COMPUTER ASSISTED METHOD FOR THE EVALUATION OF CARDIAC METABOLISM

Information

  • Patent Application
  • 20240266069
  • Publication Number
    20240266069
  • Date Filed
    May 19, 2022
    2 years ago
  • Date Published
    August 08, 2024
    3 months ago
Abstract
The invention relates to a computation based method for determining an individual cardiac metabolic profile in a subject and related materials, devices and mathematical model usage. The present invention therefore relates to a computation-based method for determining an individual metabolic cardiac profile of a subject comprising provision of a heart tissue sample from said subject, quantifying proteins in said sample from said subject, and applying information about quantities of said proteins to a mathematical model. In some embodiments, individual cardiac parameters and/or the metabolites of the subject are additionally introduced into the mathematical model, wherein individual cardiac parameters are determined for a plurality of cardiac workloads, including rest, stress or cardiac pacing. The invention also relates to the individual cardiac metabolic profile comprising a substrate uptake rate, a myocardial ATP consumption, a myocardial ATP production reserve, a myocardial ATP production at said cardiac workload, and a myocardial ATP production at maximal workload, wherein the myocardial ATP production reserve is calculated as the difference between the myocardial ATP-production at said cardiac workload and the myocardial ATP production at maximal workload. The invention further relates to the medical use and corresponding therapeutic methods based on the individual metabolic cardiac profile of the invention in the treatment, prevention, ascertainment, prognosis, of a medical condition associated with a cardiovascular disorder, in addition to detect a perturbation of a normal biological state of the heart from the subject. The invention further relates to the medical use and corresponding therapeutic methods based on the individual metabolic cardiac profile of the invention for the heart at physiological state and/or at pathological state. In further aspects, the invention relates to a computer program adapted to execute a mathematical modelling algorithm that will be performed by a computing device/module to produce outputs given data provided as inputs according to preceding claims, wherein said computer program, preferably MATLAB, is written in a programming language selected from a group comprising Fortran, C #, C/C++, High Level Shading Language, or Python.
Description

The invention relates to a computation based method for determining an individual cardiac metabolic profile in a subject and related materials, devices and mathematical model usage.


The present invention therefore relates to a computation-based method for determining an individual metabolic cardiac profile of a subject comprising provision of a heart tissue sample from said subject, quantifying proteins in said sample from said subject, and applying information about quantities of said proteins to a mathematical model. In some embodiments, individual cardiac parameters and/or the metabolites of the subject are additionally introduced into the mathematical model, wherein individual cardiac parameters are determined for a plurality of cardiac workloads, including rest, stress or cardiac pacing. The invention also relates to the individual cardiac metabolic profile comprising a substrate uptake rate, a myocardial ATP consumption, a myocardial ATP production reserve, a myocardial ATP production at said cardiac workload, and a myocardial ATP production at maximal workload, wherein the myocardial ATP production reserve is calculated as the difference between the myocardial ATP-production at said cardiac workload and the myocardial ATP production at maximal workload.


The invention further relates to the medical use and corresponding therapeutic methods based on the individual metabolic cardiac profile of the invention in the treatment, prevention, ascertainment, prognosis, of a medical condition associated with a cardiovascular disorder, in addition to detect a perturbation of a normal biological state of the heart from the subject. The invention further relates to the medical use and corresponding therapeutic methods based on the individual metabolic cardiac profile of the invention for the heart at physiological state and/or at pathological state.


In further aspects, the invention relates to a computer program adapted to execute a mathematical modelling algorithm that will be performed by a computing device/module to produce outputs given data provided as inputs according to preceding claims, wherein said computer program, preferably MATLAB, is written in a programming language selected from a group comprising Fortran, C #, C/C++, High Level Shading Language, or Python.


BACKGROUND OF THE INVENTION

Cardiovascular diseases are the leading cause of death worldwide and are primarily caused by an individual's lifestyle and dietary intake, as well as by inborn, genetic and non-genetic, predispositions. Smoking, high cholesterol, high blood pressure, lack of exercise and diabetes are factors that influence the occurrence of heart diseases. According to the World Health Organization (WHO), heart diseases are responsible for 12% of all deaths.


Heart diseases have assumed epidemic status worldwide, and despite advances in the development of drugs, surgical techniques, and medical practices, there are still a need to provide new and improved means of prevention, early detection, and correct assessment of an individual's heart disease, as well as to identify the appropriate course of treatment and its success. For example, monitoring of an individual's cardiac condition, to date the best means of prevention, can be accomplished through regular visits to the cardiologist, with the electrocardiogram (ECG) being the primary means of detecting changes in an individual's cardiac condition.


In recent years, numerous studies have firmly established metabolic disturbances as a cardinal feature of cardiac disease pathophysiology [1-5]. Although alterations in cardiac metabolism are understood to be an underlying component in almost all cardiac myopathies, the potential contribution of myocardial energy metabolism to the reduction in cardiac output and associated exercise intolerance is not fully understood [6]. In heart failure, gene expression of key proteins involved in cardiac energy metabolism is often downregulated (see, e.g., [8, 9]), as are levels of key metabolic enzymes (e.g., creatine kinase, CK [10]) and cardiac energy-rich phosphates (ATP, CrP). Although these findings suggest a mismatch between ATP demand and ATP supply, they do not allow to assess the degree of the mismatch. There is a high medical need to identify or predict this mismatch to determine risks for heart disease, such as valve disease, and/or heart failure.


The most common types of valve disease are aortic stenosis (AS) and mitral regurgitation (MI), which expose the heart to long-term pressure and volume overload, respectively. Pressure-volume overload triggers cardiac remodeling, which typically results in myocardial hypertrophy. Some patients tolerate this condition well for years, whereas others rapidly progress from compensated to decompensated heart failure despite similar characteristics. Therefore, it is of particular importance in the clinic to be able to predict the risk of transition from compensated to decompensate heart failure as accurately as possible. This would include a better knowledge of the metabolic status of the myocardium in heart disease. In the state of the art, cardiac magnetic resonance imaging and 31P magnetic resonance spectroscopy can previously be used to visualize whether reduced ATP delivery from mitochondria to myosin ATPase through the CK shuttle is associated with an otherwise unexplained reduced LV (left ventricle) ejection fraction in some (but not all) patients with severe AS. However, this does not allow for evidence of a significant difference in CK flow in patients with cardiac dysfunction. In the prior art, network reconstruction of the metabolic network of cardio-myocytes and modeling work on metabolic subsystems are known [15-18] as well as methods of diagnosing metabolic syndromes or chronic rejection of a cardiac allograft using genomic expression profiling, proteomic expression profiling, or a combination of genomic and proteomic expression profiling or a virtual surgical guides as a three-dimensional digital representation of the heart [65-68]. There is still a lack of a method and mathematical model to demonstrate changes in cardiac metabolism that are associated with cardiovascular abnormalities. In particular, there is a lack of a method to show a gradual reduction in myocardial ATP production capacity (MVATP) in cardiovascular tissue, especially in cardiac (dys-)function, e.g., in association with deterioration in LV systolic function.


This addresses an unmet and urgent medical need in the health care of cardiovascular abnormalities.


SUMMARY OF THE INVENTION

In light of the prior art, the technical problem underlying the invention was the provision of novel means for preventing, prognosis, ascertaining, and treating a cardiovascular related disorder or a pathophysiology state of the heart. Changes is cardiac metabolism, e.g. ATP production capacity, is an underlying component of a cardiovascular related disorder, cardiac morbidity and pathophysiology state of the heart.


One objective was to provide a computation-based model to determine an individual cardiac metabolic profile for preventing, prognosis, ascertaining, and treating a cardiovascular related disorder or a pathophysiology state of the heart. Another objective was to provide a method to process a heart tissue sample from a subject and cardiac parameter for modelling an individualized cardiac metabolic profile using a trained reference data set. Despite the high medical need, the state of the art currently does not provide means to determine the metabolic profile of the heart of a subject and thus to assess the ability of the heart tissue to increase energy supply in response to an increase in energy demand, e.g. ATP demand.


The technical problem can also be seen in the provision of means to assess to energetic capacity of the heart tissue from a subject by combining kinetic modeling with protein abundance data of metabolic enzymes determined in the heart tissue. The technical problem can also be seen in providing the means to generate a complex physiology-based mathematical model of cardiac energy metabolism that includes pathways that use energy-providing substrates. The technical problem can also be seen in providing the means to execute a mathematical modeling algorithm by a computer program.


These problems are solved by the features of the independent claims. Preferred embodiments of the present invention are provided by the dependent claims.


The invention therefore relates to computation-based method for determining an individual metabolic cardiac profile to prevent, to prognose, to ascertain and/or to treat a cardiovascular related disorder or a pathophysiology state of the heart.


The invention therefore relates to a computer-implemented method for determining an individual metabolic cardiac profile of a subject comprising:

    • a) Providing a heart tissue sample from said subject, and
    • b) Quantifying proteins in said sample from said subject, and
    • c) Applying information about quantities of said proteins from step b) to a mathematical model.


The invention also relates to a computer-implemented method for determining an individual cardiac metabolite and proteome profile of a human subject comprising:

    • a) Providing a heart tissue sample comprising proteins from said subject, and
    • b) Quantifying a protein expression level of multiple proteins in said sample from said subject using a large-scale protein quantification method, and
    • c) Applying the protein expression level from step b) to a mathematical model,
    • d) Calculating the individual cardiac metabolite and proteome profile based on protein expression level from step b) from said subject using the mathematical model in step c).


Access to human cardiac muscle samples is very challenging and thus exceptional and is of particular value to the present invention. To date, the prior art has only been able to detect proteins individually or a small number of proteins from a human heart muscle sample. For example, equal to or less than 100 proteins were detected. However, this information was not sufficient to provide an entire profile for the proteome and inferred metabolism for a human subject. Such a profile has the advantage of looking at the interactions of proteins with each other and thus correctly assessing the metabolic state of the heart and its ATP capacity and identifying pathological conditions. A particular advantage of the invention is that the human subject receives a nutritional or a therapeutic intervention that corresponds to the actual metabolic energy status and biological condition of the heart of said subject without and the treatment is selected on the basis of this condition, minimizing, if not completely avoiding, the risk of misinterpretation or mistreatment by intermediate steps and interference of the measurement results by other organs.


In this regard, the application of the method is not limited to a specific sample from one part of the heart, but rather can be applied to any cardiac muscle sample.


Furthermore, in the prior art, proteins and metabolites are often measured from a blood sample from a human subject and conclusions are drawn about the activity, metabolic status, and possible pathological conditions of the heart. However, the proteins or metabolites measured in the blood need not originate from the heart, or the measured changes in proteins need not be a response to conditions of the heart. This may lead to misinterpretation, resulting in mistreatment, or disease may be overlooked.


The present invention is based on quantified protein expression levels. Protein expression levels have the advantage over measurements of nucleic acids (e.g., with microarrays) that they accurately reflect the metabolic state of the heart, since proteins are the executive elements of metabolism, and therefore avoid misinterpretation due to the step of producing proteins from nucleic acid information.


The method described herein relate to hearts from a human subject, reflecting the autologous, metabolic state of the individual heart from said human subject. Rejection reactions, as they may occur after heart transplantation, are in particular a reaction of the immune system of the recipient of the donor heart. In particular, the immune system response is measurable by the immune cells circulating in the blood and is indicative of a rejection status. The invention provided herein is not intended to be used to determine a rejection reaction or rejection status in a human subject, such as diagnosis of chronic allograft rejection of a cardiac allograft.


In one embodiment, the individual metabolic cardiac profile of a diseased subject (patient, affected) can be compared to the individual metabolic cardiac profile of a non-diseased subject (control, normal).


The individual metabolic cardiac profile, if compared to a non-diseased subject, providing information about cardiac metabolic changes in the heart from the subjects can be used for (i) selecting a nutritional or a therapeutic intervention, and (ii) evaluating or preventing a therapeutic intervention. Cardiovascular related disorders or a perturbation of a normal biological state of the heart are characterized by cardiac metabolic changes.


In cardiovascular related disorders, gene expression of key proteins involved in cardiac energy metabolism as well as important metabolic enzymes (e.g., creatine kinase, CK) and cardiac energy-rich phosphates (ATP, CrP) are often downregulated. These findings suggest a mismatch between cardiac ATP demand and cardiac ATP production, and therefore in the individual metabolic cardiac profile. There is a high medical need to determine this mismatch to identify risks for heart diseases, such as valve disease, and/or heart failure. The individual cardiac metabolic profile comprises a substrate uptake rate, a myocardial ATP consumption, a myocardial ATP production reserve, a myocardial ATP production. It has proven very difficult in the art to determine the cardiac ATP production rate and the degree of reduction of cardiac ATP production in the heart tissue of a subject. The skilled person could not expect that using the protein and metabolic information of the model and the protein data from the subject's heart tissue, the ATP capacity at rest and maximum workload could be calculated. It was surprising that pathological conditions of the heart could not only be determined but also predicted, such as a cardiovascular disease or a perturbation of a normal biological state of a heart in an autologous situation in the human subject. Cardiovascular disorders are a large class of diseases that affect the heart and/or blood vessels (arteries and veins). In one embodiment, a cardiovascular related disorder can be one of, but not limited to, arrhythmias, vascular disease, myocardial infarction, heart failure, myocarditis, atherosclerosis, restenosis, coronary heart disease, coronary artery disease, atherosclerotic cardiovascular disease, arterial hypertension, cardiac fibrosis, stroke, sudden cardiac death syndrome, heart failure, ischemic heart disease, ischemic cardiomyopathy, myocardial infarction, coronary artery calcification. These diseases have similar causes, mechanisms, and treatments. Most cardiovascular disorders have common risk factors, including change cardiac metabolism, inflammation, fibrosis, diabetes, cholesterol, and vascular deposits. In one embodiment, the common risk factor is a change in cardiac metabolism.


In one embodiment, changes in cardiac metabolism comprise changes in cardiac enzyme activity, cardiac gene expression, cardiac substrate uptake rate, cardiac hormone concentration (e.g. insulin, catecholamines), cardiac metabolite concentration, cardiac ATP consumption, cardiac oxygen consumption, cardiac NO, cardiac ion exchange, cardiac energy-rich phosphates, and/or cardiac ATP production capacity. In one embodiment, changes in cardiac metabolism are associated to a pathological state of the heart and may lead to congestive heart failure, compromised cardiac function, cardio-embolism, vascular and cardiac damage, diastolic dysfunction, cardiac dysfunction, cardiac valve disease, reduction of the cardiac output, exercise intolerance, conduction disturbances, or sudden death.


In one embodiment, the individual metabolic cardiac profile of a subject involves metabolite concentration, hormone concentration, enzyme activity, protein expression, hormones, protein profile of a heart tissue from a subject, and/or individual parameter, wherein individual parameter comprise cardiac parameter, individual history, medication, laboratory parameter.


In one embodiment, metabolite concentrations can be obtained from database, published literature, and/or determined in a sample from a subject, wherein said sample comprise body fluid, blood, plasma, serum, heart tissue, preferably blood and/or heart tissue.


In one embodiment, the protein expression can be obtained from database, published literature, and/or determined in a sample from a subject, wherein said sample comprise body fluid, blood, plasma, serum, heart tissue, preferably blood and/or heart tissue.


In one embodiment, the enzyme activity can be obtained from database, published literature, and/or a sample from a subject, wherein said sample comprise body fluid, blood, plasma, serum, heart tissue, preferably blood and/or heart tissue.


In one embodiment, the protein profile of a subject is usually determined in the heart tissue from the subject.


In one embodiment, the hormone concentration can be obtained from database, published literature, and/or a sample from a subject, wherein said sample comprise body fluid, blood, plasma, serum, heart tissue, preferably blood and/or heart tissue.


In one embodiment, the subject is a human subject. A particular advantage of the present invention is the possible application of the method for determining the individual cardiac metabolic profile in the heart tissue of a human subject. For that, heart tissue sample from a human subject is used ex vivo. The skilled person knows about the importance and the special value of heart tissue samples from a human being and that access to these samples is a special challenge. The person skilled in the art is familiar with methods for obtaining heart tissue samples from a human being and knows that these are usually obtained as part of a planned surgery. Preferred collection and preparation of the heart tissue samples is described in the Examples. In the prior art, therefore, heart tissue samples from animals, such as mice, are generally used. The skilled person is aware of the lack of consistency of biological data from animals compared to humans and that this often leads to errors in the choice of therapeutic options, development of drugs, assessment of disease progression and nutritional recommendations. The person skilled in the art knows from the literature that protein profiles from mice can match humans about only half. This provides the invention with even more essentiality, correctness and usefulness.


In one embodiment, individual parameters, as used herein, include patient age, smoking behavior (either the mere fact of being an (inhalant) smoker or the number of cigarettes per day), systolic and/or diastolic blood pressure, HDL cholesterol level (either concentration or particle number), blood glucose concentration, triglyceride concentrations, subject sex, and (blood pressure) medication.


As generally known by a skilled person, patients with cardiovascular related diseases frequently have decreased ATP production in cardiac muscle cells as well as other abnormalities in cardiac metabolism, including cell death. Under physiological conditions, more than 95% of adenosine triphosphate (ATP) is generated from oxidative phosphorylation in the heart, mainly by utilization of fatty acids (FAs), with the remaining 5% produced by glycolysis. The high rate of ATP production and turnover in the heart is required to maintain its continuous mechanical work. Disturbances in ATP-generating processes may therefore directly affect contractile function. Characterization of cardiac metabolism in heart disease, such as heart failure (HF), revealed several metabolic changes termed metabolic remodeling, ranging from altered substrate utilization to mitochondrial dysfunction, ultimately leading to ATP deficiency and impaired contractility.


In the prior art, no method is available to measure myocardial ATP production capacity in vivo.


In one embodiment, the heart tissue sample can be a left ventricle, a right ventricle, a septum, a left atrium, a right atrium heart tissue sample obtained during a myocardium examination or cardiac surgery, preferably a cardiac catheter examination.


In one embodiment, a sample from a subject have been obtained from a subject with cardiovascular disease or pathophysiological state of the heart. In one embodiment, a sample from a subject have been obtained from a non-diseased subject (control, normal). The sample may have been obtained from another person and given to the person (or machine) performing the procedure.


In one embodiment, the heart tissue sample can be left ventricular septum biopsies specimen from patients admitted in need for aortic or mitral valve replacement surgery or from healthy donor heart control subjects.


In one embodiment, said heart tissue sample is a left ventricular septum sample.


In one embodiment, said heart tissue sample is a right ventricular septum sample.


Many suitable sample types are evident to a skilled person. In one embodiment of the invention, the sample is a heart tissue sample. In one embodiment, the heart tissue sample can be selected from a group of a left ventricle, a right ventricle, a septum, a left atrium, a right atrium heart tissue sample obtained during a myocardium examination, a heart transplantation, an insertion of a pacemaker, an insertion of a defibrillator or a cardiac surgery, preferably a cardiac catheter examination. Methods for storing and lysing of heart tissue samples and protein extraction from heart tissue samples are well-known to a skilled worker. A preferred method storing and lysing of heart tissue samples and protein extraction from of heart tissue samples is provided in the Examples.


In one embodiment, the sample is a blood sample, such as whole blood, plasma, or serum (plasma from which clotting factors have been removed). For example, peripheral, arterial or venous plasma or serum may be used. In another embodiment, the sample is urine, sweat, or other body fluid in which proteins are sometimes removed from the bloodstream. In one embodiment, metabolites are determined in blood samples. In one embodiment, hormones are determined in blood samples.


A particular advantage of the invention is the provision of a method in which, in order to determine the individual cardiac metabolic profile of a subject, the data are obtained from the cardiac tissue samples used and the individual parameters are obtained from the same subject.


In one embodiment, the method comprises additionally quantitatively determining of metabolites in plasma, blood, or serum sample, preferably plasma sample, from said subject, wherein said metabolites can be selected from a group of glucose, lactate, pyruvate, glycerol, fatty acids, glutamate, glutamine, leucin, isoleucine, valine, acetate, B-hydroxybutyrate, catecholamines, or insulin.


In one embodiment, the quantitatively determined metabolite of a diseased subject (patient, affected) can be compared to the quantitatively determined metabolites of a non-diseased subject (control, normal).


In one embodiment, the metabolite can be determined in plasma. In one embodiment, the metabolite can be determined in blood. In one embodiment, the metabolite can be determined in serum. In one embodiment, the metabolite can be determined in the heart tissue sample. The metabolite concentration may vary with time. In one embodiment, the time variation of the metabolite concentration comprises a change of the input value in a time course that both shifts the output signal in time and changes other parameters and behavior. In one embodiment, the metabolite concentration


In one embodiment, metabolite concentrations from a subject can be absent for the determination of the individual cardiac metabolic profile. Mathematical modeling can also be performed with metabolite concentrations obtained from databases and/or from the published literature and is known for a variety of kinetic models and metabolic pathways. This represents a particular advantage of the invention, as accurate calculation and modeling is possible even in the absence of data from the subject, and thus the mathematical model always provides more accurate, reproducible and reliable calculations. In one embodiment, metabolite concentrations from the subject can be added to the reference data set. In one embodiment, metabolite concentration from databases and/or from literature can be added to the reference data set.


In one embodiment, the computation-based method comprises additionally quantitatively determining of an individual cardiac parameter comprising heart rate, blood pressure, pressure-volume loops, and/or heart power.


In one embodiment, the quantitatively determined cardiac parameter of a diseased subject (patient, affected) can be compared to the quantitatively determined cardiac parameter of a non-diseased subject (control, normal).


In one embodiment, individual cardiac parameters comprise ventricular end diastolic volume, ventricular end systolic volume, stroke volume, heart rate, cardiac output, preload, afterload, contractility, ejection fraction, blood pressure, pressure-volume loops, and/or heart power.


The individual cardiac parameter, provided herein, is particularly advantage for studying the activity and regulation of the heart subject to the individual cardiac metabolic profile.


In one embodiment, the protein quantity of the heart tissue sample from the subject is determined using a protein quantification method selected from the group of mass spectrometry, large scale mass spectrometry, immunoassay, Western blot, microfluidics/nanotechnology sensor, and aptamer capture assay, preferably large scale mass spectrometry, wherein said method comprises:

    • a) Solubilizing the heart tissue sample,
    • b) Extracting proteins from solubilized heart tissue sample of step a) according to the protein quantification method, wherein said proteins are preferably fragmented into peptides,
    • c) Transferring said extracted proteins and/or peptides from step b) to a device, preferably a mass spectrometer, of said protein quantification method identifying and quantifying the proteins and/or peptides in said sample, preferably the peptides, and
    • wherein said protein quantification method provides a protein profile of said sample from the subject.


In one embodiment, the quantitatively determined protein profile of a diseased subject (patient, affected) can be compared to the quantitatively determined protein profile of a non-diseased subject (control, normal).


Several protein quantification methods are known in the prior art. In one embodiment, mass spectrometry is preferably used for quantifying proteins of the heart tissue sample from the subject, more preferably large scale mass spectrometry analyses. Mass spectrometry based proteomics has become a method of choice to study proteins in a global manner. Mass spectrometry is not inherently quantitative but methods have been developed to address this limitation to a certain extent. In one embodiment, the large scale mass spectrometry analyses is used for determining absolute protein quantities. Absolute quantification is technically more challenging than relative quantification and could so far only be performed accurately for a single or a small number of proteins at a time. Typical applications of absolute quantification are the determination of cellular copy numbers of proteins (important for systems biology) or the concentration of biomarkers in body fluids (important for medical applications). In addition, any precise method of absolute quantification, when performed in more than one sample, also provides the relative amounts of protein between these samples. Several methods for absolute quantification have emerged in recent years, including HR/AM-SIM, iSRM, AQUA, QConCAT, PSAQ, absolute SILAC, and FlexiQuant.


In one embodiment, an absolute quantification method is used. In one embodiment, proteins of the heart tissue sample are also absolutely quantified using HR/AM-SIM with an Orbitrap instrument. The protein quantification method, as used here, allows the most challenging samples (low abundance, high complexity) to be analyzed to find more compounds in less time, perform more accurate quantifications, and elucidate structures more thoroughly. The method for protein extraction and quantification as used herein is described in the Examples.


A particular advantage of the invention is use of a proteomics-based abundance of metabolic enzymes in heart tissue sample to generate the individual cardiac metabolic profile.


In one embodiment, the protein profile, the individual cardiac parameters and/or the metabolites of the subject are introduced into the mathematical model.


Another advantage of the invention is the comprehensiveness of the data on which the mathematical model of the invention is based, wherein said data comprises left ventricular septum heart tissue samples from 75 human subjects. As described in the Examples, heart tissue samples from the left ventricular septum were collected during surgical aortic or mitral valve replacement from 41 patients with aortic valve stenosis and 17 patients with mitral valve insufficiency, and 17 control subjects.


In one embodiment, the individual metabolic cardiac profile can be calculated for a plurality of cardiac workloads, including rest, stress or cardiac pacing, wherein individual cardiac parameter including heart rate, blood pressure, heart power are determined at said cardiac workloads.


In one embodiment, the individual metabolic cardiac profile can be calculated for a plurality of cardiac workloads, wherein said cardiac workload determines the heart under a physiological condition, including sleep, rest, activity, stress or cardiac pacing. The individual metabolic cardiac profile is dependent on a cardiac workload. In one embodiment, the maximal workload is also used as the highest utilization of the heart.


In one embodiment, the individual metabolic cardiac profile at the cardiac workload of a diseased subject (patient, affected) can be compared to the individual metabolic cardiac profile at the same cardiac workload of a non-diseased subject (control, normal).


A further advantage of the invention is that the mathematical modelling can be performed for a plurality of cardiac workloads, particularly for any cardiac workload, wherein the mathematical model of the invention can be adapted to the workload of the heart. This increases the accuracy of the individual metabolic cardiac profile, in particular the accuracy of the prediction for cardiovascular disease or treatment selection.


In one embodiment, the mathematical model of the individual metabolic cardiac profile of the subject comprises

    • Inputting a cardiac kinetic model and providing metabolic parameters relating to the cardiac kinetic model, and/or
    • Providing individual cardiac parameters at cardiac workload,
    • Parametrizing said mathematical model to the heart tissue sample of said subject by calculating a maximal activity Vmax of said subject, and
    • Computing a cardiac energy expenditure profile of said subject at cardiac workload,
    • wherein said individual metabolic cardiac profile of said subject is preferably compared to a non-diseased subject at cardiac workload.


In one embodiment, the mathematical model of the individual metabolic cardiac profile of the subject comprises

    • a) Loading a cardiac kinetic model and providing metabolic parameters relating to the cardiac kinetic model, wherein said model comprises reference protein expression levels and metabolic parameters (from other subjects), and
    • b) Inputting the protein expression levels quantified of said subject to the model, and
    • c) Providing optionally individual cardiac parameters at cardiac workload to the model, and
    • d) Parametrizing said mathematical model to the heart tissue sample of said subject by calculating a maximal activity Vmax of said subject by applying the protein expression levels of step b) to said model, and
    • e) Computing a cardiac energy expenditure profile of said subject at cardiac workload,


      wherein said individual metabolic cardiac profile of said subject is preferably compared to a non-diseased subject at cardiac workload.


In some embodiments of the present invention, the mathematical model comprises one or more parameters relating to the cardiac tissue sample and/or to the subject; one or more kinetic models, preferably cardiac kinetic model, protein profile data comprising data points relating to the cardiac tissue and/or the subject such that an update uses the data; one or more algorithms using one or more of the parameters, one or more kinetic models, preferably cardiac kinetic model, and the data as input, such that the algorithms enable determination of the individual cardiac metabolic profile; and code to implement the algorithms.


Data comprise protein quantities, peptide quantities, protein labels, cardiac parameter labels, numeric cardiac parameter, clinical laboratory parameter labels, numeric clinical laboratory parameter, numeric metabolites, metabolite label, cardiac workload label, cardiac kinetic model.


In one embodiment, computing the maximal activity Vmax for model parametrization for the heart tissue sample of the subject comprises

    • a) Input of the protein profile of the subject according to claim 5, and
    • b) Loading at least one reference data set, wherein said reference data set comprises a reference data set containing the quantities of data entries, wherein each data entry of the quantity contains at least one correlated compatible protein label and/or metabolite label, and
    • c) Computing the maximal enzyme activity Vmax of the subject, wherein Vmax is calculated by the formula







V

ma

x


s

ubject


=


V

ma

x


r

e

f





E

s

ubject



E

r

e

f










    • by applying protein quantities according to claim 5 of the subject to to Esubject and by applying Vmaxref and protein quantities to Eref of any of the reference data sets.





In some embodiments, the mathematical model is a metabolic model.


In one embodiment, reference data are primary data for all inputs, parameters, quantities, kinetic data, model variables (dependent or independent), even under different workloads. In some embodiments, reference data comprise published experimental data of mammalian hearts, comprise literature data, experimental data of mammalian tissue sample, preferably heart tissue sample, at physiological state and/or experimental data of mammalian tissue sample, preferably heart tissue sample, at pathological state. Reference data sets are usually stored in databases.


In some embodiments, the mathematical model was parametrized for individual heart tissue sample by proteomics-derived protein profiles of enzymes and transporter proteins by computing the maximal activity (Vmax) of the enzyme. The maximal activities vmaxnormal of the reference data set comprising the average of heart tissue samples of control subjects were obtained by fitting of the model to experimental data.


In one embodiment, Vmax values may vary due to variable protein profiles of subjects. In one embodiment, the maximum enzyme activity is proportional to the abundance of the protein.


The “Vmax” refers to the maximal activity of an enzyme that is related to the protein concentration (E) by







v

m

α

x


=


k
cαt


E





wherein kcat is the catalytic rate constant (“turnover number”) of the enzyme/transporter.


In one embodiment, time course of model variables (concentration of metabolites and ions) is governed by first-order differential equations. In one embodiment, the time-variations of small ions are modeled by kinetic equations of the Goldman-Hodgkin-Katz type. In one embodiment, the rate laws for enzymes and membrane transporters were either taken from the literature. In one embodiment, the rate laws for enzymes and membrane transporters were constructed based on published experimental data for the mammalian heart.


Kinetic equations and model parameters are usually set up for individual pathways. Numerical values for all other parameters of the enzymatic rate laws were taken from kinetic studies of the isolated enzymes reported in the literature.


In one embodiment, calculated metabolite profiles and fluxes are adjusted to experimental data from independent experiments with perfused hearts and in vivo measurements. In one embodiment, metabolite concentrations were constrained to experimentally determined ranges. In some embodiments, short-term regulation of key regulatory enzymes by the hormones insulin and catecholamines (epinephrine, nor-epinephrine) are included into the model by phenomenological mathematical functions relating the enzyme's phosphorylation state and the abundance of the GLUT4 transporter in the sarcolemma to the plasma concentrations of glucose (insulin) and the exercise level (catecholamines).


The mathematical model of the present invention shows a significant fit of model predictions to experimental data (FIG. 2). The examples demonstrate the ability of the heart to ensure cardiac functionality at varying cardiac workload and varying plasma concentrations of energy substrates.


In one embodiment, the individual cardiac metabolic profile comprises a substrate uptake rate, a myocardial ATP consumption, a myocardial ATP production reserve, a myocardial ATP production at said cardiac workload, and a myocardial ATP production at maximal workload, wherein the myocardial ATP production reserve is calculated as the difference between the myocardial ATP-production at said cardiac workload and the myocardial ATP production at maximal workload.


The present invention further relates to the use of the model for computation of the individual metabolic cardiac profile comprising computing a specific uptake rate of substrates, a specific ATP production rate at rest (MVATP(rest)), a specific ATP production rate at maximal ATP (MVATP(max)) workload, and myocardial ATP production reserve (MAPR).


Despite the high medical need, the state of the art currently does not provide means to determine the metabolic profile of the heart of a subject, e.g. the rate of ATP production MVATP in the heart and thus to assess the ability of the heart tissue to increase MVATP in response to an increase in ATP demand. Currently, no method is available to measure MVATP in vivo.


The myocardial ATP production reserve (MAPR) is calculated as the difference between the myocardial ATP-production at a cardiac workload and the myocardial ATP production at maximal workload. In some embodiments, the cardiac parameter can be determined for each cardiac workload.


The specific energetic parameters MVATP(rest), MVATP(max) and MAPR after 60 min pacing are described in the Examples for each subject tested (FIG. 3).


As described in the Examples, the computed substrate uptake profile of the normal human heart is compared with the mean of experimental data taken from several in vivo studies (FIG. 2A). The glucose uptake can be correlated to the plasma FFA concentration (FIG. 2B).


As a further advantage, the mathematical model can be used to determine changes in the substrate preference and accompanying altered metabolic capacity of the heart at the physiological or at the pathological state, as shown in the example.


As described in the Examples, through the individual cardiac metabolic profile, a correlation can be achieved between (e.g., increased) ATP production capacity, (e.g., increased) mechanical work of the pressure/volume overloaded heart tissue (e.g., left ventricle), and cardiac output. This particular energetic state of the myocardium even in hearts, if compared to a non-diseased subject, provides clinical state and ventricular function of the heart tissue from the subject (patient).


In one embodiment, a plurality of said mathematical models can be used in said computations for the heart at physiological state, including normal post-absorptive, post prandial, and fasted, and for the heart at pathological state, including ischemic or diabetic.


In one embodiment, the computations can be performed for a normal post-absorptive state (overnight fast), as described in the Examples, characterized by the following metabolite and hormone: glucose, fatty acids, lactate, glutamine, valine, leucine, isosleucine, β-hydroxybutyrate, acetoacetate, and catecholamines at rest and at workload. The concentration of said metabolites and hormones may be obtained by the skilled person from a database, from the published literature, or from a suitable sample as described herein.


In one embodiment, the method can be used for calculating prognosis of a cardiovascular related disorder, an effect of a change in nutritional interventions, activity and/or therapeutic interventions on protein expression and on the time variation of a metabolic parameter in the heart tissue sample of the subject.


In one embodiment, therapeutic intervention, nutritional intervention, activity suitable for a subject that produces a result that in and of itself helps to prevent, to treat and/or to cure a disease. These include risk factor reduction (e.g., diet, exercise, stress reduction), pharmacologic therapy (drugs), acupuncture, invasive and interventional therapies as practiced by cardiologists and surgeons (e.g., bypass surgery, transcutaneous electric nerve stimulation (TENS), spinal cord stimulation (SCS)).


In one embodiment, the method is used to prevent, ascertain, prognose or treat a cardiovascular related disorder or to detect a perturbation of a normal biological state of the heart from the subject.


In one embodiment, a cardiovascular-related disorder can be selected from a group of, arrhythmias, vascular disease, myocardial infarction, heart failure, myocarditis, atherosclerosis, restenosis, coronary heart disease, coronary artery disease, atherosclerotic cardiovascular disease, arterial hypertension, cardiac fibrosis, stroke, sudden cardiac death syndrome, heart failure, ischemic heart disease, ischemic cardiomyopathy, myocardial infarction, coronary artery calcification.


In one embodiment, a symptom of a cardiovascular related discorder can be one of, but not limited to, long-term pressure, cardiac volume overload, cardiac dysfunction, myocardial infarction, myocardial hypertrophy congestive heart failure, survived cardiac arrest, arrhythmias, cardiovascular events, chest pain, palpitations (rapid rhythms or skips), breath disabilities, fatigue, and has an increased risk of death. In some embodiments, said patients suffer from valve diseases, e.g. aortic stenosis (AS) or mitral valve insufficiency (MI)


In one embodiment, a perturbation of a normal biological state of the heart from the subject can be one of, but not limited to, a reduced gene expression of key proteins involved in cardiac energy metabolism, increased gene expression of key proteins involved in cardiac energy metabolism, decreased levels of central metabolic enzymes, increased levels of central metabolic enzymes, reduced levels of cardiac energy-rich phosphates, elevated levels of cardiac energy-rich phosphates.


In one embodiment, a treatment is successful when the levels of protein markers, metabolites, hormones, and/or cardiac ATP capacity usually increase, provided that these levels were previously decreased compared to a reference. In one embodiment, a treatment is successful when the levels of protein markers, metabolites, hormones, and/or cardiac ATP capacity usually decrease, provided that these levels were previously increased compared to a reference.


In one embodiment, the method is preferably used for calculating prognosis of a mitral valve disease of said human subject, wherein the heart tissue sample used is preferably a ventricular septum sample of the heart of said subject.


In one embodiment, the method is preferably used for calculating prognosis of an aortic stenosis of said human subject, wherein the heart tissue sample used is preferably a ventricular septum sample of the heart of said subject.


In one embodiment, the method is preferably used for calculating occurrence of a mitral valve disease of said human subject, wherein the heart tissue sample used is preferably a ventricular septum sample of the heart of said subject.


In one embodiment, the method is used for calculating occurrence of an aortic stenosis disease of said human subject, wherein the heart tissue sample used is preferably a ventricular septum sample of the heart of said subject.


In one embodiment, the method is used for calculating the effects of a therapeutic intervention in a mitral valve disease of said human subject, wherein the heart tissue sample used is preferably a ventricular septum sample of the heart of said subject.


In one embodiment, method is used for calculating the effects of a therapeutic intervention in an aortic stenosis disease of said human subject, wherein the heart tissue sample used is preferably a ventricular septum sample of the heart of said subject.


In one embodiment, the method can be used for

    • (i) Selecting a nutritional or a therapeutic intervention, and
    • (ii) Evaluating or preventing a therapeutic intervention.


In one embodiment, the individual cardiac metabolic profile can be determined during the treatment for evaluating the effectiveness of the treatment.


In one embodiment, the individual cardiac metabolic profile can be determined before treatment for selecting a treatment.


In one embodiment, the individual cardiac metabolic profile can be determined after the treatment for evaluating effectiveness of the treatment, wherein said effectiveness of the treatment comprise an improved cardiac metabolism, improved cardiac output, activity tolerance, gene expression of cardiac genes at levels of physiological cardiac state, metabolite concentration at levels of physiological cardiac state, an increased myocardial ATP reserve, preferably an increased myocardial ATP production capacity as compared to myocardial ATP production capacity before treatment.


The invention further relates to a computer program adapted to execute a mathematical modelling algorithm that will be performed by a computing device/module to produce outputs of given data provided as inputs according to preceding claims, wherein said computer program, preferably MATLAB, is written in a programming language selected from a group comprising Fortran, C #, C/C++, High Level Shading Language, or Python.


The invention further relates to a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out a mathematical modelling algorithm that will be performed by a computing device/module to produce outputs of given data provided as inputs described herein, wherein said computer program, preferably MATLAB, is written in a programming language selected from a group comprising Fortran, C #, C/C++, High Level Shading Language, or Python, and wherein the mathematical modelling algorithm provides cardiac energy expenditure profile for calculating prognosis of a cardiovascular related disorder, an effect of a change in nutritional interventions, activity and/or therapeutic interventions on protein expression and on the time variation of a metabolic parameter in the heart tissue sample of the subject.


The invention further relates to a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out a mathematical modelling algorithm that will be performed by a computing device/module to produce outputs of given data provided as inputs described herein, wherein said computer program, preferably MATLAB, is written in a programming language selected from a group comprising Fortran, C #, C/C++, High Level Shading Language, or Python, and wherein the mathematical modelling algorithm provides cardiac energy expenditure profile and said profile is used for (i) selecting a nutritional or a therapeutic intervention, and/or (ii) evaluating or preventing a therapeutic intervention.


In some embodiments, a processor-readable medium there is provided comprising code representing instructions for causing a processor to use in one or more mathematical models one or more parameters related to determining the individual cardiac metabolic profile of a subject during a cardiac workload.


In one embodiment, input into the mathematical model data comprise the protein profile of a cardiac tissue sample, the cardiac parameters, and/or metabolites of the subject relating to determination of the individual cardiac metabolic profile, loading a reference data set.


In one embodiment, executing the algorithm for mathematical modelling comprise parameterizing and updating the models to the cardiac tissue sample of the subject so that the updating uses said data; so that the algorithms enable determination of the individual cardiac metabolic profile of a subject at a cardiac workload.


In one embodiment, output of the algorithm comprises the individual cardiac metabolic profile of a subject at a cardiac workload.


As described herein, determining an individual's metabolic cardiac profile is particularly useful for the clinical prognosis, evaluation or treatment of heart diseases.


Further examples of the computation-based method for determining an individual metabolic cardiac profile are described in detail below.


DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to a computation-based method for determining an individual metabolic cardiac profile in a subject.


All words and terms used herein shall have the same meaning commonly given to them by the person skilled in the art, unless the context indicates a different meaning. All terms used in the singular shall include the plural of that term and vice versa.


In accordance with the present disclosure, there is provided herein a computation-based method for determining an individual metabolic cardiac profile from a subject, and if compared to a non-diseased subject, used to prevent, ascertain, prognose or treat a cardiovascular related disorder or to detect a perturbation of a normal biological state of the heart, in particular heart failure, valve disease, e.g. aortic stenosis and mitral valve insufficiency.


In heart failure, gene expression of key proteins involved in cardiac energy metabolism as well as important metabolic enzymes (e.g., creatine kinase, CK) and cardiac energy-rich phosphates (ATP, CrP) are often downregulated. These findings suggest a mismatch between cardiac ATP demand and cardiac ATP production, and therefore in the individual metabolic cardiac profile. There is a high medical need to determine this mismatch to identify risks for heart diseases, such as valve disease, and/or heart failure. The individual cardiac metabolic profile comprises a substrate uptake rate, a myocardial ATP consumption, a myocardial ATP production reserve, a myocardial ATP production. It has proven very difficult in the art to determine the cardiac ATP production rate and the degree of reduction of cardiac ATP production in the heart tissue of a subject.


If such a method for determining the individual metabolic cardiac profile of a subject is possible, it may help to prevent, ascertain, prognose or treat a cardiovascular related disorder or to detect a perturbation of a normal biological state of the heart or possibly enables therapeutic inventions for reversing an associated disorder, such as a cardiovascular related disorder. Such a method is found herein for determining the individual metabolic cardiac profile of a subject according to the disclosure, which is further described below.


The individual metabolic cardiac profile, if compared to a non-diseased subject, providing information about cardiac metabolic changes in the heart from the subjects can be used for (i) selecting a nutritional or a therapeutic intervention, and (ii) evaluating or preventing a therapeutic intervention. Cardiovascular related disorders or a perturbation of a normal biological state of the heart is characterized by cardiac metabolic changes.


Metabolites, Metabolic Cardiac Profile, Cardiac Parameter

In the determination of an individual metabolic profile for the assessment of the risk for the occurrence of cardiovascular diseases and/or changes in the physiological state of the heart, various clinical (“metabolites”, “cardiac parameter”) and individual parameters are usually determined.


For cardiovascular disease, “individual parameters”, as used herein, include patient age, smoking behavior (either the mere fact of being an (inhalant) smoker or the number of cigarettes per day), systolic and/or diastolic blood pressure, HDL cholesterol level (either concentration or particle number), blood glucose concentration, triglyceride concentrations, subject sex, and (blood pressure) medication.


A “metabolite” is defined as a substance being formed as intermediate or as degradation product of the subject's internal processes and can be selected from a group of glucose, lactate, pyruvate, glycerol, fatty acids, glutamate, glutamine, leucin, isoleucine, valine, acetate, B-hydroxybutyrate, catecholamines, creatine kinase, or insulin. In one embodiment, the metabolite can be determined in plasma. In one embodiment, the metabolite can be determined in blood. In one embodiment, the metabolite can be determined in serum. In one embodiment, the metabolite can be determined in the heart tissue sample. A metabolic parameter may vary with time. The “time variation of a metabolic parameter”, as used herein, comprises a change of the input value in a time course that both shifts the output signal in time and changes other parameters and behavior.


In one embodiment, the cardiac parameter, as used herein, comprise heart rate, blood pressure, pressure-volume loops, and/or heart power.


Cardiovascular Disorder, Cardiac Workload, Cardiac Energy Expenditure

The terms “disorder” or “disease”, as used herein, can be used interchangeably.


As used herein, the terms “cardiovascular disorder”, “heart disease”, “cardiac disease” are interchangeable with, or at least related to, the terms “cardiopathy” or “cardiovascular related disorders”. Cardiovascular disorders are a large class of diseases that affect the heart and/or blood vessels (arteries and veins). Cardiovascular disorders include arrhythmias, vascular disease, myocardial infarction, heart failure, myocarditis, atherosclerosis, restenosis, coronary heart disease, coronary artery disease, atherosclerotic cardiovascular disease, arterial hypertension, cardiac fibrosis, stroke, sudden cardiac death syndrome, heart failure, ischemic heart disease, ischemic cardiomyopathy, myocardial infarction, coronary artery calcification. These diseases have similar causes, mechanisms, and treatments. Most cardiovascular disorders have common risk factors, including inflammation, fibrosis, diabetes, cholesterol, and vascular deposits. The terms “myocardial” and “cardiac” are used interchangeably.


The “myocardial ATP-production” refers to ATP levels produced by cardiac cells. Cellular ATP pools depend on the balance between ATP utilization and ATP production. The heart has an absolute requirement for aerobic ATP production to maintain adequate ATP concentrations because the anaerobic capacity of the heart is limited. Cellular ATP levels decrease when there is insufficient O2 for aerobic ATP production or when there is an increase in ATP utilization (increased ATP hydrolysis) that is not offset by a parallel increase in ATP synthesis.


The heart can use a variety of substrates for oxidative regeneration of ATP, depending on availability. In the postabsorptive state, several hours after a meal, the heart utilizes fatty acids (60-70%) and carbohydrates (˜30%). After a carbohydrate-rich meal, the heart may adapt to utilize almost exclusively carbohydrates (primarily glucose). Lactate can be used in place of glucose and becomes a very important substrate during exercise. The heart can also utilize amino acids and ketones instead of fatty acids. Ketone bodies (e.g. acetoacetate) are particularly important in diabetic acidosis.


The term “individual cardiac metabolic profile” comprises a substrate uptake rate, a myocardial ATP consumption, a myocardial ATP production reserve, a myocardial ATP production at cardiac workload, and a myocardial ATP production at maximal workload. “Cardiac workload”, as used herein, is termed as the utilization of the heart under a physiological condition, including rest, stress or cardiac pacing. In one embodiment, the “maximal workload” is also used as the highest utilization of the heart. The myocardial ATP production reserve is calculated as the difference between the myocardial ATP-production at a cardiac workload and the myocardial ATP production at maximal workload. In some embodiments, the cardiac parameter can be determined for each cardiac workload. The term “cardiac parameter”, as used herein, describes the quantitatively determined physical number useful for studying the activity and regulation of the heart, comprising ventricular end diastolic volume, ventricular end systolic volume, stroke volume, heart rate, cardiac output, preload, afterload, contractility, ejection fraction, blood pressure, pressure-volume loops, and/or heart power.


The term “pathological state” and “diseased” are used interchangeably and comprise ischemic or diabetic state of the heart. In one embodiment, the individual cardiac metabolic profile is determined for the heart at pathological state. In one embodiment, the individual cardiac metabolic profile is determined for the heart at physiological state. The terms “physiological state” and “normal biological state” are used interchangeably and comprise normal post-absorptive, post prandial, and fasted states of the heart. The normal biological state of the heart comprises maintenance of cardiac homeostasis.


The term “cardia metabolic derangement”, “metabolic changes in the heart”, “changes in cardiac metabolism” are used interchangeably and comprises changes in cardiac enzyme activity, cardiac gene expression, cardiac substrate uptake rate, cardiac hormone concentration (e.g. insulin, catecholamines), cardiac metabolite concentration, cardiac ATP consumption, cardiac oxygen consumption, cardiac NO, cardiac ion exchange, cardiac energy-rich phosphates, and/or cardiac ATP production capacity. “Changes in cardiac metabolism” are associated to a pathological state of the heart and may lead to congestive heart failure, compromised cardiac function, cardio-embolism, vascular and cardiac damage, diastolic dysfunction, cardiac dysfunction, cardiac valve disease, reduction of the cardiac output, exercise intolerance, conduction disturbances, and/or sudden death.


Sample Preparation, Quantifying Metabolites, Peptides and Proteins

Quantitative proteomics requires the analysis of complex protein samples. In the case of cardiac metabolic profile determination, the ability to obtain appropriate samples for use in the mathematical model is important for the ease and accuracy of cardiac metabolic profiling.


A “provided” sample may have been obtained from another person and given to the person (or machine) performing the procedure. A “sample” (e.g., a test sample) from a subject means a sample that might be expected to have been obtained from a subject with cardiovascular disease or a non-diseased subject (“control,” “normal”). Many suitable sample types will be evident to a skilled worker. In one embodiment of the invention, the sample is a heart tissue sample. In one embodiment, the heart tissue sample can be selected from a group of a left ventricle, a right ventricle, a septum, a left atrium, a right atrium heart tissue sample obtained during a myocardium examination, a heart transplantation, an insertion of a pacemaker, an insertion of a defibrillator or a cardiac surgery, preferably a cardiac catheter examination. Methods for storing and lysing of heart tissue samples and protein extraction from heart tissue samples are well-known to a skilled worker. A preferred method storing and lysing of heart tissue samples and protein extraction from of heart tissue samples is provided in the Examples.


In one embodiment, the sample is a blood sample, such as whole blood, plasma, or serum (plasma from which clotting factors have been removed). For example, peripheral, arterial or venous plasma or serum may be used. In another embodiment, the sample is urine, sweat, or other body fluid in which proteins are sometimes removed from the bloodstream. In one embodiment, metabolites are determined in blood samples. In one embodiment, hormones are determined in blood samples.


Protein quantities are a number, e.g. an integral number, a decimal number, of proteins determined by an appropriate protein quantification method well-known to a skilled worker method or obtained from a public database or obtained from published literature. Peptide quantities are a number, e.g. an integral number, a decimal number, of proteins determined by an appropriate protein quantification method well-known to a skilled worker method or obtained from a public database or obtained from published literature. Examples for proteins and peptides with corresponding concentrations are provided herein. Metabolite concentrations are a number, e.g. an integral number, a decimal number, of proteins determined by an appropriate quantification method well-known to a skilled worker method or obtained from a public database or obtained from published literature. Examples for metabolites and corresponding concentrations are provided herein.


In one embodiment, the protein profile of the heart tissue sample is determined by a method, as provided by the Examples described herein, wherein the method comprises (i) solubilizing the heart tissue sample, (ii) extracting proteins from solubilized heart tissue sample of step (i) according to the protein quantification method, wherein said proteins are preferably fragmented into peptides, (iii) transferring said extracted proteins and/or peptides from step (ii) to a device, preferably a mass spectrometer, of said protein quantification method identifying and quantifying the proteins and/or peptides in said sample, preferably the peptides.


The properties and amino acid sequences of the proteins in the protein profiles of the subject are well-known and can be determined routinely, as well as downloaded from various known databases. See. e.g., the database, International Protein Index (IPI) at the world wide web site, ebi.ac.uk/IPI/xrefs.html, https://prosite.expasy.org. Information to some of the proteins discussed herein, is provided in the Examples. This information is accurate as of the date of filing of this application. Although much of the data presented in the Examples herein are directed to particular forms of proteins of interest (or peptides thereof), it will be evident to a skilled worker that a variety of forms of these proteins may be indicative of the presence of cardiovascular-related disorder in a subject. For example, the protein may be an intact, full-length protein. If a protein undergoes processing naturally (e.g., is converted from a pre-pro-hormone to a pro-hormone to a fully processed hormone; the N-terminal methionine is cleaved off; the signal sequence is removed, often accompanied by a post-translational modification, such as acetylation; etc.). Furthermore, in some instances, a protein of the invention may be broken down or degraded (e.g., proteins that are found in the urine). In such a case, an investigator can determine the level of one or more of the fragments or degradation products. A “peptide,” as used herein, refers to sequence of two or more amino acids, generally derived from a larger polypeptide or protein. The peptide is unique to the protein being identified, as detected by a method described herein. A “significant” difference in a value, as used herein, can refer to a difference which is reproducible or statistically significant, as determined using statistical methods that are appropriate and well-known in the art, generally with a probability value of less than five percent chance of the change being due to random variation. In general, a statistically significant value is at least two standard deviations from the value in a “normal” control subject or reference. Suitable statistical tests will be evident to a skilled worker. For example, a significant difference in the amount of a protein compared to a baseline value can be about 50% less, or 2-fold higher.


It is generally not practical in a clinical or research setting to use patient samples as sources for baseline controls. Therefore, one can use any of variety of references as described herein. Those skilled in the art are aware that a baseline or normal value need not be established for each method for determining proteins, peptides, hormones, or metabolites when it is performed, but that reference or normal values may be established by reference to some form of stored information about a previously determined reference value for a particular protein or panel of proteins, such as a reference value established by one of the methods described. Such a form of stored information may include, for example, a reference table, a listing or electronic file of population or individual data relating to “normal values” (control) or positive controls, a medical record for the patient in which data from previous evaluations are recorded, a receiver operator characteristic (ROC) curve, or any other source of data relating to reference values that is useful to the patient. In an embodiment in which the progress of a treatment is monitored, a reference value may be based on previous measurements of the same subject before the treatment was administered.


In one embodiment, the protein quantification method can be selected from a group of large-scale protein quantification, mass spectrometry, large scale mass spectrometry, immunoassay, Western blot, microfluidics/nanotechnology sensor, and aptamer capture assay, preferably large scale mass spectrometry such as inductively coupled plasma mass spectrometry, MALDI-MS/MS, LC-MS, LC-MS/MS, and ESI-MS/MS. In one embodiment, the protein quantification method is a large-scale protein quantification method that can be selected from a group of SILAC, ICAT, NeuCode SILAC, Label-free, Metal-coded tags (MeCAT), TMTduplex, TMTsixplex, TMT10plex and TMT11plex, and aminoxyTMT measured using a mass spectrometry technique.


As described herein, left ventricular septum biopsies specimens were taken from patients admitted to clinic in need for aortic or mitral valve replacement surgery or from healthy heart control subjects (controls). Protein extraction and quantitative proteomics was performed as described in the Examples. In one embodiment, the methods for protein extraction and quantitative proteomics described herein are preferably used in the present invention.


Among the many types of suitable immunoassays are immunohistochemical staining, ELISA, Western blot (immunoblot), immunoprecipitation, radioimmuno assay (RIA), fluorescence-activated cell sorting (FACS), etc. Assays used in a method of the invention can be based on colorimetric readouts, fluorescent readouts, mass spectrometry, visual inspection, etc. Assays can be carried out, e.g., with suspension beads, or with arrays, in which antibodies or cell or blood samples are attached to a surface such as a glass slide or a chip.


In one embodiment, mass spectrometry is used to determine the amount of a protein or a peptide. Mass spectrometry (MS) can also be used to determine the amount of a protein, using conventional methods. Some typical such methods are described in the Examples herein. Relative ratio between multiple samples can be determined using label free methods (as done in the present Examples), based on spectral count (and the number of unique peptides and the number of observations of each peptide). In the Examples herein, an Orbitrap Fusion (individual samples) and Q Exactive HF-X Orbitrap instrument (reference sample) was used (LC/MS/MS instrument to obtain the data. Alternatively, quantitive data can be obtained using multiple reaction monitoring (MRM), most often carried out using a triple quadripole mass spectrometer. In this case, peptides that are unique to a given protein are selected in the MS instrument and quantified. Absolute quantification can be obtained if a known labeled synthetic peptide is used. For detailed methods see, e.g., Qin Fu and JE Van Eyk, in Clinical Proteomics: from diagnostics to therapy (Van Eyk J E and Dunn M, eds), Wiley and Son Press; Current Protocols in Molecular Biology, Preparation of Proteins and Peptides for Mass Spectrometry Analysis in a Bottom-Up Proteomics Workflow, Gundry et al., chapter 10, 2009).


MS Data Analysis

MS data are preferably analysed using MaxQuant sofware package. For searching MS2 spectra against a decoy human UniProt database (HUMAN.2019-01, with isoform annotations) containing forward and reverse sequences, the internal Andromeda search engine is preferably used. The search included variable modifications of oxidation (M), N-terminal acetylation, deamidation (N and Q) and fixed modification of carbamidomethyl cysteine. Minimal peptide length was set to six amino acids and a maximum of three missed cleavages was allowed. The FDR (false discovery rate) was set to 1% for peptide and protein identifications. Unique and razor peptides were considered for quantification. Retention times were recalibrated based on the built-in nonlinear time-rescaling algorithm. MS2 identifications were transferred between runs with the “Match between runs” option, in which the maximal retention time window was set to 0.7 min. The integrated LFQ quantitation algorithm was applied. Gene Symbols assigned by MaxQuant were substituted with gene symbols of the reported UniProt IDs from the FASTA file used.


In general, molecular biology methods referred to herein are well-known in the art and are described, e.g., in Sambrook el al., Molecular Cloning: A Laboratory Manual, current edition, Cold Spring Harbor Laboratory, Cold Spring Harbor, NY, and Ausubel et al., Current Protocols in Molecular Biology, John Wiley & sons, New York, NY.


The computation-based method of the invention can be adapted for many uses. For example, it can be used to follow the progression of cardiovascular related disorders. In one embodiment of the invention, the detection is carried out both before (or at approximately the same time as), and after, the administration of a treatment, and the method is used to monitor the effectiveness of the treatment. A subject can be monitored in this way to determine the effectiveness for that subject of a particular drug regimen, or a drug or other treatment modality can be evaluated in a pre-clinical or clinical trial.


In one embodiment, a treatment is successful when the levels of protein markers, metabolites, hormones, and/or cardiac ATP capacity usually increase, provided that these levels were previously decreased compared to a reference. In one embodiment, a treatment is successful when the levels of protein markers, metabolites, hormones, and/or cardiac ATP capacity usually decrease, provided that these levels were previously increased compared to a reference.


Data Analysis: Mathematical (Kinetic) Model and Applying that Mathematical Mode


Mathematical modelling and applying that mathematical mode to data, parameter, references is preferably carried out using a version of the published mathematical algorithm [19].


In one embodiment, a mathematical model of cardiac energy metabolism is used to quantify the metabolic changes caused by the abundance changes of metabolic enzymes. In one embodiment, the mathematical model of cardiac energy metabolism includes all pathways involved in the catabolism of the energy-providing substrates glucose, lactate, fatty acids, KBs, and BCAAs, as well as in the synthesis of endogenous energy stores (glycogen, triacylglycerol). Kinetic data, pathways, metabolite fluxes, ion fluxes, and protein abundances can be downloaded from public databases and are well-known to the skilled-person, e.g., KEGG ENZYME, NIST Chemical Kinetics Database, SABIO Biochemical Reaction Kinetics Database, BRENDA, DAVID.


In one embodiment, the mathematical model also takes into account the short-term regulation of metabolic enzymes and transporters, e.g. by the hormones insulin and catecholamines. In one embodiment, the mathematical model also incorporates electrophysiological processes at the inner mitochondrial membrane including the generation of the proton gradient by the respiratory chain, the synthesis of ATP by FoF1-ATPase, and the membrane transport of various ions.


Kinetic and Enzyme Activity

Enzyme kinetics describes the study of rates of enzyme-catalyzed chemical reactions, measuring reaction rates and examining the effects of varying reaction conditions. Michaelis-Menten kinetics is one common model of enzyme kinetics.


In some embodiments, the time course of the concentration of metabolites and ions can be determined by first-order differential equations. The term “first order” usually means that the first derivative appears, but no derivatives of higher order. A first order differential equation may be an equation of the form dx/dt=f(x, t), where x denotes the vector of metabolites and hormones and t denotes the time.


In some embodiments, the time variation of small ions is modeled by Goldman-Hodgkin-Katz type kinetic equations, according to the publication of the inventors [Peterzan, M. A., et al 2020]. In one embodiment, the rate laws for enzymes and membrane transporters were either taken from the literature. In another embodiment, the rate laws for enzymes and membrane transporters were constructed based on published experimental data for the mammalian heart. The “Goldman” equation or “Goldman-Hodgkin-Katz” equation after David Eliot Goldman (1910-1998), Alan Lloyd Hodgkin and Bernard Katz can be used for calculating the membrane potential considering multiple permeating ions. The Goldman equation allows the calculation of a membrane potential for a membrane permeable to different ions, including sodium, potassium, calcium, and chloride ions. The Goldman equation is based on the principle of a steady state. The sum of all ionic currents must equal zero. Other assumptions of the Goldman equation are the independence of the ions from each other, and a linear decrease of the potential across the membrane thickness—because of the resulting constant field, this is often referred to as a “constant field equation”. It makes allowance for the fact that at rest membrane potentials the currents pass through individual channels. In the Goldman equation, the ion current is approximated as a function of ion concentration and a coefficient called permeability P. The permeability is derived from Fick's law of diffusion. Goldman, D. E. (1943): Potential, impedance, and rectification in membranes. In: Journal of General Physiology, 27:37-60]. In addition to the Goldman-Hodgkin-Katz equation, various calculations may be used, as well as Ohm's law, to further refine the model of transmembrane potential difference, such as the “Nernst” or “constant field” equation and Gibbs-Donnan equilibrium. See Selkurt, ed. (1984) Physiology 5th Edition, Chapter 1, Little, Brown, Boston, Mass. (ISBN 0-316-78038-3) and Hille at e.g., chapters 10-13.


The Goldman-Hodgkin-Katz voltage equation describes how the various ion gradients contribute to the resting membrane potential of a cell permeable to potassium, sodium, and chloride ions.


It shows that the membrane potential of a cell is not only determined by the quotients of the ion concentrations on both sides of the cell membrane, but primarily by the permeability (P) of the membrane for the respective ion. The greater the permeability (often also called conductivity) of the membrane for a particular ion, the greater the contribution of this ion to the membrane potential. Thus, in a sense, the membrane potential represents the weighted average of the equilibrium potentials for the various ions.


The permeability of the membrane to the particular ion species is determined solely by the number and activity of the corresponding ion channels conducting that ion. In the resting state, only very few open sodium, chloride or calcium channels are found in the cell membrane.


A change in the membrane potential of a cell occurs when the permeability of the membrane to an ion species changes. For example, activation of sodium channels shifts the membrane potential toward the equilibrium potential for sodium—the membrane potential becomes more positive. The membrane potential can also take on a new value when the intracellular or extracellular concentration of an ion changes. The membrane potential is affected by the extracellular concentration of potassium, sodium, chloride or calcium.


Ion channels are found in every cell type of an organism, with potassium channels being the largest and most diverse ion channel family. The activity is modulated by different physiological stimuli depending on the channel type, e.g., membrane potential changes (voltage-gated channels), G-proteins, calcium ions, nucleotides (ATP), etc. In most cells, the resting membrane potential is determined by potassium channels. Potassium channels decisively influence the frequency and time course of action potentials, as well as their transmission, especially in neurons and muscle cells, including cardiac muscle cells. They also regulate the electrical excitability of these cells and they play a crucial role in some secretory and metabolic processes, such as insulin secretion.


Drugs/active ingredients, food intake, and physical activity can affect the activity of potassium channels in different ways. For example, drugs with a channel blocker as the active ingredient usually block the channel pore directly from the intracellular or extracellular side of the membrane. In addition, however, the interaction of a channel blocker with an accessory subunit, for example, can cause the channel pore to close or not be opened by physiological stimuli. Disturbances in the opening and closing of ion channels in cardiac muscle cells can lead to disturbances in cardiac function and thus to cardiac diseases, such as cardiac arrhythmias and hypertension. Therefore, the provision of the mathematical model for the determination of the individual cardiac metabolic profile of the present invention, which includes the activation and inactivation of ion channels, has an enormous potential for the development of new and highly effective therapeutic concepts.


The term “reference data” as used here includes primary data for all inputs, parameters, quantities, kinetic data, model variables (dependent or independent), even under different workloads. In some embodiments, reference data comprise published experimental data of mammalian hearts, comprise literature data, experimental data of mammalian tissue sample, preferably heart tissue sample, at physiological state and/or experimental data of mammalian tissue sample, preferably heart tissue sample, at pathological state. Reference data sets are usually stored in databases.


Model Parametrization

“Mathematical model parametrizing”, as used herein, also describes finding and fitting a set of model parameters that describe the system and its behavior, and can usually be achieved by cross-referencing model predictions with actual measurements on the system, wherein this cross-referencing can be a comparison with a reference and/or a control. In one embodiment, model parameters, including kinetic rate constants, substrate affinities, affinities for allosteric regulators, were taken from reported kinetic studies of the isolated enzyme from mammalian heart tissue.


In some embodiments, the mathematical model was parametrized for individual heart tissue sample by proteomics-derived protein profiles of enzymes and transporter proteins by computing the maximal activity (Vmax) of the enzyme by the equation 1










V

ma

x

subject

=


V

m

ax

normal




E
subject




E
control









(
1
)







wherein custom-characterEcontrolcustom-character describes the average protein intensity of the enzyme derived from heart tissue samples of control subjects and Esubject describes the protein concentration of the enzyme in the individual subject, wherein said individual subject can be control or patient.


The “Vmax” refers to the maximal activity of an enzyme that is related to the protein concentration (E) by










v
max

=


k
cat


E





(
2
)







wherein kcat is the catalytic rate constant (“turnover number”) of the enzyme/transporter.


The maximal activities vmaxnormal of the reference data set comprising the average of heart tissue samples of control subjects were obtained by fitting of the model to experimental data. Equation (2) deduces that the maximum enzyme activity is proportional to the abundance of the protein.


In one embodiment, Vmax values may vary due to variable protein profiles of subjects.


In one embodiment, the Vmax values indicating the maximal activity of each enzyme are estimated by fitting the model to measurements of exchange fluxes and internal metabolites obtained in different experimental setups. In one embodiment, the validity of the model is tested by comparing the simulated exchange fluxes and metabolite concentrations with experimental data. Since the heart switches its substrate uptake rates depending on substrate availability, different simulations with variable substrate availability must be performed. Model simulation for selected substrate uptakes, e.g. glucose are given in the Examples.


Energetic Capacities

The present invention further relates to the use of the model for computation of the individual metabolic cardiac profile comprising computing a specific uptake rate of substrates, a specific ATP production rate at rest, a specific ATP production rate at maximal ATP workload. The “substrate” also refers to a reactant in a chemical reaction processed by an enzyme. The term “individual metabolic cardiac profile”, as used herein, also refers to the energetic capacity of the heart from the subject. In the Examples, the computation of the energetic capacities of controls and patients with valve disease, aortic valve stenosis or mitral valve insufficiency, is provided.


The term “MVATP(rest)”, as used herein, refers to the specific ATP production rate at rest. The term “MVATP(max)”, as used herein, refers to the specific ATP production rate at maximal ATP workload. The term “MAPR” (equation 3), as used herein, also refers to as myocardial ATP production reserve and characterize the capacity of the heart tissue to increase the ATP production with increasing workload









MAPR
=



MV
ATP

(
max
)

-


MV
ATP

(
rest
)






(
3
)







The term “specific energy parameters”, as used herein, subsumes MVATP(rest), MVATP(max), and MAPR for quantifying the energetic capacity per mass unit of the heart tissue sample (given in μmol/g/h). The term “total energy parameters as used herein, subsumes tMVATP(rest), tMVATP(max), and tMAPR for quantifying the energetic capacity of the heart tissue sample (given in mmol/h).











tMV
ATP

(
rest
)

=



MV
ATP

(
rest
)

×
heart


tissue


sample


mass
/
1000





(
4
)














tMV
ATP

(
max
)

=



MV
ATP

(
max
)

×
heart


tissue


sample


mass
/
1000





(
5
)












tMAPR
=

MAPR
×
heart


tissue


sample


mass
/
1000





(
6
)







In one embodiment, the computations can be performed for a normal post-absorptive state (overnight fast), as described in the Examples, characterized by the following metabolite and hormone: glucose, fatty acids, lactate, glutamine, valine, leucine, isosleucine, β-hydroxybutyrate, acetoacetate, and catecholamines at rest and at workload. The concentration of said metabolites and hormones may be obtained by the skilled person from a database, from the published literature, or from a suitable sample as described herein.


As described in the Examples, subject's MVO2 was estimated by the 2-factor approximation as described in Nelson et al. 1974 [31], wherein said subject's oxygen consumption MVO2 was used as value for computing the cardiac ATP consumption of the stationary resting state, MVATP(rest).










MV

O

2


=

γ
·
HR
·
BP





(
7
)







“HR” refers to the heart rate. “BP” refers to the peak systolic blood pressure. “y” refers to a proportionality factor. As described in the Examples, the resting MVO2 of normal hearts was found in the range of 0.8-1.2 ml/min/g [2-4]. Thus, with a mean MVO2=0.1 ml/min/g, HR=70/min and normal BP=125 mm, we set γ to 1.143×10-5 ml/mmHg/g.


In one embodiment, the metabolic response of the myocardial sample to an additional workload (pacing) was assessed by calculating the temporal changes in metabolic state triggered by an increase in ATP consumption rate above resting levels.


In one embodiment, the ATP consumption rate is also modeled by a generic hyperbolic rate law:










v
ATP

=


k
load

·

ATP

ATP
+

K
m








(
8
)







(see Examples). In one embodiment, the continuous parameter kload is also a natural number denoting the energetic demand, that can be stepwise increased until MVATP converged to the maximum, MVATP(max).


As an Example, the kinetic rate equation for the “Carrier mediated FATP” (“CD36”) can be calculated as










v

CD

36


=


V
max

CD

36


·



ffa
ext

-

c


16
cyt





1


+


ffa
ext


K
m

ffa
ext



+


c


16
cyt



K
m

c


16
cyt











(
9
)










V
max

CD

36


=


4
,
20

E

+

01


μmol
/
g
/
h









K
m

ffa
ext


=

0.000085
[
61
]









K
m

c


16
cyt



=

0.004
[
62
]


,




wherein “ffa” refers to free fatty acid, “ext” refers to extracellular, “cyt” refers to “cytosolic, “c16” refers to long-chain fatty acid with a 16-carbon backbone, e.g. palmitic acid.


In one embodiment, a mechanical burden of the heart is evaluated, wherein the internal myocardial power, which describes the energy required for cardiac contraction for the individual hearts, is calculated as described in the methods used in Lee et al. [32].


In one embodiment, model simulations are performed using MATLAB.


Computer Program

A further aspect of the invention relates to a computer program adapted to execute a mathematical modelling algorithm that will be performed by a computing device/module to produce outputs given data provided as inputs according to preceding claims, wherein said computer program, preferably MATLAB, is written in a programming language selected from a group comprising Fortran, C #, C/C++, High Level Shading Language, or Python.


In some embodiments, a “computer” or “computing device” may be used. Such a computer may be, for example, a mainframe computer, a desktop computer, a notebook or laptop computer, a portable device such as a data acquisition and storage device, or a processing device integrated into another device such as a scanner for tomography. In some cases, the computer may be a “dumb” terminal used to access data or processors over a network.


In some embodiments of the present invention, the mathematical model comprises processor-readable media comprising: one or more parameters relating to the cardiac tissue sample and/or the subject; one or more kinetic models, preferably cardiac kinetic model, protein profile data comprising data points relating to the cardiac tissue and/or the subject such that an update uses the data; one or more algorithms using one or more of the parameters, one or more kinetic models, preferably cardiac kinetic model, and the data as input, such that the algorithms enable determination of the individual cardiac metabolic profile; and code to implement the algorithms.


Also provided are one or more processors in communication with the processor-readable medium and configured to execute the code. In some embodiments of the present invention, a method is provided for applying a mathematical model that relates a state to time for a cardiac tissue sample of a subject. In some embodiments of the present invention, there is provided a method for applying a mathematical model that relates a condition for a cardiac tissue sample of a subject to cardiovascular disease or cardiovascular disorder.


In some embodiments of the present invention, the mathematical model uses the MATLAB program. In some embodiments of the present invention, there is provided a method for implementing a mathematical model that produces and updates a mathematical relationship between a protein profile of a cardiac tissue sample, parameters related to subject, metabolite concentration, and ion concentration, and a time course. In some embodiments of the present invention, there is provided a method for implementing a mathematical model that produces and updates a mathematical relationship between a protein profile of a cardiac tissue sample, parameters related to the subject, metabolite concentration, and ion concentration, and a cardiovascular disease or cardiovascular disorder. The procedure includes: 1) selecting a cardiac workload of a subject 2) selecting the protein profile of a cardiac tissue sample, cardiac parameters, and/or metabolites of the subject for determining the individual cardiac metabolic profile; 3) selecting at least one kinetic model, preferably a cardiac kinetic model; 4) selecting at least one parameter related to the kinetic model; 5) selecting a reference data set; 6) loading the reference data set containing the sets of data entries, wherein each data entry of the set contains at least one correlated compatible protein label and/or metabolite label; 7) inputting the protein profile of a cardiac tissue sample, the cardiac parameters, and/or metabolites of the subject; 8) calculating the subject's maximum enzyme activity Vmax, where Vmax is calculated according to formula X using the inputs from steps 6 and 7; 9) parameterizing the mathematical model to the subject's cardiac tissue sample by applying the subject's Vmax from step 8; 10) rerunning the model; 11) calculating a subject's cardiac energy expenditure profile that includes the data points from step 7; 12) comparing to a non-diseased subject at cardiac workload; 13) determining a subject's individual cardiac metabolic profile using steps 11 and 12; and 14) repeating steps 1,2, 7 through 12 as needed to update the model during determination of a subject's individual cardiac metabolic profile, for example at a different cardiac workload.


In some embodiments of the present invention, there is provided a processor-readable medium comprising code representing instructions for causing a processor to use in one or more mathematical models one or more parameters related to determining the individual cardiac metabolic profile of a subject during a cardiac workload; inputting into the models data comprising the protein profile of a cardiac tissue sample, the cardiac parameters, and/or metabolites of the subject relating to determination of the individual cardiac metabolic profile, loading a reference data set; parameterizing and updating the models to the cardiac tissue sample of the subject so that the updating uses said data; so that the algorithms enable determination of the individual cardiac metabolic profile of a subject at a cardiac workload.


The term “input” as used herein, describes a function to enter data for applying a mathematical model and returns a reference to the data in the form of a string. Data comprise protein quantities, peptide quantities, protein labels, cardiac parameter labels, numeric cardiac parameter, clinical laboratory parameter labels, numeric clinical laboratory parameter, numeric metabolites, metabolite label, cardiac workload label, cardiac kinetic model. The term “output”, as used herein, describes a value produced by an algorithm, preferably a human readable value, more preferably a value defining a metabolic cardiac profile.


The term “plurality”, as used herein, means the state of being numerous.


Through a mathematical model, problems and its instances (in the algorithmic sense) may be formulated, and analyzed for properties. An algorithm is usually a step-by-step process with well-defined steps, and takes an input instance of a problem instance (a mathematical model) and produces an output, wherein an algorithm can be implemented into a computer program. A computer program is generally a series of instructions, complying with the rules of a particular programming language, to perform or solve certain functions or tasks or problems with the help of a computer.


The term “execute” also means the process by which a computer or virtual machine executes the instructions of a computer program, written in a programming language, to see the output, including, wherein the programming language can be selected from a group of Java, Fortran, C, C++, Python, C #, JavaScript, VB .NET, R, PHP, High Level Shading Language, and MATLAB. In one embodiment, the mathematical modelling algorithm for calculating individual metabolic cardiac profile is programmed and executed in MATLAB or any distribute of MATLAB. In one embodiment, the mathematical modelling algorithm for calculating individual metabolic cardiac profile is programmed and executed in Python or any distribute of Python.


Medical Indications and Therapy:

In one aspect of the present invention there is provided an individual metabolic cardiac profile according to the invention as herein described for use in the treatment of a medical condition associated with changes in cardiac metabolism, wherein the medical condition associated with changes in cardiac metabolism is preferably a cardiovascular related disorder, cardiac ATP production capacity associated cardiovascular related disorder or a cardiovascular pathology.


As used herein, the “patient” or “subject” refers to a human, preferably a patient receiving dialysis, but can also be any other mammal, such as a domestic animal (e.g. a dog, cat or the like), a farm animal (e.g. a cow, sheep, pig, horse or the like) or a laboratory animal (e.g. a monkey, rat, mouse, rabbit, guinea pig or the like). The term “patient” preferably refers to a “subject” suffering from or suspected of suffering from a cardiovascular disease and/or changes in cardiac metabolism.


In the present invention “treatment” or “therapy” generally means to obtain a desired pharmacological effect and/or physiological effect. The effect may be prophylactic in view of completely or partially preventing a disease and/or a symptom, for example by reducing the risk of a subject having a disease or symptom or may be therapeutic in view of partially or completely curing a disease and/or adverse effect of the disease. In the present invention, “ascertain” means to discover cardiovascular disease, cardiac ATP production capacity associated cardiovascular related disorder or a cardiovascular pathology, abnormal cardiac ATP production, and/or changes in cardiac metabolism. In the present invention, the individual metabolic cardiac profile for “prognosis” comprise to predict the course of a disease or to predict the effect of a treatment. The term “evaluating”, as used herein, usually means determining whether expected outcomes were met and comprise measuring effectiveness of a medical care, a treatment, a nutritional intervention, and a physical activity.


In the present invention, “therapy” includes arbitrary treatments of diseases or conditions in mammals, in particular, humans, for example, the following treatments (a) to (c): (a) Prevention of onset of a disease, condition or symptom in a patient; (b) Inhibition of a symptom of a condition, that is, prevention of progression of the symptom; (c) Amelioration of a symptom of a condition, that is, induction of regression of the disease or symptom.


The phrase “therapeutically effective” is intended to include, within the scope of sound medical judgment, excessive toxicity, irritation, allergic reactions, and/or other problems or complications, but commensurate with a reasonable benefit/risk ratio. As used herein to refer to the therapeutic invention, nutritional intervention, activity suitable for a subject that produces a result that in and of itself helps to prevent, to treat and/or to cure a disease. These include risk factor reduction (e.g., diet, exercise, stress reduction), pharmacologic therapy (drugs), acupuncture, invasive and interventional therapies as practiced by cardiologists and surgeons (e.g., bypass surgery, transcutaneous electric nerve stimulation (TENS), spinal cord stimulation (SCS)).


In particular, the treatment relates to prevent or ameliorate cardiovascular related disorders or cardiac metabolic changes either by activity, nutritional intervention, cardiac surgery, drug therapy, mechanic therapeutic intervention, electronic heart regulation (e.g. cardiac pacemaker) according to the individual cardiac metabolic profile of the present invention. The prophylactic therapy as described herein is intended to encompass prevention or reduction of risk of cardiovascular related disorders or cardiac metabolic changes. In one embodiment, the individual cardiac metabolic profile can be determined during the treatment for evaluating the effectiveness of the treatment. In one embodiment, the individual cardiac metabolic profile can be determined before treatment for selecting a treatment. In one embodiment, the individual cardiac metabolic profile can be determined after the treatment for evaluating effectiveness of the treatment, wherein said effectiveness of the treatment comprise an improved cardiac metabolism, improved cardiac output, activity tolerance, gene expression of cardiac genes at levels of physiological cardiac state, metabolite concentration at levels of physiological cardiac state, an increased myocardial ATP reserve, preferably an increased myocardial ATP production capacity as compared to myocardial ATP production capacity before treatment.


As used herein, a “patient with symptoms of a cardiovascular-related disorder” is a subject who presents with one or more of, without limitation, reduced gene expression of key proteins involved in cardiac energy metabolism, increased gene expression of key proteins involved in cardiac energy metabolism, decreased levels of central metabolic enzymes, increased levels of central metabolic enzymes, reduced levels of cardiac energy-rich phosphates, elevated levels of cardiac energy-rich phosphates, long-term pressure, cardiac volume overload, cardiac dysfunction, myocardial infarction, myocardial hypertrophy congestive heart failure, survived cardiac arrest, arrhythmias, cardiovascular events, chest pain, palpitations (rapid rhythms or skips), breath disabilities, fatigue, and has an increased risk of death. In some embodiments, said patients suffer from valve diseases, e.g. aortic stenosis (AS) or mitral valve insufficiency (MI).


In some embodiments, said patient has symptoms of reduced gene expression of proteins involved in cardiac energy metabolism or symptoms of increased gene expression of proteins involved in cardiac energy metabolism or symptoms of decreased levels of central metabolic enzymes or symptoms of reduced levels of cardiac energy-rich phosphates or symptoms of increased levels of central metabolic enzymes or symptoms of elevated levels of cardiac energy-rich phosphates or symptoms of long-term pressure or symptoms of cardiac volume overload or symptoms of cardiac dysfunction or symptoms of myocardial infarction or symptoms of myocardial hypertrophy or symptoms of congestive heart failure or symptoms of survived cardiac arrest or symptoms of arrhythmia symptoms of cardiovascular events or symptoms of chest pain or symptoms of palpitations (rapid rhythms or skips) or symptoms of breath disabilities or symptoms of fatigue or symptoms of an increased risk of death.


In some embodiments, said patient has no symptoms of reduced gene expression of proteins involved in cardiac energy metabolism or no symptoms of increased gene expression of proteins involved in cardiac energy metabolism or no symptoms of decreased levels of central metabolic enzymes or no symptoms of reduced levels of cardiac energy-rich phosphates or no symptoms of increased levels of central metabolic enzymes or no symptoms of elevated levels of cardiac energy-rich phosphates or no symptoms of long-term pressure or no symptoms of cardiac volume overload or no symptoms of cardiac dysfunction or no symptoms of myocardial infarction or no symptoms of myocardial hypertrophy or no symptoms of congestive heart failure or no symptoms of survived cardiac arrest or no symptoms of arrhythmias or no symptoms of cardiovascular events or no symptoms of chest pain or no symptoms of palpitations (rapid rhythms or skips) or no symptoms of breath disabilities or no symptoms of fatigue or no symptoms of an increased risk of death.


In some embodiments, said patient at risk of developing symptoms of reduced gene expression of key proteins involved in cardiac energy metabolism or symptoms of increased gene expression of key proteins involved in cardiac energy metabolism or symptoms of decreased levels of central metabolic enzymes or symptoms of increased levels of central metabolic enzymes or symptoms of reduced levels of cardiac energy-rich phosphates or symptoms of elevated levels of cardiac energy-rich phosphates or symptoms of long-term pressure or symptoms of cardiac volume overload or symptoms of cardiac dysfunction or symptoms of myocardial infarction or symptoms of myocardial hypertrophy or symptoms of congestive heart failure or symptoms of survived cardiac arrest or symptoms of arrhythmia symptoms of cardiovascular events or symptoms of chest pain or symptoms of palpitations (rapid rhythms or skips) or symptoms of breath disabilities or symptoms of fatigue or symptoms of an increased risk of death presents changes in cardiac metabolism at therapeutically relevant level.


FIGURES

The invention is demonstrated by way of the example through the figures disclosed herein. The figures provided represent particular, non-limiting embodiments and are not intended to limit the scope of the invention.





SHORT DESCRIPTION OF THE FIGURES


FIG. 1: Reaction scheme of the metabolic model



FIG. 2: Simulated and measured myocardial substrate uptake rates in vivo



FIG. 3: MVATP(rest) and MVATP(max) for controls and patients with mitral valve disease and aortic stenosis



FIG. 4: Contribution of energy delivering substrates



FIG. 5: Correlation between tMVATP(rest) as well as tMVATP(max) and internal myocardial power (iMP) as well as cardiac output (CO) for MI patients (A-D) and AS patients (E-H)



FIG. 6: Metabolic characterization of three patients with AS





DETAILED DESCRIPTION OF THE FIGURES


FIG. 1: Reaction scheme of the metabolic model. FIG. 1.1 represents an overview of FIG. 1 for all parts shown in FIG. 1.2:A to FIG. 1.9:H. Arrows symbolize reactions and transport processes between compartments. 1) glycogen metabolism, (2) glycolysis, (3) oxidative pentose phosphate pathway in the endoplasmic reticulum and cytosol, (4) non-oxidative pentose phosphate pathway, (5) triglyceride synthesis, (6) synthesis and degradation of lipid droplets, (7) tricarbonic acid cycle, (8) respiratory chain and oxidative phosphorylation, (9) B-oxidation of fatty acids, (10) ketone body utilization, (11) glutamate metabolism, (12) mitochondrial electrophysiology (membrane transport of ions, (13) Utilization of branched-chain amino acids. Small cylinders and cubes symbolize ion channels and ion transporters. Double-arrows indicate reversible reactions, which according to the value of the thermodynamic equilibrium constant and cellular concentrations of their reactants may proceed in both directions. Reactions are labeled by the short names of the catalyzing enzyme or membrane transporter given in the small boxes attached to the reactions arrow. Metabolites are denoted by their short names. Full names and kinetic rate laws of reaction rates are outlined in Table 8. Full names of metabolites and a comparison of experimentally determined and calculated cellular metabolite concentrations are given in Table 9.



FIG. 2: Simulated and measured myocardial substrate uptake rates in vivo. (A) Substrate uptake rates at rest and at moderate pacing (50% maxVO2). The experimental data represent the mean of various studies [40-46]. They were computed from reported extraction rates (=1−arterial concentration/concentration in coronary sinus) putting the coronary blood flow to 0.8 ml/min/g and heart weight to 300 g. (B) Dependence of the glucose uptake rate from the plasma concentration of FFAs. The solid line represents model values, squares symbolize in vivo data taken from Nuutila et al. [38].



FIG. 3: MVATP(rest) and MVATP(max) for controls and patients with mitral valve disease and aortic stenosis. MVATP(rest) and MVATP(max) for controls and patients with mitral valve disease and aortic stenosis (A) Bottom values of the bars refer to MVATP(rest), top values refer to MVATP(max). The bar length indicates the myocardial ATP production reserve, MAPR=MVATP(max)−MVATP(rest), of the subject. (B-D) Box plots showing mean values, upper and lower quartiles and total span of MVATP(rest), MVATP(max) and MAPR for controls and patients with MI and AS.



FIG. 4: Contribution of energy delivering substrates. The panels A and B show the relative contribution of the energy delivering substrates to total energy expenditure at MVATP(rest) and MVATP(max) for the control group for 60 min pacing. Area of the pie charts represent total energy expenditure. Changes of substrate uptake rates of MI and AS patients relative to controls are shown at rest (C) and during maximal pacing (D). Bar plots represent the relative change of substrate uptake rates of glucose (1), lactate (2), fatty acids (3) and ketone bodies (4) for patients with MI and AS during rest and at maximal ATP production rate after 60 min of pacing. Relative uptake rates are normalized to control values (i.e. all control values are equal to 1).



FIG. 5: Correlation between tMVATP(rest) as well as tMVATP(max) and internal myocardial power (iMP) as well as cardiac output (CO) for MI patients (A-D) and AS patients (E-H). Correlation between tMVATP(rest) as well as tMVATP(max) and internal myocardial power (iMP) as well as cardiac output (CO) for MI patients (A-D) and AS patients (E-H).



FIG. 6: Metabolic characterization of three patients with AS. Relative substrate utilization rates compared to healthy controls at rest (A) and at maximal load (C) as well as the relative contribution of the different substrates (glucose (1), lactate (2), fatty acids (3) and ketone bodies (4)) to overall ATP production rate at rest (B) and maximal load (D). Area of pie diagrams represent total ATP production rate.


EXAMPLES

The invention is demonstrated through the examples disclosed herein. The examples provided represent particular embodiments and are not intended to limit the scope of the invention. The examples are to be considered as providing a non-limiting illustration and technical support for carrying out the invention.


The examples below present a physiology-based mathematical model of the myocardial energy metabolism. The model encompasses all pathways along which the possible energy-delivering substrates glucose, long-chain fatty acids, ketone bodies (KBs), acetate (AC) and branched-chain amino acids (BCAAs) are utilized. The method described herein allows to assess the capability of the left ventricular septum of patients and controls to increase MVATP in response to an increase of the ATP demand. Based on LV samples from controls and patients with MI and AS, it is shown that the ATP production capacity of the LV is reduced in patients and correlates positively with mechanical energy demand and cardiac output and is consistent with the clinical data.


Methods
Patient Characteristics

We investigated 75 human left ventricular myocardial biopsies. In patients, myocardial samples from the LV septum were collected during surgical aortic or mitral valve replacement from 41 patients with aortic valve stenosis (AS) and 17 patients with mitral valve insufficiency (MI). Patient characteristics are described in Table 1. For the controls (n=17), samples were taken from 44±15 year-old donors without cardiac diseases but whose hearts were not used for transplantation. All samples were frozen immediately in liquid nitrogen until further processing.


The study protocol was in agreement with the principles outlined in the Declaration of Helsinki and was approved by the Medical Ethics Review Committee. All patients gave written informed consent prior to inclusion.









TABLE 1







Patients Characteristics


Data are presented as total numbers and percentage in case of categorical and as mean and standard


deviation (SD) in case of numeric values. Parameter differences between the two patient groups were


evaluated by means of two-sided, two-sample Wilcoxon-rank test in case of numeric data and via


Chi-squared test with Yates' continuity correction in case of categorical data (p-values given in the


right column). ACE-inhibitor = angiotensin converting enzyme-inhibitor, AS = aortic stenosis,


BMI = body mass index, MI = mitral valve insufficiency












Patient characteristic and

SD/

SD/
p-


preoperative function parameters
AS
%
MI
%
value















Age at Surgery in years
68
9
60
14
0.032


BMI
28
4
27
3
0.343


Gender female
23
56%
6
35%
0.414


NYHA (stage I, II, III, IV)
(5, 17,
n.a.
(2, 7,
n.a.
0.593



15, 1)

6, 2)




Blood pressure systolic in mm[Hg]
140
19
131
16
0.123


Blood pressure diastolic in mm[Hg]
74
11
75
13
0.675


EDVi in ml/m2
73
17
108
34
<0.001


ESVi in ml/m2
30
11
40
14
0.015


EF in %
60
7
62
9
0.048


Cl in l/min/m2
3
1
5
2
<0.001


CO in l/min
6
2
9
4
<0.001


Internal myocardial power
13
7
13
5
1


Myocardial mass (i) in g/m2
71
20
67
15
0.484


Mean pressure gradient
56
15
4
8
<0.001


aortic valve, mm[Hg]







Mitral valve insufficiency
(41,
n.a.
(0,
n.a.



(none/mild, moderate, severe)
0, 0)

10, 7)




Aortic valve insufficiency
(36,
n.a.
(17,
n.a.



(none/mild, moderate, severe)
5, 0)

0, 0)




Serum Creatinine [mg/dl]
0.91
0.15
1.0
0.20
0.065


Hypertension
27
66%
11
65%
0.826


Dyslipidemia
8
20%
3
18%
0.839


Diabetes type 2
7
17%
2
12%
0.913


Coronary Artery Disease
1
 2%
2
12%
0.419


Atrial fibrillation paroxysmal
2
 5%
2
12%
0.709


Atrial fibrillation permanent
0
 0%
2
12%
0.149


Medication ACE inhibitor
15
37%
5
29%
0.826


Medication beta blocker
20
49%
10
59%
0.683


Medication diuretics
12
29%
5
29%
0.760









Quantitative Proteomics of Tissue Samples

Heart biopsies were taken from patients admitted in need for aortic or mitral valve replacement surgery or from healthy donor heart control subjects. Left ventricular septum biopsies were extracted at time of surgery, frozen directly in liquid nitrogen and kept at −80° C. For protein extraction, biopsies were lysed in 200 μl lysis buffer containing: 2% SDS, 50 mM ammonium bicarbonate buffer and EDTA-free Protease Inhibitor Cocktail (Complete, Roche). Samples were homogenized at room temperature using FastPrep-24™ 5G Homogenizer (MP Biomedicals) with 10 cycles of 20 s and 5 s pause between cycles. After heating the samples for 5 min at 95° C., 5 freeze-thaw cycles were applied. 25 U of Benzonase (Merck) was added to each sample and after an incubation for 30 min the lysates were clarified by centrifugation at 16,000 g for 40 min at 4° C. Protein concentration was measured (Bio-Rad DC Protein assay) and 100 μg of each sample was further processed using the SP3 clean-up and digestion protocol as previously described [20]. Briefly, each sample was reduced with dithiothreitol (10 mM final, Sigma) for 30 min, followed by alkylation with chloroacetamide (40 mM final, Sigma) for 45 min and quenching with dithiothreitol (20 mM final, Sigma). Beads (1 mg) and acetonitrile (70% final concentration) were added to each sample and after 20 min of incubation on an over-head rotor bead-bound protein were washed with 70% ethanol and 100% acetonitrile. 2 μg sequence-grade Trypsin (Promega) and 2 μg Lysyl Endopeptidase LysC (Wako) in 50 mM HEPES (pH 8) were added and after an overnight incubation at 37° C. peptides were collected, acidified with trifluoroacetic acid and cleaned up using StageTips protocol [21].


Heart Reference Sample for Matching Library

A peptide mix for each experimental group (Control, AS and MI) was generated by collecting 10 μg peptides from each individual sample belonging to the corresponding group. Equal peptide amounts from each group mixture were combined, desalted using a C18 SepPak column (Waters, 100 mg) and dried down using a SpeedVac instrument. Peptides were reconstituted in 20 mM ammonium formate (pH 10) and 2% acetonitrile, loaded on a XBridge C18 4.6 mm×250 mm column (Waters, 3.5 μm bead size) and separated on an Agilent 1290 HPLC instrument by basic reversed-phase chromatography, using a 90 min gradient with a flow rate of 1 ml/min, starting with solvent A (2% acetonitrile, 5 mM ammonium formate, pH 10) followed by increasing concentration of solvent B (90% acetonitrile, 5 mM ammonium formate, pH 10). The 96 fractions were collected and concatenated by pooling equal interval fractions. The final 26 fractions were dried down and resuspended in 3% acetonitrile/0.1% formic acid for LC-MS/MS analyses.


LC-MS/MS Analyses

Peptide samples were eluted from stage tips (80% acetonitrile, 0.1% formic acid), and after evaporating organic solvent peptides were resolved in sample buffer (3% acetonitrile/0.1% formic acid). Peptide separation was performed on a 20 cm reversed-phase column (75 μm inner diameter, packed with ReproSil-Pur C18-AQ; 1.9 μm, Dr. Maisch GmbH) using a 200 min gradient with a 250 nl/min flow rate of increasing Buffer B concentration (from 2% to 60%) on a High Performance Liquid Chromatography (HPLC) system (ThermoScientific). Peptides were measured on an Orbitrap Fusion (individual samples) and Q Exactive HF-X Orbitrap instrument (reference sample) (ThermoScientific). On the Orbitrap Fusion instrument, peptide precursor survey scans were performed at 120K resolution with a 2×105 ion count target. MS2 scans were performed by isolation at 1.6 m/z with the quadrupole, HCD fragmentation with normalized collision energy of 32, and rapid scan analysis in the ion trap. The MS2 ion count target was set to 2×103 and the max injection time was 300 ms. The instrument was operated in Top speed mode with 3 s cycle time, meaning the instrument would continuously perform MS2 scans until the list of non-excluded precursors diminishes to zero or 3 s. On the Q Exactive HF-X Orbitrap instrument, full scans were performed at 60K resolution using 3×106 ion count target and maximum injection time of 10 ms as settings. MS2 scans were acquired in Top 20 mode at 15K resolution with 1×105 ion count target, 1.6 m/z isolation window and maximum injection time of 22 ms as settings. Each sample was measured twice, and these two technical replicates were combined in subsequent data analyses.


Data were analyzed using MaxQuant sofware package (v1.6.2.6) [22]. The internal Andromeda search engine was used to search MS2 spectra against a decoy human UniProt database (HUMAN.2019-01, with isoform annotations) containing forward and reverse sequences. The search included variable modifications of oxidation (M), N-terminal acetylation, deamidation (N and Q) and fixed modification of carbamidomethyl cysteine. Minimal peptide length was set to six amino acids and a maximum of three missed cleavages was allowed. The FDR (false discovery rate) was set to 1% for peptide and protein identifications. Unique and razor peptides were considered for quantification. Retention times were recalibrated based on the built-in nonlinear time-rescaling algorithm. MS2 identifications were transferred between runs with the “Match between runs” option, in which the maximal retention time window was set to 0.7 min. The integrated LFQ quantitation algorithm was applied. Gene Symbols assigned by MaxQuant were substituted with gene symbols of the reported UniProt IDs from the FASTA file used.


Description of the Mathematical Model (CARDIOKIN1)

For the quantification of the metabolic changes caused by the abundance changes of metabolic enzymes, we developed a mathematical model of the cardiac energy metabolism, which comprises all pathways involved in the catabolism of the energy-delivering substrates glucose, lactate, fatty acids, KBs and BCAAs as well as the synthesis of endogenous energy stores (glycogen, triacylglycerol) (see FIG. 1). The model also takes into account the short-term regulation of metabolic enzymes and transporters by the hormones insulin and catecholamines and key electrophysiological processes at the inner mitochondrial membrane including the generation of the proton gradient by the respiratory chain, the synthesis of ATP by the FoF1-ATPase and the membrane transport of various ions.


The time course of model variables (=concentration of metabolites and ions) is governed by first-order differential equations. Time-variations of small ions are modeled by kinetic equations of the Goldman-Hodgkin-Katz type as used in our previous work [13]. The rate laws for enzymes and membrane transporters were either taken from the literature or constructed based on published experimental data for the mammalian heart.


Model calibration for individual hearts We used the proteomics-derived protein profiles of enzymes and transporters for model calibration by computing the maximal activities (Vmax) of the enzymes by the relation










V
max
subject

=


V
max
normal




E
subject




E
control









(
1
)







where custom-characterEcontrolcustom-character is the average protein intensity of the enzyme in the group of control hearts and ESubject is the protein concentration of the enzyme in the individual (control or patient). The maximal activities vmaxnormal of the reference model for the average normal heart were obtained by fitting of the model to experimental data. Equation (1) follows from the fact that the maximal enzyme activity is proportional to the abundance of the protein.


Energetic Capacities of Controls and Patients with Valve Diseases


We used the model to compute the specific uptake rates of substrates and the specific ATP production rate at rest, MVATP(rest), and at maximal ATP workload, MVATP(max), for the LV of controls (N=17) and patients with MI (N=17) or AS (N=41). As third parameter to characterize the capacity of the LV to increase the ATP production with increasing workload, we used the span between MVATP(max) and MVATP(rest), which we will refer to as myocardial ATP production reserve, MAPR (MAPR=MVATP(max)−MVATP(rest)). In the following, we will distinguish between specific energy parameters MVATP(rest), MVATP(max) and MAPR quantifying the energetic capacity per mass unit of the LV (given in μmol/g/h) and total energy parameters tMVATP(rest), tMVATP(max) and tMAPR quantifying the energetic capacity of the LV (given in mmol/h), i.e. tMVATP(rest)=MVATP(rest)×LV mass/1000 etc.


The computations were performed for a normal post-absorptive state (overnight fast) characterized by the following metabolite and hormone concentrations: glucose 5.8 mM [23], fatty acids 0.5 mM [24], lactate 0.8 mM [23], glutamine 0.5 mM [25, 26], valine 0.2 mM [25, 26], leucine 0.15 mM [25, 26], isosleucine 0.06 mM [25, 26], ß-hydroxybutyrate 0.08 mM [27, 28], acetoacetate 0.04 mM. The concentration of catecholamines at rest was 0.75 nM [29, 30] and increased with growing workload (Example 2).


The myocardial ATP consumption of the stationary resting state, MVATP(rest), was chosen in a way that the computed oxygen consumption (MVO2) was identical with the subject's MVO2, which we estimated by the 2-factor approximation










MV

O

2


=

γ
·
HR
·
BP





(
7
)







HR and BP are the heart rate and the peak systolic blood pressure and γ is a proportionality factor. Resting MVO2 of normal hearts was found in the range of 0.8-1.2 ml/min/g [2-4]. Thus, with a mean MVO2=0.1 ml/min/g, HR=70/min and normal BP=125 mm, we set γ to 1.143×10-5 ml/mmHg/g.


The metabolic response of the ventricle to an additional workload (pacing) was evaluated by computing the temporal changes of the metabolic state elicited by an increase of the ATP consumption rate above the resting value. The ATP consumption rate was modeled by a generic hyperbolic rate law










v
ATP

=


k
load

·

ATP

ATP
+

K
m








(
8
)







The parameter kload was stepwise increased until MVATP converged to the maximum, MVATP(max).


To evaluate the mechanical burden of the heart, we calculated the internal myocardial power, which describes the energy required for cardiac contraction for the individual hearts (see methods used in Lee et al. [32]).


All model simulations were performed using MATLAB, Release R2011b, The MathWorks, Inc., Natick, Massachusetts, United States.


Example 1: A Novel Method to Assess the Myocardial ATP Producing Capacity

Currently, no method is available to measure MVATP in vivo. Invasive techniques, such as the determination of substrate extraction rates from coronary sinus, arterial concentration differences or the oxidation rates of 14C-labeled substrates from the rates of 14CO2, have been applied in healthy subjects and patients with heart diseases [45, 47, 49]. However, such data cannot be directly converted into rates of ATP production. The same holds true for the measurement of the myocardial oxygen consumption rate MVO2 reflecting the overall myocardial oxidative metabolism. The MVO2 does not capture the glycolytic ATP contribution, which is low under normoxic conditions but may increase 5-fold during development of heart failure or even 20-fold during the transition from aerobic to anaerobic energy production [51]. Moreover, the ATP/O2 ratio may change considerably with increasing workload owing to increasing cardiac preference for carbohydrates. This makes it difficult to convert O2 consumption rates into ATP consumption rates. In addition, the maximal MVO2 can be low due to restrictions imposed to heart performance by the non-metabolic factors. To close this methodological gap, we applied here a novel approach to assess to energetic capacity of the LV of the human heart by combining kinetic modelling with protein abundance data of metabolic enzymes determined in cardiac tissue.


Except for the maximal enzyme activities (Vmax values), which may vary owing to variable gene expression, the numerical values for all other parameters of the enzymatic rate laws were taken from reported kinetic studies of the isolated enzymes. Numerical values for the Vmax values were estimated by the same procedure that was used for the calibration of our metabolic liver model [19]: Calculated metabolite profiles and fluxes were adjusted to experimental data from independent experiments with perfused hearts and in vivo measurements (see Table 2) while the metabolite concentrations were constrained to experimentally determined ranges. Short-term regulation of key regulatory enzymes by the hormones insulin and catecholamines (epinephrine, nor-epinephrine) was included into the model by phenomenological mathematical functions relating the enzyme's phosphorylation state and the abundance of the GLUT4 transporter in the sarcolemma to the plasma concentrations of glucose (insulin) and the exercise level (catecholamines) (see Example 2).









TABLE 2







Model simulations, which correctly


recapitulate metabolic measurements


obtained with perfused hearts and in human in vivo studies


FFAs = free fatty acids, KBs = ketone bodies,


BCAAs = branched-chain amino acids








Measurements
Data source





Glucose utilization at varying
[33, 34]


exogenous glucose concentrations



Lactate utilization and lactate/O2 ratio at varying
[35]


exogenous lactate concentrations



Utilization of FFAs at varying
[36, 37]


exogenous FFA concentrations



Glucose utilization in response to varying exogenous
[38]


concentration of FFAs (glucose-FFA-competition)



KBs utilization at varying exogenous β-
[39]


hydroxybutyrate concentrations



Utilization rates of glucose, lactate, FFAs, KBs and
[40-46]


BCAAs under post-absorptive resting conditions



Utilization rates of glucose, lactate, FFAs, KBs and
[40, 43, 44]


BCAAs at moderate pacing









Details of all validation simulations listed in Table 2 are given in below. As the heart switches its substrate uptake rates in dependence of substrate availability, we performed different simulations with variable substrate availability.


Glucose Uptake:

First, we simulated the glucose uptake of cardiac muscle in dependence of glucose availability. To match experimental conditions, we assumed that glucose and oxygen are the only available substrates, assumed that there are no hormones present and that the ATP demand is constant with a moderate demand. All external conditions are given in the Table 3.









TABLE 3





External conditions for simulation of cardiac glucose uptake


















Glucose [mM]
0.5-25
Valine [mM]
0


Lactate [mM]
0
Leucine [mM]
0


Fatty acids [mM]
0
Isoleucine [mM]
0


B-hydroxybuterate [mM]
0
Insulin [nM]
0-1500


Acetoacetate [mM]
0

TF (Example 2)




k-load
5









Lactate Uptake:

The next most abundant carbohydrate available to the heart is lactate. Therefore, we used the model to investigate the utilization of this important fuel, when the supply with alternative substrate is limited. We varied the external availability of lactate between 0 mM and 12 mM, keeping the glucose concentration at a low value of 2 mM and putting the fatty acid concentration to 0.1 mM (Table 4). Lactate to oxygen consumption rate (OCR) ratio increases up to 4 mM plasma lactate concentration when saturation is reached. This means that in the physiological range (<2 mM) lactate uptake is limited by substrate availability.









TABLE 4





External conditions for simulation of cardiac lactate uptake


















Glucose [mM]
2
Valine [mM]
0


Lactate [mM]
0.2-12
Leucine [mM]
0


Fatty acids [mM]
0.1
Isoleucine [mM]
0


B-hydroxybuterate [mM]
0
Insulin [nM]
1


Acetoacetate [mM]
0

TF (Example 2)




k-load
0









Fatty Acid Uptake:

Next, we checked the ability of the model to recapitulate fatty acid uptake. We monitored the fatty acid uptake when systematically varying the plasma fatty acid concentrations between 0 and 2 mM while assuming a moderate ATP demand (Table 5). As the majority of fatty acids in the plasma are bound to albumin, but only free fatty acids are taken up by the heart, we used the transfer function depicted in Example 2 to calculate the free fatty acid concentration from the plasma fatty acid concentration.









TABLE 5





External conditions for simulation of cardiac fatty acid uptake


















Glucose [mM]
7.63
Valine [mM]
0


Lactate [mM]
1
Leucine [mM]
0


Fatty acids [mM]
0-2
Isoleucine [mM]
0


B-hydroxybuterate [mM]
0
Insulin [nM]
757


Acetoacetate [mM]
0

TF (Example 2)




k-load
5









Suppression of Glucose Uptake by Plasma Fatty Acids:

After checking that the model correctly recapitulates the substrate utilization for glucose and fatty acids in the absence of the other substrate, the next step was to investigate the interplay of the different substrates. Therefore, we simulated the uptake of glucose in the presence of varying fatty acid concentrations in the plasma. With increasing fatty acid availability, the model correctly recapitulates the replacement of glucose with fatty acids. This strongly supports the view that fatty acids are the preferred substrate for the heart, and that glucose is used only when fatty acid availability is limited. (Table 6)









TABLE 6





External conditions for simulation of the uptake of glucose in


the presence of varying fatty acid concentrations in the plasma.


















Glucose [mM]
5.8
Valine [mM]
0


Lactate [mM]
0.8
Leucine [mM]
0


Fatty acids [mM]
0-1.2
Isoleucine [mM]
0


B-hydroxybuterate [mM]
0
Insulin [nM]
257


Acetoacetate [mM]
0

TF (Example 2)




k-load
2









Ketone Body Utilization:

Ketone bodies represent an important substrate for the heart especially during fasting conditions when glucose and lactate are not available or need to be saved for the utilization by other organs (i.e. gluconeogenesis form lactate in the liver or glycolysis in the brain). Assuming moderate glucose levels and moderate load, we systematically varied the plasma ketone body concentration (B-hydroxybuterate) from 0 to 5.5 mM and monitored the ketone body uptake rates. (Table 7)









TABLE 7





External conditions for simulation of the ketone body uptake.


















Glucose [mM]
4
Valine [mM]
0


Lactate [mM]
0.8
Leucine [mM]
0


Fatty acids [mM]
0-5
Isoleucine [mM]
0


B-hydroxybuterate [mM]
0
Insulin [nM]
36


Acetoacetate [mM]
0

TF (Example 2)




k-load
3









Substrate Utilization in the Human Heart:

Next, we tested whether the model correctly recapitulates substrate uptake of the human heart under physiological conditions when all substrates (glucose, lactate, fatty acids, ketone bodies and branched chain amino acids) are present at the same time. We simulated the substrate utilization rates of the human heart at rest and moderate pacing in an overnight fasted state and compared the simulated rates to experimental data for the human heart (Table 7). FIG. 2 shows that the model calculations recapitulate the substrate uptake profile of the normal human heart as reported in several in vivo studies [8-14] (FIG. 2A). At rest, lactate is utilized with the highest rate, followed by fatty acids and ketone bodies. Increased energy demand during pacing is predominantly fueled by increased uptake by carbohydrates (glucose, lactate, pyruvate), while fatty acid utilization remains almost constant. Branched chain amino acids do not contribute significantly to the energy expenditure of the heart (<1%).









TABLE 7





External conditions for simulation of the substrate


utilization rates of the human heart.


















Glucose [mM]
5.8
Valine [mM]
0.2


Lactate [mM]
0.8
Leucine [mM]
0.15


Fatty acids [mM]
0.5
Isoleucine [mM]
0.06


B-hydroxybuterate [mM]
0.08
Insulin [nM]
100


Acetoacetate [mM]
0.04

TF (Example 2)




k-load
0.5/3










FIG. 2 shows two model validations highlighting the good concordance of model predictions with experimental data. The examples demonstrate the ability of the heart to ensure cardiac functionality at varying cardiac workload and varying plasma concentrations of energy substrates. In FIG. 2A, the computed substrate uptake profile of the normal human heart is compared with the mean of experimental data taken from several in vivo studies [41-48]. At rest, lactate is utilized with the highest rate, followed by free fatty acids (FFAs) and KBs. Counted in moles ATP per moles substrate (glucose—38, lactate—18, palmitate—138, text book values), FFAs represent the dominating energy source. At moderate pacing, the uptake of the carbohydrates is more than doubled whereas the uptake of FFAs remains essentially unaltered. The energetic contribution of BCAAs was less than 1% at rest and pacing. FIG. 2B shows the relationship between glucose uptake and plasma FFA concentration. The uptake rate of glucose is suppressed with increasing levels of plasma FFAs by inhibition of glucose uptake ensuring the preferential utilization of fatty acids (FIG. 2B).


For patient-specific model calibration, we used protein intensity profiles (defined through LFQ intensities, see Methods) of 17 control hearts, 41 patients with AS and 17 patients with MI. Using two dimensional liquid chromatography prior to tandem mass spectrometry analysis we identified, in total, 9.133 distinct protein groups, from which a subset of 321 proteins was used for model calibration.


Example 2: External Conditions and Transfer Functions

Glucose-Insulin: The plasma concentrations of the hormone insulin determine the phosphorylation state of the inter-convertible enzymes. Insulin is secreted by the pancreas into the portal vein and the secretion rate is mainly controlled by the glucose concentration of the blood. Therefore, we used the empirical glucose hormone transfer function (GHT), which describes the relationship between the plasma level of glucose and the plasma levels of insulin established in Bulik et al., 2016 [63]:






Ins
=

1.55

nM
*



(

Glc
ext

)

5.7




(

Glc
ext

)

5.7

+


(

7.7

mM

)

5.7








Enzyme phosphorylation state: The concentration of insulin determines the phosphorylation state of the interconvertible enzymes [63]. The phosphorylation state γ of interconvertible enzymes is given by:






γ
=

1
-


Ins
0.65



Ins
0.65

+


(

0.4

nM

)

0.65








AMP-dependent phosphorylation: In addition to hormone dependent phosphorylation, phosphorylation in dependence of the energetic state of the cell is achieved by the AMP-dependent kinase. Therefore, we introduced AMP dependent phosphorylation by







γ
AMP

=

AMP

AMP
+
0.04






Glucose-fatty acids: The plasma concentration of fatty acids (FA) is largely determined by the rate of triglyceride lipolysis in the adipose tissue, which is mainly controlled by insulin and glucagon through the activity of the hormone sensitive lipases (HSL). Based on measured relations between the plasma levels of plasma and FA we constructed an empirical glucose-FA transfer function (GFT):







tfa
plasma

=


1.2

mM

-

1.1

mM



Glc
ext
4



Glc
ext
4

+


(

6.5

mM

)

4









Conversion of total plasma fatty acids to free plasma fatty acids: Plasma fatty acids are largely bound to plasma albumin or lipoproteins, but only free fatty acids are taken up by the heart. We calculated the free fatty acid concentration (ffαplasma) from total plasma fatty acid concentration (tfαplasma) assuming a linear relationship between the two. In this way, we can recapitulate hyperbolic saturation kinetics in the cardiac fatty acid uptake rates when depicted against total plasma fatty acid concentration or against free fatty acid plasma concentration:







ffa
plasma

=

3.125
·

10

-
4


·

tfa
plasma






Epinephrine: The plasma concentrations of the hormone epinephrine is an important determinant for the activity of glucose transport capacity in cardiomyocytes. As epinephrine increases cardiac pacing [64], we describe epinephrine levels in dependence of cardia pacing (load) by a transfer function.


Example 3: Energetic Capacities of the LV of Controls and Patients with Valve Diseases


FIG. 3 depicts the specific energetic parameters MVATP(rest), MVATP(max) and MAPR for each subject after 60 min pacing. Compared with controls, the individual variations of these parameters were much larger for the two patient groups (see box plots in FIG. 3 B-D). For MI patients, the mean value of the parameter MVATP(rest) was significantly higher (890±292 versus 761±10 μmol/g/h), while MVATP(max) was significantly lower when compared to control values (1713±245 versus 1941±238 μmol/g/h) (two-sample Kolmogorov-Smirnov test). For AS patients, the mean value of the parameter MVATP(rest) was also significantly higher (800±270 versus 761±10 μmol/g/h) and MVATP(max) was also significantly lower (1513±257 versus 1941±238 μmol/g/h). For both groups of patients, the parameter MAPR was on the average significantly lower compared to the control (826±448 in MI and 904±340 in AS versus 1180±245 μmol/g/h). Hence, both groups of patients had on the average a reduced ATP production reserve, which was caused by increased MVATP(rest) and decreased MVATP(max).


MVATP(rest) was significantly increased in the MI and AS group and MVATP(max) was significantly decreased in both groups, resulting in a significant reduction of the specific ATP production reserve MAPR (see FIG. 3). The general decrease of MVATP(max) in both groups of patients can be accounted for by a decrease of the oxidative phosphorylation capacity as none of the investigated LVs showed excessive glycolytic activity. A decreased expression of the PGC-1α/PPARα transcription cascade has been identified as an important mechanism responsible for the downregulation of the oxidative phosphorylation in the failing myocardium [3].


Example 4: Substrate Uptake of Patients at Rest and at Maximal Workload

Next, we investigated changes in the substrate preference of the LV accompanying altered metabolic capacity (see FIG. 4). In the resting state, the largest differences occurred for the uptake rates of glucose and lactate for patients with MI. Especially glucose uptake was increased by more than 20%. At rest, there was a significant decrease in lactate utilization in patients with AS. In general, variances in substrate utilization rates were large, again pointing to individually differing metabolic phenotypes. The reduction in lactate utilization was significant also at maximal load in MI and AS patients, while glucose rates were significantly reduced for patients with AS only. FIG. 4 also shows how the different substrates contribute to overall energy production. The contribution of fatty acids accounts for up to two third, while BCAAs always account for <1% of total energy expenditure and are therefore not shown.


Both groups of patients exhibited significant changes in the myocardial utilization of the main energy substrates. Generally, there was a trend towards higher uptake rates for glucose and decreased uptake rates for lactate in patients with MI, and a decrease in glucose as well as lactate utilization for AS patients. Ketone body utilization rates showed a high variability, but were in general increased in AS patients. This is in line with recent studies suggesting that increased reliance on ketone body metabolism offers a metabolic advantage in the failing heart and an ergogenic aid for exercise performance [55, 56].


Example 5: Association of MVATP with Clinical Parameters Evaluating the Mechanical Work and the Systolic Performance of the LV

In valve disease, the LV is exposed to chronic pressure load (AS) and/or volume overload (MI). This results in a higher mechanical workload, which can be quantified by the surrogate internal myocardial power estimating the power of the LV required for cardiac contraction [32]. Our analysis provided evidence for a strong correlation between tMVATP at rest and at maximal pacing and the internal myocardial power (see FIG. 5). Importantly, a significant correlation of the energy parameters has also been found with the cardiac output (see FIG. 5). Taken together, these findings demonstrate a close association between increased ATP production capacity, increased mechanical work of the pressure/volume overloaded LV and cardiac output.


The central findings of our approach are that even in patients with valvular dysfunction but preserved systolic function and no sign of heart failure, the energy metabolism is already deteriorated (see FIG. 3) and closely associated with mechanical power and systolic performance (see FIG. 5). The first finding is in line with several studies (reviewed in [52]) which have established that a reduction in the ATP production capacity already occurs in early phases of heart failure development. The second finding identifies the capability of the cardiac metabolic network to generate ATP as the key link between systolic function and energy metabolism of the LV rather than the intracellular transport capacity of energy-rich phosphates by the CK shuttle, which was found to not be significantly different in AS patients with preserved and reduced systolic function [10].


Example 6: Metabolic Profiling of Individual Patients

Despite the general trend of the energy parameters in the patients' LV outlined in the preceding section, substantial differences in the metabolic profiles of individual patients occur. As an example, FIG. 6 depicts the individual energetic profiles of three patients with AS with largely differing values of their cardiac energy parameters (see FIG. 3A). Patients A2 and A4 are characterized by impaired MAPR, while patient A13 has a MAPR comparable to healthy hearts (see FIG. 3). The impaired MAPR of patient A2 results from an increased MVATP(rest) with a normal MVATP(max), while the impaired MAPR of patient A4 results from an increased MVATP(rest) and a decreased MVATP(max). Patient A13 with a normal MAPR has normal MVATP(rest) and normal MVATP(max). The individual alterations in the energetics of the LV are also associated with marked differences in substrate utilization rates. For example, while A13 has normal MVATP(rest), its resting carbohydrate utilization rates (glucose and lactate) are strongly decreased and compensated by an increase KB utilization rate. This increased KB utilization is also maintained at MVATP(max) and is even more pronounced in A2. In contrast, patient A4 shows a decreased utilization rate for all substrates at MVATP(max).


Our analysis revealed in both groups of patients a large variability of the energy parameters (see FIGS. 3 and 6), likely reflecting larger differences in the patient-specific functional and structural response of the LV to pressure/volume overload. Whereas some patients present with signs of hypertrophy, myocardial thickening and ventricular dilation, others may show alterations in contraction time or only modest signs of remodeling [53, 54]. The large intra-individual variability of cardiac energetics in patients with valvular dysfunction necessitates an individual assessment of the metabolic status (see FIG. 6).


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TABLE 8





Information to Kinetic rate laws (Table 8 uses separate reference numbering)







Fatty acid uptake


Carrier mediated FATP










v

CD

36


=


V
max

CD

36


·


(


ffa
ext

-

c


16
cyt



)


1
+


ffa
ext


K
m

ffa
ext



+


c


16
cyt



K
m

c


16
cyt
















VmaxCD36 for numerical value see Table 10 Kmffaext = 0.000085 [1] Kmc16cyt = 0.004 [2]


(Long-chain) acyl-coa synthetase










v

ACS

1


=


V
max

ACS

1


·


c


16
cyt




c


16
cyt


+

K
m

c


16
cyt





·


atp
cyt



atp
cyt

+

K
m

atp
cyt




·


coa
cyt



coa
cyt

+

K
m

coa
cyt














VmaxACS1 for numerical value see Table 10


Kmc16cyt = 0.033 [3] Kmatpcyt = 0.320 [3] Kmcoacyt = 0.0064 [3]










v

FATP

1


=


V
max

FATP

1


·


c


16
cyt




c


16
cyt


+

K
m

c


16
cyt





·


atp
cyt



atp
cyt

+

K
m

atp
cyt




·


coa
cyt



coa
cyt

+

K
m

coa
cyt



















V
max

FATP

1


=





V
max

ACS

1


27

[
3
]




K
m

c


16
cyt




=



0.021
[
3
]




K
m

atp
cyt



=



0.85
[
3
]




K
m

coa
cyt



=

0.0083

[
3
]


















v

FATP

4


=


V
max

FATP

4


·


c


16
cyt




c


16
cyt


+

K
m

c


16
cyt





·


atp
cyt



atp
cyt

+

K
m

atp
cyt




·


coa
cyt



coa
cyt

+

K
m

coa
cyt














VmaxFATP4 = 1.3 · VmaxASC1 [4] Kmc16cyt = 0.013 [4] Kmatpcyt = 1.4 [4]


Kmcoacyt = 0.047 [4]





Beta-oxidation


Carnitine palmitoyltransferase I (muscle isoform)










v

CPT

1


=


V
max

CPT

1


·


c

16



coa
cyt

·

car
cyt





(


c

16


coa
cyt


+

K
m

c

16


coa
cyt




)

·

(


car
cyt

+

K
m

car
cyt



)













VmaxCPT1 for numerical value see Table 10










K
m

c

16


coa
cyt



=


K
0

c

16


coa
cyt



·

(

1
+


malcoa


2
imm



K
i

malcoa


2
imm





)











K0c16coacyt = 0.073 [5] Kimalcoa2imm = 0.0001 [6] Kmcarcyt = 0.19 [7]


Carnitine acylcarnitine translocase










v
CACT

=


V
max
CACT

·

(





car
mito

·
c


16


car
cyt


-

1
/


K
eq
CACT

·

car
cyt

·
c


16


car
mito






(

1
+


car
mito


K
m

car
mito




)



(

1
+


c

16


car
cyt



K
m

c

16


coa
cyt





)


+


(

1
+


car
cyt


K
m

car
cyt




)



(

1
+


c

16


car
mito



K
m

c

16


car
mito





)


-
1


)











VmaxCACT for numerical value see Table 10


KeqCACT = 1.6 [8] Kmcarmito = 5.8 [9] Kmc16carcyt = 0.001 [10] Kmcarcyt = 1.3 [11]


Kmc16carmito = 0.0051 [12]


Carnitine palmitoyltransferase 2










v

CPT

2


=


V
max

CPT

2


·

(



c

16



car
mito

·

coa
mito



-

1
/


K
eq

CPT

2


·
c


16



coa
mito

·

car
mito







(

1
+


c

16


car
mito



K
m

c

16


car
mito





)



(

1
+


coa
mito


K
m

coa
mito




)


+


(

1
+


c

16


coa
mito



K
m

c

16


coa
mito





)



(

1
+


car
mito


K
m

car
mito




)


-
1


)











VmaxCPT2 for numerical value see Table 10


KeqCPT2 = 2 [13] Kmc16carmito = 0.12 [14] Kmcoamito = 0.0055 [15] Kmc16coamito = 0.191 [16]


Kmcarmito = 0.46 [17]


Short chain acyl-coa dehydrogenase (c4) (identical to liver enzyme [18])










v


c

4

coa

-
scdh


=


V
max


c

4

coa

-
dh


·

(


c

4


coa
mito




c

4


coa
mito


+

K
m

c

4


coa
mito





)

·

(


etffad
mito



etffad
mito

+

K
m

etffad
mito




)











Vmaxc4coa-dh for numerical value see Table 10


Kmc4coamito = 0.0107 [19] Kmetffadmito = 0.0038 [19]


Short chain acyl-coa dehydrogenase (c5) (identical to liver enzyme [18])










v


c

5

coa

-
scdh


=


V
max


c

5

coa

-
dh


·

(


c

5


coa
mito




c

5


coa
mito


+

K
m

c

5


coa
mito





)

·

(


etffad
mito



etffad
mito

+

K
m

etffad
mito




)











Vmaxc5coa-dh for numerical value see Table 10


Kmc5coamito = 0.01 Kmetffadmito = 0.0038 [19]


Medium chain acyl-coa dehydrogenase (c6) (identical to liver enzyme [18])










v


c

6

coa

-
mcdh


=


V
max


c

6

coa

-
dh


·

(


c

6


coa
mito




c

6


coa
mito


+

K
m

c

6


coa
mito





)

·

(


etffad
mito



etffad
mito

+

K
m

etffad
mito




)











Vmaxc6coa-dh for numerical value see Table 10













K
m

c


6

coa
mito




=


0
.
0


0

9


4
[
19
]







K
m

etffad
mito


=


0
.
0



045

[
19
]














Medium chain acyl-coa dehydrogenase (c8) (identical to liver enzyme [18])










v


c

8

coa

-
mcdh


=


V
max


c

8

coa

-
dh


·

(


c

8


coa
mito




c

8


coa
mito


+

K
m

c

8


coa
mito





)

·

(


etffad
mito



etffad
mito

+

K
m

etffad
mito




)











Vmaxc8coa-dh for numerical value see Table 10


Kmc8coamito = 0.004 [19] Kmetffadmito = 0.0045 [19]


Medium chain acyl-coa dehydrogenase (c10) (identical to liver enzyme [18])










v


c

10

coa

-
mcdh


=


V
max


c

10

coa

-
dh


·

(


c

10


coa
mito




c

10


coa
mito


+

K
m

c

10


coa
mito





)

·

(


etffad
mito



etffad
mito

+

K
m

etffad
mito




)











Vmaxc10coa-dh for numerical value see Table 10


Kmc10coamito = 0.0054 [19] Kmetffadmito = 0.0045 [19]


Medium chain acyl-coa dehydrogenase (c12) (identical to liver enzyme [18])










v


c

12

coa

-
mcdh


=


V
max


c

12

coa

-
dh


·

(


c

12


coa
mito




c

12


coa
mito


+

K
m

c

12


coa
mito





)

·

(


etffad
mito



etffad
mito

+

K
m

etffad
mito




)











Vmaxc12coa-dh for numerical value see Table 10


Kmc12coamito = 0.0057 [19] Kmetffadmito = 0.0045 [19]


Long chain acyl-coa dehydrogenase (c10) (identical to liver enzyme [18])










v


c

10

coa

-
lcdh


=


V
max


c

10

coa

-
dh


·

(


c

10


coa
mito




c

10


coa
mito


+

K
m

c

10


coa
mito





)

·

(


etffad
mito



etffad
mito

+

K
m

etffad
mito




)

















V
max


c

10

coa

-
dh




for


numerical


value


see


Table


10



K
m

c

10


coa
mito




=


K
0

c

10


coa
mito



·

(

1
+


kc

16


coa
mito



K
i

kc

16


coa
mito





)











Kikc16coamito = 0.00047 [20] K0c10coamito = 0.0243 [19] Kmetffadmito = 0.0083 [19]


Long chain acyl-coa dehydrogenase (c12) (identical to liver enzyme [18])










v


c

12

coa

-
lcdh


=


V
max


c

12

coa

-
dh


·

(


c

12


coa
mito




c

12


coa
mito


+

K
m

c

12


coa
mito





)

·

(


etffad
mito



etffad
mito

+

K
m

etffad
mito




)

















V
max


c

12

coa

-
dh




for


numerical


value


see


Table


10



K
m

c

12


coa
mito




=


K
0

c

12


coa
mito



·

(

1
+


kc

16


coa
mito



K
i

kc

16


coa
mito





)











kikc16coamito = 0.00047 [20] K0c12coamito = 0.009 [19] Kmetffadmito = 0.0083 [19]


Long chain acyl-coa dehydrogenase (c14) (identical to liver enzyme [18])










v


c

14

coa

-
lcdh


=


V
max


c

14

coa

-
dh


·

(


c

14


coa
mito




c

14


coa
mito


+

K
m

c

14


coa
mito





)

·

(


etffad
mito



etffad
mito

+

K
m

etffad
mito




)











Vmaxc14coa-dh for numerical value see Table 10










K
m

c

14


coa
mito



=


K
0

c

14


coa
mito



·

(

1
+


kc

16


coa
mito



K
i

kc

16


coa
mito





)











Kikc16coamito = 0.00047 [20] K0c14coamito = 0.0074 [19] Kmetffadmito = 0.0083 [19]


Long chain acyl-coa dehydrogenase (c16) (identical to liver enzyme [18])










v


c

16

coa

-
lcdh


=


V
max


c

16

coa

-
dh


·

(


c

16


coa
mito




c

16


coa
mito


+

K
m

c

16


coa
mito





)

·

(


etffad
mito



etffad
mito

+

K
m

etffad
mito




)











Vmaxc16coa-dh for numerical value see Table 10










K
m

c

16


coa
mito



=


K
0

c

16


coa
mito



·

(

1
+


kc

16


coa
mito



K
i

kc

16


coa
mito





)











Kikc16coamito = 0.00047 [20] K0c16coamito = 0.0025 [19] Kmetffadmito = 0.0083 [19]


Enoyl-coa hydratase (Crontonase) (ec4)










v

ehyd
-

ec

4



=


V
max

ehyd
-

ec

4



·

(



ec

4


coa
mito


-

1
/


K
eq

ehyd
-

ec

4



·
lc


4


coa
mito





ec

4


coa
mito


+

K
m

ec

4


coa
mito





)











Vmaxehyd-ec4 for numerical value see Table 10










K
eq

ehyd
-

ec

4



=



0.25
[
21
]




K
m

ec

4


coa
mito




=


K
0

ec

4


coa
mito



·

(

1
+


kc

4


coa
mito



K
i

kc

4


coa
mito





)












K0ec4coamito = 0.013 [22] Kikc4coamito = 0.025 [23]


Enoyl-coa hydratase (Crontonase) (ec6)










v

ehyd
-

ec

6



=


V
max

ehyd
-

ec

6



·

(



ec

6


coa
mito


-

1
/


K
eq

ehyd
-

ec

6



·
lc


6


coa
mito





ec

6


coa
mito


+

K
m

ec

6


coa
mito





)



















V
max

ehyd
-

ec

6



=


V
max

ehyd
-

ec

4



·


1280

1

6

7

0


[
22
]







K
eq

ehyd
-

ec

6



=

2

[
21
]


















K
m

ec

6


coa
mito



=


K
0

ec


6

coa
mito




·

(

1
+


kc

4


coa
mito



K
i

kc

4


coa
mito





)











K0ec6coamito = 0.029 [22] Kikc4coamita = 0.025 [23]


Enoyl-coa hydratase (Crontonase) (ec8)










v

ehyd
-

ec

8



=


V
max

ehyd
-

ec

8



·

(



ec

8


coa
mito


-

1
/


K
eq

ehyd
-

ec

8



·
lc


8


coa
mito





ec

8


coa
mito


+

K
m

ec

8


coa
mito





)



















V
max

ehyd
-

ec

8



=


V
max

ehyd
-

ec

4



·


910

1

6

7

0


[
22
]







K
eq

ehyd
-

ec

8



=

2

[
21
]


















K
m

ec

8


coa
mito



=


K
0

ec

8


coa
mito



·

(

1
+


kc

4


coa
mito



K
i

kc

4


coa
mito





)











k0ec8coamito = 0.029 [22] Kikc4coamito = 0.025 [23]


Enoyl-coa hydratase (Crontonase) (ec10)










v

ehyd
-

ec

10



=


V
max

ehyd
-

ec

10



·

(



ec

10


coa
mito


-

1
/


K
eq

ehyd
-

ec

10



·
lc


10


coa
mito





ec

10


coa
mito


+

K
m

ec

10


coa
mito





)
















V
max

ehyd
-

ec

10



=




V
max

ehyd
-

ec

4



·


540
1670

[
22
]





K
eq

ehyd
-

ec

10




=

2

[
21
]
















K
m

ec

10


coa
mito



=




K
0

ec

10


coa
mito



·

(

1
+


kc

4


coa
mito



K
i

kc

4


coa
mito





)





K
0

ec

10


coa
mito




=



0.029
[
22
]




K
i

kc

4


coa
mito




=

0.025

[
23
]












Enoyl-coa hydratase (Crontonase) (ec12)










v

ehyd
-

ec

12



=


V
max

ehyd
-

ec

12



·

(



ec

12


coa
mito


-

1
/


K
eq

ehyd
-

ec

12



·
lc


12


coa
mito





ec

12


coa
mito


+

K
m

ec

12


coa
mito





)
















V
max

ehyd
-

ec

12



=




V
max

ehyd
-

ec

4



·


160
1670

[
22
]





K
eq

ehyd
-

ec

12




=

2
[
21
]
















K
m

ec

12


coa
mito



=




K
0

ec

12


coa
mito



·

(

1
+


kc

4


coa
mito



K
i

kc

4


coa
mito





)





K
0

ec

12


coa
mito




=



0.03
[
22
]




K
i

kc

4


coa
mito




=

0.025

[
23
]












Enoyl-coa hydratase (Crontonase) (ec14)










v

ehyd
-

ec

14



=


V
max

ehyd
-

ec

14



·

(



ec

14


coa
mito


-

1
/


K
eq

ehyd
-

ec

14



·
lc


14


coa
mito





ec

14


coa
mito


+

K
m

ec

14


coa
mito





)
















V
max

ehyd
-

ec

14



=




V
max

ehyd
-

ec

16



·


5
2.3


[
24
]





K
eq

ehyd
-

ec

14




=

2

[
21
]
















K
m

ec

14


coa
mito



=


K
0

ec

14


coa
mito



·

(

1
+


kc

4


coa
mito



K
i

kc

4


coa
mito





)











K0ec14coamito = 0.025 [23] Kikc4coamito = 0.025 [23]





Enoyl-coa hydratase (Crontonase) (ec16)










v

ehyd
-

ec

16



=


V
max

ehyd
-

ec

16



·

(


ec

16


coa
mito


1
/


K
eq

ehyd
-

ec

16



·
lc


16


coa
mito




ec

16


coa
mito


+

K
m

ec

16


coa
mito





)
















V
max

ehyd
-

ec

16



=




V
max

ehyd
-

ec

4



·


40
1670

[
22
]





K
eq

ehyd
-

ec

16




=

2

[
21
]
















K
m

ec

16


coa
mito



=


K
0

ec

16


coa
mito



·

(

1
+


kc

4


coa
mito



K
i

kc

4


coa
mito





)











K0ec16coamito = 0.030 [22] Kikc4coamito = 0.025 [23]


3-hydroxyacyl-coa dehydrogenase (Ic4) (identic with liver enzyme [25])










v


3

hdh

-

lc

4



=


V
max


3

hdh

-

lc

4



·

(



lc

4



coa
mito

·

nad
mito



-

1
/


K
eq


3

hdh

-

lc

4



·
kc


4



coa
mito

·

nadh
mito










(

1
+


lc

4


coa
mito



K
m

lc

4


coa
mito





)

·

(

1
+


nad
mito


K
m

nad
mito




)


+








(

1
+


kc

4


coa
mito



K
m


kc

4

coa

mito




)

·

(

1
+


nadh
mito


K
m

nadh
mito




)


-
1





)











Vmax3hdh-ic4 for numerical value see Table 10










K
eq


3

hdh

-

lc

4



=




1
0.012


[
26
]




K
m

lc

4


coa
mito




=

0.0072
[
27
]











Kmnadmito = 0.0154 [27] Kmkc4coamito = 0.0169 [28] = Kmnadhmito = 0.0118 [27]


3-hydroxyacyl-coa dehydrogenase (Ic6) (identic with liver enzyme [25])










v


3

hdh

-

lc

6



=


V
max


3

hdh

-

lc

6



·

(



lc

6



coa
mito

·

nad
mito



-

1
/


K
eq


3

hdh

-

lc

6



·
kc


6



coa
mito

·

nadh
mito










(

1
+


lc

6


coa
mito



K
m

lc

6


coa
mito





)

·

(

1
+


nad
mito


K
m

nad
mito




)


+








(

1
+


kc

6


coa
mito



K
m


kc

6

coa

mito




)

·

(

1
+


nadh
mito


K
m

nadh
mito




)


-
1





)











Vmax3hdh-lc6 for numerical value see Table 10










K
eq


3

hdh

-

lc

6



=




1

8
·

10

-
4





[
29
]




K
m

lc

6


coa
mito




=



0.0286
[
30
]




K
m

nad
mito



=

0.015

[
27
]












Kmkc6coamito 0.0057 [31] Kmnadhmito = 0.011 [27]


3-hydroxyacyl-coa dehydrogenase (Ic8) (identic with liver enzyme [25])










v


3

hdh

-

lc

8



=


V
max


3

hdh

-

lc

8



·

(



lc

8



coa
mito

·

nad
mito



-

1
/


K
eq


3

hdh

-

lc

8



·
kc


8



coa
mito

·

nadh
mito










(

1
+


lc

8


coa
mito



K
m

lc

8


coa
mito





)

·

(

1
+


nad
mito


K
m

nad
mito




)


+








(

1
+


kc

8


coa
mito



K
m


kc

8

coa

mito




)

·

(

1
+


nadh
mito


K
m

nadh
mito




)


-
1





)











Vmax3hdh-lc8 for numerical value see Table 10










K
eq


3

hdh

-

lc

8



=



1

10

-
3






K
m

lc

8


coa
mito




=



0.0163

[
28
]




K
m

nad
mito



=

0.015

[
27
]












Kmkc8coamito = 0.0031 [31] Kmnadhmito = 0.011 [27]


3-hydroxyacyl-coa dehydrogenase (Ic10) (identic with liver enzyme [25])










v


3

hdh

-

lc

10



=


V
max


3

hdh

-

lc

10



·

(



lc

10



coa
mito

·

nad
mito



-

1
/


K
eq


3

hdh

-

lc

10



·
kc


10



coa
mito

·

nadh
mito










(

1
+


lc

10


coa
mito



K
m

lc

10


coa
mito





)

·

(

1
+


nad
mito


K
m

nad
mito




)


+








(

1
+


kc

10


coa
mito



K
m


kc

10

coa

mito




)

·

(

1
+


nadh
mito


K
m

nadh
mito




)


-
1





)











Vmax3hdh-lc10 for numerical value see Table 10










K
eq


3

hdh

-

lc

10



=



1

10

-
3






K
m

lc

10


coa
mito




=



0.0029

[
27
]




K
m

nad
mito



=

0.0104

[
27
]




















K
m

kc


10

coa
mito




=


0
.
0


0

1


8
[
31
]







K
m

nadh
mito


=


0
.
0


0

1


1
[

2

7

]














3-hydroxyacyl-coa dehydrogenase (Ic12) (identic with liver enzyme [25])










v


3

hdh

-

lc

12



=


V
max


3

hdh

-

lc

12



·

(



lc

12



coa
mito

·

nad
mito



-

1
/


K
eq


3

hdh

-

lc

12



·
kc


12



coa
mito

·

nadh
mito










(

1
+


lc

12


coa
mito



K
m

lc

12


coa
mito





)

·

(

1
+


nad
mito


K
m

nad
mito




)


+








(

1
+


kc

12


coa
mito



K
m


kc

12

coa

mito




)

·

(

1
+


nadh
mito


K
m

nadh
mito




)


-
1





)











Vmax3hdh-lc12 for numerical value see Table 10










K
eq


3

hdh

-

lc

12



=



1

10

-
3






K
m

lc

12


coa
mito




=



0.0018

[
31
]




K
m

nad
mito



=

0.015

[
27
]












Kmkc12coamito = 0.0018 [31] Kmnadhmito = 0.011[27]


3-hydroxyacyl-coa dehydrogenase (Ic14) (identic with liver enzyme [25])










v


3

hdh

-

lc

14



=


V
max


3

hdh

-

lc

14



·

(



lc

14



coa
mito

·

nad
mito



-

1
/


K
eq


3

hdh

-

lc

14



·
kc


14



coa
mito

·

nadh
mito










(

1
+


lc

14


coa
mito



K
m

lc

14


coa
mito





)

·

(

1
+


nad
mito


K
m

nad
mito




)


+








(

1
+


kc

14


coa
mito



K
m


kc

14

coa

mito




)

·

(

1
+


nadh
mito


K
m

nadh
mito




)


-
1





)











Vmax3hdh-lc14 for numerical value see Table 10










K
eq


3

hdh

-

lc

14



=



1

10

-
3






K
m

lc

14


coa
mito




=



0.0015

[
31
]




K
m

nad
mito



=

0.015

[
27
]












Kmkc14coamito = 0.0013[31] Kmnadhmito = 0.011[27]


3-hydroxyacyl-coa dehydrogenase (Ic16) (identic with liver enzyme [25])










v


3

hdh

-

lc

16



=


V
max


3

hdh

-

lc

16



·

(



lc

16



coa
mito

·

nad
mito



-

1
/


K
eq


3

hdh

-

lc

16



·
kc


16



coa
mito

·

nadh
mito










(

1
+


lc

16


coa
mito



K
m

lc

16


coa
mito





)

·

(

1
+


nad
mito


K
m

nad
mito




)


+








(

1
+


kc

16


coa
mito



K
m


kc

16

coa

mito




)

·

(

1
+


nadh
mito


K
m

nadh
mito




)


-
1





)











Vmax3hdh-lc16 for numerical value see Table 10










K
eq


3

hdh

-

lc

16



=



1

10

-
3






K
m

lc


16

coa
mito





=

0.003

[
27
]



















K
m

nad
mito


=


0
.
0


1

4


5
[
27
]







K
m

kc


16

coa
mito




=


0
.
0


0

1


3
[
31
]







K
m

nadh
mito


=


0
.
0



11

[
27
]














3-ketoacyl-coa thiolase I (kc4)










v

3

kt


kc

4

coa


=


V
max


3

kt

-

kc


4
coa




·

(





coa
mito

·
kc


4


coa
mito


-

1
/


K
eq

3

kt


·

acoa
mito
2







(

1
+


coa
mito


K
m

coa
mito




)

·

(

1
+


kc

4


coa
mito



K
m


kc

4

coa

mito




)


+

(

1
+


acoa
mito


K
m

acoa
mito




)

-
1


)











Vmax3kt-kc4 for numerical value see Table 10 Keq3kt = 2500 [32] Kmcoamito = 0.0087 [33]










K
m

kc

4


coa
mito



=




K
0

kc

4


coa
mito



·

(

1
+


acoa
mito


K
i

acoa
mito




)





K
i

acoa
mito



=



0.125

[
34
]




K
0

kc

4


coa
mito




=

0.017
[
33
]

















K
m

acoa
mito


=




K
0

acoa
mito


·

(

1
+


kc

4


coa
mito



K
i

kc

4


coa
mito





)





K
0

acoa
mito



=



0.3

[
35
]




K
i

kc

4


coa
mito




=

0.0022
[
36
]












3-ketoacyl-coa thiolase II (kc4)










v

3

ktII


kc

4

coa


=


V
max


3

ktII

-

kc


4
coa




·

(





coa
mito

·
kc


4


coa
mito


-

1
/


K
eq

3

kt


·

acoa
mito
2







(

1
+


coa
mito


K
m

coa
mito




)

·

(

1
+


kc

4


coa
mito



K
m


kc

4

coa

mito




)


+

(

1
+


acoa
mito


K
m

acoa
mito




)

-
1


)











Vmax3ktll-kc4c for numerical value see Table 10 Keq3kt = 2500 [32] Kmcoamito = 0.0513 [33]










K
m

kc

4


coa
mito



=




K
0

kc

4


coa
mito



·

(

1
+


acoa
mito


K
i

acoa
mito




)





K
i

acoa
mito



=



0.125

[
34
]




K
0

kc

4


coa
mito




=

0.0135

[
33
]

















K
m

acoa
mito


=




K
0

acoa
mito


·

(

1
+


kc

4


coa
mito



K
i

kc

4


coa
mito





)





K
0

acoa
mito



=



0.3

[
35
]




K
i

kc

4


coa
mito




=

0.0022

[
36
]












3-ketoacyl-coa thiolase I (kc6)










v

3

kt


kc

6

coa


=


V
max


3

kt

-

c


6
coa




·

(



kc

6



coa
mito

·

coa
mito



-

1
/


K
eq

3

kt


·

acoa
mito

·
c


4


coa
mito





(


coa
mito

+

K
m

coa
mito



)

·

(


kc

6


coa
mito


+

K
m

kc

6


coa
mito




)



)











Vmax3kt-kc6 = 2.4 · Vmax3kt-kc4 [33] Keq3kt = 2500 [32] Kmcoamito 0.0087 [33] Kmkc6coamito =


0.0083[33]


3-ketoacyl-coa thiolase I (kc8)










v

3

kt


kc

8

coa


=


V
max


3

kt

-

kc

8



·

(



kc

8



coa
mito

·

coa
mito



-

1
/


K
eq

3

kt


·

acoa
mito

·
c


6


coa
mito





(


coa
mito

+

K
m

coa
mito



)

·

(


kc

8


coa
mito


+

K
m

kc

8


coa
mito




)



)











Vmax3kt-kc8 = 2.2 · Vmax3kt-kc4 [33] Keq3kt = 2500 [32] Kmcoamito = 0.0024[33]


Kmkc8coamito = 0.025 [37]





3-ketoacyl-coa thiolase I (kc10)










v

3

kt


kc

10

coa


=


V
max


3

kt

-

kc

10



·

(



kc

10



coa
mito

·

coa
mito



-

1
/


K
eq

3

kt


·

acoa
mito

·
c


8


coa
mito





(


coa
mito

+

K
m

coa
mito



)

·

(


kc

10


coa
mito


+

K
m

kc

10


coa
mito




)



)











Vmax3kt-kc10 = 2 3 · Vmax3kt-kc4 [33] Keq3kt = 2500 [32] Kmcoamito = 0.0087 [33]


Kmkc10coamito = 0.0018[33]


3-ketoacyl-coa thiolase I (kc12)










v

3

k

t


k

c

1

2

c

o

a


=


V

ma

x



3

k

t

-

k

c

1

2



·

(



k

c

1

2

c

o



a
mito

·

coa
mito



-



1

K

e

q


3

k

t



·

acoa
mito

·
c


10


coa
mito





(


c

o


a

m

i

t

o



+

K
m

c

o


a
mito




)

·

(


kc

12


coa

m

i

t

o



+

K
m

kc

12


coa
mito




)



)











Vmax3kt-kc12 = 2.1 · Vmax3kt-kc4 [37] Keq3kt = 2500 [32] Kmcoamito = 0.0087 [33]


Kmkc12coamito = 0.006 [37]


3-ketoacyl-coa thiolase I (kc14)










v

3

k

t


k

c

1

4

c

o

a


=


V

ma

x



3

k

t

-

k

c

1

4



·

(



k

c

1

4

c

o



a
mito

·

coa
mito



-



1

K

e

q


3

k

t



·

acoa
mito

·
c


12


coa
mito





(


c

o


a
mito


+

K
m

c

o


a

m

i

t

o





)

·

(


kc

14


coa
mito


+

K
m

k

c

1

4

c

o


a

m

i

t

o





)



)











Vmax3kt-kc14 = 1.7 · Vmax3kt-kc4 [37] Keq3kt = 2500 [32] Kmcoamito = 0.0087 [33]


Kmkc14coamito = 0.0065 [37]


3-ketoacyl-coa thiolase I (kc16)










v

3

k

t


k

c

1

6

c

o

a


=


V

ma

x



3

k

t

-

k

c

1

6



·

(



k

c

1

6

c

o



a

m

i

t

o


·

coa

m

i

t

o




-



1

K

e

q


3

k

t



·

acoa
mito

·
c


14


coa
mito





(


c

o


a
mito


+

K
m

c

o


a
mito




)

·

(


kc

16


coa
mito


+

K
m

k

c

1

6

c

o


a
mito




)



)











Vmax3kt-kc16 for numerical value see Table 10


Keq3kt = 2500 [32] Kmcoamito = 0.0087 [33] Kmkc16coamito = 0.0011 [38]


ETF-FAD


VETF-FAD = VmaxETF-FAD · (etffadh2mito · etfqmito − 1/KeqETF-FAD · etfqh2mito · etffadmito)


VmaxETF-FAD for numerical value see Table 10










K

e

q


ETF
-
FAD


=

exp
(



(



-
n

·

E
0



etffad
mito

/
etffadh



2
mito




-

n
·

E
0

etfqh



2
mito

/

etfq
mito






)

·
F


R
·
T


)










E0etfqh2mito/etfqmito = −25 mV [39] E0etffadmito/etffadh2mito = −23 mV [40] n = 2


ETF-QO










v

ETF
-
QO


=


V

ma

x


ETF
-
QO


·

(


etfqh



2
mito

·

q

m

m




-


1

K

e

q


ETF
-

Q

O




·

etfq
mito

·

qh

2

m

m





)











VmaxETF-QO for numerical value see Table 10










K

e

q


ETF
-
QO


=

exp
(



(


n
·

E
0



q

m

m


/
q


h


2

m

m





+

n
·

E
0

etfqh



2

m

i

t

o


/

etfq
mito






)

·
F


R
·
T


)










E0qmm/qh2mm = 87 mV [41] E0etfqh2mito/etfqmito = −25 mV [39] n = 2





Citric acid cycle


Pyruvate dehydrogenase complex


vpdhc = Ypdhc · Vpdhc-np










v

pdhc
-
np


=


V

ma

x


pdhc
-
np


·

(


pyr
mito



pyr
mito

+

K

m
-
pyr


pdhc
-
np




)

·

(


nad
mito



nad
mito

+

K

m
-
nad


pdhc
-
np




)

·

(


coa
mito



coa
mito

+

K

m
-
coa


pdhc
-
np




)

·

(

1
+


k
ca




ca
mito



ca
mito

+

K
a
ca





)











Vmaxpdhc-up for numerical value see Table 10










K

m
-

p

y

r



pdhc
-
np


=



0
.
0



77

[
42
]




K

m
-
nad


pdhc
-
np



=




K
0
nad

·

(

1
+


nadh
mito


K
i

nadh
mito




)





K
0
nad


=

0.07

[
42
]

















K
i

nadh
mito


=



0.3

[
43
]




K

m
-
coa


pdhc
-
np



=




K
0
coa

·

(

1
+


acoa
mito


K
i

acoa
mito




)





K
0
coa


=

0.0122

[
42
]












Kiacoamito = 0.029 [44] kca = 1.7 [45] Kaca = 0.001 [46] γpdhc = γpdhcacoa · γpdhcnadh










γ
pdhc
acoa

=


1
-



f
1

·




acoa
mito


coa
mito





acoa
mito


coa
mito


+

K
i

(


acoa
mito


coa
mito


)





[
47
]





K
i

(


acoa
mito


coa
mito


)




=



0.4

[
47
]




f
1


=

0.71

[
47
]

















γ
pdhc
nadh

=


1
-



f
2

·



nadh
mito


nad
mito





nadh
mito


nad
mito


+

K
i

(


nadh
mito


nad
mito


)








f
2



=



0.75

[
47
]




K
i

(


nadh
mito


nad
mito


)



=

0.5

[
47
]












Citrate synthase










v

c

s


=


V

ma

x


c

s


·

(


o

a


a
mito




o

a


a
mito


+

K
m

o

a


a
mito





)

·

(


a

c

o


a
mito




a

c

o


a
mito


+

K
m

acoa
mito




)
















V

ma

x


c

s


=


V
0

c

s




(

1
+


c

16


coa
mito



K
i

c

16


coa
mito





)

·

(

1
+


atp
mito


K
i

atp
mito




)












V0cs for numerical value see Table 10 Kic16coamito = 0.0042 [48] Kiatpmito = 0.7 [49]










K
m

o

a


a
mito



=




K
0

o

a


a

m

i

t

o




·

(

1
+


c

i


t
mito



K
i

cit
mito




)





K
i

cit
mito



=



1.6

[
50
]




K
0

o

a


a
mito




=

0.0036

[
49
]

















K
m

a

c

o


a
mito



=




K
0

a

c

o


a
mito



·

(

1
+


succoa
mito


K
i

succoa
mito




)





K
i

c

o


a
mito




=


0
.
0



67

[
51
]












Kiatpmito = 0.95 [51] Kisuccoamito = 0.13 [51] K0acoamito = 0.006 [52]


Aconitase










v

a

c


=


V

ma

x


a

c


·

(



cit
mito

-


1

K

e

q


a

c



·

isocit
mito




1
+


c

i


t

m

i

t

o




K
m

c

i


t
mito




+


i

s

o

c

i


t
mito



K
m

isocit
mito





)











Vmaxac for numerical value see Table 10


Keqac = 0.1 [53] Kmcitmito = 0.62 [54] Kmisocitmito = 0.2 [54]


NAD-dependent isocitrate dehydrogenase










v

idh
nad


=


V

ma

x


idh
nad


·

(


isocit
mito
n



isocit
mito
n

+


(

K
m

isocit
mito


)

n



)

·

(


nad
mito



nad
mito

+

K
m

nad
mito




)











Vmaxidhnad for numerical value see Table 10










K
m

isocit
mito


=


K
0

isocit
mito


·

(

1
-


n

adp
mito





adp
mito



adp
mito

+

K
a

adp
mito






)

·

(

1
-


n

cit
mito





cit
mito



cit
mito

+

K
a

cit
mito






)











K0isocitmito = 0.21 [55] n = 3 [55] nadpmito = 0.67 [56] Kaadpmito = 0.1 [56]





ncitmito = 0.85 [57] Kacitmito = 0.033 [57]










K
m

nad
mito


=




K
0

nad
mito


·

(

1
+


nadh
mito


K
i

nadh
mito




)





K
0

nad
mito



=



0.06

[
56
]




K
i

nadh
mito



=


0
.
0



043

[
58
]













NADP-dependen isocitrate dehydrogenase










v

idh
nadph


=


V

ma

x


idh
nadp


·

(


isocit
mito



isocit
mito

+

K
m

isocit
mito




)

·

(


nadp
mito



nadp
mito

+

K
m

nad
mito




)











Vmaxidhnadp for numerical value see Table 10










K
m

isocit
mito


=


K
0

isocit
mito


·

(

1
+


cit
mito


K
i

cit
mito




)

·

(

1
+


akg
mito


K
i

akg
mito




)
















K
0

isocit
mito


=



0.045

[
59
]




K
m

nadp
mito



=




K
0

nadp
mito


·

(

1
+


nadph
mito


K
i

nadph
mito




)





K
0

nadp
mito



=


0
.
0



46

[
59
]













Kinadphmito = 0.125 [58] Kicitmito = 0.159 [59] Kiakgmito = 0.08 [59]


α-ketogluterate dehydrogenase










v
kgdhc

=


V

m

x

kgdhc

·

(


akg
mito



akg
mito

+


K
m

akg
mito


·

(

1
+


nadh
mito


K

i

2


nadh
mito




)




)

·


(


nad
mito



nad
mito

+


K
m
nad

·

(

1
+


nadh
mito


K
i

nadh
mito




)




)

·

(


coa
mito



coa
mito

+


K
m

coa
mito


·

(

1
+


succoa
mito


K
i

succoa
mito




)




)











Vmxkgdhc for numerical value see Table 10


Ki2nadhmito = 0.0127 [60] Kmakgmito = 0.6 [61] Kmnadmito = 0.021[60] Kinadhmito = 0.0045 [60]


Kmcoamito = 0.0027 [60] Kisuccoamito = 0.0069[60]


Succinyl-Coa synthetase [62]










v


s

c

s

-
atp


=


V

ma

x


scs
-
atp


·

(







succoa
mito

·

adp
mito

·

p

mito




-







1

K
eq

suc
-
atp



·

suc
mito

·

coa
mito

·

atp
mito











(

1
+


succoa
mito


K
m

succoa
mito




)

·

(

1
+


adp
mito


K
m

adp
mito




)

·

(

1
+


p
mito


K
m

p
mito




)


+








(

1
+


s

u


c
mito



K
m

suc
mito




)

·

(

1
+


coa
mito


K
m

coa
mito




)

·

(

1
+


atp
mito


K
m

atp
mito




)


-
1





)
















V

ma

x


scs
-
atp


=


V
0

scs
-
atp


·

(


p
mito
n



p
mito
n

+

K
a

p
n




)











V0scs-atp for numerical value see Table 10


Kapn = 2.3 [63] n = 2.4 [63] Keqscs-atp = 1/0.27 [64] Kmsuccoamito = 0.041 [65]


Kmadpmito = 0.25 [65] Kmpmito = 0.72 [65] Kmsucmito = 5.1[65]


Kmcoamito = 0.032 [65] Kmatpmito = 0.055 [65]










v

scs
-
gtp


=


V

ma

x


scs
-
gtp



·


(







succoa
mito

·

gdp
mito

·

p
mito


-







1

K

e

q


scs
-
atp



·

suc
mito

·

coa
mito

·

gtp
mito











(

1
+


succoa
mito


K
m

succoa
mito




)

·

(

1
+


gdp
mito


K
m

gdp
mito




)

·

(

1
+


p
mito


K
m

p
mito




)


+








(

1
+


suc
mito


K
m

suc
mito




)

·

(

1
+


coa
mito


K
m

coa
mito




)

·

(

1
+


gtp
mito


K
m

gtp
mito




)


-
1





)
















V

ma

x


scs
-
gtp


=


V
0

scs
-
gtp


·

(


p
mito
n



p
mito
n

+

K
a

p
n




)











V0scs-gtp = 0.11 · V0scs-atp [65] Kapmito = 2.3 [63] n = 2.4 [63]


Keqscs-gtp = 1/0.27 [66] Kmsuccoamito = 0.086 [65] Kmgdpmito = 0.007 [65]


Kmpmito = 2.26[65] Kmsucmito = 0.49 [65] Kmcoamito = 0.036 [65] Kmgtpmito = 0.036 [65]


Succinate dehydrogenase










v
succdh

=


V

ma

x


s

u

c

c

a

h


·

(




suc
mito

·

q
mm


-


1

K

e

q

succdh


·

fum
mito

·

qh

2

m

m







(


suc
mito

+

K
m

suc
mito



)

·

(


q

m

m


+

K
m

q

m

m




)



)











Vmaxsuccdh for numerical value see Table 10










K
eq
succdh

=




exp

(




E
0


fum
mito

/

suc
mito



-

E
0



q

m

m


/
qh



2
mm





R
·
T


·
F

)




E
0


fum
mito

/

suc
mito




-

E
0



q

m

m


/
q


h


2

m

m





=

25


mV
















K
0

suc
mito


=



1.3

[
67
]




K
m

suc
mito



=





K
0

suc
mito


·

(

1
+


mal
mito


K
i

mal
mito




)





K
i

mal
mito



=



2.2

[
68
]




K
m

q

m

m




=


0
.
0



005

[
69
]














Fumarase










v
fum

=


V

ma

x

fum

·

(



fum
mito

-


1

K
eq
fum


·

mal
mito




1
+


fum
mito


K
m

fum
mito



+


mal
mito


K
m

mal
mito





)











Vmaxfum for numerical value see Table 10


Keqfum = 4.2 [70] Kmfummito = 0.333 [71] Kmmalmito = 0.59 [71]


Malate dehydrogenase (mitochondrial)










v

mdh
mito


=


V

ma

x


mdh
mito


·

(




mal
mito

·

nad
mito


-


1

K
eq

mdh
mito



·

oaa
mito

·

nadh
mito









(

1
+


mal
mito


K
m

mal
mito




)

·

(

1
+


nad
mito


K
m

nad
mito




)


+








(

1
+


oaa
mito


K
m

oaa
mito




)

·

(

1
+


nadh
mito


K
m

nadh
mito




)


-
1





)











vmaxmdhmito for numerical value see Table 10










K
eq

mdh
mito


=

1
·

10

-
5


·


(


h
cyt


h
mito


)


[
72
]











Kmmalmito = 0.4 [73] Kmnadmito = 0.06 [74] Kmoaamito = 0.017 [74] Kmnadhmito = 0.044 [74]


Transdehydrogenase [75]










v
tdh

=


V

ma

x

tdh

·

(



nadh
mito

·

nadp
mito


-


1

K

e

q

tdh


·

nad
mito

·

nadph
mito



)











Vmaxtdhmito for numerical value see Table 10










K
eq

tdh
mito


=




K
0
tdh

·

exp

(

-



v

m

m


·
F


R
·
T



)

·

(


h
cyt


h
mito


)





K
0
tdh


=

1.5

[
76
]











Mitochondrial electrophysiology and ATP synthesis


Chloride










I

c


l

e

d




=




P

c

l


·

A
m

·
U
·
F
·

(



cl
cy𝔱

-


cl
mito

·

exp

(

-
U

)




1
-

exp

(

-
U

)



)




U

=





v

m

m


·
F


R
·
T





P

c

l



=


5
·

10


-
1


0





m
/
s












Sodium










I

n

a

pump

=


V

ma

x



N

a

-
pump


·

(




na
cyt

·

h
mito


-


na
mito

·

h
cyt




1
+


na
cyt


K
m
na


+


na
mito


K
m
na




)











VmaxNa-pump for numerical value see Table 10










K
m

n

a


=



32.4

[
77
]




I

n


a

e

d





=


P

n

a


·

A
m

·
U
·
F
·

(



n


a
cyt


-

n



a
mito

·

exp

(
U
)






exp

(
U
)

-
1


)
















U
=





v

m

m


·
F


R
·
T





P

n

a



=



1
·

10


-
1


0





m
/
s



I

n

a



=


I

n

a

pump

+

I

n


a

e

d
















Potassium


IKpump = VmaxK-pump · (kcyt · hmito − kmito · hcyt)


VmaxK-pump for numerical value see Table 10










I

k
ed


=


P
k

·

A
m

·
U
·
F
·

(



k
cyt

-


k
mito

·

exp

(
U
)





exp

(
U
)

-
1


)















U
=





v

m

m


·
F


R
·
T





P
K


=



5
·

10


-
1


0





m
/
s



I
k


=


I
k
pump

+

I

k

e

d















F0F1 synthetase










v

F

0

F

1


=


V

ma

x


F

0

F

1


·

(




adp
mito

·

p
mito


-


1

K
eq

F

0

F

1



·

atp
mito





(


K
m

adp
mito


+

adp
mito


)

·

(


K
m

p
mito


+

p
mito


)



)
















V

ma

x


F

0

F

1


=


V

F

0

F

1


·


(

0.114
+

0.886



(



"\[LeftBracketingBar]"


V

m

m




"\[RightBracketingBar]"


)

n







(


"\[RightBracketingBar]"




V

m

m





"\[RightBracketingBar]"


)

n

+


(

K
m

V

m

m



)

n





)


[
78
]











VF0F1 for numerical value see Table 10


n = 10 [78] KmVmm = 140 mV [78]










K

e

q


F

0

F

1


=



exp

(


(


-

E
0
ATP



R
·
T


)

-


n
H

·

(



V

m

m


·
F


R
·
T


)



)

·


(


H
cyt


H
mito


)


n
H






mM

-
1












nH = 3 E0ATP = 30500 J/mol Kmadpmito = 0.025 [79] Kmpmito = 6.1 [79]


ATP-ADP nucleotide exchanger [80]










v
nex

=


V

ma

x

nex

·

(


1
-




atp
cyt

·

adp
mito




adp
cyt

·

atp
mito



·

exp

(



v

m

m


·
F


R
·
T


)




1
+



atp
cyt


adp
cyt


·

exp

(

f
·



v

m

m


·
F


R
·
T



)

·

(

1
+


adp
mito


atp
mito



)




)











Vmaxnex for numerical value see Table 10 f = 0.2


Phosphate exchanger










v

P
-
ex


=


V

ma

x


P
-
ex


·

(




p
cyt

·

h
cyt


-


p
mito

·

h
mito




(


p
cyt

+

K
m

p
cy𝔱



)


)








VmaxP-ex for numerical value see Table 10 Kmpcyt = 1.89 [81]





Complex I










v

c

x

l


=


V

ma

x


c

x

l


·

(




nadh
mito

·

q

m

m



-


1

K

e

q


c

x

l



·

nad

m

i

t

o


·

qh

2

m

m







(


nadh
mito

+

K
m

nadh
mito



)

·

(


q

m

m


+

K
m

q

m

m




)



)











VmaxcxI for numerical value see Table 10










K

e

q

cxl

=

exp



(



(


n
·

E
0

nadh
/
nad



+

n
·

E
0


Q
/
Q



H
2




+


n
H

·

V

m

m




)

·
F


R
·
T


)

·


(


h
mito


h
cyt


)


n
H













n = 2 E0nadh/nad = 320 mV [82] E0Q/QH2 = 87 mV [41]


NH = 4 Kmnadhmito = 0.0017 [83] Kmqmm = 0.013 [83]


Complex II


see succinate dehydrogenase


Complex III










v
cxIII

=


V

ma

x

cxIII

·

(



qh



2

m

m


·

cyc

o


x

m

m






-


1

K
eq
cxIII


·

q

m

m


·

cytc

red

m

m







(


q

h


2

m

m



+

K
m

q

h


2

m

m





)

·


(


cytc

o


x

m

m




+

K
m

cytc

o

x




)

2



)











VmaxcxIII for numerical value see Table 10










K
eq
cxIII

=


exp
(



(



-
n

·

E
0


Q
/
Q



H
2




+

n
·

E
0



cytC

o

x


/
c


y

t


C
red




+

n
·

v

m

m




)

·
F


R
·
T


)

·


(


h
mito


h



)


n

h
mito



·


(


h



h
cyt


)


n

h
cyt













n = 2 E0cytCox/cytCred = 255 mV [84]


E0Q/QH2 = 87 mV [41] nhmito = 2 nhcyt = 4 hø = 10−4 mM  custom-character  pH 7


Kmqh2mm = 0.013 [85] Kmcytcox = 0.014 [85]


Complex IV










v
cxIV

=


V

ma

x

cxIV

·

(


cytc
red



cytc
red

+

K
m

cytc
red




)

·

(


O
2



O
2

+

K
m

O
2




)
















V

ma

x

cxIV

=




V
0
cxIV

·

exp

(

-


dGp
·
F


R
·
T



)




dGp

=


-

v

m

m



+



R
·
T

F

·

log

(


h
cyt


h
mito


)













V0cxIV for numerical value see Table 10


Kmcytcred = 0.007 [86] Km02 = 2 mmHg


Adenylate kinase










v

ak
cyc


=


V

ma

x


ak
cyt


·

(




atp
cyt

·

amp
cyt


-


1

K
eq
ak


·

adp
cyt

·

adp
cyt






(

1
+


atp
cyt


K
m

atp
cyt




)

·

(

1
+


amp
cyt


K
m

amp
cyt




)


+


(

1
+


adp
cyt


K
m

adp
cyt




)

2

-
1


)











Vmaxakcyt for numerical value see Table 10


Keqak = 1 [87] Kmatpcyt = 0.039 [88] Kmadpcyt = 0.112 [88] Kmampcyt = 0.026 [88]


Pyrophosphatase










v
ppase

=


V

ma

x

ppase

·

(


pp
cyt



pp
cyt

+

K
m

pp
cyt




)











Vmaxppase for numerical value see Table 10 Kmppcyt = 0.016 [89]


ATP usage










v

atp
-
usage


=


V

ma

x


atp
-
usage


·

(


atp
cyt



atp
cyt

+

K
m

atp
cyt




)

·

(

1
+

k
load


)








Vmaxatp-usage for numerical value see Table 10 Kmatpcyt = 2





O2 diffusion










v

O

2
diff



=


V
max


O
2

-
diff


·

(


o


2
ext


-


o


2
cyt



)











VmaxO2-diff for numerical value see Table 10


Proton fluxes


IHpump = 4 · vcxl + 2 · VcxIII + 4 · vcxIV










I

H

e

d



=


P
H

·

A
m

·
U
·
F
·

(



H
cyt

-


H
mito

·

exp

(
U
)





exp

(
U
)

-
1


)











PH = 3 · 10−4 m/s


Mitochondrial membrane potential










v

V

m

m



=



1


0

-
1





c
m

·

A
m



·

(


-

I

C

e

d




+

I

K

e

d



+

I

H

e

d



+

I

Na
ed


+

I
H
pump

+

v

n

e

x


+

3
·

v
syn


+

F
·
10
·

v
pepT

·

Vol
cyt



)











Glycolysis


Glut1 glucose transporter (Glut1)










v

gluT

1


=




V

ma

x


gluT

1


·



glc
ext

-

glc
cyt



1
+


glc
ext


n
m

glc
ext



+


glc
cyt


K
m

glc
cyt









V

ma

x


gluT

1



=


V
0

gluT

1


·

(

1
-


c

1


6
ext
n




c

1


6
ext
n


+

K
i

c


16
ext






)












V0gluT1 for numerical value see Table 10


n = 2 [90] Kic16ext = 0.2 [90] Kmglccyt = 5 [91] Kmglcext = 5 [91, 92]


Glut4 glucose transporter (Glut4)










v

gluT

4


=


V

ma

x


gluT

4


·



glc
ext

-

glc
cyt



1
+


glc
ext


K
m

glc
ext



+


glc
cyt


K
m

glc
cyt




















V

ma

x


gluT

4


=


V
0

gluT

4


·

(

1
-


c

1


6
ext
n




c

1


6
ext
n


+

K
i

c


16
ext






)

·



(

1
-

γ
·

(

1
-


epi
ext



epi
ext

+

K
a

epi
ext





)

·

(

1
-


amp
cyt



amp
cyt

+

K
a

amp
cyt





)



)


[
93
]











V0gluT4 [94] for numerical value see Table 10n = 2 [90] Kic16ext = 0.2 [90]


Kaepiext = 200 pM Kaampcyt = 0.2 Kmglccyt = 5 [91] Kmglcext = 5 [91]


Hexokinase A










v
hkA

=


V

ma

x

hkA

·

(


glc
cyt



glc
cyt

+

K
m

glc
cyt




)

·

(


atp
cyt



atp
cyt

+

K
m

atp
cyt




)
















V

ma

x

hkA

=



V
0
hkA


1
+


glc

6


p
cyt



K
i
hk







V
0
hkA











for numerical value see Table 10


Kiglccyt = 0.05 [95] Kmglccyt = 0.25 [96]










K
m

atp
cyt


=


K
0

atp
cyt


·

(

1
+


glc6p
cyt


K
i

glc

6


p
cyt





)

·

(

1
+


adp
cyt


K
i

adp
cyt




)











K0atpcyt = 0.75 [96] Kiadpcyt = 0.22 [96] Kiglc6pcyt = 0.021 [96]


Hexokinase 1










v
hkB

=


V

ma

x

hkB

·

(


glc
cyt



glc
cyt

+

K
m

glc
cyt




)

·

(


atp
cyt



atp
cyt

+

K
m

atp
cyt




)
















V

ma

x

hkB

=




V
0
hkB


1
+


glc

6


p
cyt



K
i
hk







V
0
hkB


=



10
·


V
0
hkA


[
97
]





K
i
hk


=



0.05

[
95
]




K
m

glc
cyt



=

0.02

[
95
]


















K
m

atp
cyt


=


K
0

atp
cyt


·

(

1
+


glc

6


p
cyt



K
i

glc

6


p
cyt





)

·

(

1
+


adp
cyc


K
i

adp
cyt




)














K0atpcyt = 0.44 [95] Kiadpcyt = 0.62 [96] Kiglc6pcyt = 0.02 [95]





D-Glucose-6-phosphate isomerase (Gpi)










v
gpi

=


V

ma

x

gpi

·



glc

6


p
cyt


-


fru

6


p
cyt



K
eq
gpi




1
+


glc

6


p
cyt



K
m

glp
cyt



+


fru

6


p
cyt



K
m

fru

6


p
cyt
















Vmaxgpi for numerical value see Table 10


KeqGpi = 0.3 [98] Kmglc6pcyt = 0.55 [99] Kmfru6pcyt = 0.12 [99]


Phosphofructokinase 2 (Pfk2)


vpfk2 = Vmaxpfk2native · (1 − γPfk2) · vpfk2native + Vmaxpfk2ppfk2 · vpfk2p)


γpfk2 = γ · (1 − γamp) Vmaxpfk2native for numerical value see Table 10


Vmaxpfk2p = 2.3 · Vmaxpfk2native [100]










v

pfk

2

native

=



fru

6


p
cyt




fru

6


p
cyt


+

K
m

fru

6


p
cyt





·


atp
cyt



atp
cyt

+

K
m

atp
cyt




·

(

1
-


cit
cyt



cit
cyt

+

K
i

cit
cyt





)











Kmfru6pcyt = 0.121 [100] Kmatpcyt = 0.63 [100] Kicitcyt = 0.029 [100]










v

pfk

2

p

=



fru

6


p
cyt




fru

6


p
cyt


+

K
m

fru

6


p
cyt





·


atp
cyt



atp
cyt

+

K
m

atp
cyt




·

(

1
-


cit
cyt



cit
cyt

+

K
i

cit
cyt





)











Kmfru6pcyt = 0.061 [100] Kmatpcyt = 0.63 [100] Kicitcyt = 0.061 [100]


Fructose-2,6-bisphosphatase (FBP2)


vfbp2 = Vmaxfbp2phospho · γfbp2 · vfbp2p γfbp2 = γ · (1 − γamp)










V

ma

x


fbp


2
phospho



=




V

ma

x


fbp


2
native




[
101
]




v

fbp

2

p


=


fru

26


bp
cyt




fru

26


bp
cyt


+

K
m

fru

26


bp
cyt















Kmfru26pcyt = 0.026 [102]


Phosphofructokinase 1 (Pfk1):


vpfk1 = Vmaxpfk1 · ((1 − γPfk1) · vpfk1native + γpfk1 · vpfk1p)


γpfk1 = γ · (1 − γamp)


Vmaxpfk1 for numerical value see Table 10










v

pfk

1

native

=




fru


26
cyr
n




fru


26
cyt
n


+


(

K
a

fru


26
cyt



)

n



·


atp
cyt



atp
cyt

+

K
m

atp
cyt




·

(

1
-


f
atp




atp
cyt

n
atp




atp
cyt

n
atp


+


(

K
i

atp
cyt


)


n
atp






)

·


(

1
-


f
cit




cit
cyt

n
cit




cit
cyt

n
cit


+


(

K
i

cit
cyt


)


n
cit






)

·



(

fru

6


p
cyt


)


n

fru

6


p
cyt







(

fru

6


p
cyt


)


n

fru

6


p
cyt




+


(

K
m

fru

6


p
cyt



)


n

fru

6


p
cyt
















n = 2 [103]










K
a

fru


26
cyt



=


K
0

fru


26
cyt



·

(


atp
cyt

n

fru

26





atp
cyt

n

fru

26



+


(


K

i

fru

26



atp
cyt


·

(

1
+


cit
cyt



cit
cyt

+

K

i
atp


cit
cyt





)


)


n

fru

26





)
















K
0

fru


26
cyt



=



0
.
0



10

[
104
]




n

fru

26



=



n
0

-



cit
cyt



cit
cyt

+

K
cit

n

fru

26








n
0



=

5

[
104
]












Kcitnfru26 = 0.05 [104] Kifru26atpcyt = 3.4 [104] Kiatpcitcyt = 0.065 [104] Kmatpcyt = 0.2 [105]


fatp = 0.95 [103] natp = 6 [103] Kiatpcyt = 1.3 [103] ncit = 4 [103]


fcit = 0.485 [103] Kicitcyt = 0.192 [103]










K
m

fru

6


p
cyt



=


K
0

·

(

1
-


fru


26
cyt




fru


26
cyt


+

K

a

fru

6

p



fru


26
cyt






)

·

(

1
-


p
cyt



p
cyt

+

K

a

fru

6

p



p
cyt





)

·


(

1
+


f
atp




atp
cyt

n
atp




atp
cyt

n
atp


+


(

K

i
atp


fru

26


)


n
atp






)

·

(

1
+


k
cit




cit
cyt

n
cit




cit
cyt

n
cit


+


(

K
i

cit
cyt


)


n
cit






)











K0 = 7 [104] Kafru6pfru26cyt = 0.00015 [104] Kafru6ppcyt = 0.15 [106] natp = 2 [106]


Kiatpfru26 = 0.2 [106] fatp = 2 [106] kcit = 8 [106] ncit = 4 [106] Kicitcyt = 0.13 [106]










n

fru

6


p
cyt



=


n
0

·

(

1
-

f



fru


26
cyt




fru


26
cyt


+

K

n

fru

6

p



fru

26

cyt






)

·


(

1
+


(


f
atp




atp
cyt



atp
cyt

+

K

n

fru

6

p


fatp




)

·

(

1
-


fru

6


p
cyt




fru

6


p
cyt


+

K

n

fru

6

p



fru

6





)

·

(

1
-


p
cyt



p
cyt

+

K

n

fru

6

p


p




)



)











n0 = 1 [104] f = 0.66 [104] fatp = 2.75 [104] Knfru6pfru26cyt = 0.0001 [104]


Knfru6patp = 0.1 [104] Knfru6pfru6 = 0.4 [106] Knfru6pp = 0.5 [106]










v

p

f

k

1

p

=




f

r

u

2


6

c

y

t

n




f

r

u

2


6

c

y

t

n


+


(

K
a

fru


26

c

y

𝔱




)

n



·


a

t


p

c

y

t





a

t


p

c

y

t



+

K
m

a

t


p

cy

t






·

(

1
-


f

a

t

p





a

t


p

c

y

t


n
atp





a

t


p

c

y

t


n
atp



+


(

K
i

a

t


p

c

y

t




)


n
atp






)

·

(

1
-


f

c

i

t





c

i


t

c

y

t


n

c

i

t






c

i


t

c

y

t


n

c

i

t




+


(

K
i

c

i


t

c

y

t




)


n

c

i

𝔱







)

·



(

f

r

u

6


p

c

y

t



)


n

fru

6


p

c

y

t








(

f

r

u

6


p

c

y

t



)


n

fru

6


p

c

y

t





+


(

K
m

fru

6


p

c

y

𝔱




)


n

fru

6


p

c

y

t

















n = 2 [103]










K
a

fru


26

c

y

𝔱




=


K
0

fru


26

c

y

𝔱




·

(


a

t


p

c

γ

t


n

f

r

u

2

6






a

t


p

c

y

t


n

fru

26




+


(


K

i

fru

26



a

t


p

c

y

t




·

(

1
+


c

i


t

c

y

t





c

i


t

c

y

t



+

K

i
atp


c

i


t

c

y

t







)


)


n

fru

26





)
















K
0

f

r

u

2


6

c

y

𝔱




=



0
.
0




1
[

1

0

4

]

[
103
]




n

frτι

26



=



n
0

-



c

i


t

c

y

t





c

i


t

c

y

t



+

K

c

i

t


n

f

r

u

2

6








n
0



=

5
[
104
]












Kcitnfru26 = 0.05 [104] Kifru26atpcyt = 3.4 [104] Kiatpcitcyt = 0.065 [104]


Kmatpcyt = 0.2 [105] fatp = 0.95 [103] natp = 5 [103] Kiatpcyt = 0.9 [103]


ncit = 2 [103] fcit = 0.55 [103] Kicitcyt = 0.18 [103]










K
m

f

r

u

6


p

c

y

t




=


K
0

·

(

1
-


f

r

u

2


6

c

y

t





f

r

u

2


6

c

y

t



+

K

a

f

r

u

6

p



f

r

u

2


6

c

y

t







)

·

(

1
-


p

c

y

t




p

c

y

t


+

K

a

fru

6

p



p

c

y

t






)

·


(

1
+


f

a

t

p





a

t


p

c

y

t


n

a

t

p






a

t


p

c

y

t


n
atp



+


(

K

i
atp


f

r

u

2

6


)


n
atp






)

·

(

1
+


k

c

i

t





c

i


t

c

y

t


n

c

i

t






c

i


t

c

y

t


n

c

i

t




+


(

K
i

c

i


t

c

y

t




)


n

c

i

t







)











K0 = 5 [104] [103] Kafru6pfru26cyt = 0.00015 [104] Kafru6ppcyt = 0.15 [106]


natp = 2 [106] Kiatpfru26 = 0.2 [106] fatp = 2 [106] kcit = 8 [106]


ncit = 4 [106] Kicitcyt = 0.13 [106]










n

fru

6


p

c

y

t




=


n
0

·

(

1
-

f



f

r

u

2


6

c

y

t





f

r

u

2


6

c

y

t



+

K

n

fru

6

p



f

r

u

2


6

c

y

t








)

·


(

1
+


(


f

a

t

p





a

t


p

c

y

t





a

t


p

c

y

t



+

K

n

fru

6

p



f

a

t

p





)

·

(

1
-


f

r

u

6


p

c

y

t





f

r

u

6


p

c

y

t



+

K

n

f

r

u

6

p



f

r

u

6





)

·

(

1
-


p

c

y

t




p

c

y

t


+

K

n

fru

6

p


p




)



)











n0 = 1 [104] f = 0.66 [104] fatp = 2.75 [104] Knfru6pfru26cyt = 0.0001 [104]


Knfru6patp = 0.1 [104] Knfru6pfru6 = 0.4 [106] Knfru6pp = 0.5 [106]


Fructose-1,6-bisphosphatase (Fbp1)


vfbp1 = Vmaxvfbp1 · ((1 − γfbp1) · vfbp1native + γfbp1 · vfbp1p)


γfbp1 = γ · (1 − γamp)


Vmaxfbp1 for numerical value see Table 10










v

f

b

ρ

1


n

a

t

i

v

e


=



f

r

u

1

6

b


p

c

y

t





f

r

u

1

6

b


p

c

y

t



+

K
m

f

r

u

1

6

b


ρ
cyt





/

(

1
+


f

r

u

2

6

b


p

c

y

t

n




(

K
i

fru

26


bp

c

y

t




)

n



)











Kmfru16bpcyt = 0.0029 [107] Kifru26pcyt = 0.00113 [107] n = 1.26 [107]










v

f

b

ρ

1

p

=



f

r

u

1

6

b


p

c

y

t





f

r

u

1

6

b


p

c

y

t



+

K
m

f

r

u

1

6

b


p

c

y

t






/

(

1
+


f

r

u

2

6

b


p

c

y

t

n




(

K
i

f

r

u

2

6

b


p

c

y

t




)

n



)











Kmfru16bpcyt = 0.0019 [107] Kifru26bpcyt = 0.00113 [107] n = 1.26 [107]


Aldolase (Ald)










v
ald

=


v

ma

x

ald

·



f

r

u

1

6

b


p

c

y

t



-


1

K

e

q


a

l

d




g

r

a



p

c

y

t


·

dhap

c

y

t







(

1
+


f

r

u

1

6

b


p

c

y

t




K
m

f

r

u

1

6

b


p

cy

t






)

+


(

1
+


g

r

a


p

c

y

t




K
m

g

r

a


p

c

y

t






)

·

(

1
+


d

h

a


p

c

y

t




K
m

dhap

c

y

t





)


-
1












vmaxald for numerical value see Table 10


Keqald = 0.099 [108] Kmfru16bpcyt = 0.004 [109] Kmgrapcyt = 0.48 [110] Kmdhapcyt = 0.38 [110]


Triosephosphate isomerase (Tpi)










v

t

ρ

i


=


ν

m

ax


t

ρ

i


·



d

h

a


p

c

y

t



-


grap
cyt


K
eq
tpi




1
+


d

h

a


p

c

y

t




K
m

d



a


p

c

y

𝔱





+


gra


p

c

y

t




K
m

g

r

a


p

c

y

t

















vmaxtpi for numerical value see Table 10


Keqtpi = 0.04545 [108] Kmdhapcyt = 0.58 [111] Kmgrapcyt = 0.4 [11]


D-Glyceraldehyde-3-phosphate:NAD+ oxidoreductase (Gapdh)










v

gap

dh


=


v

m

ax


Gap

dh


*




nad
cyt

·

grap
cyt

·

p
cyt


-



1

K
eq
gapdh


·
bpg




13
cyt

·

nadh
cyt







(

1
+


nad
cyt


K
m

nad
cyt




)

·

(

1
+


grap
cyt


K
m

grap
cyt




)

·

(

1
+


p
cyt


K
m

p
cyt




)


+


(

1
+


nadh
cyt


K
m

nadh
cyt




)

·

(

1
+


bpg


13
cyt



K
m

bpg


13
cyt





)


-
1












vmaxGapdh for numerical value see Table 10 Keqgapdh = 10−4 mM−1 [112] Kmnadcyt = 0.09 [113]


Kmgrapcyt = 0.044 [114] Kmpcyt = 3.8 [115] Kmnadhcyt = 0.006 [115] Kmbpg13cyt = 0.01 [113]


Phosphoglycerate kinase (Pgk)










v
pgk

=


v

m

ax

pgk

·





adp
cyt

·
bpg



13
cyt


-



1

K
eq
pgk


·

atp
cyt

·
pg



3
cyt






(

1
+


adp
cyt


K
m

adp
cyt




)

·

(

1
+


bgp


13
cyt



K
m

bpg


13
cyt





)


+


(

1
+


atp
cyt


K
m

atp
cyt




)

·

(

1
+


pg


3
cyt



K
m

pg


3
cyt





)


-
1












vmaxpgk for numerical value see Table 10 Keqpgk = 1830 [116] Kmadpcyt = 0.35 [117] Kmbpg13cyt


0.0022 [117] Kmatpcyt = 0.151 [118] Kmpg3cyt = 1.397 [118]


2-Phospho-D-glycerate 2,3 phosphomutase (Pgm)










v

p

g

m


=


v

m

ax

pgm

·



p

g


3

c

y

t



-


1

K

e

q


p

g

m




p

g


2

c

y

t






p

g


3

c

y

t



+


K
m

pg


3

c

γ

t




·

(

1
+


p

g


2

cy

t




K
m

pg

2




)














vmaxpgm for numerical value see Table 10


Keqpgm = 0.1725 [119] Kmpg3cyt = 0.52 [120] Kmpg2 = 0.24 [120]


2-Phospho-D-glycerate hydrolase (Eno)










v

e

n

o


=


ν

m

ax


e

n

o


·



p

g


2

c

y

t



-


1

K

e

q


en

o



·

pep

c

y

t





1
+


p

g


2

c

y

t




K
m

p

g


2

c

y

t





+


p

e


p

c

y

t




K
m

p

e


p
cyt
















vmaxeno for numerical value see Table 10


Keqeno = 1.7 [121] Kmpg2cyt = 0.12 [122] Kmpepcyt = 0.37 [122]


Pyruvate kinase (Pk)










v

p

k


=


v

ma

x


P

k






p

e


p

c

y

t





p

e


p

c

y

t



+


K
m

p

e


p
cyt



·



·


a

d


p

c

y

t





a

d


p

c

y

t



+

K
m

a

d


p

c

y

t

















vmaxpk for numerical value see Table 10 Kmpepcyt = 0.08 [123] Kmadpcyt = 0.3 [123]


Pyruvate carboxylase










v

p

c


=


ν

m

ax


P

c


·


a

t



p

m

i

t

o


·

pyr

m

i

t

o






(


a

t


p

m

i

t

o



+

k
m

a

t


p

m

i

t

o





)

·

(


pyr

m

i

t

o


+

k
m

p

y


r
mito




)













vmaxPc for numerical value see Table 10 Kmatpmito = 0.14 [124] Kmpyrmito = 0.33 [124]


Lactate dehydrogenase (Ldh):










v

l

d

h


=


ν

m

ax


l

d




*



p

y



r

c

y

t


·

nadh

c

y

t




-


1

K

e

q


l

d

h



·

lac

c

y

t


·

nad

c

y

t







(

1
+


n

a

d


h

c

y

t




K
m

nadh
cyt




)

·

(

1
+


p

y


r

c

y

t




K
m

p

y


r

c

y

t






)


+


(

1
+


l

a


c

c

y

t




K
m

l

a


c

c

y

t






)

·

(

1
+


n

a


d

c

y

t




K
m

n

a


d
cyt





)


-
1












vmaxldh for numerical value see Table 10 Keqldh = 9000 [125] Kmnadhcyt = 0.0121 [126] Kmpyrcyt =


0.1 [127] Kmlaccyt = 4.4 [126] Kmnadcyt = 0.1 [126]


Lactate transport (LacT):










v
lacT

=


v

m

ax

lacT

·



l

a


c

e

x

t



-

lac
cyt



1
+


l

a


c

c

y

t




K
m

l

a


c

c

y

t





+


lac

e

x

t



K
m

lac

e

x

t
















vmaxlacT for numerical value see Table 10 Kmlaccyt = 2.5 [128] Kmlacext = 2.5 [128]


Pyruvate transport (PyrT):










v
lacT

=


v

m

ax


p

y

r

T


·



p

y


r

e

x

t



-

pyr
cyt



1
+


p

y


r

c

y

t




K
m

p

y


r

c

y

𝔱





+


pyr

e

x

t



K
m

p

y


r

e

x

t

















vmaxpyrT for numerical value see Table 10 Kmpyrext = 0.1 [128] Kmpyrcyt = 0.1 [128]


Mitochondrial pyruvate transport:










v

pyrT
mito


=


v

m

ax


p

y

r


T
mito



·



p

y



r

c

y

t


·

h

c

y

t




-

p

y



r

m

i

t

o


·

h

m

i

t

o






1
+


p

y


r

c

y

t




K
m

p

y


r

c

y

t





+


p

y


r

m

i

t

o




K
m

p

y


r

m

i

t

o

















vmaxPyrTmito for numerical value see Table 10 Kmpyrcyt = 0.15 [129] Kmpyrmito = 0.15 [129]


Mitochondrial malate-phosphate transport










v

m

a

l

p

T


=


v

m

ax


m

a

l

p

T


·

(




mal

m

i

t

o


·

p
cyt


-


mal
cyt

·

p
mito






(

1
+


mal

m

i

t

o



K
m

mal
mito




)

·

(

1
+


p

c

y

t



K
m

p

c

y

t





)


+


(

1
+


m

a


l

c

y

t




K
m

mal

c

y

t





)

·

(

1
+


p

m

i

t

o



K
m

p
mito




)


-
1


)











vmaxmalpT for numerical value see Table 10


Kmpcyt = 1.41 [130] Kmmalmito = 0.4 [131] Kmpmito = 1.41 [130] Kmmalcyt = 0.4 [131]


Malate-pyruvate antiport (MalPyrT)










v


m

a

l

-

p

y

r

T



=


v

ma

x


mal
-
pyrT


*

(




mal

m

i

t

o


·

pyr

c

y

t



-

m

a



l

c

y

t


·

pγr
mito







(

1
+


mal

m

i

t

o



K
m

m

a


l
mito





)

·

(

1
+


p

y


r

c

y

t




K
m

pyr

c

y

t





)


+


(

1
+


m

a


l

c

y

t




K
m

m

a


l

c

y

t






)

·

(

1
+


p

y


r

m

i

t

o




K
m

p

y


r

m

i

t

o






)


-
1


)











vmaxMalPyrT for numerical value see Table 10


Kmpyrcyt = 0.84 [132] Kmmalcyt = 0.7 [133] Kmpyrmito = 0.84 [132] Kmmalcyt = 0.7 [133]


Cytosolic malate dehydrogenase (Mdh)










v

m

d




=


ν

m

ax


M

d

h


·




mal
cyt

·

nad
cyt


-


1

K
eq

mdh
cyt



·

oaa
cyt

·

nadh
cyt






(

1
+


m

a


l

c

y

t




K
m

m

a


l

c

y

𝔱






)

·

(

1
+


n

a


d

c

y

t




K
m

n

a


d

c

y

t






)


+


(

1
+


o

a


a
cyt



K
m

oaa
cyt




)

·

(

1
+


n

a

d


h
cyt



K
m

n

a

d


h

c

y

t






)


-
1












vmaxMdh for numerical value see Table 10 Keqmdhcyt = 10−5 [72] Kmmalcyt = 0.47 [134]


Kmnadcyt = 0.099 [134] Kmoaacyt = 0.042 [134] Kmnadhcyt = 0.027 [134]


NADP-dependent malic enzyme (cytosol)










v

m

e


=


V

m

ax


m

e


·

(



m

a



l

c

y

t


·

nadp
cyt



-

1
/


K
eq
me

·

pyr
cyt

·

nadph
cyt

·
hco



3
cyt






(

1
+


m

a


l

c

y

t




K
m

m

a


l

c

y

t






)

·

(

1
+


n

a

d


p

c

y

t




K
m

n

a

d


p

c

y

t






)


+


(

1
+


p

y


r

c

y

t




K
m

p

y


r

c

y

t






)

·

(

1
+


n

a

d

p


h

c

y

t




K
m

nadph

c

y

t





)

·

(

1
+


h

c

o


3

c

y

t




K
m

h

c

o


3

c

y

t






)




)











Vmaxme for numerical value see Table 10


Keqme = 34.4 [135] Kmmalcyt = 0.12 [136] Kmnadpcyt = 0.0092 [136] Kmpyrcyt = 8 [137]


Kmnadphcyt = 0.0053 [136] Kmhco3cyt = 13 [137]


Nucleoside diphosphokinase (cytosolic)










v

n

d


k
cyt



=


V

ma

x


ndk

c

y

t



·

(




atp
cyt

·

gdp
cyt


-

1
/


K

e

q


n

d

k


·

adp

c

y

t


·

gtp

c

y

t








(

1
+


a

t


p

c

y

t




K
m

atp

c

y

t





)

·

(

1
+


g

d


p

c

y

t




K
m

gdp

c

y

t





)


+


(

1
+


a

d


p

c

y

t




K
m

a

d


p

c

y

t






)

·

(

1
+


g

t


p

c

y

t




K
m

g

t


p

c

y

t






)


-
1


)











Vmaxndkcyt for numerical value see Table 10 Keqndk = 1 [66]


Kmatpcyt = 1.8 [138] Kmgdpcyt = 0.049 [138] Kmadpcyt = 0.066 [138] Kmgtpcyt = 0.15 [138]


Nucleoside diphosphokinase (mito)










v

n

d


k

m

i

t

o




=


V

ma

x


ndk
mito


·

(




atp
mito

·

gdp
mito


-

1
/


K

e

q

ndk

·

adp

m

i

t

o


·

gtp
mito







(

1
+


atp

m

i

t

o



K
m

a

t


p

m

i

t

o






)

·

(

1
+


g

d


p

m

i

t

o




K
m

g

t


p

m

i

t

o






)


+


(

1
+


a

d


p

m

i

t

o




K
m

adp

m

i

t

o





)

·

(

1
+


g

t


p

m

i

t

o




K
m

gtp
mito




)


-
1


)











vmaxndkmito for numerical value see Table 10 Keqndk = 1 [66]


Kmatpmito = 1.66 [139] Kmgdpmito = 0.036 [139] Kmadpmito = 0.073 [139] Kmgtpmito = 0.15 [138]





Glycogen metabolism


Alpha-D-Glucose 1-phosphate 1,6-phosphomutase:










v
gpm

=


v

m

ax

gpm

·



g

l

c

1


p

c

y

t



-



1

K

e

q


g

p

m



·
glc


6


p

c

y

t





1
+


g

l

c

1


p

c

y

t




K
m

glc

1


p
cyt




+


g

l

c

6


p

c

y

t




K
m

glc

6


p

c

y

t

















vmaxgpm for numerical value see Table 10


Keqgpm = 16.2 [140] Kmglc1pcyt = 0.045 [141] Kmglc6pcyt = 0.67 [141]


UTP:Glucose-1-phosphate uridylyltransferase (UPGase):










v

u

p

g

a

s

e


=


v

m

ax

upgase

·





utp
cyt

·
glc


1


p
cyt


-


1

K
eq
upgase


·

udpglc
cyt

·

pp
cyt






(

1
+


u

t


p

c

y

t




K
m

u

t


p
cyt





)

·

(

1
+


g

l

c

1


p

c

y

t




K
m

glc

1


p

c

y

t






)


+


(

1
+


u

d

p

g

l


c

c

y

t




K
m

udphlc
cyt




)

·

(

1
+


p


p

c

y

t




K
m

pp

c

y

t





)


-
1












vmaxUPGase for numerical value see Table 10 Kequpgase = 0.3122 [142]


Kmutpcyt = 0.2 [142] Kmglc1pcyt = 0.055 [142] Kmudpglccyt = 0.06 [142] Kmppcyt = 0.084 [142]


Glycogen synthase (GS):


vgs = Vmaxgs · ((1 − γgs) · vgsnative + γgs · vgsp)










γ
gs

=


1
-


γ
·

(

1
-


epi

e

x

t




e

p


i

e

x

t



+

K
i
epi




)




K
i

e

p

i




=


200


pM







V

m

ax

gs


=


V
0
gs




(

store
-
glyglc

)



(

store
-
glyglc

)

+

10


mM















V0gs for numerical value see Table 10 Geben Sie hier eine Formel ein. store = 5 mM










v

g

s


n

a

t

i

v

e


=


(


u

d

p

g

l


c

c

y

t





u

d

p

g

l


c

c

y

t



+

K

m
-

n

a

t

i

v

e



udpglc
cyt




)

·

(


glc

6


p

c

y

t





g

l

c

6


p

c

y

t



+

K
a

g

l

c

6


p

c

y

t






)
















K

m
-

n

a

t

i

ν

e



udpglc

c

y

t



=



K

0
-

n

a

t

i

ν

e



u

d

p

g

l


c

c

y

t




·

(

1
-


g

l

c

6


p

c

y

t





glc

6


p

c

y

t



+

K

a

2


glc

6


p

c

y

t







)


+

K

b
-

n

a

t

i

v

e



udpglc
cyt












K0-nativeudpglccyt = 0.9 [143] Kaglc6pcyt = 0.004 [143] Ka2glc6pcyt = 0.004 [143] Kb-nativeudpglccyt =


0.2 [143]










v
gs
p

=


(


u

d

p

g

l


c

c

y

t





u

d

p

g

l


c

c

y

t



+

K

m
-
p


udpglc
cyt




)

·

(


g

l

c

6


p

c

y

t





g

l

c

6


p

c

y

t



+

K
a

g

l

c

6


p

c

y

t






)











Km-pudpglccyt = K0-pudpglccyt K0-pudpglccyt = 0.9 [143] Kaglc6pcyt =2 [143]


Glycogen phosphorylase (GP):


vgp = ((1 − γgp) · vgpnative + γgp · vgpp)


Ygp = ygs










v
gp

n

a

t

i

v

e


=


V

m

ax


gp
-
native


·



glyglc
·

p
cyt


-



1

K
eq
gp


·
glc


1


p
cyt






(

1
+

glyglc

K

m
-

n

a

t

i

ν

e


glycogen



)

·

(

1
+


p

c

y

t



K

m
-

n

a

t

i

ν

e



p

c

y

t





)


+

(

1
+


g

l

c

1


p

c

y

t




K

m
-

n

a

t

i

v

e



glc

1


p

c

y

t






)

-
1

















V


m

ax

-

n

a

t

i

v

e


gp

=



V
0

g

p




K

m
-

n

a

t

i

ν

e



p

c

y

t



·

K

m
-
native

glyplc



·

(


a

m


p

c

y

t





a

m


p

c

y

t



+

K

a
-

n

a

t

i

v

e



amp
cyt




)

·

(


g

l

y

g

l

c



g

l

y

g

l

c

+

0.1
·
store



)











V0gp for numerical value see Table 10 store = 5 mM


Ka-nativeamp = 0.0022 [144] Keqgp = 0.21(mM)−1 [145] Km-nativeglyglc = 2.5 [146] Km-nativepcyt =


500 [146]










K

m
-

n

a

t

i

ν

e



g

l

c

1


p

c

y

t




=




K
0

g

l

c

1

p


·

(

1
-


a

m


p

c

y

t





a

m


p

c

y

t



+

K

a
-

glc

1

p



a

m


p

c

y

t







)




K
0

glc

1

p



=


2

5


0
[

1

4

6

]



K

a
-
glc1p


a

m


p

c

y

t





=

0.5

[
146
]

















v
gp
p

=


V


ma

x

-
p

gp

·



glyglc
·

p

c

y

t



-



1

K

e

q


g

p



·
glc


1


p

c

y

t







(

1
+

glyglc

K

m
-
p

glycogen



)

·

(

1
+


p

c

y

t



K

m
-
p


p

c

y

t





)


+

(

1
+


g

l

c

1


p

c

y

t




K

m
-
p


glc

1


p
cyt





)

-
1

















V


ma

x

-
p

gp

=



V
0

g

p




K

m
-
p

p

·

K

m
-
p

glyglc



·

(


k
1

+


a

m


p

c

y

t





a

m


p

c

y

t



+

K

a
-
p


a

m


p

c

y

t







)

·

(


g

l

y

g

l

c



g

l

y

g

l

c

+

0.1
·
store



)











k1 = 0.5 [144] Ka-nativeamp = 0.22 [144]


Km-pglyglc = 0.27 [144] Km-ppcyt = 3.8 [144] Km-pglc1pcyt = 0.7 [146]


Nucleoside diphosphokinase (cytosolic) (udp)










v

ndk
cyt


=


V

m

ax


ndk
cyt


·

(



a

t



p

c

y

t


·

udp
cyt



-

1
/


K
eq
ndk

·

adp
cyt

·

utp
cyt







(

1
+


a

t


p

c

y

t




K
m

a

t


p

c

y

t






)

·

(

1
+


u

d


p

c

y

t




K
m

udp

c

y

t





)


+


(

1
+


a

d


p

c

y

t




K
m

adp

c

y

t





)

·

(

1
+


u

t


p

c

y

t




K
m

u

t


p

c

y

t






)


-
1


)











Vmaxndkcyt for numerical value see Table 10 Keqndk = 1 [66]


Kmatpcyt = 0.5 [147] Kmudpcyt = 0.05 [147] Kmadpcyt = 0.07 [147] Kmutpcyt = 0.15 [147]





Malate-Aspartate shuttle


Aspartate-amino transferase (mitochondrial)










v

asat
mito


=


V

m

ax


a

s

a

t


·

(



a

s



p

m

i

t

o


·

akg

m

i

t

o




-

1
/


K
eq
asat

·

oaa

m

i

t

o


·

glu

m

i

t

o








(

1
+


a

s


p

m

i

t

o




K
m

a

s


p

m

i

t

o






)

·

(

1
+


a

k


g

m

i

t

o




K
m

a

k


g

m

i

t

o






)


+


(

1
+


o

a


a

m

i

t

o




K
m

o

a


a
mito





)

·

(

1
+


g

l


u

m

i

t

o




K
m

glu

m

i

t

o





)


-
1


)











Vmaxasatfor numerical value see Table 10 Keqasat = 0.147 [148]


Kmaspmito = 0.35 [149] Kmakgmito = 1.1 [149] Kmoaamito = 1.84 [150] Kmglumito = 0.48 [150]


Aspartate-amino transferase (cytosolic)










v

a

s

a

t


=


V

ma

x


a

s

a

t


·

(



a

s



p

c

y

t


·

akg
cyt



-

1
/


K
eq
asat

·

oaa
cyt

·

glu
cyt







(

1
+


a

s


p

c

y

t




K
m

a

s


p

c

y

t






)

·

(

1
+


a

k


g

c

y

t




K
m

akg
cyt




)


+


(

1
+


o

a


a

c

y

t




K
m

o

a


a

c

y

t






)

·

(

1
+


g

l


u
cyt



K
m

g

l


u

c

y

t






)


-
1


)











Vmaxasat for numerical value see Table 10 Keqasat = 0.147 [148]


Kmaspcyt = 3.9 [149] Kmakgcyt = 0.57 [149] Kmoaacyt = 2.05 [150] Kmglucyt = 0.38 [150]


Aspartate-glutamate carrier










v
agc

=


V

ma

x

agc

·

(



a

s



p

m

i

t

o


·

glu
cyt



-

1
/


K
eq
agc

·

asp
cyt

·

glu
mito







(

1
+


a

s


p

m

i

t

o




K
m

asp
mi𝔱o




)

·

(

1
+


g

l


u

c

y

t




K
m

glu

c

y

t





)


+


(

1
+


a

s


p

c

y

t




K
m

asp

c

y

t





)

·

(

1
+


g

l


u

m

i

t

o




K
m

g

l


u
mito





)


-
1


)











Vmaxasatfor numerical value see Table 10










K

e

q


a

s

a

t


=


exp



(



-

V

m

m



·
F


R
·
T


)

·

(


H
cyt


H
mito


)




K
m

asp
mito



=


K
0

asp
mito


·

(

1
+


glu
mito


K
i

glu
mito




)

















K
0

asp
mito


=



0.05
[
151
]



K
i

glu
mito



=



0.5
[
152
]



K
m

asp
cyt



=


K
0

asp
cyt


·

(

1
+


glu
cyt


K
i

glu
cyt




)













K0aspcyt = 0.043 [152] Kiglucyt = 0.5 [152] Kmglumito = 3 [153] Kmglucyt = 3.2 [153]


Malate - α-ketogluterate carrier










v

m

a

c


=


V

m

ax


m

a

c


·

(



m

a



l

c

y

t


·

akg
mito



-

1
/


K
eq
mac

·

mal
mito

·

akg
cyt







(

1
+


m

a


l

c

y

t




K
m

m

a


l

c

y

t






)

·

(

1
+


a

k


g

m

i

t

o




K
m

akg
mito




)


+


(

1
+


m

a


l

m

i

t

o




K
m

mal
mito




)

·

(

1
+


a

k


g

c

y

t




K
m

a

k


g

c

y

t






)


-
1


)











Vmaxmac for numerical value see Table 10 Keqmac = 1


Kmmalcyt = 0.7 [154] Kmakgmito = 0.17 [154] Kmmalmito = 1.4 [154] Kmakgcyt = 0.3 [154]


Glycerol-3-phosphate dehydrogenase (cytosolic)










v
g3pdh

=


V

m

ax


g

3


pdh
cyt



·

(




dhap
cyt

·

nad
cyt


-

1
/


K
eq

g

3

pdh


·
g


3



p
cyt

·

nad
cyt







(

1
+


d

h

a


p

c

y

t




K
m

dhap

c

y

t





)

·

(

1
+


n

a

d


h

c

y

t




K
m

nadh
cyt




)


+


(

1
+


g

3


p

c

y

t




K
m

g

3


p

c

y

𝔱






)

·

(

1
+


n

a


d

c

y

t




K
m

n

a


d

c

y

t






)


-
1


)











Vmaxg3pdhcyt for numerical value see Table 10










K

e

q


g

3


pdh
cyt



=


1

3
·

10

-
4




[
155
]










Kmdhapcyt = 0.2 [156] Kmnadhcyt = 0.1 [156] Kmg3pcyt = 0.17 [156] Kmnadcyt = 0.063 [156]


Glycerol-3-phosphate dehydrogenase (mitochondrial)










v

g

3


pdh
mito



=


y

m

ax


g3pdh
mito


·

(



d

h

a



p

c

y

t


·
qh



2

m

m



-

1
/


K
eq

g

3

pdh


·
g


3



p
cyt

·

q

m

m







(

1
+


d

h

a


p

c

y

t




K
m

d

h

a


p

c

y

t






)

+

(

1
+


g

3


p

c

y

t




K
m

g

3


p

c

y

t






)

-
1


)











Vmaxg3pdhmito for numerical value see Table 10










K
eq

g

3


pdh
mito



=


K
eq

g

3

p


dh
cyt



·

exp

(



(


n
·

E
0

nad
/
nadh



+

n
·

E
0


QH
2

/
Q




)

·
F


R

·
T


)











Kmdhapcyt = 0.23 [157] Kmg3pcyt = 1.8 [158] E0nad/nadh = −320 mV [82]


E0QH2/Q = −87 mV [41] n = 2





Pentose phosphate shunt


Glucose-6-phosphate dehydrogenase










v

g

6

pdh


=


V

m

ax


g

6

pdh


·

(


(


glc

6


p
cyt




glc

6


p
cyt


+


K
m

glc


6
cyt



·

(

1
+


c

16


coa
cyt



K
i

c

16


coa
cyt





)




)

·


(


n

a

d


p

c

y

t





n

a

d


p

c

y

t



+


K
m

nadp
cyt


·

(

1
+


n

a

d

p


h

c

y

t




K
i

nadph

c

y

t





)




)


)











Vmaxg6pdh for numerical value see Table 10


Kmglc6pcyt = 0.013 [159] Kic16coacyt = 0.029 [160] Kmnadpcyt = 0.013 [159] Kinadphcyt = 0.01 [161]


6-Phosphogluconolactase










v
pgls

=


V

ma

x


ν

gls


·

(


pgl


6
cyt




pgl


6

c

y

t



+

K
m

p

g

l


6

c

y

t






)











Vmaxpglsfor numerical value see Table 10 Kmpg16cyt = 0.7 [162]


6-Phosphogluconate dehydrogenase










v

p

g

d

h


=


V

ma

x

pgdh

·

(





nadp
cyt

·
pg



6
cyt


-

1
/


K
eq
pgdh

·
ru


5



p
cyt

·

nadph
cyt







(

1
+


n

a

d


p

c

y

t





K
m

n

a

d


p

c

y

𝔱




·

(

1
+


n

a

d

p


h

c

y

t




K
i

n

a

d

p


h

c

y

t






)




)

·

(

1
+


p

g


6

c

y

t




K
m

pg


6
cyt





)


+



(

1
+


r

u

5


p

c

y

t




K
m

r

u

5


p

c

y

t






)

·

(

1
+


c

o


2

c

y

t




K
m

c

o


2

c

y

𝔱






)

·

(

1
+


n

a

d

p


h

c

y

t




K
m

nadph

c

y

t





)


-
1


)











Vmaxpgdh for numerical value see Table 10


Keqpgdh = 74 [163] Kmnadpcyt = 0.028 [159] Kinadph = 0.02 [164]


Kmpg6cyt = 0.071 [164] Kmco2cyt = 5 [165] Kmnadphcyt = 0.001 [165] Kmru5pcyt = 0.123 [165]


Ribulose-phosphate-3-epimerase










ν

r

p

e


=


V

m

ax


r

p

e


·

(



ru

5


p
cyt


-

1
/


K
eq
rpe

·
x


5


p
cyt




1
+


r

u

5


p

c

y

t




K
m

r

u

5


p

c

γ

t





+


x

5


p

c

y

t




K
m

x

5


p

c

y

t







)











Vmaxrpe for numerical value see Table 10 Keqrpe = 1.5 [166] Kmru5pcyt = 0.2 [167] Kmx5pcyt = 0.5


Ribose-phosphate-isomerase










v

r

p

i


=


V

m

ax


r

p

i


·

(



r

5


p
cyt


-

1
/


K
eq
rpi

·
ru


5


p
cyt




1
+


r

5


p

c

y

t




K
m

r

5


p

c

y

t





+


r

u

5


p

c

y

t




K
m

r

u

5


p

c

y

t







)











Vmaxrpi for numerical value see Table 10


Keqrpi = 0.32 [168] Kmr5pcyt = 9.1 [169] Kmru5pcyt = 0.78 [169]


Transladolase










v
taldo

=


V

ma

x

taldo

·

(



s

7



p

c

y

t


·

grap
cyt



-

1
/


K
eq
taldo

·
e


4



p
cyt

·
fru


6


p
cyt






(

1
+


s

7


p

c

y

t




K
m

s

7


p

c

y

𝔱






)

·

(

1
+


g

r

a


p

c

y

t




K
m

g

r

a


p

c

y

t






)


+


(

1
+


e

4


p

c

y

t




K
m

e

4


ρ
cyt





)

·

(

1
+


f

r

u

6


p

c

y

t




K
m

f

r

u

6


p

c

y

t






)


-
1


)











Vmaxtado for numerical value see Table 10 Keqtaldo = 0.95 [170]


Kms7pcyt = 0.17 [170] Kmgrapcyt = 0.038 [171] Kme4pcyt = 0.13 [172] Kmfru6pcyt = 0.3 [172]


Transketolase 1










v

t

k

e

t

o

1


=


V

m

ax


tketo

1


·


(



s

7



p

c

y

t


·

grap

c

y

t




-

1
/


K

e

q


t

k

e

t

o

1


·
r


5



p

c

y

t


·
x


5


p

c

y

t







(

1
+


s

7


p

c

y

t




K
m

s

7


p

c

y

t






)

·

(

1
+


g

r

a


p

c

y

t




K
m

grap
cyt




)


+


(

1
+


r

5


p

c

y

t




K
m

r

5


p
cyt





)

·

(

1
+


x

5


p

c

y

t




K
m

x

5


p

c

y

t






)

·

-
1




)











Vmaxtketo1 for numerical value see Table 10 Keqtketo1 = 0.845 [173]


Kms7pcyt = 0.285 [171] Kmgrapcyt = 0.38 [171] Kmr5pcyt = 0.066 [174] Kmx5pcyt = 0.15 [175]


Transketolase 2










v

t

k

e

t

o

2


=


V

m

ax


t

k

e

t

o

1


·

(



f

r

u

6



p

c

y

t


·

grap
cyt



-

1
/


K

e

q


t

k

e

t

o

2


·
e


4



p

c

y

t


·

x5p

c

y

t








(

1
+


f

r

u

6


p

c

y

t




K
m

f

r

u

6


p

c

y

t






)

·

(

1
+


g

r

a


p

c

y

t




K
m

grap

c

y

t





)


+


(

1
+


e

4


p

c

y

t




K
m

e

4


p

c

y

t






)

·

(

1
+


x

5


p

c

y

t




K
m

x

5


p

c

y

t






)

·

-
1




)











Vmaxtketo2 for numerical value see Table 10 Keqtketo2 = 0.084 [173]


Kmfru6pcyt = 0.34 [176] Kmgrapcyt = 0.38 [171] Kme4pcyt = 0.044 [177] Kmx5pcyt = 0.16 [177]





Fatty acid synthesis


Citrate-malate exchanger










ν


c

i

t

-

m

a

l



=



V

ma

x



c

i

t

-

m

a

l





K
m

c

i


t

m

i

t

o




·

K
m

m

a


l
cyt





·

(



c

i



t

m

i

t

o


·

mal
cyt



-

1
/


K
eq

cit
-
mal


·

cit
cyt

·

mal
mito







(

1
+


c

i


t

m

i

t

o




K
m

c

i


t

m

i

t

o






)

·

(

1
+


m

a


l

c

y

t




K
m

mal
cyt




)


+


(

1
+


c

i


t

c

y

t




K
m

c

i


t

c

y

t






)

·

(

1
+


m

a


l

m

i

t

o




K
m

mal
mito




)

·

-
1




)
















V

ma

x


cit
-
mal


=


V
0


c

i

t

-
mal


·

(

1
-



(

c

1

6

c

o


a

c

y

t



)

n




(

c

1

6

c

o


a

c

y

t



)

n

+


(

K
i

c

1

6

c

o


a

c

y

t




)

n




)











V0cit-mal for numerical value see Table 10 Kic16coacyt = 0.033 [178]


n = 3 [178] Keqcit-mal = 1










K
m

c

i


t

m

i

t

o




=


K
0

c

i


t
mito



·

(

1
+


s

u


c

m

i

t

o




K
i

s

u


c
mito





)

·

(

1
+


i

s

o

c

i


t

m

i

t

o




K
i

i

s

o

c

i


t
mito





)

·

(

1
+


p

e


p

m

i

t

o




K
i

p

e


p
mito





)











K0citmito = 0.14 [179] Kisucmito = 2.5 [179] Kiisocitmito = 0.08 [179] Kipepmito = 0.18 [179]










K
m

m

a


l

c

y

t




=



0
.
7



6
[
179
]



K
m

c

i


t

c

y

t





=


K
0

c

i


t

c

y

t




·

(

1
+


p

e


p

c

y

t




K
i

p

e


p

c

y

t






)












K0citcyt = 0.039 [180] Kipepcyt = 0.18 [179] Kmmalmito = 0.76 [179]


ATP dependent citrate lyase


vcit-lys = Vmaxcit-lys · ((1 − γcit-lys) · vcit-lysnative + γcit-lys · vcit-lysphospho)


γcit-lys = γ


Vmaxcit-lys for numerical value see Table 10










v


c

i

t

-

l

y

s



n

a

t

i

v

e


=



c

i


t

c

y

t

n




c

i


t

c

y

t

n


+


(

K
m

c

i


t

c

y

t




)

n



·


c

o


a

c

y

t





c

o


a

c

y

t



+

K
m

c

o


a

c

y

t






·


a

t


p

c

y

t





a

t


p

c

y

t



+

K
m

atp
cyt














Kmcitcyt = 0.154 [181] n = 0.65 [181] Kmcoacyt = 0.0026 [181] Kmatpcyt = 0.041 [181]










v


c

i

t

-

l

y

s


phospho

=



c

i


t

c

y

t

n




c

i


t

c

y

t

n


+


(

K
m

c

i


t

c

y

t




)

n



·


c

o


a

c

y

t





c

o


a

c

y

t



+

K
m

c

o


a

c

y

t






·


a

t


p

c

y

t





a

t


p

c

y

t



+

K
m

a

t


p
cyt















Kmcitcyt = 0.103 [181] n = 0.91 [181] Kmcoacyt = 0.002 [181] Kmatpcyt = 0.041 [181]


Acetyl-CoA carboxylase 1


vacc1 = γ · vacc1-p + (1 − γ) · vacc1-up










ν


a

c

c

1

-
p


=


V

m

ax



a

c

c

1

-
p


·

(


a

t


p

c

y

t





a

t


p

c

y

t



+

K
m

atp
cyt




)

·

(


a

c

o


a

c

y

t





a

c

o


a

c

y

t



+

K
m

a

c

o


a

c

y

t






)

·

(


h

c

o


3

c

y

t





h

c

o


3

c

y

t



+

K
m

h

c

o


3

c

y

t






)
















V

m

ax



a

c

c

1

-
p


=


V


a

c

c

1

-
p


·

(


c

i


t

c

y

t





c

i


t

c

y

t



+

K
a

c

i


t

c

y

t






)

·

(

1
-


malcoa

c

y

t




m

a

l

c

o


a

c

y

t



+

K
i

malcoa

c

y

t






)

·

(

1
-


c

1

6

c

o


a

c

y

t





c

1

6

c

o


a

c

y

t



+

K
i

c

1

6

c

o


a

c

y

t







)











Vacc1-p for numerical value see Table 10 Kic16coacyt = 0.0022 [182] Kacitcyt = 2.3 [183]


Kimalcoacyt = 0.0106 [182] Kmatpcyt = 0.057 [182] Kmacoacyt 0.18 [183 Kmhco3cyt = 2.25 [1.82]










v


a

c

c

1

-

u

p



=


V

ma

x



acc

1

-
up


·

(


a

t


p

c

y

t





a

t


p

c

y

t



+

K
m

a

t


p

c

y

t






)

·

(


a

c

o


a

c

y

t





a

c

o


a

c

y

t



+

K
m

acoa

c

y

t





)

·

(


h

c

o


3

c

y

t





h

c

o


3

c

y

t



+

K
m

h

c

o


3

c

y

t






)
















V

m

ax



a

cc1

-
up


=


V


a

c

c

1

-

u

p



·

(

1
+


n

u

p





c

i


t

c

y

t





c

i


t

c

y

t



+

K
a

c

i


t

c

y

t








)

·

(

1
-


m

a

l

c

o


a

c

y

t





malcoa

c

y

t


+

K
i

m

a

l

c

o


a

c

y

t







)











Vacc1-up = 2.5 · Vacc1-p [184] nup = 1.4 [184] Kacitcyt = 0.8 [184] Kmatpcyt = 0.057 [182]


Kmacoacyt = 0.18 [183] Kimalcoacyt = 0.0106 [182] Kmhco3cyt = 2.25 [182]


Malonyl-CoA decarboxylase










v

m

c

d

c


=




V

ma

x

mcdc

·

(


m

a

l

c

o


a

c

y

t





m

a

l

c

o


a

c

y

t



+

K
m

m

a

l

c

o


a
cyt





)




K
m

malcoa

c

y

t




=

0.04

[
185
]











Acetyl-CoA hydrolase










v

a

c

o

a

h


=




V

ma

x


a

c

o

a

h


·

(


a

c

o


a

c

y

t





a

c

o


a

c

y

t



+

K
m

a

c

o


a

c

y

t






)





K
m

a

c

o


a

c

y

t





=

0.153

[
186
]











TAG synthesis


Glycerol-uptake










v
glycT

=


V

m

a

x

glycT

·

(



glyc
ext

-

glyc
cyt



1
+


glyc
ext


K
m

glyc
ext



+


glyc
cyt


K
m

glyc
cyt





)











VmaxglycT for numerical value see Table 10 Kmglycext = 0.012 [187] Kmglyccyt = 0.012 [187]


Glycerol kinase










v
glycK

=


V

m

a

x

glycK

·

(


glyc
cyt



glyc
cyt

+


K
m

glyc
cyt


·

(

1
+


g

3


p
cyt



K
i

g

3


p
cyt





)




)

·

(


atp
cyt



atp
cyt

+

K
m

atp
cyt




)











VmaxglycK or numerical value see Table 10


Kmglyccyt = 0.003 [188] Kig3pcyt = 0.58 [188] KmATPcyt = 0.058 [188]


Glycerophosphate acyltransferase










v
gpat

=


V

m

a

x

gpat

·

(


g

3


p
cyt




g

3


p
cyt


+

K
m

g

3


p
cyt





)

·

(


c

16


coa
cyt




c

16


coa
cyt


+

K
m

c

16


coa
cyt





)











Vmaxgpat for numerical value see Table 10


Kmg3pcyt = 0.67 [189] Kmc16coacyt = 0.02 [189]


Acetyl glycerol-3-phosphate acyltransferase










v
agpat

=


V

m

a

x

agpat

·

(


lpa
er



lpa
er

+

K
m

lpa
er




)

·

(


c

16


coa
cyt




c

16


coa
cyt


+

K
m

c

16


coa
cyt





)











Vmaxagpat for numerical value see Table 10 Kmlpaer = 0.0065 [190] Kmc16coacyt = 0.004 [190]


Phosphatidic acid phosphatase










v
pap

=


V

m

a

x

pap

·

(


pa
er
n





pa
er
n

+

K
m

pa
er



)

n


)











Vmaxpap for numerical value see Table 10 Kmpaer = 0.35 [191] n = 2.2 [191]


Diacylglycerol acyltransferase










v
dgat

=


V

m

a

x

dgat

·

(


d

a


g
er




d

a


g
er


+

K
m

d

a


g
er





)

·

(


c

16


coa
cyt




c

16


coa
cyt


+

K
m

c

16


coa
cyt





)











Vmaxdgat for numerical value see Table 10 Kmdagcyt = 0.03 [192] Kmc16coacyt = 0.1 [193]


ATGL [194]










v
ATGL
tag

=


V


m

a

x

-
tag

ATGL

·

Sur
ld

·

γ

·

(


tag
ld



tag
ld

+

K
m

tag
ld




)











Vmax-tagATGL for numerical value see Table 10










K
m

tag
ld


=


10


Sur
ld


=


(


tag
ld

+


2
3

·

dag
ld


+


1
3

·

mag
ld


+


2
3



ce
ld



)


2
3












Hormone sensitive lipase (HSL) (dag) [195]










v
HSL
tag

=


V


m

a

x

-
tag

HSL

·

Sur
ld

·

γ

·

(


d

a


g
ld




d

a


g
ld


+

K
m

d

a


g
ld





)











Vmax-tagHSL for numerical value see Table 10










K
m

d

a


g
ld



=


10



Sur
ld


=


(


tag
ld

+



2
3

·
d


a


g
ld


+


1
3

·

mag
ld


+


2
3



ce
ld



)


2
3












Monoaclyglycerol lipase










v
magl

=


V

m

a

x

magl

·

Sur
ld

·

(


mag
ld



mag
ld

+

K
m

mag
ld




)











Vmaxmagl for numerical value see Table 10










K
m

mag
ld


=



0.51

[
196
]




Sur
ld


=


(


tag
ld

+



2
3

·
d


a


g
ld


+


1
3

·

mag
ld


+


2
3



ce
ld



)


2
3












Cholesterol ester esterase










v
cee

=


V

m

a

x

cee

·

Sur
ld

·

γ

·

(


ce
ld



ce
ld

+

K
m

ce
ld




)











Vmaxcee for numerical value see Table 10










K
m

ce
ld


=


5



Sur
ld


=


(


tag
ld

+



2
3

·
d


a


g
ld


+


1
3

·

mag
ld


+


2
3



ce
ld



)


2
3












Ketone body utilization


B-Hydroxy butyrate dehydrogenase










v



β

hdh



=


V

m

a

x




β

hdh



·



(




acac
mito

·

nadh
mito


-


1

K
eq



β

hdh




·

bhbut
mito

·

nad
mito






(

1
+



acac
mito



K
m

mito
acac



)

·


(

1
+



nadh
mito


K
m

nadh
mito




)


+



(

1
+



bhbut
mito


K
m

bhbut
mito




)

·


(

1
+



nad
mito


K
m

nad
mito




)


-

1


)












Vmaxβhdh for numerical value see Table 10










K
eq



β

hdh



=




20.3
·



h
mito


h
cyt



[
125
]





K
m

acac
mito



=




0.204

[
197
]




K
m

nadh
mito



=


K
0

nadh
mito


·

(

1
+


nad
mito


K
i

nad
mito




)













K0nadhmito = 0.017 [197] Kinadmito 0.121 [197] Kmhbutmito = 1.604 [197]










K
m

nad
mito


=





K
0

nad
mito


·

(

1
+


nadh
mito


K
i

nadh
mito




)





K
0

nad
mito



=




0.067

[
197
]




K
i

nadh
mito



=

0.066

[
197
]












Succinyl-CoA-oxaloacid CoA transferase










v
scot

=


V

m

a

x

scot

·

(




acac
mito

·

succoa
mito


-



1

K
eq
scot


·
kc


4



coa
mito

·

succ
mito







(

1
+


acac
mito



K
m

mito
acac



)

·

(

1
+


succoa
mito


K
m

succoa
mito




)


+



(

1
+


kc

4


coa
mito



K
m

kc

4


coa
mito





)

·

(

1
+


succ
mito


K
m

succ
mito




)


-
1


)











Vmaxscot for numerical value see Table 10











K
m

mito
acac

=



0.44

[
198
]




K
m

succoa
mito



=


K
0

succoa
mito


·

(

1
+


succ
mito


K
i

succ
mito




)

















K
0

succoa
mito


=




0.28

[
198
]




K
i

succ
mito



=




0.72

[
198
]




K
m

kc

4


coa
mito




=


K
0

kc

4


coa
mito



·

(

1
+


acac
mito


K
i

acac
mito




)













K0kc4coamito = 0.44 [198] Kiacacmito = 3.7 [198] Kmsuccmito = 34 [198]


Acetoacetate transport (mitochondrial)










v
acacT

=


V

m

a

x

acacT

·

(


acac
mito



acac
mito

+

K
m

acac
mito




)











VmaxacacT for numerical value see Table 10 Kmacacmito = 0.56 [199]


B-Hydroxy butyrate transport (mitochondrial)










v



β

hbT



=


V

m

a

x




β

hbT



·

(


bhbut
mito



bhbut
mito

+

K
m

bhbut
mito




)











Vmaxβhbt for numerical value see Table 10 Kmbhbutmito = 0.8 [200]


Acetoacetate export (MCT1/MCT2)










v

acac
-
ex


=


V

m

a

x


acac
-
ex


·

(



acac
ext

-

acac
cyt



1
+


acac
cyt


K
m

acac
cyt



+


acac
ext


K
m

acac
ext





)











Vmaxacac-ex for numerical value see Table 10 Kmacaccyt = 1.2 [200] Kmacacext = 1.2 [200]


B-Hydroxy butyrate export (MCT1/MCT2)










v




β

hb

-
ex



=


V

m

a

x





β

hb

-
ex



·

(



bhbut
ext

-

bhbut
cyt



1
+


bhbut
cyt


K
m

bhbut
cyt



+


bhbut
ext


K
m

bhbut
ext





)











Vmaxβhb-ex for numerical value see Table 10 Kmbhbutcyt = 0.8 [200] Kmbhbutext 0.8 [200]





Branched chain amino acid metabolism


Valine transport










v
valT

=


V

m

a

x

valT

·

(



val
ext

-

val
cyt



1
+


val
ext


K
m

val
ext



+


val
cyt


K
m

val
cyt





)











VmaxvalT for numerical value see Table 10 Kmvalext = 0.124 [201] Kmvalcyt = 0.124 [201]


Leucine transport










v
leuT

=


V

m

a

x

leuT

·

(



leu
ext

-

leu
cyt



1
+


leu
ext


K
m

leu
ext



+


leu
cyt


K
m

leu
cyt





)











VmaxleuT for numerical value see Table 10 Kmleuext = 0.119 [201] Kmleucyt = 0.119 [201]


Isoleucine transport










v
isoleuT

=


V

m

a

x

isoleuT

·

(



isoleu
ext

-

isoleu
cyt



1
+


isoleu
ext


K
m

isoleu
ext



+


isoleu
cyt


K
m

isoleu
cyt





)











VmaxisoleuT for numerical value see Table 10 Kmisoleuext = 0.0967 [201] Kmisoleucyt = 0.0967 [201]


Branched chain amino acid aminotransferase valine










v

BCAAT
-
val


=


V

m

a

x


BCAAT
-
val


·

(




val
cyt

·

akg
cyt


-


1

K
eq

BCAAT
-
val



·

aKIVA
cyt

·

glu
cyt






(

1
+


val
cyt


K
m

val
cyt




)

·

(

1
+


akg
cyt


K
m

akg
cyt




)


+


(

1
+


aKIVA
cyt


K
m

aKIVA
cyt




)

·

(

1
+


glu
cyt


K
m

glu
cyt




)


-
1


)











VmaxBCAAT-val for numerical value see Table 10 KeqBCAAT-val = 1 Kmvalcyt = 0.62 [202]










K
m

akg
cyt


=



0.63

[
203
]




K
m

aKIVA
cyt



=


K
0

aKIVA
cyt


·

(

1
+


aKICA
cyt


K
i

aKICA
cyt




)

·

(

1
+


KMeVA
cyt


K
i

KMeVA
cyt




)












K0aKIVAcyt = 0.11 [204] KiaKICAcyt = 2.1 [204] KiKMeVAcyt = 1.57 [204] Kmglucyt = 3.6 [203]


Branched chain amino acid aminotransferase leucine










v

BCAAT
-
leu


=


V

m

a

x


BCAAT
-
leu


·

(




leu
cyt

·

akg
cyt


-


1

K
eq

BCAAT
-
leu



·

aKICA
cyt

·

glu
cyt






(

1
+


leu
cyt


K
m

leu
cyt




)

·

(

1
+


akg
cyt


K
m

akg
cyt




)


+


(

1
+


aKICA
cyt


K
m

aKICA
cyt




)

·

(

1
+


glu
cyt


K
m

glu
cyt




)


-
1


)











VmaxBCAAT-leu for numerical value see Table 10


KeqBCAAT-leu = 1.75 [205] Kmleucyt = 3.8 [203] Kmakgcyt = 0.63 [203]










K
m

aKIVA
cyt


=


K
0

aKIVA
cyt


·

(

1
+


aKICA
cyt


K
i

aKICA
cyt




)

·

(

1
+


KMeVA
cyt


K
i

KMeVA
cyt




)











K0aKICAcyt = 0.14 [204] KiaKICAcyt = 4.19 [204] KiKMeVAcyt = 1.57 [204] Kmglucyt = 6.65 [203]


Branched chain amino acid aminotransferase isoleucine










v

BCAAT
-
isoleu


=


V

m

a

x


BCAAT
-
isoleu


·

(




isoleu
cyt

·

akg
cyt


-


1

K
eq

BCAAT
-
leu



·

KMeVA
cyt

·

glu
cyt






(

1
+


isoleu
cyt


K
m

isoleu
cyt




)

·

(

1
+


akg
cyt


K
m

akg
cyt




)


+


(

1
+


KMeVA
cyt


K
m

KMeVA
cyt




)

·

(

1
+


glu
cyt


K
m

glu
cyt




)


-
1


)











VmaxBCAAT-isoleu for numerical value see Table 10 KeqBCAAT-isoleu = Kmisoleucyt = 3.8 [203]










K
m

akg
cyt


=




0.63

[
203
]




K
m

KMeVA
cyt



=



K
0

KMeVA
cyt


·

(

1
+


aKICA
cyt


K
i

aKICA
cyt




)

·

(

1
+


aKIVA
cyt


K
i

aKICV
cyt




)












K0KMeVAcyt = 0.07 [204] KiaKIVAcyt 4.19 [204] KiaKICAcyt 2.1 [204] Kmglucyt = 2.45 [203]


A-ketoisovalerate transport (mitochondrial)










v

aKIVAT
mito


=


V

m

a

x


aKIVAT
mito


·

(



aKIVA
cyt

-

aKIVA
mito




aKIVA
cyt

+

K
m

aKIVA
cyt




)











VmaxaKIVATmito for numerical value see Table 10 KmaKIVAcyt = 0.025 [206]


A-ketoisocaproate transport (mitochondrial)










v

aKICAT
mito


=


V

m

a

x


aKICAT
mito


·

(



aKICA
cyt

-

aKICA
mito




aKICA
cyt

+

K
m

aKICA
cyt




)











VmaxaKICAT mito for numerical value see Table 10 KmaKICAcyt = 0.01 [206]


A-ketomethylvalerate transport (mitochondrial)










v

KMeVAT
mito


=


V

m

a

x


KMeVAT
mito


·

(



KMeVA
cyt

-

KMeVA
mito




KMeVA
cyt

+

K
m

KMeVA
cyt




)











VmaxKMeVATmito for numerical value see Table 10 KmKMeVAcyt = 0.01


Branched chain keto-amino acid dehydrogenase (aKIVA)










v

bckadh
-
aKIVA


=


V

m

a

x


bckadh
-
aKIVA


·

(


aKIVA
mito



aKIVA
mito

+

K
m

aKIVA
mito




)

·

(


nad
mito



nad
mito

+

K
m

nad
mito




)

·

(


coa
mito



coa
mito

+

K
m

coa
mito




)











Vmaxbckadh-aKIVA for numerical value see Table 10


KmaKIVAmito = 0.05 [207] Kmnadmito = 0.04 [208] Kmcoamito = 0.01 [208]


Branched chain keto-amino acid dehydrogenase (aKIVA)










v

bckadh
-
aKICA


=


V

m

a

x


bckadh
-
aKICA


·

(


aKICA
mito



aKICA
mito

+

K
m

aKICA
mito




)

·

(


nad
mito



nad
mito

+

K
m

nad
mito




)

·

(


coa
mito



coa
mito

+

K
m

coa
mito




)











Vmaxbckadh-aKICA for numerical value see Table 10


KmaKICAmito = 0.038 [209] Kmnadmito = 0.04 [208] Kmcoamito = 0.01 [208]


Branched chain keto-amino acid dehydrogenase (aKIVA)










v

bckadh
-
KMeVA


=


V

m

a

x


bckadh
-
KMeVA


·

(


KMeVA
mito



aKICA
mito

+

K
m

aKICA
mito




)

·

(


nad
mito



nad
mito

+

K
m

nad
mito




)

·

(


coa
mito



coa
mito

+

K
m

coa
mito




)











Vmaxbckadh-KMeVA for numerical value see Table 10


KmKMeVAmito = 0.035 [210] Kmnadmito = 0.04 [208] Kmcoamito = 0.01 [208]


2-methylacyl-CoA dehydrogenase (isobutyryl-CoA)










v

MBCoADH
-
IsoButCoA


=


V

m

a

x

MBCoADH

·

(


IsoButCoA
mito



IsoButCoA
mito

+

K
m

IsoButCoA
mito




)

·

(


etffad
mito



etffad
mito

+

K
m

etffad
mito




)











VmaxMBCoADH for numerical value see Table 10


KmIsoButCoAmito = 0.013 [211] Ketffadmito = 0.0083 [19]


2-methylacyl-CoA dehydrogenase (methylbutyryl-CoA)










v

MBCoADH
-
MeButCoA


=


V

m

a

x

MBCoADH

·

(


MeButCoA
mito



MeButCoA
mito

+

K
m

MeButCoA
mito




)

·

(


etffad
mito



etffad
mito

+

K
m

etffad
mito




)











VmaxMBCoADH for numerical value see Table 10


KmMeButCoAmito = 0.027 [211] Kmetffadmito = 0.0083 [19]


Enoyl-CoA hydratase (methyl acrylyl CoA)










v

ECoAH
-
MeAcrCoA


=


V

m

a

x


ECoAH
-
MeACrCoA


·

(


MeAcrCoA
mito



MeAcrCoA
mito

+

K
m

MeAcrCoA
mito




)











VmaxECoAH-MeACrCoA for numerical value see Table 10 KmMeAcrCoAmito = 0.001 [211]


Enoyl-CoA hydratase (Tiglyl CoA)










v

ECoAH
-
TigCoA


=


V

m

a

x


ECoAH
-
TigCoA


·

(


TigCoA
mito



TigCoA
mito

+

K
m

TigCoA
mito




)











VmaxECoAH-TigCoA for numerical value see Table 10 KmTigCoAmito = 0.0047 [211]


3-hydroxyisobutyryl-CoA hydrolase










v
HibCoAhyd

=


V

m

a

x

HibCoAhyd

·

(


HibCoA
mito



HibCoA
mito

+

K
m

HibCoA
mito




)











VmaxHibCoAhyd for numerical value see Table 10 KmHibCoAmito = 0.006 [212]


3-hydroxyisobutyrate dehydrogenase










v
HibDh

=


V

m

a

x

HibDh

·

(


Hib
mito



Hib
mito

+

K
m

Hib
mito




)

·

(


nad
mito



nad
mito

+

K
m

nad
mito




)











VmaxHibDh for numerical value see Table 10










K
m

Hib
mito


=



0.061

[
213
]




K
m

nad
mito



=


K
0

nad
mito


·

(

1
+


nadh
mito


K
i

nadh
mito




)












K0nadhmito = 0.023 [213] Kinadhmito = 0.0057 [213]


Methylmalonate-semialdehyde dehydrogenase










v
mmsdh

=


V

m

a

x

mmsd

·

(


mmsald
mito



mmsald
mito

+

K
m

mmsald
mito




)

·

(


nad
mito



nad
mito

+

K
m

nad
mito




)

·

(


coa
mito



coa
mito

+

K
m

coa
mito




)











Vmaxmmsd for numerical value see Table 10


Kmmmsaldmito = 0.0053 [214] Kmnadmito = 0.15 [214] Kmcoamito = 0.03 [214]


3-hydroxy-2-methylbutyryl-CoA dehydrogenase










v
HMBCDH

=


V

m

a

x

HMBCDH

·

(


MeHButCoA
mito



MeHButCoA
mito

+

K
m

MeHButCoA
mito




)

·

(


nad
mito



nad
mito

+

K
m

nad
mito




)











VmaxHMBCDH for numerical value see Table 10


KmMeHButCoAmito = 0.005 [215] Kmnadmito = 0.01 [215]


acetyl-CoA C-acyltransferase










v
MAACT

=


V

m

a

x

MAACT

·

(


MeAACoA
mito



MeAACoA
mito

+

K
m

MeAACoA
mito




)

·

(


coa
mito



coa
mito

+

K
m

coa
mito




)











VmaxMAACT for numerical value see Table 10


KmMeAACoAmito = 0.008 [216] Kmcoamito = 0.02 [216]


isovaleryl-CoA dehydrogenase










v
IVCoADh

=


V

m

a

x

IVCoADh

·

(


IsoValCoA
mito



IsoValCoA
mito

+

K
m

IsoValCoA
mito




)

·

(


etffad
mito



etffad
mito

+

K
m

etffad
mito




)











VmaxIVCoADh for numerical value see Table 10


KmIsoValCoAmito = 0.014 [217] Kmetffadmito = 0.0083 [19]


Methylcrotonoyl-CoA carboxylase










v
MECCC

=


V

m

a

x

MECCC

·

(


MeCroCoA
mito



MeCroCoA
mito

+

K
m

MeCroCoA
mito




)

·

(


atp
mito



atp
mito

+

K
m

atp
mito




)











VmaxMECCC for numerical value see Table 10


KmMeCroCoAmito = 0.0747 [218] Kmatpmito = 0.045 [218]


Methylglutaconyl-CoA hydratase










v
MEGCCH

=


V

m

a

x

MEGCCH

·

(


MeGCCoA
mito



MeGCCoA
mito

+

K
m

MeGCCoA
mito




)











VmaxMEGCCH for numerical value see Table 10 KmMeGCCoAmito = 0.0083 [219]


Hydroxymethylglutaryl-CoA lyase










v
HMGCL

=


V

m

a

x

HMGCL

·

(


HMeGCoA
mito



HMeGCoA
mito

+

K
m

HMeGCoA
mito




)











VmaxHMGCL for numerical value see Table 10 KmHMeGCoAmito = 0.0448 [220]


Propionyl-CoA carboxylase










v
PCC

=


V

m

a

x

PCC

·

(


ProCoA
mito



ProCoA
mito

+

K
m

ProCoA
mito




)

·

(


atp
mito



atp
mito

+

K
m

atp
mito




)











VmaxPCC for numerical value see Table 10 KmProCoAmito = 0.2 [221] Kmatpmito = 0.08 [222]


Methylmalonyl-CoA mutase










v
MMCM

=


V

m

a

x

MMCM

·

(


MeMalCoA
mito



MeMalCoA
mito

+

K
m

MeMalCoA
mito




)











VmaxMMCM for numerical value see Table 10 KmMeMalCoAmito = 0.133 [223]


Glutamate transport










v

gluT
mito


=


V

m

a

x


gluT
mito


·

(




glu
cyt

·

h
cyt


-


glu
mito

·

h
mito




1
+


glu
cyt


K
m

glu
cyt



+


glu
mito


K
m

glu
mito





)











VmaxgluTmito for numerical value see Table 10 Kmglucyt = 5 [224] Kmglumito = 0.25 [225]


Glutamate dehydrogenase (nad-dependent)










v
gdh

=


V

m

a

x

gdh

·

(





glu
mito

·

nad
mito


-



1

K
eq
gdh


·

akg
mito

·

nadh
mito

·
nh



3
mito









(

1
+


glu
mito


K
m

glu
mito




)

·

(

1
+


nad
mito


K
m

nad
mito




)


+







(

1
+


akg
mito


K
m

akg
mito




)




(

1
+


nadh
mito


K
m

nadh
mito




)

·

(

1
+


nh


3
mito



K
m

nh


3
mito





)








)
















V

m

a

x

gdh

=


V
0
gdh

·

(

1
-


c

16


coa
mito




c

16


coa
mito


+

K
i

c

16


coa
mito






)

·

(


A
0

+


(

1
-

A
0


)



(

1
-


mal
mito



mal
mito

+

K
i

mal
mito





)



)

·










V0gdh for numerical value see Table 10 Kic16coamito = 0.0001 [226] A0 = 0.7 [226]


Kimalmito = 2 [226] Keqgdh = 0.00387 mM [125]










K
m

glu
mito


=


K
0

glu
mito


·

(

1
+


akg
mito


K
i

akg
mito




)

·

(

1
+


nh


3
mito



K
i

nh


3
mito





)











K0glumito = 4.61 [227] Kiakgmito = 1.49 [228] Kinh3mito = 3.1 [228]










K
m

nad
mito


=




K
0

nad
mito


·

(

1
+


nadh
mito


K
i

nadh
mito




)





K
0

nad
mito



=

0.364

[
227
]











Kinadhmito = 0.0086 [228] Kmakgmito = 0.18 [229] Kmnadhmito = 0.03 [229] Kmnh3mito = 20 [229]


Stoichiometric matrix:











d
dt



acac
cyt


=




+


Vol
mito


Vol
cyt



·

v
acacT


+


v

acac
-
ex





d
dt



acac
ext



=
0
















d
dt



acac
mito


=



-

v
scot


-

v



β

hdh



-

v
acacT

+


v
HMGCL




d
dt



acetate
cyt



=


+

v
acoah


+

v
aceT


















d
dt



acoa
cyt


=


+

v

cit
-
lys



-

v

acc

1


+

v
mcdc

+

v
acoah

+

v
HMGCL

+

v
MAACT

















d
dt



acoa
mito


=



+
2

·

v

3

kt


kc

4

coa



+

2
·

v

3

ktII


kc

4

coa



+

v

3

kt


kc

6

coa


+


v

3

kt


kc

8

coa


+

v

3

kt


kc

10

coa


+

v

3

kt


kc

12

coa


+

v

3

kt


kc

14

coa


+

v

3

kt


kc

16

coa


+

v
pdhc

-

v
cs

















d
dt



adp
cyt


=


-


v
nex


10
·
F
·

Vol
cyt




+

v

ndk
cyt


+

2
·

v

ak
cyt



+

v

atp
-
usage


+

v
hka

+


v
hkb

+

v

ndk
cyt

udp

+

v

pfk

2


-

v
pfk1

-

v
pgk

-

v

p

k



+

v

cit
-
lys


+

v

acc

1


+

v
glycK

















d
dt



adp
mito


=


-

v

scs
-
atp



-


v

F

0

F

1



10
·
F
·

Vol
mito



+


v
nex


10
·
F
·

Vol
mito



+

v

ndk
mito


+

v
pc

+

v
PCC

+

v
MECCC

















d
dt



akg
cyt


=


-

v
asat


+

v
mac

-

v

BCAAT
-
val


-

v

BCAAT
-
leu


-

v

BCAAT
-
isoleu


















d
dt



akg
mito


=


+

v

idh
nad



+

v

idh
nadp


-

v
kgdhc

-

v

asat
mito


-



Vol
cyt


Vol
mito


·

v
mac


+

v
gdh

















d
dt



aKICA
cyt


=


+

v

BCAAT
-
val



-

v
aKICAT

















d

d

t




aKICA

m

i

t

o



=



+

v
aKICAT


·


V

o


l

m

i

t

o




V

o


l

c

y

t





-

v


b

c

k

a

d

h

-
aKICA


















d
dt



aKIVA
cyt


=


+

v

BCAAT
-
leu



-

v
aKIVAT

















d
dt



aKIVA

m

i

t

o



=



+

v
aKIVAT


·


V

o


l
mito



V

o


l

c

y

𝔱





-

v

bckadh
-
aKIVA


















d
dt



amp
cyt


=


+

v

ACS

1



+

v

FAB

1


+

v

FAB

4


-

v

ak
cyt


















d

d

t



a

s


p
cyt


=


-

v

a

s

a

t



+

v
agc

















d
dt



asp
mito


=


-

v

asat
mito



-



Vol
cyt


Vol
er


·

v
agc


















d
dt



atp
cyt


=



-

v

ACS

1



-

v

FAB

1


-

v

FAB

4


+


v
nex


10
·
F
·

Vol
cyt



-

v

ndk
cyt


-

v

atp
-
usage


-

v
hka

-

v
hkb

-


v

pfk

2


-

v

pfk

1


+

v
pgk

+

v

p

k



-

v

ndk
cyt

udp

-

v

cit
-
lys


-

v

acc

1


-

v
glycK

-

v

ak
cyt


















d

d

t



a

t


p

m

i

t

o



=


+

v


s

c

s

-

a

t

p




+


v

F

0

F

1



10
·
F
·

Vol

m

i

t

o




-


ν

n

e

x



10
·
F
·

Vol

m

i

t

o




-

v

ndk
mito


-

v

p

c


-

v

P

C

C


-

v

M

E

C

C

C


















d

d

t



b

h

b

u


t

c

y

t



=



+


V

o


l

m

i

t

o




Vol

c

y

t




·

v

β

h

b

T



+

v


β

h

b

-

e

x



















d

d

t



b

h

b

u


t

e

x

t



=
0















d

d

t



b

h

b

u


t

m

i

t

o



=


+

v

β

h

a

h



-

v

β

h

b

T


















d

d

t



b

p

g

1


3
cyt


=


+

v
gapdh


-

v

p

g

k


















d

d

t



c

1

0

c

o


a
mito


=


-

v


C

1

0

c

o

a

-
mcdh



-

v


c

1

0

coa

-
lcdh


+

v

3

k

t


k

c

1

2

c

o

a


















d

d

t



c

1

2

c

o


a

m

i

t

o



=


-

v


c

12

coa

-
mcdh



-

v


c

1

2

coa

-
lcdh


+

v

3

k

t


k

c

1

4

c

o

a


















d

d

t



c

1

4

c

o


a

m

i

t

o



=


-

v


c

1

4

c

o

a

-

l

c

d

h




+

v

3

k

t


k

c

1

6

c

o

a


















d

d

t



c

1

6

c

a


r

c

y

t



=


+

v

C

P

T

1



-

v

C

A

C

T


















d

d

t



c

1

6

c

a


r

m

i

t

o



=



+


V

o


l

c

y

t




V

o


l
mito




·

v
CACT


-

v

C

P

T

2


















d

d

t



c

1

6

c

o


a

c

y

𝔱



=


+

v

A

C

S

1



+

v

FATP

1


+

v

FATP

4


-

v

CPT

1


-

v
gpat

-

v

a

g

p

a

t


-

v

d

g

a

t


















d

d

t



c

1

6

c

o


a

m

i

t

o



=


+

v

C

P

T

2



-

v


c

16

coa

-
lcdh


















d

d

t



c

1


6

e

x

t



=
0















d

d

t



c

1


6

c

y

t



=


+

v

C

D

3

6



-

v

A

C

S

1


-

v

F

A

T

P

1


-

v

F

A

T

P

4


+



V

o


l

l

d




V

o


l

c

y

t




·

v

H

S

L

dag


+



V

o


l
ld



V

o


l

c

y

t




·

v

A

T

G

L


t

a

g



+



Vol
ld


Vol
cyt


·

v
magl


















d

d

t



c

4

c

o


a
mito


=


-

v


c

4

c

o

a

-
scdh



+

v

3

k

t


k

c

6

c

o

a


















d

d

t



c

6

c

o


a

m

i

t

o



=


-

v


c

6

c

o

a

-

m

c

d

h




+

v

3

k

t


k

c

8

c

o

a


















d

d

t



c

8

c

o


a

m

i

t

o



=


-

v


c

8

coa

-
mcdh



+

v

3

k

t


k

c

1

0

c

o

a


















d

d

t



c

a


r

c

γ

t



=


-

v

C

P

T

1



+

v
CACT

















d

d

t



c

a


r

m

i

t

o



=



-


V

o


l

c

y

t




Vol
mito



·

v

C

A

C

T



+

v

C

P

T

2


















d

d

t



c

i


t

c

y

t



=



+


V

o


l
mito



Vol
cyt



·

v

cit
-
mal



-

v

cit
-
lys


















d

d

t



c

i


t

m

i

t

o



=


+

v

c

s



-

v

a

c


-

v

cit
-
mal


















d

d

t




cl

c

y

t



=
0















d

d

t



c


l

m

i

t

o



=

+


I

cI
ed



10
·
F
·

Vol
mito



















a

d

t



c

o


a

c

y

t



=


-

v

F

A

B

P

1



-

v

F

A

B

P

4


-

v

A

C

S

1


+

v

C

P

T

1


-

v

cit
-
lys


+

v
acoah

+

v
gpat

+

v
agpat

+

v
dgat

















d
dt



coa
mito


=


-

v

CPT

2



-

v

3

kt


kc

4

coa


-

v

3

ktII


kc

4

coa


-

v

3

kt


kc

6

coa


-

v

3

kt


kc

8

coa


-

v

3

kt


kc

10

coa


-


v

3

kt


kc

12

coa


-

v

3

kt


kc

14

coa


-

v

3

kt


kc

16

coa


-

v
pdhc

+

v
cs

-

v
kgdhc

+

v

scs
-
atp


+

v

scs
-
gtp


-


v

bckadh
-
aKICA


-

v

bckadh
-
aKIVA


-

v

bckadh
-
KNeVA


-

v
HibDh

-

v
mmsdg

-

v
MMACT

















d
dt


c

o


2

c

y

t



=
0















d

d

t



c

o


2

m

i

t

o



=
0















d

d

t



c

y

t


c

o


x

m

m





=


-


2
·

v
cxIII



10
·
F
·

Vol
membrane




+


ν
cxIV


10
·
F
·

Vol

m

e

m

b

r

a

n

e




















d

d

t



c

y

t


c

red

m

m




=


+


2
·

v
cxIII



10
·
F
·

Vol

m

e

m

b

r

a

n

e





-


v
cxIV


10
·
F
·

Vol

m

e

m

b

r

a

n

e




















d

d

t




dag

e

r



=



+


V

o


l

c

y

t




Vol

e

r




·

v

p

a

p



-



V

o


l

c

y

t




Vol

e

r



·

v

d

g

a

t



















d

d

t



d

a


g
ld


=


+

v

A

T

G

L


t

a

g



-

v
HSL
dag

















d

d

t



d

h

a


p

c

y

t



=


+

v
ald


-

v

t

p

i


-

v

g

3

pdh


-

v

g

3

pd


h

m

i

t

o




















d

d

t



e

c

1

0

c

o


a

m

i

t

o



=


+

v


c

1

0

c

o

a

-

m

c

d

h




+

v


c

10

coa

-
lcdh


-

v

ehyd
-

ec

10



















d

d

t



ec

12


coa

m

i

t

o



=


+

v


c

12

coa

-

m

c

d

h




+

v


c

12

coa

-
lcdh


-

v

ehyd
-

ec

12



















d

d

t



e

c

1

4

c

o


a

m

i

t

o



=


+

v


c

14

coa

-
lcdh



-

v


e

hyd

-

ec

14



















d

d

t



e

c

1

6

c

o


a

m

i

t

o



=


+

v


c

1

6

coa

-
lcdh



-

v


e

h

y

d

-

e

c

1

6



















d

d

t



e

c

4

c

o


a

m

i

t

o



=


+

v


c

4

coa

-
scdh



-

v

ehyd
-

ec

4



















d

d

t



e

c

6

c

o


a
mito


=


+

v

c

6

coa



-

v

ehyd
-

ec

6



















d
dt


e

c

8

c

o


a

m

i

t

o



=


+

v


c

8

coa

-
mcdh



-

v

ehyd
-

ec

8



















d

d

t



e

4


p

c

y

t



=


+

v
taldo


+

v

t

k

e

t

o

2


















d
dt



etffad
mito


=


-

v


c

4

coa

-
scdh



-

v


c

6

coa

-
mcdh


-

v


c

8

coa

-
mcdh


-

v


c

10

coa

-
mcdh


-


v


c

12

coa

-
mcdh


-

v


c

10

coa

-
lcdh


-

v


c

12

coa

-
lcdh


-

v


c

14

coa

-
lcdh


-

v


c

16

coa

-
lcdh


+


v

ETF
-
FAD


-

v

MBCoADH
-
IsoButCoA


-

v


M

B

C

o

A

D

H

-
MeButCoA


-

v
IVCoADh

















d
dt


etffadh


2
mito


=


+

v


c

4

coa

-
scdh



+

v


c

6

coa

-
mcdh


+

v


c

8

coa

-
mcdh


+

v


c

10

coa

-
mcdh


+


v


c

12

coa

-
mcdh


+

v


c

10

coa

-
lcdh


+

v


c

12

coa

-
lcdh


+

v


c

14

coa

-
lcdh


+

v


c

16

coa

-
lcdh


-


v

ETF
-
FAD


+

v

MBCoADH
-
IsoButCoA


+

v


M

B

C

o

A

D

H

-
MeButCoA


+

v
IVCoADh

















d

d

t



e

t

f


q

m

i

t

o



=


-

v

ETF
-
FAD



+

v


E

T

F

-
QO


















d

d

t



e

t

f

q

h


2

m

i

t

o



=


+

v


E

T

F

-

F

F

D




-

v


E

T

F

-

Q

O



















d

d

t



fru

16


bp

c

y

t



=


+

v

p

f

k

1



-

v

f

b

p

1


-

v
ald

















d

d

t



f

r

u

2

6

b


p

c

y

t



=


+

v

pfk

2



-

v

f

b

p

2


















d

d

t



f

r

u

6


p

c

y

t



=


+

v
gpi


-

v

p

f

k

2


+

v

f

b

p

2


-

v

p

f

k

1


+

v

f

b

p

1


+

v

t

a

l

d

o


-

v

t

k

e

t

o

2


















d

d

t



f

u


m

m

i

t

o



=


+

v

s

u

c

c

d

h



-

v

f

u

m


















d

d

t



g

3


p

c

y

t



=


+

v

g

3

pdh



+

v

g

3

pd


h

m

i

t

o




+

v
glycK

-

v
gpat

















d

d

t



g

d


p

c

y

t



=


-

v

ndk

c

y

𝔱




+

v
pepck

















d

d

t



g

d


p
mito


=


-

v

scs
-
gtp



-

v

ndk
mito


















d

d

t



g

l


c

c

y

t



=


+

v

gluT

1



+

v

gluT

4


-

v

h

k

A


-

v

h

k

B


















d

d

t




glc

e

x

t



=
0















d

d

t



g

l

c

1


p

c

y

t



=


-

v
gpm


-

v

u

p

g

a

s

e


+

v
gp

















d

d

t



g

l

c

6


p

c

y

t



=


+

v

h

k

A



+

v
hkB

-

v

g

p

i


+

v

g

p

m


-

v

g

6

pdh


















d
dt



glu
cyt


=


+

v
asat


-

v
agc

-

v

gluT
mito


+

v

BCAAT
-
val


+

v

BCAAT
-
leu


+

v

BCAAT
-
isoleu


















d

d

t



g

l


u

e

x

t



=
0















d

d

t



g

l


u

m

i

t

o



=


+

v

a

s

a


t
mito




+



V

o


l

c

y

t




V

o


l

m

i

t

o




·

v

a

g

c



-

v

g

d

h


+



V

o


l

c

y

t




V

o


l

m

i

t

o




·

v

gluT
mito



















d
dt



glyc
cyt


=


+

v
glycT


-

v
glycK

+



Vol
ld


Vol
cyt


·

v
magl


















d

d

t




glyc

e

x

t



=
0















d
dt


glyglc

=


+

v
gs


-

v
gp

















d

d

t



g

r


a

e

x

t



=
0















d

d

t



g

r

a


p

c

y

t



=


+

v
ald


+

v

t

p

i


-

v
gapdh

-

v
taldo

-

v

tketo

1


-

v

t

k

e

t

o

2


















d
dt



gtp
cyt


=


+

v

ndk
cyt



-

v
pepck

















d

d

t



g

t


p
mito


=


+

v

scs
-
gtp



+

v

n

d


k

m

i

t

o




















d

d

t




h

c

y

𝔱



=
0















d

d

t




h

m

i

t

o



=

+



-

I
H
pump


+

I

H
ed


+

v

P
-
ex


-

I
k

p

u

m

p


-

I

n

a


p

u

m

ρ


+

3
·

v

F

0

F

1





10
·
F
·

Vol
mito



















d

d

t



h

c

o


3

c

y

t



=


0



d
dt


h

c

o


3

m

i

t

o



=


0



d
dt


h

i


b

m

i

t

o



=


+

v

H

i

b

C

o

A

h

y

d



-

v

H

i

b

D

h





















d

d

t



H

i

b

C

o


A

m

i

t

o



=


+

v

ECoAH
-
MeAcrCoA



-

v

H

i

b

C

o

A

h

y

d









1

d

t



H

M

e

G

C

o


A

m

i

t

o



=


+

v

M

E

G

C

C

H



-

v

H

M

G

C

L



















d
dt



IsoButCoA

m

i

t

o



=


+

v

bckadhh
-
aKIVA



-

v


M

B

C

oADH

-
IsoButCoA


















d

d

t



i

s

o

l

e


u

c

y

t



=


+

v

i

s

o

l

e

u

T



-

v


B

CAAT

-
isoleu


















d
dt



isoleu
ext


=
0















d
dt



isocit
mito


=


+

v
ac


-

v

idh
nad


-

v

idh
nadp


















d
dt



IsoValCoA
mito


=


+

v

bckadh
-
aKICA



-

v
IVCoADh

















d
dt


kc

10


coa
mito


=


+

v


3

hdh

-

lc

10




-

v

3

kt


kc

10

coa


















d
dt


kc

12


coa
mito


=


+

v


3

hdh

-

lc

12




-

v

3

kt


kc

12

coa


















d
dt


kc

14


coa
mito


=


+

v


3

hdh

-

lc

14




-

v

3

kt


kc

14

coa


















d
dt


kc

16


coa
mito


=


+

v


3

hdh

-

lc

16




-

v

3

kt


kc

16

coa


















d
dt


kc

4


coa
mito


=


+

v


3

hdh

-

lc

4




-

v

3

kt


kc

4

coa


-

v

3

ktII


kc

4

coa


+

v
scot

















d
dt


kc

6


coa
mito


=


+

v


3

hdh

-

lc

6




-

v

3

kt


kc

6

coa


















d
dt


kc

8


coa
mito


=


+

v


3

hdh

-

lc

8




-

v

3

kt


kc

8

coa


















d
dt



k
cyt


=
0















d
dt



k
mito


=

+



I
K
pump

+

I

k
ed




10
·
F
·

Vol
mito



















d
dt



KMeVA
cyt


=


+

v

BCAAT
-
isoleu



-

v
KMeVAT

















d
dt



KMeVA
mito


=



+

v
KMeVAT


·


Vol
mito


Vol
cyt



-

v

bckadh
-
KMeVA


















d
dt


lc

10


coa
mito


=


+

v

ehyd
-

ec

10




-

v


3

hdh

-

lc

10



















d
dt


lc

12


coa
mito


=


+

v

ehyd
-

ec

12




-

v


3

hdh

-

lc

12



















d
dt


lc

14


coa
mito


=


+

v

ehyd
-

ec

14




-

v


3

hdh

-

lc

14



















d
dt


lc

16


coa
mito


=


+

v

ehyd
-

ec

16




-

v


3

hdh

-

lc

16



















d
dt


lc

4


coa
mito


=


+

v

ehyd
-

ec

4




-

v


3

hdh

-

lc

4



















d
dt


lc

6


coa
mito


=


+

v

ehyd
-

ec

6




-

v


3

hdh

-

lc

6



















d
dt


lc

8


coa
mito


=


+

v

ehyd
-

ec

8




-

v


3

hdh

-

lc

8



















d
dt



lac
cyt


=


+

v
ldh


+

v
lacT

















d
dt



lac
ext


=


0



d
dt



leu
cyt


=


+

v
leuT


-

v

BCAAT
-
leu



















d
dt



leu
ext


=
0















d
dt



lpa
er


=



+


Vol
cyt


Vol
er



·

v
gpat


-



Vol
cyt


Vol
er


·

v
agpat


















d
dt



mag
ld


=


-

v
magl


+

v
HSL
dag

















d
dt



mal
cyt


=


+

v
malpT


+

v

mal
-
pyrT


-

v
mdh

-

v
mac

-



Vol
mito


Vol
cyt


·

v

cit
-
mal



-

v
me

















d
dt



mal
mito


=


+

v
fum


-

v

mdh
mito


-



Vol
cyt


Vol
mito


·

v
malpT


-



Vol
cyt


Vol
mito


·

v

mal
-
pyrT



+



Vol
cyt


Vol
mito


·

v
mac


+

v

cit
-
mal


















d
dt



malcoa
cyt


=



+

v

acc

1



-


v
mcdc



d
dt



MeAACoA
mito



=


+

v
HMBCDH


-

v
MAACT


















d
dt



MeAcrCoA
mito


=


+

v

MBCoADH
-
IsoButCoA



-

v

ECoAH
-
MeAcrCoA


















d
dt



MeButCoA
mito


=


+

v

bckadh
-
KMeVA



-

v

MBCoADH
-
MeButCoA


















d
dt



MeCroCoA
mito


=


+

v
IVCoADh


-

v
MECCC

















d
dt



MeGCCoA
mito


=


+

v
MECCC


-

v
MEGCCH

















d
dt



MeHButCoA
mito


=


+

v

ECoAH
-
TigCoA



-

v
HMBCDH

















d
dt



MeMalCoA
mito


=


+

v
PCC


-

v
MMCM

















d
dt



mmsald
mito


=


+

v
HibDh


-

v
mmsdh

















d
dt



na
cyt


=
0















d
dt



na
mito


=

+



I
na
pump

+

I

na
ed




10
·
F
·

Vol
mito



















d
dt



nad
cyt


=


-

v
gapdh


+

v
ldh

-

v
mdh

+

v

g

3

pdh


















d
dt



nad
mito


=


-

v


3

hdh

-

lc

4




-

v


3

hdh

-

lc

6



-

v


3

hdh

-

lc

8



-


v


3

hdh

-

lc

10



-

v


3

hdh

-

lc

12



-

v


3

hdh

-

lc

14



-

v


3

hdh

-

lc

16



-

v
pdhc

-

v

idh
nad


-


v
kgdhc

-

v

mdh
mito


+

v
tdh

+


v
cxI


10
·
F
·

Vol
mito



+

v

β

hdh


-

v

bckadh
-
aKICA


-


v

bckadh
-
aKIVA


-

v

bckadh
-
KMeVa


-

v
HibDh

-

v
mmsdh

-

v
HMBCDH

-

v
gdh

















d
dt



nadh
cyt


=


+

v
gapdh


-

v
ldh

+

v
mdh

















d
dt



nad
mito


=


+

v


3

hdh

-

lc

4




+

v


3

hdh

-

lc

6



+

v


3

hdh

-

lc

8



+


v


3

hdh

-

lc

10



+

v


3

hdh

-

lc

12



+

v


3

hdh

-

lc

14



+

v


3

hdh

-

lc

16



+

v
pdhc

+

v

idh
nad


+


v
kgdhc

+

v

mdh
mito


-

v
tdh

-


v
cxI


10
·
F
·

Vol
mito



-

v

β

hdh


+

v

bckadh
-
aKICA


+


v

bckadh
-
aKIVA


+

v

bckadh
-
KMeVa


+

v
HibDh

-

v
mmsdh

+

v
HMBCDH

+

v
gdh

















d
dt



nadp
cyt


=


-

v

g

6

pdh



-

v
pgdh

-

v
me

+

v

nadph
-
use


















d
dt



nadp
mito


=


-

v
tdh


-

v

idh
nadp


















d
dt



nadph
cyt


=


+

v

g

6

pdh



+

v
pgdh

+

v
me

-

v

nadph
-
use


















d
dt



nadph
mito


=


+

v
tdh


+

v

idh
nadp


















d
dt


o


2
cyt


=




-

1
4


·


v
cxIV


10
·
F
·

Vol
cyt




+


v

O

2
diff





d
dt


o


2
ext



=
0
















d
dt



oaa
cyt


=


v
mdh

+

v
asat

+

v

cit
-
lys


















d
dt



oaa
mito


=


+

v

mdh
mito



+

v
pc

+

v

asat
mito


-

v
cs

















d
dt



p
cyt


=


-


v

P
-
ex



10
·
F
·

Vol
cyt




+

2
·

v
ppase


+

v

atp
-
usage


+


v

fbp

2


+

v

fbp

1


-

v
gapdh

-

v
malpT

-

v
gp

+

v

cit
-
lys


+

v

acc

1


+

v
pap

















d
dt



p
mito


=


-

v

scs
-
atp



-

v

scs
-
gtp


-


v

F

0

F

1



10
·
F
·

Vol
mito



+



v

P
-
ex



10
·
F
·

Vol
mito



+

v
pc

+



Vol
cell


Vol
mito


·

v
malpT


+

v
PCC

+

v
MECCC

















d
dt



pa
er


=




+


Vol
cyt


Vol
er



·

v
agpat


-




Vol
cyt


Vol
er


·

v
pap




d
dt



pep
cyt



=



+

v
eno


-


v
pk



d
dt


pg


2
cyt



=


+

v
pgm


-

v
eno



















d
dt


pg


3
cyt


=



+

v
pgk


-


v
pgm



d
dt


pg


6
cyt



=



+

v
pgls


-


v
pgdh



d
dt


pgl


6
cyt



=


+

v

g

6

pdh



-

v
pgls



















d
dt



pp
cyt


=


+

v

ACS

1



+

v

FAB

1


+

v

FAB

4


-

v
ppase

+

v
upgase

















d
dt



propcoa
mito


=


+

v
mmsdh


+

v
MAACT

-

v
PCC

















d
dt



pyr
cyt


=


+

v
pk


-

v
ldh

-

v

mal
-
pyrT


+

v
pyrT

-

v

pyrT
mito


+

v
me

















d
dt



pyr
ext


=
0















d
dt



pyr
mito


=


-

v
pdhc


-

v
pc

+



Vol
cell


Vol
mito


·

v
pyrT


+



Vol
cell


Vol
mito


·

v

mal
-
pyrT



















d
dt



q
mm


=



-


Vol
mito


Vol
membrane



·

v

ETF
-
QO



-



Vol
mito


Vol
membrane


·

v
succdh


-



v
cxI


10
·
F
·

Vol
membrane



+


v
cxIII


10
·
F
·

Vol
membrane



+



Vol
cyt


Vol
membrane




v

g

3


pdh
mito




















d
dt


qh


2
mm


=



+


Vol
mito


Vol
membrane



·

v

ETF
-
QO



+



Vol
mito


Vol
membrane


·

v
succdh


+



v
cxI


10
·
F
·

Vol
membrane



-


v
cxIII


10
·
F
·

Vol
membrane



-



Vol
cyt


Vol
membrane




v

g

3


pdh
mito




















d
dt


r

5


p
cyt


=


-

v
rpi


+

v

tketo

1


















d
dt


ru

5


p
cyt


=


+

v
pgdh


-

v
rpe

+

v
rpi

















d
dt


s

7


p
cyt


=


-

v
taldo


-

v

tketo

1


















d
dt



suc
mito


=


+

v

scs
-
atp



+

v

scs
-
gtp


-

v
succdh

+

v
scot

















d
dt



succoa
mito


=


+

v
kgdhc


-

v

scs
-
atp


-

v

scs
-
gtp


-

v
scot

+

v
MMCM

















d
dt



tag
er


=



+


Vol
cyt


Vol
er



·

v
dgat


-

v

LD
-
syn
-
tag


















d
dt



tag
ld


=



+


Vol
er


Vol
ld



·

v

LD
-
syn
-
tag



-

v
ATGL
tag

















d
dt



TigCoA
mito


=


+

v

MBCoADH
-
MeButCoA



-

v

ECoAH
-
TigCoA


















d
dt



udp
cyt


=


-

v

ndk
cyt

udp


+

v
gs

















d
dt



udpglc
cyt


=


+

v
upgase


-

v
gs

















d
dt



utp
cyt


=


+

v

ndk
cyt

udp


-

v
upgase

















d
dt



val
cyt


=


+

v
valT


-

v

BCAAT
-
val


















d
dt



val
ext


=
0















d
dt



v
mm


=



10

-
1




c
m

·

A
m



·

(


-

I

C
ed



+

I

K
ed


+

I

H
ed


+

I

Na
ed


+

I
H
pump

+

v
ex

+

3
·

v
syn



)

















d
dt


x

5


p
cyt


=


+

v
rpe


+

v

tketo

1


+

v

tketo

2
















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TABLE 9







Metabolite concentrations (Table 9 uses separate reference numbering)











Mammalian
Modeled














Metabolite
Location
min [mM]
max [mM]
min [mM]
max [mM]
References

















ACoA
Acetyl coenzyme A
cell
<0.01
0.11
0.0061
0.0673
[1-7]


Acyl-CoA
Acyl coenzyme A
cell
<0.01
0.11
0.02
0.05
[2, 4, 7]


CoAmito
Coenzyme A
mito
0.05
2.26
0.0213
1.1477
[8, 9]


NAD+
Nicotinamide adenine dinucleotide
cell
0.59
1.45
1.13
1.14
[1, 10]


NAD+cyt
Nicotinamide adenine dinucleotide
cyt
0.51
1.39
1.13
1.13
[11]


NAD+mito
Nicotinamide adenine dinucleotide
mito
0.19
0.87
0.026
0.05
[9, 11]


NADH
Reduced nicotinamide adenine dinucleotide
cell
0.02
0.36
<0.01
0.0042
[1, 12]


NADHcyt
Reduced nicotinamide adenine dinucleotide
cyt
<0.01
0.01
<0.01
<0.01
[11]


NADHmito
Reduced nicotinamide adenine dinucleotide
mito
0.05
0.20
<0.01
0.024
[11]


P
Phosphate
cell
2.25
20.50
11.37
21.7
[2, 13-15]


Pcyt
Phosphate
cyt
2.18
7.81
5.45
15.25
[15, 16]


AMP
Adenosine monophosphate
cell
0.07
2.62
0.02
3.89
[2, 10, 17, 18]


ADP
Adenosine diphosphate
cell
0.69
4.49
0.34
2.67
[1, 2, 10, 17-19]


ADPcyt
Adenosine diphosphate
cyt
0.32
0.93
0.34
2.66
[15]


ATP
Adenosine triphosphate
cell
4.05
28.29
3.28
9.32
[1, 2, 6, 12, 13, 17, 19-25]


GDP
Guanosine diphosphate
cell
0.11
0.21
0.04
0.61
[10]


GTP
Guanosine triphosphate
cell
0.31
0.59
0.47
1.04
[10]


Glc6P
Glucose 6-phosphate
cell
0.10
0.93
0.05
0.34
[2, 27]


Fru6P
Fructose-6-phosphate
cell
0.03
0.23
<0.01
0.08
[2, 17, 27]


Fru26P2
Fructose-2,6-bisphosphate
cell
<0.01
0.01
<0.01
0.01
[17]


Fru16P2
Fructose-1,6-bisphosphate
cell
0.01
0.13
<0.01
<0.01
[2, 17, 26, 27]


DHAP
Dihydroxyacetone phosphate
cell
0.01
0.14
0.01
0.037
[2, 17]


GAP
Glyceraldehyde 3-phosphate
cell
0.02
0.09
<0.01
0.02
[2, 27]


13BPG
1,3-Bisphosphoglycerate
cell
<0.01
<0.01
<0.01
<0.01
[26]


3PG
3-Phosphoglycerate
cell
0.03
0.57
0.06
0.21
[2, 26, 27]


2PG
2-Phosphoglycerate
cell
<0.01
0.03
<0.01
0.036
[2, 27]


PEP
Phosphoenolpyruvate
cell
0.01
0.04
0.01
0.01
[2, 26, 27]


Pyr
Pyruvate
cell
0.01
6.00
0.02
1.5
[1, 2, 6, 26, 27]


Gly3P
Glycerol 3-phosphate
cell
<0.01
0.25
<0.01
0.09
[2, 26, 27]


Glc1P
Glucose 1-phosphate
cell
0.01
0.16
<0.01
0.02
[2, 26]


UDP-Glc
Uridine diphosphate glucose
cell
0.26
0.72
<0.01
2.1
[2, 16]


Cit
Citrate
cell
0.19
1.42
0.04
0.1
[1, 2, 28]


IsoCit
Isocitrate
cell
0.02
0.07
<0.01
<0.01
[2, 28]


aKG
Alpha-ketoglutarate
cell
0.05
0.29
<0.01
0.05
[1, 2, 28]


aKGmito
Alpha-ketoglutarate
mito
0.13
0.21
0.02
0.15
[9]


Suc
Succinate
cell
0.26
4.42
<0.01
0.06
[1, 2, 6]


Fum
Fumarate
cell
0.11
0.72
0.5
0.66
[1, 2]


Mal
Malate
cell
0.13
0.49
0.11
0.99
[1, 2, 28]


OA
Oxaloacetate
cell
0.02
0.05
<0.01
0.04
[2]


Asp
Aspartate
cell
3.01
10.78
<0.01
4.74
[2, 28, 29]


Gln
Glutamine
cell
10.38
26.24
10.33
10.33
[30, 31]


Glu
Glutamate
cell
4.63
18.72
<0.01
1.09
[2, 28, 29, 31]


IsoLeu
Isoleucine
cell
<0.01
0.23
0.18
0.2
[29-31]


Leu
Leucine
cell
0.07
0.37
0.33
0.39
[29, 30]


Val
Valine
cell
0.23
0.36
0.35
0.4
[29]


Acyl-Carn
Acylcarnitine
cell
0.01
0.94
0.03
0.14
[9, 32]


Acyl-Carncyt
Acylcarnitine
cyt
0.03
0.38
0.01
0.08
[8]


Acyl-Carnmito
Acylcarnitine
mito
0.00
0.22
0.08
0.44
[8]


Carn
Carnitine
cell
0.74
4.24
0.78
0.89
[2, 14, 33]


Carncyt
Carnitine
cyt
2.56
2.65
0.32
0.39
[8]


Carnmito
Carnitine
mito
1.84
2.03
2.66
3.02
[8]


TAG
Triacylglycerol
cell
3.34
9.78
1.4
2.77
[2, 34]


DAG
Diacyl-glycerol
cell
0.03
0.43
0.51
0.51
[2, 34]


MalCoA
Malonyl coenzyme A
cell
<0.01
0.02
<0.01
0.01
[3, 5, 7, 35-37]


C4CoA
Butyryl coenzyme A
cell
<0.01
0.01
<0.01
<0.01
[38]


C6CoA
Hexanoyl coenzyme A
cell
<0.01
0.01
<0.01
<0.01
[39]


C8CoA
Octanoyl coenzyme A
cell
<0.01
0.01
<0.01
<0.01
[39]


C10CoA
Decanoyl coenzyme A
cell
0.01
0.02
<0.01
<0.01
[39]


C14CoA
Myristoyl coenzyme A
cell
<0.01
<0.01
<0.01
<0.01
[4]


C16CoA
Palmitoyl coenzyme A
cell
<0.01
0.01
<0.01
<0.01
[4]





References


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TABLE 10







Estimated Vmax values













Estimated vmax


Short Name
Long Name
EC/TCDB Number
value [μmol/g/h]





v_CD36
fatty acid translocase
TCDB 4.C.1.1
4.20E+01


v_acs1
(Long-chain) acyl-coa synthetase 1
EC 6.2.1.3
2.80E+00


v_fatp1
fatty acid transport protein 1
TCDB 4.C.1.1
1.04E−01


v_fatp4
fatty acid transport protein 4
TCDB 4.C.1.1
1.35E−01


v_CPT1
Carnitine O-palmitoyltransferase 1, liver isoform
EC 2.3.1.21
7.50E-02


v_CACT
Carnitin-Acylcarnitin translocase
TCDB 2.A.29.8
5.00E+00


v_CPT2
Carnitine O-palmitoyltransferase 2, mitochondrial
EC 2.3.1.21
5.00E+01


v_c4coa_scdh
Short chain acyl-coa dehydrogenase (c4)
EC 1.3.8.1
5.00E+00


v_c6coa_mcdh
medium chain acyl-coa dehydrogenase (c6)
EC 1.3.8.7
5.25E+01


v_c8coa_mcdh
medium chain acyl-coa dehydrogenase (c8)
EC 1.3.8.7
6.25E+01


v_c10coa_mcdh
medium chain acyl-coa dehydrogenase (c10)
EC 1.3.8.7
1.20E+01


v_c12coa_mcdh
medium chain acyl-coa dehydrogenase (c12)
EC 1.3.8.7
9.75E+00


v_c10coa_lcdh
long chain acyl-coa dehydrogenase (c10)
EC 1.3.8.8
1.20E+00


v_c12coa_lcdh
long chain acyl-coa dehydrogenase (c12)
EC 1.3.8.8
9.75E−01


v_c14coa_lcdh
long chain acyl-coa dehydrogenase (c14)
EC 1.3.8.8
5.25E−01


v_c16coa_lcdh
long chain acyl-coa dehydrogenase (c16)
EC 1.3.8.8
1.20E−01


v_etf
ETF-FAD

2.50E+02


v_etfq
ETF-QO

1.25E+03


v_E_hyd_C4_CoA_MC
Enoyl-coa hydratase (Crontonase) (ec4)
EC 4.2.1.17
2.50E+03


v_E_hyd_C6_CoA_MC
Enoyl-coa hydratase (Crontonase) (ec6)
EC 4.2.1.17
3.20E+04


v_E_hyd_C8_CoA_MC
Enoyl-coa hydratase (Crontonase) (ec8)
EC 4.2.1.17
2.28E+04


v_E_hyd_C10_CoA_MC
Enoyl-coa hydratase (Crontonase) (ec10)
EC 4.2.1.17
1.35E+04


v_E_hyd_C12_CoA_MC
Enoyl-coa hydratase (Crontonase) (ec12)
EC 4.2.1.17
4.00E+03


v_E_hyd_C14_CoA_MC
Enoyl-coa hydratase (Crontonase) (ec14)
EC 4.2.1.17
2.17E+03


v_E_hyd_C16_CoA_MC
Enoyl-coa hydratase (Crontonase) (ec16)
EC 4.2.1.17
1.00E+03


v_3HdH_C4_CoA
3-hydroxyacyl-coa dehydrogenase (Ic4)
EC 1.1.1.35
5.75E+10


v_3HdH_C6_CoA
3-hydroxyacyl-coa dehydrogenase (Ic6)
EC 1.1.1.35
5.75E+10


v_3HdH_C8_CoA
3-hydroxyacyl-coa dehydrogenase (Ic8)
EC 1.1.1.35
5.75E+10


v_3HdH_C10_CoA
3-hydroxyacyl-coa dehydrogenase (Ic10)
EC 1.1.1.35
5.75E+10


v_3HdH_C12_CoA
3-hydroxyacyl-coa dehydrogenase (Ic12)
EC 1.1.1.35
5.75E+10


v_3HdH_C14_CoA
3-hydroxyacyl-coa dehydrogenase (Ic14)
EC 1.1.1.35
5.75E+10


v_3HdH_C16_CoA
3-hydroxyacyl-coa dehydrogenase (Ic16)
EC 1.1.1.35
5.75E+10


v_3KT_C4_I
3-ketoacyl-coa thiolase (kc4)
EC 2.3.1.16
2.50E+00


v_3KT_C4_II
3-ketoacyl-coa thiolase (kc4)
EC 2.3.1.16
2.50E+01


v_3KT_C6
3-ketoacyl-coa thiolase (kc4)
EC 2.3.1.16
6.00E+00


v_3KT_C8
3-ketoacyl-coa thiolase (kc4)
EC 2.3.1.16
5.50E+00


v_3KT_C10
3-ketoacyl-coa thiolase (kc4)
EC 2.3.1.16
5.75E+00


v_3KT_C12
3-ketoacyl-coa thiolase (kc4)
EC 2.3.1.16
5.25E+00


v_3KT_C14
3-ketoacyl-coa thiolase (kc4)
EC 2.3.1.16
4.25E+00


v_3KT_C16
3-ketoacyl-coa thiolase (kc4)
EC 2.3.1.16
2.50E+00


v_pdhc
Pyruvate dehydrogenase complex
EC 1.2.4.1; EC 1.8.1.4; EC 2.3.1.12
1.00E−01


v_cs
Citrate synthase, mitochondrial
EC 2.3.3.1
8.00E+01


v_ac
Aconitase
EC 4.2.1.3
9.00E+04


v_icdh_nad
NAD-dependent isocitrate dehydrogenase
EC 1.1.1.41
2.70E+01


v_icdh_nadp
NADP-dependent isocitrate dehydrogenase
EC 1.1.1.42
4.50E+00


v_akdhc
α-ketogluterate dehydrogenase
EC 1.2.4.2; EC 1.8.1.4; EC 2.3.1.61
4.50E+02


v_succoas_atp
Succinyl-Coa Synthetase (ATP)
EC 6.2.1.4; EC 6.2.1.5; EC 6.2.1.5
2.25E+04


v_succoas_gtp
Succinyl-Coa Synthetase (GTP)
EC 6.2.1.4; EC 6.2.1.4; EC 6.2.1.5
2.48E+03


v_succdh
Succinate dehydrogenase
EC 1.3.5.1
9.00E+03


v_fum
Fumerase
EC 4.2.1.2
1.80E+05


v_mdh
Malate dehydrogenase, mitochondrial
EC 1.1.1.37
9.00E+04


v_tdh
NAD(P) transhydrogenase, mitochondrial
EC 1.6.1.2
3.60E+03


v_ATP_use
ATP usage

1.20E−01


v_Phos
Phosphate carrier protein, mitochondrial
TCDB 2.A.29.4.2
7.72E+10


v_syn
F0F1 synthetase
EC 3.6.3.14
6.40E-06


v_ex
ATP-ADP nucleotide exchanger
TCDB 2.A.29
7.20E-07


v1
Complex I
EC 1.6.5.3
6.72E-07


v3
Complex III
EC 1.10.2.2
2.40E-06


v4
Complex IV
EC 1.9.3.1
9.60E-04


v_ak_cyt
Adenylate kinase
EC 2.7.4.3
8.00E+03


v_02_diff
O2 diffusion

8.00E+01


v_ppase
Pyrophosphatase
EC 3.6.1.1
8.00E−02


I_C_ED
Chloride electro diffusion

8.00E−01


IK_P
Sodium pump

2.40E−05


I_K_ED
Sodium electro diffusion

8.00E−01


I_Na_P
Potassium pump

1.60E-04


I_Na_ED
Sodium electro diffusion

8.00E−01


I_H ED
Mitochondrial uncoupling protein
TC 2.A.29.24.1; TC 2.A.29.24.3;
8.00E−01




TC 2.A.29.3.2; TC 2.A.29.3.4;





TC 2.A.29.3.5



v_gpi
Glucose-6-phosphate isomerase
EC 5.3.1.9
3.51E+03


v_ald
Fructose-bisphosphate aldolase B
EC 4.1.2.13
1.17E+03


v_tpi
Triosephosphate isomerase 1
EC 5.3.1.1
1.17E+03


v_gapdh
Glyceraldehydephosphate dehydrogenase
EC 1.2.1.12
1.76E+05


v_pgk
Phosphyglyceratekinase (Pgk)
EC 2.7.2.3
5.85E+02


v_pgm
2-Phospho-D-glycerate 2,3 phosphomutase (Pgm)
EC 5.4.2.1
5.85E+05


v_eno
2-Phospho-D-glycerate hydrolase (Eno)
EC 4.2.1.11
1.17E+03


v_glcT1
Glucose transporter type 1
TC 2.A.1.1
4.15E-04


v_glcT4
Glucose transporter type 4
TC 2.A.1.1
6.31E−03


v_hk1
Hexokinase
EC 2.7.1.1
4.68E−02


v_hk2
Hexokinase
EC 2.7.1.1
4.68E−03


v_fbp2
Phosphofructokinase 2 (FBP2)
EC 2.7.1.105; EC 3.1.3.46; EC 3.1.3.46
4.68E−03


v_pfk2
Phosphofructokinase 2 (Pfk2)
EC 2.7.1.105; EC 3.1.3.46; EC 3.1.3.46
1.17E−02


v_fbp1
Fructose-1,6-bisphosphatase (Fbp1)
EC 3.1.3.11
1.17E+00


v_pfk1
Phosphofructokinase 1 (Pfk1)
EC 2.7.1.11
5.85E−01


v_pk
Pyruvate kinase (Pk)
EC 2.7.1.40
5.85E−02


v_pc
Pyruvate carboxylase; mitochondrial
EC 6.4.1.1
1.17E−02


v_mal_pyrT
Malate-pyruvate antiport (MalPyrT)

4.68E−01


v_me_nadp
Identifier nicht gefunden

1.17E+01


v_ldh
Lactate dehydrogenase
EC 1.1.1.27
1.17E+05


v_mdh_cyt
Malate dehydrogenase, cytoplasmic
EC 1.1.1.37
1.17E+03


v_lacT
Lactate transport (LacT)
TCDB 2.A.1.13.1; TCDB 2.A.1.13.5;
1.17E−02




TCDB 2.A.1.13.6; TCDB





2.A.1.13.7; TCDB 2.A.1.13.9



v_pyrT
pyruvate transport (pyrT)
TCDB 2.A.1.13.1
1.17E−02


v_pyrT_mito
Mitochondrial pyruvate transport
TCDB 2.A.1.13.1
1.17E+05


v_ndk_cyt
Nudiki (cytosolic)
EC 2.7.4.6
1.17E+04


v_ndk_mito
Nudiki (mitochondrial)
EC 2.7.4.6
1.17E+06


v_ASAT_mito
Aspartate aminotransferase, mitochondrial
EC 2.6.1.1
1.50E+02


v_ASAT_in
Aspartate aminotransferase, cytoplasmic
EC 2.6.1.1
1.50E+02


v_asp_glu_T
aspartate -glutamate carrier
TCDB 2.A.29.14.1
2.25E−01


v_mal_akg_T
Malate - α-ketogluterate carrier
TCDB 2.A.29.2.13
1.50E+06


v_g3pdh_cyt
Glycerol-3-phosphate dehydrogenase (cytosolic)
EC 1.1.1.8
1.50E+06


v_g3pdh_mito
Glycerol-3-phosphate dehydrogenase (mitochondrial)
EC 1.1.5.3
3.00E-10


v_g6pd
Glucose-6-phosphate 1-dehydrogenase
EC 1.1.1.49
5.00E-06


v_pglase
6-phosphogluconolactonase
EC 3.1.1.31
3.00E−05


v_pgdh
6-phosphogluconate dehydrogenase; decarboxylating
EC 1.1.1.44
1.00E−01


v_rpe
Ribulose-phosphate 3-epimerase
EC 5.1.3.1
5.00E−03


v_rpi
Ribose-5-phosphate isomerase
EC 5.3.1.6
1.00E−02


v_taldo
Transaldolase
EC 2.2.1.2
1.00E−02


v_tkl1
Transketolase 1
EC 2.2.1.1
1.00E+02


v_tkl2
Transketolase 2
EC 2.2.1.1
1.00E+00


v_Cit_Mal
Citrate-malate exchanger
TCDB 2.A.29.7.2
3.00E−03


v_Cit_Lys
ATP dependent citrate lyase
EC 2.3.3.8
1.00E−05


v_ACC1
Acetyl-CoA carboxylase 1
EC 6.4.1.2
1.40E−05


v_Mal_CoA_dc
Malonyl-CoA decarboxylase
EC 4.1.1.9
1.00E-06


v_glycerol_uptake
Glycerol-uptake

7.50E−03


v_glycerol_kinase
Glycerol kinase
EC 2.7.1.30
3.60E−03


v_gpat
Glycerol-3-phosphate acyltransferase
EC 2.3.1.15
3.00E−03


v_agpat
Acetyl glycerol-3-phosphate acyltransferase
EC 2.3.1.51
4.50E−03


v_PAP
Phosphatidic acid phosphatase
EC 3.1.3.4
9.00E−03


v_dgat
Diacylglycerol acyltransferase
EC 2.3.1.20
1.05E−02


v_ld_syn
LD synthesis (tag)

3.00E−03


v_atgl
ATGL
EC 3.1.1.3
3.00E−04


v_hsl
Hormone-sensitive lipase
EC 3.1.1.79
3.00E−04


v_magl
Monoacylglycerol lipase
EC 3.1.1.23
3.00E−04


v_g16pi
alpha-D-Glucose 1-phosphate 1,6-phosphomutase
EC 5.4.2.2
1.20E+04


v_upgase
UTP:Glucose-1-phosphate uridylyltransferase (UPGase)
EC 2.7.7.9
9.00E+00


v_ndkutp
Nudiki (cytosolic) (udp)
EC 2.7.4.6
6.00E+01


v_gs
Glycogen synthase (GS)
EC 2.4.1.11
3.00E−04


v_gp
Glycogen-phosphorylase (GP)
EC 2.4.1.1
1.80E−02


v_acac_cytT
Acetoacetate export (MCT1/MCT2)
TCDB 2.A.1.13.1; TCDB 2.A.1.13.5;
2.85E−02




TCDB 2.A.1.13.6; TCDB





2.A.1.13.7; TCDB 2.A.1.13.9



v_bhbut_cytT
B-Hydroxy butyrate export (MCT1/MCT2)
TCDB 2.A.13.1
2.85E−02


v_acac_mito_ex
Acetoacetate transport (mitochondrial)
TCDB 2.A. 13.1
8.55E−02


v_bhbut_mito_ex
B-Hydroxy butyrate transport (mitochondrial)
TCDB 2.A.13.1
8.55E−02


v_bHBDH
D-beta-hydroxybutyrate dehydrogenase, mitochondrial
EC 1.1.1.30
5.70E+03


v_scot
Succinyl-CoA:3-ketoacid coenzyme A transferase 1,
EC 2.8.3.5
5.70E+01



mitochondrial




v_valT
valine transporter

1.00E−01


v_leuT
leucine transporter

1.00E−01


v_isoleuT
isoleucine transporter

1.00E−01


v_BCAAT_val
Branched-chain-amino-acid aminotransferase
EC 2.6.1.42
1.00E−01


v_BCAAT_leu
Branched-chain-amino-acid aminotransferase
EC 2.6.1.42
1.00E−01


v_BCAAT_isoleu
Branched-chain-amino-acid aminotransferase
EC 2.6.1.42
1.00E−01


v_BCKADH_aKIVA
Branched-chain alpha-keto acid dehydrogenase
EC 1.2.4.4
1.00E−01


v_BCKADH_aKICA
Branched-chain alpha-keto acid dehydrogenase
EC 1.2.4.4
1.00E−01


v_BCKADH_KMeVA
Branched-chain alpha-keto acid dehydrogenase
EC 1.2.4.4
1.00E−01


v_MBCoADH_IsoButCoA
2-methylacyl-CoA dehydrogenase
EC 1.3.99.12
1.00E+01


v_MBCoADH_MeButCoA
2-methylacyl-CoA dehydrogenase
EC 1.3.99.12
1.00E+01


v_ECoAH_MeAcrCoA
Enoyl-CoA hydratase, mitochondrial
EC 4.2.1.17
1.00E+03


v_ECoAH_TigCoA
Enoyl-CoA hydratase, mitochondrial
EC 4.2.1.17
1.00E+01


v_HibCDA_HibCoA
3-hydroxyisobutyryl-CoA hydrolase, mitochondrial
EC 3.1.2.4
1.00E+01


v_HibCDH_HBA
3-hydroxyisobutyryl-CoA hydrolase, mitochondrial
EC 3.1.2.4
1.00E+01


v_MMSDH_MMSALD
Methylmalonate-semialdehyde dehydrogenase, mitochondrial
EC 1.2.1.27
1.00E+01


v_HMBCDH_MeHButCoA
Methylmalonate-semialdehyde dehydrogenase, mitochondria
EC 1.2.1.27
1.00E+01


v_MAACT_MeAACoA
3-ketoacyl-CoA thiolase, mitochondrial
EC 2.3.1.16
1.00E+01


v_IVCoADH_isoValCoA
Isovaleryl-CoA dehydrogenase, mitochondrial
EC 1.3.8.4
1.00E+01


v_MECCC_MeCroCoA
Methylcrotonoyl-CoA carboxylase, mitochondrial
EC 6.4.1.4
1.00E+01


v_MEGCCH_MeGCCoA
Methylglutaconyl-CoA hydratase, mitochondrial
EC 4.2.1.18
1.00E+01


v_HMGCL_HMeGCoA
Hydroxymethylglutaryl-CoA lyase, mitochondrial
EC 4.1.3.4
1.00E+01


v_PCC_PropCoa
Propionyl-CoA carboxylase, mitochondrial
EC 6.1.4.3
1.00E+01


v_MMCM_MeMalCoa
Methylmalonyl-CoA mutase, mitochondrial
EC 5.4.99.2
1.00E+01








Claims
  • 1. A computer-implemented method for determining an individual metabolic cardiac profile of a subject comprising a) providing a heart tissue sample from said subject,b) quantifying proteins in said sample to obtain protein quantities of the heart tissue sample, andc) applying information about the protein quantities from b) to a mathematical model.
  • 2. The computer-implemented method according to claim 1, wherein said heart tissue sample is a left ventricle, a right ventricle, a septum, a left atrium, and/or a right atrium heart tissue sample obtained from said subject during a myocardium examination or cardiac surgery.
  • 3. The computer-implemented method according to claim 1, wherein said method further comprises quantitatively determining metabolites in a plasma, blood, or serum sample from said subject, wherein said metabolites are selected from the group consisting of glucose, lactate, pyruvate, glycerol, fatty acids, glutamate, glutamine, leucin, isoleucine, valine, acetate, B-hydroxybutyrate, catecholamines, insulin and combinations thereof.
  • 4. The computer-implemented method according to claim 1, wherein the method further comprises quantitatively determining of an individual cardiac parameter of the subject comprising heart rate, blood pressure, pressure-volume loops, and/or heart power.
  • 5. The computer-implemented method according to claim 1, wherein the protein quantities of the heart tissue sample from the subject are determined using a protein quantification method selected from the group consisting of mass spectrometry, large scale mass spectrometry, immunoassay, Western blot, microfluidics/nanotechnology sensor, and aptamer capture assay, wherein said method comprises: a) solubilizing the heart tissue sample to obtain a solubilized heart tissue sample,b) extracting proteins from the solubilized heart tissue sample of a) according to the protein quantification method, wherein said proteins are optionally fragmented into peptides,c) transferring said extracted proteins and/or peptides from b) to a device of said protein quantification method and identifying and quantifying the proteins and/or peptides in said sample,wherein said protein quantification method provides a protein profile of said sample from the subject.
  • 6. The computer-implemented method according to claim 5, wherein the protein profile, individual cardiac parameters and/or the metabolites of the subject are introduced into the mathematical model.
  • 7. The computer-implemented method according to claim 1, wherein said individual cardiac metabolic profile comprises a substrate uptake rate, a myocardial ATP consumption, a myocardial ATP production reserve, a myocardial ATP production at a cardiac workload, and a myocardial ATP production at maximal workload, wherein the myocardial ATP production reserve is calculated as a difference between the myocardial ATP-production at said cardiac workload and the myocardial ATP production at said maximal workload.
  • 8. The computer-implemented method according to claim 5, wherein the mathematical model of the individual metabolic cardiac profile of the subject comprises inputing a cardiac kinetic model and providing metabolic parameters relating to the cardiac kinetic model, and/orproviding individual cardiac parameters at cardiac workload,parametrizing said mathematical model to the heart tissue sample of said subject by calculating a maximal activity Vmax of said subject, andcomputing a cardiac energy expenditure profile of said subject at cardiac workload,wherein said individual metabolic cardiac profile of said subject is optionally compared to a non-diseased subject at cardiac workload.
  • 9. The computer-implemented method according to claim 8, wherein computing the maximal activity Vmax for model parametrization for the heart tissue sample of the subject comprises a) input of the protein profile of the subject, andb) loading at least one reference data set, wherein said reference data set comprises a reference data set containing the quantities of data entries, wherein each data entry of the quantity contains at least one correlated compatible protein label and/or metabolite label, andc) computing the maximal enzyme activity Vmax of the subject, wherein Vmax is calculated by the formula
  • 10. The computer-implemented method according to claim 1, wherein said individual metabolic cardiac profile is calculated for a plurality of cardiac workloads, including rest, stress or cardiac pacing, wherein individual cardiac parameter including heart rate, blood pressure, heart power are determined at said cardiac workloads.
  • 11. The computer-implemented method according to claim 1, wherein a plurality of said mathematical models are used in said computations for the heart at physiological state, including normal post-absorptive, post prandial, and fasted, and for the heart at pathological state, including ischemic or diabetic.
  • 12. The computer-implemented method according to claim 1, and calculating, via the computer-implemented method, prognosis of a cardiovascular related disorder, an effect of a change in nutritional interventions, activity and/or therapeutic interventions on protein expression and on the time variation of a metabolic parameter in the heart tissue sample of the subject.
  • 13. The computer-implemented method according to claim 1, and preventing, ascertaining, prognosing or treating, via the computer-implemented method, a cardiovascular related disorder or detecting a perturbation of a normal biological state of the heart from a subject.
  • 14. The computer-implemented method according to claim 1, and, via the computer-implemented method, (i) selecting a nutritional or a therapeutic intervention, and(ii) evaluating or preventing a therapeutic intervention.
  • 15. A computer program adapted to execute a mathematical modelling algorithm that will be performed by a computing device/module to produce outputs of given data provided as inputs according to claim 1, wherein said computer program, is written in a programming language selected from the group consisting of Fortran, C #, C/C++, High Level Shading Language, and Python.
  • 16. The computer-implemented method according to claim 2, wherein said heart tissue sample is obtained during a cardiac catheter examination.
  • 17. The computer-implemented method according to claim 3 wherein the metabolites are quantitively determined in the plasma sample from said subject.
  • 18. The computer-implemented method according to claim 5, wherein the protein quantification method is large scale mass spectrometry, said proteins are fragmented into peptides, the extracted peptides from b) are transferred to a mass spectrometer and the peptides in said sample are quantified.
  • 19. The computer program according to claim 15, said computer program is MATLAB.
Priority Claims (2)
Number Date Country Kind
21174633.4 May 2021 EP regional
21181803.4 Jun 2021 EP regional
PCT Information
Filing Document Filing Date Country Kind
PCT/EP2022/063620 5/19/2022 WO