Patent Application
20250164474
Detection and quantification of biomarkers at extremely low levels is important to disease detection, monitoring and treatment. While numerous approaches have been developed, the enzyme-linked immunosorbent assay remains “gold standard” method for the detection of protein biomarkers in both clinical use and basic research. However, its dynamic range (log 3), detection limit (picomolar range) and assay time (3-8 h) fall short of the requirement of early disease diagnosis in clinical settings. Recently, the development of single-molecule imaging has made it possible to visualize individual binding complexes, leading to greatly improved sensitivity, reliability and more depth of information compared to conventional methods. Newer methods—including single-molecule enzyme-linked immunosorbent assays (SiMoAs), single-molecule recognition through equilibrium Poisson sampling (SIMREPS), single-molecule augmented capture (SMAC) and time-resolved digital immunoassay (TD-immunoassay)—have been developed to improve detection limit. However, to enable single molecule detection, all of these methods need to amplify the original binding signal, by means of enzymatic amplification, fluorescence or nanoparticle labeling. These signal-amplification techniques suffer from inherent limitations. Methods based on enzyme amplification and gold nanoparticle labeling are limited by matrix effects and unwanted background signal arising from nonspecific reagent binding to assay substrate. Fluorescence-based methods are limited by photobleaching and ubiquitous autofluorescence of sample matrix components. Such limitations make these single-molecule assays incapable of measuring biomarkers directly in undiluted complex sample matrices, especially in whole blood. Moreover, these assays predominantly rely on end-point detection and fail to fully exploit real-time kinetic data. As most interactions occurring on the sensor surface follow first-order binding kinetics, and replicate measurements at the same time point follow a Poisson distribution, real-time data at each time point can contribute meaningfully to the final outcome. Therefore, fully leveraging real-time kinetic information can significantly enhance the precision and reliability of the final results.
Accordingly, there is a need for additional methods for the detection and quantification of low-abundance blood biomarkers.
In some aspects, the present disclosure provides a single-molecule immunoassay is a reliable technique for the detection and quantification of low-abundance blood biomarkers, which are important for early disease diagnosis and biomedical research. However, current single-molecule methods predominantly rely on end-point-detection and necessitate signal amplification via labelling, which brings a variety of unwanted effects, like matrix effect and autofluorescence interference. In some aspects, the present disclosure provides a real-time mass imaging-based label-free single-molecule immunoassay (LFSMiA). Featuring plasmonic scattering microscopy-based mass imaging, a 2-step sandwich assay format-enabled background reduction, minimization of matrix effect by dynamic tracking of single binding events, and fully leveraging real-time data for improved measurement precision through a Gaussian Bayes algorithm, the LFSMiA enables ultra-sensitive and direct protein detection at single-molecule level in neat blood sample matrices. We demonstrated that the LFSMiA can measure interleukin-6 (IL-6) and prostate-specific antigen (PSA) in buffer, undiluted serum and whole blood with sub-femtomolar limit of detection and eight log of dynamic ranges. Moreover, comparable performance was achieved with an inexpensive miniaturized setup. To show its translational potential to clinical settings and point-of-care diagnostics, we examined the detection of N-terminal pro b-type natriuretic peptide (NT-proBNP) in patient whole blood samples using the LFSMIA and realized a strong linear correlation (r>0.99) with standard clinical lab results. These and other attributes of the present disclosure will be apparent upon a complete review of the specification, including the accompanying figures.
In some aspect, the present disclosure provides a method of detecting a target molecule. The method includes contacting a sample comprising the target molecule with a substrate that comprises a plurality of capture antibodies, or antigen binding portions thereof, that specifically bind to the target molecule to form captured target molecules, wherein the plurality of capture antibodies, or antigen binding portions thereof, are unlabeled; contacting the captured target molecules with a plurality of detection antibodies, or antigen binding portions thereof, that bind to the captured target molecules to form target molecule complexes, wherein the plurality of detection antibodies, or antigen binding portions thereof, are unlabeled; taking a series of dynamically tracked real-time images of the target molecule complexes over one or more selected periods of time to produce imaged target molecule complexes; and, quantifying an amount of target molecules in the sample using the imaged target molecule complexes, thereby detecting the target molecule.
In some embodiments, the detection antibodies, or antigen binding portions thereof, specifically bind to a first epitope of the target molecules, wherein the capture antibodies, or antigen binding portions thereof, specifically bind to a second epitope of the target molecules, and wherein the first and second epitopes differ from one another. In some embodiments, the target molecule complexes each comprise a single bound target molecule. In some embodiments, the quantifying step comprises filtering in terms of position, molecular weight, binding duration, and/or binding frequency of detected binding events in the imaged target molecule complexes, and determining and fitting a time course of a total count of specific binding of the detection antibodies, or antigen binding portions thereof, using a Gaussian Bayes algorithm. In some embodiments, the quantifying step comprises digitally counting the imaged target molecule complexes in the images to quantify the amount of target molecule in the sample. In some embodiments, the quantifying step comprises determining a concentration of the target molecule in the sample. In some embodiments, the target molecule is a compound selected from the group consisting of: an interleukin-6 (IL-6) molecule, a prostate-specific antigen (PSA) molecules, and a N-terminal pro b-type natriuretic peptide (NT-proBNP) molecule. In some embodiments, the sample comprises buffer, serum, and/or whole blood.
In some embodiments, the method includes flowing the captured target molecules through a plasma separator prior to contacting the captured target molecules with the plurality of detection antibodies, or antigen binding portions thereof. In some embodiments, the plurality of capture antibodies, or antigen binding portions thereof, are disposed on a surface of a solid support. In some embodiments, the method includes performing at least a portion of the method in a microfluidic device or system. In some embodiments, the method includes obtaining the sample from a subject. In some embodiments, the method includes administering, or discontinuing administering, therapy to the subject based at least in part on the amount of target molecule in the sample obtained from the subject. In some embodiments, the method includes generating a therapy recommendation for the subject based at least in part on the amount of target molecule in the sample obtained from the subject.
In another aspect, the present disclosure provides microfluidic device that comprises a body structure comprising at least one microfluidic channel disposed at least partially in the body structure; a sample inlet area disposed at least partially in the body structure and in fluid communication with the microfluidic channel, wherein the sample inlet area is configured to receive sample aliquots that comprise mixtures of substantially unprocessed target molecules and a plurality of detection antibodies, or antigen binding portions thereof, that specifically bind to the target molecules in the sample; an assay area disposed at least partially in the body structure and in fluid communication with the microfluidic channel; a plurality of capture antibodies, or antigen binding portions thereof, disposed on a surface of the assay area, wherein the capture antibodies, or antigen binding portions thereof, specifically bind to the target molecules when the target molecules are conveyed from the sample inlet area to the assay area through at least a portion of the microfluidic channel into contact with the plurality of capture antibodies, or antigen binding portions thereof, to form captured target molecules; and, wherein the detection antibodies, or antigen binding portions thereof, specifically bind to the target molecules in the captured target molecules when the detection antibodies, or antigen binding portions thereof, are conveyed from the sample inlet area to the assay area through at least a portion of the microfluidic channel into contact with the captured target molecules to form target molecule complexes; wherein the microfluidic device is configured to operably connect to a fluid conveyance mechanism that effects fluid conveyance through the microfluidic channel to and/or from the sample inlet area and the assay area; and wherein the microfluidic device is configured to operably interface with a detection mechanism that images the target molecule complexes in the assay area to produce imaged target molecule complexes such that a controller operably connected to the detection mechanism quantifies an amount of target molecule in the sample aliquots from the imaged target molecule complexes.
In some embodiments, the detection antibodies, or antigen binding portions thereof, specifically bind to a first epitope of the target molecules, wherein the capture antibodies, or antigen binding portions thereof, specifically bind to a second epitope of the target molecules, and wherein the first and second epitopes differ from one another. In some embodiments, the target molecule complexes each comprise a single bound target molecule. In some embodiments, the controller comprises a processor, and a memory communicatively coupled to the processor, the memory storing non-transitory computer executable instructions which, when executed on the processor, perform operations comprising: digitally counting the imaged target molecule complexes in the images to quantify the amount of target molecule in the sample aliquots. In some embodiments, the amount of target molecule in the sample aliquots comprises a concentration of the target molecule in the sample aliquots.
In some embodiments, the detection mechanism comprises a bright-field microscope. In some embodiments, a kit comprises the microfluidic device. In some embodiments, the sample inlet area comprises a sample inlet port. In some embodiments, a microfluidic chip or cartridge comprises the microfluidic device. In some embodiments, a point-of-care device or system comprises or is configured to receive the microfluidic device. In some embodiments, the target molecule is a compound selected from the group consisting of: an interleukin-6 (IL-6) molecule, a prostate-specific antigen (PSA) molecules, and a N-terminal pro b-type natriuretic peptide (NT-proBNP) molecule. In some embodiments, the sample comprises buffer, serum, and/or whole blood. In some embodiments, a system comprises the microfluidic device.
In another aspect, the present disclosure provides a computer readable media comprising non-transitory computer executable instruction which, when executed by at least electronic processor, perform at least: taking a rolling average of a raw image sequence to remove background noise to produce denoised images; converting the denoised images to probability images; identifying candidate pixels of a binding event in one or more frames of the probability images to produce identified candidate pixels; fitting a Gaussian function pixels of the denoised images with the same coordinates as the identified candidate pixels to produce a Gaussian fitting; filtering out invalid binding events and determining positions and intensities of valid binding events based on the Gaussian fitting to produce detected binding events; and, mapping the detected binding events in all frames of the denoised images over time with respect to spatial locations of the detected binding events.
In order for the present disclosure to be more readily understood, certain terms are first defined below. Additional definitions for the following terms and other terms may be set forth throughout the specification. If a definition of a term set forth below is inconsistent with a definition in an application or patent that is incorporated by reference, the definition set forth in this application should be used to understand the meaning of the term.
As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. Thus, for example, a reference to “a method” includes one or more methods, and/or steps of the type described herein and/or which will become apparent to those persons skilled in the art upon reading this disclosure and so forth.
It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting. Further, unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains. In describing and claiming the methods, systems, and devices, the following terminology, and grammatical variants thereof, will be used in accordance with the definitions set forth below.
About. As used herein, “about” or “approximately” or “substantially” as applied to one or more values or elements of interest, refers to a value or element that is similar to a stated reference value or element. In certain embodiments, the term “about” or “approximately” or “substantially” refers to a range of values or elements that falls within 25%, 20%, 19%, 18%, 17%, 16%, 15%, 14%, 13%, 12%, 11%, 10%, 9%, 8%, 7%, 6%, 5%, 4%, 3%, 2%, 1%, or less in either direction (greater than or less than) of the stated reference value or element unless otherwise stated or otherwise evident from the context (except where such number would exceed 100% of a possible value or element).
Administer: As used herein, “administer” or “administering” a therapeutic agent (e.g., an immunological therapeutic agent) to a subject means to give, apply or bring the composition into contact with the subject. Administration can be accomplished by any of a number of routes, including, for example, topical, oral, subcutaneous, intramuscular, intraperitoneal, intravenous, intrathecal and intradermal.
Antibody: As used herein, the term “antibody” refers to an immunoglobulin or an antigen-binding domain thereof. The term includes but is not limited to polyclonal, monoclonal, monospecific, polyspecific, non-specific, humanized, human, canonized, canine, felinized, feline, single-chain, chimeric, synthetic, recombinant, hybrid, mutated, grafted, and in vitro generated antibodies. The antibody can include a constant region, or a portion thereof, such as the kappa, lambda, alpha, gamma, delta, epsilon and mu constant region genes. For example, heavy chain constant regions of the various isotypes can be used, including: IgG1, IgG2, IgG3, IgG4, IgM, IgA1, IgA2, IgD, and IgE. By way of example, the light chain constant region can be kappa or lambda. The term “monoclonal antibody” refers to an antibody that displays a single binding specificity and affinity for a particular target, e.g., epitope.
Antigen Binding Portion: As used herein, the term “antigen binding portion” refers to a portion of an antibody that specifically binds to a target molecule, e.g., a molecule in which one or more immunoglobulin chains is not full length, but which specifically binds to a target molecule. Examples of binding portions encompassed within the term “antigen-binding portion of an antibody include (i) a Fab fragment, a monovalent fragment consisting of the VLC, VHC, CL and CH1 domains: (ii) a F(ab′)2 fragment, a bivalent fragment comprising two Fab fragments linked by a disulfide bridge at the hinge region; (iii) a Fd fragment consisting of the VHC and CH1 domains; (iv) a Fv fragment consisting of the VLC and VHC domains of a single arm of an antibody, (v) a dAb fragment, which consists of a VHC domain; and (vi) an isolated complementarity determining region (CDR) having sufficient framework to specifically bind, e.g., an antigen binding portion of a variable region. An antigen binding portion of a light chain variable region and an antigen binding portion of a heavy chain variable region, e.g., the two domains of the Fv fragment, VLC and VHC, can be joined, using recombinant methods, by a synthetic linker that enables them to be made as a single protein chain in which the VLC and VHC regions pair to form monovalent molecules (known as single chain Fv (scFV)). Such single chain antibodies are also encompassed within the term “antigen binding portion” of an antibody. The term “antigen binding portion” encompasses a single-domain antibody (sdAb), also known as a “nanobody” or “VHH antibody,” which is an antibody fragment consisting of a single monomeric variable antibody domain. These antibody portions are obtained using conventional techniques known to those with skill in the art, and the portions are screened for utility in the same manner as are intact antibodies.
Binding: As used herein, the term “binding” or “binding interaction”, typically refers to a non-covalent association between or among two or more entities. “Direct” binding involves physical contact between entities or moieties; “indirect” binding involves physical interaction by way of physical contact with one or more intermediate entities. Binding between two or more entities can be assessed in any of a variety of contexts—including where interacting entities or moieties are studied in isolation or in the context of more complex systems (e.g., while covalently or otherwise associated with a carrier entity and/or in a biological system or cell).
Binding Moiety: As used herein, the term “binding moiety” refers to a portion of a chemical compound or structure that selectively or preferentially binds to another chemical compound or structure. In some embodiments, for example, a surface (e.g., a solid surface of a microfluidic cavity or channel) is functionalized or conjugated with binding moieties (e.g., capture antibodies or antigen binding portions thereof), which selectively or preferentially bind to target molecules.
Data set. As used herein, “data set” refers to a group or collection of information, values, or data points related to or associated with one or more objects, records, and/or variables. In some embodiments, a given data set is organized as, or included as part of, a matrix or tabular data structure. In some embodiments, a data set is encoded as a feature vector corresponding to a given object, record, and/or variable, such as a given test or reference subject. For example, a medical data set for a given subject can include one or more observed values of one or more variables associated with that subject.
Detect: As used herein, the term “detect,” “detecting,” or “detection” refers to an act of determining the existence or presence of one or more target analytes (e.g., a target molecule in a sample.
Epitope: As used herein, “epitope” refers to the part of an antigen to which an antibody and/or an antigen binding portion binds.
N-terminal prohormone B-type natriuretic peptide: As used herein, the term “N-terminal prohormone B-type natriuretic peptide” or “NT-proBNP” refers to a prohormone with a 76 amino acid N-terminal inactive protein that is cleaved from the molecule to release B-type natriuretic peptide (BNP, also known as brain natriuretic peptide 32).
Sample: As used herein, “sample” or “fluidic sample” refers to a tissue or organ from a subject; a cell (either within a subject, taken directly from a subject, or a cell maintained in culture or from a cultured cell line); a cell lysate (or lysate fraction) or cell extract; or a solution containing one or more molecules derived from a cell or cellular material (e.g., a polypeptide), which is assayed as described herein. A sample may also be any body fluid or excretion (for example, but not limited to, blood, urine, stool, saliva, tears, bile) that contains cells, cell components, or non-cellular fractions.
Subject. As used herein, “subject” refers to an animal, such as a mammalian species (e.g., human, dog, cat) or avian (e.g., bird) species. More specifically, a subject can be a vertebrate, e.g., a mammal such as a mouse, a primate, a simian or a human. Animals include farm animals (e.g., production cattle, dairy cattle, poultry, horses, pigs, and the like), sport animals, and companion animals (e.g., pets or support animals). In certain embodiments, the subject is a human. In certain embodiments, the subject is a companion animal, including, but not limited to, a dog or a cat. A subject can be a healthy individual, an individual that has or is suspected of having a disease or a predisposition to the disease, or an individual that is in need of therapy or suspected of needing therapy. The terms “individual” or “patient” are intended to be interchangeable with “subject.”
System: As used herein, “system” in the context of analytical instrumentation refers a group of objects and/or devices that form a network for performing a desired objective.
In some aspects, the present disclosure provides a real-time label-free single-molecule immunoassay (LFSMiA) based on mass imaging, which enables ultra-sensitive and direct protein detection in neat blood sample matrices. This novel LFSMiA employs plasmonic scattering microscopy (PSM), a technique capable of detecting scattered light from single molecules based on their mass property, to monitor the formation of individual biomarker immunocomplexes on the sensor surface. In some embodiments, a 2-step sandwich assay format is adopted in the LFSMiA to separate sample incubation from detection antibody binding. In this way, a sample in a complex matrix can be directly incubated with the capture antibody functionalized sensor surface and the sample matrix is washed away at the end of incubation to reduce background signal. As such, PSM can specifically extract and track the binding of single detection antibody in pure buffer to the biomarker molecules captured on the sensor surface. Moreover, the LFSMiA exhibits reduced susceptibility to matrix effects, such as interference from molecules structurally similar to the biomarker or heterophilic antibodies, by dynamically tracking binding events and utilizing binding kinetics data to distinguish between specific and nonspecific interactions. In some embodiments, we also use a Gaussian Bayes algorithm to fit the real-time binding data, providing improved detection accuracy. Additionally, the label-free nature of this assay eliminates complications associated with labeling reagents, which can hinder binding efficiency and lead to nonspecific interactions. To the best of our knowledge, the LFSMiA is also the first technology to realize label-free detection of protein biomarkers at single-molecule level. To validate this novel method, we have demonstrated detection of interleukin-6 (IL-6, an important infection and inflammation biomarker) and prostate-specific antigen (PSA, a widely used prostate cancer biomarker) in both pure buffer and neat serum. We also evaluated the clinical application of LFSMiA with N-terminal pro b-type natriuretic peptide (NT-proBNP), an important biomarker for heart failure, and demonstrated excellent linear correlation with clinical lab results measured with the commercial Elecsys proBNP II assay. To highlight the technology's potential for point-of-care diagnostics, we developed an inexpensive and miniaturized version of PSM microscope, which achieved comparable assay performance. Our method is also the first to realize sub-femtomolar biomarker detection in undiluted whole blood sample. Therefore, we believe that the LFSMiA will be a promising method of revolutionizing in vitro molecular diagnostics. These and other attributes will be apparent upon a complete review of this specification, including the accompanying figures.
In some embodiments, the assays of the present disclosure can be done at low concentrations of biomarker (e.g., femtomolar), are ultrasensitive and involve the direct detection of protein biomarkers. In some embodiments, the assays of the present disclosure involve label-free single molecule detection, which eliminates the cost and issues of labeling. In some embodiments, the present disclosure provides imaging based sandwich assays, can be tested in whole blood, and show strong linear correlation with current technologies and their clinical lab reported value for biomarkers in serum samples.
To illustrate,
To further illustrate,
As described herein, a plurality of capture antibodies, or antigen binding portions thereof, is typically disposed on a surface of assay area 208 in which the capture antibodies, or antigen binding portions thereof, specifically bind to the target molecules when the target molecules are conveyed from sample inlet area 206 to assay area 208 through at least a portion of a microfluidic channel through optional plasma separator 210 into contact with the plurality of capture antibodies, or antigen binding portions thereof, to form captured target molecules. As additionally shown, device 200 also includes optional nanoparticle (NP) reservoir 212 disposed at least partially in body structure 202 and in fluid communication with microfluidic channel 204. In some embodiments, NP reservoir 212 is configured to contain NPs that each comprise a second recognition moiety that binds to the first recognition moiety of the detection antibodies, or antigen binding portions thereof, of the captured target molecules when the NPs are conveyed from NP reservoir 212 to assay area 208 through at least a portion of microfluidic channel 204 into contact with the captured target molecules to form captured NP-target molecule complexes.
As additionally shown in
The present disclosure also provides various systems and computer program products or machine readable media. In some aspects, for example, the methods described herein are optionally performed or facilitated at least in part using systems, distributed computing hardware and applications (e.g., cloud computing services), electronic communication networks, communication interfaces, computer program products, machine readable media, electronic storage media, software (e.g., machine-executable code or logic instructions) and/or the like. To illustrate,
As understood by those of ordinary skill in the art, memory 606 of the server 602 optionally includes volatile and/or nonvolatile memory including, for example, RAM, ROM, and magnetic or optical disks, among others. It is also understood by those of ordinary skill in the art that although illustrated as a single server, the illustrated configuration of server 602 is given only by way of example and that other types of servers or computers configured according to various other methodologies or architectures can also be used. Server 602 shown schematically in
As further understood by those of ordinary skill in the art, exemplary program product or machine readable medium 608 is optionally in the form of microcode, programs, cloud computing format, routines, and/or symbolic languages that provide one or more sets of ordered operations that control the functioning of the hardware and direct its operation. Program product 608, according to an exemplary aspect, also need not reside in its entirety in volatile memory, but can be selectively loaded, as necessary, according to various methodologies as known and understood by those of ordinary skill in the art.
As further understood by those of ordinary skill in the art, the term “computer-readable medium” or “machine-readable medium” refers to any medium that participates in providing instructions to a processor for execution. To illustrate, the term “computer-readable medium” or “machine-readable medium” encompasses distribution media, cloud computing formats, intermediate storage media, execution memory of a computer, and any other medium or device capable of storing program product 608 implementing the functionality or processes of various aspects of the present disclosure, for example, for reading by a computer. A “computer-readable medium” or “machine-readable medium” may take many forms, including but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media includes, for example, optical or magnetic disks. Volatile media includes dynamic memory, such as the main memory of a given system. Transmission media includes coaxial cables, copper wire and fiber optics, including the wires that comprise a bus. Transmission media can also take the form of acoustic or light waves, such as those generated during radio wave and infrared data communications, among others. Exemplary forms of computer-readable media include a floppy disk, a flexible disk, hard disk, magnetic tape, a flash drive, or any other magnetic medium, a CD-ROM, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wave, or any other medium from which a computer can read.
Program product 608 is optionally copied from the computer-readable medium to a hard disk or a similar intermediate storage medium. When program product 608, or portions thereof, are to be run, it is optionally loaded from their distribution medium, their intermediate storage medium, or the like into the execution memory of one or more computers, configuring the computer(s) to act in accordance with the functionality or method of various aspects disclosed herein. All such operations are well known to those of ordinary skill in the art of, for example, computer systems.
In some aspects, program product 608 includes non-transitory computer-executable instructions which, when executed by electronic processor 604, perform at least: conveying fluid through a microfluidic channel of an device as described herein to and/or from a sample inlet area and an assay area using a fluid conveyance mechanism; taking images of target molecule complexes in an assay area to produce imaged target molecule complexes using a detection mechanism; and quantifying an amount of target molecule in sample aliquots using imaged target molecule complexes.
Typically, imaging is obtained using microfluidic device or subassembly 218. As shown, microfluidic device or subassembly 218 includes a fluid conveyance mechanism for flowing samples and other reagents through microfluidic channels, as described herein. Target molecule complexes are counted using the optical imaging system shown, which includes an objective lens and a CCD camera.
In LFSM-immunoassay, individual biomarkers of interest were pulled down by a capture antibody which was immobilized on a gold-coated glass slide via a polyethylene glycol (PEG) linker (
Ultra-sensitive quantitation was achieved by the optimized data analysis approach (
The relationship between molecular weight (MW) and image intensity of particles for PSM had been demonstrated previously. Here, several pure protein samples were measured to determine such a relationship on our setup (
To assess the intrinsic sensitivity of LFSMiA, we first applied it to interleukin-6 (IL-6) detection, a key factor in hematopoiesis, immunomodulation and inflammation processes, in pure buffer (1×PBS containing 1% BSA) and bovine serum. A series of standard buffer solutions or spiked bovine serum samples with different concentrations of IL-6 were flowed through the microfluidic channel for 2 hours to react with the capture antibody pre-functionalized on the sensor surface. Next, 10 nM detection antibody was injected for 10 mins to bind with IL-6 captured by the surface antibody, which is monitored by PSM (
The standard curves of IL-6 detection in pure buffer and bovine serum were determined with 3 replicates for each concentration (
Simple, rapid and sensitive assays are always needed in clinical setting. To show the applicability of our assay for clinical use, it was evaluated for NT-proBNP detection, a key clinical biomarker of heart failure. As NT-proBNP naturally presents in human blood circulation, we first measured the baseline level of NT-proBNP in the human plasma pool used for spiking, which was determined to be 8.23 pg/mL. A series of standard samples with different concentrations of NT-proBNP were prepared by spiking recombinant NT-proBNP into the human plasma pool with baseline level corrected. To evaluate the background level, horse serum was used as blank control without human NT-proBNP. Similar to IL-6 experiment, these standard samples were introduced into the microfluidic channel for 10 mins (
To evaluate the translational potential of LFSMiA for diagnostic applications, a cross-validation between the Roche's Elecsys proBNP II assay, an FDA approved routine clinical diagnostic testing for heart failure, was conducted. Serum samples from 28 patients were measured using both the Elecsys proBNP II assay and LFSMiA. The measured concentration of our method was strongly correlated with those of the Elecsys proBNP II assay (
As modern medicine greatly depends on clinical testing for disease diagnosis and monitoring, a simple assay for direct analysis of whole blood components is always preferred. Detection method using whole blood as sample matrix could not only reduce the loss of biomarkers caused by physiolysis and manual operation, but also minimize total assay time by eliminating sample preparation steps. Recent single-molecule technologies, like single molecule enzyme-linked immunosorbent assay and single molecule fluorescence microscopy, either requires removal of blood cells or have to dilute whole blood to achieve reliable detection due to matrix effects or extreme background autofluorescence. Biomarker detection at single molecule level in undiluted whole blood was accomplished by our method owes to three important features: 1) The use of microfluidic flow helps to reduce blocking effect caused by red blood cells. 2) The label-free nature, together with the two-step assay format, dramatically lowers the background signal by separating signal readout from biomarker surface capture in whole blood, enabling reliable detection of single binding events. 3) Real-time PSM imaging removes nonspecific background signals and reduces matrix effects.
To validate the capability of this method for direct detection in whole blood, we conducted experiments using the label-free digital immunoassay for the detection of interleukin-6 (IL-6) and prostate-specific antigen (PSA). Bovine whole blood was spiked with varying concentrations of IL-6 and PSA, and these samples were analyzed using the label-free digital immunoassay, following the same protocol used in IL-6 detection. The temporal profiles for IL-6 and PSA detection are shown in
These results confirm the feasibility and robust performance of the LFSMiA for ultra-sensitive biomarker detection. To our knowledge, this is the first demonstration of rapid, digital protein detection using label-free single-molecule technology. Our method exhibits sensitivity comparable to other single-molecule assays, with the added advantage of detecting individual biomarkers directly in undiluted complex clinical fluids such as serum, plasma, and whole blood—a capability not previously reported in single-molecule technologies.
To assess the applicability of the LFSMiA in point-of-care (POC) settings, we developed an affordable label-free single-molecule microscope (LFSMiA-lite) with compact dimensions of 40×15×40 cm, constructed using commercially available optical components. The total cost of the setup is approximately USD 2,000 (
First, we established the relationship between molecular weight and particle image intensity using the new LFSMiA-lite system, enabling the determination of threshold values for optimized data analysis (
To demonstrate the clinical translational potential and POC applicability of LFSMiA-lite, we employed it for rapid NT-proBNP detection in whole blood. A series of bovine whole blood samples spiked with varying concentrations of NT-proBNP were analyzed using LFSMiA-lite, following the same procedure used in previous NT-proBNP detection experiments. The resulting temporal profiles are shown in
Recent advancements in digital immunoassay techniques have primarily focused on endpoint detection, relying on the counting of final single-molecule events. The inherent relative counting error is fundamentally limited by √{square root over (N)} (where N represents the total counts), which defines the digital noise constraint in such assays. One of the most significant distinctions between LFSMiA and other assays is that LFSMiA operates as a real-time assay. By fully utilizing both kinetic and statistical information, LFSMiA effectively surpasses the digital noise limitation inherent in traditional digital immunoassays.
To demonstrate the improvements brought by the Gaussian process model, we first compared the limit of detection (LOD) with and without the use of the model, as illustrated in
In this work, we have developed a label-free digital kinetic immunoassay that addresses the limitations of current single-molecule immunoassays, enabling specific, rapid, and ultrasensitive detection of molecular biomarkers in complex sample matrices including undiluted serum, plasma, and whole blood. By integrating a Gaussian Bayes algorithm, the assay fully exploits kinetic information to enhance both sensitivity and precision. We validated the LFSMiA using a commercially available and well-characterized IL-6 antibody pair, achieving sub-femtomolar detection in pure buffer, undiluted serum, and whole blood. The assay demonstrated an impressive dynamic range of eight logs, surpassing the performance of most existing technologies. The results of IL-6 detection across different sample matrices reveal that interfering substances in real biological samples can impact the limit of detection (LOD) and sensitivity of the assays. In addition, the LFSMiA for rapid NT-proBNP detection in plasma exhibited superior sensitivity, a broader dynamic range, and significantly shorter sample-to-answer time compared to the gold-standard ELISA. When applied to serum samples from heart failure patients, the LFSMiA showed excellent correlation with FDA-approved routine clinical diagnostic tests, demonstrating significant potential for clinical translation. The successful ultra-sensitive detection of multiple clinically important biomarkers in undiluted whole blood highlights the potential of the LFSMiA for point-of-care (POC) testing, as it eliminates the need for sample preparation and the associated risk of biomarker loss. The inexpensive, compact label-free microscope (LFSMiA-lite) that we developed and optimized for digital immunoassays proved to be as effective as the laboratory-based microscopy. Applied to whole blood samples from heart failure patients, LFSMiA-lite, using a 40 μL sample volume and a total assay time of 20 minutes, produced results that strongly correlated with those obtained using clinical diagnostic assays. Thus, the LFSMiA represents a highly promising platform for clinical diagnostics and offers significant potential for POC diagnostics.
The focus of this work is to introduce a new single-molecule technology with acceptable analytical performance that can overcome the limitations of signal amplification with labeling. LFSMiA reports the total binding events N (T) of detection antibody on the surface as output signal, which is defined as
where kon is the association rate constant of the detection antibody, [A]t and [P]t are the concentrations of free analyte and detection antibody at time t. Therefore, the signal of LFSMiA would still increase even after detection antibody binding reaches dynamic equilibrium, which makes it superior to conventional endpoint assay for detecting low-abundance biomarkers. It is worth noting that the accuracy and sensitivity of LFSMiA are primarily limited by the number of the binding event numerated, which could be improved by increasing FOV or reaction time. We compared the results for the reaction time of 5 min or 10 min and it shows that longer reaction time would improve the accuracy and sensitivity (
LFSMiA still suffer from some limitations. In the current set-up, LFSMiA uses an incident illumination intensity of ˜2 kW/cm2 to image single detection antibody with acceptable signal-to-noise ratio (SNR). Higher SNR can be obtained by increasing the incident intensity, which could improve the accuracy of dynamic counting of single binding events. However, the protein molecules on the surface could be damaged due to photothermal effect.
As a sandwich assay, the affinity of antibodies would influence the performance of LFSMiA. Most commercial antibodies with nanomolar KD are compatible with LFSMiA. However, antibody with kon lower than 104 M−1s−1 would result in insufficient number of binding events detected in the assay time. We could improve the binding kinetics of such antibody by construct multivalent antibody via DNA assisted super assembly technique.
Despite these limitations, LFSMiA shows obvious advantages compared with existing label-based digital immunoassays, such as SiMoAs, SIMREPS and SMAC. The label-free nature of LFSMiA avoids the cost associated with fluorescence probes. By adding an air objective on the top of imaging area, LFSMiA could be simply achieved on commercial SPR systems, which could ease the adoption of LFSMiA. The ability to detect individual biomarker in undiluted complex clinical fluids simplify the workflow of clinical testing and is POC compatible. Compared with label-free methods like (iSCAMS) and SPR, LFSMiA excels at distinguishing between specific binding of detection antibody to analyte and nonspecifically absorbed biomolecules from the complex media. Therefore, LFSMiA is a reliable technique for fundamental biological research with the potential of moving digital immunoassay into clinical application.
Human cardiac troponin T (cTnT, catalog no. 8RTT5) was purchased from HyTest Ltd. Bovine serum albumin (BSA, catalog no. A7638-5G) and immunoglobulin G (IgG, catalog no. 12511-10 MG) were purchased from Sigma-Aldrich. Human colostrum immunoglobulin A (IgA, catalog no. SIA1901-R22) and human plasma immunoglobulin M (IgM, catalog no. IP2020-03) were purchased from Athens Research and Technology. IL-6 monoclonal capture antibody (clone no. MQ2-13A5, catalog no. 14-7069) and detection antibody (clone no. MQ2-39C3, catalog no. 13-7068) were purchased from ThermoFisher Scientific. Recombinant human IL-6 protein (catalog no. 206-IL) was purchased from R&D Systems. PSA monoclonal capture antibody (clone no. M612165, catalog no. 10-P21A), detection antibody (clone no. M612166, catalog no. 10-P20A) and purified native human PSA protein (catalog no. 30-1205) were purchased from Fitzgerald Industries. Human NT-proBNP capture antibody (catalog no. BRJNBNPS108), detection antibody (catalog no. BRJNBNPS102) and recombinant protein (catalog no. GRCBNPS101) were purchased from Fapon International Limited. Reagent diluent (catalog no. DY995), streptavidin conjugated horseradish peroxidase (streptavidin-HRP, catalog no. DY998), stop solution (catalog no. DY994) and high-binding microplate (catalog no. DY990) were purchased from R&D systems. Gender unspecified pooled K2EDTA plasma from healthy human donors and gender unspecified pooled bovine whole blood were purchased from BioIVT Elevating Science. Heat-inactivated horse serum (catalog no. 26050) was purchased from ThermoFisher Scientific. ACS grade denatured ethanol (catalog no. BDH1158) was purchased from VWR International. N-hydroxysuccinimide (NHS, catalog no. 130672), N-(3-dimethylaminopropyl)-N-ethylcarbodiimide hydrochloride (EDC, catalog no. 03450), Amicon Ultra-0.5 mL centrifugal filters, 6-mercapto-1-hexanol (catalog no. 725226) and 8-mercaptooctanoic acid (catalog no. 675075) were purchased from Sigma-Aldrich (St. Louis, MO). Sylgard 184 Clear Silicone Elastomer Kit (catalog no. DC4019862) was purchased from Krayden Inc.
47 nm gold coated 24×50 mm2 glass coverslip was used as the substrate of the sensor chip. The gold substrate was thoroughly rinsed with ethanol and deionized water sequentially and annealed using hydrogen flaming. The annealed gold substrate was then immersed overnight in an ethanol solution containing 100 μM 8-mercaptooctanoic acid (MOA) and 10 mM 6-mercapto-1-hexanol (MCH). After the gold substrate was thoroughly rinsed with ethanol and deionized water, a layer of 50 μm thick double-sided tape with a 3×36 mm2 straight channel was adhered to the gold surface. Then, a 24×40 mm2 glass coverslip with 2 drilled holes located at the 2 ends of the straight channel was placed onto the double-sided tape and pressed to form an enclosed microfluidic channel. To enable convenient fluid dispensing, 2 Polydimethylsiloxane (PDMS) pieces each with a punched through hole were bonded to the top surface of the glass coverslip with the through holes aligned. Finally, epoxy glue was applied to all the edges both of the top glass coverslip and the 2 PDMS pieces and cured for 1 hour at room temperature to secure and seal the sensor chip.
The capture antibodies for IL-6, NT-proBNP and PSA were preprocessed by buffer exchanging into MOPS buffer (5 mM MOPS, pH 7.4) with 5 spin cycles using Amicon centrifugal filters. 100 μL of an aqueous solution containing 5 mM EDC and 10 mM NHS was injected into the microfluidic channel and incubated for 5 min. Later, this procedure was repeated 2 more times to activate the carboxylic acid functional groups on the sensor surface. The channel was flushed with 100 μL MOPS buffer. In a 1-hour total incubation time, 100 μg/mL capture antibody in MOPS buffer was injected 3 times respectively at 0, 5 and 15 min with 20 μL volume used each time. Then, 100 μL aqueous solution containing 1 M ethanolamine with pH of 9.6 was injected to quench the unreacted NHS esters. Lastly, 100 μL of 1× phosphate buffered saline (PBS) was injected to flush the channel. The sensor chips were prepared prior to experiments and used within the same day.
For IL-6 detection in pure buffer, human recombinant IL-6 was spiked into 1× reagent diluent (1% BSA in 1×PBS) to reach final concentrations of 1, 10, 100, 103, 104, 105, 106, and 107 fM. For IL-6 detection in horse serum, 1, 10, 100, 103, and 104 fM of recombinant IL-6 were spiked into the horse serum. For IL-6 or PSA detection in bovine whole blood, the recombinant proteins of IL-6 or PSA were spiked so that the final plasma concentrations for each whole blood samples were 1, 10, 100, 103, and 104 fM. The corresponding samples matrices without spiking were used as blank control to measure their background level. These spiked samples were injected through the sensor chips for 2 hours with a flow rate of 10 μL/min. Following a flushing step with 1× PBS, the chips were installed onto PSM. 3 mL of 10 nM detection antibody in 1×PBS was flowed through the microfluidic channel for 10 min driven by gravity pump while PSM was recording images of the sensor surface in real time. The PSM images were then analyzed using an in-house dynamic tracking algorithm to count the number of detection antibodies binding to the sensor surface.
To generate the NT-proBNP calibration curve in human plasma and bovine whole blood, recombinant human NT-proBNP protein was spiked into the pooled human plasma or bovine whole blood to obtain spike-in concentrations of 1, 10, 100, 103, 104 and 105 pM. Baseline level of NT-proBNP in the human plasma pool used for spiking were 0.97 pM, which was measured using conventional ELISA. As such, the corrected concentrations were 1.97, 10.97, 100.97, 103, 104 and 105 pM. These standard samples were injected through the sensor chips for 10 min with a flow rate of 50 μL/min and 5 μL/min for plasma and whole blood sample respectively, and then measured using PSM following the same procedure as in IL-6 detection. Under a protocol approved by the Mayo Clinic Institutional Review Board and Biospecimens Subcommittee (IRB #19-002558/Bio00017399), 28 patient serum and whole blood samples were deidentified and provided by Mayo Clinic Arizona and measured using the LFSM-immunoassay. The patient samples were residual volume from routine clinical testing of NT-proBNP by Roche's Elecsys proBNP II assay. They were transported in icebox to our lab, stored at 4° C. and tested within 6 days.
To measure the baseline NT-proBNP level in the spiking human plasma pool, a 96 well microplate was coated overnight with 100 μL of 2 μg/mL capture antibody of NT-proBNP in 1×PBS. After washed 3 times with 200 μL of 0.05% PBST (1×PBS containing 0.05% v/v Tween 20), the plate wells were blocked with 200 μL 1× reagent diluent for 1 hour. Then, a series of horse serum standard samples with spike-in NT-proBNP concentrations of 25, 50, 100, and 200 pg/mL were prepared. Horse serum without spiking was used as 0 pg/mL blank control. A mixture of 50 μL NT-proBNP-spiked horse serum standard sample or the human plasma and 50 μL biotinylated detection antibody (2 μg/mL) was incubated in the wells for 1 hour. Following another washing step as previously, 100 μL streptavidin-HRP solution was incubated in the wells for 20 min. Washed again with 0.05% PBST, the wells were reacted with 100 μL TMB substrate solution for 20 min. Lastly, 50 μL stop solution was added, followed by reading the absorbance of each well using a microplate reader (EnVision 2104, Perkin Elmer).
For lab used PSM, a 120 mW diode laser (L660P120, Thorlabs) with a central wavelength at 660 nm was used as the light source. The light was first collimated by a 20× objective and the beam size was reduced by a lens group. The sized beam was then focused on the prism surface by a short-focus lens with an incident angle of 71° to reach SPR. The scattered light from the biomolecule and gold surface was collected by a 60× air objective (Olympus, LUCPLFLN60X, NA=0.7) equipped with a 180 mm tube lens to form an image on a CMOS camera (MQ013MG-ON, XIMEA). More details could be found in
For LFSMiA-lite, the basic principle was similar to the lab used setup. However, we changed the light source to a cheaper 100 mW diode laser and 60× air objective. We also simplified the lens group and the structure of the setup to minimize the size and cost for the lite setup.
The raw image sequence was recorded by XIMEA Cam Tool and then was processed by custom written Matlab scripts (further details are provided herein).
Protocol of LFSM-immunoassay. The gold substrate was first dipped in an ethanol solution with 100 μM 8-mercaptooctanoic acid (MOA) and 10 mM 6-mercapto-1-hexanol (MCH) overnight. After rinsed by ethanol and DI water for three times, the gold chip was made into microfluidic sensor chip following the procedure described in the main text. 60 μL EDC and NHS mixed solution (5 mM and 10 mM in DI water) was injected 3 times into the microfluidic channel at 0, 5 and 10 min in a 15-min total incubation time. The sensor was then cleaned by 200 μL MOPS buffer. Capture antibody with a concentration of 100 μg/mL in MOPS buffer was injected three times to improve the efficiency of surface modification. The capture antibody coated sensor was then exposed to test sample, after quenched by 1 M ethanolamine with PH of 9.6. After washing by 500 μL PBS buffer to remove the bubble in the channel, 3 mL detection antibody solution was flowed through the sensor for 10 min, during which the binding was recorded by PSM imaging.
Binding event detection. The binding event was extracted following the procedure shown in
where (x0, y0) is the position of the binding event in the differential image, (σx, σy) are standard deviations of the 2D Gaussian model which contains the morphological information of the binding particle, A is the intensity of the binding particle and c is the offset constant. The pixels would be rejected if the ratio between σx and σy was smaller than 0.7 or larger than 1.43 as the binding particle is not single molecule1. The binding event of single particle appears as a brightening Gaussian blob and then gradually disappears in several consecutive frames (
where I is imaging intensity, M is the accurate intensity of binding event, k is a constant represent the speed of the binding event and t0 is the accurate time the particle hit the surface. The binding event which did not appear in 5 continuous frames would be considered as nonspecific binding and deleted. Based on the relationship between MW and image intensity (
Determination of the threshold for binding time. As the clinical sample contains proteins with various sizes, label-free imaging could not confidently distinguish the dissociation event of detection antibody and that of protein with similar size after the sensor was incubated in complex sample. We analyzed the binding of IL-6 detection antibody to surface captured IL-6 (
As shown in support video, the main difference between nonspecific binding and specific binding is that the nonspecific binding would hit the same place on the sensor surface more times. To estimate the probability of two detection antibody binding to the same area on the surface, we can assume that the surface is composed of 1000 blocks with evenly distributed antigen molecules. So, the probability for a detection antibody binding to a certain block is 0.001. The probability of the event where n detection antibodies in a total of 100 detection antibodies bind to the same block can be calculated as
The probabilities for n=0, 1 and 2 are 0.9048, 0.0906 and 0.0045 respectively. Therefore, the probability for several detection antibodies binding to the same position is low and a threshold of binding frequency can be used to distinguish specific binding and nonspecific binding. We used different thresholds of binding time to process the data of IL-6 detection in pure buffer and whole blood. The standard curves were shown in
Comparison of LFSM-immunoassay at different counting time. We studied the influence of counting time on the detection limit and the precision by comparing the standard curves of NT-proBNP detection under clinical setting for counting time of 5 and 10 mins. The first 5 mins data in
The effect of detection antibody concentration on NT-proBNP detection. We compared NT-proBNP detection results for detection antibody concentrations of 10 nM and 50 nM. The number of binding events in blank experiment are similar for the two concentrations (
NT-proBNP concentration in pooled human plasma. As NT-proBNP is a stable protein and exists in the blood of both patients and healthy people, the endogenous concentration of NT-proBNP in pooled human plasma should be determined to get the accurate spiked concentration. The concentration of NT-proBNP in human plasma pool was measured to be 8.23 pg/mL by conventional ELISA (
Comparison of standard curves of IL-6 detection in whole blood with/without filtering by our real-time counting algorithm. To demonstrate the ability of our algorithm to remove nonspecific binding, standard curve of IL-6 detection in whole blood without applying intensity and binding time filtering to the binding events was shown in
Gaussian process model for binding event. From a statistical perspective, we model the real-time binding event with a stochastic process indexed by time, and the measured binding counts are viewed as observations of the underlying binding process at the designated time points. As the binding process is continuous over time and it contains the dependence between count values at any two time points, a Gaussian process becomes a natural fit for the binding process. Gaussian process modeling is a famous supervised machine learning method due to its flexibility to generate smooth realizations. The associated covariance kernel function controls the dependence among function values, which allows the estimation to borrow information from the neighborhood. In particular, we implemented Gaussian process model under a Bayesian framework to not only obtain the binding count estimates but also provide quantification of uncertainties (posterior standard deviation) in the obtained estimates.
Gaussian process modeling of binding event. We describe the binding process as a continuous real-valued function of time, defined as ƒ: →
, a mapping from the time interval
of interest to the real line
. We assume that the binding count function follows a zero-mean Gaussian process ƒ:
→
as ƒ˜GP(0, c(⋅, ⋅)) with a bivariate covariance kernel function c(⋅, ⋅):
×
→
+, here
+ denotes the positive part of the real line. The covariance kernel function only produces positive correlation by default. The type of covariance kernel function determines the correlation level between the binding counts measured at two different time points, which will be chosen later. As there is no evidence that the binding process follows a certain trend, we set the mean of Gaussian process to be constant zero over time. By the definition of a Gaussian process, at the designated time points {t1, . . . , tn}, the evaluated binding counts [ƒ(t1), . . . , ƒ(tn)] jointly have a n-dimensional multivariate normal distribution as
where the mean vector is a n-dimensional zero vector 0n and the variance-covariance matrix is a n×n symmetric and positive definite matrix with its (i, j)-th element
=c(ti, tj) for 1≤i,j≤n. As the binding process is expected to be relatively smooth, we consider a squared-exponential covariance kernel function of the form
where >0 is the associated length-scale parameter that controls the correlation level between the function evaluations at different locations. The squared-exponential kernel function is commonly used to generate smooth GP realizations which contains strong dependence. Implementing the squared-exponential kernel in Equation 1 yields that ƒn˜N(0n,
), where
is the correlation matrix with its (i, j)-th element
=cSE(x, y;
) for any 1≤i, j≤n.
Bayesian inference. The main goal is to recover the binding counts from the noised observations as well as to quantify the uncertainty in the estimates. We specifically take a Bayesian approach for estimation due to its advantage in uncertainty control. Given the data Y, one may define a likelihood function Pθ(Y) that links the data and the assumed model associated with unknown parameter θ to be estimated. Under a Bayesian framework, one may treat the unknown parameter θ as random quantities that are endowed with some distribution Π(θ), named as the prior distribution. The prior distribution is determined to incorporate the a priori knowledge on the parameter. Bayesian inference is conducted through the posterior distribution which combines the prior information and the likelihood. That being said, the posterior distribution is obtained by applying the Bayes' rule,
The posterior distribution Π(θ|Y) is a well-defined distribution of the parameter θ conditioning on the data Y. As follows, we will specify the likelihood function that links the binding count observations and the Gaussian process model. The prior distributions of the associated unknown parameters shall be provided as follows.
Gaussian process hierarchical model. We denote the collected data points {yi, i=1, . . . , n} of size n are noisy observations of the binding process at given time points {ti, i=1, . . . , n}. We also assume that the measurement error, systematic error, and other unknown errors are random and additive to the true binding count values. Under the above assumptions, we now propose our Bayesian hierarchical model
Equation 4 describes the likelihood function that links the observations {yi, i=1, . . . , n} to the assumed Gaussian process values {ƒ(ti), i=1, . . . , n} evaluated at time {ti, i=1, . . . , n}. We assume that the additive unknown random errors E's are independently and identically distributed (i.i.d.) with a centered normal distribution with some positive variance parameter σ2. The variance σ2 is assumed to be unknown and is assigned with an Inverse-Gamma (IG) prior. As the binding function ƒ is modeled with a Gaussian process associated with a squared-exponential covariance kernel function, Equation 1 implies a multivariate normal prior distribution for [ƒ(t1), . . . , ƒ(tn)] defined in Equation 5, where the correlation matrix is defined in Equation 2, and the associated length-scale parameter
is also assumed to be unknown. We consider a Uniform prior on
. In addition, in Equation 5, the prior covariance matrix contains a positive scale parameter
to control the magnitude of the variances, as the matrix
only controls correlations. The scale
is unknown and is endowed with an Inverse-Gamma prior. More details on prior distributions are discussed in the hyper parameter specification section.
Hyperparameter specification. To simplify the fitting process, we standardize the observed binding counts to ensure that the observations are on the same scale in different cases, and also scale the time points to be all within [0, 1]. Specifically, for the error variance parameter σ2, we specify that σ2˜IG(ασ, ασ) with ασ=0.01. This prior is considered as weakly informative6 in the sense that the prior does not enforce a strong subjective preference on the value of σ2, thus the posterior lets the data to update σ2. The standardized binding counts in different cases range mainly in [−2, 2] with a unit standard deviation. A proper prior on ƒn shall assign the major amount of the prior probability on the values of ƒn which roughly are the same scale as standardized binding counts. It is easy to see that the values of ƒn depend on the scale of t, the prior standard deviation. Therefore, the prior distribution of is determined such that ƒn is also on the same scale as the standardized binding counts. Based on this discussion, we consider
˜IG(
,
) with
=5 so that the prior mean is 1.25 and the prior standard deviation is approximately 0.7, also, there is around 0.9 prior probability that the prior standard deviation of ƒn is less than 1.5. Our empirical results indicate that the performance of the model is not sensitive to the choice of
provided
∈(2, 10). At least, for the length-scale parameter
associated with the Gaussian process, we consider the prior choice
˜Unif(
,
) with
=0.1,
=2. This setting allows for the correlation between two furthest time points in [0, 1] varying in (5*10−5, 0.6), allowing both a weak and strong long-range dependence possibly in the covariance matrix. The Uniform prior distribution is also noninformative so that the posterior distribution lets the data update the parameter
.
Posterior Inference. For simplicity of notation, we rewrite the likelihood function in Equation 4 in a matrix form. Denoted all of observed binding counts by Y=[y1, . . . , yn] at the time points T=[t1, . . . , tn], then the likelihood function Pƒ
The posterior distribution is proportional to the product of the likelihood function and prior density functions, however the evidence (the normalizing constant) is intractable. Thus, it is not feasible to directly use the joint posterior distribution for inference since the posterior distribution does not commit to a standard distribution family. Instead, we implemented the Markov Chain Monte Carlo (MCMC)7 method to draw a set of posterior samples of size S,
We used the posterior sample mean as the estimate of the binding counts, as
The posterior standard deviation in estimating {circumflex over (ƒ)}(ti) is estimated by the standard deviation of the posterior samples
Equation 8 and 9 are used to provide posterior estimates of binding counts with S=1000 posterior samples when analyzing the real data.
Posterior computation. Markov Chain Monte Carlo (MCMC) algorithm generates Markov Chain samples iteratively, of which the distribution converges to the target (posterior) distribution as the number of iterations goes to infinity. In practice, it is justified that the distribution of the MCMC samples approximates the posterior distributions, we consider using the Gibbs sampling technique which is one of the common MCM algorithms used for Bayesian inference8. The Gibbs sampler iteratively samples the unknown parameters separately from their conditional posterior distributions, forming an updating circle: 1) sample from [ƒn|σ2, ,
]; 2) sample from [
|ƒn, σ2,
]; 3) samples from [σ2|ƒn,
,
] and 4) sample from [
|σ2,
, ƒn]. It is verified that the joint distribution of samples drawn from the updating circle also converges to the true posterior distribution. The detailed conditional distributions and corresponding sampling procedures are laid out as follows
In fitting the real binding count data, we implemented 3000 iterations and discard the first 2000 iterations as burn-ins, and stored the last 1000 iterations as our posterior samples. Our empirical results also indicated that the Markov chain mixed well, the details are omitted here.
Some further aspects are also defined in the following clauses:
Although this disclosure contains many specific embodiment details, these should not be construed as limitations on the scope of the subject matter or on the scope of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments. Certain features that are described in this disclosure in the context of separate embodiments can also be implemented, in combination, in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments, separately, or in any suitable sub-combination. Moreover, although previously described features may be described as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can, in some cases, be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination.
Particular embodiments of the subject matter have been described. Other embodiments, alterations, and permutations of the described embodiments are within the scope of the following claims as will be apparent to those skilled in the art. While operations are depicted in the drawings or claims in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed (some operations may be considered optional), to achieve desirable results.
Accordingly, the previously described example embodiments do not define or constrain this disclosure. Other changes, substitutions, and alterations are also possible without departing from the spirit and scope of this disclosure.
This application claims priority to, and the benefit of, U.S. Provisional Patent Application Ser. No. 63/602,087, filed Nov. 22, 2023, the disclosure of which is incorporated herein by reference.
This invention was made with government support under R01GM140193 awarded by the National Institutes of Health. The government has certain rights in the invention.
| Number | Date | Country | |
|---|---|---|---|
| 63602087 | Nov 2023 | US |
