Patent Application
20090145201
The present disclosure generally relates to microfluidic processing of compounds and analysis of reaction products. More specifically, the present disclosure relates to microfluidic devices and methods for reduce the effects of compound adsorption inside microfluidic channels.
Drug discovery requires many different measurements on molecules that have highly diverse chemical structures. Due to the large cost of drug discovery, there are many efforts to miniaturize the instruments and components used in these measurements, including the storage and handling of molecules.
A primary goal of miniaturization is to reduce the volume of reagent or solutions required for the process. Two consequences of miniaturization are that the ratio of surface area to volume increases, and the diffusion distance from the center of the volume to the surface of the volume also decreases.
As an example with a solution containing several solutes, if a first solute (S1) in the solution adsorbs to the surface of the container, then the concentration of S1 free in solution will decline with time. Subsequently, the ratio of S1 in relation to all other components, such as a second solute (S2) will change with time as well.
Many measurements made in drug discovery rely on knowledge of the concentration of a test molecule. Examples include:
This phenomenon is most striking in microfluidic and other miniaturized systems in which the ratio of surface area to volume is many orders of magnitude larger than is found in more conventional approaches, such as for example, dispensing and mixing of solutions in microtiter plates. Thus, adsorption of molecules in microfluidic systems and other miniaturized devices can be a major. obstacle to miniaturization.
The problem of compound adsorption to surfaces potentially affects devices other than microfluidic channels. For example, compounds are typically stored, mixed, and studied in many different components such as pipette tips, microwells (such as in microtiter plates), tubes, vials, and other components. The adsorption of compounds to the surfaces of these components will affect the concentrations of those compounds in solution, especially if the concentration is low (to study potent compounds) and if the volume is small, which will occur in any miniaturization scheme.
One approach known in the art for decreasing the adsorption of solutes to the surfaces is to treat the surface—to alter its chemistry—so as to reduce adsorption. See Doherty et al., 2003 for a review of related applications in capillary electrophoresis. Alterations of surface chemistry have been used extensively to control the adsorption, or “sticking”, of proteins (see e.g. Rossier et al., 2000; Yang and Sundberg, 2001; and Becker and Locascio, 2002). One approach taken for proteins in microfluidic and other miniaturized systems has been to “PEGylate” the surface, that is to attach a layer of polyethylene glycol (PEG) to the surface (see e.g. Yang and Sundberg, 2001). PEGylation covers the surface with a hydrophilic material that ostensibly prevents adsorption of many biological proteins and cells, both prokaryotic and eukaryotic. Similar approaches have used detergents, especially non-ionic detergents, like the block copolymers, variably named “PLURONIC®” (BASF, Florham Park, N.J., U.S.A.) or “SYNPERONIC®” (ICI, New Castle, Del., U.S.A.), composed of blocks of polyethylene oxide-polypropylene oxide-polyethylene oxide (PEO-PPO-PEO) in which the hydrophilic PEO is similar to PEG (see Desai and Hubbell, 1991; Bridgett et al., 1992; Desai and Hubbell, 1992; Tan et al., 1993; Dewez et al, 1996; Dewez et al., 1997; Green et al., 1998; Detrait et al., 1999; Bromberg and Salvati, Jr., 1999; O'connor et al., 2000; Bevan and Prieve, 2000; Webb et al., 2001; Liu et al., 2002; Brandani and Stroeve, 2003; De Cupere et al., 2003; Musoke and Luckham, 2004).
These approaches have not proven completely effective. In fact, all attempts by applicants to PEGylate the surface of a microfluidic channel, to cover the surface with pluronics, or to otherwise make the surface more hydrophilic have actually made the surface even “stickier”, that is, adsorption is increased rather than decreased.
Another difficulty with engineering the surface chemistry is that the surface is typically designed to reduce specific chemical interactions with a single solute or a small number of solutes. However, a primary practice in drug discovery is to use a large and chemically diverse library of compounds. This prevents such tailored engineering.
It is desirable, therefore, in miniaturization to have device architectures and surface chemistries in which adsorption of solutes, especially drug-like organic molecules, is minimized.
According to a first embodiment of the presently disclosed subject matter, a microfluidic analysis channel is provided. In one embodiment, the analysis channel comprises an inlet having a first cross-sectional area for passage of fluid therethrough; and an analysis region in fluid communication with the inlet and having a second cross-sectional area for passage of fluid from the inlet to the analysis region, the second cross-sectional area being greater than the first cross-sectional area, whereby adsorption of a compound in fluid in the analysis region is decreased and a reduction of concentration of the compound at a center axis region in the analysis region is minimized.
According to a second embodiment of the presently disclosed subject matter, a microfluidic device is provided. In some embodiments, the microfluidic device comprises at least one microscale channel for passage of fluid therethrough having a first cross-sectional area; and an analysis channel in fluid communication with the microscale channel and having a second cross-sectional area, the second cross-sectional area being greater than the first cross-sectional area, whereby adsorption of a compound in fluid in the analysis channel is decreased and a reduction of concentration of the compound at a center axis region in the analysis channel is minimized. In some embodiments, the microfluidic device comprises a controlled dispersion element in fluid communication with and located upstream of the analysis channel. In some embodiments, the controlled dispersion element is an expansion channel. In some embodiments, the microfluidic device is comprised of a polymer, quartz, or silicon.
In some embodiments, the analysis channel can further comprise an expansion region beginning at the inlet and having an upstream cross-sectional area approximately equivalent to the inlet first cross-sectional area and a downstream cross-sectional area approximately equivalent to the second cross-sectional area. In some embodiments, the downstream cross-sectional area is at least two times greater than the upstream cross-sectional area and in some embodiments, the downstream cross-sectional area is between about two times and about five hundred times larger than the upstream cross-sectional area.
In some embodiments, the analysis region has an aspect ratio of height to width equal to 1. In some embodiments, the analysis region further comprises a detection area located along at least a portion of a center axis region of the analysis region.
According to a third embodiment of the presently disclosed subject matter, a method for decreasing adsorption of a compound in a fluid and minimizing reduction of concentration of the compound in a microfluidic device is provided. In some embodiments, the method comprises providing a microfluidic device comprising an analysis channel, which comprises: an inlet having a first cross-sectional area for passage of fluid therethrough; and an analysis region in fluid communication with the inlet and having a second cross-sectional area for passage of fluid from the inlet to the analysis region, the second cross-sectional area being greater than the first cross-sectional area; and passing a fluid comprising a compound through the inlet and into the analysis region, whereby adsorption of the compound in the fluid in the analysis region is decreased and a reduction of concentration of the compound at a center axis region in the analysis region is minimized.
In some embodiments, the method further comprises analyzing the compound or a product resulting from interaction of the compound with at least one other compound in the detection area. In some embodiments, analyzing the compound or the product utilizes confocal optics focused at the detection area. Further, in some embodiments, analyzing the compound or the product comprises determining steady-state kinetic constants; Michaelis constants (Km); kinetic isotope effects on enzyme catalyzed reactions; dose-responses of inhibitors or activators on enzyme or receptor activity (IC50 and EC50 value); mechanisms of inhibition of an enzyme catalyzed reaction and associated inhibition constants (slope inhibition constant (Kis) and intercept inhibition constant (Kii)); interaction factors between multiple inhibitors (α); kinetic mechanisms of multi-substrate enzyme reactions; capacity of receptor binding (Bmax); pH effects on enzyme catalysis; pH effects on enzyme binding; binding constants (Kd); binding stoichiometry; or combinations thereof.
In some embodiments, the compound or the product is fluorescently labeled. Further, in some embodiments where the compound is fluorescently labeled, analyzing the compound or the product comprises measuring fluorescence intensity, polarization fluorescence, fluorescence resonance energy transfer (FRET), fluorescence lifetime, or combinations thereof.
According to a fourth embodiment of the presently disclosed subject matter, a method for making concentration dependent measurements in a microfluidic device is provided. In some embodiments, the method comprises flowing a fluid stream comprising at least one compound through at least one microscale channel of a microfluidic device; continuously varying the concentration of the compound within the fluid stream; flowing the fluid stream through an analysis channel in fluid communication with the microscale channel, the analysis channel comprising: an inlet having a first cross-sectional area for passage of the fluid stream therethrough; an analysis region in fluid communication with the inlet and having a second cross-sectional area for passage of the fluid stream from the inlet to the analysis region, the second cross-sectional area being greater than the first cross-sectional area, whereby adsorption of the compound in the fluid stream in the analysis region is decreased and a reduction of concentration of the compound at a center axis region in the analysis region is minimized; and a detection area located within the analysis region; and measuring the fluid stream at the detection area along at least a portion of the continuously varying concentration gradient of the compound.
In some embodiments, flowing the fluid stream comprising at least one compound through at least one microscale channel of the microfluidic device comprises a first compound flowing within a first fluid stream through a first microfluidic channel and a second compound flowing within a second fluid stream through a second microfluidic channel. In some embodiments, the first and second microfluidic channels merge at a merge region, thereby flowing the first fluid stream into contact with the second fluid stream to form a merged fluid stream.
In some embodiments of the method, continuously varying the concentration of the compound within the fluid stream comprises creating a continuous concentration gradient for the first and second compounds through controlled variation of volumetric flow rates of the first and second fluid streams. In some embodiments, the first and second fluid streams are driven by a first and second pump, respectively. Further, in some embodiments, varying volumetric flow rate of the first and second fluid streams comprises controlling speeds of the first pump and the second pump, respectively. Still further, in some embodiments, the first and second pumps can be synchronized to maintain an overall constant volumetric flow rate while varying individual volumetric flow rates of the first and second fluid streams.
In some embodiments, the method comprises a third compound flowing within a third fluid stream through a third microfluidic channel, wherein the third fluid stream merges with the merged fluid stream at a second merge region. In some embodiments, a time in transit from the second merge region to the analysis channel is sufficient to permit diffusional mixing of the compounds. Further, in some embodiments, the volumetric flow rate of the third pump is constant. Still further, in some embodiments, the combined volumetric flow rate of the three pumps is constant.
In some embodiments, the first, second, and third pumps are displacement pumps. Further, in some embodiments, controlling speeds of the first and second pumps comprises reducing sharp transitions within the continuous concentration gradient. Still further, in some embodiments, controlling speeds of the first and second pumps comprises creating a continuous concentration gradient having multiple slopes. Even further, in some embodiments, controlling speeds of the first and second pumps comprises creating a logarithmic continuous concentration gradient.
In some embodiments, measuring the fluid stream comprises determining steady-state kinetic constants; Michaelis constants (Km), kinetic isotope effects on enzyme catalyzed reactions; dose-responses of inhibitors or activators on enzyme or receptor activity (IC50 and EC50 value); mechanisms of inhibition of an enzyme catalyzed reaction and associated inhibition constants (slope inhibition constant (Kis) and intercept inhibition constant (Kii)); interaction factors between multiple inhibitors (α); kinetic mechanisms of multi-substrate enzyme reactions; capacity of receptor binding (Bmax); pH effects on enzyme catalysis; pH effects on enzyme binding; binding constants (Kd); binding stoichiometry; or combinations thereof.
In some embodiments, the compound is fluorescently labeled. Further, in some embodiments where the compound is fluorescently labeled, measuring the fluid stream comprises measuring fluorescence intensity, polarization fluorescence, fluorescence resonance energy transfer (FRET), fluorescence lifetime, or combinations thereof.
Therefore, it is an object to provide devices and methods for reducing effects of molecule adsorption within microfluidic channels.
An object of the presently disclosed subject matter having been stated hereinabove, and which are achieved in whole or in part by the present disclosure, other objects will become evident as the description proceeds when taken in connection with the accompanying drawings as best described hereinbelow.
Microfluidic chips, systems, and related methods are described herein which incorporate improvements for reducing or eliminating effects of molecule adsorption within microfluidic channels. These microfluidic chips, systems, and methods are described with regard to the accompanying drawings. It should be appreciated that the drawings do not constitute limitations on the scope of the disclosed microfluidic chips, systems, and methods.
As used herein, the term “microfluidic chip,” “microfluidic system,” or “microfluidic device” generally refers to a chip, system, or device which can incorporate a plurality of interconnected channels or chambers, through which materials, and particularly fluid borne materials can be transported to effect one or more preparative or analytical manipulations on those materials. A microfluidic chip is typically a device comprising structural or functional features dimensioned on the order of mm-scale or less, and which is capable of manipulating a fluid at a flow rate on the order of μl/min or less. Typically, such channels or chambers include at least one cross-sectional dimension that is in a range of from about 1 μm to about 500 μm. The use of dimensions on this order allows the incorporation of a greater number of channels or chambers in a smaller area, and utilizes smaller volumes of reagents, samples, and fluids for performing the preparative or analytical manipulation of the sample that is desired.
Microfluidic systems are capable of broad application and can generally be used in the performance of biological and biochemical analysis and detection methods. The systems described herein can be employed in research, diagnosis, environmental assessment and the like. In particular, these systems, with their micron scales, nanoliter volumetric fluid control systems, and integratability, can generally be designed to perform a variety of fluidic operations where these traits are desirable or even required. In addition, these systems can be used in performing a large number of specific assays that are routinely performed at a much larger scale and at a much greater cost.
A microfluidic device or chip can exist alone or may be a part of a microfluidic system which, for example and without limitation, can include: pumps for introducing fluids, e.g., samples, reagents, buffers and the like, into the system and/or through the system; detection equipment or systems; data storage systems; and control systems for controlling fluid transport and/or direction within the device, monitoring and controlling environmental conditions to which fluids in the device are subjected, e.g., temperature, current and the like.
As used herein, the term “channel” or “microfluidic channel” can mean a cavity formed in a material by any suitable material removing technique, or can mean a cavity in combination with any suitable fluid-conducting structure mounted in the cavity such as a tube, capillary, or the like.
As used herein, the terms “compound” and “reagent” are used interchangeably and generally mean any flowable composition or chemistry. The result of two compounds or reagents merging or combining together is not limited to any particular response, whether a biological response or biochemical reaction, a dilution, or otherwise.
In referring to the use of a microfluidic chip for handling the containment or movement of fluid, the terms “in”, “on”, “into”, “onto”, “through”, and “across” the chip generally have equivalent meanings.
As used herein, the term “communicate” (e.g., a first component “communicates with” or “is in communication with” a second component) and grammatical variations thereof are used herein to indicate a structural, functional, mechanical, electrical, optical, or fluidic relationship, or any combination thereof, between two or more components or elements. As such, the fact that one component is said to communicate with a second component is not intended to exclude the possibility that additional components may be present between, and/or operatively associated or engaged with, the first and second components.
As used herein, the terms “measuring”, “sensing”, and “detecting” and grammatical variations thereof have interchangeable meanings; for the purpose of the present disclosure, no particular distinction among these terms is intended.
As used herein, the term “fluid” generally means any flowable medium such as liquid, gas, vapor, supercritical fluid, combinations thereof, or the ordinary meaning as understood by those of skill in the art.
As used herein, the term “vapor” generally means any fluid that can move and expand without restriction except for at a physical boundary such as a surface or wall, and thus can include a gas phase, a gas phase in combination with a liquid phase such as a droplet (e.g., steam), supercritical fluid, the like, or the ordinary meaning as understood by those of skill in the art.
Embodiments disclosed herein comprise hardware and/or software components for controlling liquid flows in microfluidic devices and measuring the progress of miniaturized biochemical reactions occurring in such microfluidic devices. As the description proceeds, it will become evident that the various embodiments disclosed herein can be combined according to various configurations to create a technologic system or platform for implementing micro-scale or sub-micro-scale analytical functions. One or more of these embodiments can contribute to or attain one or more advantages over prior art technology, including: (1) 1000-fold reduction in the amount of reagent needed for a given assay or experiment; (2) elimination of the need for disposable assay plates; (3) fast, serial processing of independent reactions; (4) data readout in real-time; (5) improved data quality; (6) more fully integrated software and hardware, permitting more extensive automation of instrument function, 24/7 operation, automatic quality control and repeat of failed experiments or bad gradients, automatic configuration of new experimental conditions, and automatic testing of multiple hypotheses; (7) fewer moving parts and consequently greater robustness and reliability; and (8) simpler human-instrument interface. As the description proceeds, other advantages may be recognized by persons skilled in the art.
Referring now to
Referring to
In one exemplary yet non-limiting embodiment and as shown in
In some embodiments for which a plurality of pumps are provided (e.g., pumps PA-PC in
The ability to produce very low flow-rate, stable displacement flows to generate concentration gradients, believed to be 3-4 orders of magnitude slower than that heretofore attainable, provides a number of advantages. Chips can be fabricated from any material, and surface chemistry does not need to be carefully controlled, as with electro-osmotic pumping. Any fluid can be pumped, including fluids that would be problematic for electro-osmotic flows (full range of pH, full range of ionic strength, high protein concentrations) and for pressure driven flows (variable viscosities, non-Newtonian fluids), greatly simplifying the development of new assays. Variations in channel diameters, either from manufacture variability or from clogging, do not affect flow rates, unlike electro-osmotic or pressure flows. Computer control and implementation of control (sensors and actuators) are simpler than for pressure flows, which require sensors and actuators at both ends of the channel. Displacement-driven flows provide the most-straighfforward means for implementing variable flows to generate concentration gradients.
The ability to pump at ultra-low flow rates (nl/min) provides a number of advantages in the operation of certain embodiments of microfluidic chip MFC and related methods disclosed herein. These low flow rates enable the use of microfluidic channels with very small cross-sections. Higher, more conventional flow rates require the use of longer channels in order to have equivalent residence times (required to allow many biochemical reactions or biological responses to proceed) or channels with larger cross-sectional areas (which can greatly slow mixing by diffusion and increase dispersion of concentration gradients). In addition, reagent use is decreased because, all other parameters being equal, decreasing the flow rate by half halves the reagent use. Smaller channel dimensions (e.g., 5-30 μm) in the directions required for diffusional mixing of reagents permits even large molecules to rapidly mix in the microfluidic channels.
Referring again to
Suitable examples of such a microfluidic chip MFC are disclosed in co-pending, commonly owned U.S. Provisional Applications entitled MICROFLUIDIC SYSTEMS, DEVICES AND METHODS FOR REDUCING DIFFUSION AND COMPLIANCE EFFECTS AT A FLUID MIXING REGION, U.S. Provisional Application No. 60/707,220 (Attorney Docket No. 447/99/3/1); MICROFLUIDIC SYSTEMS, DEVICES AND METHODS FOR REDUCING NOISE GENERATED BY MECHANICAL INSTABILITIES, U.S. Provisional Application No. 60/707,245 (Attorney Docket No. 447/99/3/2); MICROFLUIDIC SYSTEMS, DEVICES AND METHODS FOR REDUCING BACKGROUND AUTOFLUORESCENCE AND THE EFFECTS THEREOF, U.S. Provisional Application No. 60/707,386 (Attorney Docket No. 447/99/3/3); and MICROFLUIDIC CHIP APPARATUSES, SYSTEMS, AND METHODS HAVING FLUIDIC AND FIBER OPTIC INTERCONNECTIONS, U.S. Provisional Application No. 60/707,246 (Attorney Docket No. 447/99/4/2), the contents of which are incorporated herein in their entireties. As described therein, to provide internal channels, microfluidic chip MFC can comprise two body portions such as plates or layers, with one body portion serving as a substrate or base on which features such as channels are formed and the other body portion serving as a cover. The two body portions can be bonded together by any means appropriate for the materials chosen for the body portions. Non-limiting examples of bonding techniques can include thermal bonding, anodic bonding, glass frit bonding, adhesive bonding, and the like. Non-limiting examples of materials used for the body portions can include various structurally stable polymers such as polystyrene and polycarbonate, metal oxides such as sapphire (Al2O3), silicon, and oxides, nitrides or oxynitrides of silicon (e.g., SixNy, glasses such as SiO2, or the like). In advantageous embodiments, the materials can be chemically inert and biocompatible relative to the reagents to be processed, or can include surfaces, films, and coatings or are otherwise treated so as to be rendered inert and/or biocompatible. The body portions can be constructed from the same or different materials. To enable optics-based data encoding of analytes processed by microfluidic chip MFC, one or both body portions can be optically transmissive or include windows at desired locations. The channels can be formed by any suitable micro-fabricating techniques appropriate for the materials used, such as the various etching, masking, photolithography, ablation, and micro-drilling techniques available. The channels can be formed, for example, according to the methods disclosed in a co-pending, commonly owned U.S. Provisional Application entitled MICROFLUIDIC CHIP APPARATUSES, SYSTEMS, AND METHODS HAVING FLUIDIC AND FIBER OPTIC INTERCONNECTIONS, U.S. Provisional Application No. 60/707,246 (Attorney Docket No. 447/99/4/2), the content of which is incorporated herein in its entirety. In some embodiments, the size of the channels can range from approximately 5 to 500 μm in cross-sectional area.
As shown in
First input channel ICA through which a first fluid stream can flow and second input channel ICB through which a second fluid stream can flow terminate or meet at a first T-junction region or merging point MP1. From first merging point MP1, a first mixing channel MC1 traverses through microfluidic chip MFC over a distance sufficient to enable passive mixing within a merged fluid stream of reagents RA and RB introduced by first input channel ICA and second input channel ICB. In some embodiments, the mechanism for passive mixing is thermal or molecular diffusion that depends on time and diffusion distance. Accordingly, microfabricated active mixers, which can be a source of noise, complexity, unreliability and cost are not required but could be provided. In the present exemplary embodiment, third input channel ICC and first mixing channel MC1 terminate or meet at a second T-junction region or merging point MP2, from which a second mixing channel MC2 traverses through microfluidic chip MFC over a distance sufficient for mixing.
Second mixing channel MC2 communicates with a process/reaction channel or aging loop AL. Aging loop AL has a length sufficient for prosecuting a reaction or other interaction between reagents after the reagents have been introduced in two or more of first input channel ICA, second input channel ICB and/or third input channel ICC, merged at first mixing point MP1 and/or second mixing point MP2, and thereafter mixed in first mixing channel MC1 and/or second mixing channel MC2. For a given area of microfluidic chip MFC, the length of aging loop AL can be increased by providing a folded or serpentine configuration as illustrated in
As further illustrated in
After an experiment has been run and data have been acquired, the reaction products flow from aging loop AL to any suitable off-chip waste site or receptacle W. Additional architectural details and features of microfluidic chip MFC are disclosed in co-pending, commonly owned U.S. Provisional Applications entitled MICROFLUIDIC SYSTEMS, DEVICES AND METHODS FOR REDUCING DIFFUSION AND COMPLIANCE EFFECTS AT A FLUID MIXING REGION, U.S. Provisional Application No. 60/707,220 (Attorney Docket No. 447/99/3/1); MICROFLUIDIC SYSTEMS, DEVICES AND METHODS FOR REDUCING NOISE GENERATED BY MECHANICAL INSTABILITIES, U.S. Provisional Application No. 60/707,245 (Attorney Docket No. 447/99/3/2); MICROFLUIDIC SYSTEMS, DEVICES AND METHODS FOR REDUCING BACKGROUND AUTOFLUORESCENCE AND THE EFFECTS THEREOF, U.S. Provisional Application No. 60/707,386 (Attorney Docket No. 447/99/3/3); and MICROFLUIDIC CHIP APPARATUSES, SYSTEMS, AND METHODS HAVING FLUIDIC AND FIBER OPTIC INTERCONNECTIONS, U.S. Provisional Application No. 60/707,246 (Attorney Docket No. 447/99/4/2), the contents of which are incorporated in their entireties.
An example of a method for generating and mixing concentration gradients using sample processing apparatus SPA illustrated in
Once sample processing apparatus SPA has been prepared, concentration gradients can be run through microfluidic chip MFC. Two or more of pumps PA, PB and/or PC can be activated to establish separate flows of different reagents RA, RB and/or RC into microfluidic chip MFC for combination, mixing, reaction, and measurement. A variety of combining strategies can be employed, depending on the number of inputs into microfluidic chip MFC and the corresponding number of pumps PA-PC, on their sequence of mixing determined by the geometry of fluidic channels in microfluidic chip MFC, and on the sequence of control commands sent to the pumps PA-PC. Using a microfluidic chip MFC with three inputs as illustrated in
In accordance with one embodiment of the method, the total or combined volumetric flow rate established by the active pumps PA, PB and/or PC can be maintained at a constant value during the run, in which case the transit time from mixing to measurement is constant and, consequently, the duration of reaction is held constant. In addition, the ratio of the individual flow rates established by respective pumps PA, PB and/or PC can be varied over time by individually controlling their respective servo motors 12, thereby causing the resulting concentration gradient of the mixture in aging loop AL to vary with time (i.e. concentration varies with distance along aging loop AL). The concentration gradient of interest is that of the analyte relative to the other components of the mixture. The analyte can be any molecule of interest, and can be any form of reagent or component. Non-limiting examples include inhibitors, substrates, enzymes, fluorophores or other tags, and the like. As the reaction product passes through detection point DP with a varying concentration gradient, the detection equipment samples the reaction product flowing through according to any predetermined interval (e.g., 100 times per second). The measurements taken of the mixture passing through detection point DP can be temporally correlated with the flow ratio produced by pumps PA, PB and/or PC, and a response can be plotted as a function of time or concentration.
Referring to
Sample processing apparatus SPA can be useful for a wide variety of applications, due at least in part to the simplicity of the technique for concentration gradient mixing described hereinabove and the ubiquity of concentration gradients in assays. Non-limiting examples of applications include enzyme kinetics, clinical diagnostics for neo-natal care (e.g., blood enzyme diagnostics with microliter samples), toxicity studies for drug development (e.g., P450 assays or S9 fraction assays), flow cytometry, cell-based assays, and gradient elution for mass spectrometry.
In some embodiments, sample processing apparatus SPA provides for characterizing biochemical reactions. In some embodiments, characterizing the biochemical reaction comprises determining:
(1) steady-state kinetic constants, such as Michaelis constants for substrates (Km), maximum velocity (Vmax), and the resultant specificity constant (Vmax/Km or kcat/Km);
(2) binding constants for ligands (Kd) and capacity of receptor binding (Bmax);
(3) kinetic mechanisms of a bi- or multi-substrate enzyme reactions;
(4) effect of buffer components, such as salts, metals and any inorganic/organic solvents and solutes on enzyme activity and receptor binding;
(5) kinetic isotope effect on enzyme catalyzed reactions;
(6) effect of pH on enzyme catalysis and binding;
(7) dose-responses of inhibitors or activators on enzyme or receptor activity (IC50 and EC50 values);
(8) mechanisms of inhibition of enzyme catalyzed reactions and associated inhibition constants (slope inhibition constant (Kis) and intercept inhibition constant (Kii));
(9) binding constants (Kd);
(10) binding stoichiometry; or
(11) combinations thereof.
The amount of data points and accuracy of collection for the above noted exemplary applications, when performed using the sample processing apparatus SPA described herein, are superior to that observed in any heretofore known data collection techniques. In particular, the sample processing apparatus SPA provides directly measurable continuous concentration gradients by accurately varying the volumetric flow rates of multiple reagent streams simultaneously by a precisely known amount. Therefore, it is known by direct observation what the expected concentration gradients are, rather than having to calculate the gradients indirectly. Alternatively, an inert “tracer” dye can be added to one of the reagent streams, and the concentration of this tracer dye measured downstream such that the concentration of the tracer dye reports the proportion of the reagent stream, including any noise or dispersion in the system This allows for more accurate data collection than is possible with previously described devices for the applications listed above and others. The pump mechanisms described herein facilitate the use of continuous concentration gradients, in that in one embodiment, the pump mechanisms operate by flow displacement, which provides more precise volume control.
Referring now to
Generally, excitation source ES can be any suitable continuum or line source or combination of sources for providing a continuous or pulsed input of initial electromagnetic energy (hv)0 to detection area or point DP (
Wavelength selector WS2 is utilized as appropriate for the analytical technique being implemented, and can comprise one or more filters or monochromators that isolate a restricted region of the electromagnetic spectrum and provide a filtered signal (hv)2 for subsequent processing. Radiation detector RD can be any appropriate photoelectric transducer that converts the radiant energy of filtered analytical signal (hv)2 into an electrical signal I suitable for use by signal processing and readout device SPR. Non-limiting examples can include photocells, photomultiplier tubes (PMTs), avalanche photodiodes (APDs), photodiode arrays (PDAs), and charge-coupled devices (CCDs). In particular, for fluorescence measurements, a PMT or APD can be operated in a photon counting mode to increase sensitivity or yield improved signal-to-noise ratios. Advantageously, radiation detector RD is enclosed in an insulated and opaque box to guard against thermal fluctuations in the ambient environment and keep out light.
Signal processing and readout device SPR can perform a number of different functions as necessary to condition the electrical signal for display in a human-readable form, such as amplification (i.e., multiplication of the signal by a constant greater than unity), phase shifting, logarithmic amplification, ratioing, attenuation (i.e., multiplication of the signal by a constant smaller than unity), integration, differentiation, addition, subtraction, exponential increase, conversion to AC, rectification to DC, comparison of the transduced signal with one from a standard source, and/or transformation of the electrical signal from a current to a voltage (or the converse of this operation). In addition, signal processing and readout device SPR can perform any suitable readout function for displaying the transduced and processed signal, and thus can include a moving-coil meter, a strip-chart recorder, a digital display unit such as a digital voltmeter or CRT terminal, a printer, or a similarly related device. Finally, signal processing and readout device SPR can control one or more other components of sample processing apparatus SPA as necessary to automate the mixing, sampling/measurement, and/or temperature regulation processes of the methods disclosed herein. For instance, signal processing and readout device SPR can be placed in communication with excitation source ES, pumps PA-PC and thermal control unit TCU via suitable electrical lines to control and synchronize their respective operations, as well as receive feedback from the encoders typically provided with pumps PA-PC.
As appreciated by persons skilled in the art, the signal processing, readout, and system control functions can be implemented in individual devices or integrated into a single device, and can be implemented using hardware (e.g., a PC computer), firmware (e.g., application-specific chips), software, or combinations thereof. The computer can be a general-purpose computer that includes a memory for storing computer program instructions for carrying out processing and control operations. The computer can also include a disk drive, a compact disk drive, or other suitable component for reading instructions contained on a computer-readable medium for carrying out such operations. In addition to output peripherals such as a display and printer, the computer can contain input peripherals such as a mouse, keyboard, barcode scanner, light pen, or other suitable component known to persons skilled in the art for enabling a user to input information into the computer.
Referring now to
Fluorescence measuring apparatus FMA can be configured such that multiple excitation wavelengths are simultaneously introduced into a sample containing multiple signal fluorophores inside microfluidic chip MFC. This can be done by using a multiple bandpass filter as a wavelength selector WS1 or by using multiple lasers as excitation light sources. Similarly multiple bandpass dichroic mirrors and multiple wavelength selectors WS2 can be used to transmit the fluorescence from individual fluorophores to multiple signal processing and readout devices SPR.
In the embodiment illustrated in
As described above, sample processing apparatus SPA is useful for characterizing biochemical reactions on a microscale level, including for example determining potency of inhibitors (IC50). In a typical IC50 experiment, and with reference to
PA: inhibitor+tracer dye (e.g., ALEXA FLUOR 700™, Invitrogen, Carlsbad, Calif., U.S.A.)+enzyme substrate+buffer
PB: enzyme substrate+buffer
PC: coupling enzymes+target enzyme+AMPLEX RED® (10-acetyl-3,7-dihydroxyphenoxazine, from Invitrogen),
AMPLEX RED® is a non-fluorescent precursor that is converted to highly fluorescent resorufin by the action of the target enzyme and the coupling enzymes. The pump flow rates can be varied as follows:
Again, it is the complimentary actions of pumps PA and PB that create the concentration gradient of inhibitor and tracer dye at mixing point 1 MP1 which then travels to mixing point 2 MP2 where it is combined with the target enzyme.
Considering again
When the concentration of inhibitor I and its associated tracer dye TD in solution are high, inhibitor I can adsorb to walls W. As the concentration of inhibitor I decreases in the declining region of the concentration gradient (the molecules TD and I are swept to the right in
Adsorption of hydrophobic molecules can occur when the surface of a microfluidic channel also is hydrophobic. Microfluidic chips can be made from many materials, such as polymers, which can have hydrophobic surfaces. Many plastics have surface energies of 30 to 40 dyne/cm (more hydrophilic surfaces have higher surface energies), whereas water has a surface energy of about 73 dyne/cm. Many molecules measured in drug discovery have a clogP greater than about 4 indicating that they are highly hydrophobic. ClogP is a calculated version of “log P”, which is the log of the partition coefficient (water to octanol) for a molecule. LogP can be considered a measure of a molecule's hydrophobicity, with higher logP indicating greater hydrophobicity. Thus, it can be anticipated that hydrophobic binding of these compounds to a plastic surface can result in many molecules of interest to the drug industry showing behavior similar to
As shown in
The presently disclosed subject matter provides apparatuses and methods for using the same that can decrease the interference of adsorption to concentration dependent measurements, such as in a biochemistry reaction including IC50 determinations, by altering the geometry of a microfluidic channel. Although adsorption may not be eliminated, the change in concentration caused by adsorption can be minimized. In general terms, the effects of adsorption on measurements can be minimized by reducing the channel surface area to fluid volume within the channel ratio (S/V). This both decreases the amount of adsorption to the surface and increases diffusion distances, as described herein below. However, as a high surface area to volume ratio can be an unavoidable consequence of the miniaturization of microfluidics, the geometries provided by some embodiments of the presently disclosed subject matter to minimize adsorption consequences are most unexpected by persons in the field of microfluidics. The presently disclosed subject matter provides for, in some embodiments, using large channel diameters in regions of the microfluidic chip most affected by adsorption of reaction components, that is, in regions where measurements are taken. In some embodiments of the presently disclosed subject matter, and with reference to the microfluidic chip embodiment shown in
As such, the presently disclosed subject matter can provide in some embodiments a microfluidic analysis channel that can comprise an inlet having a first cross-sectional area for passage of fluid therethrough and an analysis region in fluid communication with the inlet and having a second cross-sectional area for passage of fluid from the inlet to the analysis region. The second cross-sectional area can be greater than the first cross-sectional area whereby adsorption of a compound in fluid in the analysis region is decreased and whereby reduction of concentration of the compound at a center axis region in the analysis region is minimized. In some embodiments, the second cross-sectional area can be at least two times larger than the first cross-sectional area. Further, in some embodiments, the second cross-sectional area can be between about two times and five hundred times larger than the first cross-sectional area. The analysis channel can be in fluid communication with one or more upstream microfluidic channels, as for example, the analysis channel can be in direct fluid communication with the upstream mixing channel MC2, which in turn can provide fluid communication with the remaining microfluidic channels on microfluidic chip MFC. In some embodiments, the analysis channel has a surface area to volume ratio value of about 1/10th or less a surface area to volume ratio value of an upstream microscale channel, such as for example mixing channel MC2. The analysis channel in some embodiments can comprise an expansion region beginning at the inlet and having an upstream cross-sectional area approximately equivalent to the inlet first cross-sectional area and a downstream cross-sectional area approximately equivalent to the second cross-sectional area. In some embodiments, the downstream cross-sectional area can be between about two times and about five hundred times larger than the upstream cross-sectional area. Further, in some embodiments, the analysis region can comprise a detection area located along at least a portion of a center axis region of the analysis region.
Turning now to
A consequence of increasing analysis channel AC cross-section by increasing channel diameter is that the ratio (S/V) of channel surface area to fluid volume within the channel is decreased, relative to a narrower channel. For example, to measure a reaction 3 minutes after mixing, with a volumetric flow rate of 30 nL/min, the reaction should be measured at a point in the channel such that microfluidic channel spanning from the mixing point MP to the detection area DA encloses 90 nL. For an analysis channel with square cross-section and a diameter of 25 μm, this point is about 144 mm downstream from mix point MP. This channel has a surface area of 1.44×10−5 square meters, yielding a surface to volume ratio S/V equal to 1.6×105 m−1. For a channel with a diameter of 250 μm, the measurement is made 1.44 mm downstream from mix point MP. This wider channel has a surface area of 1.44×10−6 square meters, yielding a S/V equal to 1.6×104 m−1, which is 1/10th the S/V of the narrower channel. This alone can decrease ten-fold the removal of compound per unit volume by adsorption.
This geometry change can also decrease the radial diffusive flux of compound. Flow in these small channels is at low Reynolds number, so diffusion from a point in the fluid is the only mechanism by which compound concentration changes radially in a microfluidic channel. Increasing the radius of the channel, thereby decreasing the radial diffusive flux, therefore, means that the concentration of compound at center axis region CR of analysis region AR can be less affected by adsorption than in the smaller upstream channels.
Thus, increasing the cross-sectional area of analysis region AR of analysis channel AC can both decrease the amount of adsorption at the wall per unit volume and decrease the rate of flux of compound from center axis region CR to any of channel walls W. Both together mean that the concentration at center axis region CR can decrease more slowly due to adsorption of compound.
Further, in all embodiments, the surface area of all channels exposed to compounds, not just analysis channel AC, can preferably be kept minimal, especially those channels through which concentration gradients flow. This can be accomplished by making channels as short as practicable. Additionally, when the volume contained by a channel must be defined (e.g. where the channel must contain a volume of 50 nL), it is best to use larger diameters/shorter lengths wherever possible to reduce S/V.
Another consequence of increasing analysis channel AC cross-section by increasing channel diameter is that the length of the channel down which the fluid flows can be reduced. In the disclosure above, a channel with a 25 μm diameter was 144 mm long so as to enclose 90 nl whereas the channel with 250 μm diameter was only 1.44 mm long. This shorter channel can be much easier to fabricate and has a much smaller footprint on a microfluidic chip. An analysis channel having an increased cross-sectional area and decreased S/V as disclosed herein is simple to fabricate, acts passively without moving parts, and actually simplifies the design and fabrication of a microfluidic device because such an analysis channel measuring only a few millimeters in length can replace a serpentine analysis channel SAC as shown in
Analysis channel AC can approximate a circular cross-section as closely as possible to produce the smallest ratio of surface area to volume, and also to produce the largest diffusion distance from center axis region CR to a channel wall W. However, microfluidic channels may not be circular in cross-section due to preferred manufacturing techniques. Rather, they can be more likely square in cross-section, with the exact shape depending on the technique used to form the channels. For such channels, a cross-section of analysis channel AC, particularly within analysis region AR, can have an aspect ratio as close to one as possible or, more precisely stated, the distance from center axis region CR to channel wall W can be as nearly constant in all radial directions as possible.
The reduced noise in measurements performed in analysis channel AC having increased cross-sectional area can result from the larger axial dispersion that occurs in analysis channel AC relative to the axial dispersion that occurs in the narrow serpentine analysis channel SAC. This larger axial dispersion causes noise in the concentration gradient to be dissipated, i.e. the noise in the concentration gradient is filtered out. The noise is a local fluctuation in the concentration gradient. Short regions of the gradient can be steeper than desired. Dispersion can cause concentration gradients to dissipate, with steeper gradients dissipating more rapidly. Thus, the locally steep regions of the gradient (i.e. the noise), can dissipate more rapidly than declining gradient DG overall.
The increased axial dispersion in analysis channel AC can in some instances create artifacts and systematic errors in certain measurements. For example, consider the gradient presented in
This region of maximum difference occurs where measurements often must be made for many inhibitors because an IC50 determination can span 2-3 logs of concentration, and for a set of inhibitors with varying IC50, many will have IC50s near the bottom of the gradient, thus data from this area are often used for IC50 determinations. Errors here can therefore be problematic.
One problem with the dispersion observed in the region of maximum difference RMD is that enzyme in this region of the fluid experiences a time-varying concentration of inhibitor. Consider a volume of fluid that travels from mixing point 2 MP2 to detection area DA in microfluidic chip MFC depicted in
This time-varying concentration of inhibitor violates the assumptions of steady-state enzyme kinetics that underlie the mathematical methods used to calculate the inhibitor's IC50 with regard to the enzyme. Thus, any determinations of the IC50, or any other measurement assuming constant concentrations, from such a gradient could suffer from errors arising from dispersion.
This error can be reduced by the inclusion of a “controlled dispersion element” (CDE) in some embodiments between mixing point 1 MP1 and mixing point 2 MP2. A controlled dispersion element can take on a number of geometric forms that facilitate dispersion of the reagents combined at mixing point 1 MP1. Controlled dispersion elements according to some embodiments are described in more detail in co-pending, commonly owned U.S. Provisional Application entitled MICROFLUIDIC SYSTEMS, DEVICES AND METHODS FOR REDUCING NOISE GENERATED BY MECHANICAL INSTABILITIES, U.S. Provisional Application No. 60/707,245 (Attorney Docket No. 447/99/3/2), the content of which is incorporated herein in its entirety. In some embodiments, a CDE can be a serpentine channel or an expansion channel that increases dispersion of the gradient at a point in a microfluidic chip. In the exemplary experiments described herein, insertion of a CDE after mixing point 1 MP1 to thoroughly mix the inhibitor and substrate and before these reagents combine with enzyme at mixing point 2 MP2 in the microfluidic chip MFC can reduce the above described data errors due to dispersion. The result of such a controlled dispersion element is that the majority of the dispersion in the gradient occurs upstream of mixing point 2 MP2 before the gradient of inhibitor is mixed with the enzyme at mixing point 2 MP2, thereby preventing data errors due to improper dispersion of reagents prior to analysis at detection area DA.
Dispersion does not occur linearly with time. Consider
Now turning to
The error arising from the dispersion in analysis channel AC can also be minimized by generating a gradient that has no sharp transitions. Dispersion causes time-varying concentrations at sharp transitions, so elimination of these transitions minimizes time-varying concentrations. Thus, the pumps can generate a gradient that approximates a gradient that has already dispersed. For example, pumps PA and PB (
Other gradients can be used as well. For example, by creating a gradient with two or more slopes by controlling pump flow rates, sharp transitions can be reduced.
Pump-controlled gradients with reduced transitions and controlled dispersion elements can be combined to further reduce errors in measurements arising from dispersion.
The presently disclosed subject matter further provides methods for using the novel apparatuses described herein. In some embodiments, methods for decreasing adsorption of a compound in a fluid and minimizing reduction of concentration of the compound in a microfluidic device are provided.
In other embodiments of the presently disclosed subject matter, methods for making concentration dependent measurements in a microfluidic device are provided. In some embodiments, the method comprises flowing a fluid stream comprising at least one compound through at least one microscale channel of a microfluidic device, continuously varying the concentration of the compound within the fluid stream, flowing the fluid stream through an analysis channel in fluid communication with the microscale channel, and measuring the fluid stream at the detection area along at least a portion of the continuously varying concentration gradient of the molecule.
In some embodiments, the analysis channel is a novel analysis channel as disclosed herein and comprises an inlet having a first cross-sectional area for passage of the fluid stream therethrough, an analysis region in fluid communication with the inlet and having a second cross-sectional area for passage of the fluid stream from the inlet to the analysis region, the second cross-sectional area being greater than the first cross-sectional area, whereby adsorption of the compound in the fluid stream in the analysis region is decreased and a reduction of concentration of the compound at a center axis region in the analysis region is minimized, and a detection area located within the analysis region.
In some embodiments of the methods, analyzing a product in the analysis region comprises utilizing confocal optics so that data can be collected at a center axis region of the analysis channel, which provides data the least impacted by adsorption effects at the channel walls.
In some embodiments of the methods, analyzing a product or making concentration dependent measurements comprises determining steady-state kinetic constants; Michaelis constants (Km), kinetic isotope effects on enzyme catalyzed reactions; dose-responses of inhibitors or activators on enzyme or receptor activity (IC50 and EC50 value); mechanisms of inhibition of an enzyme catalyzed reaction and associated inhibition constants (slope inhibition constant (Kis) and intercept inhibition constant (Kii)); interaction factors between multiple inhibitors (α); kinetic mechanisms of multi-substrate enzyme reactions; capacity of receptor binding (Bmax); pH effects on enzyme catalysis; pH effects on enzyme binding; binding constants (Kd); binding stoichiometry; or combinations thereof. Disclosure related to analyzing reaction products or making concentration dependent measurements is provided in U.S. Provisional Application entitled MICROFLUIDIC METHODS AND APPARATUSES FOR FLUID MIXING AND VALVING, U.S. Provisional Application No. 60/707,329 (Attorney Docket No. 447/99/2/4); U.S. Provisional Application entitled METHODS FOR CHARACTERIZING BIOLOGICAL MOLECULE MODULATORS, U.S. Provisional Application No. 60/707,328 (Attorney Docket No. 447/99/5/1); and U.S. Provisional Application entitled METHODS FOR MEASURING BIOCHEMICAL REACTIONS, U.S. Provisional Application No. 60/707,370 (Attorney Docket No. 447/99/5/2).
In some embodiments of the methods, an analyzed molecule is fluorescently labeled. Further, in some embodiments, measuring or analyzing the fluorescently labeled molecule comprises measuring fluorescence intensity, polarization fluorescence, fluorescence resonance energy transfer (FRET), fluorescence lifetime, or combinations thereof.
In some embodiments of the methods, continuous concentration gradients of reagents are generated by controlled variation of volumetric flow rates of pumps dispensing fluid streams comprising the reagents, as described in detail hereinabove. Further, in some embodiments, continuous concentration gradients of one or more reagents are created having multiple slopes (see, e.g.
In some embodiments, the presently disclosed subject matter further provides apparatuses and methods for making and using the same that can decrease the interference of adsorption to concentration dependent measurements, such as in biochemistry reactions (including IC50 determinations), by reducing adsorption of molecules to microfluidic channel walls. In some embodiments, the presently disclosed subject matter provides microfluidic chips comprising channels and chambers with treated surfaces exhibiting reduced adsorption of molecules to channel walls, such as for example hydrophilic surfaces, and methods of preparing and using the same. In some embodiments, methods of preparing hydrophilic surfaces by treating hydrocarbon-based plastics, such as for example polycarbonate, with fluorine gas mixtures are provided. In some exemplary embodiments, the methods comprise contacting a mixture of fluorine gas and an inert gas with the surface to be treated, then flushing the surface with air. This treatment results in plastic surfaces of increased hydrophilicity (increased surface energy). Hydrophobic solutes, in particular known and potential drug compounds, in solutions in contact with these treated hydrophilic plastic surfaces are less likely to be adsorbed onto the more hydrophilic surfaces. Plastics comprising the treated surfaces are useful in providing many improved drug discovery and biochemical research devices for handling, storing, and testing solutions containing low concentrations of hydrophobic solutes.
Additional details and features of hydrophilic surfaces in microfluidic systems and methods of making and using the same are disclosed in co-pending, commonly owned U.S. Provisional Application entitled PLASTIC SURFACES AND APPARATUSES FOR REDUCED ADSORPTION OF SOLUTES AND METHODS OF PREPARING THE SAME, U.S. Provisional Application No. 60/707,288 (Attorney Docket No. 447/99/9).
Further, in some embodiments of the presently disclosed subject matter, microfluidic systems are provided comprising an analysis channel with an enlarged cross-sectional area and a reduced surface area to volume ratio and, further comprising channels and chambers with hydrophilic surfaces.
The following is a detailed derivation and description of underlying mathematics supporting the use of analysis channels having increased cross-sectional areas and reduced S/V ratios when compared to standard microscale channels to reduce the deleterious effects of molecule adsorption to walls within microscale channels.
Symbols used in this description and relevant dimensions:
There are at least three options for reducing molecule adsorption or effects thereof to the inner walls of microfluidic channels: (1) stop the sticking with an appropriate universally “non-sticky” plastic or coating, (2) correct for sticking algorithmically, and (3) design of the channel geometry/architecture to reduce sticking and/or its effects. The presently disclosed subject matter addresses the problem through novel exploitation of option 3 as described herein in detail.
The phenomenon of adsorption is a convolution of the following phenomena:
Most treatments of this phenomenon examine only axial diffusion and dispersion, using the equations of Taylor-Aris which define an effective diffusion, or “dispersion”, coefficient, D′. This is a single term that encompasses the effects of axial diffusion and radial diffusion (coupled to the velocity gradient) to describe the net flux (“dispersion”) axially. It does not examine how sticking at the wall creates a radial concentration gradient which causes diffusion from the volume of fluid to the wall. Rather, most treatments make the simplifying assumption that a volume of fluid in a channel instantaneously comes to equilibrium radially because radial diffusion distances are small.
This simplifying assumption is not valid in large diameter channels, such as in the novel analysis channels disclosed herein because the diffusion distance from centerline to wall becomes large such that the volume does not go to equilibrium. Thus, the strategy adopted herein is to examine those channels for which the assumption of instantaneous radial mixing is probably not valid (e.g. large diameter channels, such as for example the novel analysis channels disclosed herein) and then to try to determine if such geometries can reduce the effects of sticking. The advantage of this approach is that it will work even if sticking, or adsorption, occurs. The more specific strategy attempted with this description is to see if diffusive flux from the centerline of the flow to the wall can be reduced. Thus, adsorption will not affect data gathered in a large diameter analysis channel if the concentration at the centerline remains unaffected and if data gathering is restricted to an area near or at the centerline.
There are a few interacting phenomena to consider when channel diameters are changed. These are primarily driven by the phenomenon in fluid mechanics known as “continuity of flow”. This states that for the flow of an incompressible fluid in a non-compliant channel (e.g. water in microfluidic channels), the volumetric flow rate, Q, is constant at all points along the channel. Volumetric flow rate, e.g. nl/min, is given by:
Q=VA (Eq. 1)
where V is the average velocity in the channel, and A is the cross-sectional area of the channel. The effect of increasing the diameter is thus to increase A and to decrease V. This leads to a number of interacting complexities:
Δ2=(A2/A1)Δ1, where Δ=dC/dx. (Eq. 0)
The remainder of this description will develop some simple equations that describe these phenomena such that scaling relationships can be achieved. The description does not attempt a coupled solution of all the interacting differential equations.
Expansion channels share some of the underlying physics of large diameter analysis channels described herein, with certain distinct differences. Expansion channels are intended to increase dispersion in a channel. Further, at the end of an expansion channel, the channel diameter is again constricted so that, once again, any radial concentration differences are quickly dissipated by diffusion, as herein described above.
The description hereinbelow directed to the novel large diameter analysis channels disclosed herein relates to examining what happens after an expansion, but without the subsequent constriction that occurs in an expansion channel. Thus, this description is for the purpose of determining if diffusive flux from the centerline of the flow to the wall can be reduced such that adsorption at the wall is of little consequence at the centerline where data are collected. One of skill in the art will appreciate that measurements at the centerline must be performed with confocal optics or equivalent technology, or measurements distant from the centerline, where adsorption will have a larger effect, will corrupt measurements.
Diffusion is at the heart of these phenomena, so one must bear in mind that fluids containing molecules are mixed/flowed with very different diffusion coefficients, D. Some examples values of D are:
The diffusion equation referred to frequently hereinbelow is Fick's law, given by
where F is the diffusive flux (moles/s) in the direction perpendicular to the cross-sectional area, A, across which the diffusion occurs; D is the diffusion coefficient for the molecule in question, and dC/dx is the concentration gradient.
Taylor and Aris derived a description for an “effective” diffusion coefficient, D′, that allows calculation of the average axial flux in a flow where the velocity gradient from centerline to wall generates radial concentration gradients. This is
The flow considered with regard to the description herein is a transition to a channel with a different cross-sectional area. Specifically, we are comparing dispersion on transition from a small channel to a large channel. As equation 1 states, this will cause the average velocity V to change. It is best to restate equation 3 using volumetric flow rate Q by substituting equation 1 into equation 3. This gives:
Again, this describes axial flux averaged over the area of the channel. The term on the left gives the contribution to D′ from the diffusion coefficient D. The term on the right gives the contribution to D′ from the parabolic velocity gradient. Basically, as the radius gets larger, D′ approaches D such that axial flux is dominated by diffusion. This is a somewhat counterintuitive result—the dispersion coefficient gets smaller as the channel gets wider. The typical form of Taylor-Aris dispersion (equation 3) states that dispersion increases with increasing radius. The result arises from the fact that the average velocity V decreases due to continuity as the radius r increases.
The point of equivalency, that is, the point where the left- and right-hand terms contributes equally, occurs where
Typical numbers for exemplary flows include:
Q=30 nl/min=(30×10−12 m3/60 s)=5×10−13 m3/s
As described earlier, a goal is to examine scaling relationships as the channel diameter is increased, including how axial flux, F, scales with radius. To simplify later derivations, equation 4 can be simplified to:
where Φ=48π.
The axial flux of a molecule is given by Fick's Law (equation 2) into which we substitute the dispersion coefficient as given by equation 6:
F=D′AΔ (Eq. 7)
where Δ=dC/dx. Consider the situation in which flow begins in a first channel segment 1 and flows into a second channel segment 2. The axial flux at two points in the two segments can be examined as a ratio:
where the subscripts 1 and 2 indicate channel segments 1 and 2, respectively. By continuity, as explained earlier, the axial concentration gradient becomes steeper when the channel diameter increases. It increases as the ratio of the areas (Equation 0), so equation 8 becomes:
The ratio of A2 to A1 is then set to k, such that:
A2=kA1 (Eq. 10)
and substituting this into equation 9 yields:
Substituting equation 6 into equation 11 yields:
This is not a very clean equation. Basically, it states that k will have different effects on Ψ for different values of D, Q, and the first radius A1.
The relative values of ΦD2A1 and Q2 will determine how the system behaves. If ΦD2A1<<Q2, then the solution approaches:
If ΦD2A1>>Q2, then the solution approaches:
The point of equivalency of flows for a small molecule (MW˜500) is:
This is identical to equation 5, except for the subscript on the radius. This is an unexpected result. Equation 4 gives the radius where D′=2D, with larger radii giving D′→D and smaller radii giving D′>D. Equation 15 gives the segment 1 radius at which Equation 12 applies, with smaller radii giving
Ψ→1/k
Again, for flows with small molecules the point of equivalency is:
r1=76.5 μm
This places one into the regime of ΦD2A1<<Q2 for an initial channel with radius r1 of 12 μm so the relation Ψ=1/k applies. This says that if one increases the area of a channel by a factor of 10 (k=10) on entering an expansion, then the axial flux increases by 10 (F2=10F1). Put in terms of channel radius, if one increases the radius by a factor of 10 then one increases the axial flux by a factor of 100.
Rather than use these approximations, equation 12 can be used to calculate Ψ and plot this against different increasing k. This is done in
Q=30 nl/min=(30×10−12 m3/60s)=5×10−13 m3/s
D=3×10−6 cm2s=3×10−10 m2/s
A1=12 μm
As expected, it behaves approximately like 1/k (e.g. Ψ˜0.1 when k=10). Thus, two results are known:
r1=12 μm then D′=2.25e−5 cm2/s
r2=100 μm then D′=4.76e−6 cm2/s
A goal at hand is to identify if increasing the diameter will cause radial diffusion to decrease more rapidly than axial flux increases. In other words, a determination is desired as to whether radial diffusion decreases with a power larger than 2. If not, a situation could exist in which the axial flux dissipates concentration gradients too quickly.
To summarize the above description:
Δ2=(A2/A1)Δ1, where Δ=dC/dx; (Eq. 0)
A description of the above summary of findings follows, staring with those points addressing axial flux.
Point 4: The analysis hereinabove permits dismissal of this issue this in large channels, such as for example the novel analysis channels disclosed herein. The velocity gradient contributes only minimally to dispersion in large channels.
Point 3a: The increase in the axial concentration gradient on transition into a larger channel dominates the transition, with ratio of axial flux in the small and large channels increasing varying with 1/k.
Point 3c. The axial velocity is given by Vmax=2V. This will impact the timing of measurements (e.g. aging time and dilute time) if measurements are restricted to the centerline by confocal optics in a large channel; however, it will have no impact on measurements in a small channel. For example, aging time are currently estimated by dividing the volume of a segment of channel divided by the volumetric flow rate Q. The implicit assumption of this estimate is that the time of arrival is given by the average velocity V, not by the maximum velocity Vmax, which is a reasonable assumption if radial concentration gradients are dissipated instantaneously in the channels. They are in small channels, but not in large channels.
The remaining summary points address radial diffusion.
Point 1: The diffusion distance increases linearly with r. The time required for a molecule to diffuse a given distance increases with the square of the distance, so flux to the wall should drop rapidly with increasing radius.
Point 2: As described in equation 0, the surface area per unit volume varies with 1/r. Thus, the rate of removal of compound at the wall, per unit volume, decreases with 1/r. For example, consider the situation in which one wants to watch a reaction for 3 minutes at 30 nl/min. The total volume in the channel is, thus, 90 nl. For exemplary 25 μm diameter channels, this yields a channel length of 0.144 m (14.4 cm). If one increases the diameter to 250 μm, then the length of channel enclosing 90 nl drops to 1.44 mm, or by a factor of 100. The surface area of the channel enclosing the 90 nl is 1.44e−5 m2 and 1.44e−6 m2 so the surface area is now 1/10th smaller, and the “sink” of compound in the larger channel is now 1/10th that of the smaller channel.
Point 3b: The radial concentration gradient will become shallower, just as the axial concentration gets steeper, on transition into a larger channel. However, it will not increase linearly with r or with A, as the axial concentration gradient did, because of the geometry of the channel.
It will be understood that various details of the presently disclosed subject matter may be changed without departing from the scope of the disclosed subject matter. Furthermore, the foregoing description is for the purpose of illustration only, and not for the purpose of limitation.
This application claims the benefit of U.S. Patent Application Ser. No. 60/707,366, filed Aug. 11, 2005, the disclosure of which is incorporated herein by reference in its entirety. The disclosures of the following U.S. Provisional Applications, commonly owned and simultaneously filed Aug. 11, 2005, are all incorporated by reference in their entirety: U.S. Provisional Application entitled MICROFLUIDIC APPARATUS AND METHOD FOR SAMPLE PREPARATION AND ANALYSIS, U.S. Provisional Application No. 60/707,373 (Attorney Docket No. 447/99/2/1); U.S. Provisional Application entitled APPARATUS AND METHOD FOR HANDLING FLUIDS AT NANO-SCALE RATES, U.S. Provisional Application No. 60/707,421 (Attorney Docket No. 447/99/2/2); U.S. Provisional Application entitled MICROFLUIDIC BASED APPARATUS AND METHOD FOR THERMAL REGULATION AND NOISE REDUCTION, U.S. Provisional Application No. 60/707,330 (Attorney Docket No. 447/99/2/3); U.S. Provisional Application entitled MICROFLUIDIC METHODS AND APPARATUSES FOR FLUID MIXING AND VALVING, U.S. Provisional Application No. 60/707,329 (Attorney Docket No. 447/99/2/4); U.S. Provisional Application entitled METHODS AND APPARATUSES FOR GENERATING A SEAL BETWEEN A CONDUIT AND A RESERVOIR WELL, U.S. Provisional Application No. 60/707,286 (Attorney Docket No. 447/99/2/5); U.S. Provisional Application entitled MICROFLUIDIC SYSTEMS, DEVICES AND METHODS FOR REDUCING DIFFUSION AND COMPLIANCE EFFECTS AT A FLUID MIXING REGION, U.S. Provisional Application No. 60/707,220 (Attorney Docket No. 447/99/3/1); U.S. Provisional Application entitled MICROFLUIDIC SYSTEMS, DEVICES AND METHODS FOR REDUCING NOISE GENERATED BY MECHANICAL INSTABILITIES, U.S. Provisional Application No. 60/707,245 (Attorney Docket No. 447/99/3/2); U.S. Provisional Application entitled MICROFLUIDIC SYSTEMS, DEVICES AND METHODS FOR REDUCING BACKGROUND AUTOFLUORESCENCE AND THE EFFECTS THEREOF, U.S. Provisional Application No. 60/707,386 (Attorney Docket No. 447/99/3/3); U.S. Provisional Application entitled MICROFLUIDIC CHIP APPARATUSES, SYSTEMS, AND METHODS HAVING FLUIDIC AND FIBER OPTIC INTERCONNECTIONS, U.S. Provisional Application No. 60/707,246 (Attorney Docket No. 447/99/4/2); U.S. Provisional Application entitled METHODS FOR CHARACTERIZING BIOLOGICAL MOLECULE MODULATORS, U.S. Provisional Application No. 60/707,328 (Attorney Docket No. 447/99/5/1); U.S. Provisional Application entitled METHODS FOR MEASURING BIOCHEMICAL REACTIONS, U.S. Provisional Application No. 60/707,370 (Attorney Docket No. 447/99/5/2); U.S. Provisional Application entitled PLASTIC SURFACES AND APPARATUSES FOR REDUCED ADSORPTION OF SOLUTES AND METHODS OF PREPARING THE SAME, U.S. Provisional Application No. 60/707,288 (Attorney Docket No. 447/99/9); U.S. Provisional Application entitled BIOCHEMICAL ASSAY METHODS, U.S. Provisional Application No. 60/707,374 (Attorney Docket No. 447/99/10); U.S. Provisional Application entitled FLOW REACTOR METHOD AND APPARATUS, U.S. Provisional Application No. 60/707,233 (Attorney Docket No. 447/99/11); and U.S. Provisional Application entitled MICROFLUIDIC SYSTEM AND METHODS, U.S. Provisional Application No. 60/707,384 (Attorney Docket No. 447/99/12).
| Filing Document | Filing Date | Country | Kind | 371c Date |
|---|---|---|---|---|
| PCT/US06/31165 | 8/10/2006 | WO | 00 | 5/16/2007 |
| Number | Date | Country | |
|---|---|---|---|
| 60707366 | Aug 2005 | US |
