Methods and apparatus for simultaneously detecting large range of protein concentrations

Abstract

To provide methods and apparatus for simultaneously detecting a quantity and / or concentration within a large range of protein.SOLUTION: Some embodiments described herein relate to a method that includes separating an analyte-containing sample via electrophoresis in a capillary. The capillary is loaded with a chemiluminescence agent, such as luminol, that is configured to react with the analyte (e.g., HRP-conjugated proteins) to produce a signal indicative of a concentration and / or quantity of analyte at each location along the length of the capillary. A first image of the capillary containing the analytes and the chemiluminescence agent is captured over a first period of time. A second image of the capillary containing the analytes and the chemiluminescence agent is captured over a second, longer, period of time. A concentration and / or quantity of a first population of analytes at a first location is determined using the first image, and a concentration and / or quantity of a second population of analytes at a second location is determined using the second image.SELECTED DRAWING: None

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Provisional Patent Application No. 62 / 427,624, filed November 29, 2016, the disclosure of which is hereby incorporated by reference in its entirety. [Background technology]

[0002] Several known techniques and devices are suitable for separating proteins by chromatography and electrophoresis. For example, U.S. Patent Nos. 9,304,133 and 9,400,277, both entitled "Methods and Devices for Analyte Detection," the disclosures of both of which are incorporated by reference in their entireties, describe the separation of proteins by capillary electrophoresis.

[0003] In some cases, it may be necessary or desirable to determine the amount and / or concentration of an analyte at one or more locations. There are several known methods for measuring the amount and / or concentration of an analyte using enhanced chemiluminescence (ECL) techniques. For example, the amount of protein trapped on the inner wall of a capillary can be measured using an antibody with horseradish peroxidase (HRP) enzyme that reacts with luminol within the capillary to produce a chemiluminescent signal measurable in photons / second and / or detections / second.

[0004] Traditional ECL techniques involve introducing luminol into a capillary and capturing one or more images of the capillary as HRP-conjugated proteins react with the luminol. Traditional ECL techniques may be suitable in situations where each peak contains a similar amount of protein and / or where the separation results in a single peak. However, traditional ECL techniques have a poor dynamic range. Similarly, traditional ECL techniques are not suitable in situations where the separation produces multiple peaks and at least two peaks contain significantly different amounts of protein. In such situations, peaks with higher concentrations of protein may saturate and / or disable the detector, peaks with higher concentrations may consume all available luminol, and / or peaks with lower concentrations of protein may become undetectable. All of these may reduce the accuracy with which the amount and / or concentration of a protein can be determined. Therefore, there is a need for methods and devices for simultaneously detecting a wide range of protein amounts and / or concentrations. [Brief explanation of the drawings]

[0005] BRIEF DESCRIPTION OF THE DRAWINGS [Figure 1] 1 is a schematic diagram of an instrument operable to measure a wide range of amounts and / or concentrations of analytes in accordance with an embodiment. [Figure 2] 1 is a flowchart of a method for determining the concentration and / or amount of an analyte population according to an embodiment. [Figure 3] 1 is a plot of a simulation of light produced by ECL techniques detected over time. [Figure 4] 1 illustrates a comparison between known techniques for determining the concentration and / or amount of an analyte and a method for determining the concentration and / or amount of an analyte according to the methods described herein. [Figure 5] 1 illustrates a comparison between known techniques for determining the concentration and / or amount of an analyte and a method for determining the concentration and / or amount of an analyte according to the methods described herein. [Figure 6]1 is a plot of simulated measurement error based on luminol consumption and mass transfer coefficient according to an embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0006] Detailed Description A particular challenge in quantifying proteins in multiple techniques using ECL technology is selecting an appropriate exposure time for imaging the capillary. Exposure times that are too short and peaks with low abundance and / or low protein concentration can prevent detection and / or accurate quantification. Exposure times that are too long and peaks with high abundance and / or high protein concentration can saturate and / or disable the detector, wash out nearby peaks, and / or consume all available luminol. One possible compromise solution is to take several relatively short exposures sequentially. The intensity of each peak can then be plotted against time, and the initial intensity (e.g., measured in photons / second) can be extrapolated using a mathematical model of the expected variation of signal versus time. The concentration and / or amount of protein in the peak can be determined based on the initial intensity. However, such techniques can be subject to significant statistical errors at low protein concentrations and systematic errors at high protein concentrations.

[0007] Some embodiments described herein relate to a method comprising electrophoretically separating an analyte-containing sample in a capillary. A chemiluminescent agent, such as luminol, configured to react with an analyte (e.g., an HRP-conjugated protein) is placed in the capillary to generate a signal indicative of the concentration and / or amount of the analyte at each location along the length of the capillary. A first image of the capillary containing the analyte and the chemiluminescent agent is taken for a first time period. A second image of the capillary containing the analyte and the chemiluminescent agent is taken for a second time period, the second time period being longer than the first time period. Similarly, the second image of the capillary has a longer exposure time than the first image of the capillary. The concentration and / or amount of a first population of analytes at the first location is determined using the first image, and the concentration and / or amount of a second population of analytes at the second location is determined using the second image. In some embodiments, a chromogenic detection agent can be used in the method instead of a chemiluminescent agent.

[0008] Some embodiments described herein relate to a method that includes separating a sample containing a first population of analytes and a second population of analytes by capillary electrophoresis. Separating the sample can result in the first population of analytes migrating to a first location along the length of the capillary and the second population of analytes migrating to a second location along the length of the capillary. Images of the capillary are taken with different exposure times. The first image can be selected such that the intensity of a first optical signal indicative of the concentration and / or amount of the first population of analytes exceeds a predetermined threshold. The initial intensity of the first optical signal can be determined by dividing the intensity of the first optical signal detected in the first image by the exposure time of the first image. The initial intensity of the first optical signal can be used to calculate the concentration and / or amount of the first population of analytes. The second image can be selected such that the intensity of the second optical signal exceeds a predetermined threshold (e.g., the same predetermined threshold). The initial intensity of the second optical signal can be determined by dividing the intensity of the second optical signal detected in the second image by the exposure time of the second image. The initial intensity of the second optical signal can be used to calculate the concentration and / or amount of the second population of analytes.

[0009] Some embodiments described herein relate to an apparatus configured to perform electrophoretic separation of multiple populations of analytes (e.g., proteins) disposed in a capillary. A detector is configured to capture images of multiple locations along the length of the capillary. Similarly, the detector may be operable to perform full-row imaging of the capillary. A computational entity (e.g., a processor and / or memory) is configured to select a first image captured by the detector based on the intensity of a first signal at the first location along the length of the capillary exceeding a predetermined threshold. The intensity of the first signal is indicative of the concentration and / or amount of the first population of analytes located at the first location. The concentration and / or amount of the first population of analytes can be calculated, for example, based on the intensity of the first signal. A second image captured by the detector can be selected based on the intensity of a second signal at a second location along the length of the capillary exceeding a predetermined threshold (e.g., the same predetermined threshold). The second image can have an exposure time that is different from the exposure time of the first image. The intensity of the second signal is indicative of the concentration and / or amount of a second population of analytes located at the second location, which concentration and / or amount can be calculated, for example, based on the intensity of the second signal and the second exposure time.

[0010] 1 is a schematic diagram of an instrument for measuring the concentration and / or amount of an analyte (e.g., a protein) according to an embodiment. The instrument includes a capillary 110, an electrode 115, and a detector 120. The capillary 110 can bridge two reservoirs 140. Each reservoir can be, for example, an anolyte reservoir, a catholyte reservoir, and / or a sample reservoir.

[0011] The instrument can be configured to draw analytes containing a sample into capillary 110 or to otherwise receive capillary 110 containing a sample. A potential capable of effecting electrophoretic separation of the sample can be applied to both ends of capillary 110 by electrodes 115. Similarly, populations of analytes can migrate to different locations along capillary 110 as a result of the potential applied by electrodes 115. Populations of analytes with similar properties (e.g., mobility, isoelectric point, etc.) can form peaks or bands in capillary 110.

[0012] As discussed in more detail herein, the instrument is capable of determining the concentration and / or amount of analyte in each peak. In some cases, a first peak 152 at a first location in the capillary 110 may contain a significantly greater amount and / or higher concentration of analyte than a second peak 154 at a second location in the capillary 110. Similarly, the first peak 152 may contain 3, 5, 10, 50, 100, or more times the amount of analyte as the second peak 154.

[0013] Detector 120 (e.g., a camera, a charge-coupled device (CCD), a complementary metal-oxide-semiconductor (CMOS) detector, etc.) is configured to capture an image of capillary 110, the analytes within capillary 110, and / or photons emitted by the ECL reaction within capillary 110. Detector 120 may be a full-column detector. Similarly, detector 120 may be operable to capture the entire length of capillary 110, a substantial portion (e.g., at least 80%) of the length of capillary 110, the entire separation region of capillary 110, and / or capture an image containing at least two different locations separated along the length of the capillary (e.g., locations associated with first peak 152 and second peak 154).

[0014] The processor 162 and the memory 164 are communicatively coupled to the detector 120. The processor 162 and the memory 164 may collectively be referred to as a computational entity. The processor 162 may be, for example, a general-purpose processor, a field-programmable gate array (FPGA), an application-specific integrated circuit (ASIC), a digital signal processor (DSP), and / or the like. The processor 162 may be configured to retrieve data from and / or write data to a memory, such as the memory 164, which may be, for example, a random access memory (RAM), a memory buffer, a hard drive, a database, an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), a read-only memory (ROM), a flash memory, a hard disk, a floppy disk, cloud storage, and / or various others. Processor 162 and memory 164 are configured to select exposure times for detector 120, receive images from detector 120, select images received from detector 120 for analysis, and / or calculate concentrations and / or amounts of analyte populations, as described in further detail herein.

[0015] In some embodiments described herein, a chemiluminescent agent (e.g., luminol) is injected into the capillary prior to imaging the capillary and / or before each image of the capillary is taken. Similarly, the instrument may include a luminol injector 115. The processor 162 may be operable to flow luminol (or any other suitable chemiluminescent agent) from the luminol injector 115 through the capillary. The capillary 110 may contain HRP, which may be coated on the walls of the capillary 110. An analyte (or population of analytes) may be configured to bind to the HRP to form an HRP-conjugated analyte. After injection of the luminol, the luminol diffuses to the walls of the capillary and emits photons detectable by the detector 120 in response to the HRP-conjugated analyte. The photons emitted by the enhanced chemiluminescence (ECL) reaction between the luminol and the HRP are indicative of the population of the analyte.

[0016] Because a typical capillary has an inner diameter (ID) of 100 μm and a typical length of 5 cm, luminol diffuses only a small fraction along the length of the capillary over the time that detector 120 takes a measurement (e.g., exposure), but impacts the capillary walls many times. Thus, the local signal is indicative of the local presence of the HRP-conjugated analyte, but is not dependent on the presence of other signals or other analytes along the length of the capillary that are more than about 1 mm away. Similarly, in the example where peak 152 is located more than about 1 mm from peak 154, the intensity of light emitted from peak 152 is independent of the intensity of light emitted from peak 154.

[0017] The initial light intensity (photons / second) of an ECL reaction is proportional to the amount of protein (e.g., analyte) at a particular location (e.g., peak) within the capillary. Therefore, if the initial light intensity can be determined, the concentration and / or amount of protein can be determined. However, several challenges can arise in accurately determining the initial light intensity. Because luminol is consumed by the chemiluminescent reaction, when the amount of available luminol is low, for example, in capillary-based techniques, the initial light intensity is often determined by measuring the light intensity multiple times and analyzing the decay curve to determine the initial light intensity. Multiple exposures are made using a detector, and the curve is fitted to intensity versus time and extrapolated back to the initial point. At low concentrations of protein, relatively long exposures are desirable because the total intensity is lower and the chemiluminescence decays more slowly. However, at high concentrations of protein, shorter exposures are desirable because the total intensity is higher and the chemiluminescence decays more rapidly. However, in many cases, capillaries may contain high concentrations of protein in some regions and low concentrations in other, possibly nearby, regions. In such cases, prolonged exposures can cause the high-concentration regions to "burn out" and consume all or most of the available luminol during exposure, resulting in erroneous low-concentration readings and / or masking of nearby low-concentration signals. Conversely, short exposures are susceptible to significant statistical errors at low protein concentrations. Thus, there is a need for systems and methods that accurately determine protein quantity over a high dynamic range. Similarly, there is a need to accurately characterize cylinders (e.g., capillaries) that contain regions with both high and low protein concentrations. The instrument described above with reference to FIG. 1 may be operable to implement methods for accurately determining quantity and / or concentration over a high dynamic range.

[0018] Figure 2 is a flow chart of a method for determining the amount and / or concentration of an analyte according to an embodiment. The method of Figure 2 can be performed by the apparatus described above with reference to Figure 1. The method includes separating a sample at 210, introducing luminol into the sample at 215, and taking an image of the capillary at 220.

[0019] In some embodiments, luminol can be placed into the capillary multiple times at 215. Each time luminol is placed into the capillary, at least one exposure can be taken at 220. The exposure length can be variable. For example, each time luminol is placed into the capillary, the exposure duration can be doubled, e.g., from 1 second to 2 seconds to 4 seconds, etc., up to 256 seconds or any other suitable maximum exposure duration. Any suitable progression of exposure duration is possible. For example, each exposure can have a duration of any integer multiple (or any other multiple) of the previous exposure duration.

[0020] By varying the exposure time, it is possible to generate at least one exposure suitable for any concentration of protein with good signal-to-noise with very little signal decay (i.e., the integrated signal versus exposure duration is still linear). Along the same lines, a high exposure duration may be particularly suitable for characterizing low protein concentrations, while a low exposure duration may be suitable for characterizing high protein concentrations. In some cases, hardware and / or runtime constraints may limit the exposure duration. For example, very low concentrations may be limited by a maximum exposure duration, while very high concentrations may be limited by a minimum exposure duration.

[0021] Thus, at 230, a first image for determining the concentration and / or amount of a first population of analytes can be selected. The first population of analytes can be disposed at a first location along the capillary. In some embodiments, once a signal indicative of the first population of proteins is detected, the detector can continue capturing data (e.g., photon counts) until a predetermined threshold (e.g., 25,000 counts) is exceeded. In such embodiments, the exposure time is determined by the time required to reach the predetermined threshold. In other embodiments, a series of exposure durations (e.g., 1 second, 2 seconds, 4 seconds, 8 seconds, etc.) can be predetermined as discussed above. Regardless of how the exposure duration is determined, a first image for determining the amount of a first population of analytes can be selected by identifying the image having the shortest exposure duration in which the signal at the first location exceeds a predetermined intensity threshold. As discussed above, the initial intensity of the enhanced chemiluminescence reaction is indicative of the amount and / or concentration of the analyte at that location. Thus, at 235, the amount of the first population of analyte can be determined by dividing the intensity (photon number or counts) of the signal detected in the first image by the exposure duration (seconds).

[0022] The selection of an image to determine the concentration and / or amount of the analyte population can be repeated for each position along the peaked capillary. For example, a second population of analytes can be disposed at a second position. The second image can be selected at 240 by identifying an image in which the signal at the second position exceeds a predetermined intensity threshold. The signal detected in the second image can be divided by the exposure duration of the second image, and the amount of the second population of analytes can be determined at 245.

[0023] An image can thus be selected for each peak or band, and the concentration and / or amount of analyte within each peak can similarly be determined. By selecting images in which the signal associated with a particular peak exceeds a predetermined threshold, the trade-off inherent in selecting an appropriate exposure time required for known ECL techniques can be mitigated. For example, a very short exposure time (e.g., 1 second) can be used to determine the amount of the peak with the highest initial intensity (and thus concentration and / or amount). Such a short exposure may be too short to determine the amount of other peaks in the capillary. Similarly, the other peaks may be below the detection threshold and / or have a low signal-to-noise ratio for an image with a short exposure time. As another example, a relatively long exposure time (e.g., 64 seconds) can be used to determine the amount of a peak with a low initial intensity (and thus concentration and / or amount). Such a long exposure may not be suitable for determining the concentration and / or amount of other peaks with higher concentrations and / or greater amounts of analyte. For example, over a 64 second measurement (exposure), a high intensity peak may consume all locally available luminol and / or significant nonlinearity in the high intensity decay may introduce a relatively large measurement error.

[0024] In some cases, the shortest nominal exposure duration can be selected by selecting the shortest exposure for which at least one peak exceeds a predetermined count threshold. The predetermined count threshold can be uniform throughout the capillary and can be related to an initial luminol concentration that is independent of the concentration of any particular subpopulation. At this predetermined count threshold, signals above the predetermined threshold will typically have a suitable signal-to-noise ratio without significant signal decay.

[0025] As discussed above, multiple images of the capillary can be taken, and the images can have different durations. In some cases, a series of exposures can be employed, with each exposure having the same or nearly the same exposure duration. The first series of exposures can have, for example, the shortest nominal exposure duration. For example, each exposure in the first series of exposures can have an exposure duration of 1 second. The second series of exposures can each have an exposure duration of, for example, 2 seconds, etc. In some cases, the exposure duration of each exposure in a series of exposures can differ from the nominal exposure duration. For example, if the second series of exposures has a nominal exposure duration of 2 seconds, exposures can be taken with exposure durations of 1.6 seconds, 1.8 seconds, 2.0 seconds, 2.4 seconds, etc. Similarly, the exposure durations of the exposures in a series of exposures can be weighted around the nominal exposure duration of the series. In this way, a smooth transition can be achieved from one nominal exposure duration to another. As described in more detail herein, light intensity can be determined by dividing the integrated signal (number of photons and / or counts detected) by the actual exposure duration.

[0026] Some embodiments described herein utilize the following mathematical model of luminol diffusion and reaction in a round capillary, which predicts luminol concentration as a function of time (t), radial position (r) within the capillary, and various reaction rate-to-diffusivity ratios (mass transfer Biot number Bi) for capillaries with radii (b). This model indicates that if the integrated signal is measured when approximately 15% of the luminol has been consumed (i.e., 15% of the maximum integrated signal), the error in approximating the initial reaction rate (proportional to the target protein concentration) is within a narrow range (15-25%) for Bi < 0.5. For Bi < 0.1, the error is equal to the % luminol consumed (a reaction-limited process). Because only ratios of target concentrations are meaningful (units are arbitrary), any fixed percentage error cancels out at such ratios.

number

[0027] The above model, discussed in more detail herein, and Figure 6 demonstrate that by selecting an image of each population of analytes whose signal exceeds a predetermined threshold (e.g., each position along the capillary), the decay of that signal over exposure time can be linearly approximated. The initial intensity can then be calculated by dividing the intensity of that image by the exposure duration.

[0028] The actual decay over the exposure time is exponential. Therefore, the higher the predetermined threshold, the less accurate the linear approximation. However, the lower the predetermined threshold, the lower the signal-to-noise ratio. Therefore, selecting an appropriate predetermined threshold balances linearity and noise. Table 1 below presents experimental data used to select an appropriate predetermined threshold. The experimental data reveal that by selecting a signal intensity of approximately 25% of the sensor's saturation level as the predetermined threshold, the ratio of the linear slope to the actual decay is less than 0.89, which is a suitable tradeoff. Other suitable thresholds may be between 30% of the sensor's saturation level and 20% of the sensor's saturation level.

[0029] [Table 1]

[0030] To minimize spatial variations in linearization errors (and discontinuous jumps in the intensity curve), additional interpolation steps can be used. Signals captured in multiple images with distinct exposure times can be used. After selecting the image in which the signal is closest to the predetermined threshold (or the image with the shortest exposure time in which the signal exceeds the predetermined threshold), additional images, such as immediately preceding and / or subsequent images (e.g., images with the next longest and / or next shortest exposure durations), are analyzed and used to interpolate the predicted exposure time that will result in the target threshold. Similarly, a predicted exposure time to reach the predetermined threshold can be calculated. The predicted exposure time may not correspond to the exposure time of the image actually captured. In such embodiments, the initial intensity can be calculated by dividing the predetermined threshold by the predicted exposure time. In some embodiments, the predicted exposure time can be calculated by linearly interpolating between the measurement just below the predetermined threshold and the measurement just above the predetermined threshold. [Example]

[0031] Example 1 FIG. 3 shows signal levels simulated using the techniques described herein. FIG. 3 depicts three intensity levels: "low," "medium," and "high." The medium intensity level has four times the intensity of the low intensity level, and the high intensity level has four times the intensity of the medium intensity level. The predetermined count threshold may be 25,000. This may be determined, for example, based on the sensitivity and / or saturation of the detector, as discussed above. Similarly, a count threshold of 25,000 may be 25% of the saturation level of the sensor. A nominal exposure duration of 16 seconds may be selected for low intensity signals, a nominal exposure duration of 4 seconds may be selected for medium intensity signals, and a nominal exposure duration of 1 second may be selected for high intensity signals. Intensity (photons / second) is determined by dividing the integrated signal by the exposure duration.

[0032] [Table 2]

[0033] Example 2 The techniques described herein can increase the dynamic range of protein concentration analysis compared to known techniques. For example, Figures 4 and 5 illustrate known methods for determining protein concentration, labeled "multi-image." This demonstrates the "burnout" phenomenon that occurs when processing a wide range of protein concentrations. Burnout occurs because high concentrations of protein consume the luminol available for the chemiluminescence reaction during a measurement (exposure) suitable for accurately resolving low protein concentrations. Similarly, the exposure duration required to resolve low protein concentrations is too long to detect the decay of chemiluminescence at high protein concentrations.

[0034] 4 and 5 also illustrate "HDR" (high dynamic range) analysis using the techniques described herein, demonstrating the ability to detect both high (636 μg / mL) and low (63.6 pg / mL) concentrations of protein without the significant systematic underestimation of high signals exemplified by the original multi-image technique.

[0035] As described above, burnout can adversely affect known techniques for determining protein concentration. However, the techniques described herein can work with burnout. For example, because luminol diffuses very slowly through a capillary, when the exposure duration is increased from short to long, regions with high protein concentrations can be accurately quantified using short exposure durations. As the exposure duration increases, regions with high protein concentrations may become depleted of available luminol. As a result, signals near low concentrations with lower intensity would otherwise be masked by the brighter signal associated with high concentrations (e.g., sensor nulling), but may be resolvable and / or more accurately detectable during longer exposure durations taken after the locally available luminol has been consumed at high concentrations. Therefore, when a high-concentration peak is relatively close to a low-concentration peak, it may be desirable to capture multiple images without replenishment of luminol.

[0036] While various embodiments have been described above, it should be understood that they have been presented by way of example only, and not limitation. Although the methods described above show certain events occurring in a particular order, the order of certain events may be changed. Additionally, some of the events may occur simultaneously, possibly in parallel processes, while others may occur sequentially as described above.

[0037] While specific embodiments have been shown and described, it will be understood that various changes in form and detail may be made. While various embodiments have been described as having particular features and / or combinations of components, other embodiments may have any of the features and / or combinations of components of any of the embodiments discussed above. For example, in some embodiments, luminol can be topped off between a series of exposures, e.g., by flowing luminol into the capillary between exposures and / or by continuously flowing luminol into the capillary. In some cases, flow within the capillary can be prevented during exposures, e.g., by balancing hydrostatic pressures at both ends of the capillary, by eliminating the electrophoresis process during imaging, or by other methods.

Claims

1. Separating a sample containing multiple analytes in a capillary by electrophoresis, A detection agent configured to react with the aforementioned plurality of analytes is placed in the capillary, The method involves imaging a plurality of images of the capillary containing the plurality of analytes and the detection agent, wherein each of the plurality of images is imaged over different exposure times, and the detection agent is added after each of the plurality of images is imaged. Selecting a first image from among the plurality of images that is closest to the threshold and exceeds the threshold, and has a first exposure time having a first signal count at a first position along the capillary, Selecting from among the plurality of images a second image having a second exposure time having a second signal count at the first position along the capillary, wherein the second exposure time is closest to the first exposure time among the plurality of images. From among the plurality of images, a third image is selected that has a third exposure time and a first signal count at a second position along the capillary, which is closest to and exceeds the threshold. The process involves selecting a fourth image from among the plurality of images, having a fourth exposure time that has a second signal count at the second position along the capillary, wherein the fourth exposure time is closest to the third exposure time among the plurality of images. Based on the first and second images, the concentration of a first population of analytes is determined from the plurality of analytes at the first position along the capillary. Based on the third and fourth images, the concentration of the second population of analytes from the plurality of analytes at the second position along the capillary is determined, A method that includes this.

2. The method according to claim 1, wherein determining the concentration of the first population of the analyte at the first position along the capillary is based on the average of the first image and the second image.

3. The method according to claim 1, wherein determining the concentration of the first population of the analyte at the first position along the capillary is based on a weighted average of the first signal count of the first image and the second signal count of the second image, based on proximity to the threshold.

4. The method further includes determining a first rate of change of the first signal at the first position by dividing the first signal at the first position by the first exposure time, and determining a second rate of change of the second signal at the first position by dividing the second signal at the first position by the second exposure time. The method according to claim 1, wherein determining the concentration of the first population of the analyte at the first position along the capillary is based on a weighted average of the first rate of change of the first signal and the second rate of change of the second signal, based on the proximity of the first signal count and the second signal count to the threshold.

5. The method according to claim 1, wherein the second exposure time of the second image is shorter than the first exposure time of the first image.

6. The method according to claim 1, wherein the second exposure time of the second image is longer than the first exposure time of the first image.

7. The further includes determining a subset of the plurality of images in which the signal count at the first position along the capillary is less than a second threshold, The method according to claim 1, wherein the first image and the second image are part of the subset of the plurality of images.

8. The method according to claim 7, wherein the second threshold is twice the value of the threshold.

9. The method according to claim 8, wherein determining the concentration of the first population of the analyte at the first position along the capillary is based on a weighted average of the subsets of the plurality of images.

10. The method according to claim 1, wherein each of the plurality of images has an exposure time twice the exposure time of the immediately preceding image among the plurality of images.

11. The method according to claim 1, further comprising balancing the hydrostatic pressure at both ends of the capillary while each of the plurality of images is being captured, thereby preventing dynamic pressure flow of the detection agent.

12. The method according to claim 1, wherein the detection agent is one of a chemiluminescent agent or a color-developing agent.

13. The method according to claim 1, wherein the concentration of the first group of the analyte at the first position along the capillary is at least three times higher than the concentration of the second group of the analyte at the second position along the capillary.

14. The method according to claim 1, wherein the detection agent is luminol.

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