Quantification of targets using cycle-by-cycle data collected on a digital polymerase chain reaction platform

Abstract

A method for quantification of a target molecule of a biological sample distributed across a plurality of partitions is provided. The method includes receiving fluorescent emission data generated by a polymerase chain reaction (PCR) for each partition of a set of partitions and identifying a partition quantity metric for each partition in the set of partitions to generate a set of partition quality metrics. Each partition quantity metric correlates to a number of target molecules within its respective partition based on the fluorescent emission data. The set of partition quantity metrics is used to determine a state of target molecule amplification within each partition of the set of partitions. The method further includes determining a quantity of the target molecule in the biological sample based on the set of partition quantity metrics.

Description

Docket No. TP388508WO1QUANTIFICATION OF TARGETS USING CYCEE-BY-CYCLE DATA COLLECTED ON A DIGITAL POLYMERASE CHAIN REACTION PLATFORMCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is an International Application claiming the benefit of U.S. Provisional Application No. 63 / 717,505, filed November 7, 2024, which is incorporated herein by reference.BACKGROUND

[0002] Previously, polymerase chain reaction (PCR) systems have been used to monitor progress, measure, and / or analyze biological and biochemical reactions for sequencing and genotyping, for example. Real-time quantitative PCR (qPCR) systems have been widely used. More recently, digital PCR (dPCR) techniques have been used to detect and quantify the concentration of rare alleles, to provide absolute quantitation of nucleic acid samples, and to measure low fold-changes in nucleic acid concentration.

[0003] In qPCR, a sample is thermally cycled and fluorescence signal from a sample is monitored. Fluorescence signals are monitored over several cycles of PCR to amplification and quantification. However, qPCR can only provide relative quantification information.

[0004] In dPCR, a solution containing a biological sample with molecules of a particular target polynucleotide or nucleotide sequence may be subdivided into a large number of partitions, such that each partition generally contains either a small number of molecules of the target nucleotide sequence or none with the target nucleotide sequence. When the partitions are subsequently thermally cycled in a PCR protocol, procedure, or experiment, the partitions containing molecules with the target nucleotide sequence are amplified and produce a positive detection signal, while the partitions containing no molecules of the target nucleotide sequence are not amplified and produce no detection signal. Using Poisson’s probability distribution, the number of target molecules in the original solution may be determined by the number of partitions that have no detectable signal. Although, dPCR is able to determine absolute quantification, dynamic range is limited by the number of partitions used. Further, usually a fluorescent intensity threshold is used to determine which samples are considered positive and negative detectionDocket No. TP388508WO1 based on the fluorescent intensity value measured at a single PCR cycle, which can lead to errors. Thus, errors in a dPCR result may occur if determining a positive and negative detection is not accurate.

[0005] As such, a method for overcoming the limitations of both qPCR and dPCR to provide more accurate quantification results of target molecules is desired.SUMMARY

[0006] In one exemplary embodiment, a method for quantification of a target molecule of a biological sample distributed across a plurality of partitions is provided. The method includes receiving fluorescent emission data generated by a polymerase chain reaction (PCR) for each partition of a set of partitions and identifying a partition quantity metric for each partition in the set of partitions to generate a set of partition quality metrics. Each partition quantity metric correlates to a number of target molecules within its respective partition based on the fluorescent emission data. The set of partition quantity metrics is used to determine a state of target molecule amplification within each partition of the set of partitions. The method further includes determining a quantity of the target molecule in the biological sample based on the set of partition quantity metrics.

[0007] In another exemplary embodiment, a system for quantification of a target molecule of a biological sample distributed across a plurality of partitions is provided. The system includes a detector configured to receive fluorescent emission data generated by a polymerase chain reaction (PCR) for each partition of a set of partitions and compute a partition quantity metric for each partition in the set of partitions to generate a set of partition quality metrics. Each partition quantity metric correlates to a number of target molecules within its respective partition based on the fluorescent emission data. The set of partition quantity metrics is used to determine a state of target molecule amplification within each partition of the set of partitions. The processor is further configured to determine a quantity of the target molecule in the biological sample based on the set of partition quantity metrics.

[0008] In yet another exemplary embodiment, a computer-readable medium is provided encoded with computer-readable instructions, which when executed by a processor of a computer, causesDocket No. TP388508WO1 the computer to carry out a method for quantification of a target molecule of a biological sample distributed across a plurality of partitions. The method includes receiving fluorescent emission data generated by a polymerase chain reaction (PCR) for each partition of a set of partitions and identifying a partition quantity metric for each partition in the set of partitions to generate a set of partition quality metrics. Each partition quantity metric correlates to a number of target molecules within its respective partition based on the fluorescent emission data. The set of partition quantity metrics is used to determine a state of target molecule amplification within each partition of the set of partitions. The method further includes determining a quantity of the target molecule in the biological sample based on the set of partition quantity metrics.

[0009] In yet another exemplary embodiment, a system comprising a processor, and a storage medium configured to store instructions is provided. The instructions, executable by a processor, cause the system to carry out a method for quantification of a target molecule of a biological sample distributed across a plurality of partitions. The method includes receiving fluorescent emission data generated by a polymerase chain reaction (PCR) for each partition of a set of partitions and identifying a partition quantity metric for each partition in the set of partitions to generate a set of partition quality metrics. Each partition quantity metric correlates to a number of target molecules within its respective partition based on the fluorescent emission data. The set of partition quantity metrics is used to determine a state of target molecule amplification within each partition of the set of partitions. The method further includes determining a quantity of the target molecule in the biological sample based on the set of partition quantity metrics.DESCRIPTION OF THE FIGURES

[0010] FIG. 1 illustrates a flowchart showing a method of using cycle-by-cycle PCR data along with dPCR data to generate a quantification result according to various embodiments described herein.

[0011] FIG. 2 illustrates a flowchart of a method of generating a quantification result according to various embodiments described herein.

[0012] FIG. 3 illustrates an exemplary computing system that various embodiments described herein may be implemented.Docket No. TP388508WO1

[0013] FIG. 4 is a block diagram that illustrates a polymerase chain reaction (PCR) instrument, upon which embodiments of the present teachings may be implemented.

[0014] FIG. 5 illustrates an exemplary optics system that can be used to image the sample support device according to embodiments of the present teachings.

[0015] FIG. 6 illustrates a sample support device including a plurality of partitions according to various embodiments described herein.

[0016] FIG. 7 illustrates an exemplary cycle-by-cycle PCR fluorescence data according to various embodiments described herein.

[0017] FIG. 8 illustrates using exemplary derivative analysis to determine an exponential region according to various embodiments described herein.

[0018] FIG. 9 illustrates using threshold analysis to determine a partition quantity metric according to various embodiments described herein.

[0019] FIGS. 10A-10C illustrate an exemplary cycle-by-cycle analysis to determine positive and negative of target determination across a plurality of partitions according to various embodiments described herein.

[0020] FIGS. 11 A and 1 IB illustrate an exemplary analysis to determine PCR efficiency according to various embodiments described herein.

[0021] FIGS. 12A and 12B illustrate an exemplary analysis to determine PCR efficiency according to various embodiments described herein.

[0022] FIG. 13 illustrates estimated assay efficiency compared to theoretical assay efficiency according to various embodiments described herein.

[0023] FIG. 14 illustrates an exemplary method for assay calibration based on assay efficiency according to various embodiments described herein.

[0024] FIG. 15 illustrates an exemplary method for assay calibration based on assay efficiency according to various embodiments described herein.Docket No. TP388508WO1

[0025] FIG. 16 illustrates a graph showing the difference between theoretical PCR efficiency and corrected predicted PCR efficiency for calibration according to various embodiments described herein.

[0026] FIGS. 17A-17B illustrate an exemplary graph showing effects of array size on PCR efficiency according to various embodiments described herein.

[0027] FIG. 18 illustrates an exemplary estimation of a partition quantity metric of a single target molecule according to various embodiments described herein.

[0028] FIG. 19 illustrates exemplary assay calibration results according to various embodiments described herein.

[0029] FIGS. 20A-20C illustrate an exemplary low concentration quantification according to various embodiments described herein.

[0030] FIGS. 21A-21C illustrate an exemplary medium concentration quantification according to various embodiments described herein.

[0031] FIGS. 22A-22C illustrate an exemplary high concentration quantification according to various embodiments described herein.

[0032] FIG. 23 illustrates an exemplary graph comparing an estimate quantity versus expected quantity according to various embodiments described herein.

[0033] FIGS. 24A-24B illustrate an exemplary comparison between the precision of quantification results from dPCR and quantification methods according to various embodiments described herein.

[0034] FIG. 25 illustrates a flowchart of developing an assay for use in generating a quantification result with cycle-by-cycle data according to various embodiments described herein.

[0035] FIG. 26 illustrates a flowchart of a user generating a quantification result with cycle-by- cycle data according to various embodiments described herein.Docket No. TP388508WO1DETAILED DESCRIPTION

[0036] To provide a more thorough understanding of the present invention, the following description sets forth numerous specific details, such as specific configurations, parameters, examples, and the like. It should be recognized, however, that such description is not intended as a limitation on the scope of the present invention but is intended to provide a better description of the exemplary embodiments.

[0037] As mentioned above, there is a desire to provide an increased dynamic range and sensitivity than either qPCR or dPCR can provide alone. Various embodiments described herein combine the strengths of qPCR and dPCR to alleviate some limitations of using qPCR and dPCR alone. Using various embodiments of the present teachings, target molecular species present in extremely low amounts can be more accurately detected and quantified while, using the same technology and methods, quantification can be accurately performed when target molecular species are present at extremely high concentrations as well as at all concentrations between these extremes. In other words, various embodiments described herein can provide more accurate estimates of target molecular quantities from a few molecules to hundreds of billions of molecules.

[0038] Although qPCR is a widespread technology and provides valuable and substantial information regarding target molecule quantity, it only provides a quantity relative to a standard quantity and reliability degrades rapidly below 50 copies per microliter. Thus, a disadvantage for qPCR is that it is difficult to detect and quantify molecules of interest when they are at very low levels. Further, accuracy of qPCR depends on many factors such as accurate fluorescence background determination, generating a standard curve using multiple samples at different known concentrations, and an accurate cycle threshold (Ct or Cq) to determine a relative quantity of the target molecule.

[0039] Further, compared to qPCR, dPCR can provide a more sensitive and accurate assessment of whether molecules of a particular species are present in a sample. Moreover, dPCR can provide an absolute quantification result. However, since dPCR relies on the amplitude of the last PCR cycle, misinterpretations, such as false positives or false negatives, may occur. The dynamic range of dPCR is also limited by the number of partitions since current methods rely onDocket No. TP388508WO1 the presence of negative partitions (no molecules of the species of interest) to generate an estimate of target molecule quantity.

[0040] Thus, it is desirable to improve target molecule quantification by overcoming some of the limitations of both technologies. Various embodiments described herein provide a way to bridge qPCR and dPCR to provide more accurate and reliable target molecule quantifications. For example, a partition quantity metric (PQM) is determined from cycle-by-cycle data (CBC data) which correlates to the number of target molecules in the partition. Using the PQM to determine the partitions positive for the target molecule along with an estimate of the number of target molecules in each partition, a more accurate quantification result of the target molecule is achieved.

[0041] Furthermore, according to various embodiments described herein, a quantification result may be generated with CBC fluorescent emission data of at least one dye channel. In other embodiments, CBC fluorescent emission data from multiple dye channels may be used to generate a quantification result for each dye channel.

[0042] According to various embodiments described herein, quantification methods may be used for multiplex nucleic acid detection assays, where each detectable label is assigned to a different target. The presence and / or amount of each target can then be determined by measuring the signal emitted from a detectable label in separate “detection channels” each corresponding to a specific property of the corresponding emitted signal. For example, in the context of fluorescence-emitting dyes as a detectable label, the separate detection channels can correspond to the emission wavelength spectrum associated with each dye. Disclosed herein are systems and methods quantification of target molecules using multiplexed nucleic acid detection assays that rely on polymerase chain reaction (PCR) processes by enabling determination of separate detectable signals, each associated with a different assay target nucleic acid, within the same detection channel (e.g., within a channel sensitive to emission (e.g, fluorescence emission) within a defined spectral range).

[0043] In various embodiments, one rare target molecule may be quantified according to the methods and systems described in the present teachings. In some embodiments, the rare targetDocket No. TP388508WO1 molecule may be quantified among one or more abundant molecules. Tn some embodiments, multiple rare target molecules may be quantified. In some embodiments, multiple rare targets may be quantified among one more abundant molecules. A rare target molecule may be <0.005% of the sample, for example.

[0044] According to various embodiments described herein, some of the shortcomings of dPCR and qPCR are improved and several advantages are provided. In dPCR, an estimate of target molecule quantity is generated using the number of negative partitions and the Poisson distribution. However, in situations when target molecule concentration is too high for a reliable assessment by dPCR, and too low for a reliable assessment by qPCR, target molecule quantity estimation may be improved according to various embodiments described herein. In other words, embodiments of the present teachings provide greater quantification accuracy in the concentration ranges where the accuracy of either dPCR or qPCR are degraded.

[0045] Another advantage in using various embodiments of the present teachings is that only a single sample, without the need to know its concentration, is needed to calibrate the quantification method. In contrast, qPCR requires a number of samples at different known concentrations to generate a “standard curve” for calibration. Multiple samples with known relative concentration may also be used to calibrate the quantification method in some embodiments of the present teachings.

[0046] Another advantage is that various embodiments described herein provide a large linear dynamic range. A dynamic range of 10 logs may be achieved, potentially eliminating the need to titrate samples during sample preparation and enables conserving on sample and consumable usage. In other examples, a dynamic range of 11 logs may be achieved. Further, high sensitivity, e.g., < 0.01%, < 0.005%, can be achieved.

[0047] Another advantage is that various embodiments enable the use of adaptive algorithms to minimize spectral crosstalk and, hence, enable higher degrees of multiplexing.

[0048] In various embodiments, the devices, instruments, systems, and methods described herein may be used to detect one or more types of target molecules, or biological components of interest. These target molecules may include, but are not limited to. DNA sequences, RNADocket No. TP388508WO1 sequences, genes, oligonucleotides, proteins, or cells (e.g., circulating tumor cells), the latter two of which have been converted to molecules amenable to PCR amplification, and example of which is using the proximity ligation assay. In various embodiments, such target molecules may be used in conjunction with various PCR, qPCR, and / or dPCR methods and systems in applications such as fetal diagnostics, multiplex dPCR, viral detection and quantification standards, genotyping, sequencing validation, mutation detection, detection of genetically modified organisms, rare allele detection, copy number variation, quantification of genetic material, quantification of proteins, assessment of viral particles containing intact copies of genetic material of interest, and proximity ligation assays. Further, an artificial intelligencebased algorithm to characterize CBC data according to various embodiments may be used to improve positive and negative determinations of partitions as well as improving the accuracy of, or creating the metrics used to estimate target molecule quantity in each partition.

[0049] Definitions• Array: a set of partitions associated with a well.• Assay: a solution of chemicals designed to examine a specific pattern of DNA or RNA sequence.• Assay efficiency (aEff): PCR efficiency of a target: at each PCR cycle, the number of target molecules increases by (1+aEff).• CBC data: cycle by cycle data, RFU values for each cycle of PCR from one channel.• Channel: a band of wavelengths of electromagnetic energy.• dPCR realm: sample concentration where there is at least one negative partition (in practice, numerous negative partitions).• dqPCR: digital quantitative PCR, methods that combine dPCR and qPCR techniques, such as methods according to various embodiments described herein.• Exponential region: the part of the PCR fluorescence emission signal where bona fide PCR amplification can first be detected.Docket No. TP388508WO1• k-profile: a listing of k values (i.e., the number of target molecules in a partition) paired with the number of partitions with that number of target molecules.• PQM: partition quantity metric.• PQMcv: the coefficient of variation of PQM values within a well.• PQMofl: PQM for the case that there is one target molecule in the partition.• Partition (P): the subdivision used by the digital PCR (dPCR) system.• Set of partitions: a number of partitions included in the well and used for analysis. The set of partitions is at least one partition. The set of partitions may also include all or some of the partitions in the well.• Multiplexed assay: a collection of assays, each addressing a distinct DNA pattern, all delivered in the same reaction vessel.• PCR: polymerase chain reaction.• qPCR realm: sample concentration where there are no negative partitions (in practice, if there are a small number of negative partitions).• Relative Fluorescence Unit (RFU): the fluorescence energy collected in a channel relative to background fluorescence.• Target molecule: a specific pattern of nucleotides making up a molecule of genetic material.• Well: a collection of partitions into which a single sample is loaded.

[0050] According to various embodiments described herein, a method for combining dPCR and qPCR ideas to provide a more accurate estimate of the number of one or more unique target molecules present in a sample is provided. Embodiments of the present teachings include methods and systems, for example, but not limited to, for:Docket No. TP388508WO11. Examining, for each partition, each fluorescent label used in the PCR reaction (one label for each target molecule), the cycle-by-cycle (CBC) data to determine whether a bona fide PCR amplification occurred. If so, calculate a partition quantity metric (PQM) that is correlated with how many molecules of a given species was present in a partition before PCR was initiated. A Ct value may be the PQM;2. Determining the total number of molecules injected into a dPCR well given the collection of the set of PQM values across the partitions of the dPCR well; and3. Estimating parameter values used by (1) and (2), i.e., PQMofl and aEff.

[0051] The terms “determine,” “calculate,” and “estimate” are used synonymously herein. These terms are not intended to imply an exact level of measurement precision. Thus, where a value is “determined,” “calculated,” or “estimated” using the embodiments described herein, it will be understood that such a value may include some degree of inherent error due to factors such as detection instrument tolerances, rounding, chemical reaction variability, and other inherent measurement imperfections known and understood by those of skill in the art.

[0052] FIG. 1 is a flowchart illustrating an exemplary method 100 for quantification of a target molecule of a biological sample according to various embodiments described herein. In step 102, the method includes receiving fluorescent emission data generated by a polymerase chain reaction (PCR) for each partition of a set of partitions. The set of partitions includes the partitions of the plurality of partitions from which fluorescent data was collected. The fluorescent emission data may be received for each cycle of PCR in some embodiments of the present teachings. Also, in some embodiments, some cycles of PCR may be used for quantification. For example, at least two, five, or fifteen cycles, for example, may be used for quantification.

[0053] In step 104, a partition quantity metric (PQM) for each partition in the set of partitions is identified to generate a set of partition quality metrics. Each PQM correlates to a number of target molecules within its respective partition based on the fluorescent emission data. In this example, a PQM is used for a quantity analysis. It should be appreciated that other values correlating to the number of target molecules within its respective partition may also be usedDocket No. TP388508WO1 according to various embodiments. A weight measurement of each partition, for example, may indicate a quantity of target molecule within each respective partition and used in the quantification analysis described in this document.

[0054] The set of partition quantity metrics is used to determine a state of target molecule amplification within each partition of the set of partitions. A state of target molecule amplification may be the partition includes a positive or negative of target molecule amplification. In other words, a state of target molecule amplification may be there is a positive indication that the target molecule was present and was amplified. On the other hand, a state of target molecule amplification may be that there is a negative indication that the target molecule was not amplified within the partition. The set of PQMs may also be further used to confirm the state of target molecule amplification determined to further improve accuracy.

[0055] The PQM is an estimation derived from the cycle-by-cycle fluorescence data and correlates with the number of target molecules in a partition. Further, a PQM estimation for the case that there is one target molecule in the partition may be used in determining a target molecule quantity in a well. This is referred to as PQMofl in this document. PQMof 1 is an estimate based on the vast majority of partitions that, presumably, only have one target molecule. In practice, PQM values of a single target molecule in a partition can have much higher values than that assigned to PQMofl . These partitions should be assigned to the value of PQMofl to fit the mathematical underpinnings of the quantification estimates because, theoretically, no partition with only one target molecule should have a PQM greater than PQMofl.

[0056] CBC data analysis to estimate PQM: using multi-resolution techniques (multiple sizes of smoothing window) allows for increased accuracy in determining PQM. Low resolutions allow for avoiding spurious peaks in derivatives of the PCR fluorescence emission signal such that the peak(s) that stand out are more likely associated with bona fide PCR amplification. Following this analysis with high resolutions allow for better localization of the region where bona fide PCR amplification can be first detected.

[0057] CBC data analysis to estimate PQM: local efficiency metrics (cycle-by-cycle multiplicative increases in signal level) allows for increased accuracy in determining PQM. This is achieved by requiring that efficiency lie within a reasonable range. This requirement canDocket No. TP388508WO1 eliminate some cases for which signal characteristics, as measured by other metrics, appear to be associated with bona fide PCR amplification.

[0058] The ratio of the mean and variance of PQM (PQMcv) has a near linear relationship with assay efficiency (aEff) for efficiencies 0.5 to 1. The slope and intercept of this relationship is dependent on the number of negative partitions and the total number of partitions (array size). For a given array size, this dependence, as a function of the number of negative partitions, can be accurately modeled by multi-layered polynomials. Hence, this model estimates the slope and intercept needed to estimate aEff from the PQMcv value. It is best to compute these polynomials for each potential array size.

[0059] In some embodiments, the PQM is a cycle threshold (Ct) value, where the Ct value is the PCR cycle where fluorescent emission data meets a fluorescent detection threshold. Method 100 may also include determining an exponential amplification region of the fluorescent emission data for each partition. Determining the exponential amplification region may be based on calculating the derivatives of the fluorescent emission data. For example, at least a zeroth, first, and second derivative of the fluorescent emission data can be used to determine a baseline for the fluorescent emission data. In other embodiments, a third derivative may also be used.

[0060] In some embodiments, the method may also include determining, based on the partition quantity metric for each partition, if the partition is positive for amplification of the target molecule.

[0061] In step 106, a quantity of the target molecule in the biological sample based on the set of partition quantity metrics for each partition is determined. A k-profile may also be generated and stored. According to various embodiments, a k-profile shows the number of partitions that are estimated to have k target molecules. For example, in the k-profile, the number of partitions containing zero target molecules is estimated, the number of partitions containing one target molecule is estimated, the number of partitions containing two target molecules is estimated, and so on. The k-profile may be taken to be an empirical observation of a Poisson process. In various embodiments, this process is described by the Poisson distribution:Docket No. TP388508WO1

[0062] , where P(k) is the probability of there being k target molecules in a partition, 5 is an index for sizes of partitions where there are N different sizes, and k(s) is the average number of target molecules across the partitions corresponding to the sthpartition size.

[0063] The method may further include determining a concentration of the target in the biological sample based on the quantity of target molecules in each partition. An exemplary method 200 of estimating the target molecule concentration in the biological sample is illustrated in FIG. 2.

[0064] First, in decision 202, an estimated concentration is determined. In some embodiments, a low concentration is determined when no partition of the set of partitions has more than one target molecule. Further, in some embodiments, a medium concentration is determined when at least one partition of the set of partitions has more than one target molecule and there is at least one partition that contains no target molecules. In some embodiments, a high concentration is determined when every partition of the set of partitions includes target molecules.

[0065] Using the estimated low, medium, and high concentration determinations, a quantity or concentration of the target molecule in the biological sample can be calculated. For a low concentration, the quantity of the target molecules is the number of partitions determined to have positive amplification in step 204.

[0066] For a medium concentration, in step 206, X is determined by finding the value of X where the Poisson distribution is maximally consistent with the X-profile. Then, in step 208, using , the concentration of the target molecule is determined by X multiplied by a number of partitions in the set.

[0067] In step 201, for cases when there is a high concentration, the concentration is determined based on a median of the partition quantity metrics across the set of partitions compared to a reference median, where the reference median is based on theoretical calculations using a predetermined theoretical target concentration. According to various embodiments described herein, a predetermined theoretical target concentration is a theoretical concentration used inDocket No. TP388508WO1 numerical simulations to determine a corresponding partition quantity metric value. In some embodiments, the reference median is based on a numerical simulation using: an estimate of a partition quantity metric when a partition includes a single target molecule (PQMofl). an estimate of PCR process efficiency (aEff), and the predetermined theoretical target concentration, wherein the predetermined theoretical target concentration is based on a case where there should be some partitions including no target molecules and some partitions including target molecules according to the Poisson distribution.

[0068] In various embodiments, determining the quantity of a target molecule in a biological sample includes determining an efficiency of the PCR process. PCR process efficiency is based on the following governing PCR process equation:F(cy)=Fo(l+aF )cy

[0069] , where cy is cycle number, o is the number of target molecules before the PCR process begins, and aEff s the efficiency of the PCR process. Determining the efficiency of the PCR process may be based on a quantity of a first biological sample when no partition of the set of partitions has more than one target molecule, a quantity of a second biological sample when every partition of the set of partitions includes target molecules, and a relative concentration between the first and the second biological samples is known. Determining efficiency may be further based on comparing a first partition quantity metric median of the first biological sample and a second partition quantity metric median of the second biological sample. Determining PCR efficiency can further include determining a slope of a regression line fit to the partition quantity metric medians of at least the first and the second biological samples. In some embodiments, PQM medians of more than two biological samples may be used to fit a regression line to find an efficiency.

[0070] Further, in some embodiments, PCR process efficiency can be based on analyzing the set of partitions for a single biological sample, where the concentration of target molecules is at a level such that at least 15% of the set of partitions include no target molecules, at least 20% of the set of partitions include only one target molecule, and at least 15% of the set of partitions include more than one target molecule. Although, one skilled in the art will recognize this is an example and many other concentrations may be used to determine PCR process efficiency.Docket No. TP388508WO1

[0071] PCR process efficiency (aEff) can be also based on a coefficient of variation of the partition quantity metric, where the coefficient of variation of the partition quantity metric (PQMcv) is based on a ratio of a mean and a standard deviation of the partition quantity metric. According to various embodiments described herein, the coefficient of variation of the partition quantity metric is mapped to an estimate of efficiency of the PCR process using a multi-layered polynomial transformation function where independent variables are the number of partitions that have no target molecules and the total number of partitions in the set of partitions. The multi-layered polynomial transformation function is determined by a numerical simulation using the Poisson distribution and the governing PCR process equation given above. The multilayered polynomial transformation function generates an estimate of the slope and intercept that converts the value of the PQMcv to a value for aEff.

[0072] Determining the efficiency of the PCR process may also be based on a plurality of biological samples, and includes using relative concentrations between the plurality of biological samples, and efficiency estimates for the plurality of biological samples, to determine an estimate of efficiency of the PCR process that is most consistent with the relative concentrations.

[0073] Various embodiments of the methods and systems of the present teachings will be further described in examples given below.

[0074] Those skilled in the art will recognize that the operations of the various embodiments may be implemented using hardware, software, firmware, or combinations thereof, as appropriate. For example, some processes can be carried out using processors or other digital circuitry under the control of software, firmware, or hard-wired logic. (The term “logic” herein refers to fixed hardware, programmable logic and / or an appropriate combination thereof, as would be recognized by one skilled in the art to carry out the recited functions.) Software and firmware can be stored on computer-readable media. Some other processes can be implemented using analog circuitry, as is well known to one of ordinary skill in the art. Additionally, memory or other storage, as well as communication components, may be employed in embodiments of the invention.

[0075] FIG. 3 is a block diagram that illustrates a computer system 300 that may be employed to carry out processing functionality, according to various embodiments, upon which embodimentsDocket No. TP388508WO1 of a thermal cycler system (FIG. 4) may utilize. Computing system 300 can include one or more processors, such as a processor 304. Processor 304 can be implemented using a general or special purpose processing engine such as, for example, a microprocessor, controller or other control logic. In this example, processor 304 is connected to a bus 302 or other communication medium.

[0076] Further, it should be appreciated that a computing system 300 of FIG. 3 may be embodied in any of a number of forms, such as a rack-mounted computer, mainframe, supercomputer, server, client, a desktop computer, a laptop computer, a tablet computer, handheld computing device (e.g., PDA, cell phone, smart phone, palmtop, etc.), cluster grid, netbook, embedded systems, or any other type of special or general purpose computing device as may be desirable or appropriate for a given application or environment. Additionally, a computing system 300 can include a conventional network system including a client / server environment and one or more database servers, or integration with LIS / LIMS infrastructure. A number of conventional network systems, including a local area network (LAN) or a wide area network (WAN), and including wireless and / or wired components, are known in the art. Additionally, client / server environments, database servers, and networks are well documented in the art.

[0077] Computing system 300 may include bus 302 or other communication mechanism for communicating information, and processor 304 coupled with bus 302 for processing information.

[0078] Computing system 300 also includes a memory 306, which can be a random-access memory (RAM) or other dynamic memory, coupled to bus 302 for storing instructions to be executed by processor 304. Memory 306 also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor 304. Computing system 300 further includes a read only memory (ROM) 308 or other static storage device coupled to bus 302 for storing static information and instructions for processor 304.

[0079] Computing system 300 may also include a storage device 310, such as a magnetic disk, optical disk, or solid-state drive (SSD) is provided and coupled to bus 302 for storing information and instructions. Storage device 310 may include a media drive and a removable storage interface. A media drive may include a drive or other mechanism to support fixed or removable storage media, such as a hard disk drive, a floppy disk drive, a magnetic tape drive, anDocket No. TP388508WO1 optical disk drive, a CD or DVD drive (R or RW), flash drive, or other removable or fixed media drive. As these examples illustrate, the storage media may include a computer-readable storage medium having stored therein particular computer software, instructions, or data.

[0080] In alternative embodiments, storage device 310 may include other similar instrumentalities for allowing computer programs or other instructions or data to be loaded into computing system 300. Such instrumentalities may include, for example, a removable storage unit and an interface, such as a program cartridge and cartridge interface, a removable memory (for example, a flash memory or other removable memory module) and memory slot, and other removable storage units and interfaces that allow software and data to be transferred from the storage device 310 to computing system 300.

[0081] Computing system 300 can also include a communications interface 318. Communications interface 318 can be used to allow software and data to be transferred between computing system 300 and external devices. Examples of communications interface 318 can include a modem, a network interface (such as an Ethernet or other NIC card), a communications port (such as for example, a USB port, a RS-232C serial port), a PCPARTITION1A slot and card, Bluetooth, etc. Software and data transferred via communications interface 318 are in the form of signals which can be electronic, electromagnetic, optical or other signals capable of being received by communications interface 318. These signals may be transmitted and received by communications interface 318 via a channel such as a wireless medium, wire or cable, fiber optics, or another communications medium. Some examples of a channel include a phone line, a cellular phone link, an RF link, a network interface, a local or wide area network, and other communications channels.

[0082] Computing system 300 may be coupled via bus 302 to a display 312, such as a cathode ray tube (CRT) or liquid crystal display (LCD), for displaying information to a computer user. An input device 314, including alphanumeric and other keys, is coupled to bus 302 for communicating information and command selections to processor 304, for example. An input device may also be a display, such as an LCD display, configured with touchscreen input capabilities. Another type of user input device is cursor control 316, such as a mouse, a trackball or cursor direction keys for communicating direction information and command selections toDocket No. TP388508WO1 processor 304 and for controlling cursor movement on display 312. This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allows the device to specify positions in a plane. A computing system 300 provides data processing and provides a level of confidence for such data. Consistent with certain implementations of embodiments of the present teachings, data processing and confidence values are provided by computing system 300 in response to processor 304 executing one or more sequences of one or more instructions contained in memory 306. Such instructions may be read into memory 306 from another computer- readable medium, such as storage device 310. Execution of the sequences of instructions contained in memory 306 causes processor 304 to perform the process states described herein. Alternatively, hard-wired circuitry may be used in place of or in combination with software instructions to implement embodiments of the present teachings. Thus, implementations of embodiments of the present teachings are not limited to any specific combination of hardware circuitry and software.

[0083] The term "computer-readable medium" and “computer program product” as used herein generally refers to any media that is involved in providing one or more sequences or one or more instructions to processor 304 for execution. Such instructions, generally referred to as “computer program code” (which may be grouped in the form of computer programs or other groupings), when executed, enable the computing system 300 to perform features or functions of embodiments of the present invention. These and other forms of computer-readable media may take many forms, including but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media includes, for example, solid state, optical or magnetic disks, such as storage device 310. Volatile media includes dynamic memory, such as memory 306. Transmission media includes coaxial cables, copper wire, and fiber optics, including the wires that comprise bus 302.

[0084] Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, or any other magnetic medium, a CD-ROM, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, PROM, and EPROM, a FLASH-EPROM, any other memory sample support device or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can read.Docket No. TP388508WO1

[0085] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 304 for execution. For example, the instructions may initially be carried on magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computing system 300 can receive the data on the telephone line and use an infra-red transmitter to convert the data to an infra-red signal. An infra-red detector coupled to bus 302 can receive the data carried in the infra-red signal and place the data on bus 302. Bus 302 carries the data to memory 306, from which processor 304 retrieves and executes the instructions. The instructions received by memory 306 may optionally be stored on storage device 310 either before or after execution by processor 304.

[0086] It will be appreciated that, for clarity purposes, the above description has described embodiments of the invention with reference to different functional units and processors. However, it will be apparent that any suitable distribution of functionality between different functional units, processors or domains may be used without detracting from the invention. For example, functionality illustrated to be performed by separate processors or controllers may be performed by the same processor or controller. Hence, references to specific functional units are only to be seen as references to suitable means for providing the described functionality, rather than indicative of a strict logical or physical structure or organization.

[0087] In various embodiments, the devices, instruments, systems, and methods described herein may be used to detect one or more types of biological components of interest. These biological components of interest may be any suitable biological target including, but are not limited to, DNA sequences (including cell-free DNA), RNA sequences, genes, oligonucleotides, molecules, proteins, biomarkers, cells (e.g., circulating tumor cells), or any other suitable target biomolecule.

[0088] In various embodiments, such biological components may be used in conjunction with various PCR, qPCR, and / or dPCR methods and systems in applications such as fetal diagnostics, multiplex dPCR. viral detection and quantification standards, genotyping, sequencing validation, mutation detection, detection of genetically modified organisms, rare allele detection, and copy number variation. Embodiments of the present disclosure are generally directed to devices,Docket No. TP388508WO1 instruments, systems, and methods for monitoring or measuring a biological reaction for a large number of small volume samples. As used herein, samples may be referred to as sample volumes, or reactions volumes, for example.

[0089] While generally applicable to quantitative polymerase chain reactions (qPCR) where a large number of samples are being processed, it should be recognized that any suitable PCR method may be used in accordance with various embodiments described herein. Suitable PCR methods include, but are not limited to, digital PCR, allele- specific PCR, asymmetric PCR, ligation-mediated PCR, multiplex PCR, nested PCR, qPCR, genome walking, and bridge PCR, for example.

[0090] Various embodiments described herein may utilize PCR instrument 400 with reference to FIG. 4. PCR instrument 400 may include control system 420 to control the functions of the detection system, heated cover, and thermal block assembly. Control system 420 may be accessible to an end user through user interface 422 of PCR instrument 400 in FIG. 4. Also, a computing system 300, as depicted in FIG. 3, may serve as to provide the control the function of PCR instrument 400 in FIG. 4, as well as the user interface function. Additionally, computing system 300 of FIG. 3 may provide data processing, display and report preparation functions. All such instrument control functions may be dedicated locally to the PCR instrument, or computer system 300 of FIG. 3 may provide remote control of part or all of the control, analysis, and reporting functions, as will be discussed in more detail subsequently. Instrument control functions may be provided on the instrument, accessible through a graphical user interface (GUI). Further, in various embodiments, data analysis controls may be provided on the instrument, accessible through a GUI. In various embodiments, data analysis of the results of the system may be performed at a local computer system, connected to the instrument. In other embodiments, data analysis functions may be accessed over a network by a user. Data from performing biological reactions by the system, according to various embodiments, may be stored on a server system to be accessible by users over a network.

[0091] As mentioned above, an instrument that may be utilized according to various embodiments, but is not limited to, is a polymerase chain reaction (PCR) instrument. FIG. 4 is a block diagram that illustrates a PCR instrument 400, upon which embodiments of the presentDocket No. TP388508WO1 teachings may be implemented. PCR instrument 400 may include a heated cover 410 that is placed over a plurality of samples 412 contained in a sample support device (not shown). In various embodiments, a sample support device may be a sample support device, or glass or plastic slide with a plurality of partitions, which partitions have a cover between the partitions and heated cover 410. Some examples of a sample support device may include, but are not limited to, a sample support device according to embodiments of the present teachings, a multiwell plate, such as a standard micro titer 96- well, a 384-well plate, or a microcard, or a substantially planar support, such as a glass or plastic slide. The partitions in various embodiments of a sample support device may include depressions, indentations, ridges, and combinations thereof, patterned in regular or irregular arrays formed on the surface of the substrate.

[0092] Various embodiments of PCR instruments include a sample block 414, elements for heating and cooling 416, a heat exchanger 418, control system 420, and user interface 422. Various embodiments of a thermal block assembly according to the present teachings comprise components 414-418 of PCR instrument 400 of FIG. 4.

[0093] According to other embodiments of the present teachings, the thermal block assembly includes thermal electric devices such that substantial uniform heat transfer is provided throughout the thermal block assembly.

[0094] As mentioned above, detection of the target may include fluorescence detection, detection of positive or negative ions, pH detection, voltage detection, or current detection, for example. As such, a detection system, according to various embodiments described herein may include an optical system, an electrical detection system, an ion detection system, or a pH detection system, for example. According to various embodiments, the detection system may be integrated in the sample support device.

[0095] Referring to FIG. 5, as mentioned above, a system 500 may be used optically view, inspect, detect, or measure one or more targets contained in the partitions. Partitions can included in a sample support device 508, which may be contained in a carrier. Sample support device 508 may be sample support device 600 (FIG. 6) according to various embodiments. System 500 comprises an optical head or system 502. System 500 may further comprise aDocket No. TP388508WO1 controller, computer, or processor 304 configured, for example, to operate various components of optical system 502 or to obtain and / or process data provided by system 500. For example, processor 304 may be used to obtain and / or process optical data provided by one or more photodetectors of optical system 502. In other embodiments, processor 304 may transmit data to one or more computing systems for further processing. Data may be transmitted from processor 304 to the computing systems, via a network, in some embodiments.

[0096] In certain embodiments, system 500 further comprises a thermal control system 506 comprising, for example, a thermal cycler configured to perform a PCR procedure or protocol on at least some of the samples contained in sample support device 508. Systems 502, 506 may combined or coupled together into a single unit, for example, in order to perform a qPCR and / or a dPCR procedure or protocol on at least some of the samples contained in sample support device 508. In such embodiments, computer 504 may be used to control systems 502, 506 and / or to collect or process data provided or obtained by either or both systems 502. 506. In other embodiments, system 502 and system 506 may be independent units.

[0097] In certain embodiments, optical system 502 comprises a light source 510 and an associated excitation optic system 512 configured to illuminate at least some of samples contained in the partitions of sample support device 508. Excitation optical system 512 may include one or more lenses 514 and / or one or more filters 516 for conditioning light directed to the samples. Optical system 502 may further comprise a photodetector 520 and an associated emission optic system 522 configured to receive optical data emitted by at least some of samples contained in the partitions of sample support device 508. For example, when system 500 is configured to perform a qPCR and / or a dPCR procedure, the sample may contain fluorescent dyes that provide a fluorescent signal that varies according to an amount of target nucleotide sequence contained in various of the through-holes of sample support device 508. Emission optical system 522 may include one or more lenses 524 and / or one or more filters 526 for conditioning light directed to the samples.

[0098] According to various embodiments, optical system 502 may have a focal length of 15 mm and a working distance of 60 mm, where the working distance of the distance from theDocket No. TP388508WO1 sample support device to the camera lens. Furthermore, in various embodiments, the overall system F-number is less than or equal to 3.

[0099] In the illustrated embodiment of FIG. 5, excitation / emission optical systems 512, 522 both comprise one or more common optical elements. For example, excitation / emission optical systems 512, 522 both comprise a beamsplitter 530 that reflects excitation light and transmits emission light from the samples to photodetector 520. In certain embodiments, excitation / emission optical systems 512, 522 both comprise a field lens (not shown) disposed between beamsplitter 530 and sample support device 508, which may be used improve optical performance, for example, to provide more even illumination and reading of light to and from the samples contained in sample support device 508. In certain embodiments, for example where even illumination is less critical (e.g., some dPCR applications), the common field lens may be omitted, as shown in the illustrated embodiment of FIG. 5. Omission of the field lens may help to reduce the size and complexity of optical system 502.

[0100] As described below, in accordance with various embodiments described herein, partitions may include, but are not limited to, through-holes, wells, indentations, spots, cavities, sample retainment regions, droplets, and reaction chambers, for example.

[0101] In certain embodiments, a dPCR protocol, assay, process, or experiment included distributing or dividing an initial sample or solution into at least ten thousand partitions, at least a hundred thousand partitions, at least one million partitions, or at least ten million of partitions. Each partition may have a volume of a few nanoliters, about one nanoliter, or that is less than or equal to one nanoliter (e.g., less than or equal to 100 picoliters, less than or equal to 10 picoliters, and / or less than or equal to one picoliter). When the number of target nucleotide sequences contained in the initial sample or solution is very small (e.g., less than 1000 target molecules, less than 100 target, less than 10 target molecules, or only one or two target molecules), it may also be important in certain cases that the entire content, or nearly the entire content, of the initial solution be contained in or received by the sample volumes or partitions being processed.

[0102] Furthermore, as used herein, thermal cycling may include using a thermal cycler, isothermal amplification, thermal convention, infrared mediated thermal cycling, or helicase dependent amplification, for example. In some embodiments, the sample support device may beDocket No. TP388508WO1 integrated with a built-in heating element. Tn various embodiments, the sample support device may be integrated with semiconductors.

[0103] According to various embodiments, detection of a target may be, but is not limited to, fluorescence detection, detection of positive or negative ions, pH detection, voltage detection, or current detection, alone or in combination, for example.

[0104] With reference to FIG. 6, in certain embodiments of the present teachings a sample support device 600 comprises a substrate 602 and a plurality of partitions. Sample support device 600 may also be referred to as an article, device, array, slide, chip, substrate, or platen, for example.

[0105] According to various embodiments of the present disclosure, partitions may be, but are not limited to, wells, droplets, cavities, indentations, spots, reaction chambers, sample retainment regions, or through-holes, for example, located in substrate 602. Partitions may be any structure that allows a sample to be independent of other samples located on the substrate. In other embodiments, a sample support structure may be a tube or channel for allowing a flow of partitions, or droplets. In the example of FIG. 6, substrate 602 comprises a first surface 610 and an opposing second surface 612.

[0106] The partitions 604 are configured to provide sufficient surface tension by capillary action to hold respective liquid samples containing a biological sample to be processed or examined. In FIG. 6, partitions 604 may be through holes.

[0107] Substrate 602 may be a flat plate or comprise any form suitable for a particular application or design. Substrate may comprise, in total or in part, any of the various materials known in the fabrication arts including, but not limited to, a metal, glass, ceramic, silicon material, or the like. Additionally, or alternatively, substrate 602 may comprise a polymer material such as an acrylic, styrene, polyethylene, polycarbonate, and polypropylene material. Substrate 602 and partitions 604 may be formed by one or more of machining, injection molding, hot embossing, laser drilling, photolithography, or the like.

[0108] QUANTIFICATION ANALYSIS OVERVIEWDocket No. TP388508WO1

[0109] Quantification analysis according to various embodiments described herein can be described in three stages.

[0110] The first stage is to visually examine processed cycle-by-cycle (CBC) data. By the user examining the CBC data, some threshold may be manually changed to improve positive and negative determination accuracy. However, default thresholds may result in sufficiently accurate determination of CBC data and manual adjustment is not needed. However, it is useful to examine the processed CBC data in case altering two threshold parameter values will result in more accurate positive and negative determination according to various embodiments described herein.

[0111] The second stage is performing an assay calibration. For a calibration, one or more wells of CBC data is selected to perform a calibration analysis. For each well that can be used as an assay calibrator, a file of parameters is generated. A well can be used as an assay calibrator if the number of negative partitions falls within a range that is appropriate for the total number of partitions associated with the well. The parameter values generated in this stage assume that positive and negative determination of the CBC data is sufficiently accurate.

[0112] The third stage is generating quantification estimates and confidence intervals using a set of parameters generated by the assay calibration step. If a full dilution series of data is available that spans the desired dynamic range for an assay, this step can be used with all of the parameter files to choose the one that generates the most accurate results. If that choice has already been made, this generates the final results for each sample submitted.

[0113] Stage 1: Analyzing Cvcle-bv-CvcIe Fluorescence Data

[0114] The first stage includes analyzing the CBC data for each partition and each channel according to various embodiments described herein. Based on characteristics of the CBC data, it is determined whether a partition may be positive or negative for amplification based on the fluorescence emission data. If it may be a positive, a metric is extracted from the data that is correlated with the number of target molecules in the partition and called the partition quantity metric (PQM). PQM is a large number (beyond the number of PCR cycles executed) for a negative.Docket No. TP388508WO1

[0115] By examining the statistics of the PQM, some potential positives may be, instead, recognized as negatives.

[0116] Scaling

[0117] The channel- specific scale of quantification analysis data may vary across wells because of system properties that have nothing to do with the particular characteristics of an assay or the quantity of target(s) in a sample. The range of the CBC data between the exponential region of the data and the end of it is estimated by attributing the exponential region to that point where the data consistently increases by a threshold factor relative to the previous cycle and this is observed for a number of cycles. The scale for a well is based on the statistical characteristics of the range estimate over all the positive partitions of the well. To be deemed a positive, the range must exceed an absolute threshold.

[0118] CBC Processing

[0119] For each partition, CBC data may be converted into a metric where the metric can be used to infer how many target molecules are in the partition. The key is to detect if there appears to be bona fide amplification and, if so, determine when that amplification shows up in the data. When the amplification shows up earlier in the data, there are more target molecules in the partition. Data may also be mildly or extremely noisy. For the latter, the first step is an attempt to correct for the noise. For example, if there is an unrealistic jump in the CBC data, the jump is removed by lowering the data down to the value before the jump. A key way the method according to various embodiments described herein avoids getting fooled by noise is to examine the data at multiple resolutions. At low resolution, many noise fluctuations can be ignored while higher resolutions allow better localization of the exponential region of PCR amplifications (a region starting at the point where amplification can be first detected and extending over a number of cycles, the length of which is related to the PCR efficiency of an assay). The method uses an interplay between second derivative information and the data itself (zeroth derivative) to derive the metric finally used. The second derivative aids in baselining the data (i.e., removing the linear trend in the data before amplification first becomes detectable). Where the zeroth derivative, after baselining, crosses a threshold a metric is assigned to a target for a given partition as the partition quantity metric, the PQM.Docket No. TP388508WO1

[0120] With a well's worth of PQM values collected, if there are enough positive PQM values, it is possible to eliminate spurious positives if they occur at low PQM values that would be "impossible" (highly improbable) when considering the distribution of the positive PQM values. It is not so clear that this can be done with high PQM values compared to the observed distribution because of the possibility of delayed bona fide amplifications.

[0121] FIG. 7 depicts localizing the start of the exponential region and assigning range according to various embodiments described herein. Graph 700 shows CBC fluorescence emission data. Here, the ratio of signal changes from cycle to cycle consistently positive with most exceeding a threshold (1stderivative multiples):3*64820* 218276,2558|-QQ J 22]

[0123] The exponential range of amplification is determined to be from about cycle 19 to cycle 39.

[0124] Partition Quantity Metric Extraction

[0125] A derivative analysis of the CBC data shown in FIG. 7 to determine a PQM is illustrated in FIG. 8. The low-resolution version is shown.

[0126] From the zeroth derivative 802, it can be observed that amplification signal is rotated clockwise. By examining the first derivative multiples 804, it can be observed that the CBC data consistently and substantially increases from cycle 19 onward. From the second derivative 806. we can observe that the curvature of the CBC data peaks around cycle 22.

[0127] Thus, the derivative analysis suggests exponential amplification becomes observable somewhere between cycle 18 and 22Docket No. TP388508WO1

[0128] FIG. 9 depicts baselining and extraction of PQM for which PQM is chosen to be the standard Ct value used in qPCR. In graph 900, the baseline used is the cycles 1 to 18. The zeroth derivative baselined 902 can be compared to the unbaselined zeroth derivative 802. A Ct threshold 904 is set at 0.005 which results in a standard Ct determined to be between 23 and 24 cycles. Thus, the PQM value for this partition of FIG. 9 is around 23.3 according to various embodiments described herein. The Ct threshold may be determined for each assay by methods well known for performing qPCR, set high enough to avoid noise in the baseline but low enough to be within the exponential region of the PCR fluorescence emission signal. For the present teachings, dqPCR offers an alternative where the Ct threshold can be automatically set to a reasonable value by, for example, setting it to 15% of the median value for the maximum range between the exponential region and the last PCR cycle.

[0129] As used in this document, a well includes all the partitions containing a single sample. FIGS. 10A-10C illustrate a well-level CBC analysis for all the partitions included in the well. Graph 1002 illustrates the CBC data from all partitions determined to have positive amplification for the target molecule. Graph 1006 illustrates the CBC data from all partitions determine to have no amplification for the target molecule (negative partitions for the target). Graph 1004 illustrates the CBC data from partitions that appear to have positive amplification but have been determined to have no amplification because their PQM values, given the PQM values for the vast majority of the partitions determined to have positive amplification, are extremely unlikely based on the Poisson distribution.

[0130] Well-Specific Scaling Outline1. Get rid of rejected partitions based on image analysis2. For each target a. For each partition i. Assign a data range value and baseline level for the data as follows: ii. Examine first derivative in early portion of the CBC data normalized by rough estimate of range (max -min of data)Docket No. TP388508WO11 . Tf significantly positive (could be an up-swoop at the start of the dataO a. Find when derivl flattens out i. If it flattens out at a fairly early but not too early cycle number, assume signal is a very early riser1. The range assigned is simply the difference between max and min of the data2. The baseline level is the min ii. If the signal does not appear to be a very early riser1. Re-estimate range from point where derivl flattens out and re-normalize derivl using data from that point on2. Search for when derivl consistently is above a threshold for a number of cycles a. When found, use the start point of this and the max at later cycles as the range b. Baseline is level at the start point2. If not significantly positive (could be a down-swoop at the start of the data or flat a. Re-estimate range from point where derivl flattens out and re-normalize derivl using data from that point on b. Search for when derivl consistently is above a threshold for a number of cyclesDocket No. TP388508WO1 i. When found, use the start point of this and the max at later cycles as the range ii. Baseline is level at the start point b. Apply a threshold to identify those partitions with a large enough range to be considered a positive c. Use statistics (e.g., median) on baseline levels and ranges of presumed positives to determine scale factors

[0131] Cycle-By-Cycle Data Processing Outline1. Get scale factors from the scaling algorithm2. Eliminate blips3. Bail if data range too small4. Bail if too many zero crossings after skipped cycles (and halfway up the range)5. Pad data on both ends (linear extrapolation) so quirks with smoothing don't corrupt data where it counts6. Get smoothed data using high resolution window7. See if it is a very early riser8. Use the smoothed data to compute 1st and 2nd derivative normalized with scaling9. Use smoothed data to remove possible down-swoop in early cycles10. Use smoothed data and low-resolution window to get low resolution smoothed data and derivatives normalized with scaling11. Bail if smoothness of the data is too poor12. Analyze the low resolution second derivative:Docket No. TP388508WO1 a. Find the peaks (heights and locations) b. Toss those too close to the ends of the data c. Set a flag if there are a "large" number of comparably large 2nd derivative peaks d. Bail if the max 2nd derivative peak is small and there are many comparable peaks e. Toss peaks that are too small f. Toss peaks where amplitude range following them are too small g. Toss those that are not followed by a sufficiently deep valley h. Score the "quality" of the peaks and pick the earliest peak that has a reasonable13. "quality" a. If there is a peak of reasonable quality, use weighted average to estimate the location of the peak i. Compute the efficiency of the assay using the high resolution 2nd derivative; flag the data if the efficiency estimate is far from expected values14. Bail if there was no 2nd derivative peak of reasonable "quality"15. Update smoothness assessment using 2nd derivative peak location (ctProxy, an example of a PQM metric)16. Bail if smoothness following ctProxy is too poor17. Use ctProxy to remove any up-swoop in early cycles18. Use ctProxy to baseline the data (by defining where the baseline stops) a. Use deviation from median to adjust baseline startDocket No. TP388508WO119. Check for reasonable baselined data. If appears rotated clockwise, adjust ctProxy to be earlier20. Re-check range is large enough after baselining the data. Bail if not.21. Use direct estimate of efficiency on baselined data, bail if efficiency is far from expected22. Determine standard Ct value (ctStd, another example of a PQM metric), i.e., the point at which baseline-detrended data crosses a given threshold level

[0132] Stage 2: Assay calibration

[0133] According to various embodiments described herein, there are two key factors that are needed to estimate the number of target molecules in a partition: 1) the PQM value for the case that there is a single target molecule in a partition (PQMofl); 2) the PCR efficiency of the assay (aEff) where 100% means that, at each cycle, the PCR process doubles the number of target molecules. There are two ways to estimate these parameters: multiple sample and single sample.

[0134] Multiple Sample

[0135] According to various embodiments described herein, for this method, it is desirable to have one sample deep in the digital realm (meaning there are few positive partitions) and one in the qPCR realm (meaning there are no negative partitions). For the digital realm sample, the vast majority, if not all, partitions will only have one target molecule. This means that the PQMofl can be determined using a statistic of the PQM values for that sample, e.g., a median. The aEff value can be estimated if the relative quantity of target between the two samples is known. The digital realm sample provides an absolute count of target molecules for the well. Moreover, along with the value for the relative quantity of the sample in the qPCR realm, the absolute count of target molecules can be calculated for the qPCR-realm sample. Combining these values with a measure of the difference in PQM values between the two samples and the median values, the governing equation for the PCR process can be solved for an estimate of aEff. Random resampling methods, e.g.. bootstrap, jackknife, etc., of the PQM values can be used to estimate confidence intervals for the two parameters.Docket No. TP388508WO1

[0136] Single Sample

[0137] According to various embodiments described herein, PQMofl and aEff can be estimated from a single sample if the number of negative partitions falls within a particular range that is specific to the total available partitions. The number of negative partitions must be high enough that there are a substantial percentage of partitions with a single target molecule and low enough where there are a significant number of partitions with more than one molecule.PQMofl can be estimated by examining the statistics of the portion of PQM values that are at the upper end of the distribution. aEff can be estimated using a multi-layered set of polynomial functions with the following independent variables: the coefficient of variation of the PQM values across the set of partitions (the mean divided by the standard deviation of the PQM values), the total number of partitions, and the total number of positive partitions (or, equivalently, the total number of negative partitions since the number of negative partitions is simply the total number of partitions minus the number of positive partitions). Bootstrap resampling of the PQM values can be used to estimate a confidence interval for the aEff estimate.

[0138] aEff Estimation Function

[0139] Determining the parameters of this function can be done by simulation using a Poisson process random number generator and the governing equation for the PCR process examined over numerous values for assay efficiency (assigned aEff). In these simulations, estimated aEff can be compared with assigned aEff and parameters of the multi-layered aEff estimation function can be adjusted to minimize the difference between the two.

[0140] PCR Efficiency Estimation

[0141] FIGS. HA and 1 IB graphs 1102 and 1104 are two examples showing PQMcv as a function of theoretical aEff (theoEff) for two different values of the number of positive partitions in the case of an array with 20480 partitions. In these examples, there is a reasonable linearity. Thus, there is a simple path to estimate assay efficiency. The graphs show that slopes and intercepts clearly depend on the number of positive partitions.Docket No. TP388508WO1

[0142] FIG. 12A and 12B, graph 1202 shows the value of the slope and graph 1204 the value of the intercept of the linear relationship between theoEff and PQMcv for each possible value for the number of positive partitions in an array of 20480 partitions: i.e., slope and intercepts of the family of functions theoEff(PQMcv I numPos ). These values are traced out in blue in the two graphs. However, orange traces cover much of the blue traces. The orange traces are polynomial functions fit to the blue traces. In the case of graph 1202, i.e., the slope values, a piecewise continuous fit is used, one 7-degree polynomial for lower values of numPos and another 7-degree polynomial for higher values of numPos. In the case of graph 1204, i.e., the intercept values, one 7-degree polynomial is used.

[0143] [FIG. 13 illustrates how estimated assay efficiency (colored lines) deviates from the theoretical value (black lines) when using the slopes and intercepts generated by the polynomial functions shown in FIGS 12A and 12B to convert simulated PQMcv values into estimates of aEff. The theoretical efficiency values are shown from 50-100% at 5% intervals. The purpose of showing these results is to clarify why an additional correction is needed.

[0144] FIG. 14 shows the relationship between the estimate of assay efficiency described through FIGS. 11 and 12 and the actual value, i.e., theoEff. The relationship is charted across theoEff values from 0.5 to 1 and for different numbers of negative partitions. For a given number of negative partitions, the curve can be modeled by a quadratic function. These functions can be used to further reduce the difference between estimated PCR efficiency and theoEff.

[0145] FIG. 15 shows estimated assay efficiency (colored lines) and theoretical values (black lines) after making the quadratic corrections shown in FIG 14; the theoretical values are completely covered by the final estimated assay efficiency values (aEff). Graph 1500 shows that aEff is within 1% of theoEff for assay efficiencies 51% to 100%, in intervals of 3%.

[0146] FIG. 16 shows an overlay of all the cases shown in FIG. 15 after subtracting off the theoretical value, the difference between the corrected-predicted efficiency (aEff) and theoEff after the numNeg- specific quadratic correction. Graph 1602 shows that aEff is well within 1% of theoEff from numNegs= 43 to 20336 in the case of an array with 20480 partitions.Docket No. TP388508WO1

[0147] FIGS. 17A and 17B illustrate the sensitivity to array size. Tn these graphs, 100 partitions were rejected from an array of 20480 partitions, but parameters of the estimation functions for aEff for a 20480 array are still used (instead of parameters for 20380 partitions). The graphs show that accuracy of aEff estimates degrades considerably. In practical use of dqPCR, effective array size likely deviates from the presumed array size because partitions can be rejected for many different reasons. e.g„ dust particles, blocked partitions so reactants cannot be loaded into it, system non-uniformities, etc. The implication from this information is that aEff estimation functions should be specific to effective array size.

[0148] Assay Calibration, PQMofl Estimation

[0149] FIG. 18 provides information concerning the estimation of PQMofl. In graph 1800, the fraction of negative partitions is graphed against the fraction of one target molecule partitions among positive partitions. Further, five different array sizes are overlayed, from 5000 to 20480 partitions; it turns out they are exactly the same across array sizes so the graphs completely overlap. The graphs show that when the number of negative partitions exceed -20% of array size, -40% or more of the positive partitions will only have a single molecule. As such, the following estimate can be made: With the number of negative partitions exceeding 20% of array size, from the pool of positive partitions, we can take the top 40% PQM values. Then, a statistic of these PQM values (e.g., median) can suffice as an estimate of PQMofl according to various embodiments described herein.

[0150] FIG. 19 shows an example chart 1900 of calibration results. In this example, an assay calibration was performed on a number of wells of data (11 shown). Three of the wells could not be used to generate assay calibrations. Further, the highlighted well shows reasonable assay efficiency values and relatively low confidence interval width. The key point from chart 1900 is that a single sample, with concentration of the target molecule in the right range, can be used to generate parameters needed to determine molecular quantities. In other words, multiple samples or one sample may be used to generate calibration parameters according to various embodiments described herein. In some embodiments, technical replicates of one sample could be used to reduce variability (not shown).

[0151] Assay Calibration OutlineDocket No. TP388508WO1

[0152] In some embodiments, to perform an assay calibration, efficiency estimation may be precomputed from vector of Ct values to provide parameters needed to estimate assay efficiency from a vector of PQM values (PQM values for each partition of a well).1. For a number of array sizes a. For number of negative partitions from 1 to arraySize- 1 i. For a number of efficiencies1. Generate a theoretical vector of PQM values based on Poisson distribution2. calling out probability of each k (after defining the PQM value for one molecule in a partition)3. From the theoretical vector of PQMs compute mean / sdev (PQMcv) ii. Fit a line to efficiency as a function of PQMcv b. Form a piecewise continuous polynomial fit to efficiency slope as a function of number of negative partitions (two pieces) (7-degree polynomials work) c. Fit a polynomial to efficiency intercept as a function of number of negative partitions (7-degree polynomial works) d. Add a polynomial correction to efficiency predicted by above slope and intercept, (a quadratic fit works) to get final efficiency as a function of the efficiency given by slope and intercept (this is done by, again, generating a theoretical PQM vector, feeding that into estimating efficiency based on the slope and intercepts above, and correcting that efficiency by the correction polynomial to get a final efficiency estimate that is more accurate.)

[0153] This is all precomputed so that, given an array size and the number of negative partition's, the efficiency can be estimated.Docket No. TP388508WO1

[0154] Assay Calibration Steps1. Eliminate rejected partitions from primary analysis2. For all wells a. For each target i. Determine scale ii. For all partitions1. Process CBC data, obtaining PQM values iii. Refine +- calling by examining PQM statistics across the well iv. Bail on this target if number of negative partitions is not within range (appropriate for the array size) to do an assay calibration, v. Compute the median PQM value for an appropriate portion of the higher PQM values to estimate PQMofl (the appropriate proportion depends on the number of negative partitions and total number of partitions) vi. Compute (mean of PQMs) / (standard deviation of PQMs) (PQMcv) vii. Convert this metric to an estimate of assay efficiency through the multilayered polynomial functions (where additional independent variables are effective array size and the number of positive partitions) viii. Perform bootstrap resampling to estimate confidence interval for the assay efficiency estimate and PQMofl estimate

[0155] Stage 3: Quantity estimation

[0156] With estimates for PQMofl and aEff and their confidence intervals in hand, a quantity and confidence interval for this quantity can be estimated for an unknown sample. The following is done for each target of each well: PQM values are computed for all partitionsDocket No. TP388508WO1 deemed viable. Positive PQM values that are so low that they are highly improbable are mapped to negatives. PQMofl and aEff parameter values are used to convert each PQM value to an estimate of k, the number of target molecules in a partition. This process creates a k-profile which is, for each k value, the number of partitions that have k target molecules. A Poisson distribution is fit to the k-profile. In other words, the Poisson distribution is estimated.

[0157] According to various embodiments described herein, low concentration may be when no partition of the set of partitions has more than one target molecule. According to various embodiments described herein, medium concentration may be when at least one partition of the set of partitions has more than one target molecule and there is at least one partition that contains no target molecules. According to various embodiments described herein, high concentration may be when every partition of the set of partitions includes target molecules

[0158] For low values of , or a low concentration, the quantity in the well is estimated by counting the number of positive partitions. For medium values of , the quantity is estimated by multiplying A by the number of partitions. For high values of A, the quantity is based on the difference between a statistical value of the observed PQM values (e.g., a median) and the same statistic computed with theoretical PQM values. The theoretical PQM values are generated by simulation using a reference number of negative partitions. The confidence interval for the quantity estimate uses the confidence intervals estimated for PQMofl and aEff and the exact confidence interval for A of the Poisson distribution.

[0159] Quantification - Low Concentration Example

[0160] FIGS. 20A-20C illustrate an example when quantity of target molecules is determined where there is a low concentration of target molecule in the set of partitions. According to various embodiments described herein, low concentration may be when no partition of the set of partitions has more than one target molecule. With the high number of negative partitions, it is likely that all the positive partitions only have one target molecule in them. As such, quantity can be determined by simply counting the number of positive partitions. In FIG. 20, graph 2002 shows the curves of the positive partitions. Graph 2004 shows the curves of the partitions flagged for human review with colors indicating tentative determination with blue indicating a positive partition, red a negative partition. Graph 2006 shows the curves of theDocket No. TP388508WO1 partitions determined to be negative for the target molecule. Tn this example, there are eight partitions showing a positive amplification of the target molecule and one positive flagged for review. As such, the quantity of the target is eight molecules, possibly 9 pending a human reviewer’s determination.

[0161] Quantification - Medium Concentration Example

[0162] According to various embodiments described herein, medium concentration may be when at least one partition of the set of partitions has more than one target molecule and there is at least one partition that contains no target molecules. With a medium number of negative partitions, some positive partitions can have more than one target molecule (k >1). FIGS. 21A- 20C show an example where the set of partitions has a medium concentration.

[0163] Graph 2102 shows the PQM values range between approximately 23 to 38.PQMofl is estimated to be 26. This value, along with aEff for this assay, is used to construct the k-profile. Note, all PQM values above PQMofl are assigned to k=l.

[0164] A Poisson distribution is fit to the k-profile, giving an estimate of 2 and array size multiplied by 2 estimates the quantity of target molecules. In this case, the quantity is estimated to be 14583 with confidence interval [14330, 14833] (2 = 0.71, array size = 20480).

[0165] Quantification - High Concentration Example

[0166] FIGS. 22A-22C illustrate determining a quantity of target molecules in a high concentration sample. With a low number of negative partitions, all positive partitions have substantially more than one target molecule (k »1).

[0167] Graph 2202 shows that PQM values range between approximately 19 to 23. In this case, using the median PQM value and its difference from a theoretical reference value based on PQMofl and aEff, a quantity of target molecule is estimated. Here, the quantity is estimated to be 333200 target molecules with confidence interval [302517, 363057].Docket No. TP388508WO1

[0168] FIG. 23 illustrates a comparison of estimates versus expected quantity of target molecules in a sample. The circles represent log 10 of estimated quantity. Plot line 2302 represents the expected quantity for 100% accurate estimates.

[0169] In this example, data from four technical replicates at each concentration were used. Presumed quantity is based on intended concentrations. Starting from a sample of known concentration, a series of dilutions is done to generate samples at the lower concentrations.

[0170] Quantity Estimation Outline1. Eliminate rejected partitions from primary analysis2. For all wells a. For each target i. Determine scale ii. For all partitions1. Process CBC data, obtaining PQM values iii. Refine +- calling by examining PQM stats across well1. If a lot of negatives, positives are probably 1 molecule so identify false positives by a fixed value below the 1 molecule PQM2. If a lot of positives, can use the stats of the PQM and known efficiency of the assay to flag false positive partitions a. If stats (e.g., median -mdev where mdev is the half width of 95% confidence interval around the median) are significantly different from efficiency predictions, flag that conditionDocket No. TP388508WO1 b. Tn any case, use the lowest of the two as the criterion to identify a false positive (i.e., stats-based or efficiency predicted for lowest reasonable PQM) iv. Several possible metrics:1. PQM can be the location of the 2nd derivative peak identified as first bona fide exponential region (ctProxy)2. PQM can be the location where baselined CBC data crosses a threshold (ctStd)3. Each of these can be converted to a quant in these ways after imposing a ceiling of PQMofl on observed PQMs: a. Convert each PQM value to a k value where k is derived from Poisson distribution, PQMofl value and observed PQM i. Add up all the k values across the positive partitions b. Use the number of negative partitions to estimate of the Poisson distribution and convert to quant by multiplying with the number of partitions c. Create a k-profile (k values and count of partitions with each k) based on translating the PQM values to k, i. Fit a Poisson distribution to the k-profile number of partitions to estimate quant or just count positives when lambda is at level where likelihood of k=2 is nilDocket No. TP388508WO1 d. Difference between observed median PQM and a theoretical median PQM at a reference number of negative partitions. i. Use the reference number of negative partitions and array size to determine the reference value ii. With the reference X, array size, PQMof 1 from calibration, and estimated assay efficiency, generate simulated PQM values iii. Compute the reference median using the simulated PQM values iv. The difference between observed PQM median and reference PQM median combined with assay efficiency generates an estimate of quant e. Hybrid of method (3) and (4) i. When estimated lambda is below a threshold, use method (3) otherwise use method (4). ii. The final method used is this one using ctStd as the PQM

[0171] Using Cycle threshold (Ct) Metrics for Quantification

[0172] As mentioned above, a PQM may be based on a Ct value according to various embodiments described herein. There are two common types of Ct values are: ctProxy: the most relevant second derivative maximum of the amp-curve; and ctStd: the standard Ct, i.e., the point at which an appropriately baselined amp-curve crosses a threshold.

[0173] As mentioned above, a PQM may be based on a Ct value according to various embodiments described herein. There are two types of Ct values in these teachings: ctProxy: theDocket No. TP388508WO1 most relevant second derivative maximum of the amp-curve; and ctStd: the standard Ct, i.e., the point at which an appropriately baselined amp-curve crosses a threshold (the common definition of a Ct value). In practice, it appears that ctStd may be the more reliable metric to use as the PQM.

[0174] The second approach is ctMedian, which is the median Ct relative to theoretical median Ct for reference negatives. In this approach, a single molecule Ct and assay efficiency generates theoretical Ct distribution across the array of partitions for a reference number of negative partitions. In the following examples, the reference number used is 100 negative partitions.

[0175] The third approach is using ctHiProbK, which is the most frequent Ct predicts X. Here, the Ct predicts k, and the most frequent k can predict X. In practice, the k for which the probability of k does not violate Poisson is used. In other words, the k with highest probability that is within Poisson bounds is used.

[0176] In FIGS. 24A and 24B show precision graphs 2400 and 2410 comparing dPCR to quantification methods according to various embodiments described herein. Precision of a quantification is defined as the maximum deviation of the 95% confidence interval from the actual quantity divided by the quantity. A value of zero means an estimate of quantity is expected to be exact, a value of -5 means an estimate of quantity is expected to deviate no more than 5% from the actual quantity 95% of the time. Precision is reported for a wide range of 2 values and several array sizes. Graph 2400 corresponds to an array size of 100000 and, moving rightward, 28000, 20480, 10240, and 8500. Graph 2400 shows the precision currently reported in commercial products. Graph 2410 shows the precision of the quantification methods described herein. It can be observed that, for quantification methods according to various embodiments described herein, precision better than 10% is extended to a much wider range of 2 values compared to the current state of the art.

[0177] Assay Development

[0178] FIG. 25 shows an exemplary flowchart of developing an assay according to various embodiments of the present disclosure. An objective of the assay developer is to sell aDocket No. TP388508WO1 kit of chemical reagents that will allow their customers to examine biological samples to obtain results that detect the presence or absence of a target molecular species and / or determine the quantity of that target in the samples. An optimal assay design is determined by performing many quantification analysis runs with many variations of the assay and many biological samples according to various embodiments described herein. When an optimal design is identified, that assay is run on many biological samples to determine quantification analysis parameters and establish assay performance according to various embodiments. Each sample might be ran at numerous quantity levels.

[0179] A quantification analysis run according to various embodiments described herein generally consists of running a plate where each well in the plate gets one specimen and this specimen is distributed to a large number of partitions associated with the well. All data collected during a run is submitted to primary analysis that converts readings into a fluorescence value for each partition and each PCR cycle and each channel (where a channel is defined as a specific interval of wavelengths of electromagnetic energy). It is this data that is submitted to quantification analysis according to various embodiments described herein. In this document, this data will be called CBC data (cycle-by-cycle data).

[0180] In doing a quantification analysis, the assay developer seeks to determine parameter values that will reliably yield accurate quantifications throughout the quantity range of interest and, for multiple targets, throughout the relative quantity range of interest. With this in mind, the assay developer compares the results of the quantification analysis to the known quantities of the targets of interest determined by other means; e.g., by diluting a specimen to generate a series of known relative quantities or mixing multiple specimens, each consisting of a different target, in known ratios.

[0181] An example of this process is shown as method 2500 in FIG. 25. In step 2502, cycle-by-cycle (CBC) fluorescence emission data is received for each partition. Using the CBC data, and absolute minimum threshold 2504 for a positive partition, a calibration is performed in step 2506. If at decision 2508, an assay calibration is not generated, further samples in a different concentration range detectable by dPCR and qPCR may be submitted in step 2510 to perform the assay calibration 2506 again.Docket No. TP388508WO1

[0182] If at decision 2508, an assay calibration result is generated, then it is determined, at decision 2512, whether multiple assay calibrations are available and if there are samples in the qPCR realm for which the concentration, relative to samples in the dPCR realm, are known. If such a collection of samples is not available, then, in step 2514, an assay calibration maybe manually chosen. However, if such a collection of samples is available, then the best assay calibration is chosen: the best assay calibration is that which minimizes the difference between estimated quantities using that assay calibration and the known relative quantities in step 2516. The final assay calibration would be included with the assay kit provided to the end users.

[0183] An assay calibration consists of the following parameters for each channel: parameters relating to the scale of the CBC data, the primary one being the threshold for the standard Ct value; PQMofl and its confidence interval; assay efficiency and its confidence interval associated with the PQM.

[0184] Next, in step 2518, samples are run on an instrument to generate CBC data. This CBC data is used in estimating quantity in step 2520 according to various embodiments described herein. In step 2522, for each well and channel, an estimated quantity along with a confidence interval is generated and provided to the user.

[0185] Assay User

[0186] As opposed to a developer, an objective of the assay user is to use the results of a test for the presence or absence of a particular target and / or the quantity of that target. The assay user purchases kits from an assay developer. In some situations, the assay user can also be an assay developer.

[0187] The quantification analysis runs that are done are determined by the number of samples for which a test result is sought.

[0188] Exemplary method 2600 of an assay user is depicted in FIG. 26. In step 2602, samples are run on an instrument to collect CBC data. For the assay user perspective, the quantification analysis is simpler in the sense that there is, ideally, no need to determine the quantification analysis parameters. The parameter values provided by the assay developer are assumed to be sufficient. Assay developer assay calibration parameters 2604 are provided to runDocket No. TP388508WO1 the quantification analysis. However, an assay calibration may be performed by the assay user.In step 2610, an optional assay calibration is performed. In the assay calibration, the assay calibration parameters are validated against the assay developer parameters in step 2612. If it is determined that the assay calibration did not pass in decision 2614, then a message to re-run the calibration and / or notify the assay developer is triggered in step 2616.

[0189] The user may proceed with the quantification analysis in step 2606 without running an assay calibration or when the assay calibration parameters have been successfully validated. In step 2608, an estimated number or concentration of target molecules in the sample are generated and provided to the assay user.

[0190] Examples

[0191] The following numbered examples are embodiments:1. A method for quantification of a target molecule of a biological sample distributed across a plurality of partitions, the method comprising: receiving fluorescent emission data generated by a polymerase chain reaction (PCR) for each partition of a set of partitions; identifying a partition quantity metric for each partition in the set of partitions to generate a set of partition quality metrics, wherein each partition quantity metric correlates to a number of target molecules within its respective partition based on the fluorescent emission data, and wherein the set of partition quantity metrics is used to determine a state of target molecule amplification within each partition of the set of partitions; and determining a quantity of the target molecule in the biological sample based on the set of partition quantity metrics.2. The method of example 1, wherein the partition quantity metric is a cycle threshold (Ct) value, wherein the Ct value is the PCR cycle where fluorescent emission data meets a fluorescent detection threshold.Docket No. TP388508WO13. The method of any one of the examples 1 to 2, wherein receiving fluorescent emission data generated by PCR for each partition of the set of partitions is for at least five cycles of PCR.4. The method of any one of the examples 1 to 3, wherein receiving fluorescent emission data generated by PCR for each partition of the set of partitions is for each cycle of PCR.5. The method of any one of the examples 1 to 4, further comprising: determining an exponential amplification region of the fluorescent emission data for each partition.6. The method of any one of the examples 1 to 5, further comprising: determining, based on the partition quantity metric for each partition, if the partition is positive for amplification of the target molecule.7. The method of any one of the examples 1 to 6, further comprising: determining, based on the set of partition quantity metrics, if each partition is positive for amplification of the target molecule.8. The method of any one of the examples 1 to 7, further comprising: determining a concentration of the target in the biological sample based on the quantity of target molecule in each partition.9. The method of any one of the examples 1 to 8, wherein determining the exponential amplification region is based on at least a zeroth, first, and second derivative of the fluorescent emission data to determine a baseline.10. The method of example 9, wherein determining the exponential amplification is further based on a third derivative of the fluorescent emission data.11. The method of any one of the examples 1 to 10, further comprising: generating a k-profile, wherein a k-th entry in the k-profile is a number of partitions that are estimated to have k target molecules.Docket No. TP388508WO112. The method of any one of the examples 1 to 11 , wherein the quantity of the target molecule is determined based on a Poisson distribution.13. The method of example 12, wherein the Poisson distribution is:, where P(k) is the probability of there being k target molecules in a partition, is an index for sizes of partitions where there are N different sizes, and (s) is the average number of target molecules across the partitions corresponding to the sthpartition size.14. The method of any one of the examples 1 to 13, wherein the concentration is a low concentration when no partition of the set of partitions has more than one target molecule.15. The method of example 14, wherein the quantity of the target molecules is the number of partitions determined to have positive amplification.16. The method of any one of the examples 1 to 13, wherein the concentration is a medium concentration when at least one partition of the set of partitions has more than one target molecule and there is at least one partition that contains no target molecules.17. The method of example 16. wherein the concentration of the target molecule is determined by A. multiplied by a number of partitions in the set.18. The method of example 17, wherein A is determined based on finding the value of A where the Poisson distribution is maximally consistent with the ^-profile.19. The method of any one of the examples 1 to 13, wherein the concentration is a high concentration when every partition of the set of partitions includes target molecules.20. The method of example 19, wherein the concentration is determined based on a median of the partition quantity metrics across the set of partitions compared to a reference median, wherein the reference median is based on a predetermined theoretical target concentration.Docket No. TP388508WO121 . The method of example 20, wherein the reference median is based on a numerical simulation using: an estimate of a partition quantity metric when a partition includes a single target molecule, an estimate of PCR process efficiency, and the predetermined theoretical target concentration, wherein the predetermined theoretical target concentration is based on a case where there are some partitions including no target molecules and some partitions including target molecules.22. The method of example 21, the PCR process efficiency is based on the following governing PCR process equation:F(cy)=Fo(l+aEff, where F(cy) is the number of target molecules at cycle number cy, Fo is the number of target molecules before the PCR process begins, and ciEff the efficiency of the PCR process.23. The method of any one of the examples 1 to 22, wherein determining the quantity of target molecule includes determining an efficiency of the PCR process.24. The method of any one of the examples 1 to 23, wherein determining the efficiency of the PCR process is based on a quantity of a first biological sample when no partition of the set of partitions has more than one target molecule, a quantity of a second biological sample when every partition of the set of partitions includes target molecules, and a relative concentration between the first and the second biological samples is known.25. The method of example 24, wherein determining efficiency is further based on comparing a first partition quantity metric median of the first biological sample and a second partition quantity metric median of the second biological sample.26. The method of example 24 or 25, wherein determining efficiency further includes determining a slope of a regression line fit to the partition quantity metric medians of at least the first and the second biological samples.27. The method of any one of the examples 1 to 23, wherein determining the efficiency of the PCR process is based on analyzing the set of partitions for a single biological sample, whereinDocket No. TP388508WO1 the concentration of target molecules is at a level such that at least 15% of the set of partitions include no target molecules, at least 20% of the set of partitions include only one target molecule, and at least 15% of the set of partitions include more than one target molecule.28. The method of example 27, wherein determining the efficiency of the PCR process is based on a coefficient of variation of the partition quantity metric, wherein the coefficient of variation of the partition quantity metric is based on a ratio of a mean and a standard deviation of the partition quantity metric across positive partitions among the set of partitions.29. The method of example 28, wherein the coefficient of variation of the partition quantity metric is mapped to an estimate of efficiency of the PCR process using a multi-layered polynomial transformation function where other independent variables are a number of partitions that have no target molecules and a total number of partitions in the set of partitions.30. The method of example 29, wherein the multi-layered polynomial transformation function is determined by a numerical simulation using the Poisson distribution and the governing PCR process equation of example 22.31. The method of any one of the examples 27 to 30, wherein determining the efficiency of the PCR process is based on a plurality of biological samples, and determining the efficiency of the PCR process further includes using relative concentrations between the plurality of biological samples, and efficiency estimates for the plurality of biological samples, to determine an estimate of efficiency of the PCR process that is most consistent with the relative concentrations.32. The method of any one of the examples 1 to 31, wherein determining the quantity of target molecules in a multiplexed assay is determined for each channel independently.33. The method of example 32, wherein a channel can contain signals from a plurality of different target molecules.34. A system for quantification of a target molecule of a biological sample distributed across a plurality of partitions, the system comprising: a detector configured to receive a fluorescent emission data generated by a polymerase chain reaction (PCR) from each partition of a set of partitions;Docket No. TP388508WO1 a memory configured to store the fluorescent emission data; and a processor configured to: receive fluorescent emission data generated by a polymerase chain reaction (PCR) for each partition of a set of partitions; compute a partition quantity metric for each partition in the set of partitions to generate a set of partition quality metrics, wherein each partition quantity metric correlates to a number of target molecules within its respective partition based on the fluorescent emission data, and wherein the set of partition quantity metrics is used to determine a state of target molecule amplification within each partition of the set of partitions; and determine a quantity of the target molecule in the biological sample based on the set of partition quantity metrics.35. The system of example 34, wherein the processor is further configured to: display, on a user interface, the quantity of target molecule to a user.36. The system of example 34 or 35, wherein the partition quantity metric is a cycle threshold (Ct) value, wherein the Ct value is the PCR cycle where fluorescent emission data meets a fluorescent detection threshold.37. The system of any one of the examples 34 to 36, wherein receiving fluorescent emission data generated by PCR for each partition of the set of partitions is for at least five cycles of PCR.38. The system of any one of the examples 34 to 36, wherein the processor is configured to receive fluorescent emission data generated by PCR for each partition of the set of partitions for each cycle of PCR.39. The system of any one of the examples 34 to 38, wherein the processor is further configured to: determine an exponential amplification region of the fluorescent emission data for each partition.Docket No. TP388508WO140. The system of any one of the examples 34 to 39, wherein the processor is further configured to: determine, based on the partition quantity metric for each partition, if the partition is positive for amplification of the target molecule.41. The system of any one of the examples 34 to 40, wherein the processor is further configured to: determining, based on the set of partition quantity metrics, if each partition is positive for amplification of the target molecule.42. The system of any one of the examples 34 to 41, wherein the processor is further configured to: determine a concentration of the target in the biological sample based on the quantity of target molecule in each partition.43. The system of any one of the examples 34 to 42, wherein the processor is configured to determine the exponential amplification region based on at least a zeroth, first, and second derivative of the fluorescent emission data to determine a baseline.44. The system of example 43, wherein the processor is configured to determine the exponential amplification further based on a third derivative of the fluorescent emission data.45. The system of any one of the examples 34 to 44, wherein the processor is further configured to: generate a k-profile, wherein a k-th entry in the k-profile is a number of partitions that are estimated to have k target molecules.46. The system of any one of the examples 34 to 45, wherein the quantity of the target molecule is determined based on a Poisson distribution.Docket No. TP388508WO147. The system of example 46, wherein the Poisson distribution is:, where P(k) is the probability of there being k target molecules in a partition, s is an index for sizes of partitions where there are N different sizes, and (s) is the average number of target molecules across the partitions corresponding to the sthpartition size.48. The system of any one of the examples 34 to 47, wherein the concentration is a low concentration when no partition of the set of partitions has more than one target molecule.49. The system of example 48, wherein the quantity of the target molecules is the number of partitions determined to have positive amplification.50. The system of any one of the examples 34 to 47, wherein the concentration is a medium concentration when at least one partition of the set of partitions has more than one target molecule and there is at least one partition that contains no target molecules.51. The system of example 50, wherein the concentration of the target molecule is determined by A multiplied by a number of partitions in the set.52. The system of example 51, wherein A is determined based on finding the value of A where the Poisson distribution is maximally consistent with the A-profile.53. The system of any one of the examples 34 to 47, wherein the concentration is a high concentration when every partition of the set of partitions includes target molecules.54. The system of example 53, wherein the concentration is determined based on a median of the partition quantity metrics across the set of partitions compared to a reference median, wherein the reference median is based on a predetermined theoretical target concentration.55. The system of example 54, wherein the reference median is based on a numerical simulation using: an estimate of a partition quantity metric when a partition includes a singleDocket No. TP388508WO1 target molecule, an estimate of PCR process efficiency, and the predetermined theoretical target concentration, wherein the predetermined theoretical target concentration is based on a case where there are some partitions including no target molecules and some partitions including target molecules.56. The system of example 55, the PCR process efficiency is based on the following governing PCR process equation:F(cy)=F0(l+aF / / )cy, where F(cy) is the number of target molecules at cycle number cy, Fo is the number of target molecules before the PCR process begins, and aEff s the efficiency of the PCR process.57. The system of any one of the examples 34 to 55, wherein the processor is configured to determine the quantity of target molecule based on determining an efficiency of the PCR process.58. The system of any one of the examples 56 to 57, wherein the processor is configured to determine the efficiency of the PCR process based on a quantity of a first biological sample when no partition of the set of partitions has more than one target molecule, a quantity of a second biological sample when every partition of the set of partitions includes target molecules, and a relative concentration between the first and the second biological samples is known.59. The system of example 58, wherein the processor is configured to determine efficiency further based on comparing a first partition quantity metric median of the first biological sample and a second partition quantity metric median of the second biological sample.60. The system of example 58 or 59, wherein the processor is configured to determine efficiency based on determining a slope of a regression line fit to the partition quantity metric medians of at least the first and the second biological samples.61. The system of any one of the examples 34 to 57, wherein the processor is configured to determine the efficiency of the PCR process based on analyzing the set of partitions for a single biological sample, wherein the concentration of target molecules is at a level such that at leastDocket No. TP388508WO115% of the set of partitions include no target molecules, at least 20% of the set of partitions include only one target molecule, and at least 15% of the set of partitions include more than one target molecule.62. The system of example 61, wherein the processor is configured to determine the efficiency of the PCR process based on a coefficient of variation of the partition quantity metric, wherein the coefficient of variation of the partition quantity metric is based on a ratio of a mean and a standard deviation of the partition quantity metric.63. The system of example 62, wherein the coefficient of variation of the partition quantity metric is mapped to an estimate of efficiency of the PCR process using a multi-layered polynomial transformation function where other independent variables are a number of partitions that have no target molecules and a total number of partitions in the set of partitions.64. The system of example 63, wherein the multi-layered polynomial transformation function is determined by a numerical simulation using the Poisson distribution and the governing PCR process equation of example 56.65. The system of any one of the examples 61 to 64, wherein the processor is configured to determine the efficiency of the PCR process based on a plurality of biological samples, and determining the efficiency of the PCR process further includes using relative concentrations between the plurality of biological samples, and efficiency estimates for the plurality of biological samples, to determine an estimate of efficiency of the PCR process that is most consistent with the relative concentrations.66. The system of any one of the examples 34 to 65, wherein determining the quantity of target molecules in a multiplexed assay is determined for each channel independently.67. The system of example 66, wherein a channel can contain signals from a plurality of different target molecules.68. A computer-readable medium encoded with computer-readable instructions, which when executed by a processor of a computer, causes the computer to carry out a method forDocket No. TP388508WO1 quantification of a target molecule of a biological sample distributed across a plurality of partitions, the method comprising: receiving fluorescent emission data generated by a polymerase chain reaction (PCR) for each partition of a set of partitions; identifying a partition quantity metric for each partition in the set of partitions to generate a set of partition quality metrics, wherein each partition quantity metric correlates to a number of target molecules within its respective partition based on the fluorescent emission data, and wherein the set of partition quantity metrics is used to determine a state of target molecule amplification within each partition of the set of partitions; and determining a quantity of the target molecule in the biological sample based on the set of partition quantity metrics.69. The computer-readable medium of example 68, wherein the partition quantity metric is a cycle threshold (Ct) value, wherein the Ct value is the PCR cycle where fluorescent emission data meets a fluorescent detection threshold.70. The computer-readable medium of any one of the examples 68 to 69, wherein receiving fluorescent emission data generated by PCR for each partition of the set of partitions is for at least five cycles of PCR.71. The computer-readable medium of any one of the examples 68 to 69, wherein receiving fluorescent emission data generated by PCR for each partition of the set of partitions is for each cycle of PCR.72. The computer-readable medium of any one of the examples 68 to 71, further comprising: determining an exponential amplification region of the fluorescent emission data for each partition.73. The computer-readable medium of any one of the examples 68 to 72, further comprising:Docket No. TP388508WO1 determining, based on the partition quantity metric for each partition, if the partition is positive for amplification of the target molecule.74. The computer-readable medium of any one of the examples 68 to 73, further comprising: determining, based on the set of partition quantity metrics, if each partition is positive for amplification of the target molecule.75. The computer-readable medium of any one of the examples 68 to 74, further comprising: determining a concentration of the target in the biological sample based on the quantity of target molecule in each partition.76. The computer-readable medium of any one of the examples 68 to 75, wherein determining the exponential amplification region is based on at least a zeroth, first, and second derivative of the fluorescent emission data to determine a baseline.77. The computer-readable medium of example 76, wherein determining the exponential amplification is further based on a third derivative of the fluorescent emission data.78. The computer-readable medium of any one of the examples 68 to 77, further comprising: generating a k-profile, wherein a k-th entry in the k-profile is a number of partitions that are estimated to have k target molecules.79. The computer-readable medium of any one of the examples 68 to 78, wherein the quantity of the target molecule is determined based on a Poisson distribution.80. The computer-readable medium of example 79, wherein the Poisson distribution is:, where P(k) is the probability of there being k target molecules in a partition, 5 is an index for sizes of partitions where there are N different sizes, and (s) is the average number of target molecules across the partitions corresponding to the sthpartition size.Docket No. TP388508WO181 . The computer-readable medium of any one of the examples 68 to 80, wherein the concentration is a low concentration when no partition of the set of partitions has more than one target molecule.82. The computer-readable medium of example 71, wherein the quantity of the target molecules is the number of partitions determined to have positive amplification.83. The computer-readable medium of any one of the examples 68 to 80, wherein the concentration is a medium concentration when at least one partition of the set of partitions has more than one target molecule and there is at least one partition that contains no target molecules.84. The computer-readable medium of example 83, wherein the concentration of the target molecule is determined by X multiplied by a number of partitions in the set.85. The computer-readable medium of example 84, wherein is determined based on finding the value of X where the Poisson distribution is maximally consistent with the ^-profile.86. The computer-readable medium of any one of the examples 68 to 80, wherein the concentration is a high concentration when every partition of the set of partitions includes target molecules.87. The computer-readable medium of example 86, wherein the concentration is determined based on a median of the partition quantity metrics across the set of partitions compared to a reference median, wherein the reference median is based on a predetermined theoretical target concentration.88. The computer- readable medium of example 87, wherein the reference median is based on a numerical simulation using: an estimate of a partition quantity metric when a partition includes a single target molecule, an estimate of PCR process efficiency, and the predetermined theoretical target concentration, wherein the predetermined theoretical target concentration is based on a case where there are some partitions including no target molecules and some partitions including target molecules.Docket No. TP388508WO189. The computer-readable medium of example 88, the PCR process efficiency is based on the following governing PCR process equation:F(cy)=F0(l+aEff, where F(cy) is the number of target molecules at cycle number cy, Fo is the number of target molecules before the PCR process begins, and aEff s the efficiency of the PCR process.90. The computer-readable medium of any one of the examples 68 to 89, wherein determining the quantity of target molecule includes determining an efficiency of the PCR process.91. The computer-readable medium of any one of the examples 68 to 90, wherein determining the efficiency of the PCR process is based on a quantity of a first biological sample when no partition of the set of partitions has more than one target molecule, a quantity of a second biological sample when every partition of the set of partitions includes target molecules, and a relative concentration between the first and the second biological samples is known.92. The computer-readable medium of example 91. wherein determining efficiency is further based on comparing a first partition quantity metric median of the first biological sample and a second partition quantity metric median of the second biological sample.93. The computer-readable medium of example 91 or 92, wherein determining efficiency further includes determining a slope of a regression line fit to the partition quantity metric medians of at least the first and the second biological samples.94. The computer-readable medium of any one of the examples 68 to 90, wherein determining the efficiency of the PCR process is based on analyzing the set of partitions for a single biological sample, wherein the concentration of target molecules is at a level such that at least 15% of the set of partitions include no target molecules, at least 20% of the set of partitions include only one target molecule, and at least 15% of the set of partitions include more than one target molecule.Docket No. TP388508WO195. The computer-readable medium of example 94, wherein determining the efficiency of the PCR process is based on a coefficient of variation of the partition quantity metric, wherein the coefficient of variation of the partition quantity metric is based on a ratio of a mean and a standard deviation of the partition quantity metric across positive partitions among the set of partitions.96. The computer- readable medium of example 95, wherein the coefficient of variation of the partition quantity metric is mapped to an estimate of efficiency of the PCR process using a multilayered polynomial transformation function where other independent variables are a number of partitions that have no target molecules and a total number of partitions in the set of partitions.97. The computer-readable medium of example 96, wherein the multi-layered polynomial transformation function is determined by a numerical simulation using the Poisson distribution and the governing PCR process equation of example 89.98. The computer-readable medium of any one of the examples 94 to 97, wherein determining the efficiency of the PCR process is based on a plurality of biological samples, and determining the efficiency of the PCR process further includes using relative concentrations between the plurality of biological samples, and efficiency estimates for the plurality of biological samples, to determine an estimate of efficiency of the PCR process that is most consistent with the relative concentrations.99. The computer-readable medium of any one of the examples 68 to 98, wherein determining the quantity of target molecules in a multiplexed assay is determined for each channel independently.100. The computer- readable medium of example 99, wherein a channel can contain signals from a plurality of different target molecules.101. A system comprising a processor, and a storage medium configured to store instructions, executable by a processor, to cause the system to carry out a method for quantification of a target molecule of a biological sample distributed across a plurality of partitions, the method comprising:Docket No. TP388508WO1 receiving fluorescent emission data generated by a polymerase chain reaction (PCR) for each partition of a set of partitions; identifying a partition quantity metric for each partition in the set of partitions to generate a set of partition quality metrics, wherein each partition quantity metric correlates to a number of target molecules within its respective partition based on the fluorescent emission data, and wherein the set of partition quantity metrics is used to determine a state of target molecule amplification within each partition of the set of partitions; and determining a quantity of the target molecule in the biological sample based on the set of partition quantity metrics.102. The system of example 101, wherein the partition quantity metric is a cycle threshold (Ct) value, wherein the Ct value is the PCR cycle where fluorescent emission data meets a fluorescent detection threshold.103. The system of any one of the examples 101 to 102, wherein receiving fluorescent emission data generated by PCR for each partition of the set of partitions is for at least five cycles of PCR.104. The system of any one of the examples 101 to 102, wherein receiving fluorescent emission data generated by PCR for each partition of the set of partitions is for each cycle of PCR.105. The system of any one of the examples 101 to 104, wherein the method further comprises: determining an exponential amplification region of the fluorescent emission data for each partition.106. The system of any one of the examples 101 to 105, wherein the method further comprises: determining, based on the partition quantity metric for each partition, if the partition is positive for amplification of the target molecule.Docket No. TP388508WO1107. The system of any one of the examples 101 to 106, wherein the method further comprises: determining, based on the set of partition quantity metrics, if each partition is positive for amplification of the target molecule.108. The system of any one of the examples 101 to 107, wherein the method further comprises: determining a concentration of the target in the biological sample based on the quantity of target molecule in each partition.109. The system of any one of the examples 101 to 108, wherein determining the exponential amplification region is based on at least a zeroth, first, and second derivative of the fluorescent emission data to determine a baseline.110. The system of example 109, wherein determining the exponential amplification is further based on a third derivative of the fluorescent emission data.111. The system of any one of the examples 101 to 110, wherein the method further comprises: generating a k-profile, wherein a k-th entry in the k-profile is a number of partitions that are estimated to have k target molecules.112. The system of any one of the examples 101 to 111, wherein the quantity of the target molecule is determined based on a Poisson distribution.113. The system of example 112, wherein the Poisson distribution is:, where P(k) is the probability of there being k target molecules in a partition, 5 is an index for sizes of partitions where there are N different sizes, and (s) is the average number of target molecules across the partitions corresponding to the sthpartition size.Docket No. TP388508WO1114. The system of any one of the examples 101 to 113, wherein the concentration is a low concentration when no partition of the set of partitions has more than one target molecule.115. The system of example 114, wherein the quantity of the target molecules is the number of partitions determined to have positive amplification.116. The system of any one of the examples 101 to 113, wherein the concentration is a medium concentration when at least one partition of the set of partitions has more than one target molecule and there is at least one partition that contains no target molecules.117. The system of example 116, wherein the concentration of the target molecule is determined by X multiplied by a number of partitions in the set.118. The system of example 117, wherein A is determined based on finding the value of A where the Poisson distribution is maximally consistent with the A-profile.119. The system of any one of the examples 101 to 113, wherein the concentration is a high concentration when every partition of the set of partitions includes target molecules.120. The system of example 119, wherein the concentration is determined based on a median of the partition quantity metrics across the set of partitions compared to a reference median, wherein the reference median is based on a predetermined theoretical target concentration.121. The system of example 120, wherein the reference median is based on a numerical simulation using: an estimate of a partition quantity metric when a partition includes a single target molecule, an estimate of PCR process efficiency, and the predetermined theoretical target concentration, wherein the predetermined theoretical target concentration is based on a case where there are some partitions including no target molecules and some partitions including target molecules.122. The system of example 121, the PCR process efficiency is based on the following governing PCR process equation:F(cy )=Fo( 1+aEf f)cyDocket No. TP388508WO1, where F(cy) is the number of target molecules at cycle number cy, Fo is the number of target molecules before the PCR process begins, and aEff s the efficiency of the PCR process.123. The system of any one of the examples 101 to 122, wherein determining the quantity of target molecule includes determining an efficiency of the PCR process.124. The system of any one of the examples 101 to 123, wherein determining the efficiency of the PCR process is based on a quantity of a first biological sample when no partition of the set of partitions has more than one target molecule, a quantity of a second biological sample when every partition of the set of partitions includes target molecules, and a relative concentration between the first and the second biological samples is known.125. The system of example 124, wherein determining efficiency is further based on comparing a first partition quantity metric median of the first biological sample and a second partition quantity metric median of the second biological sample.126. The system of example 124 or 125, wherein determining efficiency further includes determining a slope of a regression line fit to the partition quantity metric medians of at least the first and the second biological samples.127. The system of any one of the examples 101 to 123, wherein determining the efficiency of the PCR process is based on analyzing the set of partitions for a single biological sample, wherein the concentration of target molecules is at a level such that at least 15% of the set of partitions include no target molecules, at least 20% of the set of partitions include only one target molecule, and at least 15% of the set of partitions include more than one target molecule.128. The system of example 127, wherein determining the efficiency of the PCR process is based on a coefficient of variation of the partition quantity metric, wherein the coefficient of variation of the partition quantity metric is based on a ratio of a mean and a standard deviation of the partition quantity metric across positive partitions among the set of partitions.129. The system of example 128, wherein the coefficient of variation of the partition quantity metric is mapped to an estimate of efficiency of the PCR process using a multi-layeredDocket No. TP388508WO1 polynomial transformation function where other independent variables are a number of partitions that have no target molecules and a total number of partitions in the set of partitions.130. The system of example 129, wherein the multi-layered polynomial transformation function is determined by a numerical simulation using the Poisson distribution and the governing PCR process equation of example 122.131. The system of any one of the examples 127 to 130, wherein determining the efficiency of the PCR process is based on a plurality of biological samples, and determining the efficiency of the PCR process further includes using relative concentrations between the plurality of biological samples, and efficiency estimates for the plurality of biological samples, to determine an estimate of efficiency of the PCR process that is most consistent with the relative concentrations.132. The system of any one of the examples 101 to 131. wherein determining the quantity of target molecules in a multiplexed assay is determined for each channel independently.133. The system of example 132, wherein a channel can contain signals from a plurality of different target molecules.134. A method for quantification of a target molecule of a biological sample distributed across a plurality of partitions, the method comprising: performing a quantity analysis to determine an indication of quantity of target molecule within each partition of the plurality of partitions; generating a k-profile, wherein a k-th entry in the k-profile is a number of partitions that are estimated to have k target molecules; and determining a concentration of the target molecule in the biological sample based on the k- profile.135. The method of example 134, wherein the quantity analysis is weighing each partition of the plurality of partitions to determine the indication of quantity of target molecule within each partition.Docket No. TP388508WO1

[0192] Although the present invention has been described with respect to certain exemplary embodiments, examples, and applications, it will be apparent to those skilled in the art that various modifications and changes may be made without departing from the invention.

Claims

Docket No. TP388508WO1CLAIMSWhat is claimed is:

1. A method for quantification of a target molecule of a biological sample distributed across a plurality of partitions, the method comprising: receiving fluorescent emission data generated by a polymerase chain reaction (PCR) for each partition of a set of partitions; identifying a partition quantity metric for each partition in the set of partitions to generate a set of partition quality metrics, wherein each partition quantity metric correlates to a number of target molecules within its respective partition based on the fluorescent emission data, and wherein the set of partition quantity metrics is used to determine a state of target molecule amplification within each partition of the set of partitions; and determining a quantity of the target molecule in the biological sample based on the set of partition quantity metrics.

2. The method of claim 1, wherein the partition quantity metric is a cycle threshold (Ct) value, wherein the Ct value is the PCR cycle where fluorescent emission data meets a fluorescent detection threshold.

3. The method of any one of the claims 1 to 2, wherein receiving fluorescent emission data generated by PCR for each partition of the set of partitions is for at least five cycles of PCR.

4. The method of any one of the claims 1 to 3, wherein receiving fluorescent emission data generated by PCR for each partition of the set of partitions is for each cycle of PCR.

5. The method of any one of the claims 1 to 4, further comprising: determining an exponential amplification region of the fluorescent emission data for each partition.Docket No. TP388508WO16. The method of any one of the claims 1 to 5, further comprising: determining, based on the partition quantity metric for each partition, if the partition is positive for amplification of the target molecule.

7. The method of any one of the claims 1 to 6. further comprising: determining, based on the set of partition quantity metrics, if each partition is positive for amplification of the target molecule.

8. The method of any one of the claims 1 to 7, further comprising: determining a concentration of the target in the biological sample based on the quantity of target molecule in each partition.

9. The method of any one of the claims 1 to 8. wherein determining the exponential amplification region is based on at least a zeroth, first, and second derivative of the fluorescent emission data to determine a baseline.

10. The method of claim 9, wherein determining the exponential amplification is further based on a third derivative of the fluorescent emission data.

11. The method of any one of the claims 1 to 10, further comprising: generating a k-profile. wherein a k-th entry in the k-profile is a number of partitions that are estimated to have k target molecules.

12. The method of any one of the claims 1 to 11, wherein the quantity of the target molecule is determined based on a Poisson distribution.

13. The method of claim 12, wherein the Poisson distribution is:Docket No. TP388508WO1, where P(k) is the probability of there being k target molecules in a partition, s is an index for sizes of partitions where there are N different sizes, andis the average number of target molecules across the partitions corresponding to the sthpartition size.

14. The method of any one of the claims 1 to 13, wherein the concentration is a low concentration when no partition of the set of partitions has more than one target molecule.

15. The method of claim 14, wherein the quantity of the target molecules is the number of partitions determined to have positive amplification.

16. The method of any one of the claims 1 to 13, wherein the concentration is a medium concentration when at least one partition of the set of partitions has more than one target molecule and there is at least one partition that contains no target molecules.

17. The method of claim 16, wherein the concentration of the target molecule is determined by multiplied by a number of partitions in the set.

18. The method of claim 17, wherein X is determined based on finding the value of where the Poisson distribution is maximally consistent with the ^-profile.

19. The method of any one of the claims 1 to 13, wherein the concentration is a high concentration when every partition of the set of partitions includes target molecules.

20. The method of claim 19, wherein the concentration is determined based on a median of the partition quantity metrics across the set of partitions compared to a reference median, wherein the reference median is based on a predetermined theoretical target concentration.

21. The method of claim 20, wherein the reference median is based on a numerical simulation using: an estimate of a partition quantity metric when a partition includes a single target molecule, an estimate of PCR process efficiency, and the predetermined theoretical targetDocket No. TP388508WO1 concentration, wherein the predetermined theoretical target concentration is based on a case where there are some partitions including no target molecules and some partitions including target molecules.

22. The method of claim 21, the PCR process efficiency is based on the following governing PCR process equation:F(cy)=F0(l+a-F / )cy, where F(cy) is the number of target molecules at cycle number cy, Fo is the number of target molecules before the PCR process begins, and aEff the efficiency of the PCR process.

23. The method of any one of the claims 1 to 22, wherein determining the quantity of target molecule includes determining an efficiency of the PCR process.

24. The method of any one of the claims 1 to 23, wherein determining the efficiency of the PCR process is based on a quantity of a first biological sample when no partition of the set of partitions has more than one target molecule, a quantity of a second biological sample when every partition of the set of partitions includes target molecules, and a relative concentration between the first and the second biological samples is known.

25. The method of claim 24, wherein determining efficiency is further based on comparing a first partition quantity metric median of the first biological sample and a second partition quantity metric median of the second biological sample.

26. The method of claim 24 or 25, wherein determining efficiency further includes determining a slope of a regression line fit to the partition quantity metric medians of at least the first and the second biological samples.

27. The method of any one of the claims 1 to 23, wherein determining the efficiency of the PCR process is based on analyzing the set of partitions for a single biological sample, wherein the concentration of target molecules is at a level such that at least 15% of the set ofDocket No. TP388508WO1 partitions include no target molecules, at least 20% of the set of partitions include only one target molecule, and at least 15% of the set of partitions include more than one target molecule.

28. The method of claim 27, wherein determining the efficiency of the PCR process is based on a coefficient of variation of the partition quantity metric, wherein the coefficient of variation of the partition quantity metric is based on a ratio of a mean and a standard deviation of the partition quantity metric across positive partitions among the set of partitions.

29. The method of claim 28, wherein the coefficient of variation of the partition quantity metric is mapped to an estimate of efficiency of the PCR process using a multi-layered polynomial transformation function where other independent variables are a number of partitions that have no target molecules and a total number of partitions in the set of partitions.

30. The method of claim 29, wherein the multi-layered polynomial transformation function is determined by a numerical simulation using the Poisson distribution and the governing PCR process equation of claim 22.

31. The method of any one of the claims 27 to 30, wherein determining the efficiency of the PCR process is based on a plurality of biological samples, and determining the efficiency of the PCR process further includes using relative concentrations between the plurality of biological samples, and efficiency estimates for the plurality of biological samples, to determine an estimate of efficiency of the PCR process that is most consistent with the relative concentrations.

32. The method of any one of the claims 1 to 31. wherein determining the quantity of target molecules in a multiplexed assay is determined for each channel independently.

33. The method of claim 32, wherein a channel can contain signals from a plurality of different target molecules.Docket No. TP388508WO134. A system for quantification of a target molecule of a biological sample distributed across a plurality of partitions, the system comprising: a detector configured to receive a fluorescent emission data generated by a polymerase chain reaction (PCR) from each partition of a set of partitions; a memory configured to store the fluorescent emission data; and a processor configured to: receive fluorescent emission data generated by a polymerase chain reaction (PCR) for each partition of a set of partitions; compute a partition quantity metric for each partition in the set of partitions to generate a set of partition quality metrics, wherein each partition quantity metric correlates to a number of target molecules within its respective partition based on the fluorescent emission data, and wherein the set of partition quantity metrics is used to determine a state of target molecule amplification within each partition of the set of partitions; and determine a quantity of the target molecule in the biological sample based on the set of partition quantity metrics.

35. The system of claim 34, wherein the processor is further configured to: display, on a user interface, the quantity of target molecule to a user.

36. The system of claim 34 or 35, wherein the partition quantity metric is a cycle threshold (Ct) value, wherein the Ct value is the PCR cycle where fluorescent emission data meets a fluorescent detection threshold.

37. The system of any one of the claims 34 to 36. wherein receiving fluorescent emission data generated by PCR for each partition of the set of partitions is for at least five cycles of PCR.

38. The system of any one of the claims 34 to 36, wherein the processor is configured to receive fluorescent emission data generated by PCR for each partition of the set of partitions for each cycle of PCR.Docket No. TP388508WO139. The system of any one of the claims 34 to 38, wherein the processor is further configured to: determine an exponential amplification region of the fluorescent emission data for each partition.

40. The system of any one of the claims 34 to 39, wherein the processor is further configured to: determine, based on the partition quantity metric for each partition, if the partition is positive for amplification of the target molecule.

41. The system of any one of the claims 34 to 40, wherein the processor is further configured to: determining, based on the set of partition quantity metrics, if each partition is positive for amplification of the target molecule.

42. The system of any one of the claims 34 to 41, wherein the processor is further configured to: determine a concentration of the target in the biological sample based on the quantity of target molecule in each partition.

43. The system of any one of the claims 34 to 42, wherein the processor is configured to determine the exponential amplification region based on at least a zeroth, first, and second derivative of the fluorescent emission data to determine a baseline.

44. The system of claim 43, wherein the processor is configured to determine the exponential amplification further based on a third derivative of the fluorescent emission data.

45. The system of any one of the claims 34 to 44, wherein the processor is further configured to:Docket No. TP388508WO1 generate a k-profile, wherein a k-th entry in the k-profile is a number of partitions that are estimated to have k target molecules.

46. The system of any one of the claims 34 to 45, wherein the quantity of the target molecule is determined based on a Poisson distribution.

47. The system of claim 46, wherein the Poisson distribution is:, where P(k) is the probability of there being k target molecules in a partition, 5 is an index for sizes of partitions where there are N different sizes, and X(s) is the average number of target molecules across the partitions corresponding to the sthpartition size.

48. The system of any one of the claims 34 to 47, wherein the concentration is a low concentration when no partition of the set of partitions has more than one target molecule.

49. The system of claim 48, wherein the quantity of the target molecules is the number of partitions determined to have positive amplification.

50. The system of any one of the claims 34 to 47, wherein the concentration is a medium concentration when at least one partition of the set of partitions has more than one target molecule and there is at least one partition that contains no target molecules.

51. The system of claim 50, wherein the concentration of the target molecule is determined by X multiplied by a number of partitions in the set.

52. The system of claim 51, wherein X is determined based on finding the value of X where the Poisson distribution is maximally consistent with the k-profile.

53. The system of any one of the claims 34 to 47, wherein the concentration is a high concentration when every partition of the set of partitions includes target molecules.Docket No. TP388508WO154. The system of claim 53, wherein the concentration is determined based on a median of the partition quantity metrics across the set of partitions compared to a reference median, wherein the reference median is based on a predetermined theoretical target concentration.

55. The system of claim 54, wherein the reference median is based on a numerical simulation using: an estimate of a partition quantity metric when a partition includes a single target molecule, an estimate of PCR process efficiency, and the predetermined theoretical target concentration, wherein the predetermined theoretical target concentration is based on a case where there are some partitions including no target molecules and some partitions including target molecules.

56. The system of claim 55, the PCR process efficiency is based on the following governing PCR process equation:F(cy)=F0(l+aF / / )cy, where F(cy) is the number of target molecules at cycle number cy, Fo is the number of target molecules before the PCR process begins, and aEffis the efficiency of the PCR process.

57. The system of any one of the claims 34 to 55, wherein the processor is configured to determine the quantity of target molecule based on determining an efficiency of the PCR process.

58. The system of any one of the claims 56 to 57, wherein the processor is configured to determine the efficiency of the PCR process based on a quantity of a first biological sample when no partition of the set of partitions has more than one target molecule, a quantity of a second biological sample when every partition of the set of partitions includes target molecules, and a relative concentration between the first and the second biological samples is known.Docket No. TP388508WO159. The system of claim 58, wherein the processor is configured to determine efficiency further based on comparing a first partition quantity metric median of the first biological sample and a second partition quantity metric median of the second biological sample.

60. The system of claim 58 or 59, wherein the processor is configured to determine efficiency based on determining a slope of a regression line fit to the partition quantity metric medians of at least the first and the second biological samples.

61. The system of any one of the claims 34 to 57, wherein the processor is configured to determine the efficiency of the PCR process based on analyzing the set of partitions for a single biological sample, wherein the concentration of target molecules is at a level such that at least 15% of the set of partitions include no target molecules, at least 20% of the set of partitions include only one target molecule, and at least 15% of the set of partitions include more than one target molecule.

62. The system of claim 61, wherein the processor is configured to determine the efficiency of the PCR process based on a coefficient of variation of the partition quantity metric, wherein the coefficient of variation of the partition quantity metric is based on a ratio of a mean and a standard deviation of the partition quantity metric.

63. The system of claim 62, wherein the coefficient of variation of the partition quantity metric is mapped to an estimate of efficiency of the PCR process using a multi-layered polynomial transformation function where other independent variables are a number of partitions that have no target molecules and a total number of partitions in the set of partitions.

64. The system of claim 63, wherein the multi-layered polynomial transformation function is determined by a numerical simulation using the Poisson distribution and the governing PCR process equation of claim 56.

65. The system of any one of the claims 61 to 64, wherein the processor is configured to determine the efficiency of the PCR process based on a plurality of biological samples, andDocket No. TP388508WO1 determining the efficiency of the PCR process further includes using relative concentrations between the plurality of biological samples, and efficiency estimates for the plurality of biological samples, to determine an estimate of efficiency of the PCR process that is most consistent with the relative concentrations.

66. The system of any one of the claims 34 to 65. wherein determining the quantity of target molecules in a multiplexed assay is determined for each channel independently.

67. The system of claim 66, wherein a channel can contain signals from a plurality of different target molecules.

68. A computer-readable medium encoded with computer-readable instructions, which when executed by a processor of a computer, causes the computer to carry out a method for quantification of a target molecule of a biological sample distributed across a plurality of partitions, the method comprising: receiving fluorescent emission data generated by a polymerase chain reaction (PCR) for each partition of a set of partitions; identifying a partition quantity metric for each partition in the set of partitions to generate a set of partition quality metrics, wherein each partition quantity metric correlates to a number of target molecules within its respective partition based on the fluorescent emission data, and wherein the set of partition quantity metrics is used to determine a state of target molecule amplification within each partition of the set of partitions; and determining a quantity of the target molecule in the biological sample based on the set of partition quantity metrics.

69. The computer-readable medium of claim 68, wherein the partition quantity metric is a cycle threshold (Ct) value, wherein the Ct value is the PCR cycle where fluorescent emission data meets a fluorescent detection threshold.Docket No. TP388508WO170. The computer-readable medium of any one of the claims 68 to 69, wherein receiving fluorescent emission data generated by PCR for each partition of the set of partitions is for at least five cycles of PCR.

71. The computer-readable medium of any one of the claims 68 to 69, wherein receiving fluorescent emission data generated by PCR for each partition of the set of partitions is for each cycle of PCR.

72. The computer-readable medium of any one of the claims 68 to 71, further comprising: determining an exponential amplification region of the fluorescent emission data for each partition.

73. The computer-readable medium of any one of the claims 68 to 72, further comprising: determining, based on the partition quantity metric for each partition, if the partition is positive for amplification of the target molecule.

74. The computer-readable medium of any one of the claims 68 to 73, further comprising: determining, based on the set of partition quantity metrics, if each partition is positive for amplification of the target molecule.

75. The computer-readable medium of any one of the claims 68 to 74, further comprising: determining a concentration of the target in the biological sample based on the quantity of target molecule in each partition.

76. The computer-readable medium of any one of the claims 68 to 75, wherein determining the exponential amplification region is based on at least a zeroth, first, and second derivative of the fluorescent emission data to determine a baseline.Docket No. TP388508WO177. The computer-readable medium of claim 76, wherein determining the exponential amplification is further based on a third derivative of the fluorescent emission data.

78. The computer-readable medium of any one of the claims 68 to 77, further comprising: generating a k-profile, wherein a k-th entry in the k-profile is a number of partitions that are estimated to have k target molecules.

79. The computer-readable medium of any one of the claims 68 to 78, wherein the quantity of the target molecule is determined based on a Poisson distribution.

80. The computer-readable medium of claim 79, wherein the Poisson distribution is:, where P(k) is the probability of there being k target molecules in a partition, 5 is an index for sizes of partitions where there are N different sizes, and (s) is the average number of target molecules across the partitions corresponding to the sthpartition size.

81. The computer-readable medium of any one of the claims 68 to 80, wherein the concentration is a low concentration when no partition of the set of partitions has more than one target molecule.

82. The computer-readable medium of claim 71, wherein the quantity of the target molecules is the number of partitions determined to have positive amplification.

83. The computer-readable medium of any one of the claims 68 to 80, wherein the concentration is a medium concentration when at least one partition of the set of partitions has more than one target molecule and there is at least one partition that contains no target molecules.Docket No. TP388508WO184. The computer-readable medium of claim 83, wherein the concentration of the target molecule is determined by X multiplied by a number of partitions in the set.

85. The computer-readable medium of claim 84, wherein X is determined based on finding the value of k where the Poisson distribution is maximally consistent with the ^-profile.

86. The computer-readable medium of any one of the claims 68 to 80, wherein the concentration is a high concentration when every partition of the set of partitions includes target molecules.

87. The computer-readable medium of claim 86, wherein the concentration is determined based on a median of the partition quantity metrics across the set of partitions compared to a reference median, wherein the reference median is based on a predetermined theoretical target concentration.

88. The computer-readable medium of claim 87, wherein the reference median is based on a numerical simulation using: an estimate of a partition quantity metric when a partition includes a single target molecule, an estimate of PCR process efficiency, and the predetermined theoretical target concentration, wherein the predetermined theoretical target concentration is based on a case where there are some partitions including no target molecules and some partitions including target molecules.

89. The computer-readable medium of claim 88, the PCR process efficiency is based on the following governing PCR process equation:F(cy)=Fo( 1 +aEff")cy, where F(cy) is the number of target molecules at cycle number cy, FQ is the number of target molecules before the PCR process begins, and aEff the efficiency of the PCR process.

90. The computer-readable medium of any one of the claims 68 to 89, wherein determining the quantity of target molecule includes determining an efficiency of the PCR process.Docket No. TP388508WO191. The computer-readable medium of any one of the claims 68 to 90, wherein determining the efficiency of the PCR process is based on a quantity of a first biological sample when no partition of the set of partitions has more than one target molecule, a quantity of a second biological sample when every partition of the set of partitions includes target molecules, and a relative concentration between the first and the second biological samples is known.

92. The computer-readable medium of claim 91, wherein determining efficiency is further based on comparing a first partition quantity metric median of the first biological sample and a second partition quantity metric median of the second biological sample.

93. The computer-readable medium of claim 91 or 92, wherein determining efficiency further includes determining a slope of a regression line fit to the partition quantity metric medians of at least the first and the second biological samples.

94. The computer-readable medium of any one of the claims 68 to 90, wherein determining the efficiency of the PCR process is based on analyzing the set of partitions for a single biological sample, wherein the concentration of target molecules is at a level such that at least 15% of the set of partitions include no target molecules, at least 20% of the set of partitions include only one target molecule, and at least 15% of the set of partitions include more than one target molecule.

95. The computer-readable medium of claim 94, wherein determining the efficiency of the PCR process is based on a coefficient of variation of the partition quantity metric, wherein the coefficient of variation of the partition quantity metric is based on a ratio of a mean and a standard deviation of the partition quantity metric across positive partitions among the set of partitions.

96. The computer-readable medium of claim 95, wherein the coefficient of variation of the partition quantity metric is mapped to an estimate of efficiency of the PCR process using a multi-layered polynomial transformation function where other independent variables are aDocket No. TP388508WO1 number of partitions that have no target molecules and a total number of partitions in the set of partitions.

97. The computer-readable medium of claim 96, wherein the multi-layered polynomial transformation function is determined by a numerical simulation using the Poisson distribution and the governing PCR process equation of claim 89.

98. The computer-readable medium of any one of the claims 94 to 97, wherein determining the efficiency of the PCR process is based on a plurality of biological samples, and determining the efficiency of the PCR process further includes using relative concentrations between the plurality of biological samples, and efficiency estimates for the plurality of biological samples, to determine an estimate of efficiency of the PCR process that is most consistent with the relative concentrations.

99. The computer-readable medium of any one of the claims 68 to 98, wherein determining the quantity of target molecules in a multiplexed assay is determined for each channel independently.

100. The computer-readable medium of claim 99, wherein a channel can contain signals from a plurality of different target molecules.

101. A system comprising a processor, and a storage medium configured to store instructions, executable by a processor, to cause the system to carry out a method for quantification of a target molecule of a biological sample distributed across a plurality of partitions, the method comprising: receiving fluorescent emission data generated by a polymerase chain reaction (PCR) for each partition of a set of partitions; identifying a partition quantity metric for each partition in the set of partitions to generate a set of partition quality metrics, wherein each partition quantity metric correlates to a number of target molecules within its respective partition based on the fluorescent emission data, andDocket No. TP388508WO1 wherein the set of partition quantity metrics is used to determine a state of target molecule amplification within each partition of the set of partitions; and determining a quantity of the target molecule in the biological sample based on the set of partition quantity metrics.

102. The system of claim 101. wherein the partition quantity metric is a cycle threshold (Ct) value, wherein the Ct value is the PCR cycle where fluorescent emission data meets a fluorescent detection threshold.

103. The system of any one of the claims 101 to 102, wherein receiving fluorescent emission data generated by PCR for each partition of the set of partitions is for at least five cycles of PCR.

104. The system of any one of the claims 101 to 102, wherein receiving fluorescent emission data generated by PCR for each partition of the set of partitions is for each cycle of PCR.

105. The system of any one of the claims 101 to 104, wherein the method further comprises: determining an exponential amplification region of the fluorescent emission data for each partition.

106. The system of any one of the claims 101 to 105, wherein the method further comprises: determining, based on the partition quantity metric for each partition, if the partition is positive for amplification of the target molecule.

107. The system of any one of the claims 101 to 106, wherein the method further comprises: determining, based on the set of partition quantity metrics, if each partition is positive for amplification of the target molecule.Docket No. TP388508WO1108. The system of any one of the claims 101 to 107, wherein the method further comprises: determining a concentration of the target in the biological sample based on the quantity of target molecule in each partition.

109. The system of any one of the claims 101 to 108, wherein determining the exponential amplification region is based on at least a zeroth, first, and second derivative of the fluorescent emission data to determine a baseline.

110. The system of claim 109, wherein determining the exponential amplification is further based on a third derivative of the fluorescent emission data.

111. The system of any one of the claims 101 to 110, wherein the method further comprises: generating a k-profile, wherein a k-th entry in the k-profile is a number of partitions that are estimated to have k target molecules.

112. The system of any one of the claims 101 to 111, wherein the quantity of the target molecule is determined based on a Poisson distribution.

113. The system of claim 112, wherein the Poisson distribution is:, where P(k) is the probability of there being k target molecules in a partition, s is an index for sizes of partitions where there are N different sizes, and (s) is the average number of target molecules across the partitions corresponding to the sthpartition size.

114. The system of any one of the claims 101 to 113, wherein the concentration is a low concentration when no partition of the set of partitions has more than one target molecule.Docket No. TP388508WO1115. The system of claim 114, wherein the quantity of the target molecules is the number of partitions determined to have positive amplification.

116. The system of any one of the claims 101 to 113, wherein the concentration is a medium concentration when at least one partition of the set of partitions has more than one target molecule and there is at least one partition that contains no target molecules.

117. The system of claim 116, wherein the concentration of the target molecule is determined by X multiplied by a number of partitions in the set.

118. The system of claim 117, wherein X is determined based on finding the value of X where the Poisson distribution is maximally consistent with the ^-profile.

119. The system of any one of the claims 101 to 113, wherein the concentration is a high concentration when every partition of the set of partitions includes target molecules.

120. The system of claim 119, wherein the concentration is determined based on a median of the partition quantity metrics across the set of partitions compared to a reference median, wherein the reference median is based on a predetermined theoretical target concentration.

121. The system of claim 120, wherein the reference median is based on a numerical simulation using: an estimate of a partition quantity metric when a partition includes a single target molecule, an estimate of PCR process efficiency, and the predetermined theoretical target concentration, wherein the predetermined theoretical target concentration is based on a case where there are some partitions including no target molecules and some partitions including target molecules.

122. The system of claim 121, the PCR process efficiency is based on the following governing PCR process equation:F(cy)=Fo(l+aEf f)cyDocket No. TP388508WO1, where F(cy) is the number of target molecules at cycle number cy, Fo is the number of target molecules before the PCR process begins, and aEffis the efficiency of the PCR process.

123. The system of any one of the claims 101 to 122, wherein determining the quantity of target molecule includes determining an efficiency of the PCR process.

124. The system of any one of the claims 101 to 123, wherein determining the efficiency of the PCR process is based on a quantity of a first biological sample when no partition of the set of partitions has more than one target molecule, a quantity of a second biological sample when every partition of the set of partitions includes target molecules, and a relative concentration between the first and the second biological samples is known.

125. The system of claim 124, wherein determining efficiency is further based on comparing a first partition quantity metric median of the first biological sample and a second partition quantity metric median of the second biological sample.

126. The system of claim 124 or 125, wherein determining efficiency further includes determining a slope of a regression line fit to the partition quantity metric medians of at least the first and the second biological samples.

127. The system of any one of the claims 101 to 123, wherein determining the efficiency of the PCR process is based on analyzing the set of partitions for a single biological sample, wherein the concentration of target molecules is at a level such that at least 15% of the set of partitions include no target molecules, at least 20% of the set of partitions include only one target molecule, and at least 15% of the set of partitions include more than one target molecule.

128. The system of claim 127, wherein determining the efficiency of the PCR process is based on a coefficient of variation of the partition quantity metric, wherein the coefficient of variation of the partition quantity metric is based on a ratio of a mean and a standard deviation of the partition quantity metric across positive partitions among the set of partitions.Docket No. TP388508WO1129. The system of claim 128, wherein the coefficient of variation of the partition quantity metric is mapped to an estimate of efficiency of the PCR process using a multi-layered polynomial transformation function where other independent variables are a number of partitions that have no target molecules and a total number of partitions in the set of partitions.

130. The system of claim 129. wherein the multi-layered polynomial transformation function is determined by a numerical simulation using the Poisson distribution and the governing PCR process equation of claim 122.

131. The system of any one of the claims 127 to 130, wherein determining the efficiency of the PCR process is based on a plurality of biological samples, and determining the efficiency of the PCR process further includes using relative concentrations between the plurality of biological samples, and efficiency estimates for the plurality of biological samples, to determine an estimate of efficiency of the PCR process that is most consistent with the relative concentrations.

132. The system of any one of the claims 101 to 131, wherein determining the quantity of target molecules in a multiplexed assay is determined for each channel independently.

133. The system of claim 132, wherein a channel can contain signals from a plurality of different target molecules.

134. A method for quantification of a target molecule of a biological sample distributed across a plurality of partitions, the method comprising: performing a quantity analysis to determine an indication of quantity of target molecule within each partition of the plurality of partitions; generating a k-profile. wherein a k-th entry in the k-profile is a number of partitions that are estimated to have k target molecules; and determining a concentration of the target molecule in the biological sample based on the k-profile.Docket No. TP388508WO1135. The method of claim 134, wherein the quantity analysis is weighing each partition of the plurality of partitions to determine the indication of quantity of target molecule within each partition.

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