US20130304390A1 - Systems and Methods for the Analysis of Proximity Binding Assay Data - Google Patents

Systems and Methods for the Analysis of Proximity Binding Assay Data Download PDF

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US20130304390A1
US20130304390A1 US13/885,995 US201113885995A US2013304390A1 US 20130304390 A1 US20130304390 A1 US 20130304390A1 US 201113885995 A US201113885995 A US 201113885995A US 2013304390 A1 US2013304390 A1 US 2013304390A1
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sample data
values
background corrected
background
calibration
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Harrison Leong
Nivedita Sumi Majumdar
Elana E. Swartzman
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Life Technologies Corp
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    • G06F19/18—
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16B—BIOINFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR GENETIC OR PROTEIN-RELATED DATA PROCESSING IN COMPUTATIONAL MOLECULAR BIOLOGY
    • G16B20/00—ICT specially adapted for functional genomics or proteomics, e.g. genotype-phenotype associations
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16B—BIOINFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR GENETIC OR PROTEIN-RELATED DATA PROCESSING IN COMPUTATIONAL MOLECULAR BIOLOGY
    • G16B40/00—ICT specially adapted for biostatistics; ICT specially adapted for bioinformatics-related machine learning or data mining, e.g. knowledge discovery or pattern finding

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  • the present disclosure generally relates to methods for analyzing proximity binding assay (PBA) data to overcome the shortcomings of traditional methods for quantification using the analysis of amplification data for oligonucleotides.
  • PBA proximity binding assay
  • the sensitive quantitation of a biomolecule at low levels in a sample is highly desirable for several applications.
  • sensitive quantification is useful to monitor the dynamic expression levels of an intact, post-translationally modified protein in a particular cell or tissue sample or samples.
  • the amount of sample of interest for example, the number of cells or mass of tissue, may be very small. Additionally, the number of copies of the target protein of interest may be very low. In such cases, an assay for the presence of a protein in sub-femtomole concentrations may be needed.
  • proximity binding assays as a class of analyses offer the advantages of the sensitivity and specificity of biorecognition binding, along with the exponential signal amplification offered by a variety of oligonucleotide amplification reactions, such as the polymerase chain reaction (PCR).
  • PCR polymerase chain reaction
  • a system, method, and computer-readable medium for analyzing proximity binding assay data using calibration data. Analyzing the proximity binding assay data includes calculating a target protein quantity from this data.
  • the system includes a thermal cycler instrument and a processor in communication with the thermal cycler instrument.
  • the method includes steps that use a thermal cycler instrument and a processor.
  • a non-transitory and tangible computer-readable storage medium is encoded with instructions that are executed on a processor.
  • the instructions executed on the processor perform a method for analyzing proximity binding assay data.
  • the method includes providing a system of distinct software modules that includes a measurement module and an analysis module.
  • a thermal cycler instrument performs a proximity binding assay on at least one test sample, at least one reference sample, a background sample, and one or more calibration samples.
  • the thermal cycler instrument generates proximity binding assay data.
  • This proximity binding assay data includes at least one set of test sample data, at least one set of reference sample data, a background sample data set, and one or more sets of calibration sample data.
  • a processor receives this data from the thermal cycler instrument. In the computer program product, the processor receives this data using the measurement module.
  • the processor is configured to perform a number of steps.
  • the processor determines cycle threshold (Ct) values for at least one set of test sample data and at least one set of reference sample data. These may include successive dilutions of the sample.
  • the processor calculates background corrected Ct values for each value in the test sample data set and the reference sample data set using a value in the background sample.
  • the processor determines a linear range for the background corrected Ct values as a function of sample dilution.
  • the processor calculates a linear regression line for each linear range that is determined.
  • the processor estimates one or more parameter values of an exponential model (EM) fold change formula from the one or more sets of calibration sample data.
  • EM exponential model
  • the processor further detects and removes outlier Ct values before determining the linear range for the background corrected Ct values.
  • the processor determines the linear range for the background corrected Ct values by calculating a weighted sum.
  • the weighted sum is a sum of the normalized slope, the normalized linearity, and the normalized position for a plurality of the background corrected Ct values.
  • the processor then ranks the plurality of the background corrected Ct values based on the calculated weighted sum.
  • the processor determines the linear range by extending a line in two directions from a background corrected Ct value with the highest ranked weighted sum until a threshold is reached in each direction.
  • the processor further calculates a confidence interval for the target protein quantity.
  • FIG. 1 is a flow chart that depicts various embodiments of methods for the analysis of proximity binding assay (PBA) data.
  • PBA proximity binding assay
  • FIG. 2A-FIG . 2 C depict various embodiments of a proximity binding assay.
  • FIG. 3 depicts an exemplary apparatus for generating PBA data according to various embodiments described herein.
  • FIG. 4 is an exemplary block diagram that illustrates a computer system according to various embodiments upon which embodiments of methods for the analysis of PBA data may be implemented.
  • FIG. 5 depicts exemplary graphs of Ct values as a function of log of quantity of test sample for an exemplary proximity binding assay according to various embodiments described herein.
  • FIG. 6 depicts the exemplary graphs of FIG. 5 that have been corrected for background according to various embodiments of methods for the analysis of PBA data.
  • FIG. 7 depicts exemplary graphs of Ct values including detected outliers according to various embodiments for detecting outliers.
  • FIG. 8 depicts exemplary graphs of Ct values as a function of log of quantity that are assessed to determine a linear range.
  • FIG. 9 depicts the intersection of exemplary regression lines of two samples with background corrected Ct values according to various embodiments for calculating confidence intervals.
  • FIG. 10 depicts an exemplary system for analyzing PBA data according to various embodiments.
  • FIG. 11 depicts a flowchart showing a method for analyzing PBA data according to various embodiments.
  • FIG. 12 depicts a system of software modules for performing a method for analyzing PBA data according to various embodiments.
  • FIGS. 13A-13D illustrate a method for determining a linear range for the background corrected Ct values of a method for analyzing PBA data, according to various embodiments.
  • proximity binding assays offer the advantages of the sensitivity and specificity of biorecognition binding, along with the exponential signal amplification offered by a variety of oligonucleotide amplification reactions.
  • Amplification reactions may be, but are not limited to, polymerase chain reaction (PCR).
  • PCR polymerase chain reaction
  • the class of proximity binding assays has reaction kinetics governed by an additional step of the binding of a biorecognition probe (BRP) with a target molecule, as will be discussed in more detail subsequently.
  • BRP biorecognition probe
  • various embodiments of proximity binding assays may require methods for the analysis of PBA data that are particularly suited to the unique characteristics of such data.
  • proximity binding assays may be characterized by a biorecognition binding event, as depicted in FIG. 2A , in which a biorecognition probe (BRP) binds to a target biomolecule.
  • BRP biorecognition probe
  • examples of biorecognition binding may include, but are not limited by oligonucleotide-oligonucleotide, protein-protein, ligand-receptor, antigen-antibody, lectin-polysaccharide, aptamer-protein, enzyme-substrate, and cofactor-protein.
  • a BRP may enable signal amplification in order to provide for the detection of the target molecule.
  • BRPs may be prepared so that strands in proximity to one another after the binding of the BRPs to a target are of opposite orientation.
  • BRPs as shown in FIG. 2B , one population of BRP may have 3′ strands of an oligonucleotide sequence coupled to it, while a second population of BRP may have 5′ strands of an oligonucleotide sequences coupled to it, so that the strands in proximity to one another after binding are of the same orientation.
  • a PBA as shown in FIG.
  • the BRPs may be designed so that at least the free distal end sequences are complementary, so that the binding of complementary sequences produces a target for extension, as shown in FIG. 2C .
  • the proximal 3′ and 5′ ends may be ligated, as shown in FIG. 2D , forming a target for ligation.
  • sequence detection data may be generated.
  • Other methods for detecting oligonucleotides brought into proximity for various embodiments of proximity binding assays include, for example, but not limited by, restriction digestion, and polymerase extension.
  • the term “amplifying”, “amplification” and related terms may refer to any process that increases the amount of a desired nucleic acid.
  • Any of a variety of known amplification procedures may be employed in the present teachings, including PCR (see for example U.S. Pat. No. 4,683,202), as well as any of a variety of ligation-mediated approaches, including LDR and LCR (see for example U.S. Pat. No. 5,494,810, U.S. Pat. No. 5,830,711, U.S. Pat. No. 6,054,564).
  • Some other amplification procedures include isothermal approaches such as rolling circle amplification and helicase-dependant amplification.
  • the amplification may comprise a PCR comprising a real-time detection, using for example a labeling probe.
  • labeling probe generally, according to various embodiments, refers to a molecule used in an amplification reaction, typically for quantitiative or real-time PCR analysis, as well as end-point analysis. Such labeling probes may be used to monitor the amplification of the target polynucleotide.
  • oligonucleotide probes present in an amplification reaction are suitable for monitoring the amount of amplicon(s) produced as a function of time.
  • Such oligonucleotide probes include, but are not limited to, the 5′-exonuclease assay TaqMan® probes described herein (see also U.S. Pat. No.
  • peptide nucleic acid (PNA) light-up probes self-assembled nanoparticle probes
  • ferrocene-modified probes described, for example, in U.S. Pat. No. 6,485,901; Mhlanga et al., 2001, Methods 25:463-471; Whitcombe et al., 1999, Nature Biotechnology. 17:804-807; Isacsson et al., 2000, Molecular Cell Probes. 14:321-328; Svanvik et al., 2000, Anal Biochem.
  • Labeling probes can also comprise black hole quenchers (Biosearch), Iowa Black (IDT), QSY quencher (Molecular Probes), and Dabsyl and Dabcel sulfonate/carboxylate Quenchers (Epoch).
  • Labeling probes can also comprise two probes, wherein for example a fluorophore is on one probe, and a quencher on the other, wherein hybridization of the two probes together on a target quenches the signal, or wherein hybridization on target alters the signal signature via a change in fluorescence.
  • Labeling probes can also comprise sulfonate derivatives of fluorescenin dyes with a sulfonic acid group instead of the carboxylate group, phosphoramidite forms of fluorescein, phosphoramidite forms of CY 5 (available for example from Amersham).
  • intercalating labels are used such as ethidium bromide, SYBR® Green I (Molecular Probes), and PicoGreen® (Molecular Probes), thereby allowing visualization in real-time, or end point, of an amplification product in the absence of a labeling probe.
  • the target may be a protein.
  • a BRP may be directed to a polypeptide primary, secondary, or tertiary structure, such as an aptamer or antibody, or may be directed to a group such as any of a variety of chemical resulting from the in vivo or in vitro modification of a polypeptide structure.
  • a thermal cycling instrument may include a heated cover 314 that is placed over a plurality of samples 316 contained in a sample support device.
  • a sample support device may be a glass, plastic, composite, metal, or any other suitable substrate material having a plurality of sample regions, which sample regions may have a cover between the sample regions and heated cover 314 .
  • Some examples of a sample support device may include, but are not limited by, sample tubes or vials, a multi-well plate, such as a standard microtiter plate (i.e.
  • a thermal cycler instrument 300 may include a thermal block assembly, which may include a sample block 318 , as well as elements for heating and cooling 320 , and a heat exchanger 322 .
  • thermocycler instrument may include temperature blocks which may be at the same or different temperatures and wherein a capillary, tube, channel, or other conduit may be located in the thermocycler, so that a sample may flow through the different temperature blocks as opposed to remaining stationary.
  • a thermal cycling system 300 may have a detection system.
  • a detection system may have an illumination source that emits electromagnetic energy (not shown), a detector or imager 310 , for receiving electromagnetic energy from samples 316 in sample support device, and optics 312 , which may be located between the illumination source and detector or imager 310 .
  • a control system 324 may be used to control, for example, but not limited by, the functions of the detection, heated cover, and thermal block assembly.
  • the control system 324 may be accessible to an end user through user interface 326 of a thermal cycler instrument 300 .
  • a computer system 500 as depicted in FIG.
  • computer system 500 may serve as to provide control of various functions of a thermal cycler instrument. Additionally, computer system 500 may provide data processing, display and report preparation functions. All such instrument control functions may be dedicated locally to the thermal cycler instrument, or computer system 500 may provide remote control of part or all of the control, analysis, and reporting functions, as will be discussed in more detail subsequently.
  • FIG. 4 is a block diagram that illustrates a computer system 500 that may be employed to carry out processing functionality, according to various embodiments, upon which embodiments of a thermal cycler system 300 of FIG. 3 may utilize.
  • Computing system 500 can include one or more processors, such as a processor 504 .
  • processor 504 can be implemented using a general or special purpose processing engine such as, for example, a microprocessor, controller or other control logic.
  • processor 504 is connected to a bus 502 or other communication medium.
  • a computing system 500 of FIG. 4 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, hand-held 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.
  • a computing system 500 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.
  • client/server environments, database servers, and networks are well documented in the art.
  • Computing system 500 may include bus 502 or other communication mechanism for communicating information, and processor 504 coupled with bus 502 for processing information.
  • Computing system 500 also includes a memory 506 , which can be a random access memory (RAM) or other dynamic memory, coupled to bus 502 for storing instructions to be executed by processor 504 .
  • Memory 506 also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor 504 .
  • Computing system 500 further includes a read only memory (ROM) 508 or other static storage device coupled to bus 502 for storing static information and instructions for processor 504 .
  • ROM read only memory
  • Computing system 500 may also include a storage device 510 , such as a magnetic disk, optical disk, or solid state drive (SSD) is provided and coupled to bus 502 for storing information and instructions.
  • Storage device 510 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, an optical disk drive, a CD or DVD drive (R or RW), flash drive, or other removable or fixed media drive.
  • the storage media may include a computer-readable storage medium having stored therein particular computer software, instructions, or data.
  • storage device 510 may include other similar instrumentalities for allowing computer programs or other instructions or data to be loaded into computing system 500 .
  • 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 510 to computing system 500 .
  • Computing system 500 can also include a communications interface 518 .
  • Communications interface 518 can be used to allow software and data to be transferred between computing system 500 and external devices.
  • Examples of communications interface 518 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 PCMCIA slot and card, Bluetooth, etc.
  • Software and data transferred via communications interface 518 are in the form of signals which can be electronic, electromagnetic, optical or other signals capable of being received by communications interface 518 . These signals may be transmitted and received by communications interface 518 via a channel such as a wireless medium, wire or cable, fiber optics, or other 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.
  • Computing system 500 may be coupled via bus 502 to a display 512 , such as a cathode ray tube (CRT) or liquid crystal display (LCD), for displaying information to a computer user.
  • a display 512 such as a cathode ray tube (CRT) or liquid crystal display (LCD)
  • An input device 514 is coupled to bus 502 for communicating information and command selections to processor 504 , for example.
  • An input device may also be a display, such as an LCD display, configured with touchscreen input capabilities.
  • cursor control 516 is Another type of user input device, such as a mouse, a trackball or cursor direction keys for communicating direction information and command selections to processor 504 and for controlling cursor movement on display 512 .
  • 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 500 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 500 in response to processor 504 executing one or more sequences of one or more instructions contained in memory 506 . Such instructions may be read into memory 506 from another computer-readable medium, such as storage device 510 . Execution of the sequences of instructions contained in memory 506 causes processor 504 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.
  • Non-volatile media includes, for example, solid state, optical or magnetic disks, such as storage device 510 .
  • Volatile media includes dynamic memory, such as memory 506 .
  • Transmission media includes coaxial cables, copper wire, and fiber optics, including the wires that comprise bus 502 .
  • 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 chip or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can read.
  • Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 504 for execution.
  • 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 500 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 502 can receive the data carried in the infra-red signal and place the data on bus 502 .
  • Bus 502 carries the data to memory 506 , from which processor 504 retrieves and executes the instructions.
  • the instructions received by memory 506 may optionally be stored on storage device 510 either before or after execution by processor 504 .
  • test, reference and non-protein control (NPC) samples may be run, and the data may be collected and analyzed using computer system 500 .
  • NPC non-protein control
  • an end user may wish to assess the up or down regulation of a protein or proteins in a cell line.
  • test samples of a cell line subjected to various conditions may be run.
  • the determination may be relative quantitation (RQ), in which a reference may be a cell line control that has a target protein or proteins in a defined state.
  • RQ relative quantitation
  • the determination may be absolute quantification, in which a reference is a set of samples for which target proteins are of a known quantity.
  • binding may be influenced by variables in a reaction matrix.
  • antigen-antibody binding is known to be influenced by such matrix effects.
  • an NPC may be run, in which a target molecule is absent, and the control is designed to compensate for background and matrix effects.
  • the protocols for generating data for test, reference, and NPC samples are not constrained with respect to the manner in which the data may be generated.
  • samples as indicated in step 105 of method 100 may be run in the same run on the same instrument on the same day, while for other embodiments of method 100 , test, reference, and NPC samples may be run on different days and/or on different instruments.
  • the determination of threshold cycle or Ct values for all samples at all input quantities may be done.
  • the Ct is the cycle number for an oligonucleotide amplification reaction at which the fluorescence generated for a sample exceeds a defined threshold.
  • the threshold cycle is defined as the cycle number of an oligonucleotide amplification reaction at which a sufficient number of amplicons have accumulated to provide for analytical detection above noise.
  • a variety of approaches may be taken to determine a Ct value.
  • U.S. Pat. No. 7,228,237 to Woo et al discloses various embodiments for automatic threshold setting for oligonucleotide amplification reactions, and is incorporated herein by reference in its entirety.
  • a plot of the Ct values as a function of sample quantity for PBA data generated for the analysis of the protein OCT3/4 in a NTERA-2 cell line is shown.
  • a sample quantity may be, for example but not limited by, the number of cells or the concentration of a biomolecule.
  • each point represents a serial dilution of an NTERA-2 cell sample taken for analysis.
  • a proximity binding assay is an assay in which oligonucleotide-labeled BRP is a monoclonal or polyclonal antibody. This is shown in FIG. 2 .
  • the exemplary PBA data shown in FIG. 2 was generated with an embodiment of a proximity binding assay utilizing an antibody-based BRP and qPCR analysis using TAQMAN® PCR reagents
  • the average Ct value for the NPC samples or background samples associated with a particular set of samples may be subtracted from the average Ct values for each data point in the dilution series for each sample.
  • An example of the background corrected Ct (bcCt) or delta Ct ( ⁇ Ct) values for each data point for each curve for the OCT3/4 protein in the NTERA-2 cells is shown in FIG. 6 .
  • the graphs for the data presented are normally of parallel orientation for the linear phase of an amplification reaction. As can be seen in FIG.
  • the PBA data for this exemplary analysis of OCT3/4 in NTERA cells is atypical of such amplification data, since the linear phases of the curves are not parallel.
  • various embodiments of analysis of PBA data specifically address the atypical nature of data generated for such analyses.
  • a data point is flagged as an outlier if it deviates from its replicate group median by more than N standard deviations.
  • N is specified by a user and a standard deviation may be estimated using data for one dilution or across all dilutions, for example.
  • N is set through an outlier sensitivity control. Outlier detection is applied to each replicate group of bcCt values.
  • Additional outlier detection methods may be applied, for example, for cases where there are replicate data points above and below a bcCt threshold (0.5 for example), the points in the minority (either the points above or the points below the threshold) are considered outliers if they differ from the median of the majority group by more than N standard deviations. The standard deviation is based on the majority groups (each dilution has a majority group but may not have a minority group). If there is a tie, for example, no outlier is called.
  • An example of outlier detection using this additional detection method applied to a group of bcCt values is shown in plot 700 of FIG. 7 . Data points 710 are detected as outliers in plot 700 .
  • the linear range of the relationship between the bcCt values and the input quantity is determined for all samples except NPC.
  • the underlying structure of the PBA data is roughly a sigmoid function rising from left to right in a bcCt vs. log(input quantity) plot, where input quantity increases from left to right.
  • One goal is to determine the maximum and minimum log(input quantity) values (x values) such that, between these x values, there is a linear relationship between bcCt and log(input quantity). All points with the same x value are considered to be in a replicate group.
  • the linear range of the relationship between the bcCt values and the log(input quantity) is determined by assessing each data point or each group of data points based on slope, linearity, and position.
  • bcCt values 810 - 860 are plotted as a function of log (input quantity).
  • bcCt values 820 and 830 are chosen over 840 and 850 for the linear range, for example.
  • bcCt values 810 - 860 are median bcCt values calculated at each input quantity where data is available. Not all median bcCt values may be assessed for the linear range. For example, only median bcCt values above a criterion threshold may be assessed.
  • An exemplary criterion threshold can include, but is not limited to, the noise level or a level below which a thermal cycler instrument cannot record a Ct value. Assuming bcCt values 810 - 860 are above the criterion threshold, each value is assigned a measure of slope, linearity, and position. The slope for each value is calculated for a line extended to one or more adjacent values, for example.
  • the linearity for each value is calculated by fitting a line to the value and two or more adjacent values, for example.
  • the position for each value is the x position, for example.
  • the measures of slope, linearity, and position for each value are normalized across the data set. In other words, the slope for each value is divided by the maximum slope found for any value, and the linearity for each value is divided by the maximum linearity found for any value.
  • the normalized position is, for example, calculated as the difference between the maximum x position of any value and the position of the value divided by the difference between the maximum x position of any value and the minimum x position of any value.
  • a weighted sum of the normalized slope, the normalized linearity, and the normalized position are calculated for bcCt values 810 - 860 .
  • a weighted sum can also be calculated for a group of two or more bcCt values. The weighted sum is calculated according to the following equation, for example:
  • W2 and W1 are chosen, for example, to heavily weight slope, moderately weight linearity, and lightly weight position. Heavily weighting the slope and moderately weighting the linearity is designed to capture the rising phase of a sigmoid function while avoiding the early and late plateau regions and the curved portions. Lightly weighting the position is designed to capture a rising phase of the sigmoid function at a lower x value if there are multiple rising phases.
  • bcCt values 810 - 860 are placed in rank order.
  • a linear range is found by attempting to extend a line from the bcCt value of highest rank.
  • adjacent bcCt values are evaluated by computing the angle sub tended by the new candidate point and the closest two points of the linear range, for example. If the sub tended angle is within a threshold value close to 180°, then the linear range is extended in that direction. If the sub tended angle is not within a threshold value close to 180°, then the end of the linear range in that direction is found.
  • a distinguishing characteristic of a proximity binding assay is that, in general, log-linear segments of dilution series curves for samples with different amounts of the target protein are not parallel.
  • FIG. 6 shows an example of this for target protein OCT3/4 protein in the NTERA-2 cells.
  • the per-cell protein content is known to decrease with time as the cells differentiate into neurons in response to incubation with trans-retinoic acid. If the generation of ligation product (LP) were only dependent on the starting quantity of the target protein, the log-linear regions of these curves would be parallel.
  • LP ligation product
  • a mathematical description of the proximity binding assay must account for two processes: 1) The formation of LP and 2) the PCR amplification of LP.
  • the governing equation for TaqManTM monitored PCR is given by:
  • c init,LP initial concentration of ligation product prior to PCR
  • E LP PCR efficiency of the ligation product
  • log-linear regression lines are calculated for all linear ranges of bcCt values versus input quantity.
  • the linear regression lines are calculated to determine the slope and y intercept values for bcCt values versus input quantity used in equation 3.
  • a calibration method is performed to estimate values for the pure LP intercepts.
  • a direct approach can be used to estimate the pure LP intercepts.
  • linear regression lines are calculated from data collected from a dilution series of LP made from a standard solution of LP. This requires developing and adding the standard solution of LP to the proximity binding assay.
  • a dilution series of LP is not needed if it is known that the LP concentration of the standard solution is 1 or it is assumed that the slope of the LP dilution series Ct versus LP concentration curve is known (approximately ⁇ 3.32 for 100% PCR efficiency).
  • the y intercept values for log-linear regression lines of Ct values versus concentration of ligation product is determined as the Ct value at the ligation product concentration of 1.
  • a quantitative result is calculated using the EM fold change of equation 3 after it has been calibrated using calibration samples.
  • the values for variables 4 and 5 are calculated directly.
  • a relative target protein quantity is then calculated for two cell types using equation 3, the EM fold change.
  • An absolute quantity is calculated if the absolute quantity of the reference sample is known.
  • an indirect approach can also be used to estimate the variables of the EM fold change.
  • An indirect approach can provide an estimate using the proximity binding assay as described if there are a pair of calibration samples for which the relative protein quantity is a known value, f, and the log-linear regions of the pair are not parallel. If it is assumed that all concentration-independent variability between samples other than that caused by differences in target protein quantity can be accounted for by the C T values at zero cell input, i.e., a constant offset accounts for this variability, since variables (4) and (5) are simply constant offsets for the LP dilution series, it follows that
  • the EM threshold can be calculated using equation 7.
  • the EM threshold can be used to find the relative quantity for any pair of reference and test samples. Substituting the relationships in equations 6 and 7 back into equation 3 yields the following formula for relative target protein quantity parameterized by the EM threshold:
  • an estimate of absolute or relative protein quantity is calculated using the theoretical model of equation 8, for example, after the indirect calibration method, described above, is used to determine the value for the EM threshold of equation 7, for example.
  • a confidence interval is estimated for the result found in step 160 .
  • the result found in step 160 is calculated, for example, using equation 3 or equation 8.
  • the calibration samples used in conjunction with equation 3 or equation 8 are assumed to be statistically independent of the reference and test samples for which a quantitative result is sought.
  • a confidence interval is found by assuming that estimates of the parameters of equation 3 or 8 are normally distributed. It is assumed that input data are normally distributed about the linear regression lines with the same variability for all dilutions.
  • Equations 11 and 12 can be rewritten as
  • Regression lines 910 for a first sample and regression lines 920 for a second sample are shown plotted in plot 900 of FIG. 9 . Their respective confidence interval boundaries are 911 and 912 for the first sample and 921 and 922 for the second sample.
  • the EM threshold is shown as the horizontal line 930 and its confidence interval as line 940 and line 950 .
  • FIG. 1 illustrates which pair of points to pick to minimize or maximize equation 14 while remaining within the confidence regions for sample 1, sample 2, and the EM threshold. For example, in the figure
  • x c - M EM th - B ⁇ A ⁇ ( 19 ) x c ⁇ ⁇ 2 - L , x c ⁇ ⁇ 2 - H , x c ⁇ ⁇ 1 - L , and ⁇ ⁇ x c ⁇ ⁇ 1 - H ( 20 )
  • FIG. 10 shows a system 1000 for analyzing PBA data, in accordance with various embodiments.
  • System 1000 includes thermal cycler instrument 1010 and computing system 1020 .
  • Thermal cycler instrument 1010 and computing system 1020 may each comprise the exemplary computing system illustrated in FIG. 4 , in various embodiments.
  • thermal cycler instrument 1010 may include a processor to perform the methods according to various embodiments described herein.
  • Thermal cycler instrument 1010 performs a proximity binding assay on at least one test sample, at least one reference sample, a background sample, and one or more calibration samples.
  • Thermal cycler instrument 1010 generates at least one set of test sample data, at least one set of reference sample data, a background sample data set, and one or more sets of calibration sample data.
  • Computing system 1020 is in communication with thermal cycler instrument 1010 in some embodiments.
  • Computing system 1020 receives from thermal cycler instrument 1010 the at least one set of test sample data, the at least one set of reference sample data, the background sample data set, and the one or more sets of calibration sample data.
  • Computing system 1020 determines Ct values for the at least one set of test sample data and the at least one set of reference sample data.
  • Computing system 1020 calculates background corrected Ct values for each value in the test sample data set and the reference sample data set using a corresponding value in a background sample data set.
  • Computing system 1020 determines a linear range for the background corrected Ct values as a function of sample quantity for each set of test sample data and reference sample data.
  • Computing system 1020 calculates a linear regression line for each linear range that is determined. Computing system 1020 estimates one or more parameter values of an exponential model (EM) fold change formula from the one or more sets of calibration sample data. Finally, computing system 1020 calculates a target protein quantity and a confidence interval for this quantity using the linear regression lines calculated for the test sample data and the reference sample data and the one or more estimated parameter values of the EM fold change formula estimated from the one or more sets of calibration sample data.
  • EM exponential model
  • computing system 1020 further detects and removes outlier Ct values before determining a linear range for the background corrected Ct values.
  • Computing system 1020 detects outlier Ct values by determining if a background corrected Ct value deviates from its replicate group median by more than a number of dilution-series standard deviations.
  • the standard deviation is calculated based on a majority of background corrected Ct values in a replicate group above or below a threshold.
  • a minority of background corrected Ct values in the replicate group are considered outliers if the minority of background corrected Ct values differ from the median of the majority of background corrected Ct values by more than a specified number of standard deviations.
  • computing system 1020 determines the linear range for the background corrected Ct values by performing three steps.
  • step 1 a weighted sum of the normalized slope, the normalized linearity, and the normalized position is calculated each of a plurality of the background corrected Ct values.
  • step 2 the plurality of the background corrected Ct values are ranked based on the calculated weighted sum.
  • step 3 a linear range is extended in two directions from a background corrected Ct value with the highest ranked weighted sum until a threshold is reached in each direction.
  • the one or more sets of calibration sample data are generated from a standard solution of ligation product (LP).
  • the one or more parameter values estimated for the EM fold change formula include one or more pure LP intercepts.
  • the one or more sets of calibration sample data are generated from at least a pair of calibration samples for which the relative protein quantity is known.
  • the one or more parameter values estimated for the EM fold change formula include an EM threshold.
  • computing system 1020 further calculates a confidence interval for the target protein quantity.
  • computing system 1020 may be performed, in various embodiments, by computing system 500 ( FIG. 4 ) included in thermal cycler instrument 1010 .
  • FIG. 11 depicts a flowchart showing a method 1100 for analyzing PBA data, in accordance with various embodiments.
  • a proximity binding assay is performed on at least one test sample, at least one reference sample, at least one background sample, and at least one calibration sample using a thermal cycler instrument.
  • At least one set of test sample data set, reference sample data set, background sample data set, and calibration sample data set are generated using a thermal cycler instrument.
  • PBA data is received for a plurality of samples from the thermal cycler instrument using processor 504 ( FIG. 4 ).
  • the PBA data includes the at least one set of test sample data, the at least one set of reference sample data, the background sample data set, and the one or more sets of calibration sample data, for example.
  • step 1130 Ct values are determined for the at least one set of test sample data, the at least one set of reference sample data, and the at least one set of calibration data using processor 504 .
  • step 1140 background corrected Ct values are calculated for each value in the test sample data set, the reference sample data set using a corresponding value in a background sample data set using processor 504 .
  • Background corrected Ct values are calculated for each value in the calibration sample data set using a corresponding value in a background sample data set using processor 504 if the indirect approach is used for calibration.
  • a linear range is determined for the background corrected Ct values as a function of sample quantity for each set of test sample data and reference sample data using processor 504 .
  • a linear range is determined for the background corrected Ct values as a function of sample quantity for each set of calibration sample data using processor 504 if the indirect approach is used for calibration.
  • step 1160 a linear regression line is calculated for each linear range that is determined using processor 504 .
  • step 1170 one or more parameter values of an exponential model (EM) fold change formula are estimated from the one or more sets of calibration sample data using processor 504 .
  • EM exponential model
  • a target protein quantity is calculated using the linear regression lines calculated for the test sample data and the reference sample data and the one or more parameter values of the EM fold change formula estimated from the one or more sets of calibration sample data using processor 504 .
  • a computer program product includes a non-transitory and tangible computer-readable storage medium encoded with a program with instructions being executed on a processor so as to perform a method for analyzing PBA data. This method may be performed by a system that may include one or more distinct software modules in some embodiments.
  • FIG. 12 shows a system 1200 distinct software modules for analyzing PBA data, in accordance with various embodiments.
  • System 1200 includes measurement module 1210 and analysis module 1220 .
  • Measurement module 1210 receives PBA data for a plurality of samples from a thermal cycler instrument.
  • the PBA data includes at least one set of test sample data, at least one set of reference sample data, at least one background sample data point, and at least one set of calibration sample data.
  • Analysis module 1220 determines cycle threshold (Ct) values for the at least one set of test sample data and the at least one set of reference sample data. Analysis module 1220 calculates background corrected Ct values for each value in the test sample data set and the reference sample data set using a corresponding value in a background sample data set. Analysis module 1220 determines a linear range for the background corrected Ct values as a function of sample quantity for each set of test sample data, and reference sample data. Analysis module 1220 calculates a linear regression line for each linear range that is determined. Analysis module 1220 estimates one or more parameter values of an exponential model (EM) fold change formula from the one or more sets of calibration sample data. Analysis module 1220 calculates a target protein quantity using the linear regression lines calculated for the test sample data and the reference sample data and the one or more parameter values of the EM fold change formula for which parameter values have been estimated from the one or more sets of calibration sample data.
  • Ct cycle threshold
  • One method of calibration requires two or more samples for which the relative amount of target protein between the samples is known. In the absence of such samples, an example method to construct an approximation of such samples is to mix samples that are positive and negative for the target protein to form various ratios. For example, for a stem cell protein such as Lin28, Ntera2 cells, known to contain Lin28, can be mixed with Raji cells, known to be devoid of Lin28.
  • EM threshold can be generated from each possible pair of known samples.
  • An “optimal” EM threshold can be determined by taking, for example, the mean of these estimates. Other alternatives can be, for example, the median, a trimmed mean (after excluding highest and lowest values), a trimmed median, etc.
  • FIGS. 13A-13D illustrate a method for determining a linear range for the background corrected Ct values of a method for analyzing PBA data, according to various embodiments.
  • the results of a previous method, described in WO 2011/017567, entitled “Methods for the Analysis of Proximity Binding Assay Data,” filed on Aug. 5, 2010 and incorporated herein by reference, for determining a linear range are compared to the results of the method described herein.
  • FIGS. 13A & 13C show the results obtained from the method described herein.
  • FIGS. 13B & 13D show the results obtained from the previous method.
  • the linear range is shown as the portion of the line between the two vertical lines.
  • the method described herein can be used to capture early linear region that is part of the transition from the baseline level to the plateau portion of the sigmoid dilution series curve.
  • Table 1 shows improved performance between the fold change estimation between the previous method and the method described herein based on a theoretical model.
  • the previous method (described in WO 2011/017567) bases a threshold parameter, the quantification threshold (QT), on noise levels and recommends setting it to 2.
  • QT quantification threshold
  • the present method based on the theoretical model suggests a means to determine QT by performing calibration experiments.

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