Classifications

• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F18/00—Pattern recognition
• • C—CHEMISTRY; METALLURGY
  • C12—BIOCHEMISTRY; BEER; SPIRITS; WINE; VINEGAR; MICROBIOLOGY; ENZYMOLOGY; MUTATION OR GENETIC ENGINEERING
  • C12Q—MEASURING OR TESTING PROCESSES INVOLVING ENZYMES, NUCLEIC ACIDS OR MICROORGANISMS; COMPOSITIONS OR TEST PAPERS THEREFOR; PROCESSES OF PREPARING SUCH COMPOSITIONS; CONDITION-RESPONSIVE CONTROL IN MICROBIOLOGICAL OR ENZYMOLOGICAL PROCESSES
  • C12Q1/00—Measuring or testing processes involving enzymes, nucleic acids or microorganisms; Compositions therefor; Processes of preparing such compositions
  • C12Q1/68—Measuring or testing processes involving enzymes, nucleic acids or microorganisms; Compositions therefor; Processes of preparing such compositions involving nucleic acids
  • C12Q1/6844—Nucleic acid amplification reactions
  • C12Q1/6851—Quantitative amplification
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
  • G06F2218/08—Feature extraction
  • G06F2218/10—Feature extraction by analysing the shape of a waveform, e.g. extracting parameters relating to peaks

Definitions

• the present invention relates generally to data processing systems and methods, and more particularly to systems and methods for identifying statistically linear data in a data set of an amplification process, such as polymerase chain reaction (PCR).
• PCR polymerase chain reaction
• the quantity may correspond to the number of parts of a DNA strand that have been replicated, which dramatically increases during an amplification stage or region.
• Other experimental processes exhibiting amplification include bacterial growth processes.
• the quantity is detected from an experimental device via a data signal, whose data points are analyzed to determine information about the amplification. As part of the data analysis, it is important to know if amplification has potentially occurred; otherwise, effort might be wasted on analyzing non-amplifying data. If the data is statistically linear, then amplification has not occurred.
• the data from the amplification detection device would be a monotonic and continuous signal, thus one could easily identify whether the data, or portions thereof, has statistically linear behavior.
• the signal from the amplification device typically contains noise, thus making identifying a behavior of the signal difficult.
• the noise manifests itself in each data point in the signal from the device having random fluctuations that occur on top of the true signal, e.g. the actual number of DNA strands.
• the data requires processing to allow for identifying of linear behavior.
• a typical prior method for processing data to determine if it is statistically linear is with a linear least squares (LSQ) fit.
• the correlation value of the LSQ fit can be used to determine whether there is an adequate fit.
• a correlation value of 0 is related to a bad fit, thus the data is not linear, and a value of 1 suggests a good fit for linearity.
• the problem is that in the presence of noise, the correlation value can be close to 0 or 1 for data that looks statistically linear. Additionally, the correlation value does not correspond to a physical value that may provide additional insight and efficacy. Thus, the correlation value is not an acceptable criterion, particularly for data that can be extremely noisy.
• embodiments of the present invention provide methods and systems directed to processing data to determine whether the data exhibits statistically linear behavior.
• Statistically linear data means that the data generally does not curve downward or upward or otherwise display amplification. Such data typically appears to be roughly linear with a large noise signal superposed upon it.
• the data may be received from real-time PCR processes or other processes exhibiting amplification or growth.
• a method of processing data typically includes receiving an original set of data points having a signal component and a noise component.
• the original data set is fit to a linear function.
• the fit is accomplished by calculating a linear least squares fit to the data set.
• the method also includes calculating a residual between the original data set and the linear fit, and calculating a measure of the residual between the original data set and the linear fit.
• the measure is a standard deviation.
• the method also typically includes estimating the noise component present in the data set by calculating a smoothed data set and calculating the residual between the smoothed data set and the original data set.
• a smoothed data point is based on values of original data points that are local to that smoothed data point.
• a low pass filter is used to calculate the smoothed data set.
• Exemplary low pass filters include a Savitzy-Golay filter, a digital filter, or digital smoothing polynomial filter.
• a value of a smoothed data point is an average of original data points within a window around the smoothed data point.
• the method also typically includes calculating a measure of the residual of the estimated noise, and comparing the measures to determine whether the original data set exhibits statistically linear behavior.
• the comparing may include calculating a ratio of the first and second measure to determine if the ratio is smaller or greater than a pre defined value.
• the pre-defined value is of order 1.
• the method is implemented in a processor, such as a processor in a stand-alone computer, a network attached computer or a data acquisition device such as a real-time PCR machine.
• a processor such as a processor in a stand-alone computer, a network attached computer or a data acquisition device such as a real-time PCR machine.
• a real-time PCR machine is the iCycler iQ System provided by Bio-Rad Laboratories.
• an information storage medium having a plurality of instructions adapted to direct an information processing device to perform an operation of processing data to determine whether the curve exhibits linear behavior.
• the information storage medium is a RAM or ROM unit, hard drive, CD, DVD or other portable medium.
• a PCR detection system includes a detector for producing an original set of data points having a signal component and a noise component and includes logic for processing data to determine whether the data exhibits linear behavior.
• Figure 2 illustrates a real-time PCR data set exhibiting noise and statistically linear behavior.
• Figure 3 illustrates a real-time PCR data set exhibiting noise and amplification.
• Figure 4 illustrates a method of processing a data set to determine whether the data set exhibits statistically linear behavior according to an embodiment of the present invention.
• Figure 5A illustrates a linear fit to a data set exhibiting statistically linear behavior.
• Figure 5B illustrates a linear fit to a data set exhibiting amplifying behavior.
• Figure 6A illustrates a smoothed data set of real-time PCR data according to an embodiment of the present invention.
• Figure 6B illustrates an estimated noise of real-time PCR data according to an embodiment of the present invention.
• Figure 7 illustrates a system that processes real-time PCR data according to an embodiment of the present invention.
• the present invention provides techniques for processing a data set and identifying whether the data set is statistically linear, as well as distinguishing such a linear data set from a data set containing an amplification signal.
• the present invention is particularly useful for processing data from PCR growth or amplification processes to identify and remove statistically linear data prior to further analysis of the data. It should be appreciated, however, that the teachings of the present invention are applicable to processing any data set or curve that may include noise, and particularly curves that should otherwise exhibit growth or amplification such as a bacterial growth process.
• Figure 1 shows an example of a PCR curve 100, where intensity values 110 vs. cycle number 120 are plotted for a typical PCR process.
• the values 110 may be any physical quantity of interest, and the cycle number may be any unit associated with time or number of steps in the process.
• Such amplification curves typically have a linear region 130 followed by an amplification region 140 and then by an asymptotic region 150, as shown in FIG. 1. There also might be additional types of behavior such as downward curving data.
• An amplification region may have exponential, sigmoidal, high order polynomial, or other type of logistic function or logistic curve that models growth.
• amplification region 140 it is important to identify the position and shape of amplification region 140. For example, in a PCR process, it may be desirable to identify the onset of amplification, which occurs at the end of the baseline region (linear region 130). A step in identifying the location is to identify if a possible amplification region even exists, as a PCR process may not show any amplification. However, since realtime PCR data has noise, the identification of whether the data set might exhibit amplification, or equivalently that it is not statistically linear, can be difficult.
• Figure 2 illustrates a linear region 230 of a real-time PCR curve 200 made from a data set with data points 240 that include a signal and noise. Note that even for devices that produce a constant signal, this data must be broken into data points for analysis. The noise causes the fluctuations in the data points. Overall, the data is generally moving upward (i.e. positive slope) in a linear fashion. However, as curve 200 is very non-linear from point to point, the generally linear behavior cannot be determined by directly analyzing curve 200 at any one point along the curve. A direct analysis of curve 200 would falsely determine that the data does not exhibit statistically linear behavior. Embodiments of the present invention effectively determine whether data exhibits statistically linear behavior.
• Figure 3 illustrates a real-time PCR curve 300 that exhibits amplification. Initially, the data exhibits linear behavior in region 330 and in later cycles there is amplification in region 340. Embodiments of the present invention robustly and with, consistent accuracy differentiate between PCR curve 200 having only linear behavior and PCR curves possibly having an amplifying region, such as PCR curve 300.
• FIG. 4 illustrates a method 400 of processing data to determine whether the data exhibits statistically linear behavior according to an embodiment of the present invention.
• the data set is composed of data points and represents a curve having a signal component and a noise component.
• the data set is first collected or received.
• the data set may be received through many mechanisms.
• the data set may be acquired by a processor (executing instructions) resident in a PCR data acquiring device such as an iCycler iQ device or similar PCR analysis device.
• the data set may be provided to the processor in real time as the data is being collected, or it may be stored in a memory unit or buffer and provided to the processor after the experiment has been completed.
• the data set may be provided to a separate system such as a desktop computer system via a network connection (e.g., LAN, VPN, intranet, Internet, etc.) or direct connection (e.g., USB or other direct wired or wireless connection) to the acquiring device, or provided on a portable medium such as a CD, DVD, floppy disk or the like to a stand-alone computer system.
• a network connection e.g., LAN, VPN, intranet, Internet, etc.
• direct connection e.g., USB or other direct wired or wireless connection
• the data may be analyzed.
• a linear fit to the data set is calculated.
• a fit defines a merit function S that measures the agreement or difference between the data set and the fit, where small values of the merit function typically represent better parameters for the fit.
• the merit function is the squares of the difference between the data values Y and the fit function /(*,) , where for N data
• Figure 5 A shows a linear fit 510 of the PCR curve 200.
• Figure 5B shows a linear fit 550 of PCR curve 300.
• Merit functions may include different weight contributions or normalization factors to the merit function for different data points.
• Merit functions may also scale data point values or take a function of data points before a difference is taken. The difference may be taken between the data at one x value and f ⁇ x) at a different x value.
• a term in the merit function may represent the length of a line from data curve to the linear fit, such that the line is perpendicular to the linear fit. This occurs at a difference cycle number unless the linear fit has a slope of 0.
• a residual R between the data and the linear fit is calculated.
• the residual R is a set of values corresponding to an error in the data points from the linear fit.
• the residual is related to the values used to determine the merit function of the linear fit.
• the residual is a different value.
• errors 520 are used to calculate values of the residual R between curve 200 and linear fit 510.
• errors 560 are used to calculate values of the residual R between curve 300 and linear fit 550.
• step 420 a measure o ⁇ of the residual between the data and the linear fit is calculated.
• the measure is a single value made from the set of values that are the residual.
• embodiments may have a weighting value for each value of the residual, and other embodiments may subject each residual value or all residual values to additional or other functions.
• weighting value for each value of the residual
• other embodiments may subject each residual value or all residual values to additional or other functions.
• One skilled in the ail will recognize the many different measures that could be used.
• an estimated noise component present in the data set is calculated.
• the data is presumed to consist of two components, a true signal and noise.
• the noise is the difference between the true signal and the actual data point.
• the true signal can never be directly measured as noise is always added or present when a signal is detected.
• the true signal is estimated as a smoothed data set composed of smoothed data points.
• Figure 6A shows a smoothed data set 670 of PCR curve 300.
• a value of a smoothed data point is based on a function G of a plurality of original data points that are local to that smoothed data point.
• the term local relates to how far away the x value of the data points are from the data point being calculated. For example, a point may be local to another point if they differ by a preset number (window) of cycles.
• a window of three and five cycles has proved adequate, but other windows may be used, such as 10 or 20 cycles or more.
• a variable window value may also be used, i.e. each smoothed data point may be calculated with a different window.
• a window having fractions of a cycle may be used, for example where fractional data points are interpolated.
• a window may also not be symmetric around a data point, i.e. one point before and three points after that data point may be used.
• a point ceases to be local once the difference in the x value approaches the total scale used, i.e. total number of cycles.
• the function G is a moving average or low pass filter.
• the function G may take an average of the original data points within a prescribed ⁇ L+K number of cycles, e.g. a centered mean.
• G(x L ) T] ⁇ - ,
• L is the index of the smoothed data point being calculated and K is the window used.
• a residual between the smoothed data and the original data is calculated.
• This residual is defined to be the estimated noise.
• the residual between the smoothed data and the original data may be defined in the same manner as the residual between the original data and the linear fit, or the residuals may be defined in a different manner.
• Figure 6B shows an estimated noise component 680 associated with PCR curve 300 and smoothed data set 670. A superposition of noise component 680 on signal 670 gives the data curve 300.
• a measure ⁇ 2 of the residual between the smoothed data and the original data is calculated.
• the ⁇ 2 value is used as a measure of the amplitude of intrinsic noise.
• ⁇ 2 is a standard deviation.
• the measures ⁇ j and ⁇ 2 may be defined in a similar or different fashion.
• the first measure ⁇ j is compared to the second measure ⁇ 2 to determine whether the data set exhibits linear behavior.
• a ratio of O 1 and ⁇ 2 is taken. If the ratio is smaller or greater than a pre-defined value then the data is determined to exhibit linear behavior. For example, if ⁇ i/ ⁇ 2 is less than a value of order one, e.g. 1.5, the data is determined to be linear. Equivalent! y, the expression ⁇ i ⁇ Co* ⁇ 2 may be used. This expression states that the measure of the difference between the data and a linear fit must be less than a constant times the measure of the estimated noise present in the data. In some embodiments, the value of C 0 may vary.
• the constant Co is related to the fact that the definition of noise, as well as other values, is not unique.
• the value for Co may be obtained by examining large numbers of data sets to obtain a reasonable value for this number. Studies have indicated a value of 1.5 works well for the constant (co), when a standard deviation of a standard residual is used. When other residuals and measures of the residual are used, other values might be more suitable. In general, a value of C 0 on the order of 1 should work well.
• code and instructions for controlling a processor to implement the data processing techniques of the present invention are stored on a computer-readable or information storage medium such as a RAM or ROM unit, hard drive, CD, DVD or other portable medium.
• FIG. 7 illustrates a system 700 according to one embodiment of the present invention.
• the system as shown includes a sample 705, such as bacteria or DNA, within a sample holder 710.
• a physical characteristic 715 such as a fluorescence intensity value, from the sample is detected by detector 720.
• a signal 725 is sent from detector 720 to logic system 730.
• the data from signal 725 may be stored in a local memory 735 or an external memory 740 or storage device 745.
• an analog to digital converter converts an analog signal to digital form.
• Logic system 730 may be, or may include, a computer system, ASIC, microprocessor, etc. It may also include or be coupled with a display (e.g., monitor, LED display, etc.) and a user input device (e.g., mouse, keyboard, buttons, etc.). Logic system 730 and the other components may be part of a stand alone or network connected computer system, or they may be directly attached to or incorporated in a thermal cycler device. Logic system 730 may also include optimization software that executes in a processor 750.
• logic system 730 includes instructions for processing data and identifying statistically flat data.
• the instructions are preferably downloaded and stored in a memory modules 735, 740, or 745 (e.g., hard drive or other memory such as a local or attached RAM or ROM), although the instructions can be provided on any software storage medium such as a floppy disk, CD, DVD, etc.
• a memory modules 735, 740, or 745 e.g., hard drive or other memory such as a local or attached RAM or ROM
• computer code for implementing aspects of the present invention can be implemented in a variety of coding languages such as C, C++, Java, Visual Basic, and others, or any scripting language, such as VBScript, JavaScript, Perl or markup languages such as XML.
• a variety of languages and protocols can be used in the external and internal storage and transmission of data and commands according to aspects of the present invention.

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• 2006
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