Method and apparatus for evaluating qPCR curves
By employing probability density functions and fitting techniques, the baseline drift and noise interference issues of qPCR curves were resolved, enabling reliable identification and concentration determination of DNA strand amplification in noisy environments, thus improving the accuracy and reliability of qPCR.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-02-25
- Publication Date
- 2026-04-07
AI Technical Summary
Existing qPCR curves are inaccurate due to baseline drift and noise interference, making it difficult to reliably identify the amplification of DNA strands and determine their concentration.
The probability density function is used to analyze the qPCR curve. By fitting the sigmoid function and using techniques such as k-means algorithm and filters, baseline drift and noise interference are removed, characteristic points of the qPCR curve are identified, and the ct-value is determined to determine the presence or absence of DNA strands.
It improves the accuracy and reliability of qPCR curves, enabling accurate identification of DNA strand amplification under noise interference, and reduces sensitivity to baseline drift and noise.
Smart Images
Figure CN115104157B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the use of polymerase chain reaction (PCR) methods, particularly for detecting the presence of pathogens. Furthermore, this invention relates to the evaluation of qPCR measurements. Background Technology
[0002] To detect DNA strands in substances under investigation, such as serum or similar substances, PCR methods are performed in automated systems. A PCR system is capable of amplifying and detecting identified DNA strands that are to be detected, for example, those that should belong to a pathogen. PCR methods generally involve cyclically using denaturation, annealing, and extension steps. Specifically, during PCR, the DNA double helix unfolds into single strands, which are then replenished by nucleotide accumulation to replicate the DNA strand in each cycle.
[0003] qPCR can be used to quantify pathogen load in a proven manner. For this purpose, the nucleotides are at least partially equipped with fluorescent molecules that activate fluorescence properties when linked to a single strand of the DNA segment to be detected. The fluorescence intensity can be determined after each cycle based on the double-stranded structure, and this intensity depends on the number of DNA segments produced.
[0004] During amplification, a qPCR curve can be derived from the obtained intensity values. This qPCR curve exhibits a sigmoid-like change when the target DNA strand is present in the material under study. The measured qPCR curve can contain artifacts, so multiple parallel measurements are typically performed to allow for a more accurate assessment of the qPCR curve by averaging the measured values.
[0005] Of particular interest is the ability to identify, based on the measured qPCR curve, whether DNA strand amplification has occurred, and, if so, to estimate the initial concentration of the DNA strand to be detected. Summary of the Invention
[0006] According to the present invention, a method according to claim 1 and an apparatus and qPCR system according to the parallel claims are specified for performing a qPCR method.
[0007] An alternative design is proposed in the dependent claims.
[0008] According to the first aspect, a method for running a quantitative polymerase chain reaction (qPCR) method is specified, which includes the following steps:
[0009] - Perform qPCR cycles cyclically;
[0010] - Measure the intensity values after or during each qPCR cycle to obtain a qPCR curve composed of intensity values;
[0011] - The probability density function is established based on the intensity value;
[0012] - The presence or absence of the DNA strand to be detected depends on the presence of one or more features of the probability density function;
[0013] - The qPCR method relies on the presence or absence of the DNA strand to be detected.
[0014] The qPCR method involves cyclically repeating denaturation, annealing, and extension steps. In denaturation, the entire double-stranded DNA in the material to be studied unfolds into two single strands at high temperature. In the annealing step, one of the added primers is ligated to a single strand, the primer pre-defined as the starting point for amplification of the DNA segment to be detected. In the extension step, a second complementary DNA segment is formed by free nucleotides on the primer-coated single strand. After each of these cycles, the amount of DNA in the DNA segment to be detected is ideally doubled.
[0015] By using qPCR, fluorescent molecules, acting as labels, are loaded into the DNA strand to be detected. The intensity over time is then measured by measuring the fluorescence intensity after each extension step. The resulting qPCR curve has three distinct phases: a baseline, where the fluorescence intensity emitted by the loaded label is not yet distinguishable from the background fluorescence; an exponential phase, where the fluorescence intensity rises above the baseline and is thus visible, where the fluorescence signal increases exponentially in proportion to the amount of DNA strand to be detected by doubling the DNA strand in each cycle; and a plateau phase, where the reagents, i.e., the primers and free nucleotides, are no longer present at the desired concentration and doubling no further occurs.
[0016] For demonstrating, for example, the ability to identify a pre-defined, detectable DNA segment corresponding to a pathogen, the so-called ct (cycle threshold) value is crucial. The ct value determines the onset of the exponential phase and is obtained by exceeding a specific limit (which is determined for each individual DNA segment to be detected and is the same for all samples used for that DNA segment), or computationally by the second derivative of the qPCR curve in the exponential phase, corresponding to the intensity of the steepest rise in the qPCR curve. If the target value is known, the initial concentration of the detectable DNA segment in the substance under investigation can be determined by inverse calculation.
[0017] In reality, qPCR curves are highly inaccurate and subject to significant fluctuations. Baseline drift occurs, accompanied by an increase in background fluorescence during measurement cycles. That is, the fluorescence signal increases even when no amplification is occurring. Other factors negatively affecting the accuracy of qPCR curves include thermal noise and fluctuations in reagent concentration, cavitation in fluorescence volume, and artifacts.
[0018] Traditional qPCR systems involve software-based correction of the qPCR curve and the ability to smooth the curves by averaging multiple measurements of samples under identical conditions. However, this requires increased resources.
[0019] The idea behind the above method is to use a probability density function to determine whether the qPCR curve exhibits a sigmoid-like or linear change. The use of the probability density function can also reliably predict, even in highly noisy qPCR curves, whether amplification, or replication, of the DNA strand to be detected has occurred, or whether the qPCR curve is simply rising due to baseline drift.
[0020] The probability density function indicates the frequency with which intensity values exist. For this purpose, a Gaussian distribution is assumed around each measured intensity value of the qPCR curve, at each fulcrum of the curve. Because of the sigmoid form of the qPCR curve (where DNA strands have been replicated), the probability density function has multiple cycles with similar intensity values not only in the baseline range but also in the plateau phase. Therefore, the probability density function of the qPCR curve has two maxima, with a minimum value between them.
[0021] In the non-amplification case (resulting in the deletion-qPCR curve), that is, in the absence of a replicated DNA strand in the qPCR curve, the change in the qPCR curve is determined solely by the rise in the baseline. This results in only one maximum value in the probability density function.
[0022] The sigmoid-like variation curve of the qPCR curve can be particularly inferred when the maximum value is higher at low intensity values than at high intensity values, the ratio of the minimum value between the maximum values to the first maximum value is lower than a predetermined threshold, and the peak width around the second maximum value is relatively large.
[0023] The above method can reliably identify whether amplification has occurred.
[0024] If the qPCR curve is known to correspond more to a sigmoid-like curve than a linear curve, then the sigmoid function can be fitted to the qPCR curve, and the parameters of the sigmoid function can be used to determine the ct-value. This allows for reliable determination of the ct-value even in the presence of highly noisy qPCR curves during amplification.
[0025] Furthermore, the probability density function can be established based on modified intensity values, which depend on or correspond to intensity values that are corrected for the baseline drift of the PCR method by the proportion of fluorescence.
[0026] In particular, it is possible to determine the baseline drift and fluorescence fraction by using a k-means algorithm to obtain an intensity value that should be assigned to the baseline region of the q-PCR curve. The intensity value to be assigned to the baseline region is linearized by linear interpolation, and the curve of the intensity value change of the linearized baseline drift is subtracted from the measured qPCR curve.
[0027] According to one implementation, the modified intensity value can be obtained by smoothing the measured qPCR curve using a filter, particularly a moving average filter.
[0028] It can be configured such that the determination of the presence or absence of the DNA strand to be detected depends on the presence of at least one of the following features of the probability density function:
[0029] - The ratio of the function value of the probability density function with the first maximum value to the function value of the second maximum value is greater than 1;
[0030] - The ratio of the function value of a local minimum between these maximum values to the function value of the first maximum value is less than 0.7, especially less than 0.6; and
[0031] - The peak width around the second maximum value in the density function is greater than a pre-given reference value. This peak width can be determined using the so-called "half-prominence method." In this method, half the value of the maximum value is first determined. Then, a point called the half-center point is selected, which is the same size as the maximum value in the horizontal (X-) direction and has half the value of the maximum value in the vertical (Y) direction. The intersection of the density curve and the horizontal line is then determined by the half-center point. The distance between the two points closest to the half-center point determines the peak width as a reference value.
[0032] In addition, it is possible to run the qPCR method, which involves confirming the presence of the DNA strand to be detected.
[0033] - Signal notification: Ability to calculate ct-value, and / or
[0034] - The ct-value is obtained from the existence function of the given parameters. Attached Figure Description
[0035] The implementation methods are described in more detail below with reference to the accompanying drawings. Wherein:
[0036] Figure 1 A schematic diagram of the PCR method cycle is shown;
[0037] Figure 2 A schematic diagram of a typical qPCR curve with intensity value variation is shown;
[0038] Figure 3 The measured change curves of the qPCR curve are shown;
[0039] Figure 4a and Figure 4b For substances that cannot be proven, or for substances that can be proven, ideal variation curves of qPCR curves are shown; and
[0040] Figure 5 A flowchart illustrating the method for performing qPCR measurements is shown;
[0041] Figure 6 The presence-qPCR curves measured show the Gaussian distribution of each modified intensity value and the resulting probability density function; and
[0042] Figure 7a and Figure 7bThe ideal presence-qPCR curve and the ideal deletion-qPCR curve show the characteristics of the corresponding probability density function. Detailed Implementation
[0043] Figure 1 A schematic diagram of a known PCR method is shown, which includes denaturation, annealing, and extension steps.
[0044] In the annealing step S1, at a high temperature, for example above 90°C, the double-stranded DNA in the material is cleaved into two single strands. In the subsequent annealing step S2, primers are attached to the single strands at designated DNA locations, marking the beginning of the DNA strand segment to be detected. These primers indicate the starting point for amplification of the DNA strand segment. In the extension step S3, starting at the primer-marked locations, complementary DNA strand segments are formed at the single strands by the addition of free nucleotides to the material, thus completing the double-stranded structure by the end of the extension step.
[0045] By assigning fluorescent molecules to free nucleotides or primers that exhibit fluorescence only when linked to DNA strand segments, an intensity value can be obtained through appropriate measurement after extension step S3 by determining the fluorescence intensity. The measured intensity of the fluorescent light is assigned an intensity value.
[0046] Steps S1 to S3 are performed cyclically and intensity values are recorded to obtain an intensity value change curve as a qPCR curve.
[0047] The intensity value variation curve has, under ideal conditions, Figure 2 The variation curve shown is (Verlauf). Figure 2 The normalized intensity is shown as a curve relating to the cycle index Z. This curve is divided into three segments: a baseline segment B, where the fluorescence of the loaded fluorescent molecule is not yet distinguished from the background fluorescence; an exponential segment E, where intensity values are observed and increase exponentially; and a plateau segment P, where the increase in intensity values flattens out because the reagent used (a solution containing nucleotides) is exhausted and no further linkage with the cleaved single strands occurs.
[0048] exist Figure 3 The diagram exemplifies the intensity value variation curves obtained in actual measurements as qPCR curves. Dramatic fluctuations were identified, which can be caused by background fluorescence, thermal noise, fluctuations in reagent concentration, and small bubbles and artifacts in the fluorescence volume. It was also identified that determining the baseline, exponential, and plateau segments of the qPCR curve is not straightforward.
[0049] Figure 4a and Figure 4b The ideal variation curves of qPCR curves are shown in the absence of the DNA strand to be verified, or in the presence of the DNA strand to be verified.
[0050] exist Figure 5 A flowchart illustrating a method for evaluating qPCR curves is shown below. This method can be implemented on a data processing device that provides the qPCR process on a qPCR system and provides intensity values from the qPCR system with each cycle, indicating the intensity of the fluorescence of the substance. The method described below can be executed in software and / or hardware within the data processing device.
[0051] In step S11, a qPCR curve is provided with the intensity values measured by qPCR in the qPCR system. Intensity values are typically measured by detecting the sample with a camera and evaluating the grayscale level, or color level, and intensity value.
[0052] The qPCR curve measured in step S12 is smoothed by means of a filter, especially a moving average filter, in such a way that for each value, the average of one and several values of the intensity values immediately following and subsequently recorded is used, such as, for example, the average of the preceding and following two to five adjacent values.
[0053] In step S13, a clustering algorithm is used to determine three curve regions: the baseline region, the exponential region, and the plateau region. To this end, the baseline centroid, exponential region centroid, and plateau region centroid are initially placed on the qPCR curve plot. The initial centroid positions can be roughly determined based on the understanding of the sigmoid function curve. The baseline centroid C1, exponential region centroid C2, and plateau region centroid C3 can be placed using the following basic knowledge: the baseline region has low intensity values, the exponential region has medium intensity values, and the plateau region has high intensity values. Each point is then assigned to the nearest centroid on the measured qPCR curve, thus classifying it.
[0054] The k-means algorithm specifies the iterative adjustment of the centroid C by using the average value of the measurement points that constitute the qPCR curve and are associated with the corresponding centroid.
[0055] ,in
[0056] (S) k(The number of measurement points assigned to the corresponding centroid) Now, the measurement points of the qPCR curve can be reassigned to the changed centroids using the spacing method.
[0057] ,for
[0058] And among them
[0059] for Minimum.
[0060] This method is implemented iteratively until the allocation of points and clusters no longer changes or the maximum number of iterations has been reached.
[0061] Next, each measurement point of the measured qPCR curve is reassigned to a newly calculated centroid point belonging to the baseline centroid, the exponential region centroid, and the plateau region centroid.
[0062] In step S14, a linear curve of intensity values can be established by interpolating the points of the qPCR curve that belong to the baseline region, i.e., the obtained baseline centroid. The linearized qPCR baseline curve corresponds to the effect of the baseline change curve on the entire qPCR measurement. Therefore, the linearized qPCR baseline curve is subtracted from the entire measured qPCR curve. Thus, baseline rise is eliminated from the qPCR curve.
[0063] In the next step S15, the remaining qPCR curves are standardized so that the points on the qPCR curves are between 0 and 1 as modified intensity values.
[0064] The probability density function is then constructed in step S16. This probability density function represents the probability of a modified intensity value appearing in the standardized linearized qPCR curve. For this purpose, the modified intensity value for each cycle is assigned a Gaussian distribution around the corresponding modified intensity value. The probability density function corresponds to the sum of all Gaussian distributions of the modified intensity values.
[0065] In cases of successful amplification, multiple cycles with similar modified intensity values exist not only in the baseline region but also in the plateau region. This results in two eigenvalues when summed over a Gaussian distribution to form a probability density function. Conversely, in the non-amplified case, the baseline merely determines the variation curve of the qPCR curve, thus the presence of two eigenvalues is generally not expected.
[0066] Figure 6 The curves for the measured presence-qPCR curves exemplify the Gaussian distribution of each modified intensity value x and the resulting probability density function PDF.
[0067] Figure 7a and Figure 7b The ideal presence-qPCR curve and the ideal deletion-qPCR curve (the left curve plotted with the modified intensity value F on the cycle exponent z, respectively) show the characteristics of the corresponding probability density function (the right curve).
[0068] Due to noise in the non-amplified case, the probability density function will also exhibit two maxima. However, the amplified-non-amplified case can be distinguished only when at least one of the following criteria is present:
[0069] - The maximum value of the probability density function for low intensity values is greater than the maximum value of the probability density function for higher intensity values;
[0070] - It is a significant local minimum between the two maximum values.
[0071] - The width of the second maximum value is relatively high.
[0072] In step S17, it is checked whether the generated probability density function traces back to the presence-qPCR curve. This can be done by checking whether the ratio of the size of the first maximum value (the function value of the probability density function) to the size of the second maximum value is greater than 1; whether the ratio of the size of the local minimum value between the maximum values to the size of the first maximum value is less than 0.7, especially less than 0.6; and whether the width of the peak around the second maximum value is greater than a reference value, such as 8.
[0073] The width of the reference value is obtained by plotting a probability density distribution on a normalized scale of 0 to 100 using the so-called "width-half-prominence" method. This method first determines half the value of the maximum value. The point that is equal to the maximum value in horizontal (X-) magnitude and has half the maximum value in vertical (Y-) magnitude is called the half-center point. The intersection of the probability density function and the horizontal line is then determined by the half-center point. The distance between the two closest half-center points determines the width of the peak. The reference value can vary depending on the probability density distribution used and the method used to plot the density.
[0074] If it is determined in step S17 that the generated probability density function backtracks to the existence-qPCR- curve (or in other words, yes), then the sigmoid function can be fitted to the qPCR curve in step S18 according to the following rules:
[0075]
[0076] In the next step S19, the ct-value can now be determined in a manner known per se by the maximum value of the second derivative of the fitted sigmoid function.
[0077] If it is determined in step S17 that the generated probability density function backtracks to the presence-qPCR curve (or: no), then the missing strand to be detected can be signaled in step S20.
Claims
1. A method for running a quantitative polymerase chain reaction (qPCR) method, comprising the following steps: - Perform qPCR cycles cyclically; - Measure fluorescence for each qPCR cycle to obtain a qPCR curve consisting of intensity values (I); - A probability density function (PDF) is constructed from the intensity value (I), where, The probability density function (PDF) is established based on a modified intensity value, wherein the modified intensity value depends on or corresponds to the intensity value, wherein the intensity value is corrected for the fluorescence fraction of the baseline drift curve of the PCR method. - The presence or absence of the DNA strand to be detected is determined by the presence of one or more features of the probability density function (PDF); - The qPCR method is run based on the presence or absence of the DNA strand to be detected. The determination of the presence or absence of the DNA strand to be detected depends on the presence of at least one of the following features of the probability density function (PDF): - The ratio of the function value of the probability density function (PDF) at the first maximum value to the function value at the second maximum value is greater than 1; - The ratio of the function value of a local minimum between these maximum values to the function value of the first maximum value is less than 0.7; and - The peak width around the second maximum value in the probability density function (PDF) is greater than a pre-given reference value.
2. The method according to claim 1, wherein, The ratio of the function value of a local minimum between these maximum values to the function value of the first maximum value is less than 0.
6.
3. The method according to claim 2, wherein, The baseline drift fraction of fluorescence is determined by using a clustering algorithm to obtain intensity values that should be assigned to the baseline region of the qPCR curve. The intensity values to be assigned to the baseline region are linearized by linear interpolation, and the curve of the linearized intensity values of the baseline drift is subsequently subtracted from the measured qPCR curve.
4. The method according to claim 2 or 3, wherein, The modified intensity value is obtained by smoothing the measured qPCR curve using a filter.
5. The method according to claim 4, wherein, The modified intensity value is obtained by smoothing the measured qPCR curve using a moving average filter.
6. The method according to any one of claims 1 to 3, wherein, The qPCR method is run as follows: If the presence of the DNA strand to be detected is confirmed, - Signal notification enables the calculation of ct-values, and / or - The ct-value is obtained from the existence function of the given parameters.
7. An apparatus for running a quantitative polymerase chain reaction (qPCR) method, wherein, The device is configured to perform the following steps: - Perform qPCR cycles cyclically; - Measure fluorescence for each qPCR cycle to obtain a qPCR curve consisting of intensity values (I); - A probability density function (PDF) is established from the intensity value, wherein the probability density function (PDF) depends on the modified intensity value, wherein the modified intensity value depends on or corresponds to the intensity value, wherein the intensity value is corrected by the proportion of fluorescence in the baseline drift curve of the PCR method. - The presence or absence of the DNA strand to be detected is determined by the presence of one or more features of the probability density function (PDF); - The qPCR method is run based on the presence or absence of the DNA strand to be detected. The determination of the presence or absence of the DNA strand to be detected depends on the presence of at least one of the following features of the probability density function (PDF): - The ratio of the function value of the probability density function (PDF) at the first maximum value to the function value at the second maximum value is greater than 1; - The ratio of the function value of a local minimum between these maximum values to the function value of the first maximum value is less than 0.7; and - The peak width around the second maximum value in the probability density function (PDF) is greater than a pre-given reference value.
8. The apparatus for running a quantitative polymerase chain reaction (qPCR) method according to claim 7, wherein, The device is configured to perform the determination of the presence or absence of a DNA strand segment to be detected, depending on the presence of at least one of the following features of the probability density function (PDF): - The ratio of the function value of the probability density function (PDF) at the first maximum value to the function value at the second maximum value is greater than 1; - The ratio of the function value of a local minimum between these maximum values to the function value of the first maximum value is less than 0.6; as well as - The peak width around the second maximum value in the probability density function (PDF) is greater than a pre-given reference value.
9. A computer program product configured to perform all the steps of the method according to any one of claims 1 to 6.
10. An electronic storage medium having a computer program stored thereon, wherein, When the computer program is executed, it performs all the steps of the method according to any one of claims 1 to 6.
Citation Information
Patent Citations
Curve Processor Algorithm for the Quality Control of (RT-) qPCR Curves
US20130189702A1