Method for determining the minimum number of droplets required for droplet digital PCR analysis

Abstract

This invention provides a method for determining the minimum number of droplets required for droplet-based digital PCR analysis, relating to the field of PCR detection technology. The method includes: obtaining target parameters, including gene copy number, theoretical droplet number, target confidence level, and target error; and determining the minimum number of droplets corresponding to the target parameters based on a pre-established theoretical model relating droplet number to confidence level and error. The theoretical model relating droplet number to confidence level and error is based on the n-fold Bernoulli distribution theory and Chebyshev's inequality. This method theoretically determines the minimum number of droplets required for droplet-based digital PCR analysis, alleviating the problem of currently determining the minimum droplet number only empirically. It is easy to understand and implement, thereby improving the consistency and reliability of the analytical results.

Description

Technical Field

[0001] This invention relates to the field of PCR detection technology, and in particular to a method for determining the minimum number of droplets required for droplet-based digital PCR analysis. Background Technology

[0002] Digital PCR (polymerase chain reaction) is a third-generation PCR technology. Its principle involves distributing a PCR reaction system into numerous tiny reaction units. Each microreactor contains one or more copies of the target nucleic acid template, resulting in "single-molecule template" PCR amplification. After amplification, positive units are identified by the endpoint fluorescence signal, and the copy number of the target gene in the original sample is calculated using statistical methods. Digital PCR allows for precise absolute quantification without relying on control samples or standard curves, exhibiting superior sensitivity, specificity, and accuracy compared to quantitative real-time PCR, and has attracted increasing attention.

[0003] The droplet-based digital PCR system divides the reaction system containing nucleic acid molecules into tens of thousands of nano-level droplets. After the amplification reaction, an image is taken, and the brightness of the droplets indicates their positivity or negativity. The number of bright and dark droplets is then statistically analyzed to obtain the copy number of the target gene. Clearly, the number of bright and dark droplets directly affects the final analysis results. However, during image processing, abnormal droplets are often found due to various reasons, such as overlap, size, or brightness abnormalities. These are generally discarded and not included in the statistics. Because the number of droplets is usually in the tens of thousands, it is generally believed that removing a small number of abnormal droplets will not affect the final analysis results. However, there is currently no theoretical definition of "a small number," and an empirical value is generally given, which directly affects the consistency and reliability of the analysis results. Summary of the Invention

[0004] The purpose of this invention is to provide a method for determining the minimum number of droplets required for droplet digital PCR analysis, thereby improving the consistency and reliability of the analysis results.

[0005] This invention provides a method for determining the minimum number of droplets required for droplet-based digital PCR analysis, comprising:

[0006] Obtain the target requirement parameters, which include gene copy number, theoretical droplet number, target confidence level, and target error;

[0007] Based on the pre-established theoretical model relating droplet number, confidence level, and error, the minimum number of droplets corresponding to the target parameter is determined; the theoretical model relating droplet number, confidence level, and error is based on the n-fold Bernoulli distribution theory and Chebyshev's inequality.

[0008] Furthermore, based on the pre-established theoretical model relating droplet number, confidence level, and error, the minimum number of droplets corresponding to the target parameter is determined, including:

[0009] When both the gene copy number and the theoretical droplet number are known, the target probability of a single droplet being negative can be calculated based on the gene copy number and the theoretical droplet number.

[0010] Given the target confidence, target error, and target probability, determine the minimum number of droplets that satisfy the model with the following inequality:

[0011] n≥(1-p1)p1 / [(1-α)ɛ 2 ],

[0012] Where n is the number of droplets, p1 is the probability that a single droplet is negative, α is the confidence level, and the percentile ɛ of n is the error e.

[0013] Furthermore, the target probability of a single droplet being negative, calculated based on the gene copy number and the theoretical droplet number, includes:

[0014] Substituting the gene copy number and the theoretical droplet number into the following formula, the target probability p1 of a single droplet being negative is calculated:

[0015] p1 = (1 - 1 / n0) s ,

[0016] Where n0 is the theoretical number of droplets and s is the gene copy number.

[0017] Furthermore, the above-mentioned determination of the minimum number of droplets corresponding to the target parameter based on the pre-established theoretical model relating droplet number, confidence level, and error also includes:

[0018] When the gene copy number and / or theoretical droplet number are unknown, the target confidence level and target error are substituted into the following formula for the minimum droplet number to calculate the minimum droplet number n. min :

[0019] n min =0.25 / [(1-α)ɛ 2 ].

[0020] Furthermore, the above inequality model is established through the following process:

[0021] Based on the n-fold Bernoulli distribution theory, a statistical model for droplet digital PCR was established.

[0022] An inequality model was established based on the droplet-based digital PCR statistical model and Chebyshev's inequality.

[0023] Furthermore, based on the n-fold Bernoulli distribution theory, the above-mentioned statistical model for droplet-based digital PCR is established, including:

[0024] Calculate the probability that a single droplet is positive: 1 - p1;

[0025] The number of negative droplets Y among n droplets follows an n-fold Bernoulli distribution: Y∽B(n, p1);

[0026] When the number of negative droplets is j, the statistical model for droplet-based digital PCR is:

[0027] P(Y=j)=C n j p1 j (1-p1) (n-j) .

[0028] Furthermore, based on the droplet-based digital PCR statistical model and Chebyshev's inequality, the above-mentioned inequality model is established, including:

[0029] Substituting the mean np1 and variance expression n(1-p1)p1 of the n-fold Bernoulli distribution into Chebyshev's inequality, we get: P(|Y-np1| <e)≥1-(1-p1)p1 / (nɛ 2 ), where Y is the number of negative droplets among the n droplets;

[0030] At a confidence level of α, the following inequality holds: 1 - (1 - p1)p1 / (nɛ 2 )≥α;

[0031] Based on the above formula, we obtain the inequality model.

[0032] Furthermore, the method for determining the minimum number of droplets required for the above-mentioned droplet digital PCR analysis also includes:

[0033] Based on the inequality model, the curves showing the minimum number of droplets as a function of the droplet negative probability were plotted under specified confidence levels and errors; where the droplet negative probability refers to the probability that a single droplet is negative.

[0034] Furthermore, the method for determining the minimum number of droplets required for the above-mentioned droplet digital PCR analysis also includes:

[0035] Based on the formula for the minimum number of droplets, a curve showing the change of the minimum number of droplets with error at a specified confidence level was plotted.

[0036] Furthermore, the method for determining the minimum number of droplets required for the above-mentioned droplet digital PCR analysis also includes:

[0037] Based on the formula for the minimum number of droplets, a curve showing the change in the minimum number of droplets as a function of confidence level under a specified error was plotted.

[0038] The method for determining the minimum number of droplets required for droplet-based digital PCR analysis provided in this invention includes: obtaining target parameters, which include gene copy number, theoretical droplet number, target confidence level, and target error; determining the minimum number of droplets corresponding to the target parameters based on a pre-established theoretical model relating droplet number to confidence level and error; wherein the theoretical model relating droplet number to confidence level and error is based on the n-fold Bernoulli distribution theory and Chebyshev's inequality. This theoretically determines the minimum number of droplets required for droplet-based digital PCR analysis, alleviating the problem of currently determining the minimum number of droplets solely based on experience. It is easy to understand and implement, thereby improving the consistency and reliability of the analytical results. Attached Figure Description

[0039] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0040] Figure 1 A flowchart illustrating a method for determining the minimum number of droplets required for droplet-based digital PCR analysis, provided in an embodiment of the present invention.

[0041] Figure 2 This invention provides a curve showing the variation of the minimum number of droplets with the negative probability of droplets at a confidence level of 0.95 and an error of 2%.

[0042] Figure 3 This invention provides a curve showing the variation of the minimum number of droplets with error at a confidence level of 0.95.

[0043] Figure 4 This invention provides a curve showing the change in the minimum number of droplets with confidence level at an error of 2%. Detailed Implementation

[0044] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] Currently, the minimum number of droplets required for droplet-based digital PCR analysis is determined empirically, which affects the consistency and reliability of the analytical results. Therefore, this invention provides a method for determining the minimum number of droplets required for droplet-based digital PCR analysis. Based on the n-fold Bernoulli distribution theory and Chebyshev's inequality, a theoretical model is established between the number of droplets and the confidence level and error. This theoretically determines the minimum number of droplets required for droplet-based digital PCR analysis, alleviating the problem of determining the minimum droplet number only empirically. This method is easy to understand and implement.

[0046] To facilitate understanding of this embodiment, the following provides a detailed description of a method for determining the minimum number of droplets required for droplet-based digital PCR analysis disclosed in this embodiment of the invention.

[0047] This invention provides a method for determining the minimum number of droplets required for droplet-based digital PCR analysis, which can be performed by an electronic device with data processing capabilities. See also... Figure 1 The diagram shows a flowchart of a method for determining the minimum number of droplets required for droplet-based digital PCR analysis. This method mainly includes the following steps S102 to S104:

[0048] Step S102: Obtain the target requirement parameters, which include gene copy number, theoretical droplet number, target confidence level, and target error.

[0049] Step S104: Based on the pre-established theoretical model relating droplet number, confidence level, and error, determine the minimum number of droplets corresponding to the target parameter requirements.

[0050] The theoretical model relating droplet number to confidence level and error is based on the theory of n-fold Bernoulli distribution and Chebyshev's inequality.

[0051] In some possible embodiments, the theoretical model relating the number of droplets to confidence level and error includes the following inequality model:

[0052] n≥(1-p1)p1 / [(1-α)ɛ 2 ],

[0053] Where n is the number of droplets, p1 is the probability that a single droplet is negative, α is the confidence level, and the percentile ɛ of n is the error e.

[0054] When both the gene copy number and the theoretical number of droplets are known, the target probability of a single droplet being negative can be calculated first based on the gene copy number and the theoretical number of droplets. Then, the target confidence, target error, and target probability are substituted into the above inequality model to calculate the minimum number of droplets that satisfy the inequality model.

[0055] In one possible implementation, the gene copy number and the theoretical number of droplets can be substituted into the following formula to calculate the target probability p1 of a single droplet being negative:

[0056] p1 = (1 - 1 / n0) s ,

[0057] Where n0 is the theoretical number of droplets and s is the gene copy number.

[0058] When at least one of the gene copy number and the theoretical number of droplets is unknown, the probability of a single droplet being negative is unknown, i.e., p1 is unknown. In this case, calculations can only be performed in extreme cases, i.e., when 1-p1=p1, the right-hand side of the inequality model takes its maximum value, and the following formula for the minimum number of droplets can be derived:

[0059] n min =0.25 / [(1-α)ɛ 2 ].

[0060] Substituting the target confidence level and target error into the above formula for the minimum number of droplets, the corresponding minimum number of droplets can be calculated. For example, when α=0.95 and ε=0.02, n min =12500. As can be seen from the formula for the minimum number of droplets, the required minimum number of droplets increases with increasing confidence level and decreases with increasing allowable error.

[0061] In this embodiment of the invention, target requirements parameters are first obtained, including gene copy number, theoretical droplet number, target confidence level, and target error. Then, based on a pre-established theoretical model relating droplet number to confidence level and error, the minimum number of droplets corresponding to the target requirements parameters is determined. The theoretical model relating droplet number to confidence level and error is based on the n-fold Bernoulli distribution theory and Chebyshev's inequality. This theoretically determines the minimum number of droplets required for droplet-based digital PCR analysis, alleviating the problem of currently determining the minimum droplet number only empirically. It is easy to understand and implement, thereby improving the consistency and reliability of the analytical results.

[0062] To facilitate understanding, this embodiment of the invention also provides the process of establishing a theoretical model relating the number of microdroplets to confidence level and error, as detailed below:

[0063] a) Based on the n-fold Bernoulli distribution theory, establish a statistical model for droplet-based digital PCR.

[0064] Step a1: Calculate the probability that a single droplet is positive;

[0065] Let the gene copy number be s, where one copy represents an independent target DNA fragment, and the theoretical number of droplets generated be n. For a given droplet, the probability of a specific target DNA fragment entering is 1 / n. Let X be the total number of DNA fragments entering the given droplet. Then we have:

[0066] P(X=k)=C s k p k (1-1 / n) s-k

[0067] When k=0, no target DNA fragment enters the droplet, the droplet is negative, and the probability p1 is:

[0068] p1 = P(X = 0) = (1 - 1 / n) s (1)

[0069] The probability of a positive result is 1- .

[0070] Step a2: Based on the n-fold Bernoulli distribution theory, establish a statistical model for droplet digital PCR.

[0071] For all droplets, let Y be the number of negative droplets among the n droplets, following an n-fold Bernoulli distribution. Then, Y∽B(n, p1). When the number of negative droplets is j, we have:

[0072] P(Y=j)=C n j p1 j (1-p1) (n-j) .

[0073] b) Based on the statistical model of droplet digital PCR and Chebyshev's inequality, a theoretical model is established between the number of droplets and the confidence level and error.

[0074] Step b1: Given the confidence level and error magnitude;

[0075] In this embodiment, such as confidence level Take 0.95, and let the error e be the percentile of n. Right now n, when percentile At that time, e = 0.01n.

[0076] Step b2: Based on Chebyshev's inequality, establish a theoretical model relating the number of droplets to confidence level and error, and calculate the minimum number of droplets.

[0077] By the Chebyshev's inequality, we have:

[0078] P(|Y - E(Y)| < e) ≥ 1 - D(Y) / e 2

[0079] where E(Y) is the mean of Y, |Y - E(Y)| is the error of Y, and D(Y) is the variance of Y.

[0080] Substituting the mean np1 and the variance expression n(1 - p1)p1 of the n-fold Bernoulli distribution into the Chebyshev's inequality, we get:

[0081] P(|Y - np1| < e) ≥ 1 - (1 - p1)p1 / (nɛ 2 )

[0082] At the confidence level of , we have:

[0083] 1 - (1 - p1)p1 / (nɛ 2 ) ≥ α

[0084] In this way, we can ensure that P(|Y - E(Y)| < e) ≥ α, so we can get:

[0085] n ≥ (1 - p1)p1 / [(1 - α)ɛ 2 (2)

[0086] When the gene copy number s and the theoretical number of droplets n are unknown, p1 is unknown. At this time, we can only calculate in extreme cases. That is, when 1 - p1 = p1, the right expression of formula (2) takes the maximum value, and the formula for the minimum number of droplets can be obtained as:

[0087] n min = 0.25 / [(1 - α)ɛ 2 (3)

[0088] Furthermore, the above method further includes: according to the above inequality model, drawing a curve of the minimum number of droplets versus the negative probability of droplets at a specified confidence level and a specified error; where the negative probability of droplets refers to the probability that a single droplet is negative. For example, according to formula (2), the minimum number of droplets required for different negative probabilities of droplets is calculated at a confidence level of 0.95 and an error of 2%, thus obtaining a change curve as shown in Figure 2 .

[0089] Furthermore, the above method further includes: according to the above formula for the minimum number of droplets, drawing a curve of the minimum number of droplets versus the error at a specified confidence level. For example, according to formula (3), the minimum number of droplets required for different errors is calculated at a confidence level of 0.95, thus obtaining a change curve as shown in Figure 3 .

[0090] Furthermore, the above method also includes: plotting the curve of the minimum droplet number as a function of confidence level under a specified error, based on the above formula for the minimum droplet number. For example, the minimum droplet number required for different confidence levels at an error of 2% was calculated according to equation (3), thus obtaining the following... Figure 4 The curve shown represents the change.

[0091] It is evident that the minimum number of droplets required increases with increasing confidence and decreases with increasing error. Given a certain confidence level and error, the minimum number of droplets required is highest when the droplet negative probability is 50%, which is in line with expectations.

[0092] In all examples shown and described herein, any specific values ​​should be interpreted as merely exemplary and not as limitations; therefore, other examples of exemplary embodiments may have different values.

[0093] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining the minimum number of droplets required for droplet-based digital PCR analysis, characterized in that, include: Obtain the target requirement parameters, which include gene copy number, theoretical droplet number, target confidence level, and target error; Based on a pre-established theoretical model relating droplet number, confidence level, and error, the minimum number of droplets corresponding to the target parameter is determined; wherein, the theoretical model relating droplet number, confidence level, and error is established based on the n-fold Bernoulli distribution theory and Chebyshev's inequality; The step of determining the minimum number of droplets corresponding to the target parameter based on a pre-established theoretical model relating droplet number, confidence level, and error includes: When both the gene copy number and the theoretical droplet number are known, the target probability of a single droplet being negative is calculated based on the gene copy number and the theoretical droplet number. Given the target confidence level, the target error, and the target probability, determine the minimum number of droplets that satisfy the following inequality model: n≥(1-p1)p1 / [(1-α)ɛ 2 ], Where n is the number of droplets, p1 is the probability that a single droplet is negative, α is the confidence level, and the percentile ɛ of n is the error e; The calculation of the target probability that a single droplet is negative based on the gene copy number and the theoretical droplet number includes: Substituting the gene copy number and the theoretical droplet number into the following formula, the target probability p1 of a single droplet being negative is calculated: p1=(1-1 / n0) s , Wherein, n0 is the theoretical number of droplets, and s is the gene copy number; The step of determining the minimum number of droplets corresponding to the target parameter based on a pre-established theoretical model relating droplet number, confidence level, and error further includes: When the gene copy number and / or the theoretical droplet number are unknown, the target confidence level and the target error are substituted into the following minimum droplet number formula to calculate the minimum droplet number n. min : n min =0.25 / [(1−α)ε 2 ]。 2. The method for determining the minimum number of droplets required for droplet-based digital PCR analysis according to claim 1, characterized in that, The inequality model is established through the following process: Based on the n-fold Bernoulli distribution theory, a statistical model for droplet digital PCR was established. Based on the aforementioned droplet-based digital PCR statistical model and Chebyshev's inequality, the inequality model is established.

3. The method for determining the minimum number of droplets required for droplet-based digital PCR analysis according to claim 2, characterized in that, The statistical model for droplet-based digital PCR, based on the n-fold Bernoulli distribution theory, includes: Calculate the probability that a single droplet is positive: 1 - p1; The number of negative droplets Y among n droplets follows an n-fold Bernoulli distribution: Y∽B(n, p1); When the number of negative droplets is j, the statistical model for droplet-based digital PCR is: P(Y=j)=C n j p1 j (1-p1) (n-j) 。 4. The method for determining the minimum number of droplets required for droplet-based digital PCR analysis according to claim 2, characterized in that, The establishment of the inequality model based on the droplet-based digital PCR statistical model and Chebyshev's inequality includes: Substituting the mean np1 and variance expression n(1-p1)p1 of the n-fold Bernoulli distribution into Chebyshev's inequality, we get: P(|Y-np1| <e)≥1-(1-p1)p1 / (nɛ 2 ), where Y is the number of negative droplets among the n droplets; At a confidence level of α, the following inequality holds: 1 - (1 - p1)p1 / (nɛ 2 )≥α; Based on the above formula, the inequality model is obtained.

5. The method for determining the minimum number of droplets required for droplet-based digital PCR analysis according to claim 1, characterized in that, The method for determining the minimum number of droplets required for droplet-based digital PCR analysis also includes: Based on the inequality model, a curve showing the change of the minimum number of droplets with the negative probability of droplets under a specified confidence level and a specified error is plotted; wherein, the negative probability of droplets refers to the probability that a single droplet is negative.

6. The method for determining the minimum number of droplets required for droplet-based digital PCR analysis according to claim 1, characterized in that, The method for determining the minimum number of droplets required for droplet-based digital PCR analysis also includes: Based on the formula for the minimum number of droplets, a curve showing the change of the minimum number of droplets with error at a specified confidence level was plotted.

7. The method for determining the minimum number of droplets required for droplet-based digital PCR analysis according to claim 1, characterized in that, The method for determining the minimum number of droplets required for droplet-based digital PCR analysis also includes: Based on the formula for the minimum number of droplets, a curve showing the change in the minimum number of droplets as a function of confidence level under a specified error was plotted.

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