Manufacturing of polymerase chain amplification kits to optimize amplification denaturation stages

Abstract

Disclosed is a method for digitally simulating polymerase chain amplification of at least one target, comprising simulating a plurality of successive amplification cycles, each cycle comprising, in order: a hybridization stage; an extension stage; then, a denaturation stage; wherein for each cycle: the hybridization phase comprises: obtaining, for said cycle, initial values of a concentration vector of a plurality of nucleic acid molecules in single strand form; calculating a concentration matrix of a partial duplex formed by hybridization of the plurality of nucleic acid molecules in the single strand form; the denaturation stage includes multiplying a denaturation tensor of the extended duplex by a concentration vector of the extended duplex obtained by applying the extension stage to the concentration of the duplex.

Description

TECHNICAL FIELD

[0001] The present disclosure is in the field of polymerase chain amplification. More specifically, the present disclosure is in the field of polymerase chain amplification kit design and manufacturing. BACKGROUND

[0002] Polymerase chain amplification or polymerase chain reaction (PCR) is a reaction that allows the doubling of nucleic acid molecules, such as DNA or RNA. In each reaction cycle, each nucleic acid molecule is replicated. PCR amplification thus allows nucleic acid molecules to be doubled exponentially, with the nucleic acid concentration potentially doubling with each reaction cycle.

[0003] This allows PCR amplification to reach relatively high concentrations from even very small amounts of nucleic acids, allowing their detection. PCR amplification is thus used in many biomedical applications, particularly pathogen detection and characterization, as it can transform trace amounts of nucleic acids representing a pathogen into detectable amounts.

[0004] PCR amplification is referred to as singleplex amplification when its purpose is to amplify a single nucleic acid, or multiplex amplification when its purpose is to amplify multiple different nucleic acids simultaneously. The molecules to be amplified can be referred to as “targets”, and the amplified molecules can be referred to as “amplicons”, it being understood that amplicons themselves can be amplified in one or more subsequent cycles.

[0005] PCR amplification is usually performed in a PCR kit, with different temperatures being applied to trigger successive steps of the amplification cycle. The PCR kit initially contains primers that initiate amplification.

[0006] The success and speed of PCR amplification depend on many parameters of the PCR kit, in particular the duration and temperature of the different reaction steps, the sequence of the primers initially present in the kit, their concentration, the concentration of monovalent and divalent salts, the length of the oligonucleotides in solution, the length of the expected amplicon (shorter amplicons also allow shorter cycle times), etc.

[0007] In general, when designing a PCR kit, the designer performs the following steps: a) determining a list of specific potential targets (i.e. not shared with other microorganisms) for each microorganism; b) selecting potential primers from a list of possible primers based on experience; c) performing tests under real conditions; d) repeating the process if the PCR performance is not satisfactory.

[0008] This approach is even more difficult when targeting multiple targets. The design of a kit is thus long and complex, and depends on the specific working expertise of each designer.

[0009] It is also impossible to predict the reaction on paper, because the designer would quickly be overwhelmed by the number of reactions, to the point that the human mind could not possibly simulate what actually happens during a PCR process on paper.

[0010] For example, considering the fact that hybridization between different molecules can occur at different positions, it is impossible to solve a system of differential equations representing the hybridization phase a priori. The methods of the prior art also do not allow a numerical simulation of such a system in a reasonable time, due to the presence of many differential equations that are linked to each other. This greatly reduces the possibility of designing and, in turn, improving PCR kits.

[0011] There is therefore a need for a method for predicting the progress of the denaturation phase, including when there are multiple hybridizations, in order to facilitate the selection of parameters that favor the amplification of one or more targeted targets. SUMMARY

[0012] The present disclosure improves this situation.

[0013] The present application proposes a method for numerically simulating a polymerase chain reaction of at least one target, said method comprising simulating a plurality of successive amplification cycles, each cycle comprising in succession: a hybridization phase between at least one target and a plurality of primers; an elongation phase; then a denaturation phase; wherein the hybridization phase comprises for each cycle: obtaining an initial value of a concentration vector of a plurality of single-stranded nucleic acid molecules comprising at least one target and a plurality of primers for said cycle; initializing a concentration matrix of duplexes formed by hybridization of a plurality of single-stranded nucleic acid molecules; calculating the evolution of the concentration matrix in the hybridization phase in successive time steps by applying to the concentration matrix a matrix differential equation representing the kinetics of the formation of said duplexes as a function of the concentrations of a plurality of nucleic acid molecules, said matrix differential equation being parameterized by at least one association matrix comprising an association constant associated with each duplex and a dissociation matrix comprising a dissociation constant associated with each duplex.

[0014] The term "at least one target" means at least one nucleic acid in the sequence to be amplified. According to various embodiments of the application, the amplification can involve a single target, in which case the amplification is referred to as "singleplex" amplification, or can involve a plurality of targets, in which case the amplification is referred to as "multiplex" amplification.

[0015] The term "single-stranded nucleic acid molecule" is understood to mean a nucleic acid molecule in single-stranded form that is not paired with a complementary single-stranded molecule.

[0016] The term "association constant" (also called "association rate constant"), usually denoted k on is understood to mean the rate constant representing the rate of the reaction that binds two single-stranded nucleic acid molecules into a duplex.

[0017] The expression "dissociation constant" (also called "dissociation rate constant"), usually denoted k off , is understood to mean the rate constant representative of the rate of the reaction dissociating a duplex into two single-stranded nucleic acid molecules.

[0018] This makes it possible to simulate all the phases of hybridization between the target, the amplicon and the primers (i.e. the equilibrium between the association and dissociation reactions). Thus, it is possible to model the entire kinetics of the polymerase chain reaction, integrating the intermediate products and cross-reactions.

[0019] This specific modeling of the polymerase chain reaction thus makes it possible to validate the design of a polymerase chain reaction device, or conversely, to identify undesirable reactions, so as to modify the parameters affecting the amplification reaction (initial concentrations of primers, salts, phase times and temperatures, etc.).

[0020] Similarly, simulating the phases of hybridization according to a single matrix differential equation allows the kinetics of the system to be resolved using conventional computing power.

[0021] According to another aspect, a method of manufacturing a kit for characterizing microorganisms contained in a sample using a polymerase chain reaction is proposed, the kit comprising a plurality of validated primers, in which method the plurality of primers and the concentration vector of the plurality of primers are obtained by the simulation method according to one of the embodiments of the application.

[0022] This makes it possible to manufacture a device that reproduces the simulated reaction. The device produced in this way will allow the multiplication of the target as simulated previously.

[0023] According to another aspect, a kit for a polymerase chain reaction is proposed, manufactured by the manufacturing method according to one of the embodiments of the application.

[0024] According to another aspect, a computer program is proposed, comprising instructions for carrying out all or part of the processes defined herein, when this program is run by a processor.

[0025] According to another aspect, a non-transitory computer-readable recording medium is proposed, on which such a program is recorded.

[0026] According to another aspect, a method for characterizing microorganisms contained in a sample is proposed, comprising: preparing the sample so as to carry out a PCR on the prepared sample, the preparation comprising a step of adding a kit manufactured according to the kit manufacturing method defined herein; carrying out a PCR on the prepared sample; characterizing the microorganisms on the basis of the results of the PCR.

[0027] The features set out in the following paragraphs can optionally be implemented independently of one another or in combination with one another:

[0028] Advantageously, wherein said differential equations comprise a mass conservation equation of the form or any other mathematically equivalent formulation: wherein: represents the time elapsed since the beginning of the hybridization phase; the symbol and denote the concentrations of the two single-stranded nucleic acid molecules indexed i and j in the concentration vector of the plurality of nucleic acid molecules; the symbol denotes the concentration of the duplex formed by the pair of single-stranded nucleic acid molecules indexed x and y in the concentration vector of the plurality of nucleic acid molecules; the symbols and denote the values of at and .

[0029] This allows to obtain a more accurate simulation of the hybridization phase by taking into account the mass conservation.

[0030] Advantageously, wherein said matrix differential equations have the form: wherein: H is the concentration matrix of the duplexes; T0is the initial value of the cycle of the concentration vector of the plurality of molecules; K on is the association matrix; K off is the dissociation matrix; the operator denotes a two-dimensional matrix of i rows and j columns whose all elements are equal to 1 ; the operator “diag()” denotes an operator that takes as a parameter a square matrix and extracts from it a vector whose dimension is the number of rows or columns of the square matrix and which contains all the elements of the diagonal of the square matrix.

[0031] For example, the operator denotes an N-dimensional horizontal vector containing only 1 s, while the operator denotes an N-dimensional vertical vector containing only 1 s.

[0032] For example, the diag(H) operator converts the N x N square matrix H into an N-dimensional vector that includes in order all the elements on the diagonal of N. For example, if then .

[0033] This allows to integrate the differential equations of all the hybridization reactions into a single matrix equation in which T is replaced by T0, providing faster matrix calculations.

[0034] Advantageously, each association matrix or dissociation matrix comprises a plurality of elements, and each element of an association matrix or each element of a dissociation matrix related to a pair of molecules belonging to said plurality of molecules is: zero if the free enthalpy variation related to the hybridization reaction of the molecules forming the pair is greater than a threshold value; equal to the association constant or to the dissociation constant of the hybridization reaction of said pair of molecules, respectively.

[0035] This allows to take into account in the simulation only the main hybridization reactions. This makes it possible to obtain at the same time a better accuracy of the kinetics of the hybridization reactions taken into account, and a reduced complexity of the differential equations solving. This also makes it possible to take into account the differential kinetics between different reactions depending on whether the free enthalpy value between two reactions of interest is favorable or not.

[0036] Advantageously, said threshold value is selected from at least two predetermined threshold values, the lowest threshold value being reserved to the pair of molecules comprising an amplicon and a primer.

[0037] Because the threshold value and the free enthalpy variation are negative, the highest threshold value corresponds to a lower threshold value. Thus, the hybridization reaction between a primer and an amplicon is preferentially taken into account. The term "lower threshold value" is understood as a value closer to zero. The threshold value and the free enthalpy variation being negative, this also corresponds to a lower absolute threshold value.

[0038] This allows to preferentially take into account in the simulation the hybridization between a primer and an amplicon, which allows to simulate the initial few cycles of amplicon-primer hybridization during which the amplicon concentration is much lower than the primer concentration, compared to the hybridization reactions between e.g. a primer and other primers.

[0039] Advantageously, said method comprises a preceding step of defining a plurality of molecules comprising: initializing a plurality of single-stranded nucleic acid molecules as the molecules initially present in the polymerase chain reaction; performing an initial simulation of a plurality of cycles of the polymerase chain reaction, each cycle of the initial simulation comprising: obtaining in said plurality of molecules the hybridization reactions of the molecules forming each pair of molecules having an affinity lower than a threshold value; simulating a hybridization phase comprising said hybridization reactions; simulating an elongation phase; simulating a denaturation phase; adding to said plurality of molecules additional molecules obtained at the end of the hybridization, elongation and denaturation phases.

[0040] The term "additional molecules" is understood to mean molecules that are not present at the beginning of the cycle, but that are produced at the end of the hybridization, elongation and denaturation cycle.

[0041] This makes it possible to take into account only the molecules having a significant affinity that will actually be encountered during the polymerase chain reaction, just to build the concentration vector, the association matrix and the dissociation matrix. Thus, this provides a more reliable and less resource-consuming simulation of the PCR amplification reaction.

[0042] Advantageously, the preliminary step of defining the plurality of molecules comprises performing 3 to 7 initial simulation cycles.

[0043] This gives a good compromise between the number of molecules added and their importance. For example, molecules added after the 3rd, 5th or 7th cycle can be considered as unlikely to induce a significant reaction. Thus, a predefined number of cycles between 3 and 7, for example equal to 5, can limit the number of molecules used for the simulation and reduce the associated computational complexity, while maintaining the reliability of the simulation.

[0044] Advantageously, the method comprises, at the end of the simulation of the plurality of cycles, a subsequent step of displaying the time evolution of the concentration of at least one of said molecules.

[0045] This makes it possible to visualize the evolution of the concentration of at least one molecule, for example an amplicon, and thus to validate or modify the design of the polymerase chain reaction accordingly.

[0046] Advantageously, the method comprises a subsequent step of validating or modifying the initial values of the plurality of primers and of the concentration vector of the plurality of primers in the first cycle of the reaction, by comparing a value representative of the kinetics of the reaction to a threshold value.

[0047] This makes it possible to validate the primers initially present and the associated concentrations that indeed allow the desired target to be multiplied with sufficiently strong kinetics of the reaction, and to avoid generating unwanted reactions with strong kinetics, or conversely, to modify the list of primers and / or their concentrations.

[0048] Advantageously, the value representative of the kinetics is a value chosen from the following: threshold cycle; crossing point; final concentration of nucleic acid molecules amplified by the reaction; concentration of amplicon at the end of the reaction.

[0049] The term "cycle threshold" (or "Ct", also called "quantification cycle", or "Cq") is understood to mean the number of cycles required for the concentration of the amplicon to reach a reference concentration. The threshold can for example correspond to a certain concentration, at or above which the molecule is detectable.

[0050] The term "crossing point" (or "Cp", or "Take Off Point" or "TOP") is understood to mean the cycle at which the value of the second derivative of the concentration of the amplicon reaches its maximum.

[0051] The term "amplicon concentration at the end of the reaction" refers to the concentration of amplicon when the reaction is considered to be complete, for example when a period of concentration stabilization is reached. Such a stabilization period can for example be detected by linear regression on an affine straight line.

[0052] Advantageously, the modification of the plurality of primers comprises: identifying a preferential target based on the results of the polymerase chain reaction simulation; identifying, from the binding or dissociation matrix, single-stranded nucleic acid molecules forming pairs of primers associated with the target; performing at least one polymerase chain reaction modification chosen from the group consisting of: in the initial concentration vector, decreasing the initial concentration of the single-stranded nucleic acid molecules forming pairs of primers associated with the target; changing the concentration of salt; changing the hybridization temperature of at least one cycle; changing the hybridization time of at least one cycle.

[0053] This makes it possible to identify reactions between molecules present during the PCR reaction that compete with the amplification of a given target and to decrease the initial concentration of the molecules that generate these reactions, or to modify the sequence of the associated molecules accordingly, in order to facilitate the amplification of the given target.

[0054] Advantageously, the sample is taken from an animal or a human being, the method comprising selecting an antimicrobial agent according to the characteristics of the microorganisms present in the sample and administering the antimicrobial agent to the animal or human being.

[0055] Advantageously, the sample is taken from an inanimate object, the method comprising selecting an antimicrobial agent according to the characteristics of the microorganisms present in the sample and administering the antimicrobial agent to the inanimate object.

[0056] The application proposes a method for numerically simulating a polymerase chain reaction on at least one target, the method comprising simulating a plurality of successive amplification cycles, each cycle comprising in succession: a hybridization phase between at least one target and a plurality of primers; an extension phase; then a denaturation phase; wherein, for each cycle: the hybridization phase comprises: obtaining a cyclic initial value of a concentration vector of a plurality of single-stranded nucleic acid molecules comprising at least one target and a plurality of primers; calculating a concentration matrix of partial duplexes formed by hybridization of the plurality of single-stranded nucleic acid molecules, each element of the matrix representing the concentration of a duplex formed by hybridization of a pair of the plurality of single-stranded nucleic acid molecules, regardless of the hybridization position of the pair; the denaturation phase comprises: multiplying the concentration vector of extended duplexes resulting from the application of the extension phase to the duplex concentration by a denaturation tensor of extended duplexes to obtain an initial value of the concentration vector of the plurality of single-stranded nucleic acid molecules for the next cycle.

[0057] Using a single concentration value for all duplexes between a pair of nucleic acid molecules, regardless of the pairing position, makes it possible to reduce the number of equations to be solved to calculate the denaturation and to make the problem of simulating the denaturation solvable.

[0058] According to another aspect, a method is proposed for preparing a kit for characterizing microorganisms contained in a sample using a polymerase chain reaction, the kit comprising a plurality of validated primers, in which method the plurality of primers and the concentration vector of the plurality of primers are obtained by the simulation method defined herein.

[0059] This makes it possible to manufacture devices that reproduce the simulated reaction. Devices produced in this way will allow for the multiplication of targets as previously simulated.

[0060] In another respect, a kit for polymerase chain reaction is proposed, which is manufactured by the method defined herein.

[0061] According to another aspect, a computer program is proposed that includes instructions for performing all or part of the methods defined herein when the program is run by a processor.

[0062] On the other hand, a non-transient computer-readable recording medium on which such a program is recorded is proposed.

[0063] According to another aspect, a method for characterizing microorganisms contained in a sample is proposed, comprising: preparing a sample for PCR of the prepared sample, said preparation comprising the step of adding a kit manufactured according to a method defined herein; performing PCR on the prepared sample; and characterizing the microorganisms based on the PCR results.

[0064] The features described in the following paragraphs may be implemented, either independently or in combination:

[0065] Advantageously, at least one duplex is generated by two primer pairs; the extension phase simulates the concentration of each duplex generated by the two primer pairs as a single concentration of the extended duplex generated by the two primer pairs; the coefficients of the denaturation tensor are defined to allocate the concentration of each extended duplex generated by the two primer pairs to single-stranded nucleic acid molecules, corresponding to the extension of the duplex generated by the two primer pairs in two directions.

[0066] This simplifies the simulation of the reaction generated by the pairing of two primers, thereby further reducing the computational complexity of the simulation.

[0067] Advantageously, for each hybridization reaction between the two primers: the concentration of the extended duplex includes the concentration of the extended virtual duplex, which is equal to the sum of the concentrations of the extended duplex formed by the hybridization of the two primers along each of the two directions; the coefficient of the denaturation tensor of the extended duplex, corresponding to the concentration distribution of the extended virtual duplex for each of the two primers and for each of the two single-stranded nucleic acids produced by the extension along one of the two directions, is equal to 0.5.

[0068] This makes it possible to effectively simulate the reactions produced by primer hybridization while limiting the complexity of the simulation.

[0069] Advantageously, for each set of multiple hybridization reactions of single-stranded nucleic acids via primers at several positions, respectively: the concentration of the duplex and the concentration of the extended duplex each include the concentration of the virtual duplex equal to the sum of the concentrations of the duplexes formed by the multiple hybridization reactions, and the concentration of the extended virtual duplex equal to the sum of the concentrations of the extended duplexes formed by the extension of the duplexes formed by the multiple hybridization reactions; the coefficients of the denaturation tensor of the extended duplex corresponding to the concentration distribution of the extended virtual duplex of each single-stranded nucleic acid associated with one of the multiple hybridization reactions are respectively equal to the interaction energy of the multiple hybridization reactions divided by the ratio of the total interaction energy of all multiple hybridization reactions with the single-stranded nucleic acid.

[0070] The term "virtual double-strand concentration" refers not to the concentration of double-stranded molecules in a real molecule, but rather to the concentration of multiple double-stranded molecules produced by hybridization of the same primers at multiple different positions on the same single-stranded nucleic acid molecule. The concentration of virtual double-stranded molecules is equal to the sum of the concentrations of real double-stranded molecules produced by the hybridization reactions of primers and single-stranded nucleic acid molecules at different positions.

[0071] The term "concentration of extended virtual double helices" refers to the concentration of extended double helices, which do not correspond to actual molecules but rather to multiple extended double helices. These extended double helices are produced by the extension of double helices formed by hybridization of the same primers at multiple different positions on the same single-stranded nucleic acid molecule. The concentration of extended virtual double helices is equal to the sum of the concentrations of extended actual double helices produced by the hybridization reactions of primers and single-stranded nucleic acid molecules at different positions, thus forming the extension of the double helix.

[0072] The term "single-stranded nucleic acid associated with one of the multiple hybridization reactions" refers to nucleic acids generated by denaturation of the extended double helix itself, which is generated by the extension of a double helix formed by one of the multiple hybridization reactions, i.e., hybridization of primers at a specific position.

[0073] This makes it possible to simulate multiple hybridization with the same nucleic acid as if it were a single reaction, while obtaining a reliable estimate of the nucleic acid concentration produced by these multiple hybridizations at the end of the cycle.

[0074] Therefore, this makes it possible to greatly facilitate, or even realize, the calculation of concentration evolution while maintaining satisfactory simulation accuracy.

[0075] Advantageously, the extension stage includes obtaining the concentration of the extended duplex by multiplying the concentration of the duplex by the extension factor.

[0076] The term "extension factor" refers to the fraction of a given double-stranded molecule that is extended during the extension phase, and it ranges between 0 and 1.

[0077] This makes it possible to take into account every possible difference in the different double-strand extension processes.

[0078] Advantageously, the extension phase further includes updating the concentration vector of the duplex, representing the concentration of the non-extended duplex at the end of the extension phase; the denaturation phase further includes multiplying the duplex concentration vector by the denaturation tensor of the non-extended duplex to update the initial value of the concentration vector of the plurality of single-stranded nucleic acid molecules for the next cycle.

[0079] This simulates the denaturation of unextended duplexes and integrates the concentrations of both unextended and denatured duplexes under the initial conditions of the next cycle.

[0080] Tensor analysis also ensures that the mutation is under control.

[0081] Advantageously, during the denaturation phase, the same denaturation coefficient is applied to both the non-extended duplex and the corresponding extended duplex to update the concentration vectors of multiple single-stranded nucleic acid molecules and the duplex concentration for the next cycle.

[0082] The term "denaturation coefficient" refers to the fraction of a given double-stranded molecule that has been denatured during the denaturation phase, and it ranges between 0 and 1.

[0083] This makes it possible to accurately simulate the denaturation stage.

[0084] Advantageously, the method includes subsequent steps of verifying or modifying the initial values ​​of a plurality of primers and the concentration vector of the plurality of primers in the first cycle of the reaction by comparing a value representing the reaction kinetics with a threshold.

[0085] This makes it possible to verify the initially existing primers and their associated concentrations (which indeed allow for the multiplication of the desired target with sufficiently strong reaction kinetics) and avoid generating unwanted reactions with strong kinetics, or conversely, modifying the list of primers and / or their concentrations.

[0086] Advantageously, the sample is taken from an animal or human, and the method includes selecting an antimicrobial agent based on the characteristics of the microorganisms present in the sample and administering the antimicrobial agent to the animal or human.

[0087] Advantageously, the sample is taken from an inanimate object, and the method includes selecting an antimicrobial agent based on the characteristics of microorganisms present in the sample and applying the antimicrobial agent to the inanimate object. Attached Figure Description

[0088] Other features, details, and advantages will become apparent from the following detailed description and analysis of the accompanying drawings, in which: Figure 1

[0089] [Figure 1 Examples of polymerase chain reaction kits that can be manufactured by practicing the present invention are shown. Figure 2

[0090] [ Figure 2 This shows an example of a polymerase chain reaction that can be simulated according to a set of implementation schemes. Figure 3

[0091] [ Figure 3 This shows an example of temperature changes during a PCR amplification cycle. Figure 4

[0092] [ Figure 4 The image shows an example of a method according to a set of embodiments of the present invention. Figure 5

[0093] [ Figure 5 This image shows an example of the hybridization stage in one of the embodiments of the present invention. Figure 6

[0094] [ Figure 6 This image shows an example of a denaturation stage in one of a set of embodiments of the present invention. Figure 7

[0095] [ Figure 7 The illustration shows examples of hybridization, extension, and denaturation reactions in three consecutive cycles of PCR amplification in one embodiment of the present invention. Figure 8

[0096] [ Figure 8 The illustration shows an example of a method according to a set of embodiments of the present invention, which integrates the verification or modification of PCR amplification parameters. Figure 9

[0097] [ Figure 9 The illustration shows an example of a method according to a set of embodiments of the present invention, which integrates the validation or modification of PCR amplification parameters and the manufacture of a validated PCR amplification kit. Figure 10

[0098] [ Figure 10 The image shows an example of a method for characterizing microorganisms using a PCR amplification kit manufactured according to a set of embodiments of the present invention. Figure 11

[0099] [Figure 11 The illustration shows an example of visualizing the kinetics of multiple PCR reactions according to a set of embodiments of the present invention. Figure 12

[0100] [ Figure 12 The illustration shows an example of visualizing the kinetics of multiple PCR reactions under two different experimental conditions according to a set of embodiments of the present invention. Detailed Implementation

[0101] Now for reference Figure 1 .

[0102] Figure 1 Examples of a reagent kit K1 for polymerase chain reaction (PCR) that can be manufactured to implement the present invention are shown, such as kits for the FilmArray and Spotfire platforms manufactured and sold by the applicant of this application. Such kits are described, for example, in patents US 8,394,608 or US 9,932,634, which are incorporated herein by reference.

[0103] The kit K1 forms part of the testing device Tst1, which is designed to test for the presence of one or more microorganisms, such as one or more viruses, bacteria, fungi, and antibiotic resistance genes.

[0104] For this purpose, the testing device Tst1 includes a swab 1 for collecting nasal samples from patients.

[0105] The sample can then be supplied at the input of kit K1 for PCR amplification, thereby amplifying one or more nucleic acids representing the microorganisms whose presence is being sought, such as those described in the aforementioned literature. Therefore, even if the initial concentration of microorganisms in the collected sample is low, the amount of nucleic acid output by PCR amplification is sufficient to detect their presence, thus, for example, detecting the presence of microorganisms in the collected sample.

[0106] As PCR amplification proceeds, the amplicon can produce increasingly stronger fluorescence, for example, by integrating a fluorophore by forming a double-stranded sequence, and the number of double-stranded sequences containing the fluorophore increases with amplification.

[0107] Therefore, the Tst1 test kit can detect the presence of microorganisms, even if their concentration in the initial sample is very low.

[0108] The test kit Tst1 is provided only as a non-limiting example, and the invention can be applied to different types of test kits associated with different sampling methods. For example, sampling can be performed on humans, animals, or inanimate objects, and can enable the characterization of one or more microorganisms. Characterization of one or more microorganisms can allow for the selection of antimicrobial agents for administration to humans or animals, or for application to inanimate objects. Similarly, the invention is applicable to the step of amplifying a target portion of the genome by PCR prior to complete genome sequencing, such as amplifying the r16S portion in the context of microbial metagenomic identification.

[0109] Figure 2 An example of a polymerase chain reaction that can be simulated according to a set of implementation schemes is shown.

[0110] The polymerase chain reaction (PCR) consists of multiple consecutive cycles: Cyc21, Cyc22, Cyc23...Cyc2n. For better readability of the diagram, only the first cycle, Cyc21, will be described in detail.

[0111] The PCR reaction 2 is performed in a PCR kit, for example, in kit K1. The PCR kit initially comprises: - One or more nucleic acid sequences to be amplified, or "targets", such as Figure 2 The target, Targ2, is shown. The nucleic acid of the sequence to be amplified can initially be obtained from a sample, for example, via a swab (Swab1). -dNTP2 nucleotides; -PolyM2 polymerase; - Primer AM2.

[0112] The PCR reaction described in this article is a "single" reaction designed to amplify a single target, Targ2. However, the invention is not limited to this example and can also be applied to "multiplex" reactions designed to amplify multiple different targets simultaneously.

[0113] Each PCR amplification cycle includes: - The denaturation phase, denoted as Denat21 for Cyc21, occurs during which the double-stranded nucleic acid is separated into two single-stranded nucleic acids. In an instance of Cyc21 cycling, the target Targ2 initially exists as a double-stranded nucleic acid. During the denaturation phase, it is separated into two single-stranded nucleic acids, Nuc21 and Nuc22. - In the hybridization phase, denoted as Hybr21 for Cyc21, primers hybridize with single-stranded nucleic acids during this period. In an example of the Hybr21 phase, primers AM21 and AM22 hybridize with single-stranded nucleic acids Nuc21 and Nuc22, respectively. - The extension phase, denoted as Elong21 for cycle 21, is during which nucleotides complete the primer to form a double-stranded nucleic acid identical to the initial target, called an amplicon, referred to as Amp21 and Amp22 in the case of the Elong21 phase.

[0114] Therefore, at the end of the PCR amplification cycle, the single target Targ2 makes it possible to generate two identical amplicons, Amp21 and Amp22, which can themselves replicate in the next cycle. In each amplification cycle, the amplicons replicate as follows: the single target Targ2 results in two amplicons at the end of the first cycle (Cyc21), four amplicons at the end of the second cycle (Cyc22), eight amplicons at the end of the third cycle (Cyc23), and so on.

[0115] It should be noted that Figure 2 The amplifications shown are provided purely as a non-limiting example of amplifications that can be simulated by the present invention.

[0116] This invention can simulate other amplifications, such as multiplex amplification of different types of targets. Applications of this invention to specific PCR sequences have been described. This invention is applicable to any number of PCR sequences, where the input of a PCR consists of the output of the preceding PCR sequences.

[0117] The order of the stages can also be different. For example, the simulation can begin with the hybridization stage instead of the denaturation stage for each cycle. In this case, the cycle would include the hybridization stage, the subsequent extension stage, and the final denaturation stage.

[0118] Now for reference Figure 3 .

[0119] Figure 3 An example of temperature changes during a PCR amplification cycle is shown.

[0120] The Grph3 graph more precisely represents the evolution of temperature over time, using two consecutive cycles of PCR amplification, Cyc31 and Cyc32, as an example. Specifically, different stages of PCR amplification are activated by temperature changes within the amplification kit. In this example, the temperature profile is identical between cycles, and cycle cyc31 will be discussed in detail.

[0121] Typically, the temperature changes during a PCR amplification cycle are as follows: -During the hybridization phase, the temperature is initially at the first temperature, while the extension phase occurs simultaneously; Then the temperature rapidly rises to a second, higher temperature, triggering the denaturation phase, and then returns to the level of the first temperature in the hybridization phase of the next cycle.

[0122] In the instance of the Cyc31 loop: - The hybridization and extension phase of Hybr31 is activated by a first temperature of 60°C, lasting for T. hybr ; The denaturation phase of Denat31 is activated by a higher temperature, which is 96°C in this instance.

[0123] Figure 3 The durations and temperatures shown are provided purely as examples without limitation; the invention is applicable to PCR amplification performed at a variety of different durations and temperatures. Figure 3 In the example where hybridization and extension occur simultaneously, other PCR amplification reactions use three different temperatures to trigger the hybridization, extension, and denaturation phases, respectively. The temperature and duration of each phase affect the amplification reaction.

[0124] Therefore, the amplification reaction is affected by many parameters, such as: - The temperature and duration of each stage of the reaction (which can be fixed or vary depending on the cycle); -Primer selection and concentration; - Concentrations of monovalent and divalent salts; - Expected length of the amplicon; -wait.

[0125] These different factors can also lead to unexpected reactions, for example: - When two primers hybridize together, a primer dimer is formed; - Multiple hybridization occurs when primers hybridize not only to one end of a single-stranded nucleic acid but also to other positions, such as in the middle of a strand. In this case, extension will only occur on a portion of the strand, producing new amplicon.

[0126] The parameters of amplification can therefore promote or conversely slow down the desired amplification (called a specific reaction), or hinder it when unwanted / unexpected reactions (called non-specific reactions) occur, or even prevent the reaction from proceeding normally. Therefore, one of the purposes of simulating PCR amplification reactions is to model the amplification reaction as accurately as possible based on the environmental parameters of the reaction, in order to validate or conversely modify the design of the kit (i.e., the parameter values ​​used to promote a given amplification reaction—such as primer selection and concentration, temperature and duration of reaction phases, salt concentration, etc.).

[0127] However, the complexity of PCR amplification reaction kinetics, particularly the interactions between many reaction products and byproducts, makes such simulation difficult in practice. Therefore, one of the objectives of this disclosure is to provide a method for simulating PCR amplification reactions that can be performed in practice to simulate PCR reactions based on given parameters and to validate or modify the reaction parameters accordingly.

[0128] Figure 4 Examples of methods according to a set of embodiments of the present invention are shown.

[0129] Method P4 is a method for numerically simulating polymerase chain reactions of at least one target. According to various embodiments of the invention, it can be amplification of a single target, or "single" amplification, or amplification of multiple targets, or "multiplex" amplification.

[0130] The simulation includes multiple consecutive amplification cycles, each cycle consisting of a hybridization phase S41, an extension phase S42, and a denaturation phase S43.

[0131] The simulation can execute a finite number of loops. For example, each loop can be identified by a loop index ncyc, which increments between each loop in step S45.

[0132] At the end of each loop, the stopping criteria can be verified. For example: - Simulation can be performed for a predetermined number of cycles, NCyc. In this case, at the end of each cycle, the cycle index ncyc can be compared with the predetermined number of cycles, NCyc, and if ncyc >= NCyc, the criterion is validated (or, if ncyc < NCyc, a new cycle is started). - Amplicon concentrations can be compared between two cycles, and the simulation stops when a minimum number of cycles is reached and the difference in amplicon concentrations after two consecutive cycles is below a predetermined threshold. In other words, the criterion includes the number of cycles in which the reaction is considered complete. - The simulation can be stopped once the concentration of a given amplicon is above a threshold, such as the threshold for amplicon detectability; -wait.

[0133] Figure 4 An example is shown where the stopping criterion is reaching the cycle number NCyc. However, this example is provided only as a non-restrictive one. As mentioned above, one or more different criteria can be used to detect the end of the simulation.

[0134] In the remainder of the instruction manual, some of the symbols described below will be used to describe several simulation instances.

[0135] The concentration of the target molecule will be recorded in the vector of records shown below. middle: Equation 1

[0136] In the above vector, elements ...... This represents the concentration of possible amplicons (specific and non-specific) produced during PCR amplification. It should be noted that since the target and amplicons correspond to the same molecule, these values ​​correspond to the sum of the target and the concentration of amplicons for a given target. (Element) ...... In itself, it represents the concentration of possible primers. The unit of the vector elements can be mol·L. −1 .

[0137] Its concentration can be obtained in different ways and recorded in a vector. The concentrations of various molecules, particularly the concentrations of amplicon and various primers present in the simulation kit.

[0138] For example, its concentration is recorded in a vector. Multiple molecules can be obtained from a list of molecules defined by expert users.

[0139] However, it can be difficult to estimate a priori all the molecules formed during a PCR reaction, taking into account all possible reactions, such as reactions between reaction byproducts.

[0140] Therefore, the concentration recorded in the vector is determined through an initial simulation with a finite number of cycles. The initial simulation aimed to identify the molecules present in the amplification kit after a limited number of cycles, regardless of their concentration.

[0141] Therefore, the plurality of molecules can be initialized as if they were originally present in the polymerase chain reaction (especially amplicon and primer), and the initial simulation can then include a series of consecutive cycles of simulation involving the following steps: - To obtain hybridization reactions of molecules forming each molecular pair with an affinity below a threshold (or an absolute value above a threshold, since affinity is negative) from the plurality of molecules. In other words, the step includes identifying molecular pairs with an affinity below a threshold (or an absolute value above a threshold) from the molecules initially present in the initial simulation cycle, that is, molecular pairs that can be considered to react together; - The simulation includes the hybridization phase of the hybridization reaction. This initial simulated hybridization phase only includes the identification of the duplexes formed by the identified hybridization reaction; - Simulated extension stage. This initial simulated hybridization stage only includes identifying the extended duplexes obtained from the duplexes identified in the preceding steps; - Simulate the denaturation stage. This initial simulation of the denaturation stage includes identifying the molecule obtained by denaturing the duplexes acquired in the first two steps, as well as the extended duplexes; - Add additional molecules obtained at the end of the hybridization, extension, and denaturation phases to the plurality of molecules. This step includes adding molecules obtained at the end of the cycle that were not previously present in the plurality of molecules.

[0142] Therefore, in each cycle, new molecules produced by the reactions of the previous cycle can be added to a pool of already identified molecules, which themselves can generate new reactions. Thus, after a finite number of initial simulation cycles, it becomes possible to identify all the molecules that play a significant role in the simulation.

[0143] The initial number of iterations in the simulation can be set in several ways. For example: - It can be a predetermined number of initial simulation cycles; - The number of molecules added at the end of each cycle can be counted, and the initial simulation can be stopped when the number of molecules added at the end of a given cycle is zero or low, for example, if the number of molecules added is less than a given threshold. -wait.

[0144] The inventors have discovered that the initial number of simulation cycles can be between 3 and 7, for example, equal to 5, which is sufficient to obtain a definite list of molecules that have a significant impact on PCR results.

[0145] This presents a good trade-off between the number of molecules added and their importance. For example, molecules added after the 3rd, 5th, or 7th cycle might be considered less likely to elicit a significant response. Therefore, a predefined number of cycles between 3 and 7, such as a predefined number of cycles equal to 5, can limit the number of molecules used in the simulation and reduce the associated computational complexity while maintaining the reliability of the simulation.

[0146] Furthermore, a limited number of cyclic simulations are sufficient because molecules that appear after only a few cycles are unlikely to produce significant reactions compared to reactions that have undergone multiple cycles. Specifically, their very low concentrations, compared to competing molecules already present in the mixture, do not allow for significant multiplication.

[0147] Therefore, this initial simulation makes it possible to consider only the molecules that will actually be encountered in large quantities during the amplification reaction. This allows for more reliable and less resource-intensive simulations of the reaction.

[0148] Now for reference Figure 5 .

[0149] Figure 5 Examples of the hybridization stage in a set of embodiments of the present invention are shown.

[0150] exist Figure 5In the example, the hybridization phase S41 of a given cycle includes a first sub-step S411, which is to obtain the initial values ​​of the cycle for the concentration vector of multiple single-stranded nucleic acid molecules containing multiple amplicons and multiple primers. .

[0151] The concentration vector can be, for example, the vector described above. For example, the initial value of the vector. It can correspond to: - The initial concentration of molecules before the amplification reaction begins, if the simulated cycle is the first cycle; otherwise, it is 0 for molecules appearing in the next cycle. - If this cycle is not the first cycle, it corresponds to the molecular concentration at the end of the previous cycle.

[0152] The simulation of the hybridization phase aims to model the hybridization reactions that occur during the cycling process. Hybridization occurs between each pair of molecules capable of hybridization. and The following balance relationship between them is controlled: Equation 2

[0153] It should be noted here that an equation must be established such that every possible hybridization reaction between a pair of molecules indexed as i and j (i and j can be equal) is represented as a vector. The functions of molecules present in the sample are taken into consideration.

[0154] These equilibrium equations can be rewritten as the following differential equations: Equation 3

[0155] In the equation above: -symbol and Let each represent a vector involved in a given hybridization reaction. The concentration of a pair of single-stranded nucleic acid molecules with indices i and j; -symbol Represents the vector The concentration of the double strand formed by the hybridization of a pair of single-stranded nucleic acid molecules with indices i and j; -symbol and Representing vectors respectively The binding and dissociation constants of the hybridization reaction of a pair of single-stranded nucleic acid molecules with indices i and j.

[0156] The above differential equation applies to a pair of vector molecules that are considered to produce a hybridization reaction. Each reaction between them. Therefore, in some cases, the number of differential equations can be very large.

[0157] These molecular pairs that are considered to produce a hybridization reaction can be, for example, those molecular pairs whose hybridization reaction is related to a change in free enthalpy ΔG below a predetermined threshold (or whose absolute value is above the threshold and whose free enthalpy change is negative).

[0158] Therefore, only the major hybridization reactions are considered in the simulation. This makes it possible to obtain better accuracy in the hybridization reaction kinetics and reduce the complexity of solving the differential equation system. It also allows for consideration of the differential kinetics between different reactions based on whether the free enthalpy is more favorable or unfavorable between the two target reactions.

[0159] The predefined threshold can be the same for all reactions, or it can be selected from different thresholds depending on the situation. For example, the threshold can be selected from at least two predefined thresholds, with the lowest threshold reserved for molecular pairs containing amplicon and primer pairs.

[0160] In other words, the threshold for the free enthalpy change of the hybridization reaction between the amplicon and primer (above which the hybridization reaction is not considered in the simulation) is lower (closer to 0) than that of other reactions (therefore, the absolute value is below the threshold, and the free enthalpy change threshold is negative). This allows the simulation to preferentially consider hybridization between primers and amplicon, as well as hybridization between primers and other primers, thus allowing the simulation of the first few cycles of amplicon-primer hybridization, during which the amplicon concentration is much lower than the primer concentration.

[0161] In one set of embodiments of the present invention, the differential equation comprises a mass conservation equation of the following form: Equation 4 Equation 5

[0162] in: - This represents the time elapsed since the start of the hybridization stage; -symbol and These represent the concentration vectors of multiple nucleic acid molecules. The concentrations of the two single-stranded nucleic acid molecules with indices i and j in the middle; -symbol Represents a concentration vector of multiple nucleic acid molecules The index in the table represents the concentration of the double strand formed by the hybridization of a pair of single-stranded nucleic acid molecules, x and y. -symbol and express hour and value

[0163] The above equation links the concentration of each single-stranded nucleic acid molecule to the concentration of all duplexes formed through hybridization, demonstrating that hybridization does not modify the total number of single strands of each type. This can be represented as a vector. This type of mass conservation equation is established for each single-stranded nucleic acid molecule present in the sample.

[0164] It should be noted that the above mass conservation equation is provided only as a non-limiting example. According to various embodiments of the invention, equivalent formulas of the mass conservation equation can be used, i.e., other equations reflecting the concentration evolution of single-stranded nucleic acid molecules and duplexes without changing the total number of single strands of each type.

[0165] Integrating the mass conservation equation into the differential equation can refine the equation, allowing for a more accurate simulation of the hybridization phase, thus yielding an equation with as many unknowns as there are unknowns.

[0166] Substituting the hybridization reaction between a pair of single-stranded nucleic acid molecules into the differential equation (e.g., equation 3), and substituting the two mass conservation equations for the two molecules in the pair, the equation can be rewritten in the following form: Equation 6

[0167] To solve a system of differential equations, such as Figure 5 One of the principles behind the simulation of the hybridization stage shown is to represent these equations in the form of matrix differential equations.

[0168] Therefore, in Figure 5 In the example, the simulation of the hybridization stage S41 includes a second sub-step S412, namely, initializing the concentration matrix. Or a double strand formed by the hybridization of multiple single-stranded nucleic acid molecules .

[0169] The matrix can be an N×N matrix formed as follows (N is a vector). (length) - Each row and each column corresponds to one nucleic acid molecule; --Each cell includes the concentration of duplexes formed by the hybridization of nucleic acid pairs in the row and column to which that cell belongs. A triangle can be used to count the concentration of a given duplex only once; otherwise, it will be counted in both the cells at coordinates i,j and j,i.

[0170] Therefore, the matrix It can be written as: Equation 7

[0171] exist Figure 5 In an example, a given hybridization phase S41 of a cycle includes a third sub-step S413, which is to calculate the evolution of the concentration matrix during the hybridization phase by applying the matrix differential equation representing the duplex formation kinetics as a function of the concentration of multiple single-stranded nucleic acid molecules to the concentration matrix in successive time steps.

[0172] The calculation of matrix evolution can be performed, for example, as follows: The calculation is performed for a number of time steps, Npdt, corresponding to the duration of the hybridization phase. For example, the time step can have a duration between 1 and 10 milliseconds. For instance, the time step can be chosen to find a trade-off between computational convergence, computational speed, and result accuracy. - The time step index npdt is initialized to 1; - At each time step, perform the sub-step S413 to calculate the evolution of the concentration matrix; - At the end of the calculation, sub-step S414 verifies that the time step index npdt is indeed lower than the time step number Npdt; - If the time step index npdt is less than the time step number Npdt, then in sub-step S412, the time step index npdt is incremented, and then a new iteration is performed in sub-step S413 for calculating the evolution of the concentration matrix. - When the time step index npdt equals the time step number Npdt, the simulation of the hybridization stage terminates, and the simulation of the extension stage S42 begins.

[0173] Therefore, the simulation of the hybridization phase can be accomplished by simulating Npdt consecutive time steps of the hybridization reaction, each time step including vector-based simulation at the end of the previous time step. The molecular concentration is used to calculate the matrix differential equation.

[0174] This example of a continuously computed loop is provided only as a non-limiting example of a loop instruction for the computational hybridization phase. More generally, in the context of this invention, any computational loop instruction that allows the hybridization phase to be simulated according to a desired time step can be used. For example, the time step index can be initialized to 0, and the loop instruction exit condition in step S414 can be adjusted, etc.

[0175] The matrix differential equation is parameterized by at least one binding matrix containing the binding constant associated with each duplex and at least one dissociation matrix containing the dissociation constant associated with each duplex.

[0176] Therefore, the associative matrix contains all the associative coefficients included in equations 3 and 5. According to the matrix... Based on the principle of the same concentration, the binding coefficient and dissociation coefficient can be integrated into the binding matrix and dissociation matrix (e.g., the binding matrix and dissociation matrix are square matrices, where each row and each column corresponds to a molecule, each cell of the binding matrix includes the binding constant between the molecule in that row and column and the part of the duplex, and each cell of the dissociation matrix includes the dissociation constant associated with the dissociation reaction from the duplex to the molecular pair associated with that row and column).

[0177] Therefore, the combination matrix and the dissociation matrix can be written as follows: Equation 8 (for associative matrices) as well as: Equation 9 (for the associative matrix).

[0178] The unit of the combined constant can be m 3 .mol -1 .s -1 (or L.mol) -1 .s -1 The unit of the dissociation constant can be s. −1 .

[0179] As described above, in one set of embodiments of the invention, only certain hybridization reactions are taken into consideration. In this case, the binding constant and dissociation constant are therefore integrated only for reactions deemed sufficiently important (i.e., reactions that have the greatest impact on the simulation). For example, this can be achieved by defining each element of the binding matrix or each element of the dissociation matrix, said element being associated with a pair of molecules belonging to said matrix, said element being defined as: - Zero, if the change in free enthalpy (ΔG) associated with the hybridization reaction of the molecules forming the pair is greater than the threshold (or the absolute value is less than the threshold). Otherwise, they are equal to the binding constant or dissociation constant of the hybridization reaction of the molecular pair, respectively.

[0180] In other words, for less important reactions, such as if the change in free enthalpy (ΔG) associated with the hybridization reaction of molecules forming pairs is above a given threshold (or the absolute value is below that threshold), the values ​​of the binding constant and dissociation constant in the matrix will be equal to 0.

[0181] Therefore, considering only the main reactions reduces the complexity of the simulation while benefiting from good simulation accuracy.

[0182] As mentioned above, the threshold used to take hybridization reactions into account and thus integrate the binding constant and dissociation constant into the matrix can be the same for all reactions, or it can differ depending on whether the reaction is an amplicon-primer hybridization reaction or another type of hybridization reaction (e.g., primer-primer).

[0183] Therefore, by means of the combination matrix and the dissociation matrix, the evolution of the double-chain concentration matrix can be written in the form of a matrix differential equation, and substep S413 can therefore include solving a matrix differential equation for a given time step.

[0184] Therefore, solving matrix differential equations makes it possible to model the entire kinetics of chain expansion, including cross-reactions with intermediates. Solving a single matrix differential equation also makes it possible to solve system dynamics using conventional computing power.

[0185] This allows for the complete simulation of amplification (especially hybridization reactions that cannot be satisfactorily simulated in existing solutions), enabling the verification or, conversely, modification of parameters affecting the amplification reaction (primers, initial salt concentration, duration of phases, and temperature, etc.).

[0186] When the mass conservation equation is taken into account, it can be written as a matrix differential equation (which integrates multiple differential equations (e.g., equation 6 for each reaction)): Equation 10

[0187] in: -H is the concentration matrix of the double strand; -T0 is the initial value for the cycle of concentration vectors of multiple molecules; -K on It is a combined matrix; -K off It is the dissociation matrix; - It is an identity matrix of size N; - It is the Hadamard product; -diag() represents the diagonal operator, used to convert an N x N square matrix into a vector of size N, which contains all the elements along the diagonal of the matrix. Therefore,

[0188] It can be noted that T has been replaced by T0 in the differential equation, which enables faster matrix calculations.

[0189] Now for reference Figure 6 and 7 .

[0190] Figure 6 Examples of two stages, extension and modification, are shown in one set of embodiments of the invention.

[0191] Figure 7 This illustrates an example of a series of hybridization, extension, and denaturation reactions occurring in three consecutive cycles of a PCR amplification reaction. Figure 7 The reaction shown better illustrates Figure 6 The simulation steps of the extension and transformation stages are shown.

[0192] Figure 7 A simplified example of a single-target amplification reaction is shown.

[0193] Figure 7 More specifically, it shows a series of hybridization, extension and denaturation reactions that occur in a given environment, with new reactions appearing in cycles 2 and 3 as new byproducts are generated.

[0194] exist Figure 7 In this example, the simulation initially includes (the start of the hybridization phase in cycle 1): -The "sense" and "antisense" single-stranded nucleic acids of the target, respectively and ; - A "meaningful" primer and two "antonym" primers and ;

[0195] In the first cycle, the reaction is as follows: -React71: The first position with the primer Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be denatured into two single-stranded nucleic acids. and ; -React72: At the second position with the primer Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be denatured into two single-stranded nucleic acids. and Although the molecules that pair in React71 and React72 are the same, these reactions are different because pairing occurs at two different sites, so in the case of React72, elongation occurs over a shorter distance. This is known as "multiple hybridization." The change in enthalpy of free energy ΔG associated with these two reactions may also be different. Therefore, Reactions React71 and React72 each produce two independent single-chain molecules. and ; - React 73: With primers Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be denatured into two single-stranded nucleic acids. and ; -React74: and Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be denatured into two single-stranded nucleic acids. and ; - React 75: and Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be denatured into two single-stranded nucleic acids. and Although the pairing primers in React74 and React75 are the same, these reactions are different because the extension does not occur on the same strand: in the case of React74, the "antisense" strand is extended, while in the case of React75, the "sense" strand is extended.

[0196] At the end of this second cycle, new reaction byproducts are thus added to the existing products: , , , , .

[0197] In the second cycle, in addition to the five reactions React71 to React75 that already occurred in the first cycle, the presence of these new byproducts generated six new reactions: -React76: With primers Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be denatured into two single-stranded nucleic acids. and ; - React77: With primers Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be denatured into two single-stranded nucleic acids. and ; - React78: The first position with the primer Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be denatured into two single-stranded nucleic acids. and ; -React79: At the second position with the primer Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be denatured into two single-stranded nucleic acids. and Although the molecules paired in React78 and React79 are the same, these reactions are different because pairing occurs at two different positions, so in the case of React79, elongation occurs over a shorter distance. This is known as "multiple hybridization." Therefore, Reactions 78 and 79 each produce two independent single-stranded molecules. and ; - React 710: and Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be denatured into two single-stranded nucleic acids. and ; - React 711: and Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be denatured into two single-stranded nucleic acids. and Although the products of React 710 and React 711 are the same, these reactions are different because the paired molecules are different, and the elongation does not occur on the same chain: in the case of React 710, the "antense" chain is extended, while in the case of React 711, the "sense" chain is extended. It should also be noted that although... and For simulation purposes, they are treated as two different molecules associated with two different concentrations, but they are actually the same molecule.

[0198] At the end of this second cycle, new reaction byproducts are thus added to the existing products: , , and .

[0199] In the third cycle, in addition to the 11 reactions React71 to React711 that had already occurred in the second cycle, the presence of these new byproducts generated 4 new reactions: -React712: With primers Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be transformed Two single-stranded nucleic acids and ; - React 713: With primers Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be denatured into two single-stranded nucleic acids. and ; -React714: With primers Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be denatured into two single-stranded nucleic acids. and Although the products of React712 and React714 are the same, these reactions are different because the paired molecules are different, and the elongation does not occur on the same chain: in the case of React712, the "antense" chain is extended, while in the case of React714, the "sense" chain is extended. It should also be noted that although... and For simulation purposes, they are treated as two different molecules associated with two different concentrations, but they are actually the same molecule. -React715: With primers Pairing to produce a bilayer Then the double strand will be extended into an extended double strand. It will be denatured into two single-stranded nucleic acids. and Although the products of React 713 and React 715 are the same, these reactions are different because the paired molecules are different, and the elongation does not occur on the same chain: in the case of React 713, the "antense" chain is extended, while in the case of React 715, the "sense" chain is extended. It should also be noted that although... and For simulation purposes, they are treated as two different molecules associated with two different concentrations, but they are actually the same molecule.

[0200] exist Figure 6 As shown and Figure 7 One principle behind simulating the hybridization and denaturation stages in the illustrated embodiment of the invention is to simulate multiple multiple hybridization reactions (e.g., reactions React71 and React72, or React76 and React77) as a single reaction producing multiple reaction products, and then use the denaturation tensor to allocate the concentrations of the multiple hybridization reaction products for the next simulation cycle. Therefore, the concentrations of duplexes and extended duplexes corresponding to different pairing positions are represented by a single value.

[0201] By disregarding pairing positions and using a single concentration value for all duplexes between a pair of nucleic acid molecules, it is possible to reduce the number of equations required to solve for denaturation and make the problem of simulating denaturation solvable.

[0202] In one set of embodiments of the invention, certain reactions are caused by two primers pairing to form a doublet. In this case, bidirectional extension can occur. For example, this is the case with reactions React74 and React75. In this case, in some embodiments of the invention, the extension phase simulates extending such a doublet into a single extended doublet, and defines coefficients of the denaturation tensor such that the concentration of the single extended doublet produced by the pairing of the two primers produces a reaction product corresponding to bidirectional extension.

[0203] This simplifies the simulation of the reaction generated by the pairing of two primers, thereby further reducing the computational complexity of the simulation.

[0204] Therefore, in Figure 7In some examples, the reaction can be represented by the following equation, where: - Represents the elongation constant associated with each reaction; - Represents the denaturation constant associated with each reaction; - Represents the respective weights associated with the molecules produced by several reactions, when, for simulation purposes, the concentration of the extended duplex actually represents the concentration of multiple different duplexes; - The three consecutive arrows for each reaction represent hybridization, extension, and denaturation; - The molecule to the right of the last arrow represents the denatured product. To improve the readability of the equation, only the new molecules are shown.

[0205] Reactions React71 and React72 can be represented by the following equations: Equation 11

[0206] Note the two concentrations of the double strand in this multiple hybridization case. and From a single concentration This indicates the two concentrations of the extended double strand. and From a single concentration This indicates that the respective weights are applied in the variant tensor. This makes it possible to update the concentrations of the two molecules. and The weights of the reactions generated by the two pairings are also taken into consideration.

[0207] The React73 reaction is represented by the following equation: Equation 12

[0208] Reactions React74 and React75 can be represented by the following equations: Equation 13

[0209] Note that in reactions produced by the pairing of two primers (primer dimers), there are two concentrations of extended double strands. and From a single concentration This indicates the two concentrations of the extended double strand. and From a single concentration This indicates that the respective weights are applied in the variant tensor. This makes it possible to update the concentrations of the two molecules. and .

[0210] The use of weights is as follows: an equation representing multiple reactions, such as equation 13, can be associated with multiple weights (e.g., weights stored in a variable tensor), which represent the relative importance of different reactions. For example, for equation 13, reactions React74 and React75 can be associated with weights respectively. and Related. At the end of each cycle, a single concentration The concentration of the reactants. For example, for equation 13, the concentration of molecules. Increase at the end of the loop * And the concentration of molecules Increase at the end of the loop * Therefore, weight and The sum must equal 1, therefore and This represents the relative importance of React74 and React75. For example, weights. = 0.5 and = 0.5 indicates that React74 and React75 are equally common.

[0211] The reaction React76 is represented by the following equation: Equation 14

[0212] The React77 reaction is represented by the following equation: Equation 15

[0213] Reactions React78 and React79 can be represented by the following equations: Equation 16

[0214] Note the two concentrations of the double strand in this multiple hybridization case. and From a single concentration This indicates the two concentrations of the extended double strand. and From a single concentration This indicates that the respective weights are applied in the variant tensor. This makes it possible to update the concentrations of the two molecules. and The weights of the reactions generated by the two pairings are also taken into consideration.

[0215] The React710 reaction is represented by the following equation: Equation 17

[0216] The React711 reaction is represented by the following equation: Equation 18

[0217] The reaction React712 is represented by the following equation: Equation 19

[0218] The reaction React713 is represented by the following equation: Equation 20

[0219] The reaction React714 is represented by the following equation: Equation 20

[0220] The reaction React715 is represented by the following equation: Equation 22

[0221] In one set of embodiments of the present invention: - Each molecule involved in the simulation is related to a vector. It is associated with one of the indexes; - The concentration of double strands produced during the hybridization stage in the matrix Recorded in, where they are arranged according to their position in the vector The index order in the table is such that each row and column represents a molecule.

[0222] For example, in Figure 7 In the example, matrix It can be written as: Equation 23

[0223] In the diagram above, the single-stranded molecules associated with each column and each row are recorded at the top of each column and the left side of each row, respectively. According to the equation above, in the case of multiple hybridization, a single double-strand concentration is recorded in the matrix, which actually represents the concentration of multiple double-stranded molecules corresponding to multiple pairing positions. For example: - Corresponds to line " "sum column" The unit "" contains concentration In fact, it represents concentration. and The sum; - Corresponds to line " "sum column" The unit "" contains concentration In fact, it represents concentration. and The sum of .

[0224] It should be noted that these examples are given for multiple hybridizations at two different pairing positions, but the principle can be generalized to multiple hybridizations at any number of different pairing positions greater than or equal to 2.

[0225] In one embodiment of the invention, the concentration of the extended double strand is obtained during simulation S42 of the extension phase by multiplying the concentration of the double strand by the extension constant.

[0226] For example, the stretching constant can be listed in the stretching tensor, which is based on the matrix. The same principle applies, namely, extending the tensor. Each cell contains a matrix The elongation factor of the corresponding unit's double chain. Therefore, in Figure 7 In this instance, the extended tensor will be: Equation 24

[0227] The numbering of the extension constant here refers to the vector Indexes of single-stranded nucleic acid molecules. For example, in tensors. The constants recorded in column 1 and row 11 Represents a vector Molecules with indices 1 and 11 (i.e., molecules) and The elongation coefficient of the double strand formed by hybridization, that is... Also in the matrix The extension constants are recorded in column 1 and row 11. These constants can be read from a database, for example, or obtained experimentally.

[0228] Therefore, each extension coefficient represents a coefficient between 0 and 1 for a given duplex molecule that is extended during the extension phase. For example, a coefficient of 0.5 for a given duplex means that half of the duplex molecules are extended during the extension phase. Therefore, the concentration of extended duplexes at the end of the extension phase will be half the concentration of non-extended duplexes at the beginning of the extension phase. Thus, the extension tensor consists of extension coefficients between 0 and 1.

[0229] More generally, the simulation phase of the extension phase can be performed by step S421, which involves multiplying the concentration matrix of the non-extended duplex by the extension tensor: Equation 25

[0230] in: -C represents the index of the PCR amplification cycle; - Represents the duration of the extended phase; - This represents the concentration matrix of non-extended double strands in the Cth round of PCR amplification cycle; - This represents the concentration matrix of extended double strands in the Cth round of PCR amplification cycle; - Represents the extended tensor.

[0231] Since not all duplexes are extended during the extension phase, the concentration of non-extended duplexes at the end of the cycle is equal to the concentration of non-extended duplexes at the beginning of the cycle minus the concentration of extended duplexes at the end of the phase. For example: Equation 26

[0232] The extension phase has been illustrated here using Hadamard matrix multiplication. However, this is not the only way to simulate the extension phase. For example, the extension phase can be simulated more generally by multiplying the concentration of each non-extended duplex at the start of the extension phase by the extension coefficient of that duplex. For instance, the concentration of the non-extended duplex can be incorporated into the concentration vector of the non-extended duplex, and this vector can be multiplied by the extension coefficient vector.

[0233] The sex change phase can actually include two steps: - Step S431, multiply the concentration of extended and possibly non-extended duplexes by one or more denaturation tensors, which represent the distribution of duplexes in single-stranded nucleic acid molecules; - Step S432: Multiply the concentration of the duplex or the product of the concentrations of the duplexes by the denaturation tensor, and by one or more denaturation coefficients, which represent the proportion of duplexes that are actually denatured during the denaturation stage.

[0234] In one embodiment of the invention, the denaturation phase includes multiplying the concentration of the extended duplex by the denaturation tensor of the extended duplex. The denaturation tensor of the extended duplex effectively represents the redistribution of the extended duplex into single-stranded nucleic acid molecules during the denaturation phase.

[0235] This makes it possible to simulate the denaturation of already extended duplexes and to integrate the concentrations of extended and denatured duplexes under the initial conditions of the next cycle.

[0236] In one embodiment of the invention, the denaturation stage further includes multiplying the concentration of the non-extended duplex by the denaturation tensor of the non-extended duplex.

[0237] Therefore, the simulation of the denaturation stage considers both the denaturation of the extended duplex and the denaturation of the non-extended duplex, thus allowing for more accurate simulation results.

[0238] During the simulated denaturation phase, the denaturation coefficient can also be applied to the concentration of extended / non-extended duplexes and / or the concentration of single-stranded nucleic acids obtained by multiplying the concentration of extended / non-extended duplexes by the denaturation tensor.

[0239] The denaturation coefficient represents the proportion of a given type of bistrand that actually denatures during the denaturation phase. The denaturation coefficient can be obtained, for example, from a database or through experimentation.

[0240] Therefore, each denaturation coefficient represents the coefficient of a given double-stranded molecule that was denatured during the denaturation stage, and is between 0 and 1. For example, a coefficient of 0.5 for a given double-stranded molecule means that half of the double-stranded molecule was denatured during the denaturation stage.

[0241] According to various implementation plans: - The same variation coefficient can be applied to a given extended duplex and the corresponding non-extended duplex. This allows for a good approximation of the variation while simplifying the calculation; - Two different denaturation coefficients can be applied to a given extended duplex and the corresponding non-extended duplex, respectively. This allows for more accurate simulations when the extended and non-extended duplexes undergo different denaturations.

[0242] For example, the mutation coefficients can be applied using matrix multiplication. For instance, the mutation stage can be simulated using the following equation: Equation 27 Equation 28 + Equation 29

[0243] in: - It is the Hadamard product; - It is the identity matrix; - It is a variation matrix that contains the variation coefficients associated with each duplex; - It is an extended matrix; - It is the concentration matrix of non-extended duplexes at the end of the denaturation phase in cycle C; - It is the concentration matrix of the extended duplex at the beginning of the denaturation phase in cycle C; - It is the concentration matrix of non-extended duplexes at the start of the subsequent cycle C+1; - It is the concentration matrix of the extended double strands at the start of the subsequent cycle C+1; - Represents the tensor product; - It is the modified tensor of the extended double chain; - It is a non-extended bichain deformable tensor; - It is the concentration of the extended double strand at the end of the elongation phase, expressed in vector form; - It is the concentration of non-extended duplexes at the end of the extension phase, expressed in vector form; - This represents the concentration vector of single-stranded nucleic acid molecules at the end of the extension phase in PCR amplification cycle C; - This represents the concentration vector of single-stranded nucleic acid molecules at the start of the subsequent PCR amplification cycle C+1;

[0244] Equation 27 represents the concentration of non-extended and non-denatured duplexes found at the start of the subsequent amplification cycle C+1.

[0245] Equation 28 represents the concentrations of non-denatured and extended duplexes found at the start of the subsequent amplification cycle C+1.

[0246] Equation 29 represents the distribution of single-stranded nucleic acids in the denatured duplex at the start of the subsequent amplification cycle C+1. More specifically: - This represents the distribution of extended duplexes in single-stranded nucleic acids by applying the denaturation tensor of extended duplexes; - This represents the distribution of non-extended duplexes in single-stranded nucleic acids by applying the denaturation tensor of non-extended duplexes; - This represents the application of denaturation tensors in the distribution of single-stranded nucleic acids; -Therefore, terminology The changes in single-stranded nucleic acid during the PCR amplification cycle representing index C.

[0247] It should be noted that the examples provided above are given purely as non-limiting examples, and other expressions can be applied to simulate the denaturation stage. For example, an equivalent formula for the molecular distribution from a duplex to a single-chain form can be used, multiplied by a denaturation constant. For instance, multiplying by the denaturation constant can be done using vector multiplication.

[0248] In the examples of Equations 28 and 29, the variable constants are listed based on the matrix. In the modified tensor constructed using the same principle, namely the extended tensor... Each cell contains a matrix The elongation factor of the corresponding unit's double chain. Therefore, in Figure 7 In this instance, the transformation tensor will be: Equation 30

[0249] The numbering of the extension constant here refers to the vector Indexes of single-stranded nucleic acid molecules. For example, in tensors. The constants recorded in column 1 and row 11 Represents a vector Molecules with indices 1 and 11 (i.e., molecules) and The denaturation coefficient of the double strands formed by hybridization, that is... Also in the matrix Recorded in column 1 and row 11. In this example, the same mutation coefficient is applied to both the duplex and the corresponding extended duplex (e.g., and However, in other embodiments of the invention, different denaturation coefficients can be applied to certain duplexes and extended duplexes, for example, if the denaturation kinetics between the two versions are significantly different. Denaturation coefficients can be read from a database, for example, or obtained experimentally.

[0250] Therefore, each denaturation coefficient represents the coefficient of a given double-stranded molecule that is denatured during the denaturation phase, and is between 0 and 1. For example, a coefficient of 0.5 for a given double-stranded molecule means that half of the molecules in that double-stranded molecule are denatured during the elongation phase. Therefore, the concentration of elongated / non-elongated double-stranded molecules at the end of the denaturation phase will be half the concentration at the beginning of the denaturation phase. Thus, the denaturation tensor is composed of denaturation coefficients between 0 and 1.

[0251] In the case of non-extended duplexes (i.e. duplexes produced by hybridization of two non-extended single-stranded nucleic acid molecules), the molecules are not transformed, and denaturation has the effect of restoring the two hybridized single-stranded nucleic acid molecules.

[0252] exist Figure 7 In the examples, the variations of the extended duplex are summarized in the table below, where each row includes a reference identifier for the partial duplex, which is located in the vector... The index in the diagram represents two single-stranded nucleic acid molecules whose hybridization makes the formation of a double helix possible, and which is reconstructed at the end of the denaturation phase, along with the indexes of these two molecules: Table 1

[0253] Therefore, in this example, the variable tensor of the non-extended bichain It can be written as: Equation 31

[0254] Deformation tensor of non-extended bichain In this example, it is a tensor of size 12×14: it consists of 12 rows, each corresponding to a vector. The 12 doubly linked entities are labeled to the left of each corresponding row, and arranged according to their positions in the vector. The index order label in the text. It also includes 14 columns, each corresponding to a vector. The 14 single-stranded nucleic acid molecules are labeled above each corresponding column and arranged according to their position in the vector. The index order is indicated in the table. The value "1" is written in each cell of the row belonging to the double strand and the column of the single-stranded nucleic acid produced by the denaturation of the extended double strand.

[0255] Therefore, the denaturation tensor can convert molecular concentration from [previous value] to [current value] with a single, simple algebraic operation. Distributed to the next cycle The denaturation tensor can also be used to verify the correctness of the reaction by summing each row. Specifically, the sum of the elements in each row must equal 2 (because each duplex produces two single-stranded nucleic acid molecules during the denaturation phase).

[0256] In this example, the variable tensor size of the extended bichain is also 12×14, with each row representing an extended bichain (their order being their position in the vector). (In the index), each column represents a single-stranded nucleic acid molecule (their order is based on their position in the vector). (Index in the text). In the case of a duplex corresponding to a single hybridization reaction at a single position, it is constructed as a denaturation tensor, with the value "1" written in each cell of the row belonging to the extended duplex and the column of the single-stranded nucleic acid produced by the denaturation of the extended duplex.

[0257] In one set of embodiments of the invention, in the case of multiple hybridization, i.e., hybridization of the same primer at multiple sites on the same single-stranded nucleic acid, such as in React71 and React72, or in the case of React78 and React79, the denaturation tensor of the extended duplex also contains specific coefficients.

[0258] In this case, denaturation produces not two, but at least three single-stranded nucleic acids. In the case of React71 and React72 or React78 and React79, denaturation will produce three single-stranded nucleic acids because multiple hybridization occurs at two positions, but if hybridization occurs at more positions, the same principle can be generalized to more denatured products.

[0259] In this case, the concentration of the double strand and the concentration of the extended double strand respectively include the concentration of the virtual double strand, which is equal to the sum of the concentrations of the double strands formed by the multiple hybridization reaction, and the concentration of the extended virtual double strand, which is equal to the sum of the concentrations of the extended double strands formed by the extension of the double strands formed by the multiple hybridization reaction.

[0260] For example: -In the case of multiple hybridization reactions React71 and React72: - The concentration of non-extended duplexes includes representative concentrations and The concentration of the virtual double strands of the sum ; - The concentration of the extended double strand includes a representative concentration. and The concentration of the extended virtual double strand of the sum ; - In the case of multiple hybridization reactions React78 and React79: - The concentration of non-extended duplexes includes representative concentrations and The concentration of the virtual double strands of the sum ; - The concentration of the extended double strand includes a representative concentration. and The concentration of the extended virtual double strand of the sum ;

[0261] In this case, the coefficients of the denaturation tensor of the extended duplex corresponding to the concentration distribution of the extended virtual duplex of each single-stranded nucleic acid associated with one of the multiple hybridization reactions can be equal to the interaction energy of the multiple hybridization reaction divided by the ratio of the sum of the interaction energies of all multiple hybridization reactions with the single-stranded nucleic acid.

[0262] For example, in the case of multiple hybridization reactions React71 and React72, virtual duplexes Will undergo gender reassignment: -On the one hand, transgender This is present in both React 71 and React 72. Therefore, the correlation coefficient will be 1. -On the other hand, transgender and This corresponds to reactions React71 and React72. Therefore, with molecules and The correlation coefficients must correspond to the importance of React71 and React72 respectively, that is, to the importance of the crossover of React71 and the crossover of React72. Therefore, these two coefficients can be equal to the interaction energy of the React71 crossover divided by the sum of the crossover energies of React71 and React72, and the interaction energy of the React72 crossover divided by the sum of the crossover energies of React71 and React72, respectively.

[0263] For example, if the hybridization reaction React71 has an interaction energy Furthermore, the hybridization reaction React72 possesses interaction energy. Then the modified tensor of the extended double chain is related to and The relevant weights will be equal to: -for , ; -and for , .

[0264] Therefore, multiple hybridization reactions, as well as the associated extensions and denaturations, can be simulated as a single series of reactions while maintaining the accuracy of the simulation.

[0265] In one set of embodiments of the invention, when hybridization (or "primer dimer") occurs between two primers, the denaturation tensor of the extended double strand also contains specific coefficients. Specifically, in this case, the double strand formed by the hybridization of the two primers can extend in two directions, which ultimately produces different denaturation products, such as in reactions React74 and React75.

[0266] In this case, the concentration of the extended double strand, including the concentration of the extended virtual double strand, is equal to the sum of the concentrations of the extended double strands formed by the extension of the double strand formed by the hybridization of the two primers in each of the two directions.

[0267] For example, in the case of React74 and React75 reactions, the concentration of the extended duplex can include the concentration of the extended virtual duplex. ,represent and The sum of concentrations. Therefore, the concentration of the extended virtual double strand. It does not correspond to the concentration of the real double strand, but it is useful for simulation.

[0268] The coefficients of the denaturation tensor of the extended duplex, corresponding to the concentration distribution of the extended virtual duplex to each of the two primers and to each of the two single-stranded nucleic acids generated by extension in one of the two directions, can all be equal to 0.5, indicating that the frequency of extension occurring in one of the two directions is approximately half. For example, in the case of React74 and React75, the denaturation product is the primer. and and nucleic acids and In the deformation tensor of the extended double chain, lines and , , and Therefore, all cells in the column are equal to 0.5.

[0269] This makes it possible to effectively simulate the reactions produced by primer hybridization while limiting the complexity of the simulation.

[0270] exist Figure 7 In the example, denaturation tensor coefficients can be defined for each denaturation reaction of the extended duplex to be presented in a table constructed based on the same principles as the table for the non-extended duplex: Table 2

[0271] The following situation was observed here: -For extended virtual doubly and There exists a coefficient corresponding to the multiple hybridization reaction. -For the extended virtual part of the double chain There exists a coefficient corresponding to the hybridization between primers.

[0272] In this example, the coefficients associated with the two pairs of multiple hybridization responses were set to 0.8 and 0.2.

[0273] Therefore, it is possible to construct the following modified tensor of extended bichain: Equation 32

[0274] The form of this tensor allows the concentration of the extended double strand to be allocated to single-stranded nucleic acid molecules through simple algebraic operations.

[0275] Furthermore, by verifying that the sum of the values ​​in each row equals 2, it can be confirmed that the mutation is under control.

[0276] Now for reference Figure 8 .

[0277] Figure 8 Examples of methods according to a set of embodiments of the present invention are shown, which integrate the verification or modification of PCR amplification parameters.

[0278] In one set of embodiments of the present invention, features of the PCR kit, such as the selection of multiple primers and the initial values ​​of the concentration vector of the multiple primers in the first cycle of the reaction, can be verified or modified based on simulation results.

[0279] For example, in addition to the steps in method P4, method P8 also includes: - Step S81: Display the simulation results. For example, this display may include evolution curves showing molecular concentrations, values ​​representing reaction kinetics, etc.; - Step S82, compare the value representing the reaction kinetics with the threshold; -If the comparison result is positive, proceed to step S83 to verify the primers and the initial primer concentration; - Otherwise, proceed to step S84 to modify the primers and / or the initial primer concentrations.

[0280] At the end of step S84, the simulation can be rerun based on the modified parameters.

[0281] Therefore, it makes it possible to ensure that the primer parameters and their concentrations are indeed capable of achieving the desired amplification with sufficiently high kinetics, or conversely, to modify them to meet the constraint.

[0282] Step S82 compares a value representing reaction kinetics with a threshold, which can significantly verify that a given amplification reaction will be fast enough to be detected. For example, the threshold considered could be one of the following: - Cyclic threshold (Ct); - Intersection (Cp); - The final concentration of nucleic acid molecules amplified through the reaction; - The concentration of amplicon at the end of the reaction.

[0283] Therefore, step S82 may include verifying that the Ct or Cp of the amplification reaction for a given target is greater than a reference threshold (i.e., the threshold cycle Ct or crossover point Cp is too high, which means the amplification reaction is not fast enough), which means the reaction is not fast enough.

[0284] If method P8 includes a display step S81, this is a non-limiting instance. Specifically, the display may, for example, enable an expert user to verify or refute the simulation parameters, but the comparison in step S82 may also be performed automatically without the previous display.

[0285] The changes implemented in step S84 can be accomplished in various ways. For example, they can be made manually by an expert user. Alternatively, they can be made automatically, or changes can be proposed to the expert user based on the simulation results.

[0286] The following will describe an example of the changes in step S84.

[0287] First, step S84 may include sub-step S841, which identifies preferred targets based on the results of polymerase chain reaction simulation.

[0288] For example, a preferred target could be one whose amplification kinetics are not fast enough. For example, one or more comparisons as discussed in step S82 can be performed on each target, and targets with negative comparison results (e.g., targets with Ct or Cp greater than a predetermined threshold) can be considered preferred targets because the amplification kinetics are insufficient in the current case.

[0289] Then, step S84 may include a second sub-step S842, identifying single-stranded nucleic acid molecules that pair with primers associated with the target from the binding matrix or dissociation matrix.

[0290] Therefore, substep S842 includes identifying non-target molecules that pair with primers associated with the target, i.e., molecules that compete with the target (and the amplicon generated by the target amplification) for primer pairing. Such molecules can be represented using a binding matrix. or dissociation matrix This is used for identification. Specifically, these matrices contain the coefficients of each pair of molecules linked by a sufficiently strong hybridization reaction. For example, the molecule can thus be identified as one with a primer binding constant, or one with a primer binding constant greater than a threshold.

[0291] Then, step S84 may include at least one modification to the polymerase chain reaction. This at least one modification to the polymerase chain reaction may significantly include at least one modification selected from: - In the initial concentration vector, the initial concentration of the single-stranded nucleic acid molecules that pair with the primers associated with the target decreases; - Change the salt concentration; - Change the hybridization temperature for at least one cycle.

[0292] These modifications can significantly hinder hybridization between single-stranded nucleic acid molecules and primers that pair with primers associated with the target, thereby promoting hybridization between the target (and the amplicon generated by target amplification) and primers, and thus promoting the target amplification reaction.

[0293] This example demonstrates that the amplification reaction simulation according to the present invention not only makes it possible to verify that the desired amplification has indeed been performed, but also makes it possible to modify the amplification parameters to favor the desired reaction, if Figure 8 The examples of steps S841 to S843 are based on the analysis of the combined matrix. or dissociation matrix The identification of competing reactions was performed; this example is not limiting, and other methods for identifying amplification reaction inhibitors can be used in a set of embodiments of the invention. More generally, the invention is not limited to specific methods for modifying simulation parameters.

[0294] Now for reference Figure 9 .

[0295] Figure 9 Examples of methods according to a set of embodiments of the present invention are shown, which integrate the validation or modification of PCR amplification parameters and the manufacture of a validated PCR amplification kit.

[0296] Method P9 is a manufacturing method that includes all the steps of method P8.

[0297] Method P9 further includes the step of manufacturing a kit (or "PCR kit") for characterizing microorganisms in a sample using polymerase chain reaction after validation in step S83, said kit being, for example, Figure 1 The kit shown is K1.

[0298] Therefore, the kit manufactured by method P9 includes primers and concentrations validated by method P8, meaning that simulations have shown that the desired amplification can be performed with satisfactory kinetics.

[0299] Therefore, method P9 makes it possible to manufacture kits that have been validated through simulation and allows for satisfactory amplification of the desired target.

[0300] Now for reference Figure 10 .

[0301] Figure 10 An example of method P10 for characterizing microorganisms using a PCR amplification kit manufactured according to a set of embodiments of the present invention is shown.

[0302] Method P10 includes a first step S101 of preparing a sample for PCR, said preparation including the addition of a kit (K1) manufactured according to a method such as Method P9.

[0303] The samples may be taken from humans, animals, or inanimate objects.

[0304] Then, method P10 includes step S102, which involves performing PCR on the collected samples. At the end of this step, the target nucleic acid sequence will have been amplified by PCR and will be present in sufficient quantity for characterization.

[0305] Therefore, method P10 includes a third step S103, which characterizes the microorganisms based on the PCR results.

[0306] Antimicrobial agents can be selected based on this characterization, and if the sample is taken from a living organism, it can be applied to a human or animal, or if the sample is taken from an inanimate object, it can be applied to an inanimate object.

[0307] Therefore, method P10 makes it possible to perform PCR on a sample to characterize the microorganisms contained in the sample, and, if necessary, select an antimicrobial agent suitable for that microorganism.

[0308] Since the kit has been validated through simulation to allow amplification of the characteristic nucleic acid sequence of the microorganism, the P10 method allows for amplification and thus effectively characterizes the given microorganism.

[0309] Now for reference Figure 11 .

[0310] Figure 11 The graph Gr11 is shown, which represents the evolution of Ct in the simulation of nucleic acid amplification of fungal yeast (Saccharomyces cerevisiae) as a function of the duration of the hybridization phase according to the simulation method of the present invention.

[0311] This diagram shows it more precisely: - The x-axis represents the duration of the hybridization phase. The unit is seconds; The -y axis represents the maximum test time corresponding to the hybridization phase (10 seconds in this case). With a given shorter duration of the hybridization phase The difference between .

[0312] Simulations were performed using three primer concentrations, while the nucleic acid concentration from yeast derived from fungi remained constant: - Curve Crv110 represents the concentration at 0.4 µM, Follow Simulated evolution; - Curve Crv111 represents the concentration at 0.8 µM, Follow Simulated evolution; - Curve Crv112 represents the concentration at 2 µM. Follow The simulated evolution.

[0313] For the defined duration of the hybridization phase, physical experiments corresponding to these concentrations were conducted to measure the effects under real-world conditions. The values ​​were then compared with the simulation.

[0314] The actual measured value is expressed as: - Measurements of Mes1101, Mes1102, Mes1103 and Mes1104 at a concentration of 0.4 µM; - Measurements at a concentration of 0.8 µM: Mes1111, Mes1112, Mes1113, Mes1114, Mes1115, and Mes1116; - Measurements at a concentration of 2 µM: Mes1121, Mes1122, Mes1123, Mes1124, and Mes1125.

[0315] from Figure 11 It can be seen from this: - Simulations provide accurate results that are very close to the actual measurements; - As the duration of the hybridization phase increases, Ct decreases rapidly and then approaches its minimum more slowly (using...). =0 indicates that... - When the concentration is low, the hybridization time The inflection point (from which Ct approaches its minimum value) is relatively high.

[0316] Therefore, this simulation allows for an accurate and reliable assessment of Ct. It was found that the simulation makes it possible to optimize the duration of the hybridization phase to achieve the target Ct value.

[0317] Now for reference Figure 12 .

[0318] Figure 12 Examples of visualizing the kinetics of multiple PCR reactions under two different experimental conditions are shown according to a set of embodiments of the present invention.

[0319] exist Figure 12 In the example, two simulations according to the invention were performed to reproduce the following: - Target amplification in the first multiplex amplification, using the first set of primers. The first simulation is represented by the "OPA" point. - Target amplification in the second multiplex amplification, where the first set of primers was modified. The first simulation is represented by the "OPB" point.

[0320] The simulation in this example is based on the observation that, in real-world amplification instances, modifying the first set of primers increased the amplified Ct by approximately 5.5 cycles. Therefore, two simulations were performed, one for the first set of primers and one for the modified set.

[0321] The results of these two simulations are shown in Figure Gr12, where: - The x-axis represents the index of the cycle; The -y axis represents the concentration of amplicon generated by the amplification of the target.

[0322] Therefore, the "OPA" and "OPB" points represent the simulated amplicon concentrations at the end of each cycle, using the first primer set and the modified primer set, respectively.

[0323] Note that this simulation also makes it possible to detect Ct differences over approximately 5.5 cycles. .

[0324] The results demonstrate that the PCR amplification simulation according to the present invention can reliably simulate multiplex amplification. Therefore, analysis of the simulation results optimizes the selection of amplification parameters, such as primers, primer concentrations, or phase durations, thereby validating the ability of the PCR amplification kit constructed based on the simulation parameters to produce satisfactory amplification of a given target.

[0325] This disclosure is not limited to the method embodiments, computer programs, or polymerase chain reaction kits provided for illustrative purposes only, but includes all variations that may be conceived by those skilled in the art in the context of the claims.

[0326] According to the present invention, it is possible to determine whether the initial selection of primers and their concentrations achieves appropriate amplification of the target nucleic acid molecule. In this case, the design of a kit containing said primers and their concentrations is validated, and the kit can be commercially produced.

[0327] This invention also makes it possible to design PCR amplification kits using a systematic approach. Specifically, starting from a previously identified list of possible primers and their possible concentration ranges, a grid of initial parameters is determined. For example, for each set of candidate primers for the kit, their concentration ranges are discretized in predetermined increments. The initial parameters are then this set of primers having concentration values ​​within said ranges. Each parameter is simulated, and once the entire grid has been traversed, the parameters that yield optimal performance are retained, and one or more corresponding kits are then manufactured.

[0328] This invention also makes it possible to test a set of primers in the context of multiplex PCR, and in this context test and compare alternative designs to achieve the desired performance.

[0329] The prepared kit is then used in a manner known per se. In the context of clinical applications, such as detecting pathogenic microorganisms in biological samples taken from patients (or animals), clinicians (or veterinarians, respectively) can then adjust their treatment, for example, by selecting antibiotics appropriate for the detected pathogen.

[0330] Preferably, the parameters can be obtained using methods from existing technologies. or similarly obtain and The prior art methods, such as the “nearest neighbors” methods, are disclosed, for example, in Santalucia Jr., J. (1998). A unified view of polymer, dumbbell, andoligonucleotide DNA nearest-neighbor thermodynamics. Proceedings of the National Academy of Sciences, 95(4), 1460-1465.

[0331] The simulation of PCR amplification is performed by a computer, i.e. by hardware circuitry, which includes computer memory (cache, RAM, ROM, etc.) and one or more microprocessors or processors, optionally organized as computing nodes, necessary to execute computer instructions stored in memory for performing the simulation.

Claims

1. A numerical simulation method (P4) for polymerase chain amplification of at least one target, the method comprising simulating multiple successive amplification cycles, each cycle comprising: - A hybridization phase between at least one target and multiple primers (S41); - Extension phase (S42); -The subsequent sex reassignment phase (S43); For each loop: -The hybridization phase includes: - The cycle yields initial values ​​for the concentration vector of multiple single-stranded nucleic acid molecules, which includes at least one target and multiple primers; - Calculate the concentration matrix of partial duplexes formed by the hybridization of multiple single-stranded nucleic acid molecules, where each element of the matrix represents the concentration of a duplex formed by the hybridization of a pair of the multiple single-stranded nucleic acid molecules, regardless of the hybridization position of the pair; -The mutation stage includes: - Multiply the concentration vector of the extended duplex by the deformation tensor of the extended duplex ( This process is used to obtain initial values ​​for the concentration vector of multiple single-stranded nucleic acid molecules for the next cycle, wherein the concentration vector of the extended duplex is obtained by applying the extension phase to the concentration of the duplex.

2. The method according to the preceding claim, wherein: -At least one doublet is generated by pairing between two primers; - The extension phase simulates the concentration of each duplex produced by the pairing between two primers as a single concentration of the extended duplex produced by the pairing between two primers; - Define the coefficients of the denaturation tensor to allocate the concentration of each extended duplex produced by the pairing between the two primers to the single-stranded nucleic acid molecule, corresponding to the extension of the duplex produced by the pairing between the two primers in two directions.

3. The method according to the preceding claim, wherein, For each hybridization reaction between the two primers: - The concentration of extended duplexes includes the concentration of extended virtual duplexes, which is equal to the sum of the concentrations of extended duplexes formed by the duplexes formed by the hybridization of the two primers extending in each of the two directions; - The coefficient of the denaturation tensor of the extended duplex, corresponding to the concentration distribution of each of the two primers and each of the two single-stranded nucleic acids generated by the extended virtual duplex in one of the two directions, is equal to 0.

5.

4. The method according to any one of the preceding claims, wherein, For each set of multiple hybridization reactions of single-stranded nucleic acids at multiple positions using primers, respectively: - The concentration of double strands and the concentration of extended double strands respectively include the concentration of virtual double strands equal to the sum of the concentrations of double strands formed by multiple hybridization reactions, and the concentration of extended virtual double strands equal to the sum of the concentrations of extended double strands formed by the extension of double strands formed by multiple hybridization reactions; - The coefficients of the denaturation tensor of the extended duplex corresponding to the concentration distribution of the extended virtual duplex of each single-stranded nucleic acid associated with one of the multiple hybridization reactions are respectively equal to the interaction energy of the multiple hybridization reaction divided by the ratio of the sum of the interaction energies of all multiple hybridization reactions with the single-stranded nucleic acid.

5. The method according to any one of the preceding claims, wherein the extension stage comprises: - The concentration of the extended duplex is obtained by multiplying the concentration of the duplex by the extension factor.

6. The method according to the preceding claim, wherein: - The extension phase further includes updating the concentration vector of the duplex, which represents the concentration of the non-extended duplex at the end of the extension phase; - The denaturation phase further includes multiplying the concentration vector of the duplex by the denaturation tensor of the non-extended duplex ( This is used to update the initial values ​​of the concentration vectors of multiple single-stranded nucleic acid molecules for the next cycle.

7. The method according to the preceding claim, wherein, During the denaturation phase, the same denaturation coefficient is applied to both the non-extended duplex and the corresponding extended duplex to update the concentration vectors of multiple single-stranded nucleic acid molecules and the duplex concentration for the next cycle.

8. The method (P8) according to any one of the preceding claims, comprising the subsequent steps of verifying (S83) or modifying (S84) the initial values ​​of a plurality of primers and the concentration vector of the plurality of primers in the first cycle of the reaction by comparing (S82) a value representing the reaction kinetics with a threshold.

9. A method for manufacturing a kit for characterizing microorganisms contained in a sample using polymerase chain amplification, the kit comprising a plurality of validated primers, wherein the plurality of primers and a concentration vector thereof are obtained by a simulation method according to any one of claims 1 to 7.

10. A kit for polymerase chain amplification, manufactured by the method of the preceding claim.

11. A computer program comprising, when the program is run by a processor, instructions for performing the method according to any one of claims 1 to 8.

12. A non-transient, computer-readable recording medium having a program recorded thereon, which, when run by a processor, executes the method according to any one of claims 1 to 8.

13. A method for characterizing microorganisms included in a sample, comprising: - Prepare the sample for PCR on the prepared sample, the preparation comprising the step of adding a kit manufactured according to any one of claims 1 to 8; - Perform PCR on the prepared samples; - The microorganisms were characterized based on PCR results.

14. The method of claim 13, wherein the sample is taken from an animal or human, the method comprising selecting an antimicrobial agent based on the characteristics of the microorganisms present in the sample, and administering the antimicrobial agent to the animal or human.

15. The method of claim 13, wherein the sample is taken from an inanimate object, the method comprising selecting an antimicrobial agent based on the characteristics of microorganisms present in the sample, and applying the antimicrobial agent to the inanimate object.

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