Manufacturing of polymerase chain amplification kits to optimize the amplification hybridization phase

Abstract

A process for numerical simulation of a polymerase chain reaction of at least one target, comprising the simulation of a plurality of consecutive cycles of amplification, each cycle comprising a hybridization phase, an extension phase, and then a denaturation phase, wherein the hybridization phase comprises, for each cycle, obtaining the cycle initial value of a vector of concentrations of a plurality of single-stranded nucleic acid molecules, initializing a matrix of concentrations of double helix formed by the hybridization of the plurality of single-stranded nucleic acid molecules, and calculating the transition of the concentration matrix during the hybridization phase by applying a matrix differential equation that expresses the dynamics of the double helix formation as a function of the concentrations of the plurality of nucleic acid molecules to the concentration matrix.

Description

[Technical Field]

[0001] This disclosure falls under the field of polymerase chain reactions. More specifically, this disclosure relates to the simulation and manufacture of polymerase chain reaction kits. [Background technology]

[0002] Polymerase chain amplification, or polymerase chain reaction (PCR), is a reaction that enables the proliferation of nucleic acid molecules (e.g., DNA or RNA). In each reaction cycle, each nucleic acid molecule is replicated. Therefore, PCR amplification allows nucleic acid molecules to be grown exponentially, and the nucleic acid concentration potentially doubles with each reaction cycle.

[0003] This allows PCR amplification to reach relatively high concentrations even from very small amounts of nucleic acids, making them detectable. Therefore, PCR amplification can convert trace amounts of nucleic acids representing pathogens into detectable amounts, and is used in many biomedical applications, particularly in the detection and characterization of pathogens.

[0004] PCR amplification is called singleplex amplification when the goal is to amplify a single nucleic acid, or multiplex amplification when the goal is to amplify multiple different nucleic acids simultaneously. The molecule being amplified is called the "target," and the amplified molecule is called the "amplicon." Naturally, the amplicon itself can be amplified in one or more subsequent cycles.

[0005] PCR amplification is typically performed in PCR kits that apply different temperatures to trigger consecutive steps in the amplification cycle. A PCR kit initially contains a primer to initiate amplification.

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

[0007] Generally, when designing a PCR kit, the designer follows these steps: a) For each microorganism, identify a list of specific potential targets (i.e., those not shared with other microorganisms). b) Based on experience, select potential primers from a list of possible primers. c) Perform the test under real-world conditions. d) If the PCR results are unsatisfactory, repeat the process.

[0008] This method becomes even more difficult when several targets are being targeted. Therefore, the kit design is long and complex, relying on the specific expertise of each designer.

[0009] The designers are quickly overwhelmed by the sheer number of reactions, and therefore, it is impossible for the human mind to simulate what actually happens during PCR on paper, and thus, predicting the reactions on paper is also impossible.

[0010] For example, it is impossible to a priori solve the system of differential equations that describe the hybridization of all molecules present in a PCR kit, particularly between the amplicon, primer, and intermediate. Even state-of-the-art methods cannot perform numerical simulations of such systems within a reasonable timeframe due to the existence of numerous interconnected differential equations. This significantly limits the potential for designing and, consequently, improving PCR kits. [Prior art documents] [Patent Documents]

[0011] [Patent Document 1] U.S. Patent No. 8,394,608 [Patent Document 2] U.S. Patent No. 9,932,634 [Non-patent literature]

[0012] [Non-Patent Document 1] Santalucia Jr., J. (1998), A unified view of polymer, dumbbell and oligonucleotide DNA nearest-neighbor thermodynamics, Proceedings of the National Academy of Sciences, 95(4), 1460~1465 [Overview of the project] [Problems that the invention aims to solve]

[0013] Therefore, there is a need for PCR kit design methods to predict the progress of the hybridization phase in order to facilitate the selection of parameters that promote the amplification of one or more targeted objects. [Means for solving the problem]

[0014] This disclosure aims to improve the situation.

[0015] A process has been proposed for numerical simulation of a polymerase chain reaction of at least one target, the process comprising simulation of a plurality of consecutive cycles of amplification, each cycle comprising a hybridization phase between at least one target and a plurality of primers, an extension phase, and then a denaturing phase, wherein the hybridization phase comprises, for each cycle, obtaining an initial value for the cycle of a vector of concentrations of a plurality of single-stranded nucleic acid molecules comprising at least one target and a plurality of primers, initializing a matrix of concentrations of duplexes formed by the hybridization of the plurality of single-stranded nucleic acid molecules, and calculating the evolution of the matrix of concentrations during the hybridization phase in consecutive time steps by applying a matrix differential equation that expresses the kinetics of the duplex formation as a function of the concentrations of the plurality of nucleic acid molecules, wherein the matrix differential equation is parameterized by at least one association matrix containing association constants associated with each duplex and a dissociation matrix containing dissociation constants associated with each duplex.

[0016] The term “at least one target” means at least one nucleic acid of the sequence to be amplified. According to various embodiments of the present invention, amplification may relate to a single target, in which case the amplification is called “singleplex” amplification, or amplification may relate to multiple targets, in which case the amplification is called “multiplex” amplification.

[0017] The term "single-stranded nucleic acid molecule" is understood to mean a nucleic acid molecule in a single-stranded form that is not paired with a complementary single-stranded molecule.

[0018] Generally k on The term "association constant" (also called "association rate constant") is understood to mean the rate constant that represents the reaction rate at which two single-stranded nucleic acid molecules are joined to form a double helix.

[0019] Generally k off The expression "dissociation constant" (also called "dissociation rate constant") is understood to mean the rate constant that represents the rate at which a double hemisphere dissociates into two single-stranded nucleic acid molecules.

[0020] This allows for the simulation of all hybridization phases (i.e., the equilibrium between binding and dissociation reactions) between the target, amplicon, and primer. Therefore, by incorporating cross-reactions with intermediate products, the entire dynamics of the polymerase chain reaction can be modeled.

[0021] Thus, this particular modeling of polymerase chain reactions allows for verification of the design of polymerase chain reaction devices, or conversely, identification of undesirable reactions, and ultimately, modification of parameters affecting the amplification reaction (such as initial primer concentration, salt, phase time, and temperature).

[0022] Similarly, simulating the hybridization phase according to a single matrix differential equation allows us to elucidate the system's dynamics using conventional computing power.

[0023] In another embodiment, a process is provided for producing a kit for characterizing microorganisms contained in a sample using a polymerase chain reaction, the kit comprising a plurality of identified primers, wherein the plurality of primers and their concentration vectors are obtained by a simulation process according to one embodiment of the present invention.

[0024] This makes it possible to manufacture devices that can replicate simulated reactions. These manufactured devices then enable the proliferation of pre-simulated targets.

[0025] In another embodiment, a kit for polymerase chain reaction is proposed, manufactured by a manufacturing process according to one embodiment of the present invention.

[0026] In another aspect, a computer program is proposed which includes instructions for executing all or part of a process as defined herein when the program is executed by a processor.

[0027] In another embodiment, a non-temporary computer-readable recording medium on which such a program is recorded is proposed.

[0028] In another embodiment, a process is proposed for characterizing microorganisms contained in a sample, comprising the steps of: preparing a sample for performing PCR on the prepared sample, adding a kit manufactured according to a kit manufacturing process defined herein; performing PCR on the prepared sample; and characterizing the microorganisms based on the PCR results.

[0029] The features described in the following paragraphs may be implemented optionally, independently of each other, or in combination.

[0030] Conveniently, differential equations are,

[0031]

number

[0032] A mass conservation equation of the form, where t * However, this represents the time elapsed since the start of the hybridization phase, and is denoted as T. i and T j However, the vector of concentrations of multiple nucleic acid molecules

[0033]

number

[0034] represent the concentrations of two single-stranded nucleic acid molecules with indices i and j, respectively, notation H xy is the vector of concentrations of multiple nucleic acid molecules

[0035]

Number

[0036] represent the concentration of the duplex formed by hybridization of a pair of single-stranded nucleic acid molecules with indices x and y, notation T i0 and T j0 are such that t * = 0 for T i and T j represents their values, incorporating the mass conservation equation, or any other mathematically equivalent formulation of the mass conservation equation

[0037] This allows for a more accurate simulation of the hybridization phase since mass conservation is taken into account

[0038] Advantageously, the matrix differential equation is of the following form, namely

[0039]

Number

[0040] where H is the duplex concentration matrix, T0 is the initial value of the cycle of the concentration vector of multiple molecules, K on is the binding matrix, K off is the dissociation matrix, and the operator

[0041]

Number

[0042] represents a two-dimensional matrix with i rows and j columns where all elements are equal to 1, and the operator "diag()" takes a square matrix as a parameter and extracts from the square matrix a vector whose dimension is the number of rows or columns of the square matrix and which contains all elements on the diagonals of the square matrix.

[0043] For example, operators

[0044]

number

[0045] This represents a row vector of dimension N that contains only (1), and the operator

[0046]

number

[0047] This represents a column vector of dimension N that contains only the element 1.

[0048] For example, the diag(H) operator transforms an N×N square matrix H into a vector of dimension N that contains all the elements on the diagonals of H in order.

[0049]

number

[0050] If that is the case,

[0051]

number

[0052] That is the case.

[0053] This allows all differential equations for hybridization reactions to be incorporated into a single matrix equation, and replacing T with T0 in the equation results in faster matrix calculations.

[0054] Conveniently, each binding matrix or each dissociation matrix contains elements such that each binding matrix element or dissociation matrix element relating to a pair of molecules belonging to the plurality of molecules is zero if the variation in free enthalpy related to the hybridization reaction of the molecules forming the pair exceeds a threshold, and otherwise is equal to the binding constant or dissociation constant of the hybridization reaction of the pair of molecules, respectively.

[0055] This allows only the dominant hybridization reaction to be considered in the simulation. This enables both greater accuracy in the dynamics of the considered hybridization reaction and a reduction in the complexity of solving the system of differential equations. This also allows for the consideration of differential dynamics between different reactions, depending on whether the free enthalpy values ​​are favorable or unfavorable between the two reactions of interest.

[0056] Advantageously, the threshold value is selected from at least two predefined threshold values, with the lowest threshold value reserved for pairs of molecules containing a paired amplicon and primer.

[0057] Since the threshold and free enthalpy variations are negative, the highest threshold value corresponds to a relatively low threshold value. Therefore, hybridization reactions between the primer and amplicon are given preferential consideration. The term "lowest threshold value" is understood to mean a value relatively close to zero. Since the threshold and free enthalpy variations are negative, this also corresponds to a relatively low absolute threshold value.

[0058] This allows, for example, that hybridization between a primer and an amplicon is given preferential consideration in simulations compared to hybridization reactions between a primer and other primers, which enables the simulation of the first cycle of amplicon-primer hybridization where the amplicon concentration is much lower than the primer concentration.

[0059] Advantageously, the process includes a preliminary step which defines a plurality of molecules, which initializes a plurality of single-stranded nucleic acid molecules as molecules that are initially present in a polymerase chain reaction; an preliminary simulation of a plurality of cycles of the polymerase chain reaction, wherein each cycle of the preliminary simulation obtains a hybridization reaction of molecules that form each pair of molecules among the plurality of molecules having an affinity below a threshold; a simulation of a hybridization phase including the hybridization reaction; a simulation of an extension phase; a simulation of a denaturation phase; and an addition of additional molecules obtained at the end of the hybridization phase, extension phase, and denaturation phase to the plurality of molecules.

[0060] The term "additional molecules" is understood to refer to molecules that are not present at the beginning of the cycle but are generated at the end of the hybridization, extension, and denaturation cycles.

[0061] This allows for the construction of concentration vectors, as well as binding and dissociation matrices, by considering only the molecules that actually encounter each other with considerable affinity during the polymerase chain reaction. Therefore, this results in a more reliable and less resource-intensive simulation of the PCR amplification reaction.

[0062] Conveniently, the preliminary step of defining multiple molecules involves running an initial simulation for a number of cycles between 3 and 7.

[0063] This provides a good compromise between the number of molecules added and their importance. For example, molecules added after the third, fifth, or seventh cycle may be considered less likely to cause significant reactions. Therefore, a predefined number of cycles between 3 and 7, for example equal to 5, allows for limiting the number of molecules for the simulation and reducing the complexity of the associated calculations while maintaining the reliability of the simulation.

[0064] Advantageously, the process includes a subsequent step at the end of the simulation of the multiple cycles in which the temporal evolution of the concentration of at least one of the molecules is displayed.

[0065] This allows for the visualization of the concentration progression of at least one molecule, for example, an amplicon, and its verification or modification according to the polymerase chain reaction design.

[0066] Advantageously, the process includes subsequent steps to identify or correct the initial values ​​of the concentration vectors of the multiple primers in the first cycle of the reaction by comparing values ​​representing the dynamics of the reaction with thresholds.

[0067] This ensures that the initially present primers and their associated concentrations reliably allow for the growth of the desired target with sufficiently strong reaction dynamics, thereby avoiding the generation of undesirable reactions with strong dynamics, or conversely, allowing for the modification of the primer list and / or their concentrations.

[0068] Advantageously, the values ​​representing the dynamics are selected from the threshold cycle, the crossing point, the final concentration of the nucleic acid molecules amplified by the reaction, and the concentration of the amplicon at the end of the reaction.

[0069] The term “cycle threshold” (also known as “Ct,” “quantification cycle,” or “Cq”) is understood to mean the number of cycles required for an amplicon concentration to reach a baseline concentration. The threshold may correspond, for example, to the concentration at which a molecule is detectable and the concentration above it.

[0070] The term "crossing point" (or "Cp," or otherwise "take-off point" or "TOP") is understood to refer to the cycle in which the second derivative of the amplicon's concentration reaches its maximum value.

[0071] The term "amplicon concentration at the end of a reaction" refers to the amplicon concentration when the reaction is considered complete, for example, when a concentration plateau is reached. Such a plateau can be detected, for example, by linear regression on an affine straight line.

[0072] Advantageously, the modification of multiple primers includes, based on the results of polymerase chain reaction simulations, identifying targets to be favored, identifying single-stranded nucleic acid molecules that pair with primers associated with the targets from their binding or dissociation matrices, and performing at least one modification of the polymerase chain reaction, selected from, namely, reducing the initial concentration of the single-stranded nucleic acid molecules that pair with primers associated with the targets in the initial concentration vector, changing the salt concentration, changing the hybridization temperature for at least one cycle, and changing the hybridization time for at least one cycle.

[0073] This allows for the identification of intermolecular reactions present during a PCR reaction that compete with the amplification of a given target, and enables the reduction of the initial concentrations of molecules causing these reactions or the corresponding modification of the sequences of the molecules identified as causing the reactions, in order to promote the amplification of the given target.

[0074] Advantageously, the specimen is collected from an animal or a human, and the process includes selecting an antimicrobial agent in accordance with the characterization of microorganisms present in the specimen, and administering the antimicrobial agent to the animal or the human.

[0075] Advantageously, the sample is collected from an inanimate object, and the process includes selecting an antimicrobial agent according to the characterization of microorganisms present in the sample, and administering the antimicrobial agent to the inanimate object.

[0076] A process has been proposed for numerical simulation of a polymerase chain reaction of at least one target, the process comprising simulation of multiple consecutive cycles of amplification, each cycle comprising a hybridization phase between at least one target and multiple primers, an extension phase, and a denaturing phase, wherein for each cycle, the hybridization phase comprises obtaining an initial value for the cycle of a vector of concentrations of multiple single-stranded nucleic acid molecules comprising at least one target and multiple primers, and calculating a matrix of concentrations of partial duplexes formed by the hybridization of the multiple single-stranded nucleic acid molecules, where each element of the matrix represents the concentration of the duplex formed by the hybridization of the pair of the multiple single-stranded nucleic acid molecules, regardless of the hybridization position of the pair, and the denaturing phase comprises multiplication of the extended duplex concentration vector resulting from the application of the extension phase to the duplex concentrations to obtain an initial vector value for the concentrations of the multiple single-stranded nucleic acid molecules for the next cycle, and the denaturing tensor of the extended duplexes.

[0077] Using a single concentration value for all double helix strands between pairs of nucleic acid molecules, regardless of pairing position, reduces the number of equations to be solved for denaturation calculations, making it possible to solve problems that simulate denaturation.

[0078] In another embodiment, a process is provided for producing a kit for characterizing microorganisms contained in a sample using a polymerase chain reaction, the kit comprising a plurality of identified primers, wherein the plurality of primers and the concentration vectors of the plurality of primers are obtained by a simulation process as defined herein.

[0079] This makes it possible to manufacture devices that can replicate simulated reactions. These manufactured devices then enable the proliferation of pre-simulated targets.

[0080] In another embodiment, a kit for polymerase chain reactions is proposed, which is produced by a process defined herein.

[0081] In another aspect, a computer program is proposed which includes instructions for executing all or part of a process as defined herein when the program is executed by a processor.

[0082] In another embodiment, a non-temporary computer-readable recording medium on which such a program is recorded is proposed.

[0083] In another embodiment, a process is proposed for characterizing microorganisms contained in a sample, comprising the steps of: preparing a sample for performing PCR on the prepared sample, adding a kit manufactured according to a process defined herein; performing PCR on the prepared sample; and characterizing the microorganisms based on the PCR results.

[0084] The features described in the following paragraphs may be implemented optionally, independently of each other, or in combination.

[0085] Advantageously, at least one double helix arises as a result of pairing between the two primers, and the extension phase simulates the concentration of each double helix resulting from pairing between the two primers to a single concentration of the extended double helix resulting from pairing between the two primers, and the coefficients of the denaturation tensor are defined to distribute each concentration of the extended double helix resulting from pairing between the two primers to single-stranded nucleic acid molecules corresponding to the bidirectional extension of the double helix resulting from pairing between the two primers.

[0086] This simplifies the simulation of the reaction resulting from the pairing of the two primers, further reducing the computational complexity of the simulation.

[0087] Conveniently, for each hybridization reaction between the two primers, the concentration of the extended double helix includes the concentration of the extended virtual double helix, which is equal to the sum of the concentrations of the extended double helix formed by the extension of the double helix formed by the hybridization of the two primers in each of the two directions, and the coefficients of the denaturation tensor of the extended double helix, corresponding to the distribution of the concentration of the extended virtual double helix to each of the two primers and each of the two single-stranded nucleic acids resulting from the extension in one of the two directions, are all equal to 0.5.

[0088] This allows for efficient simulation of reactions resulting from hybridization between primers, while limiting the complexity of the simulation.

[0089] Advantageously, for each set of multiple hybridization reactions of single-stranded nucleic acids by a primer at several locations, the concentrations of the double helix and the extended double helix each include a virtual double helix concentration equal to the sum of the concentrations of the double helix formed by each of the multiple hybridization reactions, and an extended virtual double helix concentration equal to the sum of the concentrations of the extended double helix formed by the extension of the double helix formed by the multiple hybridization reactions, and the coefficients of the extended double helix denaturation tensor corresponding to the distribution of the concentrations of the extended virtual double helix to each single-stranded nucleic acid associated with one of the multiple hybridization reactions are each equal to the ratio between the interaction energies of the multiple hybridization reactions divided by the sum of the interaction energies of all the multiple hybridization reactions with the single-stranded nucleic acid.

[0090] The term "virtual double-strand concentration" refers not to the concentration of actual molecules, but to the concentration of double-strands that result from the hybridization of the same primer to the same single-stranded nucleic acid molecule at several different locations. In this case, the virtual double-strand concentration is equal to the sum of the concentrations of actual double-strands created by the hybridization reactions of the primer with single-stranded nucleic acid molecules at different locations.

[0091] The term "concentration of extended virtual double helix" does not correspond to actual molecules, but rather to the concentration of extended double helix corresponding to several extended double helix resulting from the hybridization of the same primer with the same single-stranded nucleic acid molecule at several different locations, and then the extension of the double helix thus formed. In this case, the concentration of extended virtual double helix is ​​equal to the sum of the concentrations of extended real double helix created by the hybridization reactions of the primer with single-stranded nucleic acid molecules at different locations, and then the extension of the double helix thus formed.

[0092] The term "single-stranded nucleic acid associated with one of multiple hybridization reactions" refers to a nucleic acid resulting from the denaturation of the extended double helix itself, which occurs as a result of the extension of the double helix formed by the hybridization of a primer at a specific site, i.e., one of multiple hybridization reactions.

[0093] This allows us to simulate these multiple hybridizations as if they were a single reaction, while obtaining a reliable estimate of the nucleic acid concentration produced by multiple hybridizations with the same nucleic acid at the end of the cycle.

[0094] Therefore, this makes it possible to significantly simplify, or even make possible, the calculation of concentration transitions while maintaining satisfactory accuracy in the simulation.

[0095] Advantageously, the extension phase includes obtaining the concentration of the extended double chain by multiplying the concentration of the double chain by an extension coefficient.

[0096] The term "elongation coefficient" refers to the ratio between 0 and 1 of the amount of a given double-chain molecule that is elongated during the elongation phase.

[0097] This makes it possible to take into account all possible differences in the process of extension of different double hemispheres.

[0098] Advantageously, the extension phase further includes updating the double-strand concentration vector representing the concentration of the unextended double helix at the end of the extension phase, and the denaturation phase further includes multiplying the double-strand concentration vector by the denaturation tensor of the unextended double helix to update the initial values ​​of the concentration vectors of the multiple single-stranded nucleic acid molecules for the next cycle.

[0099] This simulates the denaturation of unextended double helix and incorporates the concentrations of unextended and denatured double helix under the initial conditions of the next cycle.

[0100] Furthermore, tensor analysis ensures that the denaturation is well controlled.

[0101] Advantageously, during the denaturation phase, the same denaturation coefficient is applied to the unextended and corresponding extended double helix to update the concentration vectors of multiple single-stranded nucleic acid molecules and the double-strand concentrations for the next cycle.

[0102] The term "denaturation coefficient" refers to the ratio between 0 and 1 of the given double-chain molecules that are denatured during the denaturation phase.

[0103] This makes it possible to accurately simulate the degeneration phase.

[0104] Advantageously, the process includes subsequent steps to identify or correct the initial values ​​of the concentration vectors of the multiple primers in the first cycle of the reaction by comparing values ​​representing the dynamics of the reaction with thresholds.

[0105] This ensures that the initially present primers and their associated concentrations reliably allow for the growth of the desired target with sufficiently strong reaction dynamics, thereby avoiding the generation of undesirable reactions with strong dynamics, or conversely, allowing for the modification of the primer list and / or their concentrations.

[0106] Advantageously, the specimen is collected from an animal or a human, and the process includes selecting an antimicrobial agent in accordance with the characterization of microorganisms present in the specimen, and administering the antimicrobial agent to the animal or the human.

[0107] Advantageously, the sample is collected from an inanimate object, and the process includes selecting an antimicrobial agent according to the characterization of microorganisms present in the sample, and administering the antimicrobial agent to the inanimate object.

[0108] Other features, details, and benefits will become clear upon reading the detailed description below and analyzing the attached drawings. [Brief explanation of the drawing]

[0109] [Figure 1] This figure shows an example of a polymerase chain reaction kit in which the present invention can be implemented for its manufacture. [Figure 2] This figure shows an example of a polymerase chain reaction that can be simulated according to one set of embodiments. [Figure 3] This figure shows an example of temperature fluctuations during a PCR amplification cycle. [Figure 4] This figure shows an example of a method according to one embodiment of the present invention. [Figure 5] This figure shows an example of the hybridization phase of one embodiment of the present invention. [Figure 6] This figure shows an example of a modification phase in one embodiment of the present invention. [Figure 7] This figure shows an example of a hybridization reaction, an extension reaction, and a denaturation reaction over three consecutive cycles of PCR amplification in one embodiment of the present invention. [Figure 8] This figure shows an example of a method according to one embodiment of the present invention that incorporates verification or modification of PCR amplification parameters. [Figure 9] This figure shows an example of a method according to one embodiment of the present invention, which incorporates the verification or modification of PCR amplification parameters and the manufacture of a verified PCR amplification kit. [Figure 10] This figure shows an example of a method for characterizing microorganisms using a PCR amplification kit manufactured according to one set of embodiments of the present invention. [Figure 11] This figure shows an example of visualizing the dynamics of several PCR reactions according to one embodiment of the present invention. [Figure 12] This figure shows an example of visualizing the dynamics of several PCR reactions under two different experimental conditions according to one embodiment of the present invention. [Modes for carrying out the invention]

[0110] Next, Figure 1 is referred to.

[0111] Figure 1 shows an example of Kit K1 for polymerase chain reaction, for which the present invention may be carried out for its manufacture, for example, a kit used for the FilmArray platform and Spotfire platform manufactured and sold by the applicant. Such kits are described, for example, in U.S. Patent No. 8,394,608 or U.S. Patent No. 9,932,634, which are incorporated by reference.

[0112] Kit K1 forms part of Test 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.

[0113] For this purpose, the testing device Tst1 includes a cotton swab Swab1 for collecting a nasal sample from the patient.

[0114] Then, for example, as described in the aforementioned literature, a sample can be supplied at the input of kit K1 to perform PCR amplification to amplify one or more nucleic acids representing the microorganism whose presence is being sought. Therefore, even if the initial concentration of microorganisms in the collected sample is low, the amount of nucleic acids released from the PCR amplification will be sufficient to detect the presence of those nucleic acids and, consequently, the presence of microorganisms in the collected sample.

[0115] As PCR amplification progresses, the amplicon can generate increasing fluorescence, for example, through the incorporation of a fluorescent dye (fluorophore) by the formation of double-stranded sequences, and the number of double-stranded sequences incorporating the fluorescent dye increases with amplification.

[0116] Thus, the Tst1 test kit can detect the presence of microorganisms even if the concentration of microorganisms in the initial sample is very low.

[0117] The test kit Tst1 is given purely as a non-limiting example, and the present invention can be applied to different types of test kits associated with different sample collection methods. For example, sample collection may be performed on humans, animals, or inanimate objects, and may result in the characterization of one or more microorganisms. The characterization of one or more microorganisms may enable the selection of antimicrobial agents for administration to humans or animals, or for application to inanimate objects. Similarly, the present invention applies to the step of PCR amplification of a targeted portion of a genome prior to complete genome sequencing, for example, amplification of the r16S portion in the context of microbial metagenomic identification.

[0118] Figure 2 shows an example of a polymerase chain reaction that can be simulated according to one set of embodiments.

[0119] Polymerase chain reaction (PCR) involves several consecutive cycles: Cyc21, Cyc22, Cyc23...Cyc2n. To improve readability of the diagram, only the first cycle, Cyc21, is described in detail.

[0120] The reaction PCR2 is performed in a PCR kit, for example, kit K1. The PCR kit initially includes the following: - The nucleic acids of one or more sequences to be amplified, i.e., the "targets," for example, target Targ2 shown in Figure 2. The nucleic acids of the sequences to be amplified can first be obtained from a sample, for example, via a cotton swab Swab1. - dNTP2 nucleotide - Polymerase PolyM2 - Prima AM2

[0121] The PCR reaction described herein is a "singleplex" reaction aimed at amplifying a single target, Targ2. However, the present invention is not limited to this example and can also be applied to "multiplexed" reactions aimed at simultaneously amplifying several different targets.

[0122] Each PCR amplification cycle includes the following: - A denaturation phase in which a double-stranded nucleic acid is separated into two single-stranded nucleic acids, denoted as Denat21 in the case of cycle Cyc21. In the example of cycle Cyc21, the target Targ2 initially exists as a double-stranded nucleic acid. During the denaturation phase, the target Targ2 is separated into two single-stranded nucleic acids, Nuc21 and Nuc22. - A hybridization phase in which the primer hybridizes with a single-stranded nucleic acid; in the case of cycle Cyc21, this is denoted as Hybr21. In the example of phase Hybr21, primers AM21 and AM22 hybridize with single-stranded nucleic acids Nuc21 and Nuc22, respectively. - The elongation phase, denoted as Elong21 for cycle 21, in which the nucleotides complete the primer and form double-stranded nucleic acids identical to the initial target, called amplicons Amp21 and Amp22 in the case of phase Elong21.

[0123] Thus, at the end of a PCR amplification cycle, a single target, Targ2, is able to generate two identical amplicons, Amp21 and Amp22, which can then replicate themselves in the next cycle. In each amplification cycle, the amplicons are replicated as follows: a single target, Targ2, results in the generation of 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.

[0124] It should be noted that the amplification shown in Figure 2 is given purely as a non-limiting example of amplification that can be simulated by the present invention.

[0125] Other amplifications, such as multiple amplifications that amplify different types of targets, can be simulated. The application of the present invention to specific PCRs has been described. The present invention is applicable to the sequencing of any number of PCRs, where the input to one PCR consists of the output of a previous PCR.

[0126] The order of the phases may differ. For example, the simulation may start with the hybridization phase instead of the transformation phase for each cycle. In this case, the cycle would be represented by the hybridization phase, followed by the extension phase, and finally the transformation phase.

[0127] Next, Figure 3 is referred to.

[0128] Figure 3 shows an example of temperature fluctuations during a PCR amplification cycle.

[0129] More precisely, graph Grph3 shows the temperature progression as a function of time for the example of two consecutive PCR amplification cycles, Cyc31 and Cyc32. In particular, different phases of PCR amplification are activated by temperature fluctuations within the amplification kit. In this example, the temperature profile is identical between cycles and is detailed for cycle cyc31.

[0130] Generally, the temperature changes during the PCR amplification cycle as follows: - The temperature is initially the first temperature during the hybridization phase, which is simultaneous with the extension phase. Then, the temperature rises rapidly, reaching a second higher temperature that triggers the denaturation phase, and then returns to the first temperature level for the hybridization phase of the next cycle.

[0131] In the example of cycle Cyc31, - The hybridization phase and extension phase of Hybr31 have a duration of T hybr During this time, it is activated by a first temperature of 60°C. - The denaturation phase, Denat31, is activated by higher temperatures, 96°C in this example.

[0132] The durations and temperatures shown in Figure 3 are given purely as non-limiting examples, and the present invention is applicable to PCR amplification performed at very different durations and temperatures. In the example in Figure 3, the hybridization and extension phases are simultaneous, but in other PCR amplification reactions, three different temperatures are used to trigger the hybridization, extension, and denaturation phases, respectively. The different phase temperatures and durations affect the amplification reaction.

[0133] Therefore, amplification reactions are affected by many parameters, such as the following: - Temperature and duration of each phase of the reaction (these may be fixed or may vary according to the cycle) - Primer selection and concentration - Concentrations of monovalent and divalent salts - Expected amplicon length - etc.

[0134] These various factors can also promote unexpected reactions, such as the following: - Formation of a primer dimer when two primers hybridize together. - Multi-hybridization is a reaction in which a primer hybridizes not only at one end of a single-stranded nucleic acid, but also at other locations, such as in the middle of the strand. In this case, elongation occurs only in a portion of the strand, leading to the creation of a new amplicon.

[0135] Therefore, amplification parameters can either promote or slow down the desired amplification, known as a specific reaction, or even hinder the proper progress of the reaction when undesirable / unexpected reactions, known as nonspecific reactions, interfere with it. Thus, one purpose of simulating PCR amplification reactions is to model the amplification reaction as accurately as possible according to the environmental parameters of the reaction in order to verify or modify the kit design (i.e., the parameter values ​​used to promote a given amplification reaction—for example, primer selection and concentration, reaction phase temperature and duration, salt concentration, etc.).

[0136] However, the dynamics of PCR amplification reactions, particularly the complexity of the interactions between numerous reaction products and by-products, make such simulations practically difficult. Therefore, one of the objectives of this disclosure is to provide a method for simulating PCR amplification reactions that may actually be performed, in order to simulate a PCR reaction according to given parameters and to verify or modify the reaction parameters accordingly.

[0137] Figure 4 shows an example of a method according to one embodiment of the present invention.

[0138] Process P4 is a process for numerical simulation of a polymerase chain reaction of at least one target. According to various embodiments of the present invention, it may be amplification of a single target, i.e., "singleplex" amplification, or amplification of multiple targets, i.e., "multiplex" amplification.

[0139] The simulation includes multiple consecutive amplification cycles, each cycle consisting of a hybridization phase S41, an extension phase S42, and a modification phase S43 in sequence.

[0140] The simulation may be run for a limited number of cycles. For example, each cycle may be identified by a cycle index ncyc, which is incremented in step S45 between each cycle.

[0141] At the end of each cycle, the stopping criteria can be reviewed. For example, - The simulation can run for a predetermined number of cycles, NCyc. In this case, at the end of each cycle, the cycle index ncyc can be compared to the predetermined number of cycles, NCyc. If ncyc >= NCyc, the criterion is checked (or, if ncyc < NCyc, a new cycle is started). - The amplicon concentration can be compared between two cycles, and the simulation stops when the minimum number of cycles is reached and the difference between the amplicon concentrations after two consecutive cycles is below a predefined threshold. In other words, this criterion is to detect the cycle in which the reaction is considered complete. - The simulation may be stopped as soon as the concentration of a given amplicon exceeds a threshold, for example, a threshold for the detectability of the amplicon. - etc.

[0142] Figure 4 shows an example where the termination criterion is the achievement of NCyc cycles. However, this example is given merely as an unrestricted example. As mentioned above, one or more different criteria may be used to detect the termination of the simulation.

[0143] The remainder of this explanation will describe several simulation examples using specific notation introduced below.

[0144] The concentration of the molecule of interest is represented by the vector shown below.

[0145]

number

[0146] It will be listed.

[0147]

number

[0148] In the above vector, elements Amp1, ... Amp β This represents the concentrations of possible amplicons (specific and nonspecific) generated during PCR amplification. Note that since the target and amplicons correspond to the same molecule, these values ​​correspond to the sum of the target concentration and amplicon concentration for a given target. Elements AM1, ... AM α This represents the possible primer concentration insofar as it pertains to those components. The units of the vector elements are mol.L. -1 This may be the case.

[0149] In particular, the vector includes the concentration of the amplicon and the concentrations of multiple primers present in the kit being simulated.

[0150]

number

[0151] Multiple molecules whose concentrations are listed can be obtained by different methods.

[0152] For example, vector

[0153]

number

[0154] The concentrations of multiple molecules listed can be derived from a list of molecules defined by expert users.

[0155] However, considering all possible reactions between reaction byproducts, for example, it can be difficult to a priori predict all molecules that will be formed during a PCR reaction.

[0156] For this purpose, vector

[0157]

number

[0158] The concentrations of multiple molecules listed are determined by an initial simulation with a limited number of cycles. The sole purpose of this initial simulation is to determine the molecules present in the amplification kit after the limited number of cycles, regardless of their concentrations.

[0159] For this purpose, multiple molecules can be initialized like the initial molecules in a polymerase chain reaction (particularly the amplicon and primer), and the initial simulation can include simulation of multiple consecutive cycles of the following steps. - Obtain the hybridization reaction of molecules that form each pair of molecules among the aforementioned plurality of molecules that have affinity below the threshold (or, since the affinity is a negative value, exceed the threshold in absolute terms). In other words, this step involves identifying pairs of molecules with affinity below the threshold (or high in absolute terms) from the molecules initially present in the first simulation cycle, i.e., pairs of molecules that are likely to react together. - Simulation of the hybridization phase, including the aforementioned hybridization reaction. This initial simulation hybridization phase is solely for the purpose of identifying the double chain formed by the identified hybridization reaction. - Simulation of the elongation phase. This initial simulation elongation phase is solely for the purpose of identifying the elongated double helix obtained from the double helix identified in the previous step. - Simulation of the denaturation phase. This initial simulation of the denaturation phase aims to identify the molecules obtained by denaturing the double chains and extended double chains obtained in the two previous steps. - Addition of additional molecules obtained at the end of the hybridization, extension, and denaturation phases to the aforementioned multiple molecules. This step involves adding molecules obtained at the end of the cycle that were not already present in the multiple molecules to the multiple molecules.

[0160] Thus, in each cycle, new molecules obtained as a result of the reaction in the previous cycle can be added to several already identified molecules, and these new molecules themselves can give rise to new reactions. Therefore, after a limited number of initial simulation cycles, all molecules that may play an important role in the simulation can be identified.

[0161] The number of cycles for the initial simulation can be set in various ways. For example, - The number of initial simulation cycles can be a predefined number of initial simulation cycles. - The number of molecules added at the end of each cycle can be counted, and the initial simulation may be stopped if the number of molecules added at the end of a given cycle is zero or small, for example, if the number of added molecules is below a given threshold. - etc.

[0162] The inventors found that the number of initial simulation cycles could be between 3 and 7, for example, equal to 5, and that this number was sufficient to obtain a definitive list of molecules that significantly affect the PCR results.

[0163] This provides a good compromise between the number of molecules added and their importance. For example, molecules added after the third, fifth, or seventh cycle may be considered less likely to cause significant reactions. Therefore, a predefined number of cycles between 3 and 7, for example equal to 5, allows for limiting the number of molecules for the simulation and reducing the complexity of the associated calculations while maintaining the reliability of the simulation.

[0164] Furthermore, molecules that appear only after several cycles are less likely to produce significant reactions compared to reactions that have already progressed for several cycles, so simulations with a limited number of cycles are sufficient. In particular, the concentration of molecules that appear only after several cycles is very low compared to the already present molecules that compete with them in the mixture, so it does not allow them to proliferate significantly.

[0165] Therefore, this initial simulation allows us to consider only the molecules that actually encounter a significant number of times during the amplification reaction. This enables a more reliable and less resource-intensive simulation of the reaction.

[0166] Next, Figure 5 is referred to.

[0167] Figure 5 shows an example of the hybridization phase of one embodiment of the present invention.

[0168] In the example in Figure 5, the hybridization phase S41 of a given cycle is the initial value of the cycle's concentration vector of multiple single-stranded nucleic acid molecules, including multiple amplicons and multiple primers.

[0169]

number

[0170] This includes a first substep S411 to obtain the result.

[0171] The concentration vector is, for example, the vector mentioned above.

[0172]

number

[0173] It may be so. For example, the initial value of a vector

[0174]

number

[0175] teeth, - If the simulated cycle is the first cycle, it may correspond to the initial concentration of molecules before the start of the amplification reaction, and may correspond to 0 for molecules appearing in the next cycle. - If the cycle is not the first cycle, it may correspond to the concentration of the last molecule in the previous cycle.

[0176] At that time, the simulation of the hybridization phase is intended to model the hybridization reaction that occurs during the cycle. Hybridization is the process by which molecules T can hybridize. i T j Each pair is governed by the following equilibrium relationships:

[0177]

number

[0178] Here, such an equation is, therefore, a vector

[0179]

number

[0180] It should be noted that the functions of molecules present must be established by taking into account each possible hybridization reaction between pairs of molecules having indices i and j (i and j may be equal).

[0181] These equilibrium equations can be rewritten as the following differential equations.

[0182]

number

[0183] In the above equation, - Notation T i and T j These are the vectors involved in a given hybridization reaction.

[0184]

number

[0185] This represents the concentration of the single-stranded nucleic acid molecule pair at index i and j. - Notation H ij is a vector

[0186]

number

[0187] This represents the concentration of the double hemisphere formed by the hybridization of the single-stranded nucleic acid molecule pair at indices i and j. - Notation

[0188]

number

[0189] and

[0190]

number

[0191] These are, respectively, vectors.

[0192]

number

[0193] This represents the binding and dissociation constants of the hybridization reaction of the pair of single-stranded nucleic acid molecules at indices i and j.

[0194] The differential equation described above applies to vector molecules that are thought to undergo hybridization reactions.

[0195]

number

[0196] This applies to each reaction between the pairs. Therefore, the number of differential equations can sometimes be very large.

[0197] These pairs of molecules that are thought to undergo a hybridization reaction may, for example, be pairs of molecules whose hybridization reaction is associated with a variation in free enthalpy ΔG that is below a predefined threshold (or, since the variation in free enthalpy is negative, exceeds the threshold in absolute value).

[0198] Thus, only the dominant hybridization reaction is considered in the simulation. This allows for both greater accuracy in the dynamics of the hybridization reaction and a reduction in the complexity of solving the differential equations. It also makes it possible to consider the difference dynamics between different reactions, depending on whether the free enthalpy values ​​are more favorable or unfavorable between the two reactions of interest.

[0199] The predefined threshold can be the same for all reactions or can be selected from different thresholds depending on the case. For example, the value of the threshold may be selected from the values of at least two predefined thresholds, and the value of the lowest threshold is reserved for pairs of molecules containing paired amplicon and primer.

[0200] In other words, the threshold of the free enthalpy variation above which the hybridization reaction is not taken into account in the simulation is lower (closer to 0) (and thus also lower in absolute value since the threshold of the free enthalpy variation is negative) for the hybridization reaction between the amplicon and the primer than for other reactions. This allows the hybridization between the primer and the amplicon on the one hand and between the primer and other primers on the other hand to be selectively taken into account in the simulation, and thus allows the first cycle of amplicon - primer hybridization where the amplicon concentration is much lower than the primer concentration to be simulated.

[0201] In one set of embodiments of the present invention, the differential equation incorporates a mass conservation equation of the following form.

[0202]

Number

[0203] Where - t * represents the time elapsed since the start of the hybridization phase. - Notation T i and T j are, respectively, vectors of the concentrations of a plurality of nucleic acid molecules

[0204]

Number

[0205] This represents the concentrations of two single-stranded nucleic acid molecules at indices i and j. - Notation H xy This is a vector of concentrations of multiple nucleic acid molecules.

[0206]

number

[0207] This represents the concentration of the double hemisphere formed by the hybridization of the single-stranded nucleic acid molecule pair at indices x and y. - Notation T i0 and T j0 is, t * T at = 0 i and T j This represents the value.

[0208] The above equation relates the concentration of each single-stranded nucleic acid molecule to the concentration of all the double helix molecules to which they contribute in the hybridization reaction, showing that the hybridization reaction does not modify the total number of single helix molecules of each type. This type of mass conservation equation is vector

[0209]

number

[0210] This can be established for each single-stranded nucleic acid molecule present.

[0211] It should be noted that the mass conservation equation described above is given merely as a non-limiting example. According to various embodiments of the present invention, equivalent formulations of the mass conservation equation, i.e., other equations that reflect the fact that changes in the concentrations of single-stranded nucleic acid molecules and double-stranded molecules do not change the total number of single-stranded molecules of each type, may be used.

[0212] Incorporating the mass conservation equation into the differential equations allows for the completion of equations that enable more precise simulations of the hybridization phase, thus yielding an equal number of equations as there are unknowns.

[0213] The injection of the two mass conservation equations for the two molecules of the pair into the differential equation of the hybridization reaction between pairs of single-stranded nucleic acid molecules such as Equation 3 makes it possible to rewrite the equation in the following form.

[0214]

Number

[0215] To solve the system of differential equations, one of the principles of the simulation of the hybridization phase shown in FIG. 5 is to represent these equations in the form of matrix differential equations.

[0216] For this purpose, in the example of FIG. 5, the simulation of the hybridization phase S41 is the concentration matrix H of the double strands formed by the hybridization of a plurality of single-stranded nucleic acid molecules, or

[0217]

Number

[0218] includes a second sub-step S412 that initializes.

[0219] The matrix may be an N×N matrix (where N is the length of the vector

[0220]

Number

[0221] ). - Each row and each column corresponds to a nucleic acid molecule. - Each cell contains the concentration of a double helix formed by the hybridization of nucleic acid molecule pairs in the row and column to which the cell belongs. A triangular shape may be adopted to count a given double helix concentration only once, otherwise it would be counted in both the cells at coordinates i,j and j,i.

[0222] Therefore, matrix

[0223]

number

[0224] It can be written as follows:

[0225]

number

[0226] In the example shown in Figure 5, the hybridization phase S41 of a given cycle then includes a third substep S413 in which the changes in the concentration matrix during the hybridization phase are calculated in successive time steps by applying a matrix differential equation that represents the dynamics of the double helix formation as a function of the concentrations of a plurality of single-stranded nucleic acid molecules to the concentration matrix.

[0227] The calculation of matrix transitions can be performed, for example, as follows: - The computation is performed over Npdt time steps corresponding to the duration of the hybridization phase. The time steps may have durations ranging from, for example, 1 millisecond to 10 milliseconds. The time steps may be selected, for example, to find a compromise between computation convergence, computation speed, and result accuracy. - The time step index npdt is initialized to 1. - At each time step, substep S413 is performed to calculate the transition of the concentration matrix. - At the end of the calculation, substep S414 verifies that the time step index npdt is indeed smaller than the number of time steps Npdt. - If the time step index npdt is less than the number of time steps Npdt, the time step index npdt is incremented in substep S412, and then a new iteration of substep S413 is performed to calculate the transition of the concentration matrix. - When the time step index npdt is equal to the number of time steps Npdt, the hybridization phase simulation is terminated and the extension phase S42 simulation is started.

[0228] Thus, the hybridization phase can be simulated by simulating a series of time steps of Npdt with respect to the hybridization reaction, where each time step corresponds to the last vector of the previous time step.

[0229]

number

[0230] This involves calculating matrix differential equations based on the concentrations of molecules.

[0231] This example of a continuous computation loop is merely given as a non-limiting example of a loop for computing the hybridization phase. More broadly, any computation loop that allows the hybridization phase to be simulated according to a desired number of time steps can be used in the context of the present invention. For example, the time step index can be initialized to 0, and the loop termination condition in step S414 can be adapted.

[0232] The matrix differential equation is parameterized by at least one coupling matrix containing coupling constants associated with each double chain, and at least one dissociation matrix containing dissociation constants associated with each double chain.

[0233] Therefore, the join matrix contains all the join coefficients included in equations 3 and 5. The join coefficients and dissociation coefficients are in the matrix.

[0234]

number

[0235] The concentration can be incorporated into the binding and dissociation matrices according to the same principle as the concentration (for example, the binding and dissociation matrices are square matrices where each row and each column corresponds to a molecule, and each cell in the binding matrix contains the binding constants between molecules in the row and column to a partial double chain, and each cell in the dissociation matrix contains the dissociation constants related to the dissociation reaction from the double chain to the molecular pairs associated in the row and column).

[0236] Therefore, the join matrix and the dissociation matrix are, with respect to the join constant,

[0237]

number

[0238] And with respect to the dissociation matrix,

[0239]

number

[0240] They can be written as follows.

[0241] The unit of the coupling constant is m 3 .mol -1 .s -1 (or L.mol) -1 .s -1 ) is possible, while the unit of the dissociation constant is s -1 It is possible that this is the case.

[0242] As shown above, in one set of embodiments of the present invention, only specific hybridization reactions are taken into consideration. In this case, the binding and dissociation constants are therefore incorporated only with respect to reactions that are considered sufficiently important, i.e., those that have the greatest impact on the simulation. This can be done, for example, by defining each element of the binding matrix or each element of the dissociation matrix related to the pair of molecules belonging to it as follows: - Zero if the variation in free enthalpy (ΔG) associated with the hybridization reaction of the paired molecules is above (or below) the threshold. - Otherwise, they are equal to the bonding or dissociation constants of the hybridization reaction of the pair of molecules, respectively.

[0243] In other words, the values ​​of the matrix's coupling and dissociation constants become equal to 0 for less important reactions, for example, if the variation in free enthalpy (ΔG) associated with the hybridization reaction of the paired molecules is higher (or lower in absolute value) than a given threshold.

[0244] Therefore, only the dominant response is taken into consideration, which reduces the complexity of the simulation while still benefiting from good simulation accuracy.

[0245] As shown above, the threshold for taking hybridization reactions into account and, consequently, incorporating the binding and dissociation constants into the matrix, may be the same for all reactions, or it may differ depending on whether the reaction is an amplicon-primer hybridization reaction or another hybridization reaction (e.g., primer-primer).

[0246] Thus, the transition of the double-chain concentration matrix can be written in the form of a matrix differential equation using the bond matrix and the dissociation matrix, and therefore, substep S413 can be solving a matrix differential equation with respect to a given time step.

[0247] Thus, solving matrix differential equations makes it possible to model the entire dynamics of chain amplification, including cross-reactions with intermediate products. Solving a single matrix differential equation also makes it possible to solve the system's dynamics using conventional computational power.

[0248] Therefore, the possibility of fully simulating amplification, and especially hybridization reactions that have not been satisfactorily simulated in state-of-the-art solutions, allows for the verification or modification of parameters affecting the amplification reaction (such as initial primer concentration, salt, phase duration, and temperature).

[0249] When the equation of conservation of mass is taken into consideration, the matrix differential equation can be written as follows, incorporating differential equations like Equation 6 for each reaction:

[0250]

number

[0251] During the ceremony, - H is the cardinality matrix of the double hemisphere. - T0 is the initial value of the cycle of the concentration vectors of multiple molecules. - K on This is the combination matrix. - K off This is the dissociation matrix. -

[0252]

number

[0253] This is the identity matrix of size N. -

[0254]

number

[0255] This is the Hadamard product. - diag() represents a diagonal operator that transforms a square matrix of size N×N into a vector of size N that contains all elements on the diagonals of the matrix. Therefore,

[0256]

number

[0257] That is the case.

[0258] It should be noted that in differential equations, T is replaced with T0, which allows for faster matrix calculations.

[0259] Next, Figures 6 and 7 are referred to.

[0260] Figure 6 shows an example of the two phases of extension and modification in one embodiment of the present invention.

[0261] Figure 7 shows an example of a set of hybridization, extension, and denaturation reactions that occur over three consecutive cycles of a PCR amplification reaction, and the reactions shown in Figure 7 provide a better illustration of the steps in the simulation of the extension and denaturation phases shown in Figure 6.

[0262] Figure 7 shows a simplified example of a single-target amplification reaction.

[0263] Figure 7 shows, in more detail, a series of hybridization, extension, and denaturation reactions that occur under given conditions, and new byproducts are generated, so new reactions appear consecutively in cycle 2 and then cycle 3.

[0264] In the example in Figure 7, the simulation initially includes the following (at the beginning of the hybridization phase of Cycle 1): - The target single-stranded nucleic acids, "sense" and "antisense," respectively, TFWD and T REV - One "sense" prima

[0265]

number

[0266] , as well as two "antisense" primers

[0267]

number

[0268] and

[0269]

number

[0270] During the first cycle, the reaction proceeds as follows: - React71 response: T REV However, prima

[0271]

number

[0272] Paired with it in the first position, it forms a double chain.

[0273]

number

[0274] This results in an extended double chain.

[0275]

number

[0276] It is extended into two single-stranded nucleic acids T REV and

[0277]

number

[0278] It is transformed into this. - React72 response: T REV However, prima

[0279]

number

[0280] Paired with it in the second position, it forms a double chain.

[0281]

number

[0282] This results in an extended double chain.

[0283]

number

[0284] It is extended into two single-stranded nucleic acids T REV and

[0285]

number

[0286] The molecules paired are the same in reactions React71 and React72, but the pairing occurs at two different locations, and as a result, in the case of reaction React72, the elongation takes place over a shorter distance, so these reactions are different. This is called "multihybridization". The variation in free enthalpy ΔG associated with these two reactions may also be different. Thus, reactions React71 and React72 are, in each case, two molecules in separate single-stranded forms.

[0287]

number

[0288] and

[0289]

number

[0290] Generates. - React73 response: T FWD However, prima

[0291]

number

[0292] Paired with it, it forms a double chain.

[0293]

number

[0294] This results in an extended double chain.

[0295]

number

[0296] It is extended into two single-stranded nucleic acids T FWD and ST REV It is transformed into this. - React74 response:

[0297]

number

[0298] but,

[0299]

number

[0300] Paired with it, it forms a double chain.

[0301]

number

[0302] This results in an extended double chain.

[0303]

number

[0304] It is extended into two single-stranded nucleic acids PD. REV and

[0305]

number

[0306] It is transformed into this. - React75 response:

[0307]

number

[0308] but,

[0309]

number

[0310] Paired with it, it forms a double chain.

[0311]

number

[0312] This results in an extended double chain.

[0313]

number

[0314] It is extended into two single-stranded nucleic acids PD. FWD and

[0315]

number

[0316] It is transformed into. The primers paired for reactions React74 and React75 are the same, but the elongation does not occur in the same chain; that is, in reaction React74, it is the "antisense" chain that is elongated, while in reaction React75, it is the "sense" chain that is elongated, so these reactions are different.

[0317] Thus, at the end of this first cycle, a new reaction byproduct is produced, namely,

[0318]

number

[0319] However, it is added to the already existing product.

[0320] In the second cycle, the presence of these new byproducts leads to six new reactions in addition to the five reactions from React71 to React75 that have already occurred in the first cycle. - React76 response:

[0321]

number

[0322] However, prima

[0323]

number

[0324] Paired with it, it forms a double chain.

[0325]

number

[0326] This results in an extended double chain.

[0327]

number

[0328] It is extended into two single-stranded nucleic acids, and the extended double helix is ​​made up of two single-stranded nucleic acids.

[0329]

number

[0330] and

[0331]

number

[0332] It is transformed into this. - React77 response:

[0333]

number

[0334] However, prima

[0335]

number

[0336] Paired with it, it forms a double chain.

[0337]

number

[0338] This results in an extended double chain.

[0339]

number

[0340] It is extended into two single-stranded nucleic acids, and the extended double helix is ​​made up of two single-stranded nucleic acids.

[0341]

number

[0342] and

[0343]

number

[0344] It is transformed into this. - React78 response: ST REV However, prima

[0345]

number

[0346] Paired with it in the first position, it forms a double chain.

[0347]

number

[0348] This results in an extended double chain.

[0349]

number

[0350] It is extended into two single-stranded nucleic acids ST REV and

[0351]

number

[0352] It is transformed into this. - React79 Response: ST REV However, prima

[0353]

number

[0354] Paired with it in the second position, it forms a double chain.

[0355]

number

[0356] This results in an extended double chain.

[0357]

number

[0358] It is extended into two single-stranded nucleic acids ST REV and

[0359]

number

[0360] The molecules paired are the same in reactions React78 and React79, but the pairing occurs at two different locations, and as a result, in the case of reaction React79, the elongation takes place over a shorter distance, so these reactions are different. This is called "multihybridization". Thus, reactions React78 and React79 are two molecules in separate single-stranded forms, respectively.

[0361]

number

[0362] and

[0363]

number

[0364] Generates. - React710 response: PD FWD but,

[0365]

number

[0366] Paired with it, it forms a double chain.

[0367]

number

[0368] This results in an extended double chain.

[0369]

number

[0370] It is extended into two single-stranded nucleic acids PD. REV and PD FWD It is transformed into this. - React711 response:

[0371]

number

[0372] However, PD REV Paired with it, it forms a double chain.

[0373]

number

[0374] This results in an extended double chain.

[0375]

number

[0376] It is extended into two single-stranded nucleic acids PD. REV and PD FWD It is denatured into [the following]. The products of reactions React710 and React711 are the same, but the molecules paired are different, and the extension does not occur in the same chain; that is, in reaction React710, it is the "antisense" chain that is extended, while in reaction React711, it is the "sense" chain that is extended, so these reactions are different.

[0377]

number

[0378] and

[0379]

number

[0380] It should also be noted that, for the purposes of the simulation, these are treated as two different molecules associated with two different concentrations, but in reality, they are the same molecule.

[0381] Thus, at the end of this second cycle, a new reaction byproduct is produced, namely,

[0382]

number

[0383] , and

[0384]

number

[0385] However, it is added to the already existing product.

[0386] In the third cycle, the presence of these new byproducts leads to four new reactions in addition to the 11 reactions from React71 to React711 that have already occurred in the second cycle. - React712 response:

[0387]

number

[0388] However, prima

[0389]

number

[0390] Paired with it, it forms a double chain.

[0391]

number

[0392] This results in an extended double chain.

[0393]

number

[0394] It is extended into two single-stranded nucleic acids, and the extended double helix is ​​made up of two single-stranded nucleic acids.

[0395]

number

[0396] and

[0397]

number

[0398] It is transformed into this. - React713 response:

[0399]

number

[0400] However, prima

[0401]

number

[0402] Paired with it, it forms a double chain.

[0403]

number

[0404] This results in an extended double chain.

[0405]

number

[0406] It is extended into two single-stranded nucleic acids, and the extended double helix is ​​made up of two single-stranded nucleic acids.

[0407]

number

[0408] and

[0409]

number

[0410] It is transformed into this. - React714 response:

[0411]

number

[0412] However, prima

[0413]

number

[0414] Paired with it, it forms a double chain.

[0415]

number

[0416] This results in an extended double chain.

[0417]

number

[0418] It is extended into two single-stranded nucleic acids, and the extended double helix is ​​made up of two single-stranded nucleic acids.

[0419]

number

[0420] and

[0421]

number

[0422] It is denatured into [the following]. The products of reactions React712 and React714 are the same, but the molecules paired are different, and the elongation does not occur in the same chain; that is, in reaction React712, it is the "antisense" chain that is elongated, while in reaction React714, it is the "sense" chain that is elongated, so these reactions are different.

[0423]

number

[0424] and

[0425]

number

[0426] It should also be noted that, for the purposes of the simulation, these are treated as two different molecules associated with two different concentrations, but in reality, they are the same molecule. - React715 response:

[0427]

number

[0428] However, prima

[0429]

number

[0430] Paired with it, it forms a double chain.

[0431]

number

[0432] This results in an extended double chain.

[0433]

number

[0434] It is extended into two single-stranded nucleic acids, and the extended double helix is ​​made up of two single-stranded nucleic acids.

[0435]

number

[0436] and

[0437]

number

[0438] It is denatured into [the following]. The products of reactions React713 and React715 are the same, but the molecules paired are different, and the extension does not occur in the same chain; that is, in reaction React713, it is the "antisense" chain that is extended, while in reaction React715, it is the "sense" chain that is extended, so these reactions are different.

[0439]

number

[0440] and

[0441]

number

[0442] It should also be noted that, for the purposes of the simulation, these are treated as two different molecules associated with two different concentrations, but in reality, they are the same molecule.

[0443] One principle for simulating the hybridization and denaturation phases of examples of embodiments of the present invention shown in Figure 6 and illustrated in Figure 7 is to simulate several multiple hybridization reactions (e.g., reactions React71 and React72, or reactions React76 and React77) as a single reaction producing multiple reaction products, and then use a denaturation tensor to distribute the concentrations of the multiple hybridization reaction products for the next simulation cycle. Thus, the concentrations of the double chain and the extended double chain corresponding to different pairing positions are represented by a single value.

[0444] Using a single concentration value for all double helix strands between pairs of nucleic acid molecules, regardless of pairing position, reduces the number of equations to be solved for denaturation calculations, making it possible to solve problems that simulate denaturation.

[0445] In one set of embodiments of the present invention, a particular reaction occurs as a result of the pairing of two primers into a double chain. In this case, the extension can occur in both directions. This is true, for example, of reactions React74 and React75. In this case, in some embodiments of the present invention, the extension phase simulates the extension of such a double chain into a single extended double chain, and the coefficients of the denaturing tensor are defined such that the concentration of the single extended double chain resulting from the pairing of the two primers produces reaction products corresponding to the extension in both directions.

[0446] This simplifies the simulation of the reaction resulting from the pairing of the two primers, further reducing the computational complexity of the simulation.

[0447] In the example in Figure 7, the reaction can therefore be represented by the following equation, where, - E e This represents the extension constant associated with each reaction. - E d This represents the denaturation constant associated with each reaction. - w represents the respective weights associated with the molecules resulting from several reactions, where the concentration of the extended double chain actually represents the concentration of several different double chains, for the purpose of the simulation. - The three consecutive arrows in each reaction represent hybridization, extension, and denaturation. Therefore, the molecule to the right of the last arrow represents the denaturation product. Only the new molecule is shown to improve the readability of the formula.

[0448] React 71 and React 72 are based on the formula

[0449]

number

[0450] It can be represented by:

[0451] In this case of multiple hybridization, the two concentrations of the double chain

[0452]

number

[0453] and

[0454]

number

[0455] is a single clock

[0456]

number

[0457] Represented by, the two concentrations of the extended double chain

[0458]

number

[0459] and

[0460]

number

[0461] is a single clock

[0462]

number

[0463] Represented by the application of each weight w in the denatured tensor, the concentrations of the two molecules take into account the respective weights of the reactions resulting from both pairings.

[0464]

number

[0465] and

[0466]

number

[0467] It should be noted that it will be possible to update it.

[0468] React73 is a formula

[0469]

number

[0470] It is represented by [this].

[0471] React 74 and React 75 are based on the formula

[0472]

number

[0473] It can be represented by:

[0474] In this reaction (primer-dyma) that results from the pairing of two primers, the two concentrations of the double chain

[0475]

number

[0476] and

[0477]

number

[0478] is a single concentration H PD Represented by, the two concentrations of the extended double chain

[0479]

number

[0480] and

[0481]

number

[0482] is a single clock

[0483]

number

[0484] This is represented by the application of each weight w in the denatured tensor to the concentrations PD of the two molecules. REV and PD FWD It should be noted that it will be possible to update it.

[0485] The use of weights is done, for example, as follows: an equation representing several reactions, such as equation 13, can be associated with several weights representing the relative importance of different reactions, which are stored, for example, in a denatured tensor. For example, with respect to equation 13, reactions React74 and React75 are associated with weight w, respectively. React74 and w React75 It can be associated with. At the end of each cycle, a single concentration

[0486]

number

[0487] However, this can be divided into the concentrations of the reaction products. For example, in equation 13, the concentration of the molecule PD REV However, at the end of the cycle

[0488]

number

[0489] Only the concentration of molecules is increased, and the concentration of molecules PD FWD However, at the end of the cycle

[0490]

number

[0491] It is increased by only that much. Therefore, the weight w React74 and w React75 The sum of must be equal to 1, and as a result, w React74 and w React75 This represents the importance of React 74 and React 75, respectively. For example, the weight w React74 = 0.5 and w React75 = 0.5 indicates that React 74 and React 75 are equally likely to experience this.

[0492] React76 is a formula

[0493]

number

[0494] It is represented by [this].

[0495] React77 is a formula

[0496]

number

[0497] It is represented by [this].

[0498] React 78 and React 79 use the formula

[0499]

number

[0500] It can be represented by:

[0501] In this case of multiple hybridization, the two concentrations of the double chain

[0502]

number

[0503] and

[0504]

number

[0505] is a single clock

[0506]

number

[0507] Represented by, the two concentrations of the extended double chain

[0508]

number

[0509] and

[0510]

number

[0511] is a single clock

[0512]

number

[0513] Represented by the application of each weight w in the denatured tensor, the concentrations of the two molecules take into account the respective weights of the reactions resulting from both pairings.

[0514]

number

[0515] and

[0516]

number

[0517] It should be noted that it will be possible to update it.

[0518] React710 is a formula

[0519]

number

[0520] It is represented by [this].

[0521] React711 is an expression

[0522]

number

[0523] It is represented by [this].

[0524] React712 is an expression

[0525]

number

[0526] It is represented by [this].

[0527] React713 is an expression

[0528]

number

[0529] It is represented by [this].

[0530] React714 is an expression

[0531]

number

[0532] It is represented by [this].

[0533] React715 is a formula

[0534]

number

[0535] It is represented by [this].

[0536] In one set of embodiments of the present invention, - Each molecule involved in the simulation is a vector

[0537]

number

[0538] It is associated with the index in [location]. - The concentration of the double hemisphere obtained as a result of the hybridization phase is a square matrix.

[0539]

number

[0540] It is described, and each row and each column is a vector of one of the molecules.

[0541]

number

[0542] These are represented by the order of their indices in the given system.

[0543] In the example in Figure 7, the matrix

[0544]

number

[0545] For example, it could be written as follows:

[0546]

number

[0547] In the above representation, the single-stranded molecules associated with each column and row are shown above each column and to the left of each row, respectively. According to the formula above, in the case of multihybridization, the matrix actually contains single double-strand concentrations representing the concentrations of several double-strands corresponding to several pairing positions. For example, - line “

[0548]

number

[0549] " and column "T REV The cell corresponding to " is actually concentration

[0550]

number

[0551] and

[0552]

number

[0553] Total concentration

[0554]

number

[0555] Includes. - line “

[0556]

number

[0557] " and column "ST REV The cell corresponding to " is actually concentration

[0558]

number

[0559] and

[0560]

number

[0561] Total concentration

[0562]

number

[0563] Includes.

[0564] While these examples are given for multihybridization at two different pairing locations, it should be noted that this principle can be generalized to multihybridization with any number of pairings of two or more different locations.

[0565] In one embodiment of the present invention, the concentration of the elongated double chain is obtained during the simulation S42 of the elongation phase by multiplying the concentration of the double chain by the elongation constant.

[0566] For example, the extension constant is a matrix.

[0567]

number

[0568] It can be enumerated in the elongation tensor constructed by the same principle, that is, the elongation tensor

[0569]

number

[0570] Each cell is a matrix

[0571]

number

[0572] It includes the extension coefficients of the double-stranded cells corresponding to each cell. In the example in Figure 7, the extension tensor is therefore as follows:

[0573]

number

[0574] The numbering of the extension constants here is for vectors.

[0575]

number

[0576] Refers to the index of single-stranded nucleic acid molecules in [the specified location]. For example, tensors

[0577]

number

[0578] The constants listed in column 1, row 11.

[0579]

number

[0580] is a vector

[0581]

number

[0582] Molecules with indices 1 and 11 (therefore, molecules

[0583]

number

[0584] and

[0585]

number

[0586] A double helix formed by the hybridization of ) i.e., a matrix

[0587]

number

[0588] It is also written in column 1, row 11.

[0589]

number

[0590] This represents the extension coefficient. The extension constant can be obtained, for example, from a database or experimentally.

[0591] Therefore, each elongation coefficient represents a coefficient between 0 and 1 for the molecules of a given double chain that are elongated during the elongation phase. For example, a coefficient of 0.5 for a given double chain means that half of the molecules of that double chain are elongated during the elongation phase. Thus, the concentration of the elongated double chain at the end of the elongation phase is half the concentration of the unelongated double chain at the beginning of the elongation phase. In this way, the elongation tensor consists of elongation coefficients between 0 and 1.

[0592] More broadly, the simulation phase of the extension phase can be performed by step S421, which multiplies the concentration matrix of the unextended double hemisphere by the extension tensor.

[0593]

number

[0594] During the ceremony, - C represents the index of the PCR amplification cycle. - Δt represents the duration of the extension phase. -

[0595]

number

[0596] This represents the concentration matrix of the unextended double helix in the Cth PCR amplification cycle. -

[0597]

number

[0598] This represents the concentration matrix of the extended double helix in the Cth PCR amplification cycle. -

[0599]

number

[0600] This represents an elongated tensor.

[0601] Since not all of the double helix is ​​fully elongated during the elongation phase, the concentration of the unelongated double helix at the end of the cycle is therefore equal to the concentration of the unelongated double helix at the beginning of the cycle minus the concentration of the elongated double helix at the end of the phase. For example,

[0602]

number

[0603] The elongation phase is represented here by the Hadamard matrix product. However, this is not the only way to simulate the elongation phase. For example, the elongation phase can be more broadly simulated by multiplying the concentration of each unelongated double chain at the beginning of the elongation phase by the elongation coefficient of that double chain. For example, the concentration of the unelongated double chain can be incorporated into the concentration vector of the unelongated double chain, and this vector can be multiplied by the elongation coefficient vector.

[0604] The denaturation phase may actually consist of two steps, namely: - Step S431: Multiply the concentrations of the extended double helix and, optionally, the unextended double helix by one or more denaturing tensors representing the distribution of the double helix to single-stranded nucleic acid molecules. - Step S432: Multiply the concentration of the double chain, or the concentration of the product of the double chain concentration and the denaturation tensor, by one or more denaturation coefficients that represent the proportion of the double chain that is actually denatured during the denaturation phase.

[0605] In one set of embodiments of the present invention, the denaturation phase includes multiplying the concentration of the extended double helix by the denaturation tensor of the extended double helix. The denaturation tensor of the extended double helix effectively represents the redistribution of the extended double helix to single-stranded nucleic acid molecules during the denaturation phase.

[0606] This simulates the denaturation of the elongated double helix and incorporates the concentrations of the elongated and denatured double helix under the initial conditions of the next cycle.

[0607] In one set of embodiments of the present invention, the denaturation phase further comprises multiplying the concentration of the unextended double helix by the denaturation tensor of the unextended double helix.

[0608] Therefore, the simulation of the denaturation phase takes into account not only the denaturation of the elongated double helix but also the denaturation of the unelongated double helix, thereby enabling more accurate simulation results.

[0609] When simulating the denaturation phase, the denaturation coefficient can also be applied to the concentration of the extended / unextended double helix, and / or the concentration of the single-stranded nucleic acid resulting from the multiplication of the extended / unextended double helix concentration with the denaturation tensor.

[0610] The degeneration coefficient represents the proportion of a given type of double helix that is actually degenerated during the degeneration phase. The degeneration coefficient can be obtained, for example, from a database or experimentally.

[0611] Therefore, each denaturation coefficient represents a coefficient between 0 and 1 for the given double-chain molecules that are denatured during the denaturation phase. For example, a coefficient of 0.5 for a given double-chain means that half of the molecules in this double-chain are denatured during the denaturation phase.

[0612] According to various embodiments, - The same degeneration coefficient may be applied to a given elongated double helix and its corresponding unelongated double helix. This allows for a good approximation of degeneration while simplifying calculations. - Two different degeneration coefficients may be applied to a given elongated double helix and its corresponding unelongated double helix, respectively. This allows for more accurate simulations when degeneration occurs differently for elongated and unelongated double helixes.

[0613] The transformation coefficient can be applied, for example, by matrix multiplication. For example, the transformation phase can be simulated by the following equation.

[0614]

number

[0615] During the ceremony, -

[0616]

number

[0617] This is the Hadamard product. -

[0618]

number

[0619] This is the identity matrix. -

[0620]

number

[0621] This is a degeneration matrix containing degeneration coefficients associated with each double helix. -

[0622]

number

[0623] This is the extension matrix. -

[0624]

number

[0625] This is a matrix of concentrations of unextended double helix at the end of the denaturation phase of cycle C. -

[0626]

number

[0627] This is a matrix of the concentrations of the extended double hemispheres at the beginning of the denaturation phase of cycle C. -

[0628]

number

[0629] This is the matrix of concentrations of the unextended double chain at the beginning of the next cycle C+1. -

[0630]

number

[0631] This is the matrix of concentrations of the extended double chain at the beginning of the next cycle C+1. -

[0632]

number

[0633] This represents the tensor product. -

[0634]

number

[0635] This is an extended double-stranded denatured tensor. -

[0636]

number

[0637] This is a non-extended double-stranded denatured tensor. -

[0638]

number

[0639] This is the concentration of the extended double helix at the end of the extension phase, expressed in vector form. -

[0640]

number

[0641] This is the concentration of the unextended double hemisphere at the end of the extension phase, expressed in vector form. -

[0642]

number

[0643] This represents the concentration vector of single-stranded nucleic acid molecules at the end of the extension phase of PCR amplification cycle C. -

[0644]

number

[0645] This represents the concentration vector of single-stranded nucleic acid molecules at the beginning of the next PCR amplification cycle C+1.

[0646] Equation 27 represents the concentrations of unextended and undenatured double helix found at the beginning of the next amplification cycle C+1.

[0647] Equation 28 represents the concentrations of undenatured and extended double helix found at the beginning of the next amplification cycle C+1.

[0648] Equation 29 represents the distribution of denatured double-stranded nucleic acids into single-stranded nucleic acids at the beginning of the next amplification cycle C+1. More specifically, -

[0649]

number

[0650] This represents the distribution of the extended double helix to single-stranded nucleic acid by applying a denatured tensor to the extended double helix. -

[0651]

number

[0652] This represents the distribution of unextended double helix to single-stranded nucleic acids by applying a denatured tensor to an unextended double helix. -

[0653]

number

[0654] This represents the application of a denatured tensor to the distribution of single-stranded nucleic acids. - Therefore, term

[0655]

number

[0656] This represents the variation in single-stranded nucleic acid during the PCR amplification cycle of index C.

[0657] It should be noted that the examples provided above are purely non-restrictive, and other formulations may be applied to simulate the denaturation phase. For example, equivalent formulas for the distribution of a double hemisphere to a single-stranded molecule and the multiplication of the denaturation constant may be used. For instance, the multiplication of the denaturation constant may be performed in the form of vector multiplication.

[0658] In the examples of equations 28 and 29, the variance constant is a matrix.

[0659]

number

[0660] It is listed as a denatured tensor constructed by the same principle, that is, a denatured tensor

[0661]

number

[0662] Each cell is a matrix

[0663]

number

[0664] It includes the degenerate coefficients of the double helix of the corresponding cells. In the example in Figure 7, the degenerate tensor is therefore as follows:

[0665]

number

[0666] The numbering of the transformation constants here is by vector

[0667]

number

[0668] Refers to the index of single-stranded nucleic acid molecules in [the specified location]. For example, tensors

[0669]

number

[0670] The constants listed in column 1, row 11.

[0671]

number

[0672] is a vector

[0673]

number

[0674] Molecules with indices 1 and 11 (therefore, molecules

[0675]

number

[0676] and

[0677]

number

[0678] A double helix formed by the hybridization of ) i.e., a matrix

[0679]

number

[0680] It is also written in column 1, row 11.

[0681]

number

[0682] This represents the degeneration coefficient of the double strand and the corresponding elongated double strand (for example,

[0683]

number

[0684] and

[0685]

number

[0686] The same degeneration coefficient is applied to the ). However, in other embodiments of the present invention, different degeneration coefficients may be applied to a particular double helix and an extended double helix, for example, when the dynamics of degeneration differ significantly between the two versions. The degeneration coefficient can be read from a database, for example, or obtained experimentally.

[0687] Therefore, each denaturation coefficient represents a coefficient between 0 and 1 for the given double-strand molecules that are denatured during the denaturation phase. For example, a coefficient of 0.5 for a given double-strand means that half of the molecules in that double-strand are denatured during the denaturation phase. Thus, the concentration of the extended / unextended double-strand at the end of the denaturation phase is half the concentration of the extended / unextended double-strand at the beginning of the denaturation phase. In this way, the denaturation tensor is composed of denaturation coefficients between 0 and 1.

[0688] In the case of unextended double helix (i.e., a double helix resulting from the hybridization of two unextended single-stranded nucleic acid molecules), the molecule is not transformed, and denaturation has the effect of restoring the two nucleic acid molecules to a hybridized single helix.

[0689] In the example in Figure 7, the denaturation of the extended double helix is ​​summarized in the table below, with each row containing the reference symbol for the partial double helix and the vector.

[0690]

number

[0691] This includes the index of the two single-stranded nucleic acid molecules whose hybridization enabled them to form a double helix, and which are recreated at the end of the denaturation phase, along with the index of these two molecules.

[0692] [Table 1]

[0693] Therefore, the unextended double-stranded denatured tensor

[0694]

number

[0695] In this example, it can be written as follows:

[0696]

number

[0697] Unextended double-stranded denatured tensor

[0698]

number

[0699] In this example, it is a tensor of size 12x14, that is, it is a vector

[0700]

number

[0701] The 12 double chains each contain 12 corresponding rows. The 12 double chains are described to the left of their respective rows, and the vector

[0702]

number

[0703] They are listed in the order of their indices in the vector. A mutated tensor is a vector

[0704]

number

[0705] It also includes 14 columns corresponding to each of the 14 single-stranded nucleic acid molecules. The 14 single-stranded nucleic acid molecules are listed above their respective columns, and the vector

[0706]

number

[0707] They are listed in the order of their indices. The value "1" is written to each cell belonging to the double-stranded row and the single-stranded nucleic acid column that is produced by the denaturation of this extended double-stranded structure.

[0708] Thus, a variant tensor can be transformed into a single, simple algebraic operation for the next cycle.

[0709]

number

[0710] from

[0711]

number

[0712] This allows for the distribution of molecular concentrations. The denaturation tensor form also allows for verification that the reaction is correct by summing each row. In particular, the sum of the elements in each row must be equal to 2 (since each double helix produces two single-stranded nucleic acid molecules during the denaturation phase).

[0713] The degenerate tensor of the elongated double helix is ​​also 12x14 in size in this example, and each row represents the elongated double helix as a vector.

[0714]

number

[0715] The order of those indices in the vector is shown, and each column represents a single-stranded nucleic acid molecule.

[0716]

number

[0717] These are represented in the order of their indices. For a double hemisphere corresponding to a single hybridization reaction at a single location, the denaturation tensor is constructed as a denaturation tensor in which the value "1" is written to each cell belonging to the row of the extended double hemisphere and the column of single-stranded nucleic acid produced by the denaturation of this extended double hemisphere.

[0718] In one set of embodiments of the present invention, the extended double-stranded denatured tensor also includes specific coefficients in the case of multiple hybridizations, i.e., hybridization of the same primer at several locations of the same single-stranded nucleic acid, for example, in the case of reactions React71 and React72, or React78 and React79.

[0719] In this case, denaturation produces at least three single-stranded nucleic acids, not two. In the case of reactions React71 and React72, or React78 and React79, multiple hybridization occurred at two locations, so denaturation produces three single-stranded nucleic acids, but the same principle can be extended to a greater number of denatured products in the case of hybridization at a greater number of locations.

[0720] In this case, the concentration of the double chain and the concentration of the extended double chain each include, for example, a virtual double chain concentration equal to the sum of the concentrations of the double chains formed by multiple hybridization reactions, and a virtual extended double chain concentration equal to the sum of the concentrations of the extended double chains formed by the extension of the double chains formed by multiple hybridization reactions.

[0721] for example, - For multi-hybridization reactions in React 71 and React 72, - The concentration of the unextended double chain is the concentration

[0722]

number

[0723] and

[0724]

number

[0725] The hypothetical double-stranded concentration representing the sum

[0726]

number

[0727] Includes. - The concentration of the extended double chain is the concentration

[0728]

number

[0729] and

[0730]

number

[0731] The total concentration of the extended virtual double hemisphere

[0732]

number

[0733] Includes. - For multi-hybridization reactions in React 78 and React 79, - The concentration of the unextended double chain is the concentration

[0734]

number

[0735] and

[0736]

number

[0737] The hypothetical double-stranded concentration representing the sum

[0738]

number

[0739] Includes. - The concentration of the extended double chain is the concentration

[0740]

number

[0741] and

[0742]

number

[0743] The total concentration of the extended virtual double hemisphere

[0744]

number

[0745] Includes.

[0746] In this case, the coefficient of the extended double-strand denaturation tensor corresponding to the distribution of the extended virtual double-strand concentration to each single-stranded nucleic acid associated with one of the multiple hybridization reactions may be equal to the ratio of the interaction energies of the multiple hybridization reactions, each divided by the sum of the interaction energies of all the multiple hybridization reactions with the single-stranded nucleic acid.

[0747] For example, in the case of the multihybridization reactions React71 and React72, a virtual double chain

[0748]

number

[0749] but, - On the one hand, T was present in both React 71 and React 72. REV It is transformed into this. Therefore, the associated coefficient becomes 1. - On the other hand, it corresponds to React 71 and React 72.

[0750]

number

[0751] and

[0752]

number

[0753] It is modified into a molecule.

[0754]

number

[0755] and

[0756]

number

[0757] The coefficients related to this must correspond to the respective importance of the reactions React71 and React72, i.e., the respective importance of the hybridization of React71 and the hybridization of React72. For this purpose, these two coefficients can be equal to the interaction energy of the hybridization of React71 divided by the sum of the hybridization energies of React71 and React72, and the interaction energy of the hybridization of React72 divided by the sum of the hybridization energies of React71 and React72, respectively.

[0758] For example, the hybridization reaction React71 has an interaction energy ΔG 1 It has the interaction energy ΔG of the hybridization reaction React72. 2 If it has, in the extended double-stranded denatured tensor

[0759]

number

[0760] and

[0761]

number

[0762] The weights associated with each are equal to the following: -

[0763]

number

[0764] Regarding

[0765]

number

[0766] - and

[0767]

number

[0768] Regarding

[0769]

number

[0770] Thus, multiple hybridization reactions, along with associated extension and denaturation, can be simulated as a single series of reactions while maintaining the accuracy of the simulation.

[0771] In one set of embodiments of the present invention, the denaturation tensor of the elongated double chain also includes a specific coefficient in the case of hybridization between two primers, i.e., a "primer-dyma". In particular, in this case, the double chain formed by the hybridization of two primers may be elongated in both directions, which ultimately produce different denatured products, such as in reactions React74 and React75.

[0772] In this case, the concentration of the elongated double chain includes the concentration of an elongated virtual double chain equal to the sum of the concentrations of the elongated double chains formed by the elongation in each of the two directions of the double chain formed by the hybridization of the two primers.

[0773] For example, in the case of reactions React74 and React75, the concentration of the extended double chain is,

[0774]

number

[0775] and

[0776]

number

[0777] The total concentration of the extended virtual double hemisphere

[0778]

number

[0779] It may include. Therefore, the concentration of the extended virtual double chain

[0780]

number

[0781] This does not correspond to the actual concentration of double hemispheres, but it facilitates the simulation.

[0782] Then, the coefficients of the denatured double-strand tensor, corresponding to the distribution of the elongated virtual double-strand concentration to each of the two primers and each of the two single-stranded nucleic acids resulting from elongation in one of the two directions, can all be equal to 0.5 to represent the fact that elongation occurs substantially every two times in each of the two directions. For example, in the case of reactions React74 and React75, the denatured product is the primer PD REV and PD FWD Nucleic acids

[0783]

number

[0784] and

[0785]

number

[0786] Therefore, in an extended double-stranded denatured tensor,

[0787]

number

[0788] The row and

[0789]

number

[0790] , and

[0791]

number

[0792] All cells in that column will be equal to 0.5.

[0793] This allows for efficient simulation of reactions resulting from hybridization between primers, while limiting the complexity of the simulation.

[0794] In the example in Figure 7, the coefficients of the denaturation tensor can be defined for each denaturation reaction of the extended double chain in a table constructed using the same principle as the table for the unextended double chain.

[0795] [Table 2]

[0796] The following can be observed here. - Extended virtual double helix

[0797]

number

[0798] and

[0799]

number

[0800] The existence of coefficients corresponding to multiple hybridization reactions. - Extended virtual partial double helix

[0801]

number

[0802] The existence of coefficients corresponding to hybridization between primors.

[0803] In this example, the coefficients associated with the two pairs of multiple hybridization reactions were both set to 0.8 and 0.2.

[0804] Thus, this makes it possible to construct the following denatured tensor of the extended double helix.

[0805]

number

[0806] This tensor form allows the concentration of the extended double hemisphere to be distributed to single-stranded nucleic acid molecules through simple algebraic operations.

[0807] Furthermore, by verifying that the sum of the values ​​in each row is equal to 2, it is possible to verify that the variance is well controlled.

[0808] Next, Figure 8 is referred to.

[0809] Figure 8 shows an example of a process according to one embodiment of the present invention that incorporates verification or modification of PCR amplification parameters.

[0810] In one embodiment of the present invention, the characteristics of the PCR kit, such as the selection of multiple primers and the initial values ​​of the concentration vectors of the multiple primers in the first cycle of the reaction, can be confirmed or modified based on simulation results.

[0811] For example, process P8 includes the steps of process P4, plus the following: - Step S81 displays the simulation results. This display may include, for example, a curve showing the changes in molecular concentration, values ​​representing the reaction dynamics, etc. - Step S82: Comparison of a value representing the dynamics of the reaction with a threshold value. - If the comparison is positive, proceed to step S83 to confirm the primer and initial primer concentrations. - If not, step S84 to correct the primer and / or initial primer concentrations.

[0812] At the end of step S84, the simulation can be rerun based on the modified parameters.

[0813] Thus, this ensures that the primer parameters and primer concentration allow for the desired amplification to be achieved with sufficiently high dynamics, or conversely, allows for the modification of the primer parameters and primer concentration to satisfy this constraint.

[0814] Step S82, which compares a value representing the reaction dynamics with a threshold, allows, in particular, verification that a given amplified reaction becomes fast enough to be detected. For example, the threshold considered may be one of the following thresholds: - Threshold cycle (CT) - Crossing point (Cp) - Final concentration of nucleic acid molecules amplified by the reaction - Concentration of the amplicon at the end of the reaction

[0815] Therefore, step S82 may consist of verifying that the Ct or Cp of the amplification reaction of a given target exceeds a reference threshold (i.e., the threshold cycle Ct or crossing point Cp is too high, which means the amplification reaction is not fast enough), and the Ct or Cp of the amplification reaction of a given target exceeding a reference threshold means that the reaction is not fast enough.

[0816] This is a non-limiting example if process P8 includes a display step S81. In particular, the display may allow, for example, an expert user to review or not review the simulation parameters, while the comparison in step S82 may also be performed automatically without the preceding display.

[0817] The changes in step S84 can be implemented in various ways. For example, the changes may be made manually by an expert user. Alternatively, the changes may be made automatically based on the results of the simulation, or suggested to the expert user.

[0818] An example of the changes in step S84 is described below.

[0819] First, step S84 may include a substep S841 that identifies a target to be favored, depending on the results of the polymerase chain reaction simulation.

[0820] For example, a target that should be favored may be one whose dynamics are not fast enough. For instance, one or more of the comparisons considered in step S82 can be performed on each target, and targets for which the comparison is negative (e.g., targets where Ct or Cp exceeds a predefined threshold) can be considered targets that should be favored because their amplification dynamics are currently insufficient.

[0821] Step S84 may then include a second substep S842 for identifying single-stranded nucleic acid molecules that form a pair with a primer associated with the target from a binding matrix or dissociation matrix.

[0822] Therefore, substep S842 is to identify molecules other than the target that form a pair with the primer associated with the target, i.e., molecules that compete with the target (and the amplicons resulting from the amplification of the target) to pair with the primer. Such molecules are identified by the binding matrix K on or dissociation matrix K offThis can be used to identify molecules. In particular, these matrices contain coefficients for each pair of molecules bonded by a sufficiently strong hybridization reaction. For example, a molecule can therefore be identified as having a binding constant with a primer, or a binding constant greater than the threshold with a primer.

[0823] Step S84 may then include performing at least one modification of the polymerase chain reaction. The at least one modification of the polymerase chain reaction may include, in particular, at least one selected from the following: - Reduction of the initial concentration of the single-stranded nucleic acid molecule that forms a pair with the target-related primer in the initial concentration vector. - Changing the salt concentration - Change the hybridization temperature for at least one cycle.

[0824] These modifications, in particular, make it possible to discourage hybridization of the target-related primer with the primer of a single-stranded nucleic acid molecule that pairs with it, thereby promoting hybridization of the target (and the amplicon resulting from the amplification of the target) with the primer, and thus the amplification reaction of the target.

[0825] In this example, the example from steps S841 to S843 in Figure 8 is the join matrix K on or dissociation matrix K off While the simulation of an amplified reaction according to the present invention, based on the identification of competing reactions through analysis, demonstrates that it is possible not only to verify that the desired amplification is indeed performed but also to modify the amplification parameters to favor the desired reaction, this example is not limiting, and other processes for identifying limitations on the amplified reaction may be used in one set of embodiments of the present invention. More broadly, the present invention is not limited to specific processes for modifying simulation parameters.

[0826] Next, Figure 9 is referred to.

[0827] Figure 9 shows an example of a process according to one embodiment of the present invention that incorporates verification or modification of PCR amplification parameters and the production of a verified PCR amplification kit.

[0828] Process P9 is a manufacturing process that includes all the steps of Process P8.

[0829] Process P9 further includes, at the end of the confirmation in step S83, a step of producing a kit for characterizing microorganisms in the sample using polymerase chain reaction, i.e., a "PCR kit" such as kit K1 shown in Figure 1.

[0830] Therefore, the kit produced by process P9 includes primers and concentrations confirmed by process P8, i.e., its simulations have shown that the desired amplification can be performed with satisfactory dynamics.

[0831] Thus, process P9 is verified by simulation and makes it possible to manufacture a kit that enables satisfactory amplification of the desired target.

[0832] Next, Figure 10 is referred to.

[0833] Figure 10 shows an example of process P10 for characterizing microorganisms using a PCR amplification kit manufactured according to one embodiment of the present invention.

[0834] Process P10 includes a first step S101 of preparing a sample for PCR to be performed on the prepared sample, the preparation including the step of adding a kit (K1) manufactured according to a process such as process P9.

[0835] The sample may have been taken from a human, animal, or inanimate object.

[0836] Then, process P10 includes step S102, in which PCR is performed on the collected sample. At the end of this step, the nucleic acid sequence of interest has been amplified by PCR and is present in sufficient quantity to be characterized.

[0837] Therefore, process P10 includes a third step S103 in which the microorganisms are characterized according to the PCR results.

[0838] The antimicrobial agent is selected based on its characteristics and can be administered to a human or animal if the sample is taken from a living organism, or applied to an inanimate object if the sample is taken from an inanimate object.

[0839] Thus, process P10 allows PCR to be performed on the sample to characterize the microorganisms contained in the sample and, if necessary, to select an antimicrobial agent suitable for these microorganisms.

[0840] Since the kit has been confirmed by simulation to enable amplification of nucleic acid sequences characteristic of this microorganism, the P10 method allows for amplification and, consequently, efficient characterization of a given microorganism.

[0841] Next, Figure 11 is referred to.

[0842] Figure 11 shows graph Gr11, which represents the change in Ct during a simulation of nucleic acid amplification from the fungal yeast (S. cerevisiae) using the simulation process of the present invention, as a function of the duration of the hybridization phase.

[0843] More precisely, the graph represents the following: - The x-axis represents the duration of the hybridization phase, expressed in seconds. hybr - The y-axis corresponds to the maximum time the hybridization phase was examined (10 seconds in this case). t And, C for a given shorter duration of the hybridization phaset the difference ΔC between t

[0844] Simulations were performed for three primer concentrations, and the concentration of nucleic acid from fungal yeast was kept constant. - Curve Crv110 represents the simulated evolution of ΔC with respect to a concentration of 0.4 μM as a function of t t hybr - Curve Crv111 represents the simulated evolution of ΔC with respect to a concentration of 0.8 μM as a function of t t hybr - Curve Crv112 represents the simulated evolution of ΔC with respect to a concentration of 2 μM as a function of t t hybr

[0845] In the actual case, to measure the value of ΔC t and compare it with the simulation, physical experiments corresponding to these concentrations were carried out for a specific duration of the hybridization phase.

[0846] The actual measured values are - Represented by measured values Mes1101, Mes1102, Mes1103, and Mes1104 for a concentration of 0.4 μM. - Represented by measured values Mes1111, Mes1112, Mes1113, Mes1114, Mes1115, and Mes1116 for a concentration of 0.8 μM. - Represented by measured values Mes1121, Mes1122, Mes1123, Mes1124, and Mes1125 for a concentration of 2 μM.

[0847] In Figure 11, it can be seen that - The simulation provides a precise result very close to the actual measurement. - When the duration of the hybridization phase increases, Ct decreases rapidly and then decreases more slowly, (ΔC t ​​​​​​It approaches the minimum value (represented by = 0). - Hybridization time t when Ct approaches its minimum value hybr The point of inflection is higher when the concentration is low.

[0848] Thus, the simulation enables an accurate and reliable assessment of Ct. Therefore, it can be seen that the performed simulation allows for the optimization of the duration of the hybridization phase to reach the target Ct value.

[0849] Next, Figure 12 is referred to.

[0850] Figure 12 shows an example of visualizing the dynamics of several PCR reactions under two different experimental conditions according to one embodiment of the present invention.

[0851] In the example shown in Figure 12, two simulations according to the present invention were performed to reproduce the following: - Amplification of the target in a first multiplex amplification using a first set of primers. This first simulation is represented by the "OPA" point. - Amplification of the target in the second multiplex amplification by modifying the first set of primers. This second simulation is represented by the point "OPB".

[0852] In this case, the simulation was run after it was found that, in the real-world amplification example, the amplification Ct increased by approximately 5.5 cycles after the modification of the first set of primers. Therefore, two simulations were performed: one corresponding to the first set of primers and another corresponding to the modification of the set.

[0853] The results of these two simulations are shown in graph Gr12 below. - The x-axis will represent the cycle index. - The y-axis represents the concentration of the amplicon resulting from the amplification of the target.

[0854] Therefore, the points labeled "OPA" and "OPB" represent the last simulated amplicon concentrations in each cycle when the first set of primers and the modified set of primers are used, respectively.

[0855] The simulation shows a difference in Ct ΔC over approximately 5.5 cycles. t It should be noted that it should also be possible to detect [the following].

[0856] These results demonstrate the ability of the PCR amplification simulation according to the present invention to reliably simulate the function of multiplex amplification. Therefore, analysis of the simulation results optimizes the selection of amplification parameters, such as primer, primer concentration, or phase duration, to confirm the ability of a PCR amplification kit constructed according to the simulated parameters to produce satisfactory amplification of a given target.

[0857] This disclosure is not limited to the examples of processes, computer programs, or polymerase chain reaction kits presented above for purely illustrative purposes, but rather includes all variations that can be envisioned by those skilled in the art in the context of the protection sought.

[0858] The present invention makes it possible to determine whether the initial selection of primers and their concentrations leads to the appropriate amplification of target nucleic acid molecules. In such cases, the design of a kit containing the primers and their concentrations is confirmed, and the kit can be put into production for sale.

[0859] The present invention also enables the adoption of a systematic approach to the design of PCR amplification kits. In particular, a grid of initial parameters is determined, starting from a pre-identified list of possible primers and the possible concentration ranges of those primers. For example, for each set of candidate primers for a kit, its concentration range is discretized in predetermined increments. The initial parameters are then this set of primers with concentration values ​​at the given intervals. Simulations are performed for each parameter, and once the entire grid has been examined, the parameters that yield the best performance are retained, and one or more corresponding kits are manufactured.

[0860] The present invention allows for the examination of primer sets in the context of multiplex PCR, and in this case, also enables the examination and comparison of alternative designs to achieve the expected performance.

[0861] The manufactured kit is then used in a known manner. In the context of clinical applications, for example, the detection of pathogenic microorganisms in biological specimens taken from patients (or animals), the clinician (or veterinarian, respectively) can then adapt their treatment, for example, by selecting an antibiotic appropriate for the detected pathogen.

[0862] In a preferred manner, the parameter ΔG, or similarly,

[0863]

number

[0864] and

[0865]

number

[0866] This can be obtained by state-of-the-art methods, such as the “nearest neighbors” method disclosed by Santalucia Jr., J. (1998), A unified view of polymer, dumbbell and oligonucleotide DNA nearest-neighbor thermodynamics, Proceedings of the National Academy of Sciences, 95(4), 1460-1465.

[0867] The PCR amplification simulation is performed by a computer, that is, by hardware circuitry including computer memory (cache, RAM, ROM, etc.) and one or more microprocessors or processors, organized or not organized in the form of computing nodes, which are necessary to execute computer instructions stored in memory in order to perform the simulation. [Explanation of Symbols]

[0868] K1 Kit Tst1 Inspection, Inspection Equipment Swab1 Cotton swab Cyc21, Cyc22, Cyc23...Cyc2n cycle PCR2 reaction Targ2 target PolyM2 polymerase AM2, AM21, AM22 Primer Denat21 Degeneration Phase Nuc21, Nuc22 single-stranded nucleic acid Hybr21 Hybridization Phase Amp21, Amp22 Amplifier Elongation Phase Elong21 Graph3 graph Cyc31, Cyc32 cycle Hybr31 Hybridization Phase and Extension Phase Thybr Duration Denat31 Degeneration Phase P4 process S41 Hybridization Phase S411 Substep S412 Substep S413 Substep S414 Substep S42 Extension Phase S421 Step S43 Degeneration Phase S431 Step S432 Step ncyc cycle index NCyc Predefined number of cycles Npdt time step count npdt time step index React71 response React72 Reaction React73 Reaction React74 Reaction React75 response React76 Reaction React77 Reaction React78 Reaction React79 response React710 response React711 response React712 Reaction React713 Reaction React714 Reaction React715 response P8 process S81 Step S82 Step S83 Step S84 Step S841 Substep, Step S842 Substep, Step S843 Step P9 process P10 Process S101 Step S102 Step S103 Step Gr11 Graph t hybr Duration of the hybridization phase ΔC t Difference in Ct Crv110 curve Crv111 curve Crv112 curve Mes1101, Mes1102, Mes1103, Mes1104, Mes1111, Mes1112, Mes1113, Mes1114, Mes1115, Mes1116, Mes1121, Mes1122, Mes1123, Mes1124, Mes1125 Measured values Gr12 graph

Claims

1. A process (P4) for numerical simulation of a polymerase chain reaction of at least one target, comprising simulating multiple consecutive amplification cycles, each cycle being: - Hybridization phase (S41) between at least one target and multiple primers, - Extension phase (S42), - Next, the denaturation phase (S43) The hybridization phase includes a series of steps, and the hybridization phase is performed with respect to each cycle. - A vector of concentrations of multiple single-stranded nucleic acid molecules, including the at least one target and the multiple primers. [Math 1] Initial value of the cycle [Math 2] To obtain (S411), - A matrix of double-strand concentrations formed by the hybridization of the plurality of single-stranded nucleic acid molecules. [Math 3] Initialization (S412), - Calculation (S413) of the changes in the concentration matrix during the hybridization phase in consecutive time steps by applying a matrix differential equation that expresses the dynamics of the formation of the double helix as a function of the concentrations of the plurality of nucleic acid molecules to the concentration matrix, wherein the matrix differential equation is parameterized by at least one binding matrix containing binding constants related to each double helix and a dissociation matrix containing dissociation constants related to each double helix. Process (P4), including [this].

2. The aforementioned differential equation is, [Math 4] A mass conservation equation of the form, where, - t * However, this represents the time elapsed since the start of the hybridization phase. - Notation T i and T j However, the vectors of concentrations of multiple nucleic acid molecules, respectively [Math 5] This represents the concentrations of two single-stranded nucleic acid molecules at indices i and j. - Notation H xy However, the vector of concentrations of multiple nucleic acid molecules [Math 6] This represents the concentration of the double hemisphere formed by the hybridization of the single-stranded nucleic acid molecule pair at indices x and y. - Notation T i0 and T j0 are the T * at t i = 0 and T j represent the values of The numerical simulation process according to claim 1, which incorporates the equation of conservation of mass, or any other mathematically equivalent formulation of the equation of conservation of mass.

3. The aforementioned matrix differential equation is of the following form, namely, [Number 7] It is in the form of, and in the formula, - H is the concentration matrix of the double chain, - T 0 However, the initial value of the cycle of the concentration vectors of the plurality of molecules, - K on However, the above-mentioned combination matrix is - K off However, the above dissociation matrix is, - Operator [Number 8] However, this represents a two-dimensional matrix with i rows and j columns where all elements are equal to 1. - The operator "diag()" takes a square matrix as a parameter and extracts a vector from the square matrix whose dimension is the number of rows or columns of the square matrix and which contains all the elements on the diagonals of the square matrix. The numerical simulation process according to claim 2.

4. Each bond matrix or each dissociation matrix contains elements, and each bond matrix element or each dissociation matrix element relating to a pair of molecules belonging to the plurality of molecules, - If the variation in free enthalpy (ΔG) related to the hybridization reaction of the molecules forming the pair exceeds the threshold, then it is zero. - Otherwise, they are equal to the bonding or dissociation constant of the hybridization reaction of the pair of molecules, respectively. The process according to any one of claims 1 to 3.

5. The process according to claim 4, wherein the threshold value is selected from at least two predefined threshold values, the lowest threshold value being reserved for a pair of molecules comprising a paired amplicon and a primer.

6. A preliminary step of defining the aforementioned plurality of molecules, - Initialization of the plurality of single-stranded nucleic acid molecules as the molecules initially present in the polymerase chain reaction, - Initial simulations of multiple cycles of the polymerase chain reaction, wherein each cycle of the initial simulation is - To obtain a hybridization reaction of molecules that form each pair of molecules among the plurality of molecules having affinity below a threshold, - Simulation of the hybridization phase including the aforementioned hybridization reaction, - Simulation of the extension phase, - Simulation of the degeneration phase, - Addition of additional molecules obtained at the end of the hybridization phase, the extension phase, and the denaturation phase to the plurality of molecules Initial simulation, including The process according to any one of claims 1 to 5, including a preliminary step.

7. The process according to claim 6, wherein the preliminary step of defining the plurality of molecules includes performing the initial simulation cycles between 3 and 7.

8. The process according to any one of claims 1 to 7, further comprising a subsequent step of displaying the temporal progression of the concentration of at least one of the molecules at the end of the simulation of the plurality of cycles (S81).

9. The process (P8) according to any one of claims 1 to 8, further comprising the subsequent step of confirming (S83) or correcting (S84) the initial values ​​of the plurality of primers and the concentration vectors of the plurality of primers in the first cycle of the reaction by comparing a value representing the dynamics of the reaction with a threshold (S82).

10. The value representing the aforementioned dynamics is, - Threshold cycle (Ct), - Crossing point (Cp), - Final concentration of nucleic acid molecules amplified by the above reaction, - Concentration of the amplicon at the end of the above reaction The process according to claim 9, wherein the value is selected from the following.

11. Modifying the aforementioned multiple primers - Identification of targets to be favored, based on the results of the polymerase chain reaction simulation. - Identification of a single-stranded nucleic acid molecule that forms a pair with a primer related to the target, from the binding matrix or the dissociation matrix, - The following is, in other words, - Reduction of the initial concentration of the single-stranded nucleic acid molecule that forms a pair with the primer related to the target in the initial concentration vector, - Change the salt concentration, - Change the hybridization temperature for at least one cycle, - Change the hybridization time for at least one cycle. Application of at least one modification of the polymerase chain reaction selected from The process according to claim 9 or 10, including the process described in claim 9 or 10.

12. A process (P9) for producing a kit (S91) for characterizing microorganisms contained in a sample using a polymerase chain reaction, wherein the kit comprises a plurality of identified primers, and in the process, the plurality of primers and the concentration vectors of the plurality of primers are obtained by a simulation process according to any one of claims 9 to 11.

13. A kit (K1) for polymerase chain reaction, manufactured by the process described in claim 12.

14. A computer program comprising instructions for performing a process according to any one of claims 1 to 11 when the program is executed by a processor.

15. A non-temporary computer-readable recording medium on which a program for performing the process described in any one of claims 1 to 11 is recorded when the program is executed by a processor.

16. A process (P10) for characterizing microorganisms contained in a sample, - Preparation of the sample (S101) for performing PCR on the prepared sample, comprising the step of adding a kit (K1) manufactured according to the process described in claim 12, - PCR is performed on the prepared sample (S102), - Characterization of the microorganism based on PCR results (S103) Process (P10), including the above.

17. The process according to claim 16, wherein the sample is collected from an animal or a human, and the process includes selecting an antimicrobial agent based on the characterization of the microorganisms present in the sample, and administering the antimicrobial agent to the animal or the human.

18. The process according to claim 16, wherein the sample is collected from an inanimate object, and the process includes selecting an antimicrobial agent based on the characterization of the microorganisms present in the sample, and administering the antimicrobial agent to the inanimate object.

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