Manufacture of polymerase chain amplification kits optimizing an amplification denaturation phase

Abstract

Disclosed is a method for digitally simulating a polymerase chain amplification of at least one target, comprising the simulation of a plurality of successive cycles of the amplification, each cycle comprising, sequentially: a hybridization phase; an elongation phase; then a denaturation phase; wherein, for each cycle: the hybridization phase comprises: obtaining, for the cycle, an initial value of a vector of concentrations of a plurality of nucleic acid molecules in the form of single strands; calculating a matrix of concentrations of partial duplexes formed by the hybridization of the plurality of nucleic acid molecules in the form of single strands; the denaturation phase comprises: multiplying a vector of the concentration of elongated duplexes resulting from the application of the elongation phase to the concentrations of duplexes, by an elongated duplex denaturation tensor.

Description

Description Title: MANUFACTURE OF POLYMERASE CHAIN ​​REACTION KITS OPTIMIZING A DENATURATION PHASE OF AMPLIFICATION Technical field

[0001] The present disclosure relates to the field of polymerase chain reaction. More specifically, the present disclosure relates to the field of simulation and manufacturing of polymerase chain reaction kits. Prior Art

[0002] A polymerase chain reaction (also called a polymerase chain reaction, and abbreviated as "PCR") is a reaction that allows the multiplication of nucleic acid molecules (e.g., DNA or RNA). In each reaction cycle, each nucleic acid molecule is duplicated. PCR amplification therefore allows nucleic acid molecules to multiply exponentially, with the concentration of nucleic acid doubling with each reaction cycle.

[0003] This allows PCR amplification to achieve, from even very small quantities of nucleic acids, relatively high concentrations, allowing their detection. Thus, PCR amplification is used in many biomedical applications, including the detection and characterization of pathogens, because it allows tiny quantities of nucleic acids representative of a pathogen to be transformed into detectable quantities.

[0004] A PCR amplification is called "singleplex" when it aims to amplify a single nucleic acid, or "multiplex" when it aims to amplify a plurality of different nucleic acids simultaneously. The molecules to be amplified can be called "targets" and the amplified molecules "amplicons", it being understood that an amplicon can itself be amplified at one or more subsequent cycles.

[0005] PCR amplification is usually performed in a PCR kit that uses different temperatures to trigger successive steps in the amplification cycles. The PCR kit initially contains primers to initiate amplification.

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

[0007] Generally speaking, when designing a PCR kit, the designer carries out the following steps: a) identifies for each microorganism a list of specific potential targets (i.e. not shared with other microorganisms); b) chooses, based on experience, potential primers from a list of possible primers; c) carries out tests under real conditions; d) repeats the process if the PCR performance is not satisfactory.

[0008] This methodology becomes even more difficult when multiple targets are targeted. Designing a kit is therefore long and complex and relies on the specific professional expertise of each designer.

[0009] Anticipation of reactions on paper is also impossible, because the designer is very quickly overwhelmed by the number of reactions, so it is impossible for the human mind to simulate on paper what will actually happen during PCR.

[0010] For example, it is impossible to solve a priori a system of differential equations representing the hybridization phase, taking into account the fact that hybridization between the different molecules may have occurred in different places. State-of-the-art methods also do not allow numerical simulations of such a system to be carried out in a reasonable time, due to the presence of numerous differential equations linked to each other. This considerably reduces the possibilities for designing and therefore improving PCR kits.

[0011] There is therefore a need for a method for designing PCR kits that can predict the course of denaturation phases, including in the case of multiple hybridizations, in order to facilitate the selection of parameters facilitating the amplification of one or more targeted targets. Summary

[0012] This disclosure improves the situation.

[0013] A method for numerical simulation of a polymerase chain reaction of at least one target is provided, said method comprising the simulation of a plurality of successive cycles of the amplification, each cycle comprising, sequentially: a hybridization phase between the at least one target and a plurality of primers; an elongation phase; then a denaturation phase; wherein the hybridization phase comprises for each cycle: obtaining an initial value for the cycle of a vector of concentrations of a plurality of nucleic acid molecules in the form of single strands comprising the at least one target and the plurality of primers; initializing a matrix of concentrations of duplexes formed by the hybridization of the plurality of nucleic acid molecules in the form of single strands;calculating, by successive time steps, the evolution of said concentration matrix during the hybridization phase, by applying to the concentration matrix a matrix differential equation representing the kinetics of formation of said duplexes as a function of the concentrations of the plurality of nucleic acid molecules, said matrix differential equation being parameterized by at least one association matrix comprising the association constants associated with each duplex and a dissociation matrix comprising the dissociation constants associated with each duplex.;

[0014] The term "at least one target" means at least one nucleic acid of a sequence to be amplified. According to different embodiments of the invention, the amplification may concern a single target, in which case the amplification is called "singleplex", or a plurality of targets, in which case the amplification is called "multiplex".

[0015] A "single-stranded nucleic acid molecule" means a single-stranded nucleic acid molecule unpaired with a complementary single-stranded molecule.

[0016] Association constant (also called association rate constant), usually denoted kon, is a rate constant representing the speed of the association reaction of two nucleic acid molecules in the form of single strands into a duplex.

[0017] The term "dissociation constant" (also called "dissociation rate constant" or "dissociation rate constant"), generally denoted koff, is a rate constant representing the speed of the dissociation reaction of a duplex into two single-stranded nucleic acid molecules.

[0018] This makes it possible to simulate all the hybridization phases (i.e. the equilibrium between association and dissociation reactions) occurring between the targets, the amplicons and the primers. The entire dynamics of a polymerase chain reaction can therefore be modeled, integrating cross-reactions with the intermediate products.

[0019] This specific modeling of a polymerase chain reaction thus makes it possible to validate the design of a polymerase chain reaction device, or on the contrary to identify undesirable reactions and to modify accordingly the parameters influencing the amplification reaction (initial concentration of primers, salts, duration and temperature of the phases, etc.).

[0020] Furthermore, the simulation of the hybridization phase according to a single matrix differential equation allows a resolution of the kinetics of the system using conventional computing capabilities.

[0021] According to another aspect, there is provided a method of manufacturing a kit for the characterization of microorganisms included in a sample by using a polymerase chain reaction, said kit comprising a plurality of validated primers, in which method the plurality of primers and the vector of concentrations for said plurality of primers are obtained by a simulation method according to one of the embodiments of the invention.

[0022] This allows the manufacture of a device reproducing the reaction as simulated. The device thus produced will therefore allow the multiplication of targets as previously simulated.

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

[0024] According to another aspect, there is provided a computer program comprising instructions for implementing all or part of a method as defined herein when this program is executed by a processor.

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

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

[0027] The features set out in the following paragraphs may, optionally, be implemented, independently of each other or in combination with each other:

[0028] Advantageously, in which the differential equation incorporates mass conservation equations of the form: In which: ^^ ∗represents the time elapsed since the start of the hybridization phase; the notations ^^ ^^ and ^^ ^^ denote respectively the concentrations of two nucleic acid molecules in the form of single strands of indices i and j in the vector ^̅^ of concentrations of a plurality of nucleic acid molecules; the notation ^^ ^^ ^^ denotes the concentration of a duplex formed by the hybridization of the pair of nucleic acid molecules in the form of single strands of indices x and y in the vector ^̅^ of concentrations of a plurality of nucleic acid molecules; the notations ^^ ^^0 and ^^ ^^0 denote the values ​​of ^^ ^^ and ^^ ^^ to ^^ ∗ = 0 ; or any other mathematically equivalent formulation.

[0029] This allows for a more accurate simulation of the hybridization phase, as mass conservation is taken into account.

[0030] Advantageously, which matrix differential equation is of the following form: in which: H is the concentration matrix of the duplexes; T0 is the initial value for the cycle of the concentration vector of the plurality of molecules; Kon is the association matrix; Koff is the dissociation matrix; the operator ^^ ^^, ^^ represents a two-dimensional matrix comprising i rows and j columns whose elements are all equal to 1; the operator "diag()" denotes a operator taking a square matrix as a parameter and extracting from this square matrix a vector having the dimension of the number of rows or columns of the square matrix and containing all the elements of the diagonal of the square matrix.

[0031] For example, the ^^ operator 1, ^^ represents a horizontal vector of dimension N comprising only 1s, and the operator ^^ ^^,1represents a vertical vector of dimension N comprising only 1s.

[0032] For example, the operator diag(H) transforms a square matrix H of dimension NxN into a vector of dimension N comprising all the elements of the diagonal of N, in order. For example, if ^^ =

[0456] , then ^^ ^^ ^^ ^^( ^^) =

[0005] , 7 8 9 9

[0033] This allows the differential equations for all hybridization reactions to be integrated into a single matrix equation, with replacing T with T0 in the equation allowing for faster matrix calculations.

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

[0035] This allows only the dominant hybridization reactions to be taken into account in the simulation. This allows both to obtain better precision in the kinetics of the hybridization reactions taken into account, and to reduce the complexity of solving the differential equation. This also allows to take into account the differential dynamics between the different reactions depending on whether the free enthalpy value is favorable or unfavorable between two reactions of interest.

[0036] Advantageously, the value of said threshold is chosen from at least two predefined threshold values, the lowest threshold value being reserved for pairs of molecules comprising a matched amplicon and primer.

[0037] Since the thresholds and free energy variation are negative, the higher threshold value corresponds to a lower threshold value. Hybridization reactions between primers and amplicons will therefore be preferentially taken into account. By "lower threshold value" we mean a value closer to zero. Since the thresholds and free energy variation are negative, this also corresponds to a lower absolute threshold value.

[0038] This allows hybridizations between primers and amplicons to be taken into account preferentially in the simulation, compared to hybridization reactions between primers and other primers for example, which allows the simulation of the first cycles of amplicon-primer hybridization, during which the concentration of amplicons is much lower than that of the primers.

[0039] Advantageously, the method comprises a prior step of defining the plurality of molecules comprising: an initialization of the plurality of nucleic acid molecules in the form of single strands as being the molecules initially present in the polymerase chain reaction; an initial simulation of a plurality of cycles of the polymerase chain reaction, each cycle of the initial simulation comprising: obtaining the hybridization reactions of the molecules forming each pair of molecules among said plurality of molecules having an affinity lower than a threshold; a simulation of a hybridization phase implementing said hybridization reactions; a simulation of an elongation phase; a simulation of a denaturation phase; an addition to said plurality of molecules of the additional molecules obtained at the end of the hybridization, elongation and denaturation phases.

[0040] "Additional molecules" are molecules that were not present at the beginning of a cycle, and which are generated at the end of the hybridization, elongation and denaturation cycle.

[0041] This allows the construction of a concentration vector, and association and dissociation matrices, taking into account only the molecules that will actually be encountered with significant affinities during the polymerase chain reaction. This therefore allows for a more reliable and less resource-intensive simulation of the PCR amplification reaction(s).

[0042] Advantageously, the preliminary step of defining the plurality of molecules comprises the execution of a number of cycles of the initial simulation between 3 and 7.

[0043] This provides a good compromise between the number of molecules added and their importance. For example, molecules added after the 3 e , 5 e or 7e cycle can be considered as not likely to give rise to significant reactions. A predefined number of cycles between 3 and 7, and for example equal to 5, therefore makes it possible to limit the number of molecules for the simulation, and reduce the associated computational complexity, while preserving the reliability of the simulation.

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

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

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

[0047] This makes it possible to validate that the primers initially present, and associated concentrations, allow the multiplication of the desired targets with sufficiently strong reaction kinetics, and to avoid the generation of unwanted reactions with strong kinetics or, on the contrary, to modify the list of primers and / or their concentrations.

[0048] Advantageously, the value representative of the kinetics is a value chosen from: a threshold cycle; a crossover point; a final concentration of a nucleic acid molecule amplified by the reaction; a concentration of amplicons at the end of the reaction

[0049] A "cycle threshold" (also known as "cycle of quantification" or "Ct") is the number of cycles required for an amplicon concentration to reach a reference concentration. For example, the threshold may correspond to a concentration at which the molecule is detectable.

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

[0051] The term "end-of-reaction amplicon concentration" 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, using linear regression on an affine line.

[0052] Advantageously, the modification of the plurality of primers comprises: identifying a target to be favored based on the results of the polymerase chain reaction simulation; identifying, from the association matrix or the dissociation matrix, a single-stranded nucleic acid molecule forming a pair with a primer associated with said target; carrying out at least one modification of the polymerase chain reaction chosen from: a decrease, in the initial concentration vector, of the initial concentration of said single-stranded nucleic acid molecule forming a pair with the primer associated with said target; a modification of the salt concentration; a modification of the hybridization temperature for at least one cycle; a modification of the hybridization duration for at least one cycle.

[0053] This makes it possible to identify the reactions between the molecules present during the PCR reaction which compete with the amplification of a given target, and to reduce the initial concentration of the molecule(s) which generate these reactions, or to modify the sequence of the molecule(s) in question accordingly in order to promote the amplification of the given target.

[0054] Advantageously, the sample is taken from an animal or a human being, said method comprising the choice of an antimicrobial based on the characterization of the microorganisms present in said sample, and the administration of said antimicrobial to said animal or human being.

[0055] Advantageously, the sample is taken from an inanimate object, said method comprising the choice of an antimicrobial based on the characterization of the microorganisms present in said sample, and the application of said antimicrobial to said inanimate object.

[0056] A method for numerical simulation of a polymerase chain reaction of at least one target is provided, said method comprising the simulation of a plurality of successive cycles of the amplification, each cycle comprising, sequentially: a hybridization phase between the at least one target and a plurality of primers; an elongation phase; then a denaturation phase; wherein, for each cycle: the hybridization phase comprises: obtaining an initial value for the cycle of a vector of concentrations of a plurality of single-stranded nucleic acid molecules comprising the at least one target and the plurality of primers; calculating a matrix of concentrations of partial duplexes formed by hybridization of the plurality of single-stranded nucleic acid molecules, each element of said matrix representing the concentration of the duplexes formed by hybridization of a pair of said plurality of single-stranded nucleic acid molecules, independently of the hybridization position of said pair;the denaturation phase comprises: multiplying an elongated duplex concentration vector, resulting from the application of the elongation phase to the duplex concentrations, by an elongated duplex denaturation tensor in order to obtain an initial value of a vector of concentrations of a plurality of nucleic acid molecules in the form of single strands for the following cycle.;

[0057] Using a single concentration value for all duplexes between a pair of nucleic acid molecules regardless of the pairing position reduces the number of equations to be solved for calculating denaturation, and makes the problem of simulating denaturation soluble.

[0058] According to another aspect, there is provided a method of manufacturing a kit for the characterization of microorganisms included in a sample by using a polymerase chain reaction, said kit comprising a plurality of validated primers, wherein the plurality of primers and the vector of concentrations for said plurality of primers are obtained by a simulation method as defined herein.

[0059] This allows the manufacture of a device reproducing the reaction as simulated. The device thus produced will therefore allow the multiplication of targets as previously simulated.

[0060] According to another aspect, there is provided a kit for polymerase chain reaction made by a method as defined herein.

[0061] According to another aspect, there is provided a computer program comprising instructions for implementing all or part of a method as defined herein when this program is executed by a processor.

[0062] According to another aspect, there is provided a non-transitory, computer-readable recording medium on which such a program is recorded.

[0063] According to another aspect, there is provided a method for characterizing microorganisms included in a sample, comprising: preparing the sample so as to carry out a PCR on the prepared sample, said preparation comprising a step of adding a kit manufactured in accordance with a method as defined herein; carrying out the PCR on the prepared sample; characterizing the microorganisms according to the results of the PCR.

[0064] The features set out in the following paragraphs may, optionally, be implemented, independently of each other or in combination with each other:

[0065] Advantageously, at least one duplex results from the pairing between two primers; the elongation phase simulates the concentration of each duplex resulting from the pairing between two primers into a single concentration of elongated duplex resulting from the pairing between two primers; the coefficients of the denaturation tensor are defined so as to distribute each concentration of elongated duplex resulting from the pairing between two primers into nucleic acid molecules in the form of single strands corresponding to an elongation of the duplex resulting from the pairing between the two primers in both directions.

[0066] This simplifies the simulation of reactions resulting from the pairing between two primers, in order to further reduce the computational complexity of the simulation.

[0067] Advantageously, for each hybridization reaction between two primers: the concentrations of elongated duplexes comprise a concentration of an elongated virtual duplex equal to the sum of the concentrations of the elongated duplexes formed by the elongation in each of the two directions of the duplexes formed by the hybridization of the two primers; the coefficients of the denaturation tensor of the elongated duplexes corresponding to the distribution of the concentration of the elongated virtual duplex towards each of the two primers, and each of the two nucleic acids in the form of single strands resulting from the elongation in one of the two directions are all equal to 0.5.

[0068] This makes it possible to efficiently simulate reactions resulting from hybridizations between primers, while limiting the complexity of the simulation.

[0069] Advantageously, for each set of multiple hybridization reactions of a single-stranded nucleic acid by a primer in several locations respectively: the concentrations of duplexes and the concentrations of elongated duplexes respectively comprise a concentration of a virtual duplex equal to the sum of the concentrations of the duplexes formed by the multiple hybridization reactions, and a concentration of an elongated virtual duplex equal to the sum of the concentrations of the elongated duplexes formed by the elongation of the duplexes formed by the multiple hybridization reactions;the coefficients of the denaturation tensor of the elongated duplexes corresponding to the distribution of the concentration of the elongated virtual duplex towards each nucleic acid in the form of a single strand associated with one of the multiple hybridization reactions are respectively equal to the ratio between the interaction energy of the multiple hybridization reaction divided by the sum of the interaction energies of all the multiple hybridization reactions with said single-stranded nucleic acid.;

[0070] By "concentration of a virtual duplex" is meant a concentration of a duplex not corresponding to a real molecule, but to several duplexes resulting from the hybridization of the same primer on the same nucleic acid molecule in single-strand form in several distinct locations. The concentration of the virtual duplex is then equal to the sum of the concentrations of the real duplexes created by the hybridization reactions of the primer with the nucleic acid molecule in single-strand form in the different positions.

[0071] By "concentration of a virtual elongated duplex" is meant a concentration of an elongated duplex not corresponding to a real molecule, but to several elongated duplexes resulting hybridization of the same primer to the same nucleic acid molecule in single-strand form at several distinct locations, followed by elongation of the duplexes thus formed. The concentration of the elongated virtual duplex is then equal to the sum of the concentrations of the real elongated duplexes created by the hybridization reactions of the primer with the nucleic acid molecule in single-strand form at the different positions, followed by elongation of the duplexes thus formed.

[0072] The term "single-stranded nucleic acid associated with one of the multiple hybridization reactions" means the nucleic acid resulting from the denaturation of an elongated duplex itself resulting from the elongation of the duplex formed by one of the multiple hybridizations, i.e. a hybridization of the primer at a particular location.

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

[0074] This therefore makes it possible to considerably facilitate, or even make possible, calculations of the evolution of concentrations, while maintaining satisfactory precision in the simulation.

[0075] Advantageously, the elongation phase comprises: obtaining the concentrations of the elongated duplexes by multiplying the concentrations of the duplexes by elongation coefficients.

[0076] The term "elongation coefficient" refers to the fraction, between 0 and 1, of molecules of a given duplex that are elongated during an elongation phase.

[0077] This allows to take into account every possible difference in the elongation process of the different duplexes.

[0078] Advantageously, the elongation phase further comprises updating the duplex concentration vector, representing at the end of the elongation phase the concentration of the non-elongated duplexes; the denaturation phase further comprises multiplying said duplex concentration vector by a denaturation tensor of the non-elongated duplexes to update the initial value for the following cycle of the concentration vector of the plurality of nucleic acid molecules in the form of single strands.

[0079] This makes it possible to simulate the denaturation of duplexes that have not been elongated, and to integrate the concentrations of non-elongated and denatured duplexes into the initial conditions of the following cycle.

[0080] Tensor analysis also helps ensure that denaturation is under control.

[0081] Advantageously, during the denaturation phase, the same denaturation coefficient is applied to a non-elongated duplex and to the corresponding elongated duplex to update the vector of concentrations of the plurality of nucleic acid molecules in the form of single strands, and the concentrations of duplexes for the following cycle.

[0082] The term "denaturation coefficient" refers to the fraction, between 0 and 1, of molecules of a given duplex that are denatured during a denaturation phase.

[0083] This allows the denaturation phase to be simulated precisely.

[0084] Advantageously, the method comprises a subsequent step of validating or modifying the plurality of primers and the initial value of the concentration vector for said plurality of primers in the first cycle of the reaction by comparing a value representative of the kinetics of a reaction to a threshold.

[0085] This makes it possible to validate that the primers initially present, and associated concentrations, allow the multiplication of the desired targets with sufficiently strong reaction kinetics, and to avoid the generation of unwanted reactions with strong kinetics or, on the contrary, to modify the list of primers and / or their concentrations.

[0086] Advantageously, the sample is taken from an animal or a human being, said method comprising the choice of an antimicrobial based on the characterization of the microorganisms present in said sample, and the administration of said antimicrobial to said animal or human being.

[0087] Advantageously, the sample is taken from an inanimate object, said method comprising the choice of an antimicrobial based on the characterization of the microorganisms present in said sample, and the application of said antimicrobial to said inanimate object. Brief description of the drawings

[0088] Other features, details and advantages will become apparent upon reading the detailed description below, and upon analyzing the attached drawings, in which: Fig.1

[0089] [Fig. 1] shows examples of kits for polymerase chain reaction for the manufacture of which the invention can be implemented. Fig.2

[0090] [Fig.2] shows an example of a polymerase chain reaction that can be simulated according to a set of embodiments. Fig.3

[0091] [Fig.3] shows an example of temperature variation during a PCR amplification cycle Fig.4

[0092] [Fig.4] shows an example of a method according to a set of embodiments of the invention. Fig.5

[0093] [Fig. 5] shows an example of a hybridization phase in a set of embodiments of the invention. Fig.6

[0094] [Fig. 6] shows an example of a denaturation phase in a set of embodiments of the invention. Fig.7

[0095] [Fig.7] shows an example of hybridization, elongation and denaturation reactions over 3 successive cycles of PCR amplification in a set of embodiments of the invention. Fig.8

[0096] [Fig.8] shows an example of a method according to a set of embodiments of the invention integrating a validation or modification of the parameters of the PCR amplification. Fig.9

[0097] [Fig.9] shows an example of a method according to a set of embodiments of the invention integrating a validation or modification of the parameters of the PCR amplification, and a manufacture of a validated PCR amplification kit. Fig.10

[0098] [Fig.10] shows an example of a method for characterizing a microorganism using a PCR amplification kit manufactured according to a set of embodiments of the invention. Fig.11

[0099] [Fig.11] shows an example of visualization of the kinetics of several PCR reactions according to a set of embodiments of the invention. Fig.12

[0100] [Fig.12] shows an example of visualization of the kinetics of several PCR reactions under two distinct experimental conditions according to a set of embodiments of the invention. Description of the embodiments

[0101] Reference is now made to Figure 1.

[0102] Figure 1 represents an example of a K1 kit for polymerase chain reaction for the manufacture of which the invention can be implemented, for example a kit used for the FilmArray and Spotfire platforms manufactured and marketed by the Applicant. Such a kit is for example described in document US 8,394,608 or US 9932634 incorporated by reference.

[0103] The K1 kit is part of a Tst1 test kit intended to test for the presence of one or more microorganisms, for example by one or more viruses, bacteria, fungi and antibiotic resistance genes.

[0104] For this purpose, the Tst1 test equipment includes an Ecv1 swab for taking a nasal sample from a patient.

[0105] The sample can then be provided as input to the K1 kit in order to carry out a PCR amplification, in order to amplify one or more nucleic acids representative of the microorganism(s) whose presence is sought, for example as described in the aforementioned documents. Thus, even if the initial concentration of microorganisms in the sample taken is low, the quantity of nucleic acid at the output of the PCR amplification will be sufficient to detect their presence, and therefore for example the presence of the microorganism(s) in the sample taken.

[0106] As PCR amplification progresses, amplicons can generate increasingly greater fluorescence, for example through the integration of fluorophores by the formation of a double-stranded sequence, the number of double-stranded sequences integrating fluorophores increasing with amplification.

[0107] The Tst1 test kit therefore makes it possible to detect the presence of microorganisms, even if their concentration in the initial sample is very low.

[0108] The Tst1 test kit is provided by way of non-limiting example only, and the invention may be applied to different types of test kits, associated with different sampling means. For example, the sampling may be carried out on a human being, an animal or even an inanimate object, and may result in the characterization of one or more microorganisms. The characterization of one or more microorganisms may allow the choice of an antimicrobial, with a view to its administration to a human being or an animal, or its application to the inanimate object. Similarly, the invention applies to the step of PCR amplification of a targeted part of genomes before their complete sequencing, for example an amplification of the r16S portion in the context of microbial metagenomic identification.

[0109] Figure 2 shows an example of a polymerase chain reaction that can be simulated according to a set of embodiments.

[0110] The polymerase chain reaction (PCR) consists of several successive cycles Cyc21, Cyc22, Cyc23…Cyc2n. To improve the readability of the figure, only the first Cyc21 cycle will be detailed.

[0111] The PCR2 reaction is carried out in a PCR kit, for example in the K1 kit. The PCR kit initially contains: - nucleic acids of one or more sequences to be amplified, or "target", for example the Cib2 target shown in Figure 2. The nucleic acids of the sequences to be amplified can initially come from a sample, for example via the Ecv1 swab; - dNTP2 nucleotides; - PolyM2 polymerase; - AM2 primers.

[0112] The PCR reaction shown here is a so-called "singleplex" reaction aimed at amplifying a single Cib2 target. However, the invention is not restricted to this example, and may also apply to so-called “multiplex” reactions aimed at simultaneously amplifying several distinct targets.

[0113] Each PCR amplification cycle includes: - a denaturation phase, denoted Denat21 for the Cyc21 cycle, during which the double-stranded nucleic acids are separated into two single-stranded nucleic acids. In the example of the Cyc21 cycle, a Cib2 target is initially present in the form of a double-stranded nucleic acid. During the denaturation phase, it is separated into two single-stranded nucleic acids Nuc21 and Nuc22; - a hybridization phase, denoted Hybr21 for the Cyc21 cycle, during which primers hybridize to the single-stranded nucleic acids.In the example of the Hybr21 phase, the primers AM21 and AM22 respectively hybridize with the nucleic acids in the form of single strands Nuc21 and Nuc22; - an elongation phase, noted Elong21 for cycle 21, during which nucleotides complete the primers to form nucleic acids in the form of double strands identical to the initial target, called amplicons, Amp21 and Amp22 in the case of the Elong21 phase.

[0114] Thus, at the end of a PCR amplification cycle, a single Cib2 target has generated two identical amplicons Amp21 and Amp22, which can themselves be duplicated in the next cycle. At each amplification cycle, the amplicons are thus duplicated: a single Cib2 target results in the generation of two amplicons at the end of the 1 e Cyc21 cycle, four amplicons at the end of the 2 e Cyc22 cycle, eight amplicons at the end of the 3 e Cyc23 cycle, etc.

[0115] It should be noted that the amplification shown in Figure 2 is provided as a non-limiting example only of an amplification that can be simulated by the invention.

[0116] Other amplifications can be simulated, such as multiplex amplification multiplying different types of targets. The application of the invention to a particular PCR has been described. The invention applies to a sequence of any number of PCRs, the input of a PCR consisting of the output of the previous PCR.

[0117] The order of the phases can also be different. For example, the simulation can start for each cycle with the hybridization phase rather than the denaturation phase. In this case, a cycle will be represented by a hybridization phase, followed by an elongation phase and finally a denaturation phase.

[0118] Reference is now made to Figure 3.

[0119] Figure 3 shows an example of temperature variation during a PCR amplification cycle.

[0120] The Grph3 graph more precisely represents the evolution of temperature as a function of time, for an example of two successive Cyc31 and Cyc32 PCR amplification cycles. Indeed, the different phases of PCR amplification are activated by temperature variations in the amplification kit. In this example, the temperature profile is identical between cycles, and will be detailed for cycle cyc31.

[0121] Generally speaking, the temperature evolves as follows during a PCR amplification cycle: - it is initially at a first temperature during the hybridization phase, simultaneous with the elongation phase; - then increases rapidly to reach a second, higher temperature, triggering the denaturation phase, before dropping back to the level of the first temperature for the hybridization phase of the following cycle.

[0122] In the example of the Cyc31 cycle: - the hybridization and elongation phases Hybr31 are activated by a first temperature of 60° for a duration Thybr; - the denaturation phase Denat31 is activated by a higher temperature, in this example, 96°.

[0123] The times and temperatures shown in Figure 3 are provided by way of non-limiting example only, and the invention is applicable to PCR amplifications carried out for very different times and temperatures. While in the example of Figure 3 the hybridization and elongation phases are simultaneous, in other PCR amplification reactions, three separate temperatures are used to trigger the hybridization, elongation and denaturation phases respectively. The temperatures and times of the different phases influence the amplification reaction.

[0124] The amplification reaction(s) are therefore impacted by numerous parameters such as: - the temperatures and duration of each phase of the reaction (which can be fixed or vary according to the cycles); - the choice and concentrations of primers; - the concentrations of monovalent and divalent salts; - the length of the expected amplicons; - etc.

[0125] These different factors can also promote unexpected reactions such as for example: - the formation of primer dimers, when two primers hybridize to each other; - multi-hybridization reactions when primers hybridize not only to one end of a nucleic acid in the form of single strands, but also to other locations, for example in the middle of a strand. In this case, the elongation will take place on only part of the strand, and will result in the creation of a new amplicon.

[0126] Amplification parameters can therefore facilitate, or on the contrary slow down a desired amplification, called a specific reaction, or even prevent the proper development of a reaction, when unwanted / unexpected reactions, called non-specific reactions, hinder it. One of the objectives of simulating a PCR amplification reaction is therefore to model as accurately as possible the amplification reaction according to the environmental parameters of the reaction, in order to validate, or on the contrary to modify the design of a kit (i.e. the values ​​of parameters used to favor a given amplification reaction – e.g. choice and concentration of primers, temperature and duration of reaction phases, concentration of salts, etc.).

[0127] However, the complexity of the kinetics of PCR amplification reactions, and in particular the interaction between numerous reaction products and by-products, makes such simulation difficult in practice. One of the objectives of the disclosure is therefore to provide a method for simulating a PCR amplification reaction that can be implemented in practice to simulate a PCR reaction according to given parameters, and validate or modify the reaction parameters accordingly.

[0128] Figure 4 shows an example of a method according to a set of embodiments of the invention.

[0129] The P4 method is a method for numerical simulation of a polymerase chain reaction of at least one target. According to different embodiments of the invention, it may be an amplification of a single target, or “singleplex” amplification, or an amplification of a plurality of targets, or “multiplex” amplification.

[0130] The simulation comprises a plurality of successive amplification cycles, each cycle successively comprising an S41 hybridization phase, an S42 elongation phase and a S43 denaturation phase.

[0131] The simulation can be performed for a limited number of cycles. For example, each cycle can be identified by a cycle index ncyc, incremented in a step S45 between each cycle.

[0132] At the end of each cycle, a stopping criterion can be checked. For example: - the simulation can be carried out for a predefined number of cycles NCyc. In this case, at the end of each cycle, the cycle index ncyc can be compared to the predefined number of cycles NCyc, and the criterion validated if ncyc >= NCyc (or on the contrary, a new cycle started if ncyc < NCyc); - the concentrations of the amplicons can be compared between two cycles, and the simulation stopped when a minimum number of cycles is reached, and the difference between the concentrations of the amplicons at the end of two successive cycles is lower than a threshold predefined. In other words, this criterion consists of detecting the cycle from which the reaction is considered to be finished; - the simulation can be stopped as soon as the concentration of a given amplicon is higher than a threshold, for example a detectability threshold of the amplicon; - etc.

[0133] Figure 4 shows an example where the stopping criterion is reaching a number of cycles NCyc. However, this example is provided as a non-limiting example only. As indicated above, one or more different criteria can be used to detect the end of the simulation.

[0134] In the following description, several simulation examples will be described, using certain notations introduced below.

[0135] The concentrations of the molecules of interest will be noted in a vector noted ^̅^ represented below: Equation 1

[0136] In the vector above, the elements ^^ ^^ ^^1, … ^^ ^^ ^^ ^^represent the concentrations of possible amplicons (specific and non-specific) produced during PCR amplification. It should be noted here that, since the targets and amplicons correspond to the same molecule, these values ​​correspond to the sum of the concentrations of the targets and amplicons for a given target. The elements ^^ ^^1, … ^^ ^^ ^^ represent the concentrations of the possible primers. The units of the vector elements can be mol.L -1 .

[0137] The plurality of molecules whose concentrations are noted in the vector ^̅^ can be obtained in different ways, and includes in particular the concentration of the amplicons, and of the plurality of primers present in the simulated kit.

[0138] For example, the plurality of molecules whose concentrations are noted in the vector ^̅^ can come from a list of molecules defined by an expert user.

[0139] However, it can be difficult to estimate a priori the set of molecules formed during a PCR reaction, given all possible reactions, for example between reaction by-products.

[0140] For this purpose, the plurality of molecules whose concentration is noted in the vector ^̅^ is determined by means of an initial simulation of a limited number of cycles. This initial simulation has the sole purpose of determining the molecules present in the amplification kit after the limited number of cycles, regardless of their concentration.

[0141] For this purpose, the plurality of molecules can be initialized like the molecules initially present in the polymerase chain reaction (in particular amplicons and primers), then the initial simulation can comprise the simulation of a plurality of successive cycles of the following steps: - obtaining the hybridization reactions of the molecules forming each pair of molecules among said plurality of molecules having an affinity lower than a threshold (or higher in absolute value, the affinities being negative values). In other words, this step consists of identifying, from the molecules initially present in the cycle of the initial simulation, the pairs of molecules having an affinity lower than a threshold (or higher in absolute value), that is to say the pairs of molecules which can be considered to react together; - simulation of a hybridization phase implementing said hybridization reactions.This initial simulation hybridization phase consists solely of identifying the duplexes formed by the identified hybridization reactions; - simulation of an elongation phase. This initial simulation hybridization phase consists solely of identifying the elongated duplexes obtained from the duplexes identified in the previous step; - simulation of a denaturation phase. This initial simulation of the denaturation phase consists of identifying the molecules obtained by the denaturation of the duplexes, and elongated duplexes, obtained in the two previous steps; - an addition to said plurality of molecules of the additional molecules obtained at the end of the hybridization, elongation and denaturation phases. This step consists of adding to the plurality of molecules the molecules which are obtained at the end of a cycle and which were not yet present therein.

[0142] Thus, at each cycle, new molecules resulting from the reactions of the previous cycle can be added to the plurality of molecules already identified, these new molecules being themselves likely to generate new reactions. Thus, it is possible after a limited number of initial simulation cycles to know all the molecules which could play a significant role in the simulation.

[0143] The number of cycles of the initial simulation can be defined in different ways. For example: - it can be a predefined number of cycles of initial simulation; - the number of molecules added at the end of each cycle can be counted, and the initial simulation can be stopped when the number of molecules added at the end of a given cycle is zero or low, for example if the number of molecules added is less than a given threshold. - Etc.

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

[0145] This provides a good compromise between the number of molecules added and their importance. For example, molecules added after the 3 e , 5 e or 7 e cycle can be considered as not likely to give rise to significant reactions. A predefined number of cycles between 3 and 7, and for example equal to 5, therefore makes it possible to limit the number of molecules for the simulation, and reduce the associated computational complexity, while preserving the reliability of the simulation.

[0146] Furthermore, a simulation over a limited number of cycles is sufficient, because molecules that only appear after a few cycles would not be likely to generate significant reactions, compared to reactions that have already started several cycles ago. Indeed, their very low concentration compared to the molecules already present with which they are in competition in the mixture does not allow them to multiply significantly.

[0147] This initial simulation therefore makes it possible to take into account only the molecules that will actually be encountered in significant numbers during the amplification reaction. This therefore allows for a simulation of the reaction that is both more reliable and less resource-intensive.

[0148] Reference is now made to Figure 5.

[0149] Figure 5 shows an example of a hybridization phase in a set of embodiments of the invention.

[0150] In the example of Figure 5, the hybridization phase S41 for a given cycle comprises a first sub-step S411 of obtaining an initial value ^̅^0 for the cycle of a vector of concentrations of a plurality of nucleic acid molecules in the form of single strands comprising the plurality of amplicons and the plurality of primers.

[0151] The vector of concentrations can for example be the vector ^̅^ mentioned above. The initial value ^̅^0 of the vector can for example correspond to: - the initial concentrations of the molecules before the start of the amplification reaction, if the simulated cycle is the first cycle; and 0 for the molecules appearing in the following cycles - the concentrations of the molecules at the end of the previous cycle, if the cycle is not the first cycle.

[0152] The simulation of the hybridization phase then aims to model the hybridization reactions taking place during the cycle. Hybridization is governed by the following equilibrium relationships between each pair of molecules ^^ ^^ and ^^ ^^ likely to hybridize: Equation 2

[0153] It should be noted here that such an equation must therefore be established taking into account for each possible hybridization reaction between a pair of molecules of indices i and j (i and j can be equal), depending on the molecules present in the vector ^̅^.

[0154] These equilibrium equations can be rewritten in the form of the following differential equations: Equation 3

[0155] In the equations above: - the notations ^^ ^^ and ^^ ^^denote respectively the concentrations of a pair of nucleic acid molecules in the form of single strands of indices i and j in the vector ^̅^ involved in a given hybridization reaction; - the notation ^^ ^^ ^^ denotes the concentration of a duplex formed by the hybridization of the pair of nucleic acid molecules in the form of single strands with indices i and j in the vector ^̅^; - the notations ^^^^ ^^ ^^ ^^ and ^^^^ ^^ ^^ ^^ denote respectively the association and dissociation constants of the hybridization reaction of the pair of nucleic acid molecules in the form of single strands with indices i and j in the vector ^̅^.

[0156] The differential equations noted above apply to every reaction between a pair of molecules of the vector ^̅^ which are considered to produce a hybridization reaction. The number of differential equations can therefore in some cases turn out to be very high.

[0157] These pairs of molecules which are considered to produce a hybridization reaction can, for example, be those whose hybridization reaction is associated with a variation in free enthalpy ΔG lower than a predefined threshold (or higher in absolute value, the variation in free enthalpy being negative).

[0158] Thus, only the dominant hybridization reactions will be taken into account in the simulation. This allows both to obtain a better precision of the kinetics of the hybridization reactions, and to reduce the complexity of solving the system of differential equations. This also allows to take into account the differential dynamics between the different reactions depending on whether the free enthalpy value is more or less favorable between two reactions of interest.

[0159] The predefined threshold can be the same for all reactions, or chosen from different thresholds depending on the case. For example, the threshold value can be chosen from at least two predefined threshold values, with the lower threshold value being reserved for pairs of molecules comprising a matched amplicon and primer.

[0160] In other words, the threshold of free enthalpy variation above which a hybridization reaction is not taken into account in the simulation is lower (closer to 0) for hybridization reactions between an amplicon and a primer than for the others (and therefore also lower in absolute value, the thresholds of free enthalpy variation being negative). This makes it possible to preferentially take into account in the simulation hybridizations between primers and amplicons on the one hand, and primers and other primers on the other hand, which makes it possible to simulate the first cycles of amplicon-primer hybridization, during which the concentration of amplicons is much lower than that of primers.

[0161] In one set of embodiments of the invention, the differential equations incorporate mass conservation equations of the following form: Equation 5

[0162] In which: - ^^ ∗ represents the time elapsed since the start of the hybridization phase; - the notations ^^ ^^ and ^^ ^^ respectively denote the concentrations of two nucleic acid molecules in the form of single strands with indices i and j in the vector ^̅^ of concentrations of a plurality of nucleic acid molecules; - the notation ^^ ^^ ^^ denotes the concentration of a duplex formed by the hybridization of the pair of nucleic acid molecules in the form of single strands with indices x and y in the vector ^̅^ of concentrations of a plurality of nucleic acid molecules; - the notations ^^ ^^0 and ^^ ^^0 denote the values ​​of ^^ ^^ and ^^ ^^ to ^^ ∗ = 0.

[0163] The above equations relate the concentrations of each single-stranded nucleic acid molecule to the concentrations of all duplexes to which they contribute via hybridization reactions, to demonstrate that a hybridization reaction does not change the total number of single strands of each type. Such a conservation of mass equation can be derived for each single-stranded nucleic acid molecule in the vector ^̅^.

[0164] It should be noted that the mass conservation equations noted above are provided by way of non-limiting example only. According to different embodiments of the invention, equivalent formulations of mass conservation equations, i.e., other equations reflecting that the evolution of the concentrations of nucleic acid molecules in the form of single strands and duplexes does not modify the total number of single strands of each type, can be used.

[0165] The integration of mass conservation equations into the differential equations makes it possible to complete the equations allowing more precise simulation of the hybridization phase, in order to obtain as many equations as there are unknowns.

[0166] Injecting, into a differential equation of a hybridization reaction between a pair of single-stranded nucleic acid molecules such as equation 3, the two mass conservation equations of the two molecules in the pair allows the equation to be rewritten in the following form: Equation 6

[0167] In order to solve the system of differential equations, one of the principles of the simulation of the hybridization phase as represented in Figure 5 is to represent these equations in the form of a matrix differential equation.

[0168] For this purpose, in the example of figure 5 the simulation of the hybridization phase S41 comprises a sub-second step S412 of initialization of a matrix of concentrations ^^, or ^^ of the duplexes formed by the hybridization of the plurality of nucleic acid molecules in the form of single strands.

[0169] The matrix can be an N x N matrix (N being the length of the vector ^̅^ ) formed in the following way: - each row and each column corresponds to a nucleic acid molecule; - each cell includes the concentration of the duplex formed by the hybridization of the pair of nucleic acid molecules of the row and column to which the cell belongs. A triangular form can be adopted to count only once the concentration of a given duplex, which would otherwise be counted at once in a cell with coordinates i,j and j,i.

[0170] The matrix ^^ can therefore be written: Equation 7

[0171] In the example of Figure 5, the hybridization phase S41 for a given cycle then comprises a third sub-step S413 of calculating, by successive time steps, the evolution of the concentration matrix during the hybridization phase, by applying to the concentration matrix a matrix differential equation representing the kinetics of formation of said duplexes as a function of the concentrations of the plurality of nucleic acid molecules in the form of single strands.

[0172] The calculation of the evolution of the matrix can for example be carried out in the following way: - the calculation is carried out for a number of time steps Npdt corresponding to the duration of the hybridization phase. A time step can for example have a duration between 1 and 10 milliseconds.A time step may for example be chosen to find a compromise between convergence of the calculation, calculation speed and precision of the result; - a time step index npdt is initialized to 1; - at each time step, sub-step S413 of calculating the evolution of the concentration matrix is ​​carried out; - at the end of the calculation, a sub-step S414 verifies that the index of the time step npdt is indeed less than the number of time steps Npdt; - if the index of the time step npdt is less than the number of time steps Npdt, the index of the time step npdt is incremented in sub-step S412, then a new iteration of sub-step S413 of calculating the evolution of the concentration matrix is ​​carried out; - when the index of the time step npdt is equal to the number of time steps Npdt, the simulation of the hybridization phase is finished, and the simulation of the elongation phase S42 is started.

[0173] Thus, the simulation of the hybridization phase can be done by simulating successive Npdt time steps of the hybridization reactions, each time step including the calculation of the matrix differential equation based on the concentrations of the molecules in the vector ^̅^ at the end of the previous time step.

[0174] This example of a loop of successive calculations is provided as a non-limiting example only of a loop for calculating the hybridization phase. More generally, any calculation loop making it possible to simulate the hybridization phase according to the desired number of time steps can be used within the scope of the invention. For example, the time step index can be initialized to 0 and the exit condition of the loop at step S414 adapted, etc.

[0175] The matrix differential equation is parameterized by at least one association matrix comprising the association constants associated with each duplex and at least one dissociation matrix comprising the dissociation constants associated with each duplex.

[0176] The association matrices thus contain all the association coefficients involved in equations 3 and 5. The association and dissociation coefficients can be integrated into the association and dissociation matrices according to the same principle as the concentrations in the matrix ^^ (eg the association and dissociation matrices are square matrices in which each row and each column correspond to molecules, each cell of the association matrix(es) includes the association constant between the molecules of the row and the column towards a partial duplex, and each cell of the dissociation matrix includes the dissociation constant associated with the dissociation reaction of the duplex towards the pair of molecules associated with the row and the column).

[0177] The association and dissociation matrices can therefore be written respectively: Equation 8 For the association matrix, and: Equation 9 For the dissociation matrix.

[0178] The units of association constants can be m 3 .mol -1 .s -1 (or L.mol -1 .s -1 ), while the units of dissociation constants can be s -1 .

[0179] As indicated above, in a set of embodiments of the invention, only certain hybridization reactions are taken into account. In this case, the association and dissociation constants are therefore only integrated for the reactions considered sufficiently important, i.e. the reactions which will have the greatest impact on the simulation. This can for example example can be done by defining each element of the association matrix, or each element of the dissociation matrix associated with a pair of molecules belonging as being: - zero, if the variation of free enthalpy (ΔG) associated with the hybridization reaction of the molecules forming the pair is greater than a threshold (or lower in absolute value); - respectively equal to an association constant, or to a dissociation constant of the hybridization reaction of the pair of molecules otherwise.

[0180] In other words, the values ​​of the association and dissociation constants in the matrices will be equal to 0 for less important reactions, for example if the variation of free enthalpy (ΔG) associated with the hybridization reaction of the molecules forming the pair is greater than a given threshold (or lower in absolute value).

[0181] Thus, only the dominant reactions will be taken into account, which reduces the complexity of the simulation, while benefiting from good simulation accuracy.

[0182] As indicated above, the threshold for taking into account a hybridization reaction, and therefore integrating the association and dissociation constants into the matrices, can be identical for all reactions, or different depending on whether the reaction is an amplicon-primer hybridization reaction or another hybridization reaction (primer-primer for example).

[0183] The evolution of the duplex concentration matrix can therefore, thanks to the association and dissociation matrices, be written in the form of a matrix differential equation, and sub-step S413 can thus consist of solving the matrix differential equation for a given time step.

[0184] Solving the matrix differential equation thus makes it possible to model the entire dynamics of the chain amplification, including cross-reactions with intermediate products. Solving a single matrix differential equation also allows the kinetics of the system to be solved using conventional computing capabilities.

[0185] The possibility of fully simulating amplification, and in particular hybridization reactions which were not simulated satisfactorily in state-of-the-art solutions, thus allows validation or, on the contrary, modification of the parameters influencing the amplification reaction (initial concentration of primers, salts, duration and temperature of the phases, etc.).

[0186] When the mass conservation equations are taken into account, the matrix differential equation can be written, by integrating the differential equations such as Equation 6 for each reaction: Equation 10

[0187] In which: - H is the concentration matrix of the duplexes; - T0 is the initial value for the cycle of the concentration vector of the plurality of molecules; - Kon is the association matrix; - Koff is the dissociation matrix; - is the identity matrix of size N - is the Hadamard product; - diag() represents the diagonal operator converting a square matrix of size N x N into a vector of size N comprising all the elements of the diagonal of the matrix. Thus,

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

[0189] Reference is now made to Figures 6 and 7.

[0190] Figure 6 shows an example of two elongation and denaturation phases in a set of embodiments of the invention.

[0191] Figure 7 shows an example of a set of hybridization, elongation and denaturation reactions taking place during three successive cycles of PCR amplification reaction, the reactions represented in Figure 7 allowing to better illustrate the steps of the simulations of the elongation and denaturation phases represented in Figure 6.

[0192] Figure 7 represents a simplified example of a single target amplification reaction.

[0193] Figure 7 more specifically represents series of hybridization, elongation, denaturation reactions occurring in a given context, with new reactions appearing successively in cycle 2 then in cycle 3, as new by-products are generated.

[0194] In the example of Figure 7, the simulation initially includes (start of the hybridization phase of cycle 1): - nucleic acids in the form of single strands "sense" and "antisense" of the target, respectively ^^ ^^ ^^ ^^ and ^^ ^^ ^^ ^^ ; - a “sense” primer ^^1 ^^ ^^ ^^, and two “antisense” primers ^^1 ^^ ^^ ^^and ^^2 ^^ ^^ ^^;

[0195] During the first cycle the reactions are as follows: - React71 reaction: ^^ ^^ ^^ ^^ pairs with primer ^^1 ^^ ^^ ^^in a first position to give the duplex ^^ ^ 1 ^ ^^ ^^ ^^ ^^, which will then be elongated into an elongated duplex ^^ ^ 1^ ^ ∗ ^ ^^ ^^ ^^, which will be denatured into two single-stranded nucleic acids ^^ ^^ ^^ ^^ and ^^ ^^ ^ 1 ^ ^^ ^^ ; - React72 reaction: ^^ ^^ ^^ ^^ pairs with primer ^^1 ^^ ^^ ^^in a second position to give the duplex ^^ ^ 2 ^ ^^ ^^ ^^ ^^, which will then be elongated into an elongated duplex ^^ ^ 2 ^ ^ ∗ ^ ^^ ^^ ^^, which will be denatured into two single-stranded nucleic acids ^^ ^^ ^^ ^^ and ^^ ^^ ^ 2 ^ ^^ ^^. Although the paired molecules are the same in the React71 and React72 reactions, these reactions are distinct, because the pairing occurs in two distinct positions, the elongation therefore occurs over a shorter distance in the case of the React72 reaction. In this case, we speak of "multi-hybridization". The variations in free enthalpy ΔG associated with these two reactions can also be different. The React71 and React72 reactions therefore respectively generate two molecules in the form of distinct single strands ^^ ^^ ^ 1 ^ ^^ ^^ and ^^ ^^ ^ 2 ^ ^^ ^^ ; - React73 reaction: ^^ ^^ ^^ ^^ pairs with primer ^^1 ^^ ^^ ^^ to give duplex ^^^^ ^^ ^^ ^^ ^^, which will then be elongated into an elongated duplex ^^ ^ ∗ ^ ^^ ^^ ^^ ^^, which will be denatured into two nucleic acids in single-strand form ^^ ^^ ^^ ^^ and ^^ ^^ ^^ ^^ ^^; - React74 reaction: ^^1 ^^ ^^ ^^pairs with ^^2 ^^ ^^ ^^to give the duplex ^^^^ ^^ ^^ ^^ ^^, which will then be elongated into an elongated duplex ^^ ^ ∗ ^ ^^ ^^ ^^ ^^, which will be denatured into two single-stranded nucleic acids ^^ ^^ ^^ ^^ ^^ and ^^1 ^^ ^^ ^^; - React75 reaction: ^^1 ^^ ^^ ^^pairs with ^^2 ^^ ^^ ^^to give the duplex ^^^^ ^^ ^^ ^^ ^^, which will then be elongated into an elongated duplex ^^ ^ ∗ ^ ^^ ^^ ^^ ^^, which will be denatured into two single-stranded nucleic acids ^^ ^^ ^^ ^^ ^^ and ^^2 ^^ ^^ ^^. Although the paired primers in the React74 and React75 reactions are the same, these reactions are distinct because the elongation does not occur on the same strand: in the case of the React74 reaction it is the "antisense" strand that is elongated, whereas in the case of the React75 reaction it is the "sense" strand that is elongated.

[0196] At the end of this second cycle, new reaction by-products are therefore added to the products already present: ^^ ^^ ^ 1 ^ ^^ ^^ , ^^ ^^ ^ 2 ^ ^^ ^^ , ^^ ^^ ^^ ^^ ^^ , ^^ ^^ ^^ ^^ ^^ , ^^ ^^ ^^ ^^ ^^ .

[0197] In the second cycle, the presence of these new by-products generates 6 new reactions, in addition to the 5 React71 to React75 reactions already taking place in the first cycle: - React76 reaction: ^^ ^^ ^ 1 1 ^ ^^ ^^ pairs with primer ^^1 ^^ ^^ ^^to give the duplex ^^ ^^ / ^^ ^^ ^^ ^^ ^^ which will then be elongated into an elongated duplex ^^which will be denatured into two nucleic acids in single-strand form ^^ 1 ^^ ^^ ^^ and ^^ ^^ ^ 1 ^ ^^ ^^ ; - React77 reaction: ^^ ^^ ^ 2 ^ ^^ ^^ pairs with primer ^^1 ^^ ^^ ^^to give the duplex will then be elongated into an elongated duplex ^^which will be denatured into two nucleic acids in single-strand form ^^ 2 ^^ ^^ ^^ and ^^ ^^ ^ 2 ^ ^^ ^^ ; - React78 reaction: ^^ ^^ ^^ ^^ ^^ pairs with primer ^^1 ^^ ^^ ^^in a first position to give the duplex ^^ ^ 1 ^ / ^^ ^^ ^^ ^^ ^^, which will then be elongated into an elongated duplex ^^ ^ 1 ^ / ∗ ^ ^ ^^ ^^ , which will be denatured into two single-stranded nucleic acids ^^ ^^ ^^ ^^ ^^ and ^^ 1 ^^ ^^ ^^ ; - React79 reaction: ^^ ^^ ^^ ^^ ^^ pairs with primer ^^1 ^^ ^^ ^^in a second position to give the duplex ^^ ^ 2 ^ / ^^ ^^ ^^ , which will then be elongated into an elongated duplex ^^ ^ 2 ^ / ∗^^ ^^ ^^ ^^ ^^, which will be denatured into two single-stranded nucleic acids ^^ ^^ ^^ ^^ ^^ and ^^ 2 ^^ ^^ ^^ . Although the paired molecules are the same in the React78 and React79 reactions, these reactions are distinct, because the pairing occurs in two distinct positions, the elongation therefore occurs over a shorter distance in the case of the React79 reaction. In this case, we speak of "multi-hybridization". The React78 and React79 reactions therefore respectively generate two molecules in the form of distinct single strands ^^ 1 ^^ ^^ ^^ and ^^ 2 ^^ ^^ ^^ ; - React710 reaction: ^^ ^^ ^^ ^^ ^^ pairs with ^^2 ^^ ^^ ^^ to give the duplex ^^^^ / ^^ ^^ ^^ ^^ ^^, which will then be elongated into an elongated duplex ^^ ∗ ^ ^ / ^^ ^^ ^^ ^^ ^^ , which will be denatured into two single-stranded nucleic acids ^^ ^^ ^^ ^^ ^^ and ^^ ^^ ^^ ^^ ^^ ; - React711 reaction: ^^1 ^^ ^^ ^^pairs with ^^ ^^ ^^ ^^ ^^to give the duplex ^^^^ / ^^ ^^ ^^ ^^ ^^, which will then be elongated into an elongated duplex ^^ ∗ ^ ^ / ^^ ^^ ^^ ^^ ^^ , which will be denatured into two single-stranded nucleic acids ^^ ^^ ^^ ^^ ^^ and ^^ ^^ ^^ ^^ ^^ . Although the products of the React710 and React711 reactions are the same, these reactions are distinct because the paired molecules are different and the elongation does not occur on the same strand: in the case of the React710 reaction it is the "antisense" strand that is elongated, whereas in the case of the React711 reaction it is the "sense" strand that is elongated. It should also be noted that, although ^^ ∗ ^ ^ / ^^ ^^ ^^ ^^ ^^ and ^^ ∗ ^ ^ / ^^ ^^ ^^ ^^ ^^ are considered for the purposes of the simulation as two different molecules associated with two different concentrations, they are in reality the same molecule.

[0198] At the end of this second cycle, new reaction by-products are therefore added to the products already present: ^^ 1 ^^ ^^ ^^ , ^^ 2 ^^ ^^ ^^ , ^^ 1 ^^ ^^ ^^ and ^^ 2 ^^ ^^ ^^

[0199] In the third cycle, the presence of these new by-products generates 4 new reactions, in addition to the 11 React71 to React711 reactions already taking place in the second cycle: - React712 reaction: ^^ 1 ^^ ^^ ^^ pairs with primer ^^11 ^ ^ ^^ ^^ to give the duplex ^^ ^^ ^^ ^^ ^^, which will then be elongated into an elongated duplex ^^1∗ ^ ^ ^^ ^^ ^^, which will be denatured into two single-stranded nucleic acids ^^ 1 ^^ ^^ ^^ and ^^ 1 ^^ ^^ ^^ ; - React713 reaction: ^^ 2 pairs with the primer ^^ to give the d 2 ^^ ^^ ^^ 1 ^^ ^^ ^^uplex ^^ ^^ ^^ ^^ ^^, which will then be elongated into an elongated duplex ^^ ^2 ^∗ ^^ ^^ ^^, which will be denatured into two single-stranded nucleic acids ^^ 2 ^^ ^^ ^^ and ^^ 2 ^^ ^^ ^^ ; - React714 reaction: ^^ 1 ^^ ^^ ^^ pairs with primer ^^1 ^^ ^^ ^^to give the duplex which will then be elongated into an elongated duplex ^^1∗ ^ ^ ^^ ^^ ^^, which will be denatured into two single-stranded nucleic acids ^^ 1 ^^ ^^ ^^ and ^^ 1 ^^ ^^ ^^ . Although the products of the React712 and React714 reactions are the same, these reactions are distinct because the paired molecules are different and the elongation does not occur on the same strand: in the case of the React712 reaction it is the "antisense" strand that is elongated, whereas in the case of the React714 reaction it is the "sense" strand that is elongated. It should also be noted that, although ^^ ^ 1 ^∗ 1 ^^ ^^ ^^ ^^are considered for the purposes of the simulation as two different molecules associated with two different concentrations, it is in reality the same molecule; - React715 reaction: ^^ 2 pairs with primer ^^ to give the duple 2 ^^ ^^ ^^ 1 ^^ ^^ ^^xe ^^ ^^ ^^ ^^ ^^, which will then be elongated into an elongated duplex ^^ ^ 2 ^∗ ^^ ^^ ^^, which will be denatured into two single-stranded nucleic acids ^^ 2 ^^ ^^ ^^ and ^^ 2 ^^ ^^ ^^ . Although the products of the React713 and React715 reactions are the same, these reactions are distinct because the paired molecules are different and the elongation does not occur on the same strand: in the case of the React713 reaction it is the "antisense" strand that is elongated, whereas in the case of the React715 reaction it is the "sense" strand that is elongated. It should also be noted that, although ^^ ^^ ^^are considered for the purposes of the simulation as two different molecules associated with two different concentrations, it is in reality the same molecule.

[0200] One principle of simulating the hybridization and denaturation phases in the exemplary embodiments of the invention shown in Figure 6 and exemplified in Figure 7 is to simulate several multiple hybridization reactions (e.g., React71 and React72 reactions, or React76 and React77 reactions) as a single reaction generating several reaction products, and then use a denaturation tensor to distribute the concentrations of the products of the multiple hybridization reactions for the next simulation cycle. The concentrations of the duplexes and elongated duplexes corresponding to different pairing positions are therefore represented by a single value.

[0201] Using a single concentration value for all duplexes between a pair of nucleic acid molecules regardless of the pairing position reduces the number of equations to be solved for calculating denaturation, and makes the problem of simulating denaturation soluble.

[0202] In a set of embodiments of the invention, certain reactions result from the pairing between two primers into a duplex. In this case, the elongation can occur in both directions. This is for example the case of the React74 and React75 reactions. In this case, in certain embodiments of the invention, the elongation phase simulates the elongation of such a duplex into a single elongated duplex, and the coefficients of the denaturation tensor are defined so that the Concentration of the single elongated duplex resulting from the pairing of the two primers generates reaction products corresponding to elongations in both directions.

[0203] This simplifies the simulation of reactions resulting from the pairing between two primers, in order to further reduce the computational complexity of the simulation.

[0204] In the example of Figure 7, the reactions can therefore be represented by the following equations, in which: - ^^ ^^ represents an elongation constant linked to each reaction; - ^^ ^^represents a denaturation constant linked to each reaction; - ^^ represents the respective weights associated with the molecules resulting from several reactions, when for the purposes of the simulation a concentration of elongated duplex actually represents the concentration of several distinct duplexes; - the three successive arrows for each reaction represent hybridization, elongation and denaturation; - the molecules to the right of the last arrow therefore represent the products of denaturation. In order to improve the readability of the equations, only the new molecules have been indicated.

[0205] The React71 and React72 reactions can be represented by the equation: Equation 11

[0206] Note that, in the case of this multiple hybridization, the two concentrations of duplexes ^^1 ^ ^ ^^ ^^ ^^ ^^ and ^^2 ^ ^ ^^^^ ^^ ^^ are represented by a single concentration ^^^^ ^^ ^^ ^^ ^^, the two concentrations of elongated duplexes ^^ ^ 1 ^ ^ ∗ ^ ^^ ^^ ^^ and ^^ ^ 2 ^ ^ ∗ ^ ^^ ^^ ^^ are represented by a single concentration ^^ ^ ∗ ^ ^^ ^^ ^^ ^^, and that the applications of the respective weights ^^ in the denaturation tensor allows to update the concentrations of the two molecules ^^ ^^ ^ 1 ^ ^^ ^^ and ^^ ^^ ^ 2 ^ ^^ ^^ to take into account the respective weights of the reactions from the two pairings.

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

[0208] The React74 and React75 reactions can be represented by the equation: Equation 13

[0209] Note that, in this reaction resulting from the pairing of two primers (primer dimer), the two concentrations of elongated duplexes ^^^^ ^^ ^^ ^^ ^^ and ^^^^ ^^ ^^ ^^ are represented by a single concentration ^^ ^^ ^^ , the two concentrations of elongated duplexes ^^ ^ ∗ ^ ^^ ^^ ^^ ^^and ^^ ^ ∗ ^ ^^ ^^ ^^ ^^are represented by a single concentration ^^ ^ ∗ ^ ^^ , and that the application of the respective weights ^^ in the denaturation tensor makes it possible to update the concentrations of the two molecules ^^ ^^ ^^ ^^ ^^ and ^^ ^^ ^^ ^^ ^^ .

[0210] The use of weights is done for example in the following way: an equation representing several reactions, such as equation 13 can be associated with several weights, for example stored in the denaturation tensor, representing the relative importance of the different reactions. For example, for equation 13, the reactions React74 and React75 can be associated respectively with a weight ^^^^ ^^ ^^ ^^ ^^ ^^74 and ^^^^ ^^ ^^ ^^ ^^75. At the end of each cycle, the single concentration ^^ ^ ∗ ^ ^^ is divided into concentrations of the reaction products. For example, for equation 13, the concentration of the molecule ^^ ^^ ^^ ^^ ^^ would be increased at the end of the cycle by ^^^^ ^^ ^^ ^^ ^^74* ^^ ^ ∗ ^ ^^ , and the concentration of the molecule ^^ ^^ ^^ ^^ ^^ would be increased at the end of the cycle by ^^^^ ^^ ^^ ^^ ^^75* ^^ ^ ∗ ^ ^^. The sum of the weights ^^^^ ^^ ^^ ^^ ^^74 and ^^^^ ^^ ^^ ^^ ^^75 must therefore be equal to 1, so that ^^^^ ^^ ^^ ^^ ^^74 and ^^^^ ^^ ^^ ^^ ^^75 represent the respective importance of the React74 and React75 reactions. For example, weights ^^^^ ^^ ^^ ^^ ^^74= 0.5 and ^^^^ ^^ ^^ ^^ ^^75= 0.5 would indicate that the React74 and React75 reactions are equally frequent.

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

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

[0213] The React78 and React79 reactions can be represented by the equation: Equation 16

[0214] Note that, in the case of this multiple hybridization, the two concentrations of duplexes ^^ 1 ^ ^ / ^^ ^^ ^^ ^^ ^^ ^^ 2 ^ ^ / ^^ ^^^^ ^^ ^^ are represented by a single concentration ^^^^ / ^^ ^^ ^^ ^^ ^^, the two concentrations of elongated duplexes are represented by a single concentration ^^ ∗ ^ ^ / ^^ ^^ ^^ ^^ ^^, and that the applications of the respective weights ^^ in the denaturation tensor allows to update the concentrations of the two molecules ^^ 1 ^^ ^^ ^^ and ^^ 2 ^^ ^^ ^^ to take into account the respective weights of the reactions from the two pairings.

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

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

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

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

[0219] The React714 reaction is represented by the equation: Equation 21

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

[0221] In a set of embodiments of the invention: - each molecule involved in the simulation is associated with an index in the vector ^̅^; - the concentrations of the duplexes resulting from the hybridization phase are noted in a square matrix ^^ where each row and each column represents one of the molecules, in the order of their indices in the vector ^̅^.

[0222] In the example of Figure 7, the matrix ^^ can for example be written: Equation 23

[0223] In the above representation, the single-stranded molecules bound to each column and row are noted above each column and to the left of each row, respectively. According to the equations noted above, in case of multi-hybridization, a single duplex concentration is noted in the matrix, representing in fact the concentration of several duplexes corresponding to several pairing positions. For example: - the cell corresponding to the row "^^1 ^^ ^^ ^^" and the column "^^ ^^ ^^ ^^ » includes the concentration ^^^^ ^^ ^^ ^^ ^^, actually representing the sum of the concentrations ^^ ^ 1 ^ ^^ 2 ^^ ^^ ^^ and ^^ ^^ ^^ ^^ ^^ ^^ ; - the cell corresponding to the row "^^1 ^^ ^^ ^^" and the column "^^ ^^ ^^ ^^ ^^ » includes the concentration ^^, represented 1 ^^ / ^^ ^^ ^^ ^^ ^^nt in fact the sum of the concentrations ^^ ^^ / ^^ ^^ ^^ ^^ ^^ and ^^ 2 ^ ^ / ^^ ^^ ^^ ^^ ^^.

[0224] It should be noted that these examples are given for multihybridizations at two distinct pairing positions, but this principle can be generalized to multihybridizations with pairings at any number of distinct positions greater than or equal to 2.

[0225] In a set of embodiments of the invention, obtaining the concentrations of the elongated duplexes during the simulation S42 of the elongation phase is done by multiplying the concentrations of the duplexes by elongation constants.

[0226] For example, the elongation constants can be listed in an elongation tensor constructed on the same principle as the matrix ^^ , that is, each cell of the elongation tensor ̿ ^ ̿ ^ ^ ̿ ^contains a stretch coefficient of the duplex of the corresponding cell of the matrix ^^. In the example of figure 7 the stretch tensor would therefore be: Equation 24

[0227] The numbering of the elongation constants here refers to the indices of the nucleic acid molecules in the form of single strands in the vector ^̅^. For example, the constant ^^ ^^11,1 , noted at 1 e column and the 11 e tensor line ̿ ^ ̿ ^ ^ ̿ ^ , represents the elongation coefficient of the duplex formed by the hybridization of the molecules of index 1 and 11 in the vector ^̅^ (therefore the molecules ^^ ^^ ^ 1 ^ ^^ ^^ and ^^ ^ 1 ^ ^^ ^^ ), that is to say ^^ ^ 1 ^ / ^^ ^^ ^^ ^^ ^^, also noted at 1 e column and the 11 erow of the matrix ^^. The elongation constants can for example be read from a database, or obtained experimentally.

[0228] Each elongation coefficient therefore represents the coefficient, between 0 and 1, of the molecules of a given duplex that are elongated during an elongation phase. For example, a coefficient of 0.5 for a given duplex means that half of the molecules of this duplex are elongated during the elongation phase. The concentration of elongated duplexes at the end of the elongation phase will therefore be half the concentration of non-elongated duplexes at the beginning of the elongation phase. The elongation tensor is therefore made up of elongation coefficients between 0 and 1.

[0229] More generally, the simulation phase of the elongation phase can be carried out by a step S421 of multiplication of the concentration matrix of the non-elongated duplexes by the elongation tensor: Equation 25

[0230] In which: - C represents the index of the PCR amplification cycle; - ∆ ^^ ^ represents the duration of the elongation phase: - ^^ ^^ represents the concentration matrix of non-elongated duplexes at the C-th cycle of PCR amplification; - ^^ ∗ ^^ represents the concentration matrix of the duplexes elongated at the C-th cycle of PCR amplification; - ̿ ^ ̿ ^ ^ ̿ ^ represents the elongation tensor.

[0231] Since all the duplexes have generally not been elongated during the elongation phase, the concentration of non-elongated duplexes at the end of the cycle is therefore equal to the concentration of non-elongated duplexes at the beginning of the cycle minus the concentration of elongated duplexes at the end of the phase. For example: ^^ ^^+1 (0) = ^^ ^^ (0) − ^^ ∗ ^^ (∆ ^^ ^ ) Equation 26

[0232] The elongation phase has been illustrated here using a Hadamard matrix product. However, this is not the only way to simulate an elongation phase. For example, the elongation phase can be simulated more generally by multiplying the concentration of each unextended duplex at the beginning of the elongation phase by the elongation coefficient of that duplex. For example, the concentrations of the unextended duplexes can be integrated into a concentration vector of the unextended duplexes, and this vector can be multiplied by a vector of elongation coefficients.

[0233] The denaturation phase may in practice comprise two steps: - a step S431 of multiplying the concentrations of elongated and possibly non-elongated duplexes by one or more denaturation tensors representing the distribution of the duplexes in nucleic acid molecules in the form of single strands; - a step S432 of multiplying the concentrations of the duplexes, or the product of the concentrations of the duplexes by the denaturation tensor(s) by one or more denaturation coefficients representing the rate of duplexes actually denatured during the denaturation phase.

[0234] In one set of embodiments of the invention, the denaturation phase comprises multiplying the concentrations of elongated duplexes by an elongated duplex denaturation tensor. The elongated duplex denaturation tensor practically represents the redistribution of elongated duplexes to single-stranded nucleic acid molecules during the denaturation phase.

[0235] This makes it possible to simulate the denaturation of the duplexes that have been elongated, and to integrate the concentrations of elongated and denatured duplexes into the initial conditions of the following cycle.

[0236] In one set of embodiments of the invention, the denaturation phase further comprises multiplying the concentrations of non-elongated duplexes by a denaturation tensor of the non-elongated duplexes.

[0237] Thus, the simulation of the denaturation phase takes into account both the denaturation of the elongated duplexes, but also the denaturation of the duplexes that have not been elongated, thus making it possible to obtain a more accurate simulation result.

[0238] When simulating the denaturation phase, a denaturation coefficient can also be applied to the elongated / non-elongated duplex concentrations and / or to the single-stranded nucleic acid concentrations resulting from multiplying the elongated / non-elongated duplex concentrations by the denaturation tensors.

[0239] Denaturation coefficients represent the proportion of duplexes of a given type that are actually denatured during the denaturation phase. Denaturation coefficients can, for example, be read from a database, or obtained experimentally.

[0240] Each denaturation coefficient therefore represents the coefficient, between 0 and 1, of the molecules of a given duplex which are denatured during a denaturation phase. For example, a coefficient of 0.5 for a given duplex means that half of the molecules of this duplex are denatured during the denaturation phase.

[0241] According to different embodiments: - the same denaturation coefficient can be applied to a given elongated duplex, and to the corresponding non-elongated duplex. This allows a good approximation of the denaturation, while simplifying the calculations; - two distinct denaturation coefficients can be applied respectively to a given elongated duplex, and to the corresponding non-elongated duplex. This allows a more precise simulation, in cases where the denaturation occurs differently for the elongated duplex and the non-elongated duplex.

[0242] Denaturation coefficients can, for example, be applied through matrix multiplications. For example, the denaturation phase can be simulated by the following equations: Equation 29

[0243] In which: - ° represents the Hadamard product; - ̿ ^ ̿ ^ ^ ̿ ^ is the identity matrix; - ̿ ^ ̿ ^ ^ ̿ ^ is a denaturation matrix comprising denaturation coefficients associated with each duplex; - ̿ ^ ̿ ^ ^ ̿ ^ is the elongation matrix; - ^^ ^^ (∆ ^^ ) is the concentration matrix of non-elongated duplexes at the end of the denaturation phase in cycle C; - is the concentration matrix of elongated duplexes at the beginning of the denaturation phase in cycle C; - ^^ ^^+1(0) is the concentration matrix of the non-elongated duplexes at the beginning of the following cycle C+1; - ^^ ∗ ^^+1( 0 ) is the concentration matrix of the elongated duplexes at the beginning of the following cycle C+1; - ∙ represents the tensor product; - ^̿^ ^ ∗ ^ is the denaturation tensor of elongated duplexes; - ^̿^ ^^ is the denaturation tensor of non-elongated duplexes; - ^^ ^ ∗ ^ ^ ^ ^ ^ ^^ ^^ (∆ ^^ ) is the concentration of elongated duplexes at the end of the elongation phase, put in vector form; - ^^ ^ ^ ^ ^ ^^ ^^ ^^ (∆ ^^ ) is the concentration of non-elongated duplexes at the end of the elongation phase, put in vector form; - ^̅^ ^^ ^^ ^ ^ ^^ ^^ ( ∆ ^^ )represents the concentration vector of nucleic acid molecules in the form of single strands at the end of the elongation phase in the PCR amplification cycle C; - represents the concentration vector of nucleic acid molecules in the form of single strands at the start of the following PCR amplification cycle C+1;

[0244] Equation 27 represents the concentration of unelongated and undenatured duplexes found at the beginning of the amplification cycle following C+1.

[0245] Equation 28 represents the concentration of elongated and undenatured duplexes found at the beginning of the amplification cycle following C+1.

[0246] Equation 29 represents the distribution of single-stranded nucleic acids in the denatured duplexes at the beginning of the amplification cycle following C+1. More specifically: - ∙ ^^ ^ ∗ ^ ^ ^ ^ ^ ^^ ^^ ( ∆ ^^ )represents the distribution of elongated duplexes into single-stranded nucleic acids by applying the denaturation tensor of elongated duplexes; - ^ ^^ ^̿^ ^^ ∙ represents the distribution of unelongated duplexes into single-stranded nucleic acids by applying the unelongated duplex denaturation tensor; - ̿ ^ ̿ ^ ^ ̿ ^ ° represents the application of the denaturation tensor to the distribution of nucleic acids in the form of single strands; - the term ̿ ^ ̿ ^ ^ ̿ ^ ° [ ^^ ^ ∙ ^^ ^ ^ ^ ^ ^^ ^^ ^^ ( ∆ ^^ ) ] therefore represents the variation of nucleic acids in the form of single strands during the PCR amplification cycle of index C.

[0247] It should be noted that the examples provided above are provided as non-limiting examples only, and other formulations could be applied to simulate the denaturation phase. For example, equivalent formulas for distributing duplexes to single-stranded molecules and multiplying by denaturation constants can be used. For example, multiplication by denaturation constants can be done as vector multiplications.

[0248] In the example of Equation 28 and Equation 29, the denaturation constants are listed in a denaturation tensor constructed on the same principle as the matrix ^^, i.e. each cell of the elongation tensor ̿ ^ ̿ ^ ^ ̿ ^contains an elongation coefficient of the duplex of the corresponding cell of the matrix ^^. In the example of figure 7 the denaturation tensor would therefore be: Equation 30

[0249] The numbering of the elongation constants here refers to the indices of the nucleic acid molecules in the form of single strands in the vector ^̅^. For example, the constant ^^ ^^11,1 , noted at 1 e column and the 11 e tensor line ̿ , represents the denaturation coefficient of the duplex formed by the hybridization of the molecules of index 1 and 11 in the vector ^̅^ (therefore the molecules ^^ ^^ ^ 1 ^ ^^ ^^ and ^^ ^ 1 ^ ^^ ^^ ), that is to say ^^ ^ 1 ^ / ^^ ^^ ^^ ^^ ^^, also noted at 1 e column and the 11 erow of the matrix ^^. In this example, the same denaturation coefficient is applied to the duplexes and the corresponding elongated duplexes (e.g. However, in other embodiments of the invention, distinct denaturation coefficients may be applied to certain duplexes and extended duplexes, for example if the denaturation dynamics are significantly different between the two versions. The denaturation coefficients may for example be read from a database, or obtained experimentally.

[0250] Each denaturation coefficient therefore represents the coefficient, between 0 and 1, of the molecules of a given duplex that are denatured during a denaturation phase. For example, a coefficient of 0.5 for a given duplex means that half of the molecules of this duplex are denatured during the elongation phase. The concentration of elongated / non-elongated duplexes at the end of the denaturation phase will therefore be half the concentration of elongated / non-elongated duplexes at the beginning of the denaturation phase. The denaturation tensor is therefore made up of denaturation coefficients between 0 and 1.

[0251] In the case of non-elongated duplexes (i.e., duplexes resulting from the hybridization of two nucleic acid molecules in the form of single strands that have not been elongated), the molecules have not been transformed, and denaturation has the effect of restoring the two nucleic acid molecules in the form of hybridized single strands.

[0252] In the example of Figure 7, the denaturation of elongated duplexes is summarized in the table below, where each row includes the reference of a partial duplex, its index in the vector ^^^^ ^^ ^^ ^^, the two nucleic acid molecules in single-stranded form whose hybridization has allowed to form the duplex, and which are re-created at the end of the denaturation phase, and the indices of these two molecules: Table 1

[0253] The denaturation tensor of non-elongated duplexes ^̿^ ^^ can therefore be written in this example: Equation 31

[0254] The denaturation tensor of non-elongated duplexes ^̿^ ^^ is in this example a tensor of size 12x14: it includes 12 rows corresponding respectively to the 12 duplexes in the vector ^^^^ ^^ ^^ ^^. The 12 duplexes are noted to the left of each corresponding row, and noted in the order of their indices in the vector ^^^^ ^^ ^^ ^^. It also includes 14 columns corresponding respectively to the 14 single-stranded nucleic acid molecules in the vector ^̅^. The 14 single-stranded nucleic acid molecules are noted above each corresponding column, and noted in the order of their indices in the vector ^̅^. The value "1" is inscribed in each cell belonging to the row of a duplex, and the column of a nucleic acid in the form of single strands generated by the denaturation of this elongated duplex.

[0255] The denaturation tensor thus makes it possible to distribute the concentrations of molecules from ^^^^ ^^ ^^ ^^towards for the next cycle in a single simple algebraic operation. The form of the denaturation tensor also makes it possible to verify that the reaction is correct by summing each row. Indeed, the sum of the elements of each row must be equal to 2 (since each duplex generates two nucleic acid molecules in the form of single strands during the denaturation phase).

[0256] The denaturation tensor of the elongated duplexes is also in our example of size 12x14, each row representing an elongated duplex in the order of their indices in the vector ^^ ^ ∗^ ^^ ^^ ^^, and each column represents a single-stranded nucleic acid molecule in the order of their indices in the vector ^̅^. For cases of duplexes corresponding to a single hybridization reaction at a single location, it is constructed as the denaturation tensor, by entering the value "1" in each cell belonging to the row of an elongated duplex, and the column of a single-stranded nucleic acid generated by the denaturation of this elongated duplex.

[0257] In a set of embodiments of the invention, the denaturation tensor of the elongated duplexes also contains specific coefficients in the case of multiple hybridizations, i.e. hybridization of the same primer in several locations of the same nucleic acid in the form of single strands, as for example in the case of the React71 and React72 reactions, or the React78 and React79 reactions for example.

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

[0259] In this case, the duplex concentrations and the elongated duplex concentrations respectively comprise a concentration of a virtual duplex equal to the sum of the concentrations of the duplexes formed by the multiple hybridization reactions, and a concentration of an elongated virtual duplex equal to the sum of the concentrations of the elongated duplexes formed by the elongation of the duplexes formed by the multiple hybridization reactions.

[0260] For example: - in the case of the React71 and React72 multihybridization reactions: - the concentrations of non-elongated duplexes include the concentration of representing the sum of the concentrations And - the concentrations of elongated duplexes include the concentration of virtual elongated duplex ^^ ^ ∗ ^ ^^ ^^ ^^ ^^representing the sum of the concentrations ^^ ^ 1 ^ ^ ∗ ^ ^^ ^^ ^^ ; - in the case of the React78 and React79 multihybridization reactions: - the concentrations of non-elongated duplexes include the concentration of virtual duplex ^^^^ / ^^ ^^ ^^ ^^ ^^ representing the sum of the concentrations ^^ ^ 1 ^ / ^^ ^^ ^^ ^^ ^^and ^^ ^ 2 ^ / ^^ ^^ ^^ ^^ ^^; - the concentrations of elongated duplexes include the concentration of virtual elongated duplex ^^ ^ ∗^ / ^^ ^^ ^^ ^^ ^^representing the sum of the concentrations ^^ ^ 1 ^ / ∗ ^^ ^^ ^^ ^^ ^^and ^^ ^ 2 ^ / ∗ ^^ ^^ ^^ ^^ ^^.

[0261] In this case, the coefficients of the denaturation tensor of the elongated duplexes corresponding to the distribution of the concentration of the elongated virtual duplex towards each nucleic acid in the form of a single strand associated with one of the multiple hybridization reactions can be respectively equal to the ratio between the interaction energy of the multiple hybridization reaction divided by the sum of the interaction energies of all the multiple hybridization reactions with said single-stranded nucleic acid.

[0262] For example, in the case of the multihybridization reactions React71 and React72, the virtual duplex ^^ ^ ∗ ^ ^^ ^^ ^^ ^^will be distorted: - on the one hand, towards ^^ ^^ ^^ ^^, which was present in both React71 and React72 reactions. The associated coefficient will therefore be 1; - on the other hand, towards ^^ ^^ ^ 1 ^ ^^ ^^ and ^^ ^^ ^ 2 ^ ^^ ^^ , corresponding to the reactions React71 and React72. The coefficients associated with the molecules ^^ ^^ ^ 1 ^ ^^ ^^ and ^^ ^^ ^ 2 ^ ^^ ^^ must therefore correspond to the respective importance of the React71 and React72 reactions, that is to say to the respective importance of the hybridization of React71 and the hybridization of React72. For this purpose, these two coefficients can be respectively 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.

[0263] For example, if the hybridization reaction of React71 has an interaction energy ^^ ^^ 1 , and the hybridization reaction of React72 an interaction energy ^^ ^^ 2 , the weights associated with ^^ ^^ ^ 1 ^ ^^ ^^ and ^^ ^^ ^ 2 ^ ^^ ^^ in the denaturation tensor of the elongated duplexes will be respectively equal to: 1 = ^^ ^ 1 - ^^ ^ ^^ ^^ 1 + ^^ ^^ 2 for ^^ ^^ ^ 1 ^ ^^ ^^ ; t ^^2= ^^ 2 - e ^^ ^^ ^^ 1 + ^^ ^^ 2 for ^^ ^^ ^ 2 ^ ^^ ^^ .

[0264] Thus, multiple hybridization reactions, and associated elongations and denaturations can be simulated as a single series of reactions, while preserving the accuracy of the simulation.

[0265] In one set of embodiments of the invention, the denaturation tensor of the elongated duplexes also contains specific coefficients in the case of hybridizations between two primers, or "primer dimer". Indeed, in this case, the duplex formed by the hybridization of the two primers can be elongated in both directions, which ultimately generates distinct denaturation products, as for example in the React74 and React75 reactions.

[0266] In this case, the concentrations of elongated duplexes include a concentration of a virtual elongated duplex equal to the sum of the concentrations of the elongated duplexes formed by elongation in each of the two directions of the duplex formed by the hybridization of the two primers.

[0267] For example, in the case of the React74 and React75 reactions, the concentrations of the elongated duplexes may include a concentration of a virtual elongated duplex ^^ ^ ∗ ^ ^^, representing the sum of the concentrations of ^^ ^ ∗ ^ ^^ ^^ ^^ ^^and ^^ ^ ∗ ^ ^^ ^^ ^^ ^^.Thus, the concentration of the elongated virtual duplex ^^ ^ ∗ ^ ^^ does not correspond to a concentration of a real duplex, but makes it easier to simulate.

[0268] The coefficients of the denaturation tensor of the elongated duplexes corresponding to the distribution of the concentration of the virtual duplex elongated towards each of the two primers, and each of the two single-stranded nucleic acids resulting from the elongation in one of the two directions can then all be equal to 0.5, to represent the fact that the elongation takes place approximately once in two in each of the two directions. For example, in the case of the React74 and React75 reactions, the denaturation products are the primers ^^ ^^ ^^ ^^ ^^ and ^^ ^^ ^^ ^^ ^^, as well as nucleic acids ^^1 ^^ ^^ ^^and ^^2 ^^ ^^ ^^. In the denaturation tensor of elongated duplexes, cells on the line of ^^ ^ ∗ ^ ^^ and the columns of ^^ ^^ ^^ ^^ ^^ , ^^ ^^ ^^ ^^ ^^ , ^^1 ^^ ^^ ^^and ^^2 ^^ ^^ will therefore all be equal to 0.5.

[0269] This makes it possible to efficiently simulate reactions resulting from hybridizations between primers, while limiting the complexity of the simulation.

[0270] In the example of Figure 7, the coefficients of the denaturation tensor can be defined for each denaturation reaction of an elongated duplex, in a table constructed on the same principle as the table for non-elongated duplexes: Table 2

[0271] We observe here: - The presence of coefficients corresponding to multiple hybridization reactions, for elongated virtual duplexes ^^∗ ∗ ^ ^ ^^ ^^ ^^ ^^ and ^^ ^^ / ^^ ^^^^ ^^ ^^, - the presence of coefficients corresponding to hybridization between primers for the elongated virtual partial duplex ^^ ^ ∗ ^ ^^ .

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

[0273] This therefore allows us to construct the following denaturation tensor for elongated duplexes: Equation 32

[0274] The shape of this tensor allows the concentrations of elongated duplexes to be distributed to single-stranded nucleic acid molecules by a simple algebraic operation.

[0275] Additionally, it is possible to verify that denaturation is under control by checking that the sum of the values ​​on each line is equal to 2.

[0276] Reference is now made to Figure 8.

[0277] Figure 8 shows an example of a method according to a set of embodiments of the invention integrating a validation or modification of the parameters of the PCR amplification.

[0278] In one set of embodiments of the invention, the characteristics of the PCR kit, for example the choice of the plurality of primers and the initial value of the concentration vector for said plurality of primers in the first cycle of the reaction, can be validated or modified depending on the results of the simulation.

[0279] For example, the method P8 comprises, in addition to the steps of the method P4: - a step S81 for displaying the results of the simulation. This display may for example comprise a display of curves showing the evolution of the concentrations of the molecules, values ​​representative of the kinetics of the reaction, etc.; - a step S82 for comparing a value representative of the kinetics of a reaction to a threshold; - if the comparison is positive, a step S83 for validating the primers and the initial concentrations of the primers; - otherwise, a step S84 for modifying the primers and / or the initial concentrations of the primers.

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

[0281] This therefore makes it possible to ensure that the parameters of the primers and their concentration allow the desired amplification to be achieved with sufficiently strong kinetics, or on the contrary to modify them to satisfy this constraint.

[0282] Step S82 of comparing a value representative of the kinetics of a reaction to a threshold makes it possible in particular to verify that a given amplification reaction will be sufficiently rapid to be detected. For example, the threshold considered may be one of the following thresholds: - a threshold cycle (Ct); - a crossing point (Cp); - a final concentration of a nucleic acid molecule amplified by the reaction; - a concentration of amplicons at the end of the reaction.

[0283] Thus, step S82 may consist of verifying that a Ct or Cp for an amplification reaction of a given target is greater than a reference threshold (i.e., the threshold cycle Ct, or crossing point Cp is too high, meaning that the amplification reaction is not fast enough), meaning that the reaction will not be fast enough.

[0284] If the method P8 comprises a display step S81, this is a non-limiting example. Indeed, the display can for example allow an expert user to validate or not the parameters of the simulation, but the comparison in step S82 can also be carried out automatically, without prior display.

[0285] Implementing a change in step S84 can be done in different ways. For example, the change can be done manually by an expert user. Alternatively, a change can be done automatically, or proposed to the expert user based on the results of the simulation.

[0286] An example of modification at step S84 will be described below.

[0287] First, step S84 may comprise a sub-step S841 of identifying a target to be favored based on the results of the polymerase chain reaction simulation.

[0288] For example, the target to be favored may be a target whose kinetics are not sufficiently fast. For example, one or more of the comparisons discussed for step S82 may be performed for each target, and a target for which the comparison is negative (e.g., a target whose Ct or Cp is greater than a predefined threshold) considered as a target to be favored, because the amplification kinetics are currently insufficient.

[0289] Step S84 may then comprise a second sub-step S842 of identifying, from the association matrix or the dissociation matrix, a nucleic acid molecule in single-strand form forming a pair with a primer associated with said target.

[0290] Sub-step S842 therefore consists of identifying a molecule other than the target forming a pair with a primer associated with said target, i.e. a molecule which will compete with the target (and the amplicons resulting from the amplification of the target) to pair with the primer. Such a molecule can be identified using the association matrix ^^ ^^ ^^ , or the dissociation matrix ^^ ^^ ^^ ^^ . Indeed, these matrices contain coefficients for each pair of molecules linked by a sufficiently strong hybridization reaction. The molecule can therefore, for example, be identified as a molecule having an association constant with the primer, or an association constant greater than a threshold with the primer.

[0291] Step S84 may then comprise carrying out at least one modification of the polymerase chain reaction. The at least one modification of the polymerase chain reaction may in particular comprise at least one modification chosen from: - a reduction, in the initial concentration vector, of the initial concentration of said nucleic acid molecule in the form of a single strand forming a pair with the primer associated with said target; - a modification of the salt concentration; - a modification of the hybridization temperature for at least one cycle.

[0292] These modifications make it possible in particular to disfavor the hybridization of the nucleic acid molecule in the form of a single strand forming a pair with the primer associated with said target with the primer, which thus makes it possible to favor the hybridization of the target (and of the amplicons resulting from the amplification of the target) with the primer, and therefore the amplification reaction of the target.

[0293] This example shows that the amplification reaction simulation according to the invention not only makes it possible to verify that a desired amplification is indeed carried out, but also to modify the parameters of the amplification in order to favor a desired reaction. If the example of steps S841 to S843 of figure 8 is based on an identification of a competing reaction via analysis of the association matrix ^^ ^^ ^^ , or the dissociation matrix ^^ ^^ ^^ ^^, this example is not limiting, and other methods of identifying brakes on an amplification reaction can be used in a set of embodiments of the invention. More generally, the invention is not limited to a particular method of modifying the parameters of the simulation.

[0294] Reference is now made to Figure 9.

[0295] Figure 9 shows an example of a method according to a set of embodiments of the invention integrating a validation or modification of the parameters of the PCR amplification, and a manufacture of a validated PCR amplification kit.

[0296] The P9 process is a manufacturing process comprising all the steps of the P8 process.

[0297] The method P9 further comprises, at the end of the validation in step S83, a step of manufacturing a kit for the characterization of microorganisms included in a sample by using a polymerase chain reaction, or “PCR kit” such as the kit K1 represented in figure 1 for example.

[0298] The kit manufactured by the P9 process thus includes the primers and concentrations as validated by the P8 process, i.e. whose simulation has shown that a desired amplification can be achieved with satisfactory kinetics.

[0299] The P9 process therefore makes it possible to manufacture a kit validated by simulation, and allowing satisfactory amplification of the desired targets.

[0300] Reference is now made to Figure 10.

[0301] Figure 10 shows an example of a method P10 for characterizing a microorganism using a PCR amplification kit manufactured according to a set of embodiments of the invention.

[0302] The method P10 comprises a first step S101 of preparing the sample so as to carry out a PCR on the prepared sample, said preparation comprising a step of adding a kit (K1) manufactured in accordance with a method such as the method P9.

[0303] The sample may have been taken from a human, an animal, or an inanimate object.

[0304] The method P10 then comprises a step S102 of implementing PCR on the sample taken. At the end of this step, the nucleic acid sequences of interest will have been amplified by PCR, and are present in sufficient quantities to be characterized.

[0305] The P10 process therefore includes a third step S103 of characterization of the microorganisms based on the PCR results.

[0306] An antimicrobial can be chosen based on the characterization and either administered to the human or animal if the sample was taken from a living being, or applied to an inanimate object if the sample was taken from an inanimate object.

[0307] The P10 process thus makes it possible to carry out a PCR on a sample, in order to characterize a microorganism contained in the sample, and if necessary select an antimicrobial adapted to this microorganism.

[0308] The kit having been validated by simulation to allow the amplification of the nucleic acid sequences characteristic of this microorganism, the P10 method allows amplification, and therefore effective characterization of a given microorganism.

[0309] Reference is now made to Figure 11.

[0310] Figure 11 shows a graph Gr11 representing the evolution of the Ct for a simulation of amplification of a nucleic acid from yeast of the fungus (S. cerevisiae) as a function of the duration of the hybridization phase according to a simulation method of the invention.

[0311] The graph represents more precisely: - on the x-axis, the duration of the hybridization phase ^^ℎ ^^ ^^ ^^, in seconds; - on the y-axis, the difference ^^ ^^ ^^ between the ^^ ^^ corresponding to the maximum time tested for the hybridization phase (here, 10 seconds), and the ^^ ^^ for a given duration of hybridization phase, shorter.

[0312] The simulations were carried out for 3 primer concentrations, the concentration of nucleic acid from the yeast of the fungus being kept constant: - the Crv110 curve represents the simulated evolution of the ^^ ^^ ^^as a function of ^^ℎ ^^ ^^ ^^, for a concentration of 0.4 µM; - the Crv111 curve represents the simulated evolution of the ^^ ^^ ^^ as a function of ^^ℎ ^^ ^^ ^^, for a concentration of 0.8 µM; - the Crv112 curve represents the simulated evolution of the ^^ ^^ ^^ as a function of ^^ℎ ^^ ^^ ^^, for a concentration of 2 µM.

[0313] Physical experiments corresponding to these concentrations, for certain durations of the hybridization phase were carried out, in order to measure the value ^^ ^^ ^^ on real cases and compare to simulations.

[0314] The actual measurements are represented: - by the measurements Mes1101, Mes1102, Mes1103 and Mes1104 for the concentrations of 0.4 µM; - by the measurements Mes1111, Mes1112, Mes1113, Mes1114, Mes1115 and Mes1116, for concentrations of 0.8 µM; - by the measurements Mes1121, Mes1122, Mes1123, Mes1124 and Mes1125, for concentrations of 2 µM.

[0315] Figure 11 shows that: - the simulations provide precise results, very close to the real measurements; - when the duration of the hybridization phase increases, the Ct decreases rapidly then more slowly to tend towards a minimum value (represented by ^^ ^^ ^^ = 0); - the inflection point of the hybridization duration ^^ℎ ^^ ^^ ^^from which the Ct approaches the minimum value is higher when the concentrations are low.

[0316] The simulation therefore makes it possible to evaluate the Ct precisely and reliably. We can therefore see that the simulations carried out make it possible to optimize the duration of the hybridization phase to reach a target Ct value.

[0317] Reference is now made to Figure 12.

[0318] Figure 12 shows an example of visualization of the kinetics of several PCR reactions under two distinct experimental conditions according to a set of embodiments of the invention.

[0319] In the example of Figure 12, two simulations according to the invention were executed to reproduce: - the amplification of a target within a first multiplex amplification, with a first set of primers. This first simulation is represented by the “OPA” points, - the amplification of a target within a second multiplex amplification, with a modification of the first set of primers. This first simulation is represented by the “OPB” points.

[0320] The simulation was carried out in this case, following the observation that, in a real amplification example, the Ct of an amplification was increased by approximately 5.5 cycles following the modification of the first set of primers. Two simulations, corresponding to the first set of primers, and to the modification of the set, were therefore conducted.

[0321] The results of these two simulations are represented on graph Gr12, with: - on the abscissa, the cycle index; - on the ordinate, the concentration of amplicons resulting from the amplification of the target.

[0322] The points “OPA” and “OPB” therefore show the simulated amplicon concentrations at the end of each cycle, respectively in the case where the first primer set and the modified primer set are used.

[0323] We note that the simulation also allows us to detect a difference in Ct ^^ ^^ ^^ of approximately 5.5 cycles.

[0324] This result demonstrates the ability of the PCR amplification simulation according to the invention to reliably simulate the operation of a multiplex amplification. Thus, the analysis of the simulation results makes it possible to optimize the choice of amplification parameters, for example the choice of primers, primer concentrations, or phase durations in order to validate the ability of a PCR amplification kit constructed according to the simulated parameters to generate a satisfactory amplification of a given target.

[0325] The present disclosure is not limited to the examples of method, computer program, kit for polymerase chain amplification above, only by way of example, but it encompasses all the variants that may be envisaged by those skilled in the art within the framework of the protection sought.

[0326] By means of the invention, it is possible to determine whether an initial choice of primers and their concentration leads to appropriate amplification of the target nucleic acid molecules. In such a case, the design of a kit containing said primers and their concentrations is validated and the kit can be put into production for commercialization.

[0327] The invention also makes it possible to adopt a systematic approach for the design of PCR amplification kits. In particular, starting from a list of possible primers previously identified and a range of possible concentrations for the latter, a grid of initial parameters is determined. For example, for each set of candidate primers for a kit, their concentration range is discretized with a predetermined step. An initial parameter is then this set of primers with concentration values ​​in said ranges. A simulation is launched for each of the parameters and once the entire grid has been covered, the parameter(s) giving the best performance are retained, then one or more corresponding kits are manufactured.

[0328] The invention also makes it possible to test a set of primers in the context of a multiplex PCR, and in this case to test and compare alternative designs in order to achieve the expected performances.

[0329] The manufactured kit is then used in a manner known per se. In the context of a clinical application, such as the detection of pathogenic microorganisms in a biological sample taken from a patient (or an animal), the clinician (resp. the veterinarian) can then adapt his therapy, for example choosing an antibiotic adapted to the detected pathogen.

[0330] In a privileged manner, the parameters ∆ ^^, or similarly the ^^ ^^ ^^ and ^^ ^^ ^^ ^^, can be obtained according to state-of-the-art methods, for example the so-called "Nearest Neighbors" methods disclosed for example 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.

[0331] The simulation of PCR amplification is implemented by computer, namely by means of hardware circuits comprising computer memories (cache, RAM, ROM, etc.) and one or more microprocessors or processors, organized or not in the form of calculation nodes, necessary for the execution of computer instructions stored in the memories for the implementation of said simulation.

Claims

Claims

1. A method (P4) for numerical simulation of a polymerase chain reaction of at least one target, said method comprising the simulation of a plurality of successive cycles of the amplification, each cycle comprising, sequentially: - a hybridization phase (S41) between the at least one target and a plurality of primers; - an elongation phase (S42); - then a denaturation phase (S43); wherein, for each cycle: - the hybridization phase comprises: - obtaining an initial value for the cycle of a vector of concentrations of a plurality of nucleic acid molecules in the form of single strands comprising the at least one target and the plurality of primers;- calculating a matrix of concentrations of partial duplexes formed by the hybridization of the plurality of nucleic acid molecules in the form of single strands, each element of said matrix representing the concentration of the duplexes formed by the hybridization of a pair of said plurality of nucleic acid molecules in the form of single strands, independently of the hybridization position of said pair; - the denaturation phase comprises: - multiplying an elongated duplex concentration vector, resulting from the application of the elongation phase to the duplex concentrations, by a denaturation tensor of the elongated duplexes ( ^̿^; ^ ∗^) in order to obtain an initial value of a vector of concentrations of a plurality of nucleic acid molecules in the form of single strands for the following cycle.

2. Method according to the preceding claim, in which: - at least one duplex results from the pairing between two primers; - the elongation phase simulates the concentration of each duplex resulting from the pairing between two primers into a single concentration of elongated duplex resulting from the pairing between two primers; - the coefficients of the denaturation tensor are defined so as to distribute each concentration of elongated duplex resulting from the pairing between two primers into nucleic acid molecules in the form of single strands corresponding to an elongation of the duplex resulting from the pairing between the two primers in both directions.

3. A method according to the preceding claim, wherein, for each hybridization reaction between two primers: - the concentrations of elongated duplexes comprise a concentration of an elongated virtual duplex equal to the sum of the concentrations of the elongated duplexes formed by the elongation in each of the two directions of the duplexes formed by the hybridization of the two primers; - the coefficients of the denaturation tensor of the elongated duplexes corresponding to the distribution of the concentration of the elongated virtual duplex towards each of the two primers, and each of the two nucleic acids in the form of single strands resulting from the elongation in one of the two directions are all equal to 0.

5.

4. A method according to any one of the preceding claims, wherein,for each set of multiple hybridization reactions of a single-stranded nucleic acid by a primer at several locations respectively: - the concentrations of duplexes and the concentrations of elongated duplexes respectively comprise a concentration of a virtual duplex equal to the sum of the concentrations of the duplexes formed by the multiple hybridization reactions,and a concentration of an elongated virtual duplex equal to the sum of the concentrations of the elongated duplexes formed by the elongation of the duplexes formed by the multiple hybridization reactions; - the coefficients of the denaturation tensor of the elongated duplexes corresponding to the distribution of the concentration of the elongated virtual duplex towards each single-stranded nucleic acid associated with one of the multiple hybridization reactions are respectively equal to the ratio between the interaction energy of the multiple hybridization reaction divided by the sum of the interaction energies of all the multiple hybridization reactions with said single-stranded nucleic acid.

5. A method according to any one of the preceding claims,wherein the elongation phase comprises: - obtaining the concentrations of the elongated duplexes by multiplying the concentrations of the duplexes by elongation coefficients.

6. Method according to the preceding claim, wherein: - the elongation phase further comprises updating the duplex concentration vector, representing at the end of the elongation phase the concentration of the non-elongated duplexes;, - the denaturation phase further comprises the multiplication of said duplex concentration vector by a denaturation tensor of the non-elongated duplexes ( ^̿^ ^^) to update the initial value for the next cycle of the concentration vector of the plurality of nucleic acid molecules in the form of single strands.

7. Method according to the preceding claim, in which, during the denaturation phase, the same denaturation coefficient is applied to a non-elongated duplex and to the corresponding elongated duplex to update the concentration vector of the plurality of nucleic acid molecules in the form of single strands, and the duplex concentrations for the next cycle.

8. Method (P8) according to any one of the preceding claims, comprising a subsequent step of validating (S83) or modifying (S84) the plurality of primers and the initial value of the concentration vector for said plurality of primers in the first cycle of the reaction by comparing (S82) a value representative of the kinetics of a reaction to a threshold.

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

10. A kit for polymerase chain reaction manufactured by the method according to the preceding claim.

11. A computer program comprising instructions for implementing the method according to one of claims 1 to 8 when this program is executed by a processor.

12. A non-transitory recording medium readable by a computer on which is recorded a program for implementing the method according to one of claims 1 to 8 when this program is executed by a processor.

13. A method for characterizing microorganisms included in a sample, comprising:. − Preparing the sample so as to perform a PCR on the prepared sample, said preparation comprising a step of adding a kit manufactured in accordance with a method of claim 1 to 8; − Carrying out the PCR on the prepared sample. − Characterizing the microorganisms according to the results of the PCR.

14. The method of claim 13, wherein the sample is taken from an animal or a human being, said method comprising choosing an antimicrobial according to the characterization of the microorganisms present in said sample, and administering said antimicrobial to said animal or human being.

15. The method of claim 13, wherein the sample is taken from an inanimate object, said method comprising choosing an antimicrobial according to the characterization of the microorganisms present in said sample, and applying said antimicrobial to said inanimate object.

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