In the work the general methodology of control is used for obtaining the solution of the problem of optimal annealing stage in a polymerase chain reaction in order to effectively conduct the study and the possibility of providing a multi-stage cyclic regime of temperature change. The annealing stage should occur at certain temperatures and over time, because otherwise the necessary transformations of DNA molecules may not occur. The developed model of annealing stage of the polymerase chain reaction, which takes into account the ratio of the number of single-stranded DNA, primer, single-stranded DNA bound to the primer, direct and reverse reaction rate for annealing, was used. In the model under study, the Arrhenius equation is used, which takes into account the dependence of the reaction rate on absolute temperature. The principle of Pontryagin's maximum is applied to the problem of optimal control of annealing stage and the necessary optimality condition is formulated. The direct method of numerical solving of the problem of optimal annealing control, which is implemented in the package of Java classes, is developed. In the form of graphs are presented the results of numerical simulation of the problem of optimal control of the annealing stage polymerase chain reaction. The results of numerical modeling of the optimal control of the annealing stage of polymerase chain reaction for changing the number of single-stranded DNA, the number of primers, changes in the number of single-stranded DNA that are connected to the primer and the optimal temperature value of the investigated stage are constructed. The obtained results of numerical simulation of the problem of optimal control of the annealing stage of polymerase chain reaction will help to minimize the necessary time for the implementation of this stage. The scheme of temperature setting thus constructed minimizes the required time of implementation of the annealing stage, which in the general case will ensure the achievement of the minimum time for polymerase chain reaction.
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