Study of the DNA denaturation based on the Peyrard-Bishop-Dauxois model and recurrence quantification analysis

The aim of this work was is to study of the phase transition during thermal denaturation of DNA by the method of recurrence quantification analysis, which is the most modern and efficient approach for the analysis of complex systems. To achieve the goal, the nonlinear dynamics model of the DNA denaturation is implemented, based on the Peyrard-Bishop-Dauxois approach, which allows determining the state of DNA base pairs at an arbitrary point in time. Next, the dynamics of DNA is simulated at different temperatures, and the evolution of hydrogen bond stretching during DNA heating is studied. To analyze the results obtained, the method of recurrence quantification analysis is used, which make it possible to judge the nature of the processes occurring in the system and are of particular interest in relation to the study of nonlinear DNA dynamics, in particular phase transitions, since on the basis of their analysis it is possible to identify states of repetition and fading (laminarity), the occurrence of extreme events, the presence of hidden periodicity and cyclicity. Using this method of analysis, quantitative measures are calculated in a window shifted along the main diagonal of the recurrent plot (RP). These measures quantify fine-scale RP structures. The calculations reveal the most sensitive measures to the analysis of the process under study, with the help of which the precursors of the phase transition are determined.