# American Institute of Mathematical Sciences

October  2014, 19(8): 2469-2482. doi: 10.3934/dcdsb.2014.19.2469

## Modeling DNA thermal denaturation at the mesoscopic level

 1 Dep. Ingegneria Civile Informatica Edile Ambientale e Matematica Applicata, University of Messina, Contrada Di Dio, Vill. S. Agata, 98166 Messina, Italy 2 Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa

Received  October 2013 Revised  April 2014 Published  August 2014

In this paper a mesoscopic approach is proposed to describe the process of breaking of hydrogen bonds during the DNA thermal denaturation, also known as DNA melting. A system of integro-differential equations describing the dynamic of the variable which characterizes the opening of the base pairs is proposed. In the derivation of the model non linear effects arising from the collective behavior, namely the interactions, of base pairs are taken into account. Solutions of the mesoscopic model show significative analogies with the experimental S-shaped curves describing the fraction of broken bonds as a function of temperature at the macroscopic level, althought we instead simulate the variation in time. With this respect a research perspective connecting the theoretical results to the experimental one is proposed.
Citation: Marina Dolfin, Mirosław Lachowicz. Modeling DNA thermal denaturation at the mesoscopic level. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2469-2482. doi: 10.3934/dcdsb.2014.19.2469
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##### References:
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