Modeling DNA thermal denaturation at the mesoscopic level

Marina Dolfin; Mirosław Lachowicz

doi:10.3934/dcdsb.2014.19.2469

Article Contents

2014, Volume 19, Issue 8: 2469-2482. Doi: 10.3934/dcdsb.2014.19.2469

This issue Previous Article An explicit coefficient criterion for the existence of positive solutions to the linear advanced equation Next Article Existence of weak solutions for non-local fractional problems via Morse theory

Modeling DNA thermal denaturation at the mesoscopic level

Marina Dolfin^1, and
Mirosław Lachowicz^2,

1.
Dep. Ingegneria Civile Informatica Edile Ambientale e Matematica Applicata, University of Messina, Contrada Di Dio, Vill. S. Agata, 98166 Messina
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: October 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 92B05, 35R09; Secondary: 35R09.

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