Análise da divergência na integral de transferência do modelo Peyrard-Bishop de DNA

The Peyrard-Bishop model is a classical approach to describe the molecular interaction in DNA and RNA, where the double strand is considered as perfectly flat, without the characteristic helical torsion. The model Hamiltonian has two potential terms, one which describes the interaction between the b...

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Detalles Bibliográficos
Autor: Mateus Rodrigues Leal
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2016
País:Brasil
Institución:Universidade Federal de Minas Gerais (UFMG)
Repositorio:Repositório Institucional da UFMG
Idioma:portugués
OAI Identifier:oai:repositorio.ufmg.br:1843/BUBD-AA8ETR
Acceso en línea:http://hdl.handle.net/1843/BUBD-AA8ETR
Access Level:acceso abierto
Palabra clave:Modelo Peyrard-Bishop
Convergência da integral de transferência
Modelos estatísticos de DNA
modelo Peyrard-Bishop
convergência da integral de transferencia
modelos estatísticos de DNA
Física
Descripción
Sumario:The Peyrard-Bishop model is a classical approach to describe the molecular interaction in DNA and RNA, where the double strand is considered as perfectly flat, without the characteristic helical torsion. The model Hamiltonian has two potential terms, one which describes the interaction between the bases and another taking into account the stacking between base pairs. The partition function, for a string of N pairs in DNA, results in a multiple integral of 2N variables. Using the transfer integral technique, this multiple integral can be reduced to an eigenvalue problem of dimension N with just one integral of one variable. However,for the Peyrard-Bishop Hamiltonian the form of the potentials causes a numerical divergence problem which is usually circumvented by simply truncating the integral limits. Here, we study in detail the numerical divergence of several variants of the Hamiltonian and also a mathematical method proposed recently to bypass the divergence by mapping the integral to 3D. We show that the addition of a term of torsion in the stacking potential eliminates the divergence. The conditions for the potentials to be convergent were obtained from the analysis of the transfer integral.