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

• Ano de defesa: 2016
• Autor(a) principal: Mateus Rodrigues Leal
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; UFMG
• Palavras-chave em Português: 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
• Link de acesso: http://hdl.handle.net/1843/BUBD-AA8ETR

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.