Modelos de redes unidimensionais aplicados ao estudo termodinâmico do DNA
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Data
2013-06-18
Autores
Ribeiro, Natália Fávaro [UNESP]
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Universidade Estadual Paulista (Unesp)
Resumo
Este trabalho apresenta um estudo termodinâmico de modelos de redes unidimensionais, usados para simular o DNA. Primeiramente, o modelo de Peyrard-Bishop (PB) com o potencial “Corcunda” on site foi utilizado para analisar a termodinâmica da molécula. Com o método do operador integral de transferência foram obtidas as propriedades termodinâmicas do sistema e as soluções da equação tipo – Schrödinger que emerge desse formalismo foram determinadas pelo método variacional. Com os parâmetros do potencialnormalmente utilizados na literaturao valor obtido para a temperatura de desnaturação foi extremamente alto. Por isso, são sugeridos diferentes parâmetros para descrever a termodinâmica da molécula de DNA com esse modelo. Além disso, também é estudada uma das extensões do modelo original de PB, na qual a interação de empilhamento puramente harmônica é modificada por um potencial não harmônico. São apresentados os passos e as aproximações necessárias para determinar a equação tipo – Schrödinger com massa dependente da posição que descreve as propriedades termodinâmicas desse modelo. As soluções dessa equação são determinadas a partir de uma adaptação do método variacionalpara o estudo desse problema. Para adquirir confiança na aplicação do método na solução da equação de Schrödinger com massa dependente da posição, alguns exemplos da literatura foram resolvidos.Por fim,a termodinâmica da extensão do modelo de PB foi determinada com a aplicação desse método semi - analítico. Os resultados mostraram que é possível utilizar o método variacional para solucionar esse tipo de problema e quea transição de fase da molécula ocorre em uma temperatura compatível com a apresentada na literatura
This work shows a thermodynamical study of one-dimensional lattice models, used to simulate the DNA. The Peyrard-Bishop (PB) model with the “Hump” potential on site was used to analyze the molecule thermodynamics. The thermodynamical properties of the system were obtained with the transfer integral operator method and the solutions of the type-Schrödinger equation that emerges from the formalism were determined with the variational method. With the potential parameters normally used in the literature the obtained value to the denaturation temperature was extremely high. Because of this, it is suggested different parameters to describe the thermodynamics of the DNA molecule. Besides, it is also studied an extension of the original PB model, in which the purely harmonic stacking interaction is modified to a non-harmonic potential. The steps and necessary approximations to determine the type-Schrödinger equation with position-dependent mass that describes the thermodynamical properties of this model are shown. The solutions of this equation are determined from an adaptation of the variational method to the study of this kind of problem. To gain confidence in the application of this method in the solution of the Schrödinger equation with position-dependent mass, some examples of the literature were solved. Finally, the thermodynamic of the extension of the PB model was determined with the application of this semi-analytical method. The results showed that it is possible to use the variational method to solve this kind of problem and that the phase transition of the molecule occurs in a temperature in agreement with the one present in the literature
This work shows a thermodynamical study of one-dimensional lattice models, used to simulate the DNA. The Peyrard-Bishop (PB) model with the “Hump” potential on site was used to analyze the molecule thermodynamics. The thermodynamical properties of the system were obtained with the transfer integral operator method and the solutions of the type-Schrödinger equation that emerges from the formalism were determined with the variational method. With the potential parameters normally used in the literature the obtained value to the denaturation temperature was extremely high. Because of this, it is suggested different parameters to describe the thermodynamics of the DNA molecule. Besides, it is also studied an extension of the original PB model, in which the purely harmonic stacking interaction is modified to a non-harmonic potential. The steps and necessary approximations to determine the type-Schrödinger equation with position-dependent mass that describes the thermodynamical properties of this model are shown. The solutions of this equation are determined from an adaptation of the variational method to the study of this kind of problem. To gain confidence in the application of this method in the solution of the Schrödinger equation with position-dependent mass, some examples of the literature were solved. Finally, the thermodynamic of the extension of the PB model was determined with the application of this semi-analytical method. The results showed that it is possible to use the variational method to solve this kind of problem and that the phase transition of the molecule occurs in a temperature in agreement with the one present in the literature
Descrição
Palavras-chave
Biofísica, Biologia molecular, Termodinamica, DNA, Biophysics
Como citar
RIBEIRO, Natália Fávaro. Modelos de redes unidimensionais aplicados ao estudo termodinâmico do DNA. 2013. 89 f. Tese (doutorado) - Universidade Estadual Paulista Julio de Mesquita Filho, Instituto de Biociências, Letras e Ciências Exatas de São José do Rio Preto, 2013.