Thermodynamics of DNA with “hump” Morse potential

Abstract

Resumo: A desnaturação térmica do DNA, ou seja, a separação das duas cadeias, é um fenômeno causado pela amplitude das vibrações das bases, portanto, é necessário saber como essa separação é gerada para implementar o modelo alternativo do comportamento de fusão como uma função da sequência de nucleotídeos e terapias para combater o câncer. Propomos usar o modelo de Peyrard-Bishop (PB) de DNA não linear estendido para incluir um potencial enarmônico que represente a interação de empilhamento aromático entre n-e (n-1)-enésimos pares de bases consecutivos para tratar o problema. Nós usamos métodos de diferença finita para determinar o valor médio do deslocamento para o potencial "corcunda de Morse" do modelo Peyrard-Bishop do DNA. Mostramos como o "pseudo-Schrödinger" estendido combinado com método de diferença finita pode ser usado para obter os deslocamentos do valor médio para a desnaturação térmica do DNA com o potencial Morse "da corcunda". Palavras-chave:Método das diferenças finitas, equação pseudo-Schrödinger, "corcunda" do potencial de Morse ___________________________________________________________________________ Abstract: The thermal denaturation of DNA, i.e. the separation of the two strands is a phenomenon caused by the amplitude of the vibrations of the bases, therefore it is necessary to know how such separation is generated in order to implement alternative model of the melting behavior as a function of nucleotide sequence and therapies to combat the cancer. We propose to use the extended nonlinear Peyrard-Bishop(PB) model of DNA to include an anharmonic potential representing the aromatic stacking interaction between n-and (n-1)-th consecutive base pairs to treat the problem. We use Finite-difference methods for determine the mean value of the displacement for the "hump Morse" potential of the Peyrard-Bishop model of DNA. We show how the extended "pseudoSchrödinger" combined with finite difference method can be used to obtain the mean value displacements for the thermal denaturation of DNA with "hump" Morse potential.

Dark breather using symmetric Morse, solvent and external potentials for DNA breathing

“…We have obtained the Eigen functions of the pseudo-Schrodinger equation (12) to demonstrate that the mean value breathing of DNA is zero. The analysis is based on the reference 12 .…”

“…The fluctuations or breathing of DNA can be performed numerically using the finite difference methods. Firstly, we obtain the ground state wave function of equation (12). For estimate the mean value of the fluctuations we use the formula:…”

“…The ground state wave function for the symmetric Morse potential is symmetric in consequence the mean value of the fluctuations is approximately zero (for a review, see ref. 12).…”

Statistical mechanics of DNA mutation using SUSY quantum mechanics

“…The parameters that are used to derive the DNA denaturation temperature by statistical methods are determined experimentally [5]. The thermodynamic properties of DNA under the influence of hump-Morse potential are determined [6]. The helicoidal model of the DNA is reviewed by [7].…”

Statistical Mechanics of DNA Mutation using SUSY Quantum Mechanics

“…In work [3] the degrees of freedom of DNA strands and thermodynamics of nonlinear dynamics of DNA was explored. The crucial parameters a, D required to derive the DNA denaturation temperature by statistical methods are determined experimentally in work done by [4] In another work by [5], the thermodynamic properties of DNA under the influence of hump-Morse potential are determined. The helicoidal model of the DNA is reviewed by [6].…”