Analytic results of the DNA thermal denaturation in the Peyrard-Bishop-Dauxois model

Filho, Elso Drigo; Ricotta, Regina Maria; Ribeiro, Natália Fávaro

doi:10.1088/1742-6596/1194/1/012030

Cited by 2 publications

(1 citation statement)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the case of problems that are not exactly solvable, however, it has been suggested that the variational method could be applied within the SQM formalism to evaluate the energy spectrum of diatomic molecules [3], [4]. The methodology has thus provided knowledge on quantum dots [5], nonlinear features of the Peyrard-Bishop model for the DNA [6], quantum confinement of H-bonds in the DNA [7], [8], and other algebraic potential problems, [9], including the analysis of the Fokker-Planck Equation (FPE) with a view to describing a diffusive process, such as the folding of proteins, [10], through a mapping in a Schrödinger type equation, SE, [11]- [12]. In this line the approach was applied to explore the kinetics of the time-dependent probability distributions over thermodynamic free energy profiles of protein folding, [13], and tri-stable free energy profiles to analyze the kinetics of intermediate conformations of the protein, [14].…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric Quantum Mechanics Formalism in a Modeling for Protein Folding

Drigo Filho,

Chahine,

Araujo

et al. 2023

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Recently, a mathematical method was developed to analyze the kinetics of the protein folding process, considering it as a diffusion process described by the Fokker-Planck equation and its solution, the time-dependent probability density. This work presents the main points of the methodology, based on the application of the algebraic formalism of Supersymmetric Quantum Mechanics associated with the variational method, to analyze the symmetric tri-stable free energy potential function that describes the unfolded and folded states, as well as an intermediate state of the protein.

show abstract

Section: Introductionmentioning

confidence: 99%

Supersymmetric Quantum Mechanics Formalism in a Modeling for Protein Folding

Drigo Filho,

Chahine,

Araujo

et al. 2023

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

show abstract

Quantum-tunneling transitions and exact statistical mechanics of bistable systems with parametrized Dikandé–Kofané double-well potentials

2022

View full text Add to dashboard Cite

We consider a one-dimensional system of interacting particles (which can be atoms, molecules, ions, etc.), in which particles are subjected to a bistable potential the double-well shape of which is tunable via a shape deformability parameter. Our objective is to examine the impact of shape deformability on the order of transition in quantum tunneling in the bistable system, and on the possible existence of exact solutions to the transfer-integral operator associated with the partition function of the system. The bistable potential is represented by a class composed of three families of parametrized double-well potentials, whose minima and barrier height can be tuned distinctly. It is found that the extra degree of freedom, introduced by the shape deformability parameter, favors a first-order transition in quantum tunneling, in addition to the second-order transition predicted with the $$\phi ^4$$ ϕ 4 model. This first-order transition in quantum tunneling, which is consistent with Chudnovsky’s conjecture of the influence of the shape of the potential barrier on the order of thermally assisted transitions in bistable systems, is shown to occur at a critical value of the shape-deformability parameter which is the same for the three families of parametrized double-well potentials. Concerning the statistical mechanics of the system, the associate partition function is mapped onto a spectral problem by means of the transfer-integral formalism. The condition that the partition function can be exactly integrable, is determined by a criterion enabling exact eigenvalues and eigenfunctions for the transfer-integral operator. Analytical expressions of some of these exact eigenvalues and eigenfunctions are given, and the corresponding ground-state wavefunctions are used to compute the probability density which is relevant for calculations of thermodynamic quantities such as the correlation functions and the correlation lengths. Graphic Abstract

show abstract

Analytic results of the DNA thermal denaturation in the Peyrard-Bishop-Dauxois model

Cited by 2 publications

References 32 publications

Supersymmetric Quantum Mechanics Formalism in a Modeling for Protein Folding

Supersymmetric Quantum Mechanics Formalism in a Modeling for Protein Folding

Quantum-tunneling transitions and exact statistical mechanics of bistable systems with parametrized Dikandé–Kofané double-well potentials

Contact Info

Product

Resources

About