Solitons em macromoléculas poliméricas helicoidais

Abstract

One of the challenges of Theoretical Physics is the attempt of exploring how its concepts and techniques can be applied to Biology to describe the dynamics of living matter. The complexity of the structure and organization of biological systems leads to nonlinear effects where manifestations of solitonic mechanisms are possible. An attractive way to study the propagation of vibrational energy in biopolymers such as proteins, is based on nonlinear lattices models. In the decade 1970, Davidov suggested that intramolecular vibrations modes in protein are related with interactions in the deformation of its structure and propagate along the polypeptide chain with constant velocity. This is a behavior of solitary waves (solutions of certain classes of non-linear wave equations). The basic models used to study the nonlinear dynamics of macromolecular polymer works with onedimensional anharmonic lattices. However, these molecules are three dimensional and is necessary to take into account not only longitudinal displacements but also transverse displacements of the chain. Based on the fact that, on the ground state, a macromolecular polymer takes a helical shape, we study a physical model that describes the nonlinear dynamics of polymers, in particular for a alpha-helical protein, treating with interactions between monomers of different helix, which is responsible for stabilizing the molecule’s spiral geometry. The numerical solutions of the dynamical equations obtained for this chain show that the model supports soliton solutions. We yet analyze the acceptable values of the free parameters for these solutions to exist. We show how the solutions represent a twist in the molecule and how their dynamics describes the propagation of twist along the protein chain.