Localization of energy in two components model of microtubules under viscosity

Abstract

In this paper, our interest is to describe in a more realistic way, the pattern of energy spread in microtubule (MTs) lattice through the mechanism of modulational instability (MI). The nonlinear dynamics of MTs is modeled by two components model of microtubule (MTs) under stokes and hydrodynamical viscous forces resulting from the tangential motion of the individual dimers and relative motion of interacting dimers, respectively. The dynamical equations of dimers resulting from the hamiltonian are solved through the multiple scale expansion method in the semi discrete approximation limit. We show that the nonlinear dynamics of MTs are governed by a complex Ginzburg–Landau equation that admits solitary solutions. Linear stability analysis of MI indicates under plane-wave perturbation, the constant amplitude plane wave solution becomes unstable, resulting in the generation of modulated solitary waves called breathers. Numerical analyzes show that viscosity factor promotes the formation of solitary excitations that assists energy spread in the lattice. It is thought that this excitation could initiates kinesin walk in MT-associated proteins system. This result shows that under electromechanical vibrations of MTs under viscosity factor, breathers are generated, which serves as signaling pathways in cells.