Stability analysis and discrete breather dynamics in the microtubulin lattices

Abstract

Breather is a nonlinear wave that propagates along microtubules (MTs), which are crucial for many cellular processes such as mitotic chromosome movement, intracellular transport, signalling, cell shape, and motility since depend on the hydrolysis of guanosine triphosphate (GTP), which releases energy. We look into the effects of the electric field and viscosity factors on the spread of discrete breathers along microtubules. From one end of the filament to the other, the electric field transports biologically significant information, and viscosity influences the polymerization and depolymerization of microtubules. In the present analysis, we have demonstrated that when localized modes occur at particular microtubulin lattices, several types of intrinsic surface modes exist. A linear stability analysis is also performed, and it is found that the eigenvalues strictly reside on the real and imaginary axes, supporting the stability of the generated solutions. Finally, we planned to investigate the possibility of an energy localization by breather over the microtubulin protofilament lattices.