Transport memory effects on coupled nonlinear waves in microtubule dynamics

The paper examines how microtubules (MTs) function in their biological environment, focusing on soliton-breather solutions. These solutions are nonlinear localized excitations that propagate in an angular continuous model of microtubule dynamics. Our model considers competitive effects from transport memory and nonlinearity, which arise due to collisions between tubulin dimers and particulate entities during energy processing in eukaryotic cells due to the hydrolysis of guanosine triphosphate (GTP). Our mathematical approach determines that the angular displacement of a dimer is governed by a modified system of coupled complex nonlinear Schrödinger equations. Analytical solutions are obtained and propagated in the MT lattice through direct numerical simulations, and small variations in coefficients significantly impact energy processing in cytoplasmic MTs.