Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation

TL;DR

This paper extends a microtubule dynamics model to include GTP-tubulin concentration dependence and nucleation effects, analyzing steady states and their stability using novel Evans function techniques.

Contribution

It introduces a generalized reaction convection diffusion model with variable rates and nucleation effects, employing new Evans function methods for stability analysis.

Findings

Existence of steady states under new model conditions

Stability criteria derived for these steady states

Application of Evans function as a novel stability analysis tool

Abstract

We generalize the Dogterom-Leibler model for microtubule dynamics [DL] to the case where the rates of elongation as well as the lifetimes of the elongating and shortening phases are a function of GTP-tubulin concentration. We study also the effect of nucleation rate in the form of a damping term which leads to new steady-states. For this model, we study existence and stability of steady states satisfying the boundary conditions at x = 0. Our stability analysis introduces numerical and analytical Evans function computations as a new mathematical tool in the study of microtubule dynamics.