Is Actin Filament and Microtubule Growth Reaction- or Diffusion-Limited?

TL;DR

This paper investigates whether actin filament and microtubule growth are limited by chemical reactions or diffusion, using a field-theory model to reconcile experimental data and predict a crossover density.

Contribution

It introduces a combined reaction-diffusion model and predicts a crossover point where growth limitation shifts from reaction to diffusion, explaining observed variances.

Findings

Identification of a crossover bulk density between reaction and diffusion limits

Estimation of how diffusion perturbs chemical reactions at filament tips

Explanation of large variances in growth speed

Abstract

Inside cells of living organisms, actin filaments and microtubules self-assemble and dissemble dynamically by incorporating actin or tubulin from the cell plasma or releasing it into their tips' surroundings. Such reaction-diffusion systems can show diffusion- or reaction-limited behaviour. However, neither limit explains the experimental data: while the offset of the linear relation between growth speed and bulk tubulin density contradicts the diffusion limit, the surprisingly large variance of the growth speed rejects a pure reaction limit. In this Letter, we accommodate both limits and use a Doi-Peliti field-theory model to estimate how diffusive transport is perturbing the chemical reactions at the filament tip. Furthermore, a crossover bulk density is predicted at which the limiting process changes from chemical reactions to diffusive transport. In addition, we explain and estimate larger variances of the growth speed.