Cell size, mechanical tension, and GTPase signaling in the Single Cell

TL;DR

This paper extends wave-pinning models of cell polarization to include dynamic cell size and mechanical feedback, revealing new behaviors like oscillations and changes in cell motility.

Contribution

It introduces a mathematical framework that incorporates cell size changes and mechanical tension into GTPase signaling models, expanding understanding of cell polarization dynamics.

Findings

Shrinking and growing cells can lose polarity.

Mechanical feedback influences GTPase activity and cell shape.

Novel oscillatory behaviors in Rac activity and cell size.

Abstract

Cell polarization requires redistribution of specific proteins to the nascent front and back of a eukarytotic cell. Among these proteins are Rac and Rho, members of the small GTPase family that regulate the actin cytoskeleton. Rac promotes actin assembly and protrusion of the front edge, whereas Rho activates myosin-driven contraction at the back. Mathematical models of cell polarization at many levels of detail have appeared. One of the simplest based on "wave-pinning", consists of a pair of reaction-diffusion equations for a single GTPase. Mathematical analysis of wave-pinning so far is largely restricted to static domains in one spatial dimension. Here we extend the analysis to cells that change in size, showing that both shrinking and growing cells can lose polarity. We further consider the feedback between mechanical tension, GTPase activation, and cell deformation in both static, growing, shrinking, and moving cells. Special cases (spatially uniform cell chemistry, absence or presence of mechanical feedback) are analyzed, and the full model is explored by simulations in 1D. We find a variety of novel behaviors, including "dilution-induced" oscillations of Rac activity and cell size, as well as gain or loss of polarization and motility in the model cell.