Low-dimensional manifold of actin polymerization dynamics

Abstract

Actin filaments are critical components of the eukaryotic cytoskeleton, playing important roles in a number of cellular functions, such as cell migration, organelle transport, and mechanosensation. They are helical polymers with a well-defined polarity, composed of globular subunits that bind nucleotides in one of three hydrolysis states (ATP, ADP-Pi, or ADP). Mean-field models of the dynamics of actin polymerization have succeeded in, among other things, determining the nucleotide profile of an average filament and resolving the mechanisms of accessory proteins. However, these models require numerical solution of a high-dimensional system of nonlinear ordinary differential equations. By truncating a set of recursion equations, the Brooks–Carlsson (BC) model reduces dimensionality to 11, but it still remains nonlinear and does not admit an analytical solution, hence, significantly hindering understanding of its resulting dynamics. In this work, by taking advantage of the fast timescales of the hydrolysis states of the filament tips, we propose two model reduction schemes: the quasi steady-state approximation model is five-dimensional and nonlinear, whereas the constant tip (CT) model is five-dimensional and linear, resulting from the approximation that the tip states are not dynamic variables. We provide an exact solution of the CT model and use it to shed light on the dynamical behaviors of the full BC model, highlighting the relative ordering of the timescales of various collective processes, and explaining some unusual dependence of the steady-state behavior on initial conditions.

Keywords

• actin
• polymerization dynamics
• cytoskeleton
• Drazin inverse
• polymer physics
• diffusion map