Derivation of Amplitude Equations for a Mass-Conserved Reaction-Diffusion Model of Intracellular Actin Waves

by Mr. Saar Orion Modai

Dept of Physics, BGU

at Biological and soft-matter physics

Thu, 29 May 2025, 12:10
Sacta-Rashi Building for Physics (54), room 207

Abstract

Eukaryotic cells tend to form periodic and aperiodic spatiotemporal patterns involving actin, a key cytoskeletal protein that alternates through the processes between monomeric (G-actin) and polymeric (F-actin) forms. These regulated transitions appear to be related to essential functions like structural integrity and cell migration. Yet, the mechanisms involved in these intracellular actin waves (IAWs) remain poorly understood and thus, subject to vast research. From the theoretical point of view, a plausible strategy comprises reaction-diffusion (RD) models that represent a mean-field approach and allow comparison with experimental observations via bifurcation theory. Additionally, IAWs introduce a nontrivial extension to RD systems due to the mass conservation of actin monomers and, thus, require the development of distinct theoretical insights from typical RD models employed for chemical systems.

I simplify an RD model of ventral IAWs, characterized by mass conservation and positive and negative feedback interactions. The simplification of the model attempts to find a prototypical RD model with mass conservation in the spirit of the FitzHugh-Nagumo model for RD systems. The model is analyzed using linear stability, numerical simulations, continuation, and weakly nonlinear analysis of traveling wave solutions emerging from a finite wavenumber Hopf instability. The analysis is conducted for two control parameter types: the chemical rate for which the total actin mass is fixed, and total actin mass while keeping all other parameters fixed. The results show a good agreement between amplitude equations and numerical continuation, forming the basis for future work.

Created on 24-05-2025 by Feingold, Mario (mario)
Updaded on 24-05-2025 by Feingold, Mario (mario)