Active waves from non-reciprocity and cytoplasmic exchange

TL;DR

This study provides a generic route to the emergence of nonreciprocity-driven pulsatory patterns that can be controlled by both the strength of activity and the turnover rate, and reveals analogous pulsatory patterns on impermeable domains.

Abstract

Pattern formation in active biological matter typically arises from the feedback between chemical concentration fields and mechanical stresses. The actomyosin cortex of cells is an archetypal example of an active thin film that displays such patterns. Here, we show how pulsatory patterns emerge in a minimal model of the actomyosin cortex with a single stress-regulating chemical species that exchanges material with the cytoplasm via a linear turnover reaction. Deriving a low-dimensional amplitude-phase model, valid for a one-dimensional periodic domain and a spherical surface, we show that nonlinear waves arise from a secondary parity-breaking bifurcation that originates from the nonreciprocal interaction between spatial modes of the concentration field. Numerical analysis confirms these analytical predictions, and also reveals analogous pulsatory patterns on impermeable domains. Our study provides a generic route to the emergence of nonreciprocity-driven pulsatory patterns that can be controlled by both the strength of activity and the turnover rate.

Figures (3)

• Figure 1: Phase diagrams in the $\mathrm{P}-\mathrm{R}$ plane on a one-dimensional periodic domain, obtained from (a) the reduced model [\ref{['eq:rho1_pbc']}-\ref{['eq:phi_pbc']}], and (b) numerical solutions of the full model [\ref{['eqn:conc']}-\ref{['eqn:mom']}]. Representative kymographs of the concentration field $c(x,t)$ (in the full model) are presented in panels (c-e), along with movies in the SI supplement. Here $\mu=1$ and $\mathrm{S}=5$.
• Figure 2: Properties of active travelling waves. (a) - (d): Variation of the travelling wave speed $u$ and phase $\varphi$ with $\mathrm{R}$ and $\mathrm{P}$; the predictions of the reduced-model are compared with the results of the full model. (e)-(f) Concentration and velocity profiles of the stable asymmetric travelling wave (solid-orange) and the unstable symmetric stationary pattern (dashed-black), obtained from the full model. Here $\mathrm{S} = 5$.
• Figure 3: Phase-diagram on the surface of a sphere, obtained from (a) the reduced model, and (b) the full model. Snapshots visualizing the evolution of the concentration field obtained from the full model are presented in panels (c) and (d), along with movies in the SI supplement. Here $\mu=1$, and $\mathrm{S}=4$ (reduced model) and 2 (full model).