Active waves from non-reciprocity and cytoplasmic exchange

TL;DR

This paper demonstrates how nonreciprocal interactions in a minimal model of the actomyosin cortex lead to pulsatory wave patterns, revealing a generic mechanism for pattern formation in active biological matter.

Contribution

The study introduces a low-dimensional amplitude-phase model showing that nonreciprocal interactions cause pulsatory patterns in active thin films, validated by numerical analysis.

Findings

Nonreciprocal interactions induce pulsatory waves.

Pattern formation depends on activity strength and turnover rate.

Patterns occur on both periodic and 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.