The origins of disordered actomyosin network contraction such as in the cellular cortex remain an active topic of research. We derive an agent-based mathematical model for the evolution of two-dimensional networks. A major advantage of our approach is that it enables direct calculation of the network stress tensor, which provides a quantitative measure of contractility. Exploiting this, we use simulations of disordered networks and find that both protein friction and actin filament bending are sufficient for contraction.

Asymptotic analysis of a special case of this model implies that bending induces a geometric asymmetry that enables motors to move faster close to filament plus-ends, inhibiting expansion.

We also explore a minimal model for pattern formation through biased turnover of actin filaments. The resulting discrete-time interacting particle system can be interpreted as voter model with continuous opinion space. We fully characterise the asymptotic shape of solutions which are characterised by transient clusters.

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Last updated: 18 May 2024