Collective States of Active Particles With Elastic Dipolar Interactions

Abstract

Many types of animal cells exert active, contractile forces and mechanically deform their elastic substrate, to accomplish biological functions such as migration. These substrate deformations provide a mechanism in principle by which cells may sense other cells, leading to long-range mechanical inter–cell interactions and possible self-organization. Here, inspired by cell mechanobiology, we propose an active matter model comprising self-propelling particles that interact at a distance through their mutual deformations of an elastic substrate. By combining a minimal model for the motility of individual particles with a linear elastic model that accounts for substrate-mediated, inter–particle interactions, we examine emergent collective states that result from the interplay of motility and long-range elastic dipolar interactions. In particular, we show that particles self-assemble into flexible, motile chains which can cluster to form diverse larger-scale compact structures with polar order. By computing key structural and dynamical metrics, we distinguish between the collective states at weak and strong elastic interaction strength, as well as at low and high motility. We also show how these states are affected by confinement within a channel geometry–an important characteristic of the complex mechanical micro-environment inhabited by cells. Our model predictions may be generally applicable to active matter with dipolar interactions ranging from biological cells to synthetic colloids endowed with electric or magnetic dipole moments.