Thermodynamic Control of Activity Patterns in Cytoskeletal Networks

Abstract

We aim to identify the control principles governing the adaptable formation of non-equilibrium structures in actomyosin networks. We build a phenomenological model and predict that biasing the energy dissipated by molecular motors should effectively renormalize the motor-mediated interactions between actin filaments. Indeed, using methods from large deviation theory, we demonstrate that biasing energy dissipation is equivalent to modulating the motor rigidity and results in an aster-tobundle transition. From the simulation statistics, we extract a relation between the biasing parameter and the corresponding normalized motor rigidity. This work elucidates the relationship between energy dissipation, effective interactions, and pattern formation in active biopolymer networks, providing a control principle of cytoskeletal structure and dynamics.The actin cytoskeleton is a paradigm of adaptive biomaterials that efficiently and accurately sense various environmental inputs and respond to them [1]. This adaptive behavior is in part enabled by the rich non-equilibrium morphological states that the actin cytoskeleton can adopt by varying, for example, component concentrations [2, 3]. Indeed, actin networks have been observed in the form of contractile bundles [4], branched lamellipodium [5], and contractile mesh structures [6], among many others. These varied non-equilibrium morphological states control important biophysical properties of the cell, such as its structural integrity, motility, and signaling [7, 8].Efforts to unravel the driving forces responsible for sustaining the various non-equilibrium morphological states have relied on experiments [2, 9-13], simulations [14,15], and theory [16] of model systems with limited cytoskeletal elements. For instance, a model system composed of actin filaments and myosin motors transitions between actin bundles and asters when the actin filament lengths and myosin concentrations are varied [9]. Recent in vitro experiments with light-sensitive motors demonstrate that actin networks can be patterned when the motors are activated by light [11]. Microtubule-kinesin systems have also been shown to exhibit remarkable structural changes as component concentrations are tuned [17]. However, a thermodynamic understanding of the underlying control principles is yet to be achieved.Recent work on simple active matter systems has provided pointers to how such a non-equilibrium thermodynamic control framework could be developed using dynamical bias [18][19][20][21]. Specifically, the seminal flocking transition in a Vicsek-like model is typically achieved