Biological materials, such as the actin cytoskeleton, exhibit remarkable structural adaptability to various external stimuli by consuming different amounts of energy. In this Letter, we use methods from large deviation theory to identify a thermodynamic control principle for structural transitions in a model cytoskeletal network. Specifically, we demonstrate that biasing the dynamics with respect to the work done by nonequilibrium components effectively renormalizes the interaction strength between such components, which can eventually result in a morphological transition. Our work demonstrates how a thermodynamic quantity can be used to renormalize effective interactions, which in turn can tune structure in a predictable manner, suggesting a thermodynamic principle for the control of cytoskeletal structure and dynamics.

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