Computer simulations can aid in understanding how collective materials properties emerge from interactions between simple constituents. Here, we introduce a coarse-grained model that enables simulation of networks of actin filaments, myosin motors, and crosslinking proteins at biologically relevant time and length scales. We demonstrate that the model qualitatively and quantitatively captures a suite of trends observed experimentally, including the statistics of filament fluctuations, mechanical responses to shear, motor motilities, and network rearrangements. We use the simulation to predict the viscoelastic scaling behavior of crosslinked actin networks, characterize the trajectories of actin in a myosin motility assay, and develop order parameters to measure contractility of a simulated actin network. The model can thus serve as a platform for interpretation and design of cytoskeletal materials experiments, as well as for further development of simulations incorporating active elements.

Molecular motors embedded within collections of actin and microtubule filaments underlie the dynamics of cytoskeletal assemblies. Understanding the physics of such motor-filament materials is critical to developing a physical model of the cytoskeleton and designing biomimetic active materials. Here, we demonstrate through experiments and simulations that the rigidity and connectivity of filaments in active biopolymer networks regulates the anisotropy and the length scale of the underlying deformations, yielding materials with variable contractility. We find that semiflexible filaments can be compressed and bent by motor stresses, yielding materials that undergo predominantly biaxial deformations. By contrast, rigid filament bundles slide without bending under motor stress, yielding materials that undergo predominantly uniaxial deformations. Networks dominated by biaxial deformations are robustly contractile over a wide range of connectivities, while networks dominated by uniaxial deformations can be tuned from extensile to contractile through cross-linking. These results identify physical parameters that control the forces generated within motor-filament arrays and provide insight into the self-organization and mechanics of cytoskeletal assemblies.

Living cells dynamically modulate the local morphologies of their actin networks to perform biological functions, including force transduction, intracellular transport, and cell division. A major challenge is to understand how diverse structures of the actin cytoskeleton are assembled from a limited set of molecular building blocks. Here we study the spontaneous self-assembly of a minimal model of cytoskeletal materials, consisting of semiflexible actin filaments, crosslinkers, and molecular motors. Using coarse-grained simulations, we demonstrate that by changing concentrations and kinetics of crosslinkers and motors, as well as filament lengths, we can generate three distinct structural phases of actomyosin assemblies: bundled, polarity-sorted, and contracted. We introduce new metrics to distinguish these structural phases and demonstrate their functional roles. We find that the binding kinetics of motors and crosslinkers can be tuned to optimize contractile force generation, motor transport, and mechanical response. By quantitatively characterizing the relationships between the modes of cytoskeletal self-assembly, the resulting structures, and their functional consequences, our work suggests new principles for the design of active materials.

In cells, actin-binding proteins (ABPs) sort to different regions to establish F-actin networks with diverse functions, including filopodia used for cell migration and contractile rings required for cell division. Recent experimental work uncovered a competition-based mechanism that may facilitate spatial localization of ABPs: binding of a short cross-linker protein to 2 actin filaments promotes the binding of other short cross-linkers and inhibits the binding of longer cross-linkers (and vice versa). We hypothesize this sorting arises because F-actin is semiflexible and cannot bend over short distances. We develop a mathematical theory and lattice models encompassing the most important physical parameters for this process and use coarse-grained simulations with explicit cross-linkers to characterize and test our predictions. Our theory and data predict an explicit dependence of cross-linker separation on bundle polymerization rate. We perform experiments that confirm this dependence, but with an unexpected cross-over in dominance of one cross-linker at high growth rates to the other at slow growth rates, and we investigate the origin of this cross-over with further simulations. The nonequilibrium mechanism that we describe can allow cells to organize molecular material to drive biological processes, and our results can guide the choice and design of cross-linkers for engineered protein-based materials.