A Versatile Framework for Simulating the Dynamic Mechanical Structure of Cytoskeletal Networks

Abstract

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.

Filament Rigidity and Connectivity Tune the Deformation Modes of Active Biopolymer Networks

“…To elucidate the microscopic deformation modes underlying contraction in networks with varying filament rigidity, we use agent-based simulations (34). In brief, we model actin filaments as wormlike chains interacting with cross-linkers and motors represented as linear springs with two sites (heads) that can attach and detach to the filaments via a Monte Carlo procedure.…”

Mechanical and kinetic factors drive sorting of F-actin crosslinkers on bundles

“…A simulation framework for actin and crosslinkers exhibits domain formation. Throughout this work we use AFINES (Active Filament Network Simulation), a coarse-grained molecular dynamics simulation framework built specifically for actin and ABP assemblies to investigate the mechanical properties of actin filaments and crosslinkers that might yield domain formation (schematic in Figure 1B and model details in SI: AFINES simulation) (22,23). Actin filaments are modelled as polar worm-like chains (represented as beads connected by springs) that can grow from their barbed end by increasing the rest length of the barbed end spring at a constant rate, and adding a bead when that rest length is above a threshold (as done e.g.…”

“…In the absence of filament fluctuations, we estimate θ ≈ arcsin (∆l xl /lg) where ∆l xl is the difference in length between the two crosslinkers. Since the energy cost of bending an angle θ over a distance lg for a worm-like chain is kBT Lpθ 2 /2lg (22,27), where Lp is the filament persistence length, kB is Boltzmann's constant, and T is temperature, the total energy cost to bend a filament twice is Equation (1) indicates that increasing the magnitude of mechanical parameters, such as the persistence length of filaments or the difference in length between crosslinkers, will increase the energy required to switch domain type on a filament bundle. The higher switching energy would decrease the likelihood of switching domains, and therefore increase domain lengths.…”

“…All data from this work is available from the authors upon request. Instructions and code for running and analyzing all simulations is available in the "xlink_sorting_paper" folder of https://github.com/Simfreed/AFINES (22,23). TIRF Experiments.…”

“…We model crosslinkers as Hookean springs, with two ends (heads L and R ) that can stochastically bind to and unbind from filaments. In addition to our previous implementation (22), we incorporate a bending term into the crosslinker, so that it prefers to bind perpendicularly to filaments, and have different binding rates for 1 and 2 heads. Thus, the potential energy of a crosslinker is…”