Modeling actin dynamics.

Actin monomers assemble into filaments that structurally support cells as well as drive membrane protrusion for cell movement. Within cells, some actin structures are very dynamic and turn over rapidly, while others are very stable. Even purified actin filament dynamics are complex, and researchers have often turned to mathematical models in order to interpret data, test hypotheses, make predictions, and deepen understanding. Models of actin dynamics can be broadly divided into time-dependent models and time-independent models. Most commonly, time-independent models use numerical solutions of sets of differential equations to explore the effects of key parameters on the actin cycle at steady state. Recent examples have been used to predict the nucleotide profile of steady-state filaments and to illuminate the mechanisms behind profilin's effects on actin dynamics. Time-dependent models of actin dynamics have been either Monte Carlo simulations, which track individual filaments at various levels of detail or less commonly stochastic models, which have been explored and solved analytically. These Monte Carlo and stochastic models have recently been used to investigate filament length diffusion, filament length distributions, annealing and fragmentation, and pyrene fluorescence overshoots. We do not review force production/protrusion models as they tend to reduce the complexity of actin dynamics to a single 'elongation rate' and because these models have been recently well reviewed.