A Single-Chain Model to Predict Buckling in Active Gels

Abstract

We present a single-chain theory to describe the dynamics of active actin gels, driven by motor proteins. Molecular motors create active cross-links between the semiflexible filaments. We model the semiflexible filaments as bead-spring chains; the active interactions between filaments are accounted for using a mean-field approach in which filaments have prescribed probabilities to undergo a transition from one motor attachment state into the other depending on the state of the probe filament. The level of description of the model includes the change in the end-to-end distance of the filaments, the attachment state of the filaments, and the motor-generated forces, as stochastic state variables which evolve according to a proposed differential Chapman-Kolmogorov equation. The motor-generated forces are drawn from a stationary distribution of motor stall forces that can be measured experimentally. The general formulation of the model allows accounting for physics that is not possible, or not practical, to include in available models that have been postulated on coarser levels of description. To obtain analytical results that provide insight into the microscopic mechanisms underlying the dynamics of active gels we first treat the special case of filaments as one-dimensional dumbbells, approximate the elasticity of the semiflexible filaments with a Hookean spring law, and assume that the transition rates are independent of the tension in the filaments. We show that even in this simplified form, the model predicts the buckling of individual filaments that is thought to be the underlying mechanism in the self-contraction of non-sarcomeric actin-mysoin bundles [Lenz et. al., PRL 108, 238107 (2012)]. The active dumbbell model also explains the violation of the fluctuation-dissipation theorem observed in microrheology experiments on active gels [Mizuno et. al., Science 315, 370-373 (2007)].