Modeling the collective motion of microtubules driven by mobile kinesin motors

The microtubule gliding assay is a commonly used in-vitro technique to study the collective motion of microtubules as an active fluid. When computationally modeling the movement of microtubules, a spatially uniform distribution of the motor proteins is usually assumed which represents the fixed motor positions of the experiments. Inspired by recent experiments on lipid substrates, we explore a modified setup where kinesin motors are mobile and thus activity varies spatiotemporally. We use Brownian Dynamics simulations to study the collective motions of microtubules, modeled as flexible chains of particles that "self-propel" only in the vicinity of diffusing motors, which we also simulate explicitly. With these simulations, we probe the feedback between the microtubules' active phase behavior and the motors' dynamically reconfiguring activity field. We control the degree of overlap of microtubules using a modified Weeks–Chandler–Anderson potential and show that depending on the degree of overlap and the flexibility of the chains, our model predicts that gliding assays transition between an active polar state and an active nematic state. We also explore how the active phase behavior changes with the motors' diffusion constant.