In this paper, we construct a novel nonlocal transport model that describes the evolution of microtubules (MTs) as they interact with stationary distributions of motor proteins. An advection term accounts for directed MT transport (sliding due to motor protein action), and an integral term accounts for reorientation of MTs due to their interactions with cross-linking motor proteins. Simulations of our model show how MT patterns depend on boundary constraints, as well as model parameters that represent motor speed, cross-linking capability (motor activity), and directionality. In large domains, and using motor parameter values consistent with experimentally-derived values, we find that patterns such as asters, vortices, and bundles are able to persist. In vivo, MTs take on aster patterns during interphase and they form bundles in neurons and polarized epithelial cells. Vortex patterns have not been observed in vivo, however, are found in in vitro experiments. In constrained domains, we find that similar patterns form (asters, bundles, and vortices). However, we also find that when two opposing motors are present, anti-parallel bundles are able to form, resembling the mitotic spindle during cell division. This model demonstrates how MT sliding and MT reorientation are sufficient to produce experimentally observed patterns.
Microtubules Motor proteins Pattern formation Non-local model
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