2003/11/24 by Sumithra Sankararaman, Sankararaman, Sumithra, Gautam I. Menon +3
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Micro and Nano Robotics #Microtubule and mitosis dynamics #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0311540
34 pages, 10 figures included
arxiv created 2003/11/24 · openalex publication_date 2003/11/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We model the effects of confinement on the stable self-organized patterns obtained in the non-equilibrium steady states of mixtures of molecular motors and microtubules. In experiments [Nedelec et al. Nature, 389, 305 (1997); Surrey et al., Science, 292, 1167 (2001)] performed in a quasi-two-dimensional confined geometry, microtubules are oriented by complexes of motor proteins. This interaction yields a variety of patterns, including arangements of asters, vortices and disordered configurations. We model this system via a two-dimensional vector field describing the local coarse-grained microtubule orientation and two scalar density fields associated to molecular motors. These scalar fields describe motors which either attach to and move along microtubules or diffuse freely within the solvent. Transitions between single aster, spiral and vortex states are obtained as a consequence of confinement, as parameters in our model are varied. We also obtain other novel states, including ``outward asters'', distorted vortices and lattices of asters on confined systems. We calculate the steady state distribution of bound and free motors in aster and vortex configurations of microtubules and compare these to our simulation results, providing qualitative arguments for the stability of different patterns in various regimes of parameter space. We also study the role of crowding or ``saturation'' effects on the density profiles of motors in asters, discussing the role of such effects in stabilizing single asters.