2003/07/30 by Sumithra Sankararaman, Gautam I. Menon, P. B. Sunil Kumar · 5 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Mathematical Biology Tumor Growth #Microtubule and mitosis dynamics #Nonlinear Dynamics and Pattern Formation #cond-mat.soft #cond-mat.stat-mech #q-bio.SC
paper · pdf · doi:10.1103/physreve.70.031905
11 pages Latex file, 2 figures included
arxiv created 2003/07/30 · openalex publication_date 2004/09/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We model the stable self-organized patterns obtained in the nonequilibrium steady states of mixtures of molecular motors and microtubules. In experiments [Nédélec et al., Nature (London) 389, 305 (1997); Surrey et al., Science 292, 1167 (2001)] performed in a quasi-two-dimensional geometry, microtubules are oriented by complexes of motor proteins. This interaction yields a variety of patterns, including arrangements 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. For systems in which the effects of confinement can be neglected, we present a map of nonequilibrium steady states, which includes arrangements of asters and vortices separately as well as aster-vortex mixtures and fully disordered states. 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 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. We also comment on the implications of our results for experiments.