Multiscale modeling and simulation of microtubule–motor-protein assemblies

Abstract

Microtubules and motor proteins self-organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven out of equilibrium by adenosine triphosphate–consuming motor proteins. Microscopic motor activity causes polarity-dependent interactions between motor proteins and microtubules, but how these interactions yield larger-scale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubule-motor systems in which Brownian dynamics simulations of polar microtubules driven by motors are used to study microscopic organization and stresses created by motor-mediated microtubule interactions. We identify polarity-sorting and crosslink tether relaxation as two polar-specific sources of active destabilizing stress. We then develop a continuum Doi-Onsager model that captures polarity sorting and the hydrodynamic flows generated by these polar-specific active stresses. In simulations of active nematic flows on immersed surfaces, the active stresses drive turbulent flow dynamics and continuous generation and annihilation of disclination defects. The dynamics follow from two instabilities, and accounting for the immersed nature of the experiment yields unambiguous characteristic length and time scales. When turning off the hydrodynamics in the Doi-Onsager model, we capture formation of polar lanes as observed in the Brownian dynamics simulation.

Contributions of Microtubule Dynamic Instability and Rotational Diffusion to Kinetochore Capture

“…The simulations used a hybrid Brownian dynamics-kinetic Monte Carlo scheme approach based on our previous work (28)(29)(30)(31). Brownian dynamics model the diffusive random motion of MTs and KCs; kinetic Monte Carlo models the stochastic MT dynamic instability (Supporting Material).…”

Topological Defects in a Living Nematic Ensnare Swimming Bacteria

“…Active nematics exhibit a complex spatiotemporal behavior [18] and even a long-range ordering of topological defects [19]. A theoretical understanding of active nematics was achieved by particle simulations [20], phenomenological hydrodynamic models [21,22], or by asymptotic reduction of the probabilistic Boltzmann equation for interacting particles to the Ginzburg-Landau-type model [23,24]. An equilibrium nematic liquid crystal (LC) model [25,26] supplemented by a phenomenological active stress was used in a number of works [27][28][29][30][31].…”

Molecular simulations of cellular processes

“…Simulating macromolecule stability and interactions in a eukaryotic-like cell requires a large effort for the presence of localized and pervasive structures (Neri et al 2013;Smith et al 2014;Unterberger and Holzapfel 2014;Mak et al 2015Mak et al , 2016Gao et al 2015;Nguyen et al 2016;Popov et al 2016;Reddy and Sansom 2016;Chavent et al 2016;Foffano et al 2016;Niesen et al 2017;Tachikawa and Mochizuki 2017). Future investigations will be devoted to simulating dynamical processes involving the cytoskeleton and the membranes, such as the trafficking of macromolecules and vesicles to their sub-cellular localization (Miller et al 2016).…”