Modeling density variations in two-dimensional microtubule-based active nematics

Abstract

A dense two-dimensional layer of aligned microtubules (MTs), powered by molecular motors, is a canonical laboratory model of active materials and a synthetic analog of biological systems such as bacterial turbulence, mitotic spindles, and morphogenesis. This material exhibits nematic ordering and associated topological defects, which display complex emergent dynamics, including the creation and annihilation of defects and the braiding of defects around one another in a complicated chaotic dance. Despite its prominent role in research, the MT-based active nematic material lacks a well established theoretical model that accurately captures the rich density variations prominently seen in experiments---density variations that are, in fact, the experimental signature of the nematic structure itself. The MT-system is typically modeled using two fields: the Q-tensor (encoding the order and orientation of the nematic phase) and the fluid velocity; critically, the microtubule density is assumed to be constant. This traditional model is adopted from classical Landau-de Gennes liquid crystal theory. Here, we present a fundamentally different approach to modeling MT-based active nematics that explicitly incorporates density variations, producing simulations that strongly resemble experimental videos, including the characteristic striation patterns. It also reproduces important behavior of the system confined to a circular well---behavior seen experimentally, but not captured by current theory. In crafting our model, we present an alternative to Landau-de Gennes theory for the creation and annihilation of topological defects that does not rely on the classic isotropic-nematic phase transition.