  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 ATP-consuming motor
proteins. Microscopic motor activity causes polarity-dependent interactions
between motor proteins and microtubules, but how these interactions yield such
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.
