Bridging the microscopic and the hydrodynamic in active filament solutions

Abstract

Ka -Filaments, microtubules, their networks, and supramolecular assemblies. PACS. 87.16.Nn -Motor proteins (myosin, kinesin dynein).Abstract. -Hydrodynamic equations for an isotropic solution of active polar filaments are derived from a microscopic mean-field model of the forces exchanged between motors and filaments. We find that a spatial dependence of the motor stepping rate along the filament is essential to drive bundle formation. A number of differences arise as compared to hydrodynamics derived (earlier) from a mesoscopic model where relative filament velocities were obtained on the basis of symmetry considerations. Due to the anisotropy of filament diffusion, motors are capable of generating net filament motion relative to the solvent. The effect of this new term on the stability of the homogeneous state is investigated.c EDP Sciences

Active gels as a description of the actin‐myosin cytoskeleton

“…An order of magnitude estimate of the stress in a three-dimensional gel is obtained by replacing L by the mesh size of the gel. A more detailed study of this liquid limit has been performed in a series of papers by Liverpool and Marchetti (Liverpool and Marchetti, 2005) in the limit where the actin concentration is very low.…”

“…This can be done in two ways. One can first write microscopic equations for actin filaments interacting with molecular motors and then coarse-grain these equations to a mesoscopic or a macroscopic scale to obtain the mechanical properties of the cytoskeleton at large length scales (Kruse and Julicher, 2000;Liverpool and Marchetti, 2005;Aranson and Tsimring, 2005). In this approach, one needs, however, a refined microscopic description of both the properties of actin filaments and the properties of molecular motors.…”

Hydrodynamics of isotropic and liquid crystalline active polymer solutions

“…In addition in this section we let α 0 =α 0 /48, α 1 =α 1 /48 and assume α 0 = α 1 = α, β 0 = β 1 = β. This approximation is justified by the estimate for these motor-induced parameters obtained in Appendix A using a microscopic model for the the motor-mediated filament interaction [29]. We consider separately the spatially varying hydrodynamic modes in each of the homogeneous states: isotropic, nematic and polarized phases.…”

Complex Spontaneous Flows and Concentration Banding in Active Polar Films

“…Using microscopic models of motor-filament coupling, it was estimated in [13] that β ≫ α in microtubules/kynesin mixtures, while β ≤ α in actomyosin systems. This suggests that in-vitro microtubules/kynesin mixtures may be the best candidate for the observation of the oscillating bands predicted here.…”