Bridging the microscopic and the hydrodynamic in active filament solutionsT. B. Liverpool1, 2 and M. C. Marchetti3
1 Department of Applied Mathematics, University of Leeds - Leeds LS2 9JT, UK
2 Isaac Newton Institute for Mathematical Sciences - Cambridge CB3 0EH, UK
3 Physics Department, Syracuse University - Syracuse, NY 13244, USA
received 8 June 2004; accepted in final form 27 December 2004
published online 11 February 2005
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.
87.16.Ka - Filaments, microtubules, their networks, and supramolecular assemblies.
87.16.Nn - Motor proteins (myosin, kinesin dynein).
© EDP Sciences 2005