Abstract
We describe the large-scale collective behavior of solutions of polar biofilaments and stationary and mobile crosslinkers. Both mobile and stationary crosslinkers induce filament alignment promoting either polar or nematic order. In addition, mobile crosslinkers, such as clusters of motor proteins, exchange forces and torques among the filaments and render the homogeneous states unstable via filament bundling. We start from a Smoluchowski equation for rigid filaments in solutions, where pairwise crosslink-mediated interactions among the filaments yield translational and rotational currents. The large-scale properties of the system are described in terms of continuum equations for filament and motor densities, polarization, and alignment tensor obtained by coarse-graining the Smoluchovski equation. The possible homogeneous and inhomogeneous states of the systems are obtained as stable solutions of the dynamical equations and are characterized in terms of experimentally accessible parameters. We make contact with work by other authors and show that our model allows for an estimate of the various parameters in the hydrodynamic equations in terms of physical properties of the crosslinkers.
Highlights
Soft active systems are a new and exciting class of complex fluids to which energy is continuously being supplied by internal or external sources
Biology provides many examples of such systems which include cell membranes, biopolymer solutions driven by chemical reactions, collections of living cells moving on a substrate, and the cytoskeleton of eukariotic cells [1]
In this paper we describe a derivation of the hydrodynamic equation for a solution of polar filaments and both stationary and mobile crosslinkers
Summary
Soft active systems are a new and exciting class of complex fluids to which energy is continuously being supplied by internal or external sources. The cytoskeleton is a complex three-dimensional network of long filamentary proteins (mainly F-actin and microtubules) cross-linked by a variety of smaller proteins [2, 3] Among the latter are clusters of active motor proteins, such as myosin and kinesin, that transform chemical energy from the hydrolysis of ATP (adenosine tri-phosphate) into mechanical work and are capable of ”walking” along the filaments, mediating the exchange of forces between them [4, 5, 6, 7]. Active crosslinkers sort the filaments according to polarization at a rate proportional to the mean motor stepping rate This mechanism is important in the polarized state, where it yields filament advection along the direction of polarization and allows for the onset of oscillatory structures. We conclude with a discussion of open questions and a comparison with related work
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