Polarity sorting in a bundle of actin filaments by two-headed myosins

A theoretical model is presented for sorting of the polarity of actin filaments in the presence of actin-activated ATP-hydrolysis of two-headed myosin (heavy meromyosin, HMM). In methylcellulose aqueous solution, actin filaments form a nonpolar bundlelike aggregate. Upon addition of HMM and ATP to this, the HMM-driven mutual sliding of the actin filaments is known to lead to gradual segregation of the filaments according to their polarity directions, as well as to contraction of the length of the bundle. We found crucial role of frictional drag between the actin filaments, which is not mediated by active sliding force of the two-headed myosins. We show why regions of actins with sorted polarity emerge and how they undergo coarsening in the presence of frictional drag between filaments.