Deformation and finite size effects in cooperative molecular motors

Abstract

Motor protein systems have been of considerable interest lately. In these studies muscle contraction is modeled as the sliding of two filaments made of protein particles over one another, that is the sliding of the backbone filament on the track filament. In order to make the analytical analysis easy these filaments are assumed to be of infinite length or mass. This enables the understanding of the sliding of motility assays with constant velocity and generation of constant force. However, finite size in length and mass brings fluctuationsuctuations in velocity around certain values, and changes in direction through intermittent transitions. It is possible to associate time constants to this kind of behavior. It turns out that the magnitude of the time constant being created during the process is proportional to both the length of the filament and the mass of the protein particles. Deformation phenomenon stems from internally generated forces which so far has been examined as axonemal deformations. The elastic coupling of the protein particles to the backbone has been studied separately, which in fact is also related to the generation of internal forces. Instead of focusing on the axonemal deformations, we implemented an Ising-like potential contribution to our computation to study the elastic coupling which makes the computation easier. We found out that for certain range of parameters that measures the deformation strength, one attains a better motor because of more intense force generation at the expanse of getting a lower sliding velocity.