Abstract:
Successful functioning of all living systems depends on several classes of
active enzymatic molecules known as biological molecular motors. They are
involved in processes that require the application of mechanical forces such as
cellular transport, muscle functioning, synthesis of proteins and nucleic acids
and many others. Experimental studies suggest that most biological molecular
motors function collectively by interacting with each other and moving along
linear tracks, from which they occasionally dissociate at specific locations.
We develop a theoretical model to investigate the multi-particle dynamics
of interacting molecular motors with local dissociations. It is specifically
stimulated by ribosomes motion along ribonucleic acid (RNA) molecules
during the protein synthesis when the ribosome complex might dissociate
into the solution by encountering a specially localized region on RNA. In our
theoretical approach, we model the dynamics of molecular motors as onedimensional totally asymmetric simple exclusion processes for interacting
particles. Using a cluster mean-field approach, which partially takes into
account the correlations in the system, stationary properties such as particle
currents, densities and phase diagrams are explicitly calculated. It is found that
the presence of local dissociations increases the number of possible stationary
phases. Furthermore, the strength of interactions between molecular motors,
the modification of transition rates due to interactions and the frequency
of dissociations strongly influence the dynamics of molecular motors. The
microscopic origin of these observations are discussed. Our theoretical
predictions are fully supported by Monte Carlo computer simulations.
