Exclusion and Hierarchy of Time Scales Lead to Spatial Segregation of Molecular Motors in Cellular Protrusions.

Molecular motors that carry cargo along biopolymer filaments within cells play a crucial role in the functioning of the cell. In particular, these motors are essential for the formation and maintenance of the cellular protrusions that play key roles in motility and specific functionalities, such as the stereocilia in hair cells. Typically, there are several species of motors, carrying different cargos, that share the same track. Furthermore, it was observed that in the mature stereocilia, the different motors occupy well-segregated bands as a function of distance from the tip. We use a totally asymmetric exclusion process model with two- and three-motor species, to study the conditions that give rise to such spatial patterns. We find that the well-segregated bands appear for motors with a strong hierarchy of attachment or detachment rates. This is a striking example of pattern formation in nonequilibrium, low-dimensional systems.

Traffic jams and shocks of molecular motors inside cellular protrusions.

Molecular motors are involved in key transport processes inside actin-based cellular protrusions. The motors carry cargo proteins to the protrusion tip which participate in regulating the actin polymerization and play a key role in facilitating the growth and formation of such protrusions. It is observed that the motors accumulate at the tips of cellular protrusions and form aggregates that are found to drift towards the protrusion base at the rate of actin treadmilling. We present a one-dimensional driven lattice model, where motors become inactive after delivering their cargo at the tip, or by loosing their cargo to a cargoless neighbor. The results suggest that the experimental observations may be explained by the formation of traffic jams that form at the tip. The model is solved using a novel application of mean-field and shock analysis. We find a new class of shocks that undergo intermittent collapses. Extensions with attachment and detachment events and relevance to experiments are briefly described.

Transport dynamics of molecular motors that switch between an active and inactive state.

Molecular motors are involved in key transport processes in the cell. Many of these motors can switch from an active to a nonactive state, either spontaneously or depending on their interaction with other molecules. When active, the motors move processively along the filaments, while when inactive they are stationary. We treat here the simple case of spontaneously switching motors, between the active and inactive states, along an open linear track. We use our recent analogy with vehicular traffic, where we go beyond the mean-field description. We map the phase diagram of this system, and find that it clearly breaks the symmetry between the different phases, as compared to the standard total asymmetric exclusion process. We make several predictions that may be testable using molecular motors in vitro and in living cells.