Processivity and Velocity for Motors Stepping on Periodic Tracks

Processive molecular motors enable cargo transportation by assembling into dimers capable of taking several consecutive steps along a cytoskeletal filament. In the well-accepted hand-over-hand stepping mechanism the trailing motor detaches from the track and binds the filament again in leading position. This requires fuel consumption in the form of ATP hydrolysis, and coordination of the catalytic cycles between the leading and the trailing heads. However, alternative stepping mechanisms exist, including inchworm-like movements, backward steps, and foot stomps. Whether all of these pathways are coupled to ATP hydrolysis remains to be determined. Here, in order to establish the principles governing the dynamics of processive movement, we present a theoretical framework which includes all of the alternative stepping mechanisms. Our theory bridges the gap between the elemental rates describing the biochemical and structural transitions in each head, and the experimentally measurable quantities, such as velocity, processivity, and probability of backward stepping. Our results, obtained under the assumption that the track is periodic and infinite, provide expressions which hold regardless of the topology of the network connecting the intermediate states, and are therefore capable of describing the function of any molecular motor. We apply the theory to myosin VI, a motor that takes frequent backward steps, and moves forward with a combination of hand-over-hand and inchworm-like steps. Our model reproduces quantitatively various observables of myosin VI motility measured experimentally from two groups. The theory is used to predict the gating mechanism, the pathway for backward stepping, and the energy consumption as a function of ATP concentration. Significance Statement Molecular motors harness the energy released by ATP hydrolysis to transport cargo along cytoskeletal filaments. The two identical heads in the motor step alternatively on the polar track by communicating with each other. Our goal is to elucidate how the coordination between the two heads emerges from the catalytic cycles. To do so, we created a theoretical framework that allows us to relate the measurable features of motility, such as motor velocity, with the biochemical rates in the leading and trailing heads, thereby connecting biochemical activity and motility. We illustrate the efficacy of the theory by analyzing experimental data for myosin VI, which takes frequent backward steps, and moves forward by a hand-over-hand and inchworm-like steps.