  The molecular motor myosin V exhibits a wide repertoire of pathways during
the stepping process, which is intimately connected to its biological function.
The best understood of these is hand-over-hand stepping by a swinging lever arm
movement toward the plus-end of actin filaments, essential to its role as a
cellular transporter. However, single-molecule experiments have also shown that
the motor "foot stomps", with one hand detaching and rebinding to the same
site, and backsteps under sufficient load. Explaining the complete taxonomy of
myosin V's load-dependent stepping pathways, and the extent to which these are
constrained by motor structure and mechanochemistry, are still open questions.
Starting from a polymer model, we develop an analytical theory to understand
the minimal physical properties that govern motor dynamics. In particular, we
solve the first-passage problem of the head reaching the target binding site,
investigating the competing effects of load pulling back at the motor, strain
in the leading head that biases the diffusion in the direction of the target,
and the possibility of preferential binding to the forward site due to the
recovery stroke. The theory reproduces a variety of experimental data,
including the power stroke and slow diffusive search regimes in the mean
trajectory of the detached head, and the force dependence of the
forward-to-backward step ratio, run length, and velocity. The analytical
approach yields a formula for the stall force, identifying the relative
contributions of the chemical cycle rates and mechanical features like the
bending rigidities of the lever arms. Most importantly, by fully exploring the
design space of the motor, we predict that myosin V is a robust motor whose
dynamical behavior is not compromised by reasonable perturbations to the
reaction cycle, and changes in the architecture of the lever arm.
