Motor proteins play an important
role in many biological processes
and have inspired the development of synthetic analogues. Molecular
walkers, such as kinesin, dynein, and myosin V, fulfill a diverse
set of functions including transporting cargo along tracks, pulling
molecules through membranes, and deforming fibers. The complexity
of molecular motors and their environment makes it difficult to model
the detailed dynamics of molecular walkers over long time scales.
In this work, we present a simple, three-dimensional model for a molecular
walker on a bead–spring substrate. The walker is represented
by five spherically symmetric particles that interact through common
intermolecular potentials and can be simulated efficiently in Brownian
dynamics simulations. The movement of motor protein walkers entails
energy conversion through ATP hydrolysis while artificial motors typically
rely on a local conversion of energy supplied through external fields.
We model energy conversion through rate equations for mechanochemical
states that couple positional and chemical degrees of freedom and
determine the walker conformation through interaction potential parameters.
We perform Brownian dynamics simulations for two scenarios: In the
first, the model walker transports cargo by walking on a substrate
whose ends are fixed. In the second, a tethered motor pulls a mobile
substrate chain against a variable force. We measure relative displacements
and determine the effects of cargo size and retarding force on the
efficiency of the walker. We find that, while the efficiency of our
model walker is less than for the biological system, our simulations
reproduce trends observed in single-molecule experiments on kinesin.
In addition, the model and simulation method presented here can be
readily adapted to biological and synthetic systems with multiple
walkers.