Five-Site Model for Brownian Dynamics Simulations of a Molecular Walker in Three Dimensions

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.