A Robust Mathematical Formulation for Studying Elastically Coupled Motor-Cargo Systems

Molecular motors are small, and, as a result, motor operation is dominated by high viscous friction and large thermal fluctuations from the surrounding fluid environment. The small size has made it very difficult to study the physical mechanisms of molecular motors. It is already difficult enough to see the motor itself, let alone to control the motor directly by applying an external force. In many single molecule experiments and when carrying out its biological functions, a molecular motor may be coupled elastically to a cargo that is much bigger than the motor itself. Fortunately, current experimental technologies allow us to measure the external force acting on the cargo and the position of the cargo with the precision of piconewtons and nanometers. It is not clear, however, whether the measured force and position can be simply treated as the force acting on the motor and the position of the motor itself. Thus, to interpret correctly the experimental results, we need to study the behaviors of not just the motor itself but also the elastically coupled motor-cargo systems. To facilitate the modeling study of motor-cargo systems, we must develop the corresponding numerical capability for solving the modeling equations. In this study, we develop a robust mathematical/numerical formulation for simulating elastically coupled motor-cargo systems for the full range of elasticity.