The use of an "effective potential" to describe the directed motion of a two-state molecular motor.

Force generation and directed motion of molecular motors using a simple two-state model are studied in the paper. Here we consider the asymmetric and periodic potential in the model. The symmetric and periodic potential is adopted to describe the interactions between motor proteins and filaments that are periodic and polar. The flux and the slope of the effective potential as functions of the temperature and transition rates are calculated in the two-state model. The ratio of the slope of the effective potential to the flux is also calculated. It is concluded that the directed motion of motor proteins is relevant to the effective potential. The slope of the effective potential corresponds to an average force. The non-vanishing force therefore implies that detailed balance is broken in the process of transition between different states. Moreover, we compare the theoretical relationship of load force and velocity with the experimental data. It is shown that they are consistent.