Fluctuations and randomness of movement of the bead powered by a single kinesin molecule in a force-clamped motility assay: Monte Carlo simulations.

The motility assay of K. Visscher, M. J. Schnitzer, and S. M. Block (Nature, 400:184-189, 1999) in which the movement of a bead powered by a single kinesin motor can be measured is a very useful tool in characterizing the force-dependent steps of the mechanochemical cycle of kinesin motors, because in this assay the external force applied to the bead can be controlled (clamped) arbitrarily. However, because the bead is elastically attached to the motor and the response of the clamp is not fast enough to compensate the Brownian motion of the bead, interpretation or analysis of the data obtained from the assay is not trivial. In a recent paper (Y. Chen and B. Yan, Biophys. Chem. 91:79-91, 2001), we showed how to evaluate the mean velocity of the bead and the motor in the motility assay for a given mechanochemical cycle. In this paper we extend the study to the evaluation of the fluctuation or the randomness of the velocity using a Monte Carlo simulation method. Similar to the mean, we found that the randomness of the velocity of the motor is also influenced by the parameters that affect the dynamic behavior of the bead, such as the viscosity of the medium, the size of the bead, the stiffness of the elastic element connecting the bead and the motor, etc. The method presented in this paper should be useful in modeling the kinetic mechanism of any processive motor (such as conventional kinesin and myosin V) based on measured force-clamp motility data.