  The Kinesin family of motor proteins are involved in a variety of cellular
processes that transport materials and generate force. With recent advances in
experimental techniques, such as optical tweezers which can probe individual
molecules, there has been an increasing interest in understanding the
mechanisms by which motor proteins convert chemical energy into mechanical
work. Here we present a mathematical model for the chemistry and three
dimensional mechanics of the Kinesin motor protein which captures many of the
force dependent features of the motor. For the elasticity of the tether that
attaches cargo to the motor we develop a method for deriving the non-linear
force-extension relationship from optical trap data. For the Kinesin heads,
cargo, and microscope stage we formulate a three dimensional Brownian Dynamics
model that takes into account excluded volume interactions. To efficiently
compute statistics from the model an algorithm is proposed that uses a two step
protocol that separates the simulation of the mechanical features of the model
from the chemical kinetics of the model. Using this approach for a bead
transported by the motor, the force dependent average velocity and randomness
parameter are computed and compared with the experimental data.
