  The origin of biological motion can be traced back to the function of
molecular motor proteins. Cytoplasmic dynein and kinesin transport organelles
within our cells moving along a polymeric filament, the microtubule. The motion
of the myosin molecules along the actin filaments is responsible for the
contraction of our muscles. Recent experiments have been able to reveal some
important features of the motion of individual motor proteins, and a new
statistical physical description - often referred to as ``thermal ratchets'' -
has been developed for the description of motion of these molecules. In this
approach the motors are considered as Brownian particles moving along
one-dimensional periodic structures due to the effect of nonequilibrium
fluctuations. Assuming specific types of interaction between the particles the
models can be made more realistic. We have been able to give analytic solutions
for our model of kinesin with elastically coupled Brownian heads and for the
motion of the myosin filament where the motors are connected through a rigid
backbone. Our theoretical predictions are in a very good agreement with the
various experimental results. In addition, we have considered the effects
arising as a result of interaction among a large number of molecular motors,
leading to a number of novel cooperative transport phenomena.
