  We present a simple model for the bidirectional dynamics of actin bundles
with alternating polarities in gliding assays with non-processive myosin
motors. In the model, the bundle is represented as an elastic chain consisting
of monomers with positive and negative polarities. The motion of the bundle is
induced by the pulling forces of the underlying motors which stochastically
attach to the monomers and, depending on the polarity of the monomers, pull
them in the right or left direction. We demonstrate that perfectly a-polar
chains consisting of equal numbers of monomers with positive and negative
polarities may exhibit biased bidirectional motion with non-zero drift. This
effect is attributed to the elastic tension developed in the chain due to the
action of the myosin motors. We also show that as a result of this tension, the
attachment probability of the motors is greatly reduced and becomes strongly
dependent on the length of the chain. These surprising effects point to the
necessity of considering the elasticity of the cytoskeleton in theoretical
studies of cooperative dynamics of molecular motors.
