Force { Velocity Relations of a Two { State CrossbridgeModel for Molecular

{ We discuss the force-velocity relations obtained in a two-state crossbridge model for molecular motors. They can be calculated analytically in two limiting cases: for a large number and for one pair of motors. The eeect of the strain-dependent detachment rate on the motor characteristics is studied. It can lead to linear, myosin-like, kinesin-like and anomalous curves. In particular, we specify the conditions under which oscillatory behavior may be found. Understanding the molecular mechanism underlying biological motors has recently attracted increasing interest in biology as well as in physics 1]. Motor proteins such as myosin, kinesin and dynein moving along molecular tracks are involved in a wide range of processes essential for life, e.g. cell division, muscle contraction, and intracellular transport of organelles. For many decades exclusively data from physiological measurements on muscles 2] provided experimental information for modeling molecular motors 3, 4]. In recent years, a variety of in vitro techniques allowed the observation of single motor proteins 5] and gave new insights into the basic principles underlying their operation. Not only new theoretical models for single-molecule motors 6, 7, 8, 9] were inspired by these experiments, but also new models for cooperative motors 10, 11, 13]. The theoretical models can follow two diierent goals. Either they are designed to t as many physiological experiments as possible by including many (up to six) diierent states, or one uses simpliied models (mostly with two states: attached and detached) in order to extract the generic features of motion generation and classify the motors according to their properties 10, 11]. Latter models fall into two classes, one using a speciic conformational change (power stroke) in the motor molecule 10], the other a ratchet mechanism 12, 11]. A striking result of the ratchet models was the prediction of spontaneous oscillations of cooperative motors 13], which might explain the oscillatory behavior of muscles 14]. Here we discuss the force-velocity relations of a two-state power-stroke model with strain-dependent detachment rates. Depending on the functional form of these rates, the model can show a much greater variety of phenomena than previously discussed 3, 10]. These include linear, hyperbolic, anomalous or kinesin-like force-velocity relations. In the two-state model each motor molecule has two long living states: attached and detached. This corresponds to the model described by Leibler and Huse 10] when only the time limiting steps important for mechanical properties are taken into account. Two-state models have …