EPJ E - Compare Motor Models: Two-State versus Crossbridge

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Published on 18 July 2011

Rigid two-state and crossbridge are two models of motor assemblies widely used in the literature. But up to now they had never been studied and compared systematically. In cells, motor proteins use chemical energy to generate motion and forces. This thorough comparison presented in EPJE shows that theforce response to a small displacement step is similar in both models to the delayed stretch activation observed in oscillating muscles.

Motors often interact and form clusters because they are connected to a single rigid backbone. In a muscle the backbone is made by association of the motor tails. The backbone motion results from the action of all the motors, and feeds back on each motor. Previous works suggest that motor assemblies are endowed with complex dynamical properties, which may play a role in the mechanisms of heartbeat, flagellar beating, or hearing. This paper studies two models of motor assemblies: the rigid two-state model and the classical crossbridge model widely used in muscle physiology.

Both models predict spontaneous oscillations. In the rigid two-state model, they can have a "rectangular" shape or a characteristic "cusp-like" shape that resembles cardiac sarcomere and "stick-slip" oscillations. The oscillations in the vicinity of the Hopf bifurcation threshold can be much faster than the chemical cycle. This property, not found in the crossbridge model where friction slows down motion, could be important for the description of high frequency oscillations, such as insect wingbeat. Experiments based on the response of a motor assembly to a step displacement are also well described by both theories, which predict non-linear force displacement relations, delayed rise in tension and "sarcomere give". This suggests that these effects are not directly dependent on molecular details. The authors relate the collective properties of the motors to their microscopic properties accessible in single molecule experiments and they show that a three state crossbridge model predicts instabilities even in the case of an apparent load decelerated detachment rate.