Hysteresis in cross-bridge models of muscle

Sam Walcott and Sean X. Sun

A dynamical system is said to exhibit hysteresis if its current state depends on its history. Muscle shows hysteretic properties at constant length, such as residual force enhancement after stretch. There is no generally accepted explanation for residual force enhancement. Here we examine a very simple kinetic model for the interaction between actin and myosin, the two main proteins involved in muscle contraction. We demonstrate that this model shows hysteresis at constant force. Since muscle is not a continuum but rather a group of repeating elements, called sarcomeres, arranged in series, we perform simulations of three sarcomeres. These simulations show hysteresis at constant length. This result is the first time that residual force enhancement has been demonstrated using an experimentally motivated kinetic model and multi-sarcomere simulations without passive elastic elements, damping and/or force-length relationships. We conclude by suggesting some experiments to test the model's predictions. If these experiments support the model, it becomes important to understand multiple sarcomere systems, since their behavior may be very different from most current simulations that neglect the coupling between sarcomeres.

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