The response of the cross-bridge cycle model to oscillations in intracellular calcium: A mathematical analysis

The response of smooth muscle cells to changes in blood pressure is a large component of the processes that regulate blood flow. Models of the mechanical behaviour of smooth muscle cells normally assume that the mechanical properties of the cell are dependent upon the state of attached myosin, this being determined by a four state kinetic model. An analysis of the behaviour of this kinetic model is presented here, in particular the response to oscillations in intracellular calcium. It is shown that the amplitudes of oscillation of the states in the kinetic model drop off rapidly with frequency and that at 1 Hz are of negligible magnitude. This is found to be true for a number of different combinations of model parameters, indicating that at the cardiac driving frequency the smooth muscle cell response is solely determined by the mechanical behaviour of the cells, without any influence of the biochemical processes, i.e. the response is purely passive