Hysteresis modeling for calcium-mediated ciliary beat frequency in airway epithelial cells

A hysteresis model is proposed to describe calcium-mediated Ciliary beat frequency (CBF) in airway epithelial cells. In this dynamic model, the kinetics of coupling between calcium and CBF is posited as a two-step configuration. First, Ca²+ directly binds to or indirectly acts on the axonemal proteins to modulate the activity of axonemal proteins. This step can be modeled by a Hill function in biochemistry. In the second step, the activity of axonemal proteins interacts with the sliding velocity of axonemal microtubules, the equivalent to regulating the CBF. The well-known Bouc-Wen model for hysteresis in mechanical engineering, which can only generate the stable clockwise hysteresis loops, is modified to describe the counter clockwise hysteresis loops commonly observed in the biological experiments. Based upon this new hysteresis model, the dynamic behavior of calcium-regulated CBF in epithelial airway cells is investigated through simulation studies. The numerical results demonstrate that the CBF dynamics in airway epithelial cells predicted by the hysteresis model is more consistent with the experimental observations than that predicted by previous static model in the literature.