A hysteresis model for calcium-mediated ciliary beat frequency in airway epithelial cells

A hysteresis model is proposed to describe the calcium-regulated Cilia Beat Frequency (CBF) in airway epithelial cells. In this dynamic model, the kinetics of coupling between [Ca 2+ ]i and CBF is considered as a two-step process. First, Ca 2+ directly binds to or indirectly influences the axonemal proteins to induce the conformational changes in axonemal proteins. This process can be modeled by a Hill function in biochemistry. In the second step, the conformational changes in axonemal proteins alter the sliding velocity of axonemal microtubules, the equivalent to changing the CBF. It is assumed that the hysteresis occurs in this step, and the standard linear solid (SLS) model for describing hysteresis behavior of a viscoelastic material using a linear combination of springs and dashpots to represent elastic and viscous components, respectively, is adopted to describe this process. The dynamic behavior of the CBF is investigated through simulation studies based on the hysteresis model. The numerical results demonstrate that the CBF in airway epithelial cells predicted by the hysteresis model is more consistent with the experimental observations than that predicted by previous static model.