Mathematical model for promotion of wound closure with ATP release

To computationally investigate the recent experimental finding such that extracellular ATP release caused by exogeneous mechanical forces promote wound closure, we introduce a mathematical model, the Cellular Potts Model (CPM), which is a popular discretized model on a lattice, where the movement of a "cell" is determined by a Monte Carlo procedure. In the experiment, it was observed that there is mechanosensitive ATP release from the leading cells facing the wound gap and the subsequent extracellular Ca²⁺ influx. To model these phenomena, the Reaction-Diffusion equations for extracellular ATP and intracellular Ca²⁺ concentrations are adopted and combined with CPM, where we also add a polarity term because the cell migration is enhanced in the case of ATP release. From the numerical simulations using this hybrid model, we discuss effects of the collective cell migration due to the ATP release and the Ca²⁺ influx caused by the mechanical forces and the consequent promotion of wound closure.