Traveling waves of calcium in pancreatic acinar cells: model construction and bifurcation analysis

We construct and study a model for intracellular calcium wave propagation, with particular attention to pancreatic acinar cells. The model is based on a model of the inositol trisphosphate (IP3) receptor, which assumes that calcium modulates the binding affinity of IP3 to the receptor. Two versions of the model, one simpler than the other, are studied numerically. In both versions, solitary waves in the excitable regime arise via homoclinic bifurcations in the traveling wave equations. As the background concentration of IP3 is increased, the wave speed increases, and for some values of the IP3 concentration, the initial pulse gives rise to secondary pulses that travel in both directions. This can give rise to irregular spatio-temporal behavior, or to trains of pulses. In the simpler model, these secondary waves are related to the presence of a T-point, a heteroclinic cycle, and an associated spiral of homoclinic orbits, which terminate the branch of homoclinic orbits.