Modeling intracellular calcium waves

Intracellular Ca2+ patterns are spatio-temporal concentration profiles. Living cells exhibit transitions from localized structures (called sparks or puffs) to traveling waves. Waves may form rotating spirals or target patterns.

The Ca2+ concentration changes by nonlinear release and uptake of cell organelles. Release is accomplished through channels with stochastic transitions between the states closed, open and inhibited. The transition rates depend on Ca2+. Channels are coupled by Ca2+ diffusion and spatially organized in clusters.

In most cells and for most channel types the dynamics of the spatial Ca2+ profile is faster than the channel dynamics because flux densities are large and diffusion time for distances of channel spacing is small. That allows to eliminate the reaction-diffusion equation for Ca2+ adiabatically. That reduces the model to an array of stochastic elements with state dependent transition rates and coupling over a distance of a few cluster spacings. We give simple rules for calculating the transition rates.

Our approach provides a generalized stochastic model to which many biologically detailed models for the different Ca2+ channel types can be reduced as long as they fulfill the requirement of time scale separation.

In the limit of large numbers of channels per channel cluster and strong spatial coupling, continuum models can be applied. With such a continuum model, we investigate the impact of increased mitochondrial Ca2+ cycling on pattern formation and stability. Experimental findings can be explained by a gap in the dispersion relation for wave trains.