Modeling traveling calcium waves in cellular structures.

We report a parametric simulation study of traveling calcium waves in two classes of cellular structures: dendrite-like processes and an idealized cell body. It is motivated by the hypothesis that calcium waves may participate in spatiotemporal sensory processing; accordingly, its objective is to elucidate the dependence of traveling wave characteristics (e.g., propagation speed and amplitude) on various anatomical and physiological parameters. The models include representations of inositol trisphosphate and ryanodine receptors (which mediate transient calcium entry into the cytoplasm from the endoplasmic reticulum), as well as other entities involved in calcium transport or reactions. These support traveling cytoplasmic calcium waves, which are fully regenerative for significant ranges of model parameters. We also observe Hopf bifurcations between stable and unstable regimes, the latter being characterized by periodic calcium spikes. Traveling waves are possible in unstable processes during phases with sufficiently high calcium levels in the endoplasmic reticulum. Damped and abortive waves are observed for some parameter values. When both receptor types are present and functional, we find wave speeds on the order of 100 to several hundred micrometers per second and cytosolic calcium transients with amplitudes of tens of micromolar; when ryanodine receptors are absent, these values are on the order of tens of micrometers per second and 1-6 micromolar. Even with significantly downgraded channel conductance, ryanodine receptors can significantly impact wave speeds and amplitudes. Receptor areal densities and the diffusion coefficient for cytoplasmic calcium are the parameters to which wave characteristics are most sensitive.