A mathematical calcium-induced calcium-release model

Calcium plays a key role in neurons in the regulation of subcellular processes and links the electrophysiological scale with biochemical processes taking place in the cell. In this paper we present a mathematical model for neuronal Calcium induced calcium release (CICR), taking into account synaptic calcium uptake through the plasma membrane, the cytosol and its interaction with the endoplasmic reticulum through channels called Inositol-3-phosphate (IP3) and Ryanodine Receptors (RYR) that are embedded in the endoplasmic membrane. For this model study we defined a two-dimensional model environment that represents a neuronal spine including the components mentioned above. A reaction-diffusion process is coupled with a transport term on the endoplasmic membrane to regulate endoplasmic calcium sequestration and release. The model was implemented in the simulation environment UG and employs finite-volume discretization together with multigrid solvers for the numerical solution of the underlying problem. This study shows that, depending on the behavior of the endoplasmic reticulum, calcium signals are fairly restricted to the spinal area or can extend further into the dendritic branches. Furthermore we observe signal transduction faster than by passive diffusion, giving rise to the hypothesis that, under certain cytosolic-endoplasmic configurations, CICR-signals can travel faster than by passive calcium diffusion.