Analytical solution of reaction-diffusion equations for calcium wave propagation in a starburst amacrine cell
Document Type
Article
Publication Date
1-1-2010
Abstract
A reaction-diffusion model is presented to encapsulate calcium-induced calcium release (CICR) as a potential mechanism for somatofugal bias of dendritic calcium movement in starburst amacrine cells. Calcium dynamics involves a simple calcium extrusion (pump) and a buffering mechanism of calcium binding proteins homogeneously distributed over the plasma membrane of the endoplasmic reticulum within starburst amacrine cells. The system of reaction-diffusion equations in the excess buffer (or low calcium concentration) approximation are reformulated as a nonlinear Volterra integral equation which is solved analytically via a regular perturbation series expansion in response to calcium feedback from a continuously and uniformly distributed calcium sources. Calculation of luminal calcium diffusion in the absence of buffering enables a wave to travel at distances of 120 mu m from the soma to distal tips of a starburst amacrine cell dendrite in 100 msec, yet in the presence of discretely distributed calcium-binding proteins it is unknown whether the propagating calcium wave-front in the somatofugal direction is further impeded by endogenous buffers. If so, this would indicate CICR to be an unlikely mechanism of retinal direction selectivity in starburst amacrine cells.
Keywords
Buffer, calcium, starburst amacrine cells, directional selectivity, retina, reaction-diffusion equations, CICR-based Ca(2+) waves, fire-diffuse-fire model, endoplasmic reticulum, lumen, diffusion speed
Publication Title
Journal of Integrative Neuroscience
Volume
9
Issue
3
Publisher
Imperial College Press
Publisher Location
57 SHELTON ST, COVENT GARDEN, LONDON WC2H 9HE, ENGLAND