Analytical solution of reaction-diffusion equations for calcium wave propagation in a starburst amacrine cell.
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 μm 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.
Neural Networks Research Group, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia. roman.poznanski@um.edu.my
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D025042:Amacrine Cells / Q000166:cytology / Q000187:drug effects / Q000502:physiology*; D000818:Animals; D002118:Calcium / Q000378:metabolism*; D020013:Calcium Signaling / Q000187:drug effects / Q000502:physiology*; D003198:Computer Simulation; D004058:Diffusion; D008959:Models, Neurological; D009415:Nerve Net / Q000187:drug effects / Q000502:physiology; D009433:Neural Inhibition / Q000502:physiology; D017729:Presynaptic Terminals / Q000378:metabolism; D012160:Retina / Q000166:cytology*; D014795:Visual Pathways / Q000502:physiology; D005680:gamma-Aminobutyric Acid / Q000378:metabolism / Q000494:pharmacology
D005680:gamma-Aminobutyric Acid; D002118:Calcium