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.
Optical imaging of dendritic calcium signals provided evidence of starburst amacrine cells exhibiting calcium bias to somatofugal motion. In contrast, it has been impractical to use a dual-patch clamp technique to record membrane potentials from both proximal dendrites and distal varicosities of starburst amacrine cells in order to unequivocally prove that they are directionally sensitive to voltage, as was first suggested almost two decades ago. This paper aims to extend the passive cable model to an active cable model of a starburst amacrine cell that is intrinsically dependent on the electrical properties of starburst amacrine cells, whose various macroscopic currents are described quantitatively. The coupling between voltage and calcium just below the membrane results in a voltage-calcium system of coupled nonlinear Volterra integral equations whose solutions must be integrated into a prescribed model for example, for a synaptic couplet of starburst amacrine cells. Networks of starburst amacrine cells play a fundamental role in the retinal circuitry underlying directional selectivity. It is suggested that the dendritic plexus of starburst amacrine cells provides the substrate for the property of directional selectivity, while directional selectivity is a property of the exclusive layerings and confinement of their interconnections within the sublaminae of the inner plexiform layer involving cone bipolar cells and directionally selective ganglion cells.