Analysis of dim-light responses in rod and cone photoreceptors with altered calcium kinetics

Abstract

Rod and cone photoreceptors in the retina of vertebrates are the primary sensory neurons underlying vision. They convert light into an electrical current using a signal transduction pathway that depends on Ca^{2+} feedback. It is known that manipulating the Ca^{2+} kinetics affects the response shape and the photoreceptor sensitivity, but a precise quantification of these effects remains unclear. We have approached this task in mouse retina by combining numerical simulations with mathematical analysis. We consider a parsimonious phototransduction model that incorporates negative Ca^{2+} feedback onto the synthesis of cyclic GMP, and fast buffering reactions to alter the Ca^{2+} kinetics. We derive analytic results for the photoreceptor functioning in sufficiently dim light conditions depending on the photoreceptor type. We exploit these results to obtain conceptual and quantitative insight into how response waveform and amplitude depend on the underlying biophysical processes and the Ca^{2+} feedback. With a low amount of buffering, the Ca^{2+} concentration changes in proportion to the current, and responses to flashes of light are monophasic. With more buffering, the change in the Ca^{2+} concentration becomes delayed with respect to the current, which gives rise to a damped oscillation and a biphasic waveform. This shows that biphasic responses are not necessarily a manifestation of slow buffering reactions. We obtain analytic approximations for the peak flash amplitude as a function of the light intensity, which shows how the photoreceptor sensitivity depends on the biophysical parameters. Finally, we study how changing the extracellular Ca^{2+} concentration affects the response.