The effect of photoreceptor coupling and synapse nonlinearity on signal : noise ratio in early visual processing

Electrical coupling of vertebrate photoreceptors is well known to improve the signal:noise ratio in the photoreceptor layer for large-area stimuli. For example, if N photoreceptors are perfectly coupled to each other, the signal:noise ratio is improved for stimuli illuminating more than a number M = $\surd $ N of the receptors but is made worse for small-area stimuli illuminating less than M of the N receptors. Using the model of Lamb & Simon (J. Physiol., Lond. 263, 257 (1976)), which treats the photoreceptor layer as a square array of cells, each coupled through a resistive gap junction to the four cells around it, we show that the signal:noise ratio for small-area stimuli is much greater than would be expected from a model in which receptors are assumed to be perfectly coupled. Contrary to predictions made assuming perfect coupling, receptor coupling should not prevent rods from detecting single photons, but whether the single photon signal can be detected at the bipolar cell level depends on how signals are read out of the receptor layer. The signal:noise ratio in bipolar cells postsynaptic to the photoreceptor layer is determined partly by synaptic convergence and nonlinearity in synaptic transmission from receptors. If the synaptic gain decreases with light-induced receptor hyperpolarization, as is found experimentally, then receptor coupling can improve the postsynaptic signal:noise ratio for stimuli illuminating only one receptor, even though coupling decreases the presynaptic signal:noise ratio for such stimuli. Moreover, increasing the number of coupled receptors projecting to a bipolar cell can improve the signal:noise ratio for localized stimuli if the synapse is sufficiently nonlinear (although, for the degree of nonlinearity seen in lower vertebrates, synaptic convergence makes the ratio worse for the single photon event). The fact that receptor coupling and synaptic convergence can, under some circumstances, improve the signal:noise ratio in bipolar cells suggests a principle of retinal design that may compete with the requirements of high spatial resolution.