A B s a- R A c T The dynamics of the Limulus retina may be well described by the spatiotemporal transfer function, which measures the response of the eye to moving sinusoidal gratings. We consider a model for this system, which incorporates an excitatory generator potential, and self- and lateral inhibitory processes. Procedures are described which allow estimation of parameters for the model consistent with the empirical transfer function data. Transfer functions calculated from the model show good agreement with laboratory measurements, and may be used to predict accurately the response of the eye to arbitrary moving stimuli. The model allows convenient interpretation of the transfer function measurements in terms of physiological processes which underly the response of the Limulus retina.

ABSTRACT Excitatory properties of visual cells in the lateral eye of Limulus, investigated by optic nerve recordings in situ, differ significantly from the properties of cells in the classical, excised eye preparation. The differences suggest the possibility that two receptor mechanisms function in the eye in situ: one mechanism encodes low light intensities and the other responds to high intensifies. The two mechanisms enable each ommatidium to respond over an intensity range of approximately 10 log units. This hypothesis was tested by measuring the increment threshold and the spectral sensitivity, by studying light and dark adaptation, and by analyzing the variability of the impulse discharge. Although the results do not conclusively identify two receptor mechanisms, they indicate that a process or a part of a process that functions in the eye in situ is abolished by excising the eye or cutting off its blood supply.

vary moderately about a mean level. The dynamics of such a system may conveniently be summarized by means of a spatiotemporal transfer function, which describes the response of the system to moving sinusoidal gratings. The response of the system to an arbitrary stimulus may then be calculated by adding together the system's responses to suitably weighted sinusoidal stimuli. We have measured such a spatiotemporal transfer function for the Limulus eye. We have then accurately predicted, in a parameter-free calculation, the eye's response to various stimulus patterns which move across it at several different velocities.

A B s T R A C T Patterns of optic nerve activity were computed for stationary step patterns of illumination from theoretical models of lateral inhibition based on revised Hartline-Ratliff equations. The computed response patterns contain well-defined Mach bands which match closely in amplitude and shape those recorded from single optic nerve fibers of the Limulus lateral eye. Theory and experiment show that the amplitude of the Mach bands is reduced by an inhibitory nonlinearity, the width of the Mach bands is approximately equal to the lateral dimension of the inhibitory field, but the shapes of the Mach bands are poor indices of the precise configuration of the inhibitory field. Theorems are proved establishing the equivalence of Mach-band patterns for models of different dimensions and a uniqueness condition for solutions of the piecewise linear model.

ABSTRACT Inhibition in the Limulus lateral eye in situ is qualitatively similar to that in the excised eye. In both preparations ommatidia mutually inhibit one another, and the magnitude of the inhibitory effects are linear functions of the response rate of individual ommatidia. The strength of inhibition exerted between single ommatidia is also about the same for both preparations; however, stronger effects can converge on a single ommatidium in situ. At high levels of illumination of the retina in situ the inhibitory effects are often strong enough to produce sustained oscillations in the discharge of optic nerve fibers. The weaker inhibitory influences at low levels of illumination do not produce oscillations but decrease the variance of the optic nerve discharge. Thresholds for the inhibitory effects appear to be determined by both presynaptic and postsynaptic cellular processes. Our results are consistent with the idea that a single ommatidium can be inhibited by more of its neighbors in an eye in situ than in an excised eye. Leaving intact the blood supply to the eye appears to preserve the functional integrity of the retinal pathways which mediate inhibition.

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