Theory of Delayed Lateral Inhibition in the Compound Eye of Limulus

Abstract

Although the magnitude of lateral inhibition in the retina of Limulus polyphemus depends strongly on the distance between ommatidia, the time of delay r between the response of one ommatidium and the consequent inhibition of another is independent of the distance between them and is approximately 0.1 sec. Moreover, experimental observations indicate that for intact undamaged retinae in intense spatially uniform illumination, the total inhibitory influence at a given ommatidium can exceed the excitation of that ommatidium. A simple theory combining these two known facts yields the following conclusions: The response of a healthy Limulus retina to an intense, temporally constant, and spatially uniform excitation e (in the usual Hartline-Ratliff units) should be a sustained synchronous oscillation of period 2T, with the mean response over one complete cycle equal to approximately 1/2 e. Under a broad class of circumstances the sustained oscillations should take the form of a succession of "bursts" and "rest periods", each of duration r. The oscillations can have, however, a fine structure in which there is repeated information about the duration and sequence of any short pulses of excitation which occurred within a time-interval of length r before the onset of steady excitation. Because it is repeated every 2r seconds, this information remains available in the retina for interaction with subsequent changes of excitation.The usually considered functional purposes for the much studied lateral inhibitory influences in the retina of the compound eye of Limulus polyphemus (1-21) are (i) enhancement of spatial contrast to facilitate edge detection (6,8,(10)(11)(12), (ii) tuning for significant spatial and temporal frequencies (13,14), and (iii) generation of special burst responses to "light off" and "on-off" stimuli (4). We here describe, in a preliminary way, theoretical considerations which indicate that, at least for the visual system of Limulus, lateral sensory inhibition in the retina of compound eyes has another purpose.Consider a compound eye of Limulus in a time-dependent field of illumination, and number 1,2,Y. . . ,M the approximately one thousand ommatidia of the eye. The response, r,(t), (at p at time t) is the rate of discharge at time t of impulses in the axon issuing from the eccentric cell of the p'th ommatidium.Following Hartline and Ratliff (3, 5) we define the excitatWion ep(t) to be the response which the p'th ommatidium would show if it were illuminated by itself in a standard state with the flux of light actually falling on it at time t -T, where T is the latent period between a change of illumination and the consequent change in the rate of firing; the standard state referred to here is one in which the p'th ommatidium is free from the effects of lateral inhibition but not the effects of light-adaptation and self-inhibition. [One may, for example, visualize the standard state as that obtained by light-adapting the entire eye and then holding all ommatidia other than the p'th in total darkn...

Inhibition in the Limulus lateral eye in situ.

“…The period of oscillation must indeed reflect the dynamic properties of both lateral inhibition and self-inhibition (Stevens, 1964;Purple and Dodge, 1965;Lange et al, 1966), but we make no attempt here to determine the relative contributions. Several theoretical aspects of the oscillatory responses have been investigated by Coleman and Renninger (1974, 1977. The response patterns they computed from a nonlinear integral equation agree qualitatively with the physiological results reported here.…”

Back to Basics: Towards Novel Computation and Arrangement of Spatial Sensory in Images

“…Actually, such hexagonal arrays are more common for animals and plants than any other geometric arrays, such as rectilinear orthogonal arrays. This is due to the need of a motion detection, which is obtained based on the local difference of light intensity between adjacent neighboring photoreceptor cells [8][9][10] using the lateral inhibition process [8,11]. Lateral inhibition is a contrast enhancement computation to exaggerate the light intensity differences of the neighboring cells; it is useful in an edge detection.…”

Coding and adaptation during mechanical stimulation in the leech nervous system

“…This time‐dependent contraction of the receptive field properties is reminiscent of lateral inhibition observed in the eye of many invertebrate species (Coleman & Renninger, 1974; Coleman, 1975) and in the vertebrate retina (Dowling & Werblin, 1971; Werblin, 1974; Cook & McRaynolds, 1998), and of similar mechanisms observed in the cochlea (Brownell et al 1985; Zhao & Santos‐Sacchi, 1999). This dynamic control of sensitivity and localisation seems to be a basic property of sensory transduction present across species and sensory modalities.…”