Localization of the pupil trigger in insect superposition eyes

Summary In the superposition eyes of the sphingid moth Deilephila and the neuropteran Ascalaphus, adjustment to different intensities is subserved by longitudinal migrations of screening pigment in specialized pigment cells. Using ophthalmoscopic techniques we have localized the light-sensitive trigger that controls pigment position.In both species, local illumination of a small spot anywhere within the eye glow of a dark-adapted eye evokes local light adaptation in the ommatidia whose facets receive the light. Details of the response pattern demonstrate that a distal light-sensitive trigger is located axially in the ommatidium, just beneath the crystalline cone, and extends with less sensitivity deep into the clear zone. The distal trigger in Deilephila was shown to be predominantly UV sensitive, and a UV-absorbing structure, presumably the distal trigger, was observed near the proximal tip of the crystalline cone.In Ascalaphus we also found another trigger located more proximally, which causes local pigment reaction in the ommatidia whose rhabdoms are illuminated (the centre of the eye glow). The light-sensitive trigger for this response appears to be the rhabdom itself.     

The responses of Limulus optic nerve fibers to patterns of illumination on the receptor mosaic

The inhibition that is exerted mutually among receptor units (ommatidia) of the compound eye of Limulus is less for units widely separated than for those close together. This diminution of inhibition with distance is the resultant of two factors: (1) the threshold of inhibitory action increases with increasing distance between the units involved; and (2) the coefficient of inhibitory action decreases with increasing distance. The discharge of nerve impulses from ommatidia at various distances from one another may be described quantitatively by a set of simultaneous linear equations which express the excitatory effects of the illumination on each ommatidium and the inhibitory interactions between each ommatidium and its neighbors. The values of the thresholds and coefficients of inhibitory action, which appear as parameters in these equations, must be determined empirically: their dependence on distance is somewhat irregular and cannot yet be expressed in an exact general law. Nevertheless the diminution of inhibitory influences with distance is sufficiently uniform that patterns of neural response generated by various patterns of illumination on the receptor mosaic can be predicted qualitatively. Such predictions have been verified experimentally for two simple patterns of illumination: an abrupt step in intensity, and a simple gradient between two levels of intensity (the so-called Mach pattern). In each case, transitions in the pattern of illumination are accentuated in the corresponding pattern of neural response.     

Inhibition in the Limulus lateral eye in situ

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.     

Inhibition in the eye of Limulus

In the compound lateral eye of Limulus each ommatidium functions as a single receptor unit in the discharge of impulses in the optic nerve. Impulses originate in the eccentric cell of each ommatidium and are conducted in its axon, which runs without interruption through an extensive plexus of nerve fibers to become a fiber of the optic nerve. The plexus makes interconnections among the ommatidia, but its exact organization is not understood. The ability of an ommatidium to discharge impulses in the axon of its eccentric cell is reduced by illumination of other ommatidia in its neighborhood: the threshold to light is raised, the number of impulses discharged in response to a suprathreshold flash of light is diminished, and the frequency with which impulses are discharged during steady illumination is decreased. Also, the activity that can be elicited under certain conditions when an ommatidium is in darkness can be inhibited similarly. There is no evidence for the spread of excitatory influences in the eye of Limulus. The inhibitory influence exerted upon an ommatidium that is discharging impulses at a steady rate begins, shortly after the onset of the illumination on neighboring ommatidia, with a sudden deep minimum in the frequency of discharge. After partial recovery, the frequency is maintained at a depressed level until the illumination on the neighboring receptors is turned off, following which there is prompt, though not instantaneous recovery to the original frequency. The inhibition is exerted directly upon the sensitive structure within the ommatidium: it has been observed when the impulses were recorded by a microelectrode thrust into an ommatidium, as well as when they were recorded more proximally in single fibers dissected from the optic nerve. Receptor units of the eye often inhibit one another mutually. This has been observed by recording the activity of two optic nerve fibers simultaneously. The mediation of the inhibitory influence appears to depend upon the integrity of nervous interconnections in the plexus: cutting the lateral connections to an ommatidium abolishes the inhibition exerted upon it. The nature of the influence that is mediated by the plexus and the mechanism whereby it exerts its inhibitory action on the receptor units are not known. The depression of the frequency of the discharge of nerve impulses from an ommatidium increases approximately linearly with the logarithm of the intensity of illumination on receptors in its vicinity. Inhibition of the discharge from an ommatidium is greater the larger the area of the eye illuminated in its vicinity. However, equal increments of area become less effective as the total area is increased. The response of an ommatidium is most effectively inhibited by the illumination of ommatidia that are close to it; the effectiveness diminishes with increasing distance, but may extend for several millimeters. Illumination of a fixed region of the eye at constant intensity produces a depression of the frequency of discharge of impulses from a nearby ommatidium that is approximately constant, irrespective of the level of excitation of the ommatidium. The inhibitory interaction in the eye of Limulus is an integrative process that is important in determining the patterns of nervous activity in the visual system. It is analogous to the inhibitory component of the interaction that takes place in the vertebrate retina. Inhibitory interaction results in the exaggeration of differences in sensory activity from different regions of the eye illuminated at different intensities, thus enhancing visual contrast.     

Analysis of the biphasic optokinetic response in the crab Carcinus meanas

Steplike displacements of a striped pattern elicit biphasic optokinetic responses in the crab Carcinus maenas. Both the first fast phase and the second slow phase response are caused by interactions between adjacent ommatidia. The analysis of the influence of the pattern contrast revealed that both phases can only be identified by means of their time courses. On the basis of the correlation model for movement perception experiments are deviced to elicit both phases separately. For this purpose the presentation time of the pattern prior to and the duration of the interruption of the presentation during steplike displacement had to be varied, respectively, without changing the background illumination. The experimental results verified the assumption that two independent processes underlie the two phases of the response. The contribution of both subsystems to the response can be calculated according to the correlation model. Computer simulations of the step responses under closed loop conditions describe the experimental data well. The relation between step responses and responses to uniform motion of a striped pattern are discussed.     

The relevance of the brightness to visual acuity,predation, and activity of visually hunting ground-beetles (Coleoptera,Carabidae)

Summary Carabid species of the visually hunting type living in dim habitats have larger frontal ommatidia and gain their optimal visual performance with lower light intensity than species inhabiting bright places.The latter phenomenon is based upon the mechanisms of light adaptation, which reduce the acceptance angles of the ommatidia thus increasing their visual acuity. In more sensitive ommatidia adaptation occurs with lower light intensity.The differences between the species concerning the intensity dependence of their visual performance are regarded as an effect of natural selection. Thereafter an apposition eye more sensitive to light should be advantageous in a dim environment.This hypothesis has been investigated and verified by observation of the predation behaviour of Notiophilus biguttatus confronted with Collembola: From 1 to 500 lux the hunting success of the beetles increased proportionally to the light intensity.Measurements of the activity at dawn and at dusk under natural conditions showed that the beginning and the conclusion of activity are correlated with a critical level of illumination. Notiophilus biguttatus starts being active if the illumination is sufficient for successful hunting.Supported by the Deutsche ForschungsgemeinschaftSupported by the Österreichischer Forschungsrat     

Inhibitory interaction of receptor units in the eye of Limulus

The inhibition that is exerted mutually among the receptor units (ommatidia) in the lateral eye of Limulus has been analyzed by recording oscillographically the discharge of nerve impulses in single optic nerve fibers. The discharges from two ommatidia were recorded simultaneously by connecting the bundles containing their optic nerve fibers to separate amplifiers and recording systems. Ommatidia were chosen that were separated by no more than a few millimeters in the eye; they were illuminated independently by separate optical systems. The frequency of the maintained discharge of impulses from each of two ommatidia illuminated steadily is lower when both are illuminated together than when each is illuminated by itself. When only two ommatidia are illuminated, the magnitude of the inhibition of each one depends only on the degree of activity of the other; the activity of each, in turn, is the resultant of the excitation from its respective light stimulus and the inhibition exerted on it by the other. When additional receptors are illuminated in the vicinity of an interacting pair too far from one ommatidium to affect it directly, but near enough to the second to inhibit it, the frequency of discharge of the first increases as it is partially released from the inhibition exerted on it by the second (disinhibition). Disinhibition simulates facilitation; it is an example of indirect effects of interaction taking place over greater distances in the eye than are covered by direct inhibitory interconnections. When only two interacting ommatidia are illuminated, the inhibition exerted on each (decrease of its frequency of discharge) is a linear function of the degree of activity (frequency of discharge) of the other. Below a certain frequency (often different for different receptors) no inhibition is exerted by a receptor. Above this threshold, the rate of increase of inhibition of one receptor with increasing frequency of discharge of the other is constant, and may be at least as high as 0.2 impulse inhibited in one receptor per impulse discharged by the other. For a given pair of interacting receptors, the inhibitory coefficients are not always the same in the two directions of action. The responses to steady illumination of two receptor units that inhibit each other mutually are described quantitatively by two simultaneous linear equations that express concisely all the features discussed above. These equations may be extended and their number supplemented to describe the responses of more than two interacting elements.     

The electrical responses of the retinal receptors and the lamina in the visual system of the fly musca

Slow electrical responses were recorded from receptors and from the lamina of the visual pathway of the fly Musca.

1. Receptors 1 to 6 in the retinal ommatidia are identified by their response dichroic sensitivity planes. The half-width of their angular sensitivity distributions is estimated 2.5° in dark adaptation, and found not to vary with ambient illumination. The retinula cells are only excited by light that enters the eye through their overlying corneal facets.
2. The responses of the lamina show no detectable dichroic sensitivity, though in favourable cases their angular sensitivity distributions may be as narrow as those of the receptors. It is shown that these responses are excited by light that enters the six facets of the corneal projection of the single lamina cartridge synapse. The retinula fibres of passage through the lamina, originating from ommatidial cells 7 and 8, evidently do not contribute excitation to the responses.
3. It is shown that the separate responses contributed by the individual receptors of the projection are added linearly at the lamina response compartment over a wide range of light intensities.

     

Convergence of antennal and ocellar inputs in the insect brain

Summary Unitary responses were recorded from the brain of the fleshfly, Boettcherisca peregrina, during olfactory or mechanical stimulation of the antenna, and simultaneous photic stimulation of the ocelli. Convergence from the two inputs, the antenna and the ocelli, was observed. The response to antennal stimulation was facilitated by photic stimulation in most units. The responses to the antennal stimuli were facilitated greatly at the peak of the photic response. Some units responded both to ocellar illumination and antennal stimulation. Their response to antennal stimulation seemed independent of the light-condition during the light-adapted state, but was facilitated at the onset of the ocellar illumination, and occluded just after its cessation. In addition, there were some units which responded to antennal stimulation but not to the ocellar illumination; some of them also showed facilitation of the response to antennal stimulation during ocellar illumination.     

Variation of ommatidia number as a function of worker size inCamponotus pennsylvanicus (DeGeer) (Hymenoptera: Formicidae)

Summary The relation of worker size to ommatidia number was examined in the polymorphic antCamponotus pennsylvanicus (DeGeer). Linear regression described this relationship as:Y = 260.9 + 113.6×; whereYis ommatidia number andX is head width. A log-log regression described this relationship as:Y = 323.5 + 286.9*logX(r ² = 0.98). This analysis indicated an allometric relation of ommatidia number to head width, where ommatidia numbers increase at a slower rate than head width. This relationship is discussed in terms of ethotypes associated with worker morphotypes, and the possible mechanisms regulating polymorphic development.     

Visual pattern discrimination as an element of the fly's orientation behaviour

Summary The visually guided orientation behaviour of stationarily flying Musca domestica (females) has been investigated. Under such conditions, the flight activity does not influence the visual stimulus (openloop) and the tendency of a fly to orientate towards some visual object can be recorded as a yaw torque reaction (orientation response).—Orientation responses to flickering stripes reveal two different mechanisms of visual integration, namely a local flicker detecting mechanism and a specific kind of dynamic lateral interactions (Figs. 3, 5). The lateral interactions are mediated by a field of interconnections of receptors which are separated by at least 4 to 6 vertical rows of ommatidia (Figs. 3, 8). While stimulation of not more than 3 vertical rows of ommatidia activates only flicker detection, stimuli of more than 6° width may in addition exert an excitatory or an inhibitory influence as a consequence of the associated nonlinear interactions (Figs. 5, 7). The relevance of these lateral interactions for tracking and chasing behaviour is discussed. It is suggested that the fly's visual pattern discrimination rests essentially on these lateral interactions.     

THE VISUAL ACUITY OF THE HONEY BEE

1. Bees respond by a characteristic reflex to a movement in their visual field. By confining the field to a series of parallel dark and luminous bars it is possible to determine the size of bar to which the bees respond under different conditions and in this way to measure the resolving power or visual acuity of the eye. The maximum visual acuity of the bee is lower than the lowest human visual acuity. Under similar, maximal conditions the fineness of resolution of the human eye is about 100 times that of the bee. 2. The eye of the bee is a mosaic composed of hexagonal pyramids of variable apical angle. The size of this angle determines the angular separation between adjacent ommatidia and therefore sets the structural limits to the resolving power of the eye. It is found that the visual angle corresponding to the maximum visual acuity as found experimentally is identical with the structural angular separation of adjacent ommatidia in the region of maximum density of ommatidia population. When this region of maximum ommatidia population is rendered non-functional by being covered with an opaque paint, the maximum visual acuity then corresponds to the angular separation of those remaining ommatidia which now constitute the maximum density of population. 3. The angular separation of adjacent ommatidia is much smaller in the vertical (dorso-ventral) axis than in the horizontal (anterio-posterior) axis. The experimentally found visual acuity varies correspondingly. From this and other experiments as well as from the shape of the eye itself, it is shown that the bee''s eye is essentially an instrument for uni-directional visual resolution, functional along the dorso-ventral axis. The resolution of the visual pattern is therefore determined by the vertical angular separation of those ocular elements situated in the region of maximum density of ommatidia population. 4. The visual acuity of the bee varies with the illumination in much the same way that it does for the human eye. It is low at low illuminations; as the intensity of illumination increases it increases at first slowly and then rapidly; and finally at high intensities it becomes constant. The resolving power of a structure like the bee''s eye depends on the distance which separates the discrete receiving elements. The data then mean that at low illuminations the distance between receiving elements is large and that this distance decreases as the illumination increases. Since such a moving system cannot be true anatomically it must be interpreted functionally. It is therefore proposed that the threshold of the various ommatidia are not the same but that they vary as any other characteristic of a population. The visual acuity will then depend on the distance apart of those elements whose thresholds are such that they are functional at the particular illumination under investigation. Taking due consideration of the angular separation of ommatidia it is possible to derive a distribution curve for the thresholds of the ommatidia which resembles the usual probability curves, and which describes the data with complete fidelity.     

Die Verarbeitung stationärer optischer Nachrichten im Komplexauge von Limulus

Summary The functional properties of the processing of visual information by the complex eye of Limulus was studied. The spatial distribution of activity that results in the optic nerve when the Limulus eye is exposed to a stationary optical pattern depends upon the transfer characteristics of two subsystems: the dioptric apparatus and the nervous interactions comprising the lateral inhibition system. — The transfer characteristic of the dioptric apparatus is determined by the sensitivity distribution function of single ommatidia. This distribution was measured and found to be approximately of Gauss-function type. The sensitivity falls off to 1/e at a distance of one ommatidium; thus the visual fields of adjacent ommatidia strongly overlap. As a consequence of the overlap, amplitudes of the spatial Fourier components, of which the brightness distribution of the optical surround is made up, are more and more reduced with increasing frequency in the intensity distribution on the receptor mosaic. The amplitude of the spatial frequency 1/=0,25 ( in units of interommatidial distance) is reduced to half of the maximum value, which is attained at zero frequency. It is shown that the amplitude frequency characteristic of the sensitivity distribution function has no zeros, which means that no loss of optical information results from overlap of visual fields. Thus the resolving power of the dioptric apparatus is limited only by the number of receptors per unit area. — The transfer characteristic of the lateral inhibition system in the Limulus eye depends on the distribution of the inhibitory coefficients around the individual receptors. This distribution function was determined from excitatory responses in the optic nerve elicited by a spatial light intensity step function on the receptor mosaic. It is found that this distribution is also Gaussian in form, but decays to 1/e at a distance of eight to nine ommatidia along the major axis of the eye. The average value of the inhibitory coefficients between adjacent ommatidia was found to be 0,025. The amplitude frequency response of the inhibitory system is constant for high spatial frequencies down to 1/=0,1 while amplitudes of lower frequency sinusoids are reduced down to nearly half of the maximum value at frequency zero. The amplitude frequency characteristic of the inhibitory system ensures a one to one correspondence between the intensity distribution on the receptor mosaic and the excitation distribution in the optic nerve. The overall transfer characteristic of the eye is derived from the transfer characteristics of the dioptric apparatus and the inhibitory system. This characteristic is of bandpass type with a maximum amplitude response at a frequency of 1/=0,07. The overall transfer characteristic was independently confirmed in a separate experiment. The nature of the overall transfer characteristic shows that the inhibitory system does not exactly correct for the overlap of the visual fields of single ommatidia, which in principal the system could do if the distributions of inhibitory coefficients and ommatidia sensitivity were equal. The overall transfer characteristic of the Limulus eye garantees a one to one correspondence between patterns in the optical surround and excitation distributions in the optic nerve. — The average values of the inhibitory coefficients derived from these experiments are at least a factor ten smaller than those determined directly by other investigators. Possible explanations of this discrepency are discussed. — In a separate chapter the overall transfer characteristic for eyes submerged in water is described. It was found that this characteristic does not differ from that determined in air for the eye region which was investigated in the experiments. This result is explained by two properties of the eye which are dependent on the refractive index of the surround medium and whose influences cancel each other: the visual fields of ommatidia are reduced under water, while the divergence angles between the optical axes of adjacent ommatidia also diminish.

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This research was supported in part by the United States Air Force under Grant No. AF-EOAR-62-41 and monitored by the European Office, Office of Aerospace Research.     

Electrical responses of homing pigeon and guinea pig Purkinje cells to pineal indoleamines applied by microelectrophoresis

Summary The effects of microelectrophoretically applied melatonin (aMT), 5-methoxytryptophol (ML), 5-hydroxytryptophol (HL) and noradrenaline (NA) on the electrical activity of cerebellar Purkinje and other cells during both day- and nighttime were studied in urethane-anesthetized intact and pinealectomized homing pigeons and guinea pigs.In the intact pigeon, equal numbers of Purkinje cells were excited and inhibited by aMT and ML, whilst the responses to HL were predominantly inhibitory. The responses varied significantly depending on whether the cells were tested during the day or at night (P<0.001). Pinealectomy abolished the observed day/night differences. In intact pigeons most of the other cerebellar units were inhibited by aMT and ML, whilst HL elicited an excitation in about 50% of the units.In the guinea pig most of the Purkinje cells were inhibited by aMT and ML, whereas HL caused no response in most of the units. No significant 24-h rhythmicity in response to the indoles could be observed. The responses of the other cerebellar units were more complicated. aMT caused an excitation in most of the units, whilst the predominant response caused by ML was inhibition. Only 30% of these units responded to HL; the remainder showed no measurable responses.It is apparent from these studies that pineal indoleamines may play a modulatory role in the cerebellum.Abbreviations ECG electrocardiogram - GABA gamma-aminobutyric acid     

Localization of visual pigments within rhabdoms of the compound eye of Spodoptera exempta (Insecta,Noctuidae)

Summary In the noctuid moth Spodoptera exempta, the distribution of visual pigments within the fused rhabdoms of the compound eyes was investigated by electron microscopy. Each ommatidium regularly contains eight receptor cells belonging to three morphological types: one distal, six medial, and one basal cell (Meinecke 1981); four different visual pigments — absorption maxima at approximately 355, 465, 515, and 560 nm — are known to occur within the eye (Langer et al. 1979). The compound eyes were illuminated in situ by use of monochromatic light of different wavelengths. This illumination produced a wide scale of structural changes in the microvilli of the rhabdomeres of individual cells. Preparation of eyes by freeze-substitution revealed the structural changes in the rhabdomeres to be effects of light occurring in vivo.The degree of structural changes may be considerably different in rhabdomeres within the same ommatidium; it was found to depend on the wavelength and the duration of illumination, the intensity received by the ommatidia as well as the spectral sensitivity of the receptor cells. Therefore, it was possible to estimate the spectral sensitivities of the morphological types of receptor cells. Generally, all medial cells are green receptors and all basal cells red receptors; distal cells are blue receptors in about two-thirds of the ommatidia, while in the remaining third of them distal cells are sensitive to ultraviolet light.Supported by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 114 (Bionach)     

Relevance of the single ommatidium performance in determining the oscillatory response of the Limulus retina

The response of a healthy lateral eye of Limulus to constant, uniform and sufficiently intense light stimulation, consists of a sustained oscillatory discharge, all ommatidia firing synchronously in bursts, at intervals of about 0.2 s (Barlow and Fraioli, 1978). This response has been analysed by a computer simulation, where the performance of the single unit is described by encoder models of the integrate-and-fire type, already extensively investigated. The results obtained show that the occurrence and the time features of the oscillatory response depend on the neural models adopted.     

Analysis of the Organization and Overlap of the Visual Fields in the Compound Eye of the Honeybee (Apis mellifera)

Using the results of an optical analysis, a digital computer technique was developed to analyze the relative excitation produced by arbitrary figures at the rhabdom of the receptors of a compound eye. This technique was applied to several sets of figures for the honeybee (Apis mellifera) and a reasonable agreement was found with behavioral data. Similarly, the significance of a fixed cutoff angle for a visual field was investigated. It is concluded that overlap between neighboring ommatidia is highly significant for visual processing in the apposition eye, contrary to the assumptions of the mosaic theory.     

Ein Mechanismus zur Steuerung des Lichtflusses in den Rhabdomeren des Komplexauges von Musca

Summary In the ommatidia of Musca, the light flux transmitted by each one of the rhabdomeres of sense cells no. 1 to 6 decreases as a function of time if light falls onto these rhabdomeres. With a similar time course the light flux reflected from these rhabdomeres increases. These changes take place within a few seconds following illumination. The results have been established in the intact animal using changes in the appearance of the pseudopupil as indicator and also in surviving preparations of the eye with direct inspection of the rhabdomeres.The changes are interpreted as a consequence of interactions between pigment granules in the sense cells and electromagnetic fields induced outside the rhabdomeres by light travelling on the inside: In the dark adapted situation the granules are quite distant from the rhabdomeres, the interaction is negligible. During light adaptation the granules move close to the rhabdomeres, and as a consequence, total reflection of the light in the rhabdomere is frustrated. The relatively rapid changes in the optical characteristics of the rhabdomeres are explained by the fact that the distance, the granules have to move in order to switch from one condition to the other is in principle on the order of the wavelength of light.The results indicate, that the changes in the position of the granules are induced by the excitation of the respective sense cells themselves, for instance by the degree of their depolarisation. No interaction between the sense cells of one ommatidium nor between those of different ommatidia could be found.The function of the movement of the pigment granules is interpreted as a means to protect the sense cells no. 1 to 6 against strong illumination. — Movement of pigment granules is not induced in sense cells no. 7 and 8 with light intensities which give maximal response in sense cells no. 1 to 6.

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Wertvolle Diskussionen verdanken wir Herrn Dr. K. G. Götz sowie Herrn Prof. W. Reichardt. Wir danken Fräulein T. Wiegand für Mithilfe bei den Experimenten sowie Herrn E. Freiberg für das Fertigstellen der Abbildungen.     

On oscillatory responses of the Limulus retina

Published observations of the dynamic properties of lateral and self-inhibition in the Limulus retina lead to a non-linear integral equation for the response of ommatidia located near the center of a uniformly illuminated region. Coleman and Renninger (1976, 1978) showed that when the excitation is constant in time and the sum of the inhibitory coefficients for the illuminated region exceeds a critical value, the integral equation has a stable periodic solution describing a sustained, spatially synchronized, oscillatory response in which bursts of activity alternate with silent periods. Such spatially synchronized bursting has been observed in the Limulus retina in situ by Barlow and Fraioli (1978), using the preparation of Barlow and Kaplan (1971). Employing experimental data on the temporal dependence of lateral and self-inhibition, which were then available only for the excised eye, Coleman and Renninger calculated a value of 0.34 s for the period p of the bursting response, which is significantly above the range, 0.11–0.20 s, of values of p observed for the Limulus eye in situ. Brodie et al. (1978) have recently published measurements of the temporal dependence of lateral and self-inhibition for the in situ preparation. Here we show that when the kernel functions in Coleman and Renninger's integral equation are chosen in accord with these new data, the periodic solutions of the equation have a period of approximately 0.13s, which is in the range (0.11–0.20 s) required for agreement with experiment. Other properties of the periodic solutions, i.e., their general form and the threshold levels of inhibition required for their existence, are also in accord with published observations of the behavior of the retina in situ.     

The effects of stimulus area and intensity on the on/off ratio of some locust visual interneurones

The on- and off-discharges of three types of locust visual interneurones were recorded in response to luminous discs ranging in subtense from 0.4 to 25°. For the DCMD neurone there was a clear reciprocal relationship between ON and OFF, with large on- and small off-responses at 0.4°, and the reverse at 25° disc subtense. Most of the changeover from almost pure ON to almost pure OFF discharges occurred in the subtense range up to 2°, i.e. within the acceptance angle of one ommatidium or the angle between adjacent ommatidia. This behaviour was not found at low luminance levels, where ON and OFF followed parallel courses. These findings suggest the existence of strong inhibition, augmenting rapidly with increase in target subtense, as also with luminance as shown in separate experiments. For the DCMD the off-response had the characteristics of a simple rebound excitation, following a short period of light exposure.The other visual interneurones (M and S) behaved differently. They did not show reciprocity of ON and OFF, but instead their responses followed parallel courses with increase in subtense, resembling those of the DCMD at low luminance. Nonetheless, like the DCMD, they did show peaking of the on-response at certain subtenses and luminance, although at much higher levels. The inhibitory activity defining the responses of M and S neurones appeared much less effective than that associated with the DCMD. This could be due to greater complexity in their central connexions, of which nothing is known.