1. The responses of the cockroach descending contralateral movement detector (DCMD) neurone to moving light stimuli were studied under both light- and dark-adapted conditions.

  2. With light-adaptation the response of the DCMD to two moving 2° (diam.) spots of white light is less than the response to a single spot when the two spots are separated by less than 10° (Fig. 2).

  3. With light-adaptation the response of the DCMD to a single moving light spot is a sigmoidally shaped function of the logarithm of the light intensity (Fig. 3 a). With dark-adaptation the response of a DCMD to a single moving light spot is a bell-shaped function of the logarithm of the stimulus intensity (Fig. 3b). The absolute intensity that evokes a threshold response is about one-and-a-half log units less in the dark-adapted eye than in the light-adapted eye.

  4. The decrease in the DCMD’s response that occurs when two stimuli are closer than 10°, and when a single bright stimulus is made brighter, indicates that lateral inhibition operates among the afferents to the DCMD.

  5. It is shown that this inhibition cannot be produced by a recurrent lateral inhibitory network. A model of the afferent path that contains a nonrecurrent lateral inhibitory network can account for the response/intensity plots of the DCMD recorded under both light-adapted and dark-adapted conditions.

  6. The threshold intensity of the DCMD is increased if a stationary pattern of light is present near the path of the moving spot stimulus. This is shown to be due to a peripheral tonic lateral inhibition that is distinct from the non-recurrent lateral inhibition described earlier.

  7. It is suggested that the peripheral lateral inhibition acts to adjust the threshold of afferents to local background light levels, while the proximal non-recurrent network acts to enhance the acuity of the eye to small objects in the visual field, and to filter out whole-field stimuli.

Large-field motion detector interneurones have been studied in many arthropod species (Wiersma & Yamaguchi, 1967; Bishop, Keehn & McCann, 1967; Collett, 1971; Glantz, 1974; Dvorak, Bishop & Eckert, 1975; Kien, 1975). One reason for this is that their dramatic responses to quite specific visual stimuli provide insight into the organization of that part of the visual nervous system that contains the relevant afferent pathways. This is especially true of the serially connected pair of locust visual interneurones, the lobular giant movement detector (LGMD) (O’Shea & Williams, 1974) and the descending contralateral movement detector (DCMD) (Rowell, 1971). The responses of the LGMD under specific visual stimulus regimes have helped clarify the organization of lateral inhibitory networks in the peripheral visual nervous system (Rowell & O’Shea, 1976b; Rowell, O’Shea & Williams, 1977).

Fig. 1.

Arrangement of the animal, and recording and stimulating apparatus, (a) The cockroach is mounted ventral aide up on a hemicylindrical rod. The head, legs and thorax are waxed firmly to the rod. The long axis of the head and of the compound eyes are all in the same horizontal plane, (b) Light from a tungsten lamp (T) is attenuated by a neutral density filter (ND) and focused by a lens (L) on to the tip of a fibre-optic light guide (FO). The opposite, luminous end of the light guide is moved by a carriage behind a translucent screen (TS). At either end of the excursion, the spot of light on that screen disappears as the light guide passes behind an opaque screen (OS). One eye views the spot; the other eye and the ocelli are covered with opaque wax (W). The path of motion of the spot is along a line in the same horizontal plane as the long axis of the eye. The centre of the path of the spot is 6o° lateral from directly anterior on the longitudinal body axis. This position lies in the dorsal/lateral part of the visual field of one eye. The line of the path is perpendicular to a line connecting the centre of the path with the eye. Hook electrodes record DCMD activity in the contralateral thoracic connective and convey it to recording electrodes (E).

Fig. 1.

Arrangement of the animal, and recording and stimulating apparatus, (a) The cockroach is mounted ventral aide up on a hemicylindrical rod. The head, legs and thorax are waxed firmly to the rod. The long axis of the head and of the compound eyes are all in the same horizontal plane, (b) Light from a tungsten lamp (T) is attenuated by a neutral density filter (ND) and focused by a lens (L) on to the tip of a fibre-optic light guide (FO). The opposite, luminous end of the light guide is moved by a carriage behind a translucent screen (TS). At either end of the excursion, the spot of light on that screen disappears as the light guide passes behind an opaque screen (OS). One eye views the spot; the other eye and the ocelli are covered with opaque wax (W). The path of motion of the spot is along a line in the same horizontal plane as the long axis of the eye. The centre of the path of the spot is 6o° lateral from directly anterior on the longitudinal body axis. This position lies in the dorsal/lateral part of the visual field of one eye. The line of the path is perpendicular to a line connecting the centre of the path with the eye. Hook electrodes record DCMD activity in the contralateral thoracic connective and convey it to recording electrodes (E).

Fig. 2.

Responses of the DCMDs in three animals to single and paired moving spots of light. The 2 ° spots moved across a screen at 10°/s for 5 s. •, Responses to a single spot (‘1 ‘); ◯, responses to another single spot (‘2’) that is 0 · 5 log units dimmer than the first, and moves along a parallel path 6° below the first path; □, both spots are presented simultaneously, aligned vertically and 6° apart (‘1 & 2’) ; ◼, both spots again presented simultaneously, separated by 10° (‘1 & a’). Stimuli were presented in random order, at 15 min intervals. Responses were measured as the total number of DCMD spikes during the stimulus period minus the number of DCMD spikes during the immediately previous 5 s. The animals were light-adapted (see Methods).

Fig. 2.

Responses of the DCMDs in three animals to single and paired moving spots of light. The 2 ° spots moved across a screen at 10°/s for 5 s. •, Responses to a single spot (‘1 ‘); ◯, responses to another single spot (‘2’) that is 0 · 5 log units dimmer than the first, and moves along a parallel path 6° below the first path; □, both spots are presented simultaneously, aligned vertically and 6° apart (‘1 & 2’) ; ◼, both spots again presented simultaneously, separated by 10° (‘1 & a’). Stimuli were presented in random order, at 15 min intervals. Responses were measured as the total number of DCMD spikes during the stimulus period minus the number of DCMD spikes during the immediately previous 5 s. The animals were light-adapted (see Methods).

Fig. 3.

The DCMD’s response in light-adapted and dark-adapted eyes, as a function of stimulus intensity, (a) Normalized responses of two light-adapted animals (◯, •) to a single 2° spot of light moving at 10°/s along a 50° path in the visual field. The continuous curve is the response of the model (see text) to the simulated movement of a 2° light spot across the array of 1 light-adapted ‘model photoreceptors. (Parameter values of light-adapted model photoreceptors are: Δ ρ = 2·5°; So = 0·4; g = 0·45; see Appendix 2.) (b) Responses of 14 dark-adapted animals to the same stimulus. The responses of each animal were normalized to that animal’s maximal response, and the normalized responses of the 14 animals to each intensity were averaged to yield a plot of the mean, normalized responses (±s.D.) vt. log I (•). ◯, Individual responses of 3 of the 14 animals tested. The mean of the maximal response was 185 ± 70 spikes per stimulus pass, which corresponds to 1·0 on the ordinate in (a) and (b). The continuous line is the response of the model to the same simulation as in (a), but with the model photoreceptor parameters set to ‘dark-adapted’ values (Δ ρ = 6·5°, So = 1, g = 1 ; see Appendix 2).

Fig. 3.

The DCMD’s response in light-adapted and dark-adapted eyes, as a function of stimulus intensity, (a) Normalized responses of two light-adapted animals (◯, •) to a single 2° spot of light moving at 10°/s along a 50° path in the visual field. The continuous curve is the response of the model (see text) to the simulated movement of a 2° light spot across the array of 1 light-adapted ‘model photoreceptors. (Parameter values of light-adapted model photoreceptors are: Δ ρ = 2·5°; So = 0·4; g = 0·45; see Appendix 2.) (b) Responses of 14 dark-adapted animals to the same stimulus. The responses of each animal were normalized to that animal’s maximal response, and the normalized responses of the 14 animals to each intensity were averaged to yield a plot of the mean, normalized responses (±s.D.) vt. log I (•). ◯, Individual responses of 3 of the 14 animals tested. The mean of the maximal response was 185 ± 70 spikes per stimulus pass, which corresponds to 1·0 on the ordinate in (a) and (b). The continuous line is the response of the model to the same simulation as in (a), but with the model photoreceptor parameters set to ‘dark-adapted’ values (Δ ρ = 6·5°, So = 1, g = 1 ; see Appendix 2).

The ventral nerve cord of the cockroach Periplaneta americana contains a bilateral pair of identifiable visual interneurones that are shown in the following paper (Edwards, 1982a) to be analogous to the DCMD neurones of the locust. This paper deals with the effects of lateral inhibition on the DCMD’s response.

Lateral inhibition

Lateral inhibition occurs in the visual nervous systems of many insects, including the fly (Zettler & Jarvilehto, 1971), the dragonfly (Laughlin, 1974; Frantsevich & Mokrushov, 1977), the bee (Erber & Menzel, 1977) and the locust (O’Shea & Rowell, 1975b). Because the cells that directly mediate lateral inhibition have not been identified in any insect, studies of lateral inhibition have concentrated on its effects on the visual fields and response characteristics of interneurones along the visual path. The present paper describes a set of experiments in which the response of the cockroach DCMD neurone was used to discover the effects of lateral inhibitory interactions among the visual afferents to the cell.

The cockroach DCMD neurones are a bilateral pair of large motion-sensitive interneurones, each of which has a visual field co-extensive with that of the whole of one compound eye. The DCMD cells respond to the movement of a small contrasting object with a continuous but irregular train of spikes (Edwards, 1982 a).

Visual excitation is conveyed to the DCMD of each eye by an array of parallel afferent channels (Edwards, 1982 a). Any inhibitory interactions among these afferent channels should be reflected in the response of the DCMD. Although the afferent channels cannot easily be monitored directly, the response of the DCMD neurone, which integrates the afferent excitation, can be used to infer the nature of the lateral interactions. Moreover, the response of the DCMD provides a direct measure of the global effects of a lateral inhibitory network on the two-dimensional pattern of excitation produced on the surface of the eye.

This approach has been used successfully to demonstrate that two layers of lateral inhibition are present along the afferent path to the DCMD in the locust eye (Rowell et al. 1977). The present study extends these findings to the cockroach, and examines how changes in the state of light adaptation of the eye can alter the response of the lateral inhibitory networks to particular visual stimuli.

Adult male cockroaches (Periplaneta americana) from a laboratory colony were used in all experiments. Prior to dissection, experimental animals were chilled to reduce motor activity. Hook electrodes implanted around one connective of the ventral nerve cord, usually between the pro- and mesothoracic ganglia, were used to record the spike activity of the DCMD. The animal was attached to a hemi-cylindrical aluminium rod, ventral side up, as in Fig. 1 a, so that the head and legs were immobilized, and the long axis of each compound eye was parallel to the longitudinal axis of the rod. The other end of the rod was then clamped on to a calibrated universal joint, so that the orientation of the head in space could be kept constant. The animal could be kept in this state for up to two weeks if given water and liquid food daily Recordings from the ventral nerve cord remained stable throughout this period? Spikes from the cockroach DCMD neurone are among the largest in the ventral nerve cord, but the occasional appearance of larger extraneous signals necessitated the use of a ‘window circuit’ (Model 120, W-P instruments) to ensure that only DCMD spikes were counted during the responses to visual stimuli. All experiments were performed at room temperature (20° ± 2 °C).

Light stimuli

The DCMD was stimulated by a moving spot of light provided by the luminous tip of a fibre-optic light guide (Edmund Scientific) moving behind a translucent white paper screen. The light guide was moved at a constant velocity in either direction along a linear, 15 cm path by a specially fabricated carriage. The speed could be varied continuously between 0· 5 cm/s and 10 cm/s and was monitored by the voltage dropped across a potentiometer attached to the carriage. The intensity of the light spot was measured with a calibrated photodiode (United Detector Technology, PIN 10/UV), and could be varied with neutral density filters (Eastman Kodak) between 3·54 W/cm2 and 11·2 μW/cm2.

The animal was positioned so that the stimulus path length subtended 50° at the eye, and the tip of the light guide subtended about 2° (Fig. 1b). The animal was oriented so that the longitudinal body axis was at 60° to a line perpendicular to the centre of stimulus path. The path of the light guide was in the same horizontal plane as the long axis of one of the animal’s eyes. This orientation brought the stimulus through the centre of the DCMD’s receptive field, which corresponds to the dorsolateral part of the eye, 6o° lateral from dorsal (Fig. 3, Edwards, 1982 a). The other eye and the ocelli were covered with opaque wax.

Motion of the light guide through the visual field usually evoked a brief burst of DCMD spikes at the appearance of the light (‘on’ response), an irregular, continuous discharge during the stimulus motion (movement response), and another brief burst following the disappearance of the stimulus (‘off’ response) behind an opaque screen (Edwards, 1982 a). DCMD movement response amplitudes were calculated as the total number of spikes evoked during the constant period of stimulus motion, beginning 150 ms after the appearance of stimulus ; this excluded the on and off response discharges. The spontaneous DCMD discharge that occurred during a corresponding period immediately prior to the stimulus presentation was subtracted from the original spike count to give a final value for the movement response. The stimulus velocity in these experiments was 10°/s, and so the counting period was 5 s.

In all these experiments, dark-adapted animals were stimulated in an otherwise completely darkened room; light-adapted animals were adapted to a constant level of fluorescent room lighting that was kept on during these experiments. At the experimental bench, this room lighting measured 150 μW/cm2 (Tektronix J-16 digital photometer with a J6512 irradiance head).

Computation

The model of the non-recurrent lateral inhibitory network described below was implemented in a BASIC program that contains 185 steps. The program includes seventeen 9-by-10 arrays and two 19-element vectors. The Northstar Horizon microcomputer, which has 64 Kbytes of random access memory, takes 22 min to calculate the model DCMD’s response to the stimulated motion of a fixed intensity, 2° spot across the photoreceptor array.

Inhibition excited by two moving targets

A moving light stimulus (conditioning stimulus) was used to excite afferent fibres near those stimulated by another moving light stimulus (test stimulus). Lateral interaction among the two groups of fibres was monitored by the response of the DCMD. The method is similar to that using stationary stimuli to study lateral inhibition in the optic nerve of Limulus (Hartline, Wagner & Ratliff, 1956).

The test stimulus that was presented to the light-adapted animal (see Methods) was a 2° spot of white light that moved through 50°across a white screen at 10°/s. The conditioning stimulus was a dimmer spot (– 0·5 log units) of the same diameter that moved across the screen along a parallel path at the same speed. When the two spots were presented simultaneously, separated by either 6° or 10°, their centres were aligned perpendicular to their direction of motion.

Each of the four stimulus centrifugations (test alone, conditioning alone, test and conditioning separated by 6° or by 10°) created a different pattern of stimulation in the array of photoreceptors of the eye. The normalized effective light intensities on the photoreceptors in the array of ommatidia of the eye produced by these patterns were calculated (Appendix 1) from published values of the photoreceptor acceptance angle (Δ ρ = 2·5°, Butler & Horridge, 1973a) and the interommatidial angle (· = 3°, Butler, 1973). The values for the photoreceptors in one row of ommatidia are presented in Table 1.

Table 1.

Normalized effective light intensities from 2° test and conditioning stimuli on photoreceptors in a row of ommatidia

Normalized effective light intensities from 2° test and conditioning stimuli on photoreceptors in a row of ommatidia
Normalized effective light intensities from 2° test and conditioning stimuli on photoreceptors in a row of ommatidia

Table 1 shows that when the test and conditioning stimuli are presented separately, they each provide significant stimulation (intensity greater than 1 % of maximum) to axial photoreceptors and those in neighbouring ommatidia. When presented together at 6° separation, the two stimuli create a broad bimodal pattern of stimulation among the ommatidia of the eye, while at 10° separation the stimuli create two distinct unimodal patterns.

These different stimulus patterns evoke different responses from the DCMD. As can be seen in Fig. 2, the bimodal stimulus pattern created when the two stimuli were separated by 6° evoked a smaller DCMD response than did the smaller unimodal pattern created when the test stimulus was presented alone. When the separation of the paired stimuli was increased to 10°, the response increased to the value achieved by the test stimulus alone. Similar results could be obtained with stimuli presented anywhere in the visual field of the DCMD, which is co-extensive with the field of one eye. These responses were measured as the difference between the number of spikes that occurred during the 5 s of the stimulus presentation and the number of spikes that occurred spontaneously during the 5 s period immediately preceding the presentation. The different stimulus configurations were presented in random order to detect changes in responsiveness caused by habituation (Edwards, 1982 a).

From these results, I conclude that a moving spot of light generates both excitation and inhibition in the afferent path to the DCMD. Furthermore, while the afferent excitation from a spot is directly expressed in the response of the DCMD, the inhibition is directed laterally, and reduces the DCMD’s response to a second nearby stimulus. The limited range of this inhibition (as indicated by the increased response when the stimulus separation is 10°), and the ability to evoke it with stimuli anywhere in the visual field, suggest that it is mediated by a lateral inhibitory network in which locally excited interneurones inhibit the response of neighbouring excitatory afferents.

Light adaptation and the intensity dependence of excitation and inhibition of the DCMD response

Butler & Horridge (1973 a, b) have found that both the absolute sensitivity and the angular sensitivity of cockroach photoreceptors are very different in the light- and dark-adapted states. When the eyes were adapted to ‘low-level background light’ (intensity not measured, Butler & Horridge, 1973 a) the acceptance angles of photoreceptors were found to be about 2·5°, while those of dark-adapted eyes were about 6·5° (Butler & Horridge, 1973 a). The maximal response of dark-adapted photoreceptors was twice that of light-adapted receptors, while the normalized plots of the response vs. log I for the two states were parallel sigmoidal curves separated by about one-half log unit of intensity (Butler & Horridge, 1973b).

I have found differences in the responsiveness of the DCMD when the eyes were in different states of light adaptation. Fig. 3 a presents the normalized DCMD responses (measured as before) from two light-adapted animals plotted against the log of the intensity of a moving 2° light spot. The spot moved at 10°/s for 5 s along a 50°path. The intensity of the light spot was made to vary over a 5 log-unit range during the series of trials. The stimulus intensity of any particular trial was chosen randomly, and the inter-trial interval was set at 15 min to avoid any systematic change in the DCMD’s responsiveness caused by response habituation (Edwards, 1982 a). The cell’s responsiveness was monitored throughout the course of the experiment by recording the response to a fixed-intensity stimulus presented every 10th trial. Cockroaches were light-adapted by being exposed to moderate fluorescent room lighting (150μW/cm2 at the experimental table) for at least 1 h before and during testing. The amplitude of the DCMD’s response increased from 10% to 90% of maximum over 2·5 log units of stimulus intensity, and then remained nearly constant for intensities greater than –1·9 log units (Fig. 3 a). The rising phase of this plot is identical to similar plots of the responses to monochromatic stimuli (Edwards, 1982 a).

In dark-adapted eyes, the response vs. log I function for the DCMD was completely different. It is described by the bell-shaped response vs. log I plot of Fig. 36, in which the dots represent the means of the normalized responses of 14 animals, and the bars represent one standard deviation of the mean. These responses were recorded under the same stimulus conditions that prevailed when light-adapted responses were measured, except that the animal was kept completely in the dark for over 1 h before and during the experiment. The inter-trial interval was again 15 min which allowed the eye to remain dark-adapted at the beginning of each trial. The DCMD’s response increased from 10% to 90% of the peak value over only 1·5 log units of stimulus intensity, and then decreased to near zero as the stimulus intensity was increased another 1·5 log units. The peak response was 20% greater than that recorded from light-adapted eyes (185 vs. 155 spikes), while the stimulus intensity at which the peak occurred was nearly 3 log units less in dark-adapted than in light-adapted eyes. Similarly, the stimulus intensity at which the response reached 39 spikes (0·2 on the ordinate in Fig. 3 a, b) was nearly 1·5 log units less.

Part of the increase in the DCMD’s sensitivity that results from dark-adaptation can be accounted for by the increase in sensitivity that occurs in the photoreceptors upon dark-adaptation (Butler & Horridge, 1973b). The fall in the dark-adapted response curve that occurs at high stimulus intensities, however, must be due to a neural inhibition directed against elements in the afferent pathway to the DCMD. Like the excitation, this inhibition is excited by the slow-moving spot of light. It is apparent that the inhibition has a higher effective threshold stimulus intensity than the excitation, and that the amplitude of the inhibition increases with the stimulus intensity at least until the DCMD response is extinguished. Finally, the results of Fig. 3 b, like those of Fig. 2, suggest that the inhibition dominates when the stimulus affects a large group of ommatidia in the compound eye ; this can occur with a bright 2° stimulus when the eye is dark-adapted, and photoreceptor sensitivities and acceptance angles are increased above their values in the light-adapted state.

Recurrent and non-recurrent lateral inhibition

The results presented in Figs 2 and 36 can be accounted for by the action of a lateral inhibitory network in the afferent path to the DCMD. Such a lateral inhibitory network can be organized in either of two ways: the inhibition can be recurrent, as in the lateral eye of Limulus (Hartline & Ratliff, 1958), or it can be non-recurrent (i.e. feed-forward) (Ratliff, 1965).

In a recurrent network, the inhibition directed against the lateral neighbours of any unit is an increasing function of that unit’s response (Ratliff, 1965). This organization makes it possible for the network to go into uncontrolled oscillation in response to a step increase in a spatially uniform excitation (see Discussion); such oscillation must not occur if the network is to filter visual inputs. I have shown that for the response of the network to remain stable, regardless of the pattern of excitation, the amplitude of the response of any unit of the network must always exceed the sum of the inhibition (i.e. decreases in response) produced immediately in all other units by that unit’s response (Edwards, 1982b).

A result of this last conclusion is that the sum of the responses of elements in a recurrent network cannot decrease as the net excitation of the network increases (Edwards, 1982b). If the response of the DCMD is related to the sum of all the outputs of a lateral inhibitory network, then this result, and the decrease in the DCMD’s response that occurs as the intensity is increased (Fig. 3 b), together suggest that the lateral inhibition is not mediated by a recurrent network, and must therefore be mediated by a non-recurrent network.

A model of the afferent path to the DCMD was developed that incorporates a fixed non-recurrent lateral inhibitory network that is excited by an array of light-or dark-adapted photoreceptors. This model suggests that the differences in the response vs. log I plots for the DCMD in light-and dark-adapted eyes (Fig. 3 a, b) can be accounted for by the differences in the response properties of light-and dark-adapted photoreceptors (Butler & Horridge, 1973 a, b) along with fixed non-recurrent lateral inhibition. The model also suggests how the pattern of responses created by a 2 ° light stimulus in the array of photoreceptors is transformed by a non-recurrent lateral inhibitory network into a completely different pattern of responses in an array of interneurones that provides input to the DCMD.

A model of the afferent path to the DCMD

The model has three layers of elements: (1) a hexagonal array of photoreceptors, each of which corresponds to the set of photoreceptors in one ommatidium in the compound eye; (2) two serially connected arrays of intemeuronal elements that make up the non-recurrent lateral inhibitory network; (3) a single summating interneurone that receives as converging input the responses of all the output neurones of the lateral inhibitory network. A two-dimensional diagram of this network is presented in Fig. 4.

Fig. 4.

A two-dimensional diagram of the model of the visual afferent path to the DCMD. Each model photoreceptor (P) corresponds to the photoreceptors in one ommatidium; they are separated by one interommatidia] angle (3°). They each excite an excitatory (E1) and an inhibitory cell (I) in the first layer of the non-recurrent lateral inhibitory network (N-RLIN). The excitatory cell excites one neurone (E2) in the second layer of the network, while the inhibitory cell inhibits that excited neurone’s nearest six neighbours. The outputs of the second layer cells converge on the DCMD. excitatory synaptic connexion ; inhibitory synaptic connexion.

Fig. 4.

A two-dimensional diagram of the model of the visual afferent path to the DCMD. Each model photoreceptor (P) corresponds to the photoreceptors in one ommatidium; they are separated by one interommatidia] angle (3°). They each excite an excitatory (E1) and an inhibitory cell (I) in the first layer of the non-recurrent lateral inhibitory network (N-RLIN). The excitatory cell excites one neurone (E2) in the second layer of the network, while the inhibitory cell inhibits that excited neurone’s nearest six neighbours. The outputs of the second layer cells converge on the DCMD. excitatory synaptic connexion ; inhibitory synaptic connexion.

The model photoreceptors have the same angular sensitivity function and response/ intensity function as cockroach photoreceptors; their angular separation is equal to one interommatidial angle in the cockroach eye. Each photoreceptor excites identically a pair of neurones in the first layer of the non-recurrent lateral inhibitory network; one of the pair excites one neurone in the second layer of the network, while the other inhibits that second-layer neurone’s six nearest neighbours. The response of each of those second-layer neurones, therefore, is governed by the excitation that it receives from one excitatory neurone in the first layer and the inhibition it receives from six inhibitory cells. All of the second-layer neurones excite the DCMD via rectifying synapses ; the response of the DCMD is given by the sum of the responses of the second-layer neurones that are positive. A more complete description of the model is provided in Appendix 2.

Experimental stimulations

The model was used to simulate the experiment of Figs. 3 a and b, in which the response of the DCMD to different intensities of 2° light moving at 10°/s through the visual field were recorded when the eye was light-adapted and dark-adapted. The spot of light was represented by a hexagonal array of 19 equally intense point sources having a nearest-neighbour spacing of 0·5°. The stimulus array was positioned near the centre of the array of photoreceptors and moved in increments of 0·4° across the array until a position identical to the first was encountered. The response of the model was calculated at each position, and the sum of these responses was taken to be the response of the model to the movement of the stimulus along that path. Other paths were also tested and found to give quite similar responses. The average of the responses to several paths represented the response of the model to a stimulus of that intensity. This simulation assumes that the responses of the photoreceptors, interneurones and DCMD to the slowly moving spot can be described by a quasi-static approximation, i.e. that the time-dependent properties of these units are relatively unimportant. An argument for the reasonableness of this assumption is presented in Appendix 2.

With the photoreceptor parameters set to reflect light-adapted conditions (Δ ρ = 2·5° and So = 0·4 in equation 1, g = 0·45 in equation 5 in Appendix 2), the response of the model was calculated for a range of stimulus intensities and plotted as the continuous curve in Fig. 3 a. The simulation was repeated with the photoreceptor parameters adjusted to reflect dark-adapted conditions (Δ ρ = 6·5°, 50 = 1, g = 1), to give the continuous curve in Fig. 3b. The responses from the ‘light-adapted’ simulation and experiment are each normalized to the maximum responses from the ‘dark-adapted’ simulation and experiment (Fig. 3 b), respectively.

Fig. 3 a shows that a feed-forward lateral inhibitory network can filter the information coming from an array of light-adapted photoreceptors in such a way as to cause the DCMD response to vary with log I in the same sigmoidal fashion as the experimental data. When the model photoreceptors are ‘dark-adapted’, the response of the model to different stimulus intensities changes in the same way as the response of the cell changes : the threshold intensity decreases, and the response vs. log I plot changes to a bell-shaped curve (Fig. 3b) from a sigmoidal curve.

Patterns of responses in the array of photoreceptors and in the array of interneurones

When the eye is light-adapted, the acceptance angles and sensitivities of the photoreceptors are reduced, so that the number of ommatidia in the eye affected by a 2° spot is small. This is evident in Fig. 5 a, which displays the pattern of responses of the ‘light-adapted’ model photoreceptors and the second-layer interneurones to different intensities of a 2° stimulus. At low stimulus intensities (log I = –4·3), the excitation is restricted to a single photoreceptor. A single interneurone is strongly excited, and its six nearest neighbours are inhibited. When the intensity is increased by two log units, the central photoreceptor and its six neighbours are all excited, but that excitation remains largely conlined to a single interneurone. When the intensity is increased by another two log units, the response of the central photoreceptor is saturated, as are the responses of its six neighbours. The central interneurone is inhibited at this stimulus intensity, while the six surrounding interneurones are Txcited. These excited interneurones are themselves surrounded by a ring of strongly inhibited interneurones.

Fig. 5.

Response patterns of the hexagonal array of model photoreceptors (P) and the corresponding array of second-layer interneurones (Int) of the non-recurrent lateral inhibitory network. •, Excited units; ◯, inhibited units. The responses are calculated for a 2° spot centred over the middle photoreceptor of the array. The angular separation between adjacent photoreceptors and adjacent interneurones is 3°. The response amplitude of each unit is given by the diameter of each circle. Null responses are represented by blank spaces, (b) Model photoreceptors are light-adapted. Responses to three intensities, log I = -4·3, –2·3 and – 0·3 are given. (b) Model photoreceptors are dark-adapted. Responses to log I = –4·3, – 3·3 and –2·3 are given.

Fig. 5.

Response patterns of the hexagonal array of model photoreceptors (P) and the corresponding array of second-layer interneurones (Int) of the non-recurrent lateral inhibitory network. •, Excited units; ◯, inhibited units. The responses are calculated for a 2° spot centred over the middle photoreceptor of the array. The angular separation between adjacent photoreceptors and adjacent interneurones is 3°. The response amplitude of each unit is given by the diameter of each circle. Null responses are represented by blank spaces, (b) Model photoreceptors are light-adapted. Responses to three intensities, log I = -4·3, –2·3 and – 0·3 are given. (b) Model photoreceptors are dark-adapted. Responses to log I = –4·3, – 3·3 and –2·3 are given.

The 2° spot excites many more photoreceptors in a dark-adapted eye, and they, in turn, cause many interneurones to be excited and inhibited (Fig. 5b). At low intensities (log = –4·3), the excitation of the seven strongly excited photoreceptors is transmitted to the corresponding output interneurones of the lateral inhibitory network; they are surrounded by a ring of inhibited interneurones. With ten times more light, the feed-forward inhibition overwhelms the excitation of the central unit, and a ring of positive responses is formed. When the intensity is increased by one more log unit, all the interneurones are inhibited, and the summating neurone receives no excitation in response to the bright stimulus. Total inhibition of the interneurones occurs at this intensity only for this position of the stimulus over the receptor array; as the stimulus is moved some interneurones give positive response. This causes the summating neurone to have a net positive response at this intensity (Fig. 3 b).

Inhibition produced by a tonic stimulus

The inhibitory effects described above were produced by moving spots of light. To see if inhibition could also be produced by constant, stationary stimuli, the response of the DCMD was recorded as the moving stimulus passed near a stationary pattern of light. A 2° spot of light was moved at 10°/s through a 50°path on a white screen while the rest of the room was dark and the animal was thoroughly dark-adapted. During the movement of the spot, however, a narrow bar of white light was displayed on the white screen. The bar subtended 3·6° by 75° at the eye of the animal, and was aligned parallel to and 12° below the path of the moving spot. The bar was turned on 10 s before the motion stimulus was presented, maintained on at constant intensity during the 5 s of stimulus motion, and turned off immediately afterwards. The 10 s of exposure of the eye to the bar prior to presentation of the moving stimulus allowed transient responses of other ventral cord neurones to the onset of the bar to pass so that the DCMD’s response to the moving spot could be detected. The inter-stimulus interval was 15 min, so that the bar of light was on less than 2% of the time. This permitted the eye to remain dark-adapted at the beginning of each experimental trial. All other experimental arrangements were identical to those of the experiment of Fig. 3b.

Results were similar for the seven animals tested. Normalized data from one animal are given in Fig. 6. With no bar of light, the DCMD response was similar to that of Fig. 3b. With a dim bar present (log Ibar equals –4·27, measured on the same scale as the stimulus spot, i.e. the abscissa), the stimulus intensity that evoked a response of 55 spikes during the 5 s counting period (0·3 on the ordinates in Fig. 6) was about 0·75 log units greater than without the bar present, the peak response amplitude was significantly greater, the rise to the peak (as the stimulus intensity was increased) was significantly steeper, while the fall from the peak was much more prolonged and achieved a moderate plateau value at high stimulus intensities. With a brighter bar (log Ibar = –3·42, plot III) the stimulus intensity that evoked 55 spikes was increased another 0 · 5 log units, but the rising slope of the response vs. log I plot remained steep, as did the size of the maximal response. The fall from the peak response with increased stimulus intensity became much more gradual, however, and the final plateau was about twice the amplitude of that obtained with the dimmer bar. The brightest bar (log Ibar = –2 · 40, plot IV) raised the stimulus intensity needed to evoke 55 spikes by one more log unit, but the rising phase of the plot was less steep, the maximum response was reduced, and the response did not decline from its maximum at high stimulus intensities.

Fig. 6.

The effect of tonic lateral inhibition on the DCMD’s dark-adapted response vs. log I plot. Filled circles are the normalized responses of the DCMD to different intensities of the moving 2° spot when the eye was dark-adapted and a bar of light (3·6 ° by 75 °) was parallel to and 12° below the path of the spot. The continuous curves are the responses of the ‘dark- adapted’ model when the responses of the excitatory and inhibitory neurones of the first layer of the non-recurrent network are reduced by the constants Io and I1, respectively. I. No bar present; I, = o, I1 = o. II. Dim bar of light (log 1bar = –4 · 27); Ie = 0·2, Ii = 0 · 29. III. Brighter bar of light (log Ibar= –2·40); Ie = 0·61, I1 = 0 · 57. The bar intensities are measured on the same scale as the spot intensities.

Fig. 6.

The effect of tonic lateral inhibition on the DCMD’s dark-adapted response vs. log I plot. Filled circles are the normalized responses of the DCMD to different intensities of the moving 2° spot when the eye was dark-adapted and a bar of light (3·6 ° by 75 °) was parallel to and 12° below the path of the spot. The continuous curves are the responses of the ‘dark- adapted’ model when the responses of the excitatory and inhibitory neurones of the first layer of the non-recurrent network are reduced by the constants Io and I1, respectively. I. No bar present; I, = o, I1 = o. II. Dim bar of light (log 1bar = –4 · 27); Ie = 0·2, Ii = 0 · 29. III. Brighter bar of light (log Ibar= –2·40); Ie = 0·61, I1 = 0 · 57. The bar intensities are measured on the same scale as the spot intensities.

It is clear that the bar had two major effects on the DCMD’s response to the moving spot. It reduced the response to the stimulus intensities, that had evoked the largest response without the bar present, and it dramatically increased the response to higher spot intensities that had previously evoked little or no response. It is conceivable that these effects might be due to light scattered from the bar, or they might be due to the same lateral inhibitory network invoked earlier, or to an additional lateral inhibitory network.

Light scattered from the bar might tend to reduce the contrast of the spot in the visual field of the DCMD, and thereby decrease the sensitivity of the DCMD to the spot. This effect was shown to be less important than tonic lateral inhibition by the results of the following experiment. A dark-adapted eye was stimulated with a moving spot in the presence of a bar of light that was placed on the path of the spot stimulus in the first series of trials (filled circles, Fig. 7a), and 12 ° lateral to the path in the second series (open circles). The bar subtended 2 · 5° by 75 ° at the eye so that it would cover only the path of the 2 ° stimulus when superimposed on it.

When on the path, log Ibar = –4 · 3 (on the same scale as the 2 ° stimulus intensities, but when 12 ° lateral to the path it was 2 75 log units brighter. The photoreceptors that were oriented towards the path of the spot, however, were calculated to receive about 10 times more light from the bar that was on the path than from the bar that was 12 ° lateral to it, due to the greater sensitivity of photoreceptors to on-axis light (Appendix 1). The bar of light that was superimposed on the stimulus path, therefore, should be more effective than the lateral bar in reducing the contrast of the stimulus on those photoreceptors that are oriented towards the path. Consequently, if reduced contrast were responsible for the increased threshold stimulus intensity of the DCMD in the experiments of Fig. 6, the DCMD’s threshold intensity should be increased more when the bar of light is superimposed on the stimulus path than when it is 12 ° lateral to it. Since the converse was found (Fig. 7a), the threshold shifts must be due to tonic, laterally acting neural effects, such as tonic lateral inhibition.

Fig. 7.

Controls for the effects of scattered light from the bar stimulus, (a) •, Responses of a dark-adapted DCMD to a range of intensities of a moving 2° spot in the presence of a bar of light (log Ibar, = –4 · 3, 2 5° by 75 °) superimposed on the path of the spot. ◯, Responses to the moving spot when the bar is moved 12 ° off the path, and made 2 · 75 log units brighter. The effective intensity of the laterally placed bar on photoreceptors oriented towards the spot, however, was calculated to be about 10 times less than the effective intensity of light from the superimposed bar. (b) Responses to the moving spot in the presence of a lateral bar of light (3 · 6° by 75 °, log = –2 · 40) turned on at different times before the presentation of the spot. ◯, Bar was turned on 10 s before the motion of the spot began, and remained on during that motion. •, Bar was turned on 1 min before motion of the spot began. The two stimulus paradigms were presented in random order at the different spot intensities. The continuous lines in (a) and (b) are not predictions of the model, but are fits to the data made by eye.

Fig. 7.

Controls for the effects of scattered light from the bar stimulus, (a) •, Responses of a dark-adapted DCMD to a range of intensities of a moving 2° spot in the presence of a bar of light (log Ibar, = –4 · 3, 2 5° by 75 °) superimposed on the path of the spot. ◯, Responses to the moving spot when the bar is moved 12 ° off the path, and made 2 · 75 log units brighter. The effective intensity of the laterally placed bar on photoreceptors oriented towards the spot, however, was calculated to be about 10 times less than the effective intensity of light from the superimposed bar. (b) Responses to the moving spot in the presence of a lateral bar of light (3 · 6° by 75 °, log = –2 · 40) turned on at different times before the presentation of the spot. ◯, Bar was turned on 10 s before the motion of the spot began, and remained on during that motion. •, Bar was turned on 1 min before motion of the spot began. The two stimulus paradigms were presented in random order at the different spot intensities. The continuous lines in (a) and (b) are not predictions of the model, but are fits to the data made by eye.

Light scattered from the bar might act to light-adapt the photoreceptors that respond to the moving spot, which would also raise the threshold intensity of the DCMD to the spot. To test for this possibility, the bar of light was again positioned 12 ° lateral to the path of the stimulus. The interval between the time the bar of light was turned on and the time the spot stimulus began to move was randomly alternated between 10 s and 1 min. The longer period of tonic stimulation by the bright bar (log Ibar = –2 · 40) should have caused all the affected photoreceptors to begin to light-adapt before the moving stimulus was presented. The most severely affected photoreceptors would have been oriented towards the bar. If their excitation would normally lead to a lateral inhibition of afferents responding to the spot, then as these photoreceptors light-adapt that lateral inhibition should decrease. Such a decrease in the inhibition of afferents responding to the spot should cause a decrease in the threshold intensity of the DCMD’s response to the spot stimulus. However, if tonic lateral inhibition does not exist, then prolonged exposure to the lateral bar of light should affect the response of the DCMD by light-adapting the photo-receptors that respond to the moving spot. Light-adaptation of those photoreceptors would cause the DCMD’s threshold intensity to increase. In Fig. 7b it is apparent that the longer exposure to the bright bar produced a decrease in the threshold intensity of the DCMD, which is consistent with the tonic lateral inhibition hypo-thesis.

The experiments of Fig. 7 indicate that the shifts in the DCMD’s response vs. log I plot caused by the bar stimulus (Fig. 6) are due in large part to tonic lateral inhibition excited by the bar, although scattered light from the bar may have some effect. It is conceivable that the lateral inhibition excited by the stationary bar of light is produced by the same non-current network that is responsible for the lateral inhibitory effects discussed above. However, such non-recurrent lateral inhibition produced by the bar stimulus would reduce the response to the 2 ° stimulus of elements in the second layer of the lateral inhibitory network, and would not affect the excitatory and inhibitory inputs to those units that are produced by the 2 ° light spot. In this instance, tonic lateral inhibition would reduce the response of elements that excite the DCMD, but would not increase their threshold stimulus intensities, as required by the data of Fig. 6.

These effects can be seen in a model simulation of the response of a dark-adapted eye to a moving 2 ° spot, in which all the second-layer interneurones of the non-recurrent network are tonically inhibited by a constant inhibitory post-synaptic conductance, G1(see Appendix 2). This conductance represents the tonic inhibitory conductance created by the stationary bar in cells that are responding to the moving spot. The plot of Fig. 8 (continuous curve) was calculated with G1/G1 set to 1 · 5; the excitatory and inhibitory synaptic conductances produced in the second-layer interneurones by the spot were unaffected. The model response is reduced at all stimulus intensities from the values obtained without the tonic inhibition (dashed curve). A reduction in the response of the model will occur regardless of the spatial extent of the non-recurrent lateral inhibition excited by the bar, as long as the inhibition reaches at least nearest neighbours. It is also apparent that the response vs. log intensity curve is not shifted to a higher range of stimulus intensities by the non-recurrent inhibition as required by the curves in Fig. 6. These results suggest that the lateral inhibition produced by the bar is not mediated by the same nonrecurrent network that may mediate the lateral inhibition evoked by the moving spot stimulus.

Fig. 8.

The effect on the response of the model of tonic inhibition mediated by the nonrecurrent lateral inhibitory network. Dashed curve: model response calculated for dark- adapted conditions. Continuous curve: model response under dark-adapted conditions, but with a constant inhibitory conductance (G1/G1= 1 · 5) added to the inhibitory conductances [Σ Δ G1(j)/G1] of the second-layer neurones (equation 8, appendix 2).

Fig. 8.

The effect on the response of the model of tonic inhibition mediated by the nonrecurrent lateral inhibitory network. Dashed curve: model response calculated for dark- adapted conditions. Continuous curve: model response under dark-adapted conditions, but with a constant inhibitory conductance (G1/G1= 1 · 5) added to the inhibitory conductances [Σ Δ G1(j)/G1] of the second-layer neurones (equation 8, appendix 2).

The effects of tonic lateral inhibition evident in Fig. 6 can be simulated with the model if lateral inhibition produced by the bar of light acts on the units in the first layer of the non-recurrent network, or at some more distal point along the afferent path. This tonic lateral inhibition could be mediated by another lateral inhibitory network interposed between the photoreceptors and the non-recurrent network of Fig. 4, or it might be mediated by extracellular current flow between the proximal ends of photoreceptors (Shaw, 1975, 1977). In both instances, tonic lateral inhibition would cause greater stimulus intensities to be required to produce both excitation and inhibition in the feed-forward lateral inhibitory network. As a consequence, the range of stimulus intensities over which DCMD responses could be evoked by a spot of light would be shifted to higher values.

The effect of such a distal tonic lateral inhibition on the response of the DCMD to the moving spot was simulated with the model by subtracting a constant from the responses of all the model neurones of the first layer of the non-recurrent net work. The constant inhibition of first-layer neurones can only be overcome by mcreased excitation from photoreceptors that are excited by the moving spot stimulus ; this will occur if the stimulus intensity is increased. The simulated bar inhibition in the model, therefore, acts to increase the threshold intensity of both the excitation and the non-recurrent inhibition experienced by neurones of the second layer of the network. The increases in the threshold intensities of these inputs act to increase the threshold intensity of the response of the network, and the threshold intensity of the DCMD. The continuous curves of Fig. 6 illustrate the effects of different amounts of bar-inhibition on the responses of the model to a range of spot intensities.

The best fits of the model curves to the DCMD responses were obtained by allowing the bar-inhibition (Ie) that affected the excitatory neurones in the first layer of the network to differ slightly from the bar-inhibition (I1) that affected the inhibitory neurones in that layer. To produce curve II in Fig. 6, for instance, the normalized responses of first-layer excitatory cells (Fig. 4) were reduced by 0 · 2 (= Ie), and this difference was used to calculate the excitation of second-layer cells. The normalized responses of first-layer inhibitory cells were reduced by 0 · 29 (=I1) to calculate the non-recurrent inhibition of second-layer cells. To produce curve III, these constants were 0 · 41 and 0 · 46, respectively, while for curve IV they were 061 and 0-57, respectively. It is unclear whether the small difference in the amount of bar-inhibition that affects excitation and inhibition in the non-recurrent network is a reflexion of the physiology of the system or is merely an artifact of the model; it is apparent, however, that the tonic lateral inhibition in the model has the same effect on the model’s response to the moving spot as light from the bar has on the DCMD’s response to the spot.

The effect of tonic inhibition on the thresholds of proximal afferents indicates that it mediates a form of ‘network adaptation’ (Dowling, 1977) that adjusts the sensitivity of those afferents to changing background light conditions. Tonic lateral inhibition also mediates network adaptation effects in second-order cells in the lamina of fly and dragonfly (Laughlin & Hardie, 1978). The experiment of Fig. 7b demonstrates that this inhibition, or network adaptation, can itself adapt : the tonic inhibition of the afferents that excite the DCMD decreases with time following the turn-on of the light bar stimulus. This adaptation of the tonic inhibition is probably due in large part to the adaptation of the photoreceptors that are stimulated by the bar of light ; it may also be due to other forms of network adaptation.

Organization of the afferent path to the DCMD

From the experimental results presented below, I conclude that two layers (at least) of lateral inhibition filter the signals that converge on the DCMD neurone from the photoreceptors. The more distal layer of lateral inhibition can be excited by tonic light stimuli, such as the bar stimulus. The major effect of this inhibition is to adjust the threshold stimulus intensity of more proximal afferents to the ambient light level of adjacent regions of the visual field. This allows those afferents, including the DCMD, to be most sensitive to stimuli that are close to the background in intensity (Fig. 6). Lateral inhibition performs a similar ‘network adaptation’ function’ (Dowling, 1977) for interneurones in the lamina of the fly and dragonfly (Laughlin & Hardie, 1978) and for the DCMD in the locust (Rowell & O’Shea, 1976a, b), while in the mudpuppy retina the lateral inhibition mediated by the horizontal cells adjusts the sensitivity of bipolar cells to changing levels of background illumination (Werblin, 1974).

The more proximal lateral inhibitory network acts to discriminate against large-field stimuli, and in favour of small, bright stimuli. In doing so, it should also enhance the contrast between the signal that represents the stimulus and that which represents the background, and thereby increase the spatial acuity of the eye (Fig. 5). The decrease in the DCMD’s response that occurs as the stimulus intensity is increased beyond a certain value (Fig. 3 b) is evidence that the proximal network is organized in a non-recurrent manner (see below). This organization can act to keep the excitation produced by large-field stimuli from reaching the DCMD; in doing so, it may also keep the cell from being excited by whole-field motion created by movement of the animal. The response of the cell habituates to frequent presentations of a stimulus (Edwards, 1982 a), and so the non-recurrent network may also serve to protect the DCMD from the response habituation that might accompany such whole-field stimuli. In the locust, the DCMD neurone is protected by lateral inhibition from the excitatory and habituating effects of whole-field stimuli (O’Shea & Rowell, 1975 a).

Anatomical substrates

The visual nervous system of the cockroach lacks the crystalline organization found in other insects, such as the fly and the bee (Ribi, 1975, 1977; Strausfeld, 1970). The photoreceptor axons project into the lamina in randomly organized groups of 6 – 20 fibres, which terminate in the synaptic region in an extensive fibre complex (Ribi, 1977). While one axon (the long visual fibre) projects to the medulla without branching in the lamina, the other axons terminate in the lamina and make synaptic contact there with second-order monopolar cells or centrifugal horizontal cells. The absence of a cartridge arrangement makes it difficult to determine how many ommatidia communicate with a single monopolar or horizontal cell; the lateral extent of branches from one horizontal cell is about twice that of the monopolars, while the lateral extent of monopolar dendrites is about twice that of receptor axonal branches.

From Ribi’s (1977) description of the anatomy of the lamina, it seems likely that the afferent path to the DCMD neurone includes a connexion between the photoreceptors and the monopolars in the lamina. The lamina is a possible site for distal lateral inhibition, mediated synaptically by the monopolars, or electrically, as Shaw suggests (1975), among the photoreceptor terminals. Some elements of the pathways that Strausfeld & Campos-Ortega (1977) have suggested may mediate lateral inhibition in the fly may also be present here. The horizontal cells of the cockroach lamina may also mediate a lateral inhibitory function, but the source of excitation for those cells is unclear. Finally, if the cockroach is like other insects (Strausfeld, 1976), other possible substrates for lateral inhibition should be present in the medulla.

The similar organizations of the afferent paths to the cockroach and locust DCMDs

Lateral inhibition in the locust visual system has many of the same effects on the response of the DCMD neurone that it does in the cockroach. Tonically excited lateral inhibition adjusts the response threshold of the DCMD so that it is most sensitive to stimuli near the intensity of the background (Rowell & O’Shea, 1976 b). At the same time, lateral inhibition protects the DCMD from whole-field stimulation, and is responsible for the cell’s preference for small-field stimuli (O’Shea & Rowell, 1975a; Rowell et al. 1977). The responses of the lateral inhibitory network in the locust converge on a fan-shaped cell, the lobular giant movement detector (LGMD) which transmits spikes one-for-one to the DCMD (O’Shea & Williams, 1974; O’Shea & Rowell, 1975 b). The strong similarity between the response properties of the DCMD neurones in the cockroach and locust (Edwards, 1982 a), and between the organization of the afferent pathways to the two cells, suggests the possibility that convergence of visual signals on to the DCMD neurone in cockroach may also occur by way of an LGMD neurone.

Recurrent and non-recurrent lateral inhibition

It is clear from the experimental simulations that a model that incorporates a nonrecurrent lateral inhibitory network can account for the way in which the amplitude of the DCMD’s response varies with stimulus intensity. A non-recurrent network, for instance, enables the model to give smaller responses to bright stimuli of increasing intensity (Fig. 3 b). A recurrent network cannot behave in this way; increases in the net excitation will evoke larger net responses from a recurrent network until the responses saturate (Edwards, 19826). This inability is due to the requirement that the response of the network to a constant, uniform stimulus must not oscillate. The recurrent network will not oscillate if the total inhibition that any neurone directs at its neighbours is less than the response of the cell that produced the inhibition. If this restriction is not met, the onset of a constant uniform stimulus will evoke identical large, initial responses from all the cells of the recurrent network, which will then generate larger measures of lateral inhibition. The inhibition will depress the responses of those cells below their pre-stimulus values, which will disinhibit the cells during the next increment of time. The disinhibition will evoke responses that are larger than the initial responses to the stimulus; this completes the first cycle of an exploding oscillation. If the restriction of no unbounded oscillation is met, the response to the constant uniform excitation will be a damped oscillation around a higher constant level ; the net effect of any increase in the excitation of the network will be to increase the net response of the recurrent network.

Since a non-recurrent network can account for the responses of the DCMD neurone while a recurrent network cannot, it is reasonable to conclude that the lateral inhibition that filters the inputs to the DCMD in the cockroach is organized in a non-recurrent fashion. It should be possible to extend this type of argument to the visual systems of other animals. Certain visual interneurones in the protocerebrum of the bee, for instance, have bell-shaped response vs. log I functions (Erber & Menzel, 1977). These curves are indicative of a non-recurrent inhibition in the afferent paths to the cells. The inhibition may be due to a non-recurrent lateral inhibitory network, or it may be due to simple feed-forward inhibitory inputs to the recorded cells; the possibility that recurrent lateral inhibitory networks are also present in the visual pathway is not excluded, but they are not dominant in response characteristics.

Non-recurrent networks, like recurrent networks, are able to enhance both the spatial and temporal contrast of signals produced by an array of photoreceptors. As is apparent in Fig. 5 a, enhanced spatial contrast may enhance acuity by localizing the response to a point stimulus to one afferent channel. It is also apparent from Fig. 5 that a non-recurrent network can distort the neural image of the stimulus, and at high stimulus intensities it can completely prevent whole-field patterns of excitation from reaching proximal afferents. As mentioned above, this ability can play an important role in preventing whole-field, reafferent visual excitation from reaching the DCMD.

The model of the afferent path to the DCMD

The model described here represents an attempt to identify those elements and processes in the afferent pathway to the DCMD that determine the major characteristics of the cell’s response to patterns of light on the eye. Simulations with the model demonstrate how a particular organization of these elements can account for a number of these characteristics that are seemingly unrelated. In particular, it shows how changes in the adaptation state of the photoreceptors that excite a non-recurrent lateral inhibitory network might be responsible for the very different response vs. log I plots recorded from the DCMD in light-and dark-adapted eyes.

The organization of the model into three layers (an array of photoreceptors, a non-recurrent lateral inhibitory network and a whole-field interneurone) is an idealization of what might be found in the cockroach visual nervous system. This organization was further simplified in the model to emphasize the nature of the processes involved. The model photoreceptors were given the same response properties (not including temporal properties) as photoreceptors in the eye of the cockroach. The response of neurones in the first layer of the non-recurrent network was made identical to the responses of the model photoreceptors that excite them, to emphasize the dependence of excitation and inhibition in the network on the response of each photoreceptor. Transformations of the responses of cockroach photoreceptors that may occur in the afferent path to the lateral inhibitory network were incorporated in the model into the functions of Fig. 9. These functions related the excitatory and inhibitory post-synaptic conductances of second-layer model neurones to the responses of the first-layer neurones, and thereby to the responses of the photoreceptors. The result is that the model makes explicit which aspects of its response are the result of particular properties of the photoreceptors and which are the result of the nonrecurrent lateral inhibitory network. This can be seen very clearly in plots like those in Fig. 5, which illustrate the patterns of responses that a stimulus creates in the array of photoreceptors, and the patterns of responses that the non-recurrent network creates in the array of interneurones.

Fig. 9.

Plots of the functions that relate excitatory (ΔGe/G1, continuous curve) and inhibitory (ΔG1(j)/G1, dashed curve) synaptic conductances of second-layer neurones of the model to the normalized responses of excitatory and inhibitory first-layer neurones, respectively. The synaptic conductances are normalized to the leakage conductance of the second-layer cells. These plots are used to calculate the responses of second-layer neurones of the non-recurrent network according to equation 8 (appendix 2) when the responses of the first-layer neurones are known from equation 6.

Fig. 9.

Plots of the functions that relate excitatory (ΔGe/G1, continuous curve) and inhibitory (ΔG1(j)/G1, dashed curve) synaptic conductances of second-layer neurones of the model to the normalized responses of excitatory and inhibitory first-layer neurones, respectively. The synaptic conductances are normalized to the leakage conductance of the second-layer cells. These plots are used to calculate the responses of second-layer neurones of the non-recurrent network according to equation 8 (appendix 2) when the responses of the first-layer neurones are known from equation 6.

The patterns of interneurone responses in Fig. 5 are due in large part to the fact that lateral inhibition in the non-recurrent network is restricted to neighbouring channels. If lateral inhibition were extended to more distant channels, details of the pattern, such as the amplitudes of the excitation and inhibition of different units, would undoubtedly change. It is unlikely, however, that the types of patterns seen in Fig. 5, e.g. alternate concentric rings of excited and inhibited units, would be greatly changed if the spatial extent of the non-recurrent inhibition were different.

The motion-sensitivity of the DCMD

The DCMD does not respond to stationary stimuli, but it does respond to stimuli moving as slowly as 3°/s (Edwards, 1982a). It is apparent that at some point in the afferent path a process of adaptation occurs that filters out the responses to unvarying light stimuli; this may be accomplished in part by distal tonic lateral inhibition (see below). Such a process is not incorporated explicitly in the model presented here; it is assumed that the responses to the moving spot vary more rapidly than the lower cut-off frequency of the adaptation process, and so they are not affected by it. As was mentioned earlier, it is also assumed that the spot moves slowly enough for the response of the photoreceptors to track smoothly the effective intensity of the incident light according to equation 5 (Appendix 2); i.e. the photoreceptors and model interneurones are in a quasi-steady state (Srinivasan & Bernard, 1977). The evidence at hand suggests that these are reasonable assumptions. Moreover, the ability of the model to mimic the intensity dependence of the DCMD under light-and dark-adapted conditions lends credence to this suggestion.

Effects of light-and dark-adaptation

Light-adaptation and dark-adaptation have large effects on the absolute sensitivity, the angular sensitivity and the response characteristics of cockroach photoreceptors (Butler & Horridge, 1973 a, b). Light-and dark-adaptation also have large effects on the sensitivity, the shape of the response vs. log I plot, and the maximum response amplitude of the cockroach DCMD neurone (Fig. 3). The model simulations indicate that if the responses of the photoreceptors are filtered by a non-recurrent lateral inhibitory network, then the differences in the absolute sensitivity, angular sensitivity and response amplitude of the light-and dark-adapted photoreceptors can account for the corresponding differences in the responses of the DCMD (Fig. 3). Omitted from consideration in the calculations of the model’s responses in Fig. 3, however, are (1) the relative depolarization of light-adapted photoreceptors relative to the rest potential of dark-adapted photoreceptors (noted, but not measured by Butler & Horridge, 1973 a) and (2) the response of the distal (tonic) lateral inhibition to the steady-state responses of those light-adapted photoreceptors. The model is able to predict the differences in the response of the DCMD under light-and dark-adapted conditions if both of these phenomena are ignored (Fig. 3 a). This success could be deceptive, or it could mean that the two phenomena (the tonic responses of light-adapted photoreceptors and the tonic lateral inhibition excited by the steady-state responses of those light-adapted photoreceptors) effectively cancel each other out, perhaps at the level of the cells that are post-synaptic to the photoreceptors.

Good evidence for this latter notion is provided by recent studies on the effects of light- and dark-adaptation on the responses of photoreceptors and first-order large monopolar cells (LMCs) in the fly and dragonfly (Laughlin & Hardie, 1978) Unlike the photoreceptors that excite them, LMCs have no steady-state response to the background under light-adapted conditions. This is due to a peripheral lateral inhibition that cancels the steady-state signal from the photoreceptors, possibly at the receptor terminals (Shaw, 1975), presynaptic to the LMCs. It has been suggested (Laughlin & Hardie, 1978) that this sort of inhibition may account for the insensitivity of the locust DCMD to tonic stimuli, and for the ability of the locust DCMD to adjust its threshold sensitivity to the level of background illumination (Rowell & O’Shea, 1976a). In the present instance, it is reasonable to suppose that the same distal tonic lateral inhibition that is excited by the bar of light (Fig. 6) is also excited by the steady-state responses of light-adapted photoreceptors, and acts to cancel those steady-state signals before they reach more proximal afferents to the DCMD. This neural or network adaptation (Dowling, 1977) would account for the ability of a model that ignores both the steady-state receptor response to the background light, and the accompanying distal tonic lateral inhibition, to predict the response vs. log I plot of the DCMD in light-adapted animals.

I should like to thank Dr Timothy H. Goldsmith for his advice and encouragement of this work, which was supported by NIH research grant USPHS EY 00222 to Dr Goldsmith. I should also like to thank Drs Brian Mulloney and Michael Bastiani for their helpful criticisms of the manuscript.

The effective stimulus intensity on a photoreceptor

The angular sensitivity of a photoreceptor can be approximately described by a gaussian function :
where p is the angle between a point in the visual field and the visual axis of the photoreceptor, Δ ρ is the acceptance angle, and S0 is the sensitivity when p is zero (Butler & Horridge, 1973 a). The product I0*S(p) equals the effective light intensity on a photoreceptor from a point source of intensity I0 positioned at an angle p off the visual axis.
A spot stimulus (Table 1)
If So is set equal to 1, then the (normalized) total effective light intensity on a photoreceptor from a 2 ° light spot of intensity Io centred at p off the photoreceptor’s visual axis is given by
Equation 2 was used to calculate the total relative light intensities on photoreceptors in a row of ommatidia that are at different angular distances from the test and conditioning stimuli. These intensities are presented in Table 1; the values of the acceptance angle (Δ ρ) and interommatidial angle used in the calculation are given in the text.
A bar stimulus (Fig. 7b 
The total effective light intensity on a photoreceptor from a bar of light 2-5° wide that is centred on the photoreceptor’s visual axis is given by
Ibar is the intensity/area of the bar. Since the photoreceptors are dark-adapted, assume that Δ ρ is 6·5°. Consequently, Icentred = 16·5Ibar.
When the bar is 12° lateral to the photoreceptor, and is 2·75 log units brighter, the effective intensity is

The model photoreceptors

The model photoreceptors are arranged in a hexagonal array with each separated from its nearest six neighbours by 3°, which is the interommatidial angle in the region of the eye stimulated in these experiments. The response of each model photoreceptor is governed by four parameters: the sensitivity, So; the acceptance angle, Δ ρ; the slope of the response vs. log I function, which is governed by the exponent, n; and the photoreceptor gain, g. The angular sensitivity function of cockroach photoreceptors was described above by equation 1 ; as in the cockroach eye, Δ ρ is 6-5° and So is 1·0 for dark-adapted photoreceptors, while for light-adapted photoreceptors Δ ρ is 2·5° and So is 0·4 (Butler & Horridge, 1973 a, b).

The response of a cockroach photoreceptor to a point source stimulus on the optical axis varies in a sigmoidal fashion with the logarithm of the stimulus intensity (Butler & Horridge, 1973b). The relationship between response and stimulus intensity can be accurately described by the equation
where I is the stimulus intensity, Rp is the photoreceptor response and g and n are constants (Naka & Rushton, 1962). The best fit to the response/intensity plots for cockroach photoreceptors can be obtained when n is equal to 0·75, and g equals i-o for dark-adapted eyes and 0·45 for light-adapted eyes (Butler & Horridge, 1973b).

The model elements of the non-recurrent lateral inhibitory network

Each pair of excitatory and inhibitory neurones in the first layer of the nonrecurrent lateral inhibitory network is excited by one photoreceptor (Fig. 4); the responses of both of these elements (V1e, V11) are the same as the photoreceptor that excites them, so that r
Each excitatory neurone of the first layer excites one neurone of the second layer; each inhibitory neurone of the first layer inhibits the six nearest neighbours of the excited second-layer neurone. A serially connected pair of model excitatory neurones, and the photoreceptor that excites them, together constitute one channel for excitation of the DCMD. Lateral inhibition among the channels is restricted to nearest neighbours in this model because of computer storage limitations; the results of the two-stimulus experiments (Fig. 2), however, suggest that inhibition may extend no farther than two channels from its source.
The excitation and inhibition that elements in the second layer receive from elements of the first layer assume the form of membrane conductance changes; the excitation causes an increase in a depolarizing conductance, Ge, while the inhibition causes an increase in a hyperpolarizing conductance, Gi. Each second-layer interneurone, therefore, is modelled as a single isopotential compartment that has a membrane potential, V2, governed by a constant leakage conductance, G1, and the synaptic conductances according to equation 7 :
where Ee, Ei and E1 are the excitatory, inhibitory and leakage reversal potentials, respectively. If it is assumed that the excitatory and inhibitory synaptic conductances are both zero when no light stimuli are present, and that the leakage reversal potential is halfway between the excitatory and inhibitory reversal potentials, then the normalized response of the cell to synaptic input can be given by equation 8 :
All of the variables prefixed by A denote the difference between the stimulated and the resting (absence of light stimuli) value of the parameter. The synaptic conductances are all normalized to the leakage conductance. The six inhibitory conductances [Gi/(j)] that affect each interneurone are assumed to be in parallel and to have the same reversal potential. in equation 8 represents the sum of the inhibitory conductance changes produced by the six lateral inhibitory inputs. The synaptic conductances are all normalized to the leakage conductance, GP The tonic inhibitory conductance, G1, that is used to simulate non-recurrent lateral inhibition produced by the bar stimulus (Fig. 8), is added to in equation 8.

The relations assumed between the response of the first-layer neurones and the excitatory (ΔGe/G1) and inhibitory [ΔGi(j) /G1]conductance changes that they produce in second-layer neurones are described in Fig. 9. In both instances, the conductance change is a saturating exponential function of the pre-synaptic response. This is the same kind of relation that has been found to describe the variation of post-synaptic conductance or potential as a function of pre-synaptic potential at a number of different synapses (Lily, 1956; Katz & Miledi, 1967; Kuba & Tomita, 1971, 1972; Cooke & Quastel, 1973; Laughlin, 1973; Llinas, Steinberg & Walton, 1976). The parameters that govern the exact form of these conductance functions (the relative thresholds, rates of rise and saturation amplitudes) were chosen to achieve the simulations described in the text (Fig. 3 a, b). The maximum slope of these functions is greater than that of the squid giant synapse (Katz & Miledi, 1967; Llinas et al. 1976) and smaller than that of the retinular cell to large monopolar cell (LMC) synapse in the dragonfly eye (Laughlin, 1973).

The responses of the elements of the second layer can be positive or negative, depending on whether the excitatory synaptic conductance is larger than the inhibitory, or vice versa. These elements are each assumed to excite the DCMD through a rectifying chemical synapse (Fig. 4); the response of the DCMD, therefore, is assumed to be the sum of the rectified response of each of these elements.

The response of the model to light

Equations 1 and 5 can be used to calculate the responses of all the photoreceptors in the array to a point-source stimulus located anywhere in the visual field. Larger stimuli can be simulated with arrays of point sources; the response of each photoreceptor to the stimulus array is determined by the sum of the effective light intensities of all the sources at the photoreceptors. The responses of the photoreceptors, through the responses of the elements in the first layer of the network, determine the excitatory and inhibitory synaptic conductances of each second-layer interneurone according to the plots in Fig. 9. Given these conductances, the responses of each of these interneurones can be calculated from equation 8. The response of the summating (DCMD) interneurone, and of the model, is equal to the sum of the positive responses of second-layer neurones.

This procedure can be used to calculate the response of the model to arbitrarily shaped patterns of light in the visual field. The model can only represent steadystate conditions, however; none of the parameters of the model is time-dependent. As a consequence, the model can only simulate responses to slowly varying stimuli; the rate of change of the stimulus intensity must be slow compared to the response times of photoreceptors and the normal range of cellular time-constants. The model was used to simulate experiments in which a 2° spot of light was moved through the visual field at io°/s when the eye was light-adapted and dark-adapted (Fig. 3 a, b). The effective light intensity on a light-adapted photoreceptor from a stimulus that passed through the optical axis would vary between 10% and 90% of maximum in about 200 ms; this time would increase to about 500 ms if the photoreceptors were dark-adapted. The rise time of the step response of cockroach photoreceptors is less than 50 ms for all stimuli from threshold intensity to those that are three log units brighter; a plateau response is achieved to bright stimuli (3 log units above threshold) within 150 ms (Butler & Horridge, 1973 a). The 2° spot of light moved slowly enough for it to be assumed that the responses of the photoreceptors and of the post-synaptic cells have remained in a quasi-steady state condition (Srinivasan & Bernard, 1977; Pinter, 1972).

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