The descending contralateral movement detector (DCMD) of the locust responds vigorously to small target (ca. 5°) stimuli; this response is inhibited by simultaneous or subsequent rotation of a radial grating (windmill) pattern (subtending 19-90° of visual angle) and suppressed by earlier rotation,
The excitation produced in the DCMD by rotation of a radial grating pattern depends only on the spatial frequency of the stripes of the pattern, and is independent of pattern size, and of temporal frequency over the range of low values used.
The inhibition produced by this same stimulus similarly depends only on the spatial frequency of the stripes of the pattern, independent of pattern size, and of temporal frequency over the range of low values used.
As the radial grating excitation decreases with increasing spatial frequency, the inhibition increases until limited by optical and neural resolution.
For spatial frequencies of the radial grating pattern below 0·05 cyc/deg the radial grating patterns become excitatory. Above 0·05 cyc/deg they are inhibitory. This is the point in spatial frequency below which inhibitory grating ‘backgrounds’ become excitatory targets.
Inhibition decreases as the size of the radial grating pattern is decreased below 19° visual angle; at 8° or less no inhibition can be found at any spatial frequency.
Inhibition is greater in the posterior than anterior regions of the receptive field, and greater in the ventral than the dorsal regions.
Inhibition decreases as the distance between small target and the radial grating is increased, but this is influenced by the local variations of excitation and inhibition.
Habituation is often greater for small target and low-frequency radial grating response than for inhibited small target and high frequency grating response.
These results substantiate previously proposed lateral inhibition models of the acridid movement detector system.
Extensive studies have clearly shown the preference of the acridid movement detector system for small field stimuli (Palka, 1967, 1969; Rowell, 1971; Rowell, O’Shea & Williams, 1977) and have shown the inhibition of response to small field stimuli by large field stimuli (Palka, 1972; O’Shea & Rowell, 1975). Large field stimuli can be either simple dimming (Palka, 1967) or fields of moving stripes (Palka, 1969, 1972; O’Shea & Rowell, 1975; Rowell, O’Shea & Williams, 1977; Pinter, 1977). Considerable progress has been made in anatomical localization of certain sites of this inhibition (Rowell, O’Shea & Williams, 1977; O’Shea & Rowell, 1976).
Stimuli intermediate in size between large and small field have been used to determine the visual acuity of the locust (Schistocerca gregaria) by measuring responses of the DCMD (Palka & Pinter, 1975). These stimuli were radial grating patterns, each composed of black and white stripes arranged in a windmill pattern rotated about its centre. They were used in preference to spatially truncated rectangular gratings because they do not have low spatial frequency components, which generate artifacts (Palka, 1965). As discussed in the Appendix, precision radial grating patterns contain spatial frequencies only above approximately that spatial frequency defined by the reciprocal of the chord distance subtended by one stripe cycle at the outermost edge of the pattern. This feature makes them useful for determining spatial frequency dependent properties of visual systems.
Palka (1967) observed that dimming a large uniform target blocked DCMD response to dimming of a small target, and during experiments performed to measure locust visual acuity, it was observed that the response to rotation of the radial grating pattern was never sustained, as it is to movement of a small target. These observations suggested that response to rotation of these gratings might contain both excitatory and inhibitory components, and if so, that the inhibitory components might reduce the response elicited by the simultaneous presentation of another primarily excitatory small target stimulus. The inhibition has since been studied and found to depend primarily on the spatial frequency content of the radial grating pattern (Pinter, 1977).
In this paper I attempt to determine the relationship between this excitation and inhibition as a function of spatial frequency, temporal frequency, pattern size, time, and position in the receptive field. These are important factors in deriving lateral inhibition models of the response of the DCMD to visual stimuli of any kind. Lateral inhibition is thought to be the mechanism responsible for the capability of the DCMD to discriminate between small and large field stimuli (Rowell et al. 1977).
The neurone antecedent to the DCMD is the lobula giant movement detector (LGMD) which samples activity across the entire visual field via its fan of dendrites in the lobula; the DCMD follows spikes in the LGMD one for one via an electrical synapse (O’Shea & Rowell, 1975). There is lateral inhibition peripheral to the fan of dendrites of the LGMD (preconvergence inhibition), and in addition the LGMD receives one or more direct inhibitory inputs (postconvergence inhibition) which sample activity across the entire visual field. The postconvergence inhibition appears in the LGMD as IPSPs, but only at high temporal frequencies of visual stimulation (Rowell et al. 1977).
The temporal frequency of visual stimulation by the moving spatial pattern is the emporal frequency of variation in light intensity viewed by a retinular cell of one ommatidium. In all experiments described below, the range of temporal frequency is from 0·52 to 4·7 Hz, probably below that required to produce postconvergence inhibition and IPSPs in the LGMD. The inhibition found in the experiments reported below is thus occurring peripheral to the fan of LGMD dendrites in the lobula, probably in the medulla.
It is important to note that Rowell et al. (1977) define temporal frequency as twice the frequency of the variation in light intensity. All of their numerical values of temporal frequency must be halved to compare with the results presented below.
MATERIALS, METHODS AND DEFINITIONS
Male desert locusts, Schistocerca gregaria, obtained from the colony at the University of British Columbia, Vancouver, B.C., were used in all experiments. They were mounted with wax or glue, ventral side up, and the ventral nerve cord exposed on one side only between the first and second thoracic ganglia. The nerve cord was gently lifted on a hook electrode and held in place with petroleum jelly expressed from a syringe. The ipsilateral eye and the three ocelli were covered with opaque black paint. After amplification, the spikes of the DCMD, consistently the largest seen, were selected electronically by an adjustable window circuit, electronically counted, and histogrammed, with a bin width of 10 ms. A single histogrammed trial was 1280 ms in length beginning with a silent period of 400 ms, followed by a stimulus period of 400 ms for all experiments. The interstimulus interval was 30 s, unless otherwise indicated, which appeared to be the best compromise between length of run, drift in rate of responsiveness, and gain reduction due to habituation. Except where otherwise indicated, the target motion (indicated by T in the figures) and target plus grating motion (RT) trials were interleaved, to attenuate bias due to responsiveness drift and different rates of habituation from the inhibited and uninhibited stimulus. A single run to obtain one value of inhibition (I) (as defined on page 195) and the corresponding PST histogram required 34 trials and thus about 17 min. Time between runs was approximately 5 min. First trials with or without grating motion were alternated to prevent bias. The spike count was made in the 400 ms stimulus period. These preparations were usually stable for at least 6 h, and often more (up to 2 days). For the results below, useful data were obtained from 56 preparations.
The receptive field of the DCMD is approximately a hemisphere, and motion detection has little directional preference, although small differences in sensitivity to direction of rotation can be found. These differences were not routinely investigated; usually the direction of small target motion and radial grating rotation was left constant over several experiments in order to be able to test variations of other parameters.
The coordinate system used here is that of Palka (1967). It assumes an origin for the animal’s eye looking directly lateral in the horizontal plane which approximately bisects the eye. In the horizontal plane then, directly anterior is 90° anterior and directly posterior is 90° posterior; in a transverse plane approximately bisecting the eye, directly dorsal is 90° dorsal and directly ventral is 90° ventral. The equator is then the horizontal plane and the zero meridian lies in the transverse plane bisecting the animal’s eye.
The region of greatest sensitivity lies along the equator and somewhat posterior, and for determination of functions of spatial frequency, time and habituation it was primarily this region that was tested; with the radial grating pattern at the origin and the small target just posterior to the grating. For the usual animal-to-pattern distance of 9 in. the small target subtended 5-6° in visual angle and the inhibitory radial grating pattern 37° in visual angle. Other animal-to-pattern distances ranged from 3 in. to 50 in., and in some experiments target size was changed correspondingly to preserve its angular size; little difference was observed in excitatory or inhibitory response when target size was not so changed. The small target (T in Fig. 1) was an occluding edge moving at a constant velocity of 12° (visual angle) per second across a 5·6° bright disc. The excitatory stimulus thus lasted approximately 0·5 s. The radial grating tangential velocity was 11° (visual angle) per s. The grating pattern angular rotational velocity was 37° (pattern plane angle) per s during rotation unless otherwise indicated. These were optimal parameters, chosen by test, but responses were not sensitive to variations. Calibrations were obtained with an oscilloscope and photomultiplier tube viewing the stimulus through a narrow slit.
The perceived nominal spatial frequency of a radial grating is obviously a function both of the number of stripes composing the pattern and of the visual angle the grating subtends at the eye of the animal, which is in turn a function of the absolute size of the grating and its distance from the animal. It can be shown (see Appendix) that, for a grating subtending a given angle (θ in Fig. 1), perceived nominal spatial frequency can be approximated by the variable F, obtained as follows. Each cycle of pattern delimits a portion of the perimeter of the grating, forming an arc. The chord (L in Fig. 1) of this arc subtends a certain visual angle at the eye; this angle, a in Fig. 1, measures the number of degrees of visual angle per cycle at the perimeter of the grating. The reciprocal of the angle a (i.e. cycles per degree of visual angle) is defined as F, the spatial frequency of the radial grating. In the experiments reported here, when the grating subtended a visual angle of 37°, the 90-, 40-, 20- and 10-stri^B patterns gave values of F of 0·397, 0·175, 0·088 and 0·045 cyc/deg of visual angle respectively; when the grating subtended 90 ° the 90-, 40-, 20- and 10-stripe patterns gave values of F of 0·177, 0·079, 0·040 and 0·021 cyc/deg of visual angle respectively. Note that these values are changed if either the number of stripes or the visual angle subtended by the grating is altered. The methods of fabrication, illumination and rotation of these radial gratings have been described previously (Palka & Pinter, 1975).
The moving edge in the small target had predominantly low spatial frequencies, which is the complement of the situation for precision radial grating patterns. The edge and small disc were formed by projection through a fixed aperture of a moving edge attached to a loudspeaker driven by an amplified function generator. Synchrony of the abrupt initiation of motion of the edge and rotation of the radial grating was checked by an oscilloscope and photomultiplier tube, and rechecked by observation during each experiment; a Digipulser DS-i master timer controlled these motions, the Ortec 4620/21 histogram units and the gating of the spike counters, as well as the inter-stimulus interval. A counter in the histogram units controlled the number of trials, and another counter (one flip-flop) alternated trials for interleaved runs. Spike counts were transcribed by hand from the gated electronic counter display.
The luminance of a bright bar of the radial grating pattern was 1200 lumens/m2 and that of a dark bar approximately o lumens/m2. The bright small disc had a luminance equal to that of a bright bar of the radial grating pattern. When experiments were performed in a light surround, that surround was at a luminance 1·5 log10 units below that of a bright bar, and approximately 130° minimum extent in visual angle, centred at the origin. When the disc was occluded in light-surround experiments, the occluded portion had the same luminance as the surround, but the excitatory response was approximately the same as in a dark surround.
Active controls are defined as runs where the illumination of the radial grating pattern was extinguished and a black curtain placed over it, but all else remained the same including the alternation of small target motion with simultaneous small target motion and rotation. Thus the effect of any auditory response of the DCMD could be detected. There was none, as the motor drive and relay were well insulated against sound production. The slowly moving loudspeaker cone produced no sound.
Excitation and inhibition by radial grating patterns
Excitation of the DCMD by radial grating patterns is shown in Fig. 2. The response, either in terms of total number of spikes or peak spike frequency, decreased as the number of stripes was increased, at a constant grating diameter of 37° of visual angle. (Generally peak spike frequency is a less reliable measure than spike count, and in Fig. 5 the solid triangles show the dependence of spike count E on spatial frequency for the data of Fig. 2.) The response lasted about 200 ms in response to all tested periods of rotation, and had a latency that was constant for any given number of stripes.
The effect of rotation of radial grating patterns upon the response of the DCMD to small target motion is shown in Fig. 3. In the presence of an adjacent stationary grating, the response to the small target (plots T) consisted of about 100 ms of high-frequency spiking followed by a lower spike frequency. The response was quite constant over the 80 min required for the records in Fig. 3, typical of a healthy preparation. It was also unaffected by the number of stripes in the static radial pattern. When the target was presented together with the rotation of the grating (plots RT), however, there was a reduction in number of spikes (inhibition) with gratings of 90, 40 and 20 stripes (compare each RT plot with its T plot control). The effects of the inhibition appear just after the initial high-frequency bursts and disappear about 270 ms after the onset of the response. With gratings of 10 stripes, the spike frequency was generally elevated during this period.
Figs. 4 and 5 show inhibition and excitation by radial gratings as a function of the spatial frequency of the grating, rather than as a function of time. Thus, the data of Fig. 3 are displayed as a difference in spike count as the open triangles in Fig. 4. The 10-stripe pattern (spatial frequency 0·045) is again seen to be excitatory, and it can be seen that as stripe number is increased, i.e. with gratings which produce less excitation when presented by themselves (closed triangles), there is more inhibition of the small target response.
In two experiments the effect of varying radial grating pattern rotation speed on inhibition of response to the small target was tested, at a spatial frequency of 0·169 cyc/deg and a temporal frequency of 1·4–8·6 Hz. (20-stripe pattern subtending 19° of visual angle). Inhibition was not a function of temporal frequency between 1·4 and 5·4 Hz. At 8·6 Hz there was a slight decrease in inhibition. A temporal frequency of 5·4 Hz is quite low, and Rowell et al. (1977) first saw post-convergence IPSPs at a temporal frequency of 12·5 Hz. Thus if temporal frequencies in the region of 12 Hz were employed, inhibition could actually increase due to the increase of post-convergence inhibition with increase of temporal frequency.
The dependence of inhibition (I) of the small target response by the grating on the spatial frequency of the grating is described for dark surround and light surround conditions in Figs. 4 and 5 respectively. The continuous curves, which are averages over a number of experiments, indicate that there is a transition from excitation to inhibition at about 0·05 cyc/deg (a value of F corresponding to a 10-stripe pattern subtending 33·2° of visual angle). (This will apply to harmonics of the spatial frequency as well as to the frequency itself.) When the pattern size is changed, the transition point is still approximately 0·05 cyc/deg, as can be seen by comparison of the open triangles (a pattern of 37° of visual angle) and the open circles (a pattern of 90° of visual angle) in Figs. 4 and 5. Further, to obtain the continuous curves it was necessary to use a range of pattern sizes from 90 to 19° visual angle, and in each experiment the set of points of (I) from different pattern sizes overlapped. Overlapping occurred even at the high frequency end of the curve, where the inhibition falls to zero because the radial grating pattern becomes less well resolved. The limit of acuity of the locust is approximately 1·0 cyc/deg (corresponding to a 90-stripe pattern subtending 14·4° of visual angle) (Palka & Pinter, 1975). In summary, a radial grating pattern is a localized inhibitory ‘background’ if its spatial frequency components are resolvable and do not lie below 0·05 cyc/deg, below which point it becomes excitatory. The spatial frequency of maximal inhibition is about 0·17 cyc/deg, which corresponds to a 90-stripe pattern subtending 93·1° of visual angle, or 40-stripe pattern subtending 37·7°, or a 20-stripe pattern subtending 18·6°.
To show that the excitation evoked by a radial grating pattern alone is complementary to its inhibition, the excitation due to rotation of the pattern alone has been plotted in Figs. 4 and 5, for both pattern sizes. Excitation decreased with increasing spatial frequency, and the curves overlapped for the two pattern sizes. Maximal rate of change of both inhibition and excitation with respect to spatial frequency occurred in the same region of spatial frequency. This would reinforce the hypothesis that one is a function of the other. In other words, it is possible that the grating response has a self-inhibitory component which inhibits excitatory components of the response and also inhibits the small target response. This could explain the phasic characteristic of response to rotation of radial gratings (Fig. 2).
The characteristics of excitation and inhibition reported here do not vary substantially when the surrounding stationary light background of 130° visual angle is introduced (see Methods). Initially this background was introduced as a control for stray light artifacts caused by the moving stimuli, and no significant differences in response to the radial grating or in inhibition of small target response by the radial grating were seen. However, in the light background, Fig. 5, the augmentation of small target response by the grating is considerably larger than in dark background, Fig. 4.
Inhibition was found to be independent of the initial presence of a light or dark bar of the radial grating pattern adjacent to the small target. In two experiments the possibility of a small target inhibiting another small target was tested. Invariably the response to two targets of the kind described above placed 40° apart in the visual field in areas of normal to high sensitivity was greater or equal to that for one target alone.
The region of radial grating pattern sizes where inhibition becomes strongly dependent on the visual angle subtended by the pattern is shown in Fig. 6. Inhibition decreases very sharply below a radial grating pattern size of approximately 19° visual angle, while above that size inhibition is in the region of values found for pattern sizes up to 90° visual angle. At approximately 8°, inhibition cannot be found at any spatial frequency. Spatial frequencies used for the results of Fig. 6 were in the range of 0·086– 0·472, which, by examining Figs. 4 and 5, can be seen to be the region of maximal inhibition. The radial grating patterns used were the 10-, 40- and predominantly 20-stripe patterns.
In Fig. 7 the inhibition is shown in plots RT as a function of the time of initiation of radial grating rotation, beginning with simultaneous rotation in Fig. 7 A. A distinct ‘valley’, representing the point of maximal inhibition in plots RT (compare to plots T above), can be seen 185 ms after initiation of rotation, in all cases except A. In Fig. 8D the inhibition (I) of Fig. 7 is plotted as a function of delay of rotation. The result is similar to that for the cricket (Palka, 1972), although there the greater inhibition was probably due to the much larger field of inhibitory rectangular stripes. In contrast to these results, if the radial grating is rotated first for 400 ms, then stopped and small target motion immediately initiated, only a general suppression of response to the small target is observed. This suppression, tested in several experiments, is not a function of spatial frequency except for an abrupt fall-off above 0·4 cyc/deg (approximately a 90-stripe pattern subtending 37° visual angle), which is caused by approaching resolution limits (Palka & Pinter 1975). This suppression is decreased by approximately one-third by delaying small target motion 500 ms after cessation of radial grating rotation. However, if the grating rotation is not stopped, the suppression is generally somewhat increased.
In determinations of inhibition (I) it was never found that the inhibition was a suppression caused by a higher peak spike frequency in the initial response to simultaneous target and pattern motion than target motion alone. Rather, the peak spike frequency usually followed the same dependence on spatial frequency as did spike count. This is an important point, as there are many measures of spike activity of potential significance to the nervous system. Three measures of immediate interest in the records of experiments reported here are peak initial spike frequency, average spike frequency in the initial high frequency burst, and total spike count during the stimulus. Of additional interest is whether peak initial spike frequency can influence total spike count, perhaps by adaptation. Fig. 8 A illustrates the point for the records of Fig, 3 (for which (I) is plotted in Fig. 4, open triangles). For the inhibitory spatial frequencies, above about 0·08 cyc/deg (40-stripe pattern subtending 90° of visual angle), the peak spike frequency for simultaneous target and pattern motion was less than that for target motion alone. Therefore, the inhibition (7) is not due to a greater peak spike frequency for simultaneous motion. At 0·05 cyc/deg (10-stripe pattern subtending 33·2° of visual angle) the inhibition has become excitation (see open triangles of Fig. 4) and this is reflected in the greater peak spike frequency for simultaneous motion. If instead of peak spike frequency the average spike frequency in the 100 ms initial peak of response is plotted (Fig. 8 A, solid symbols), a nearly parallel case is seen. Variations in spike frequency for target motion alone (triangles) are typical of preparation drift.
Since the computation by the nervous system of effectiveness of stimuli or points in the stimulus field is often modelled by addition of excitatory variables or subtraction by lateral inhibition, it is important to determine experimentally whether the addition or subtraction is arithmetic, i.e. linear. The inhibition or augmentation of small target response by the radial grating pattern was not a linear process in terms of spikes removed or added. For inhibitory gratings, Fig. 8B shows the number of spikes removed by the grating from the small target response as a function of the number of spikes caused by grating rotation alone for the experiment of Fig. 3. The number of spikes removed by grating rotation was always greater than the number of spikes produced by grating rotation alone. In contrast, the number of spikes added by augmenting gratings was always less than the number of spikes caused by the grating alone. This is illustrated in Fig. 8C for several experiments with maximal augmentation at low spatial frequencies. Thus the gratings were more effective inhibitors than augmentors of small target response.
In the course of these experiments the question of optimal timing of grating rotation for maximal inhibition arose. Since grating rotation preceding small target motion causes a suppression perhaps simply due to preceding neuronal activity (see above), optimal timing of inhibition was tested as in Fig. 7 for grating rotation following initiation of small target motion. For the records of Fig. 7 the inhibition (I) is plotted in Fig. 8D as a function of delay of rotation. Since the inhibition decreased with increase of delay it can be concluded that although delayed rotation produces effective inhibition, simultaneous rotation is optimally inhibitory on small target response.
O’Shea & Rowell (1975) and Rowell et al. (1977) have proposed a classical lateral inhibitory network as a model for reduced response to wide field stimuli, and a corollary to this mechanism is protection of excitatory synapses on to the LGMD from decrement for wide field stimuli. In fact the habituation in response to wide field stimuli is far less than that to small field stimuli (O’Shea & Rowell, 1975). To determine whether the inhibition due to radial gratings can be explained by the same mechanism, non-interleaved runs of simultaneous radial grating and small target motion alone were made with interstimulus interval of 10 s rather than 30 s to increase effects of habituation. In Fig. 9 A for a radial grating pattern diameter of 37° and spatial frequency yielding strong inhibition, the decrement in response to simultaneous small target and radial grating motion (triangles) is certainly less than that for small target motion alone (circles). The same can be said for Fig. 9B where spatial frequency is now lower but still inhibitory. Fig. 9C illustrates a similar experiment with an animal displaying an unusual resistance to habituation; the difference in decrement is in the same direction but much smaller. It is apparent that with radial grating inhibition, habituation is often reduced. However, in most experiments the trials with and without radial grating motion were interleaved to avoid habituation dependent bias in the inhibition (I).
An interesting prediction of differences in habituation for radial grating excitation alone can be made on the basis of the results of Fig. 9. If a salient difference for the DCMD between wide field and small field stimuli is the spatial frequency content, a low spatial frequency radial grating of the same size as one of a high spatial frequency should have a more strongly habituating response. In Fig. 10 it can be seen that the decrement in response for the low spatial frequency grating is far greater than that for the high spatial frequency grating and the prediction is fulfilled.
Distribution of inhibition and excitation in the receptive field
Determinations of a detailed receptive field map of excitation in response to a small stationary target have been made by Palka (1967). Since the radial grating pattern is a localized inhibitory stimulus, it can then be used to determine a receptive field map of inhibition. In Fig. 11 the small target was placed in the origin of the coordinate system (i.e. directly lateral in the horizontal plane 9 in. from the eye), and the radial grating pattern was placed in various positions in the receptive field, but always 40° from the small target and 9 in. from the eye, subtending 37° visual angle. Polar plots of inhibi- tion were then obtained. The majority of such plots from a series of 14 animals fell into one of the two types shown in Figs. 11 (a) and (b). Most receptive fields showed greatest inhibition in the posterior-ventral quadrant (Fig. 11 a), but several showed the strong difference between anterior-posterior and dorsal-ventral axes illustrated in Fig. 11 (b). Rarely was there strong dorsal inhibition, and posterior inhibition was usually stronger than anterior. This is seen in Fig. 11 (c), where a mean of complete polar plots for ten animals is shown. Comparing this to the map of excitation sensitivity (Palka, 1967), the anterior-posterior axis is similar but the dorsal-ventral axis is reversed. Placing the radial grating further away from the target, up to 60°, did not substantially change the distribution of inhibition sensitivity.
In attempting to measure the change of inhibition as the radial grating was moved away from the small target, the results could be affected by excitation sensitivity gradients. In the experiment of Fig. 12(a) the small target was placed 50° ventral on The dorsal-ventral meridian, and inhibition (/) measured for the grating centred at the four more dorsal points (open circles). There was a fall-off of inhibition with increasing separation between target and grating. The excitation (E) evoked by the small target at the positions shown (closed circles) was slightly smaller in the dorsal than ventral regions. In Fig. 12(b) the target was placed 50° posterior and the inhibition (I) was seen to fall off with increasing distance (open circles); the same was found for the target placed 50° anterior (open triangles), but the fall-off was less when the grating was moved into the posterior rather than the anterior region.
To assess the differences in fall-off of inhibition along the dorsal-ventral and anterior-posterior axes, the data points from a series of experiments like those of Fig. 12 were fitted by linear regression, and the average of the slopes over eight animals is shown in Table 1. When the slope is positive, fall-off of inhibition is indicated. It is notable that along the dorsal-ventral axis, the strong inhibition in the ventral region appears to outweigh any fall-off or gradient effect moving ventrally, as the slope is slightly negative. A similar effect is seen along the anterior-posterior axis, as the gradient of inhibition in the posterior direction is far less than in the anterior direction, corresponding to the greater inhibition in the posterior region than in the anterior.
Spatial frequency, temporal frequency and temporal relationships in inhibition
I have attempted here to dissect out the salient variables in grating excitation and inhibition: spatial frequency, size, contrast frequency, time of occurrence and position in the receptive field. Spatial frequency is an important variable because it can be used to economically characterize many visual stimuli, and responses put in these terms can be related to anatomically based mathematical models of the nervous system (Cowan, 1977).
In these studies temporal frequency has been varied in some cases, but has never been high enough to evoke predominantly the known (Rowell et al. 1977) temporal frequency-dependent inhibition (post-convergence inhibition) in the locust LGMD and DCMD. Rowell et al. (1977) have shown by intracellular recording techniques that IPSPs in the LGMD, mediating post-convergence inhibition, may in some cases occur at the low temporal frequencies employed in this study. Since the measure of inhibition in this study, spike count, is not dependent on recording conditions or electrode placement as in intracellular recording, spike count may be a much more sensitive measure of inhibition and it is possible that post-convergence inhibition is part of the mechanism of the inhibition found in this study.
In general, temporal frequency always has the possibility of modifying responses to moving spatial stimuli (Pinter, 1972; Srinivasan & Bernard, 1975). For example, too low a temporal frequency may reduce the response in some phasic neural channels, and too high a temporal frequency will reduce the response of any neural channel unable to transmit rapid changes in time. Here, however, nearly the same inhibition (I) was obtained at a given spatial frequency of the stimulus pattern with temporal frequency (a function of spatial frequency and velocity) differing by a factor of two. In Figs. 4 and 5 the temporal frequencies for the overlapping points all differ by a factor of two, but inhibition (I) is nearly the same and the spatial frequency dependence is preserved. Further, in two experiments the dependence of inhibition (I) over a large but low temporal frequency range (1·4 – 5·4 Hz - see Results) was tested, and no dependence on temporal frequency was found. Since there was also no effect of pattern size (Figs. 4, 5), the dependence of inhibition (I) on the radial gratings for sizes above 19° visual angle (Fig. 6) must be primarily on their spatial frequency content. Examination of Figs. 4 and 5 will also show that changing spatial frequency by a factor of four causes a change in response from maximal inhibition to augmentation; therefore a change of temporal frequency by a factor of four might be considered a large range for this study.
The time course of inhibition (I) when small target motion preceded radial grating rotation was examined in detail (Fig. 7). However, when the radial grating rotation period preceded small target motion, the inhibition (I) became numerically very large (0·8 – 0·95) and, unlike the case in Fig. 7, was not dependent on spatial frequency. For this reason it was termed a ‘suppression’. It could not be determined whether this suppression was clearly dependent on the excitation or on the inhibition evoked by the radial grating, but it was not dependent on spatial frequency as was the radial grating excitation or inhibition. The lack of dependence on spatial frequency and the time course of decay of this suppression to approximately a third of its initial value in 100 ms suggests it is due to a quite different mechanism than the inhibition caused by Simultaneous rotation of radial gratings. Rowell et al. (1977) found that the time course of decay of the post-convergence inhibition (mediated by IPSPs in the LGMD antecedent to the DCMD) was similar to that of this suppression, although they did not measure spatial frequency dependence. It is thus quite possible that the postconvergence inhibition mediates this suppression and a prediction of lack of dependence on spatial frequency of the IPSPs in the LGMD can be made by this observation. On the other hand it is also possible that the suppression is either a simple post-excitatory depression due to any excitation, or a saturated continued inhibition.
The choice of the specific small target stimulus used here was made primarily on the basis of obtaining as large an excitatory response as possible in order to measure inhibition, as inhibition by radial gratings was not observable in small excitatory responses. The radial gratings cause both excitatory and inhibitory components of response, and the excitatory component may add to the excitatory response to the small target. In many cases where the excitatory response to the small target was quite low, e.g. 3 – 5 spikes, the added excitatory component due to the radial grating appeared to obscure its inhibition of response to the small target.
In the plots T (small target response only) in Fig. 3 there is an initial large onset response after the first arrow, followed by a decay, followed by a resumption of a higher level of spike frequency. While this decay is probably an inherent property of the neural response, the possibility remains that it is partly due to the nature of the small target stimulus. At a time corresponding to the end of this decay, approximately 230 ms, the occluding edge in the 5·6° bright disc has reached the half-way point and the edge has maximal length, and zero rate of change of length. Thus it could be true that the decay is partly a function of the decreasing rate of change of length as the half-way point is approached by the edge. Dependence on rate of change of edge length could be a factor in responses to rectangular gratings viewed through a round window. However, use of a rectangular window of approximately 7·5 × 10° through which an edge of fixed length moved (T. Abrams, unpublished observations) yielded the large onset followed by a decay, followed by a resumption of a higher level of spike frequency. This suggests that the decay may be an inherent property of the neural response, perhaps a rapid adaptation due to the initial high-frequency burst.
The light background (see Methods) was used (Fig. 5) initially as a control against stray light artifacts, generated by the rotating grating, because the light background considerably reduces the contrast level of such artifacts. These artifacts were reduced so that they were imperceptible to the experimenter, but the possibility of their effects on the DCMD remained. Since these stray light artifacts were primarily of low spatial frequency content (e.g. edges, lines) the fact that the inhibitory regions of Figs. 4 and 5 are similar indicates the ineffectiveness of these stray light artifacts to the DCMD. However, the excitatory or augmenting regions of Figs. 4 and 5 are quite different, and greater augmentation is seen for light background. Since a continuous distribution of ‘harmonics’ of the nominal spatial frequency of the radial grating pattern (see Fig. 13) is present in all cases, it may exert inhibition while the nominal spatial Wequency of the pattern is excitatory, below 0·05 cyc/deg. The greater augmentation by radial gratings seen in light background (Fig. 5), might be due to the lower valudl of contrast of this distribution of harmonics with respect to the overall illuminatioIP level, and thus possibly due to their lesser effectiveness in inhibition, when the nominal spatial frequency of the grating is below 0·05 cyc/deg.
Spatial relationships in the receptive field
Since the inhibition reported here may be related to or mediated by peripheral excitatory channels, it is of considerable interest to compare the distribution of inhibition in the receptive field with the distribution of excitation determined by Palka (1967). He determined that response to dimming a small 1° test target was greatest at the centre of the eye (the origin) and along the equator, greater in the posterior than the anterior regions. The distribution of inhibition by radial gratings generally agrees with this determination (Fig. 11 c) except for a reverse distribution on the dorsal-ventral axes.
The large field inhibitory rectangular grating used by O’Shea & Rowell (1975) and Rowell et al. (1977) had a nominal spatial frequency of 0·066 cyc/deg which is in the inhibitory region of spatial frequency in Figs. 4 and 5. This grating had ventral and dorsal sections flanking the excitatory target on the equator. However, the inhibition fell off with target-to-grating distance much more rapidly than was the case for radial gratings (Fig. 12). One reason for this may be seen in Fig. 11(c), where the dorsal region would give quite weak inhibition, although the ventral region would give stronger inhibition. It may be that their rectangular gratings, which spanned the entire horizontal extent of the receptive field in the anterior-posterior direction, exerted the major inhibition only near the equator in animals with inhibitory receptive fields like that summarized in Fig. 11(c); this would give rapid fall-off of inhibition as the grating halves are moved away from the equator. For an animal with a receptive field like that of Fig. 11 (b), the fall-off would be even more rapid.
Lateral inhibition was proposed by O’Shea & Rowell (1975) and Rowell et al. (1977) as a mechanism to explain discrimination against wide field stimuli in their experiments. Their wide field stimuli were not simple large, but had also variation in contrast (nonzero spatial frequency spectrum). The motivation of some of the experiments reported here was to determine how much this discrimination depended on these two salient parameters of the wide field stimuli: size and spatial frequency. In Figs. 4– 6 it was demonstrated that changing size by a factor of four did not change dependence of inhibition (7) on spatial frequency. Thus, for the radial gratings larger in diameter than 19° visual angle the dependence of this discrimination, measured as inhibition (7), is primarily on spatial frequency, not size; this is consistent with a model of lateral inhibition. Ratliff, Knight & Graham (1969) have shown theoretically that lateral inhibition is capable of performing spatial frequency filtering including discrimination against high spatial frequencies independently of the size of the stimulus. Thus the results of the present study are consistent with the model of the acridid movement detector system of Rowel et al. (1977).
In the dragonfly, Olberg (1978) discovered many units in the ventral nerve cord which discriminated against wide field stimuli but the ventral cord contained also many units which discriminated in favour of wide field stimuli. These latter units are of interest here because they suggest the existence of other networks where lateral inhibition would be augmented or replaced by lateral summation. However, in the acridid movement detector (Rowell et al. 1977, and Figs. 9 and 10, this article), responses to wide field stimuli habituate less than to small field stimuli and the lateral inhibition is thought to protect synapses from habituation. In the dragonfly the units discriminating in favour of wide field stimuli habituated far less than those discriminating against wide field stimuli. If lateral inhibition in wide field favouring units is indeed replaced by lateral summation, these units and their antecedents must be unusually resistant to habituation and not require protection from habituation by lateral inhibition. The dragonfly units discriminating against wide field stimuli may be mediated by strongly habituating interneurones on which lateral inhibition has no effect.
Applicability of spatial frequency and Fourier analysis
In this study it is clear that the receptive field of the DCMD determined by a small dimming field will not predict the response of the DCMD to extended stimuli such as gratings. The receptive field in this case is not a point-spread function in terms of measurable quantities, and thus the Fourier transform of the receptive field function will not yield a meaningful spatial frequency transfer function. The DCMD must actually be tested by extended stimuli such as gratings. Thus, spatial Fourier analysis in its strictest sense is not applicable to the DCMD. However, the characterization of the grating is appropriately made in the spatial frequency domain as that is a way of describing it which can be generalized to other stimuli. Fourier analysis can then be applied in a restricted sense to motion of objects in a restricted region of the receptive field. Fourier analysis provides a prediction that, when not fulfilled, aids one in examining characteristics of stimuli or the structure of the nervous system in order to discover the reason for non-applicability. Fourier analysis is not simply a more complicated way of describing the receptive field, but at the very least, a motivation to relate the receptive field of a visual cell to its response to extended spatial stimuli.
Comparison to vertebrate visual systems
There are two important psychophysical results for which the presently studied simpler visual system can provide a model. The first is a study of elevation of visual thresholds to a low spatial frequency test flash in the presence of a striped background over which the eye made a saccade, or which was moved at saccadic velocities (Brooks & Fuchs, 1975). In all cases tested, the threshold to a test flash increased significantly, from 1·29 to 2·27 log10 intensity units. The spatial frequency of the stripe repetition in the 50 × 75° background frame was 0·25 cyc/deg. In a study having almost exactly the stimulus arrangement used by Rowell et al. (1977), where a small 3·5° diameter test stimulus was flanked above and below by a moving rectangular grating, Mateef, Yakimoff & Mitrani (1976) tested elevation of visual threshold to the 3·5° diameter low spatial frequency test flash for grating stripe frequency of 0·2 cyc/deg. The moving grating raised threshold by about a factor of 2·3 over that for a static grating, and fcicreasing the separation between the upper and lower flanks to n° reduced the threshold rise to insignificant values. It is interesting that both groups of investigators chose frequencies close to the inhibitory maximum for the locust. Although the optical resolving power of the locust is nearly two orders of magnitude less than that of the human, the spatial frequency of inhibitory gratings is about the same. Therefore optical factors are probably not dominant in the inhibition, but for unknown reasons the neural factors are operating similarly.
If the rise of threshold in the above psychophysical studies is caused by inhibition, the locust DCMD and human visual system have a striking parallel of inhibition of response to small objects by gratings. Further, the inhibition seems to fall off with distance between object and grating in a parallel manner to that of the DCMD. Perhaps these common properties of the two visual systems are important in all visual systems in animals which must discriminate between small objects and large textured backgrounds and distinguish between object movement, world movement and selfmovement.
This study was supported by a grant (EY 01285) from the National Eye Institute, NIH. T. Abrams, P. Neudorfer and J. Palka critically reviewed the MS.
Grating intensity patterns have wide application as test patterns for optical systems and visual systems research. Windmill or radial grating patterns have certain advantages over rectangular grating patterns. Most notable of these is the lack of low-frequency spatial spectrum components generated by spatial truncation of rectangular grating patterns (Palka, 1965; Barlow, 1965; Burtt & Catton, 1969). Radial grating patterns have been used in a study of suppression of visual response by high spatial frequency textured backgrounds (Pinter, 1977) and in determining optomotor responses (Srinivasan, 1977). However, to avoid unwanted low spatial frequency components in radial grating patterns it is necessary to fabricate them with great precision in periodicity and in this way a satisfactory measurement of compound eye visual acuity has been made (Palka & Pinter, 1975). The spatial frequency spectrum of precision radial grating patterns is important in interpreting the above studies and for any usage of them as test patterns or visual stimuli.
For Fig. 13, increasing the inner radius reduces the peak amplitude (for = 0·9r2, the peak decreases by 17%) but does not shift the initial rise nor peak position of the spectrum shown. Decreasing the inner radius affects primarily the amplitudes beyond the peak. Changing r2 only scales the spectrum in frequency.
It is clear that there are no unwanted low spatial frequencies in the spectrum of precision radial grating patterns either as a function of angular or radial spatial frequency coordinates. Moreover, the most important spectral properties of these patterns are relatively insensitive to variations of the number of stripe cycles and the inner and outer radii. Note that for any other angular variation gθ(θ) in the pattern having radial symmetry the spectrum can be calculated by equation (3).
An important requirement for grating patterns is lack of errors in the periodic spatial variation producing the high spatial frequencies. This is what the adjective ‘precision’ refers to, and, to the extent these errors are present, there will exist unwanted low spatial frequency components. These will confound any measurements made resting on the assumption there are no low-frequency components. This is especially serious when the visual system tested has a greater response to low spatial frequencies than to high ones, which is often the case. The noise in the response due to the low-frequency artifactual noise in the pattern will often far exceed the signal in the response due to the high frequency components (Palka & Pinter, 1975).
Windmill patterns (N = 4) have been used in vertebrate vision studies (Werblin & Copenhagen, 1975; Enoch, Lazarus & Johnson, 1976; Ingling et al. 1977), where the temporal frequency of contrast variation was of primary interest. Nevertheless, the spatial frequency spectrum of such a pattern may affect the response of a visual system independently of temporal frequency variation produced in individual neural channels.
The interpretation of responses to rotated radial gratings is simplest when the excitatory receptive field of the visual system tested exceeds the grating in size and has no motion directional preference, as in the present study. Truncated rectangular gratings can produce obscuring responses due to the truncation (Burtt & Catton, 1962) and this was analysed experimentally and theoretically by Palka (1965) and Barlow (1965). However, when the spatial truncation of the rectangular grating is performed by the visual system tested and not by the stimulus spatial limits, the obscuring response due to spatial truncation disappears. Yet, there do exist many experimental situations where radial gratings are preferable to rectangular gratings because of the truncation effects of the latter, but special attention must be devoted to the precision of the former.