Fast-scale adaptive changes of directional tuning in fly tangential cells are explained by a static nonlinearity

The fly lobula plate contains individually identifiable motion-sensitive neurons with large receptive fields(Hausen, 1984), which integrate directional signals according to flow patterns occurring during flight (Krapp and Hengstenberg,1996). This class of neurons, named tangential cells after their anatomy, represents an ideal system for developing and testing models of motion detection and adaptation (Egelhaaf et al., 2002). This article focuses on two important spiking tangential cells, H1 and V1.

H1 is known to modify its response characteristics depending on previous stimulation history, both over short and long time scales(Fairhall et al., 2001). The focus of this paper is on relatively short time scales and brief adaptors [for a characterization of adaptive responses to longer lasting adaptors, see Neri and Laughlin (Neri and Laughlin,2005)]. When the time scale is short, adaptive effects are sometimes referred to as `temporal dynamics' in the literature(Perge et al., 2005a). We use these two descriptions interchangeably in this paper, because the effects we report here can be accounted for without truly adaptive changes in system parameters.

We were interested in how the neuronal response to a local directional signal is affected by signals that are presented immediately before, and whether the effect of the preceding signals depend on their spatial location within the receptive field. Our stimulus consisted of a stream of two simultaneous patches that appeared at different locations and changed direction independently. By analyzing the neuronal response conditional upon the occurrence of selected combinations of directions at specific locations and time points, we could derive detailed descriptors of how the temporal and spatial interaction of two directional signals affect firing rate at scales of∼200 ms and ∼20° of visual angle.

We measured highly reproducible, spatially local temporal dynamics that appear to satisfy expectations from mechanisms with adaptive utility [e.g. redundancy reduction (Barlow,2001)]. We wished to establish whether active changes in the parameters specifying the system were required to account for the observed results. Our simple computational schemes demonstrate that these effects are largely explained by models that do not involve any adaptive change, but rather very early nonlinear operations acting before signals are further integrated by the tangential cell. We propose a physiological interpretation of these models based on the connectivity between medulla and lobula plate(Douglass and Strausfeld,1995). Because the effects we observe are closely related to those reported for macaque middle temporal (MT) area(Perge et al., 2005a; Perge et al., 2005b) and cat posteromedial lateral suprasylvian (PMLS) region(Vajda et al., 2006), we speculate that a substantially similar modeling scheme may apply to both vertebrate and invertebrate motion pathways. This speculation is supported by recent computational work on primates(Rust et al., 2006).

We recorded extracellularly from six V1, eleven H1, one V2/V3 and one H3 neuron in the contralateral (right) lobula plate of 19 female blow flies Calliphora vicina Robineau-Desvoidy 1830. Each neuron was easily identified by its firing pattern and directional preference in response to a wide-field, high-contrast sinewave grating that optimally drove the neuron(Hausen, 1984) (see V1 neuron example in Fig. 2A). The monitor (ViewSonic PT795, Walnut, CA, USA) was driven by a VSG graphics card(Cambridge Research Systems, Kent, England) at 180 Hz, covered roughly 78°×74° (width × height) and was typically centred at 40°/5° azimuth/elevation. Results on simultaneously presented patches from these experiments were presented previously(Neri, 2006). The same dataset has been analyzed for the present study, but the analysis herein does not overlap with the preceding analysis and presents results that cannot be derived from the earlier work (Neri,2006). With the exception of the preliminary tests with wide-field gratings to identify the neurons (see above), which we repeated only a small number of times (e.g. the directional tuning curve in Fig. 2A shows the mean ±s.e.m. of 4 repetitions), all other measurements come from a large number of repetitions. More specifically, s.e.m. values for Fig. 2C were computed from an average of 273 repeats per data point. Data points and s.e.m./Z-scores for Fig. 2D–K were computed from 68 repeats on average per data point, those in Fig. 3 from 125 on average per data point. Fig. 4B shows mean ± s.e.m. from an average of 302 repeats per data point, and each point on the surfaces in Fig. 6A was computed from 2150 repeats.

We obtained maps of local directional preference(Fig. 2B) using a vector white-noise reverse-correlation technique(Srinivasan et al., 1993; Neri, 2006) applied to a stream of multiple patches moving in random directions at a constant speed of 23° s^–1 (Fig. 1A, leftmost frame). Each patch subtended roughly 19°×18° (100% contrast on a 38 cd m^–2 mean luminance background, carrier spatial frequency 0.1 cycles deg.^–1, s.d. of Gaussian envelope 4°) and moved for 220 ms in one of eight possible directions at cardinal and diagonal axes. After inspection of the vector map for the entire receptive field, we chose two highly responsive locations (see Fig. 4 for a quantitative assessment of responsiveness) and stimulated them in pairs (Fig. 1A). When possible, we tested more than 1 pair for the same neuron.

Analysis and modeling (below) are presented here using compact notation. A smoother, more intuitive and descriptive account is provided in the first section of Results. The direction of the patch at location x as a function of time t is D_x(t), where 0 is downward (↓). The time-locked neuronal firing is F(t)(firing was computed by binning every 1 patch duration). The vectorτ(Ω)={t₁,t₂,...t_n}is the subset of time points for which the expression Ω is satisfied. For example, τ(D₁=0) is the subset of time points at which patch 1 was moving ↓. The relevant descriptors in this study are captured by the expression S_x,y(d₁,d₂)=〈F{τ[D_x(t)=d₁D_y(t–Δt)=d₂]}〉_t,where Δt=1 patch duration. For example, the surface plot in Fig. 1E (patches at same location) was obtained for x=y=1, the one in Fig. 1F (patches at different locations) for x=1 and y=2, and that in Fig. 1D for x=1, y=2 and Δt=0. Fig. 2H,I were obtained from Fig. 2E,F by subtracting〈 S_x,y(d₁,d₂)〉_d1from S_x,y(d₁,d₂)for every d₂ to obtain

For the model in Fig. 1C the response at time t from the filter at location x is r_x(t)=cos[D_x(t)]+cos[D_x(t–Δt)]+2,i.e. tuning is sinusoidal (peaking at ↓) and temporal integration is over two patch presentations. The final output is f(r₁+r₂)–1/10 (the subtractive term allows the output to be negative, thus simulating inhibition via firing rates below baseline), where f is the Naka–Rushton equation f(r)=r^β/(r^β+α^β)with α=〈r〉_t and β=2. The output of the basic linear model (Fig. 6B) is simply (r₁+r₂). For the model in Fig. 1D the final output is f(r₁)+f(r₂). For the model in Fig. 1E, the response from location x is

Our goal was to characterize H1/V1 responses to a directional signal at position 1 and time t (Fig. 1A, broken blue circle) as a function of the directional signal that preceded it at time t–Δt. The preceding signal could be delivered at the same location 1 (broken white circle) or at a different spatial location 2 (broken red circle), and we analyzed these two conditions separately. Fig. 2shows how we obtained the two corresponding descriptors for an example V1 neuron. As typical for V1, this cell responded most vigorously to a full-field grating moving downwards (Fig. 2A). Correspondingly, its vector map within the frontolateral visual field shows multiple locations with downward directional tuning(Fig. 2B; the map was obtained using a vector white noise reverse correlation technique, see Materials and methods). We selected the two locations within the receptive field indicated by coloured circles. Directional tuning at these locations, as tested using single patches restricted to the individual locations, was consistent with that indicated by the map (Fig. 2C).

We then stimulated the two locations simultaneously using two Gabor patches moving in random directions (Fig. 1A). At any given time t, the response to two simultaneous patches is very close to that expected from quasi-linear summation across all possible combinations of different directions[Fig. 2D; for a detailed analysis of responses to two simultaneous patches, see Neri(Neri, 2006)]. As shown in Fig. 1B, we performed the analysis for two patches that followed one another within the streaming sequence. The surface plot in Fig. 2E reports the intensity of the response to a patch presented at location 1 (whose direction is on the x axis) when preceded by a patch at the same location (whose direction is on the y axis). Fig. 2F reports the results of a similar analysis, but performed in relation to the preceding patch that appeared at the other location 2. The two surfaces clearly differ. In Fig. 2F (patches at different locations) the direction of the preceding patch is virtually irrelevant (the surface shows little variation along the y axis), the response being modulated predominantly by the patch that is currently moving when the response is recorded at time t (the surface varies along the x axis as expected from the directional tuning at location 1). In Fig. 2E (patches at same location) the response is reduced when the preceding patch was moving in the same direction as the current patch (darker pixels along the diagonal), on top of a large modulation in response to the current patch that is similar to Fig. 2F.

To bring out these effects more clearly, we factored out the expected response to both the current patch (time t) and the preceding patch(time t–Δt) in the assumption that they are integrated linearly by the neuron. This can be achieved by simply subtracting the directional response to each patch after averaging along the direction of the other patch (see Materials and methods). A similar procedure was used by Felsen et al. for experiments with same-location oriented patches in cat area 17 (Felsen et al., 2002). In simple terms, this procedure consists of taking the average across different columns (thus obtaining a directional response for the patch at time t–Δt regardless of the direction of the patch at time t) and subtracting this average from each column in the surface matrix. The outcome of the subtraction is shown in Fig. 2H,I. This leaves us with the response to the patch at time t conditional upon the direction of the patch at time t–Δt, but without contamination from the delayed response that is simply expected from the stimulation provided by the patch at time t–Δton its own. Fig. 2G shows slices across Fig. 2H (along the rows indicated by the coloured rectangles), showing the effect whereby the response is reduced by a preceding patch moving in the same direction as the patch at time t.

The second subtraction is for the expected response to the patch at time t regardless of the direction of the patch at time t–Δt, which is obtained by averaging and subtracting across rows rather than columns. The outcome of this subtraction is shown in Fig. 2J,K. For purely linear summation of the responses to the two individual patches, we expect this surface to be completely flat. This prediction is confirmed when the two patches occupy different locations(Fig. 2K), but not when they are at the same location (Fig. 2J). In the latter case we observed a clear pattern with negative modulations along the central diagonal (blue) and nearby positive modulations(red). In the rest of the paper we only focus on the two descriptors at Fig. 2J,K, because they encapsulate sequential effects for patches at same (J) and different (K)locations.

Fig. 3 shows `same' and`different' plots (analogous to Fig. 2J,K) for six more neurons, including H1, V2 and H3 as well as V1. Although noisy, these surface plots show that the main observation in Fig. 2, i.e. that strong modulations are only observed for same-location patches and not for different-locations patches, holds true for all the other neurons we recorded from. Moreover, the diagonal structure of negative and positive modulations is present in all `same' location plots. In the following we demonstrate the validity of these two claims for the entire population, one at a time. Preliminary to that, however, it is necessary to establish that the two regions we selected for testing were responsive enough to ensure that the observed lack of any effects for the `different' descriptor did not simply result as a consequence of one region being unresponsive. Fig. 4A plots the distribution for the difference in preferred direction between the two patches. For 96% of our tests the difference did not exceed 45°, and the majority of the tests involved locations with matched directional preference (peak at 0). In Fig. 4B each point plots the response ranges of the two locations that were paired in a given test, one against the other on the two axes (the largest response range within a pair was assigned to the x axis). Response range was defined as the difference between largest and smallest responses on the directional tuning curve. For a location that is not directionally selective or that is unresponsive, response range (although positive by definition) should not be significantly different from 0. It is clear from Fig. 4B that no such unresponsive locations were included in our dataset, as all response ranges are significantly greater than 0. Moreover, the responsiveness of the two locations within a pair was highly correlated (r²=0.94),meaning that the two locations we selected for testing were not only similar in directional preference but also in overall responsiveness. On average, the response range of the less responsive location within a pair was 72% of the response range of the more responsive location.

To assess whether surfaces like those shown in Fig. 3 present strong modulations, we determined the percentage of pixels that reaches statistical threshold (|Z|>2) for all double-patch tests individually. Fig. 5A plots this quantity for the `same' surfaces (on the y axis) versus`different' surfaces (on the x axis) for all neurons and tests. All points lie above the unity line, demonstrating that `same' surfaces modulated far more significantly than `different' surfaces (paired t-test for`same' versus `different' returns P<10^–10; when restricted to the V1 population P<0.002, to the H1 population P<0.001). We wished to determine whether the few modulations that reached significance in the`different' surfaces were consistent across tests and neurons. For this purpose, we computed the pixel-wise correlation between all possible pairs of surfaces for the H1 and V1 populations separately. Fig. 5B plots correlations for`same' surfaces (on the y axis) versus `different' surfaces(on the x axis), for both V1 (solid circles) and H1 (open circles). Correlations were all positive for `same' surfaces (t-test P<10^–40 for both V1 and H1), but not different from 0 on average for the `different' surfaces (P=0.08 for V1, P=0.63 for H1). This result demonstrates that the few significant modulations within `different' surfaces were not consistent across tests/neurons, confirming our claim that `different' surfaces were essentially featureless. Below we therefore focus on `same' surfaces.

We wished to determine whether the diagonal structure suggested by the`same' surface plot in Fig. 2Jwas consistently observed across the entire sample. As a starting point, we report that the modulation at the pixel indexed by the preferred direction on both axes (↓ on x and ↓ on y in Fig. 2J) was invariably negative (P<10<sup>–11</sup>) for `same' surfaces, but not different from 0 for `different' surfaces (P=0.82). We then studied the 4 immediately surrounding pixels along the diagonals, indicated by circles in Fig. 6D. If no diagonal structure is present (as is the case for the left-hand surface plotted in Fig. 6D), we expect similar modulations at the positions indicated by black circles when compared with the modulations at the positions indicated by white circles. If, however, the structure of the surface is diagonal, with a negative modulation along the central negative diagonal and positive modulations along the nearby parallel diagonals (as suggested by the surface plot in Fig. 2J), we expect negative modulations at the white positions and positive modulations at the black positions. Fig. 5C plots the modulation at the white positions (averaged between the two positions) on the y axis versus the modulation at the black positions on the x axis for all tests and neurons. Clearly the pattern conforms to the diagonal structure discussed earlier.

To further support our claim that we did observe a consistent diagonal structure across our entire dataset, we computed Fourier power spectra for all surfaces individually, and extracted power at different orientations. The presence of a diagonal structure in the surface should be reflected in the presence of larger power at the corresponding orientation in the power spectrum. Fig. 5D plots power for the orientation corresponding to the negative diagonal (on the yaxis) versus power for the orientation corresponding to the positive diagonal (on the x axis). For `same' surfaces (solid symbols) the former is larger than the latter (paired t-test P<10<sup>–7</sup>), as we expect from the diagonal structure that was already uncovered by Fig. 5C. No such difference is observed for `different' surfaces (open symbols, P=0.17). Similar results were obtained when we considered power at vertical and horizontal orientations, which did not differ from the positive diagonal. In summary, both Fig. 5C and Fig. 5Dconcur to demonstrate that the diagonal structure suggested by Fig. 2J was consistent across our entire sample and set of tests.

Fig. 6A shows `same' and`different' surfaces averaged across the entire neuronal population after realigning the preferred direction of each neuron to downward. No modulation is observed when the two patches are at different locations, but a clear pattern is observed when they are at the same location, in line with the population results at Fig. 5A,B. Specifically, in the latter case the modulation resembles a diagonally tilted Gabor function (notice the additional negative ripples within the bottom-left and top-right portions of the surface), as already demonstrated by the population analysis at Fig. 5C,D. This result is closely related to that obtained by Perge et al. for MT neurons when tested with same-location patches [compare fig. 8A in Perge et al.(Perge et al., 2005a) with the left-hand surface plot in Fig. 6A here]. In a separate study, Perge et al. also tested different locations within the centre and surround of MT neurons' receptive fields(Perge et al., 2005b). Although they did not explore inter-patch temporal dynamics to the same degree that was done here, their results were consistent with ours (see Discussion).

We emphasize that, although the averaging procedure used to obtain the surfaces in Fig. 6A relies on the assumption that the different neurons we tested can be lumped into one descriptor, this assumption is not necessary for our claims on the structure of `same' and `different' surfaces, which motivated our choice of modeling schemes described in the next section. The logic behind our modeling strategy is driven by two observations about the structure of `same' and `different'surfaces: (1) that only `same' surfaces showed consistent modulations and (2)that these modulations conformed to a diagonal structure along the negative diagonal, with a central negative modulation surrounded by positive modulations. We demonstrated the validity of both observations across our neuronal population without assuming that data from different neurons could be averaged together, so this assumption is not necessary for our conclusions. In Fig. 6A we present the grand average for reference purposes only, so that the modeling results can be directly compared to an average descriptor. We also note that our analysis could not discern any difference across neuronal types in relation to the metrics that are relevant for this study.

As a first step, we attempted to simulate the results in Fig. 6A using the very minimal model that we could design as a potential candidate for this process. This model simply consists of two linear filters applied to the two different patches (see Materials and methods). Each filter has a directional tuning curve that resembles V1, and integrates across two patch presentations(temporal integration window=2 patch durations). The responses from the two filters are summed to generate the output from the neuron (this is the same as using just one filter). This model is like that cartooned in Fig. 1C, but without the late nonlinearity (red) before the output. As we expected from the way in which we computed the two surfaces in Fig. 6A, they show no modulation for a simple linear model of this kind(Fig. 6B).

We then introduced a basic nonlinearity directly borrowed from standard spike-output nonlinear transducers (see Materials and methods). The nonlinearity was initially placed very late in the model, right before the sum from the two filters was converted into the final output(Fig. 1C). This simple nonlinearity generated clear modulations at the level of the two surfaces in Fig. 6C. The most conspicuous discrepancy with respect to the experimental results is that this simulation shows no difference between same-location and different-location conditions. This outcome is expected because the model in Fig. 1C integrates the responses from the two patches before, not after, the nonlinearity. At the level of the nonlinearity there is no distinction between the two locations.

We remedied to this failure of the simulations by simply placing the nonlinearity at an earlier stage in the model. More specifically, the responses to the two patches are now separately subjected to the nonlinear transducer before, rather than after, they are summed(Fig. 1D). This simple modification eliminated all modulations from the `different' surface, without affecting the result obtained earlier for the `same' surface(Fig. 6D). However, the outcome of this model still falls short of providing an account for the experimental results in Fig. 6A. More specifically, the surface in Fig. 6D is not oriented diagonally. This is an important failure of the model, as demonstrated by the following example. If the patch at time t is moving down to the right and it was preceded by a patch at time t–Δt that was moving in the same direction(right-most white circle in Fig. 6D), the model predicts a negative modulation that is identical to when the preceding patch at time t–Δt was moving down to the left (right-most black circle in Fig. 6D), i.e. orthogonally to the patch at time t. This is clearly not the case for the real neurons: as a consequence of the diagonal structure in the experimental data,the modulations associated with these two conditions are very different in Fig. 6A (see also Fig. 5C,D, where we showed that this result holds across the entire dataset).

We were able to capture this aspect of our data by simply placing the nonlinearity at an even earlier stage in the model, before the two linear filters corresponding to the two patch locations(Fig. 1E). We introduced a bank of four front-end linear filters with different directional tuning, one for each cardinal direction. The output of each front-end filter was nonlinearly transduced individually, after which the four outputs were summed using weights that conformed to the V1-like linear filter used in the previous models (i.e. the front-end filter preferring downward was weighed more than the other three). Although there is still room for improvement, this model does generate a diagonally oriented structure for the same-location condition. It also simulates directional preference for individual patches(Fig. 2C) and patches presented simultaneously (Fig. 2D)(simulations not shown).

Fast-scale adaptive effects have been observed in fly(Fairhall et al., 2001),macaque (Priebe and Lisberger,2002; Priebe et al.,2002; Perge et al.,2005a) and cat (Vajda et al.,2006) neurons. Particularly relevant to this study are the results of Perge et al. (Perge et al.,2005a). They showed that neurons in macaque MT respond to a sequence of moving patches presented at the same location within the receptive field in a manner that is very similar to what we observed here for fly tangential cells (compare their fig. 8A with the left-hand surface in Fig. 6A) (see also Priebe et al., 2002). Vajda et al. found similar results for neurons located in cat PMLS(Vajda et al., 2006).

Related results have also been reported for orientation tuning in monkey(Müller et al., 1999) and cat (Dragoi et al., 2000; Dragoi et al., 2001; Dragoi et al., 2002; Felsen et al., 2002) primary visual cortex, where exposure (even brief) to an adapting stimulus causes the preferred orientation of the cell to shift away from the adapting orientation. This repulsive effect was also present in our data, as demonstrated in Fig. 2G (blue and red traces show that preferred direction shifts away from the preceding direction,indicated by the colour-coded arrows).

Perge et al. (Perge et al.,2005a) did not provide quantitative simulations of their results,which they interpreted as deriving from a mixture of static nonlinearities and fast-scale adaptation. More specifically, they recognized that the reduced response to a patch preceded by another patch moving in the same direction could result as a consequence of a simple compressive nonlinearity acting on a sluggish temporal integrator (model in Fig. 1C), but speculated that positive modulations away from the central diagonal (warm-coloured streaks in Fig. 6A) may reflect specific network interactions before or within MT [p. 2114 of Perge et al.(Perge et al., 2005a)]. In a general sense this intuition was correct, because the model in Fig. 1E could be described as a small network that performs simple nonlinear processing before feeding signals to the tangential cell where spikes were recorded. Our simulations provide a computable model for implementing this idea quantitatively.

Apparently complex phenomena can unexpectedly be accounted for by extremely simple nonlinear models. A recent example in the fly literature is provided by the modeling work of Borst et al. (Borst et al., 2005), who offered a simple explanation for some fast-scale adaptive effects that had been previously reported(Fairhall et al., 2001) in H1(see also Brenner et al.,2000). Borst et al. showed that the basic Reichardt model displays quasi-instantaneous velocity gain control, and that it can explain H1 behaviour without any adaptive change in its internal parameters(Borst et al., 2005). Some effects happen on a longer timescale(Fairhall et al., 2001) and are likely to involve adaptive parameter changes.

The temporal interactions we measured in spiking tangential cells may appear to fulfill an adaptive role. For example, the reduced response to a stimulus moving in the same direction and the enhanced response to a change in stimulus direction, both of which are implied by the surface in Fig. 6A, can be interpreted within the framework of redundancy reduction and enhanced signaling of novel events (Barlow, 2001). However,similar to Borst et al.'s modeling work, our simulations show that these adaptation-like effects need not imply that the system is adaptively modifying its internal structure in response to its stimulation history. The model in Fig. 1E is static, i.e. its parameters do not vary depending on previous stimulation. Nevertheless it provides an adequate description of the data(Fig. 6E).

It is also interesting to note that the model in Fig. 1E shares similarities with a modeling framework that has recently been proposed for plaid selectivity in MT (Rust et al.,2006). Plaids involve the spatial superposition of two directional signals, which differs from the stimuli we and others have used to study temporal interactions between different patches. However the response properties of MT neurons to this class of stimuli can be characterized by surface plots similar to those in Fig. 3, where x and y axes refer to the directions of the two signals that generate the plaid [see fig. 1 in Rust et al.(Rust et al., 2006)]. The experimental surfaces are consistent with a model involving a bank of front-end filters, each subjected to a nonlinear operation (gain control normalization), followed by a weighted pooling stage and finally a spike converter [see fig. 3a in Rust et al. (Rust et al., 2006)]. The structure of this model is clearly related to Fig. 1E, despite the fact that the two models refer to different stimuli and neuronal types.

Because our stimuli consisted of multiple patches at different locations within the receptive field, we were able to study temporal interactions between patches that appeared at the same as well as at different locations. We only observed interactions for patches that appeared at the same location and one immediately after the other (we performed our analyses forΔ t>1 patch duration and found no effects). This result may not apply to macaque MT neurons, which show some rapid adaptation across different locations within the receptive field(Priebe and Lisberger, 2002). A related difference between fly and macaque motion-sensitive cells has been reported for long-lasting adaptors: in this case MT neurons adapt only locally(Kohn and Movshon, 2003),whereas fly neurons display some degree of global adaptation(Neri and Laughlin, 2005). These studies are not entirely comparable, however, not only because of species differences but also because the effect of adaptation was often measured using different metrics and stimuli; e.g. use of directional gain(Neri and Laughlin, 2005)rather than contrast gain (Kohn and Movshon, 2003).

The directional effects (or lack thereof) that we report here for patches at different locations within the receptive field have not been studied extensively in other species. As mentioned previously, these experiments were performed for patches that appeared at the same location and the results obtained were very similar to ours (Perge et al., 2005a; Vajda et al.,2006). Perge et al. (Perge et al., 2005b) conducted experiments in which different spatial regions were stimulated separately, but they focused on the comparison between the classical receptive field and the so-called `surround'. Surround responses are very different from those obtained within the classical receptive field,as there is convincing evidence that the former are controlled by mechanisms that differ from those that support responses within the receptive field(Huang et al., 2007). Perge et al. (Perge et al., 2005b) also briefly discuss interactions between patches that were both within the centre of the receptive field. They report nonlinear interactions for differently located patches that appeared at the same time (Δt=0), but no nonlinear interaction when presented successively (Δt=26 ms). These authors only tested two directions (preferred and anti-preferred) and did not report detailed data as to the consistency of this result across their sample (this question was not central to their article), but this last observation is certainly in agreement with ours [see last paragraph of their results section, p. 2056 (Perge et al.,2005b)]. In conclusion, although more data on MT is required to confirm Perge et al.'s analysis, their observations indicate that a successful simulation of their data would require the two separate pooling stages that are implemented by the model in Fig. 1E, in the same way that this modeling scheme was necessary to explain our results.

It seems reasonable to expect that, had we made our patches significantly smaller, we would have observed some interaction across different locations. The model in Fig. 1E implies that the receptive field is subdivided into regions that pool signals from the preceding stages in a spatially localized fashion. If the stimuli are sufficiently small to place the two patches within the receptive field of the front-end filters, then clearly the two patches will interact as if they had been presented at the same location. This prediction also applies to the local effects demonstrated by Kohn and Movshon(Kohn and Movshon, 2003), as well as to the original H1 study (Maddess and Laughlin, 1985) (see also de Ruyter van Steveninck et al.,1986); however, these previous studies have not tested it. We attempted to reduce patch size on a few occasions, but this required us to increase the spatial frequency of the carrier in order to preserve enough detail within the patch to confer it directional properties (as the envelope of the Gabor is reduced to approach the spatial period of the carrier, the patch turns into a blob). This resulted in suboptimal spatial frequencies for the neuron, combined with stimuli that only excited a very small portion of the receptive field. Even at 100% contrast, we failed to find stimulus parameters that drove the cell with sufficient reliability to carry out an extensive investigation of temporal interactions between pairs of very small patches. We hope to resolve this limitation in future studies.

All the building components of our models are basic standard operators in computational modeling, their physiological plausibility being straightforward. The question remains, however, as to whether the particular way in which they are assembled in Fig. 1E is interpretable in the context of the anatomy and physiology of the fly lobula plate.

For V1, a potential interpretation may be that the front-end filters represent the VS system, which is known to feed onto V1(Kurtz et al., 2001; Haag and Borst, 2004). Although VS neurons convey information predominantly via graded potentials rather than spiking, their response is nonlinear in several respects (Farrow et al., 2005; Farrow et al., 2006), so the early nonlinearity in Fig. 1Emay be implemented at the level of the VS system. There are several problems with this interpretation, however. First, the VS system is preferentially selective for downward motion, whereas the front-end layer in Fig. 1E consists of units with different directional selectivity. Despite the fact that VS receptive fields are heterogeneous in directional preference, it seems unlikely that the VS system would be able to support an extensive multi-directional input like that in Fig. 1E at every point in the receptive field of a V1 neuron. Second, VS receptive fields are very large, certainly larger than the patches we used in our stimuli. The spatial selectivity we demonstrated in Fig. 6A seems hard to reconcile with such extensive spatial pooling. Third and most importantly, a VS-like interpretation may apply to V1 but not H1, which receives direct retinotopic input from the medulla(Hausen, 1984). An interpretation based on intra-lobula network connectivity seems unlikely for H1. Because we observed very similar effects for both V1 and H1, our data argue against this class of interpretations.

An altogether different possibility is that the front-end stage in Fig. 1E is implemented at the level of the medulla, where directional selectivity has been documented(Douglass and Strausfeld, 1995)and receptive fields only represent small fractions of the visual space covered by H1 and V1 (Strausfeld and Lee,1991). These receptive fields are typically smaller than our patches of ∼20°×20°(Strausfeld and Gilbert,1992). The most likely candidates are bushy T-cells (particularly T5), small retinotopic neurons with bushy dendrites extending across a few neighbouring columns within the medulla(Douglass and Strausfeld,1995). These neurons leave the inner medulla and supply inputs onto lobula plate tangentials (Strausfeld and Lee, 1991). The spatially separate pooling of front-end signals in Fig. 1E would correspond to different compartments within the dendritic arborization of the tangential cell, which is plausible given the massive extent of these arborizations. This interpretation is consistent with previous modeling work on the emergence of directional selectivity across the medulla–lobula plate projection (Melano and Higgins,2005). Specifically, Melano and Higgins placed the relevant nonlinearity between T5 and subsequent pooling by the tangential cell [see their fig. 1b, where the nonlinearity is labeled `POS' (Melano and Higgins, 2005)].

In summary, our results on the temporal dynamics and interactions of directional signals within the receptive fields of spiking tangential cells support a simple and physiologically plausible scheme where an early nonlinearity between medulla and lobula plate generates response properties that may serve a fast-scale adaptive role. These properties, however, arise as a consequence of static nonlinearities, without requiring truly adaptive changes in the system. A similar demonstration of adaptive phenomena mediated by static nonlinearities in the fly has been recently provided for velocity gain control in H1 (Borst et al.,2005). Further work is needed to identify the exact components of this simple model, and to refine its structure in relation to empirical results that are not captured by its formulation in Fig. 1E.

This work was supported by the Royal Society (University Research Fellowship) and the Wellcome Trust (International Prize Travelling Research Fellowship).