A neuron that extracts directionally selective motion information from upstream signals lacking this selectivity must compare visual responses from spatially offset inputs. Distinguishing among prevailing algorithmic models for this computation requires measuring fast neuronal activity and inhibition. In the Drosophila melanogaster visual system, a fourth-order neuron—T4—is the first cell type in the ON pathway to exhibit directionally selective signals. Here we use in vivo whole-cell recordings of T4 to show that directional selectivity originates from simple integration of spatially offset fast excitatory and slow inhibitory inputs, resulting in a suppression of responses to the nonpreferred motion direction. We constructed a passive, conductance-based model of a T4 cell that accurately predicts the neuron’s response to moving stimuli. These results connect the known circuit anatomy of the motion pathway to the algorithmic mechanism by which the direction of motion is computed.
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We thank A. Nern for providing the driver line and image, K. Shinomiya and Janelia’s FlyEM project team for providing the reconstructed T4 cell morphology, M. Cembrowski for assistance with the NEURON simulations and E. Rogers for help with fly husbandry. We are also grateful to A. Hermundstad, J. Dudman, N. Spruston, B. Mensh and members of the Reiser lab for comments on the manuscript. This project was supported by the Howard Hughes Medical Institute.
Integrated supplementary information
(a) Top: expression pattern of the driver line used to target T4 cells (SS02344; reoriented substack of a confocal image volume). Similar images were obtained from at least 5 samples. Bottom: schematic of experimental setup. Blue square represents the full mapping stimulus grid from c. (b) Example single cell responses to ON square flashes (~11° × ~11°), presented for 140ms at each location on the indicated stimulus grid (inset). Individual trials in gray (n = 3 trials), mean in red. Inset: stimulus grid of non-overlapping squares, subtending 78.75° × 67.5° of the visual space. (c) Responses from example cell in b to bright and dark square flashes (n = 3 trials each). Note stimulus grid contains overlapping positions to map RF center more precisely. Inset: stimulus grid highlighting two of the nine stimulus positions with darker squares. This mapping procedure was performed for all the cells in the dataset.
(a) Circular mean of preferred direction for all recorded neurons (n = 17 cells). Lines connect data from the same cell, dot color depicts different speeds, and dot size the normalized mean response vector magnitude (scale in inset). (b) Histogram of the data in a, showing three distinct peaks corresponding to three of the four cardinal directions. (c) Responses from an example cell to eight different directions (rows) at four different speeds (columns). Responses were temporally aligned to the time the bar crossed the RF center. (d,e) Mean normalized vector calculated for each time point for responses in c, decomposed into magnitude (d) and angle (e). Vector was calculated from temporally aligned responses presented in c. This procedure can be considered as mimicking a downstream cell’s readout of differently tuned T4 cells with RFs centered at the same spatial position. Note, that for the two slower speeds the instantaneous PD flips by 180° after the bar passes the center (seen clearly in 10 out of 17 cells), since PD response is now hyperpolarizing while ND response is depolarizing (denoted with gray lines).
(a) Normalized peak depolarization (red) and peak hyperpolarization (blue) for all recorded neurons. Here, PD is presented from left to right, with peak depolarization aligned to position zero. A value of 4 indicates that a particular position gave the strongest depolarizing response at all four speeds, and a 2 indicates the largest hyperpolarizing response (since only the two slowest speeds were considered). (b) Angular distance between peaks of the hyperpolarization and depolarization curves in a. Black line indicates the mean.
Supplementary Figure 4 T4 responses to two-step apparent motion show null direction suppression, but no preferred direction enhancement.
Averaged baseline-subtracted responses (mean ± s.e.m.) to 160 ms flash stimuli presented along the PD-ND axis (n = 17 cells; expanded version of stimulus protocol shown in Fig. 3, applied to all recorded T4 neurons, here the five positions sampled are shifted by one position towards the leading side). Stimulus positions indicated correspond to those in Fig. 2. Apparent motion is presented as two flash stimuli timed to match their appearance during 14°/sec motion. PD motion indicated in red and ND motion in blue. Single position responses are shown in gray along the diagonal. Gray traces above and below the diagonal are time-aligned sums (computed as the superposition) of the diagonal SPFRs. Note that no enhancement for second bar responses occurs in the lower triangle, but clear suppression is present for most responses in the upper triangle.
(a) Comparison of PD and ND responses (mean ± s.e.m. , n = 31 trials, 16 cells) for measured, summed, rectified (summed after hyperpolarization removal), and scaled (rectified and central position response scaled to the magnitude of each position) traces. Data presented as measured and summed is reproduced from Fig. 4d. (b) Boxplots for Directional Selectivity Index (DSI) for the same data as in a by manipulation and speed, gray crosses represent outliers (* indicates DSI > 0 with p < 0.01, one sided unpaired t-test). The response reconstructed from amplitude-scaled versions of the SPFR at the central position (which lack the temporal sharpening of the depolarized component of trailing-edge SPFRs) do not show directional selectivity (see Methods for boxplot conventions). (c) Schematic for procedures applied in rectified and scaled versions of the SPFR sums in a.
(a) Summary of 1000 independent nonlinear least squares fits of simulation parameters (from randomized initial conditions) optimized to reproduce the measured SPFRs. Plot of sorted sum of squared errors (SSE) between each optimization result and the original SPFRs summed over all positions and all speeds. The smallest error solutions are found in distinct clusters that are color-coded and are further examined in b and c. (b) Spatial and temporal filters for excitatory and inhibitory conductances. Top: normalized conductance weights for excitatory (thicker line) and inhibitory synapses in three optimization solution-clusters. Each subplot shows resulting Gaussian distribution from 10, nearly indistinguishable, solutions (chosen at random) from each solution-cluster. Gaussian amplitudes were scaled by RM (inverse of the leak conductance), and the excitatory amplitude was further scaled by 10 for comparison. In solutions 1 and 2, the excitatory distribution is broader, and shifted towards the leading side (0 marks the leading end of the dendrite). Bottom: excitatory and inhibitory conductance pulse for 160 ms flash. In solutions 1 and 2 the excitatory conductance is much faster. Figure 5 data is based on Solution 1, example parameter values in Supplementary Table 1. (c) Comparison of measured SPFR data used for fitting and the simulation results. Only 160ms flashes are shown, but the model was fit to SPFRs at all 4 speeds. Each row shows a single solution from each solution-cluster labeled in a. The 3rd solution does not account for hyperpolarization on the trailing side and was therefore excluded from further analysis. (d) Comparison of mean measured responses to simulated predictions with parameters from solution-cluster 2 (Supplementary Table 1) to moving bars in the PD and ND. (e) Peak PD and ND responses measured in T4s, compared to the solution-cluster 2 simulation results from d. (f) DSI for the mean measured responses compared to the simulation results from d. Note that Fig. 5 b,c,d show these comparisons using solution 1 parameters.
(a) Averaged baseline-subtracted responses (mean ± s.e.m.) to 40 ms flash stimuli presented along the PD-ND axis (n = 3, same cells as in Fig. 3) in black. Single position responses are shown along the diagonal. Stimulus positions indicated correspond to those in Fig. 2. The time-aligned sum of the single position responses is shown in gray. Lines demarcate the maximal response to second bar in 3 example positions. Arrows point from summed prediction to measured response. (b) As a proxy for possible effect of calcium imaging21, the same data as in a are plotted after squaring the measured responses (in green). Gray traces represent the sum of squared single position responses. Note that in example i, the slight suppression in a, becomes an enhanced response in b, in example ii minimal enhancement becomes strong enhancement, and in example iii suppression is maintained.
Supplementary Figure 8 The space-time tilt in the T4 spatiotemporal receptive fields likely originates from the interaction of excitatory and inhibitory inputs.
Left: SPFRs from Fig. 2 (for 160 ms flashes) were replotted to approximate the spatiotemporal RF of T4 cells. Dashed line indicates stimulus onset. The RF features an excitatory lobe peaking in the center (by construction) and an inhibitory lobe following in time and offset spatially towards the trailing side. In this representation, the leading side responses appear to rise more slowly than central responses, which could conform with the temporal delay requirement of an HR-like mechanism. Center: the spatiotemporal RF plotted from simulated SPFRs generated from the (Solution 1) model parameters. Lines correspond to response traces shown in the inset. The apparent difference in onset times for different positions is the result of different response magnitudes, since the time constants at different positions in the model are identical by construction. Right: similar to center, but from simulations where the inhibitory inputs were removed. Note that in the model, removing inhibition completely removes the inseparable property of the filter, showing that the contribution of inhibition is sufficient to account for the tilt in the excitatory lobe.