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Dynamic nonlinearities enable direction opponency in Drosophila elementary motion detectors

Nature Neuroscience volume 22, pages 1318–1326 (2019)Cite this article

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Abstract

Direction-selective neurons respond to visual motion in a preferred direction. They are direction-opponent if they are also inhibited by motion in the opposite direction. In flies and vertebrates, direction opponency has been observed in second-order direction-selective neurons, which achieve this opponency by subtracting signals from first-order direction-selective cells with opposite directional tunings. Here, we report direction opponency in Drosophila that emerges in first-order direction-selective neurons, the elementary motion detectors T4 and T5. This opponency persists when synaptic output from these cells is blocked, suggesting that it arises from feedforward, not feedback, computations. These observations exclude a broad class of linear-nonlinear models that have been proposed to describe direction-selective computations. However, they are consistent with models that include dynamic nonlinearities. Simulations of opponent models suggest that direction opponency in first-order motion detectors improves motion discriminability by suppressing noise generated by the local structure of natural scenes.

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Fig. 1: Measurements of opponency and LN models for motion detection.
Fig. 2: The first-order DS neurons T4 and T5 exhibit opponent responses.
Fig. 3: Opponency persists under changes of contrast and stimulus type.
Fig. 4: Temporal tuning of opponent suppression.
Fig. 5: T4 and T5 cells with silenced synapses continue to show opponency.
Fig. 6: Feedforward models can produce DO responses.
Fig. 7: Opponency improves velocity discriminability in EMDs.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Code availability

Code for all modeling is available at https://github.com/ClarkLabCode/OpponencyModels.

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Acknowledgements

We thank J.E. Fitzgerald for alerting us to the intuitive explanation of multiplicative opponency with one biphasic filter, as well as for helpful conceptual comments and suggestions. We thank J.B. Demb, H.H. Clark, the members of the Clark Lab and our anonymous reviewers for helpful comments on the manuscript. The Arclight construct was a gift from V. Pieribone. M.S.C. was supported by an NSF GRF. D.A.C. and this research were supported by NIH R01EY026555, NIH P30EY026878, NSF IOS1558103, a Searle Scholar Award, a Sloan Fellowship in Neuroscience, the Smith Family Foundation and the E. Matilda Ziegler Foundation.

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Authors and Affiliations

  1. School of Engineering and Applied Science, Yale University, New Haven, CT, USA

    Bara A. Badwan

  2. Interdepartmental Neuroscience Program, Yale University, New Haven, CT, USA

    Matthew S. Creamer & Damon A. Clark

  3. Department of Physics, Yale University, New Haven, CT, USA

    Jacob A. Zavatone-Veth & Damon A. Clark

  4. Department of Molecular, Cellular, and Developmental Biology, Yale University, New Haven, CT, USA

    Damon A. Clark

  5. Department of Neuroscience, Yale University, New Haven, CT, USA

    Damon A. Clark

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Contributions

B.A.B., M.S.C. and D.A.C. designed experiments. B.A.B. acquired and analyzed data. B.A.B., M.S.C., J.A.Z.V. and D.A.C. analyzed models. B.A.B., M.S.C., J.A.Z.V. and D.A.C. wrote the paper.

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Correspondence to Damon A. Clark.

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Integrated supplementary information

Supplementary Figure 1 Opponency in modeling and behavior.

a) Intensity plots of the sinusoidal gratings moving in the cell’s preferred direction (PD) and anti-preferred null direction (ND), and the sum of the gratings. b) Summary of classical direction opponency. In the classic view, opponent direction-selectivity depends on opposing motion stimuli producing responses with opposite signs. c) An alternative scheme for detecting opponency in the presence of signal rectification. It considers a signal to be opponent if the addition of an ND stimulus suppresses responses to PD stimuli. d) Schematic diagram of a Hassenstein-Reichardt Correlator (HRC) model of direction-selectivity. This model multiplies the instantaneous contrast at one point in space with the delayed contrast at a second point in space to create DS signals. The delay is represented by the filter in the box on the vertical arms of the model. By subtracting two of these multiplied signals with opposite directional tuning, the final signal is DO. e) Schematic of a generic DO model. f) Schematic of LN model that creates a DS signal using a spatiotemporally oriented linear filter that is convolved with the stimulus and followed by a nonlinearity. The oriented space-time filter acts to enhance the variance of stimuli with the same orientation (direction). When the nonlinearity is purely quadratic, the result is a pure motion energy model. g) The experimental apparatus used to measure behavioral responses. The fly is tethered to pin and placed on an air-suspended ball in front of a panoramic visual display. h) Behavioral optomotor responses themselves exhibit classical opponency. The turning response to clockwise (CW) rotational sinewave gratings (blue, n = 69 flies) produces a CW response that is opposite in sign to the response to counterclockwise (CCW) sinewave gratings (orange, n = 69 flies). The combination of the two (purple, n = 19 flies) produces no response. Shaded region indicates stimulus duration.

Supplementary Figure 2 Composite sinusoidal grating contrast distributions.

a) Contrast probability density function of a single sinusoidal grating. b) Contrast probability density function of a composite sinusoidal grating with components moving in opposing directions. c) Contrast probability density function of a composite sinusoidal grating with components moving in orthogonal directions.

Supplementary Figure 3 Glider stimuli generate preferred-direction enhancement and null-direction suppression.

a) Space-time intensity plots of two-point gliders at two temporal update rates (5Hz for top panels, 60 Hz for bottom), that are either uncorrelated (left column), correlated to the right (middle column), or correlated to the left (right column). Gliders consist of binary stimuli with enforced correlations over space and time1,2. Duration of plots is 1 second; azimuthal extent is 60º. b) The responses of layer 1 T5 cells in both layers to the gliders specified in (a) (n = 10 flies for 5Hz, and n = 15 flies for 60Hz). Time traces show the cells increase their responses to gliders correlated in their PD relative to uncorrelated at both update rates. However, the response to motion in their ND only decreases relative to uncorrelated at the lower update rate. Shaded region indicates stimulus duration. c) The responses of layer 2 T5 cells to the same stimuli, showing the same phenomenon as in (b). Shaded region indicates stimulus duration. d) Averaged responses of T4 cells to the gliders with 5 Hz temporal update rate (puncorr,PD = 0.0012, puncorr,ND = 0.0002, n = 13 flies). e) Averaged responses of T4 cells to the gliders with 20 Hz temporal update rate (puncorr,PD = 0.0020, puncorr,ND = 0.85, n = 10 flies). f) Averaged responses of T4 cells to the gliders with 60 Hz temporal update rate (puncorr,PD = 0.0078, puncorr,ND = 0.074, n = 9 flies). (g-i) Averaged responses of T5 cells to the gliders, as in (d-f). In T4 and T5, the lower update rates show stronger null-direction suppression relative to uncorrelated stimuli (puncorr,PD = 0.0020, puncorr,ND = 0.0020 and n = 10 flies for 5 Hz; puncorr,PD = 0.0001, puncorr,ND = 0.010 and n = 14 flies for 20 Hz; puncorr-PD = 0.0010, puncorr,ND = 0.25, n = 15 flies for 60 Hz). (* p < 0.05, ** p < 0.01, *** p < 0.001, by a paired two-sided Wilcoxon signed-rank test).

Supplementary Figure 4 Tetanus toxin expression in T4 and T5 eliminates rotational behavioral responses to motion.

Sinewave gratings of various temporal frequencies were presented to flies and mean rotational behavioral responses were recorded. When tetanus toxin was expressed in T4 and T5, the flies failed to respond to these rotational stimuli, though genetic controls did. This shows that tetanus toxin expression successfully blocked synaptic transmission from these cells. The genotype in this experiment is identical to the genotype used to measure calcium signals in T4 and T5 in Fig. 5. (+ > TNT n = 9 flies; T4T5>GCaMP n = 9 flies; T4T5>GCaMP,TNT n = 3 flies).

Supplementary Figure 5 Linear-nonlinear models for direction-selective computations.

a) Space-time intensity plots of the sinusoidal gratings moving in one direction, the other direction, and the sum of the gratings. b) Sample spatiotemporal receptive field for a linear-nonlinear (LN) model of T4. c) Sample time traces of PD (blue), ND (orange), and PD + ND (purple) sinusoidal gratings after linear filtering by the receptive field shown in (b). d) Commonly used nonlinearities in LN models of elementary detectors include (clockwise from top left) a quadratic, an exponential, a soft rectifier, and a half-quadratic. All of these nonlinearities are expansive and static. e) LN models with expansive, static nonlinearities cannot be opponent with this suite of sinusoidal inputs (see Supplementary Notes 1 and 2). f) Motion energy linear-nonlinear model consisting of a spatiotemporal linear filter with oriented positive and negative lobes followed by a static quadratic nonlinearity. g) The components of PD and ND motion are presented as (1,1) + (2,2), and (1,2) + (2,1) respectively. h) The responses of a motion energy model to PD and ND motion compared to the sum of responses to their constituent parts. This model produces both PD enhancement and ND suppression relative to the linear prediction based on a decomposition of the stimulus. That is, \(r\left( {1,1} \right) + r\left( {2,2} \right) < r(PD)\) and \(r\left( {1,2} \right) + r\left( {2,1} \right) > r(ND)\). i) A linear-nonlinear model with a compressive (sigmoidal) nonlinearity can be tuned to produce weakly opponent responses at one contrast level, but is non-opponent when contrast is halved. j) The peak responses of T4- and T5-cells to single, full-contrast moving edges are larger than the peak responses to sinusoidal gratings, suggesting that sinusoidal grating inputs do not saturate the calcium signal.

Supplementary Figure 6 Multiplicative model intuition, model response timeseries, model parameter sweeps, and linearity tests.

a) An HRC half-correlator where the temporal filter of one arm is the derivative of the other. The model can be decomposed into separate components. Flipping the sign of the filters allows for the subtraction of the two models with each tuned to opposing directions (delayed arm switched). b) Response timeseries for the rectified multiplier model in Fig. 6b (see Methods for details on timeseries computation). c) Response timeseries for the dynamic gain model in Fig. 6c. d) The effect of sweeping the parameters of the dynamic gain model on the degree of opponency (see Methods for details on parameter sweeps for this and other models). The parameter values chosen are indicated by a red circle. e) The effect of sweeping the parameters of the dynamic gain model on the response to the sum of PD and OD gratings. f) Response timeseries for the three-input conductance model in Fig. 6d. g) As in (f), but for the three-input conductance model. h) As in (g), but for the three-input conductance model. i) The PD and ND voltage responses of the three-input model in Fig. 6d compared to a prediction of the response based on a linear model and responses to counterphase gratings at 8 different spatial phases3.

Supplementary Figure 7 Joint probability distributions of elementary motion detector responses and natural scene velocity.

See Methods for an explanation of how each distribution was computed. Marginal probabilities are shown above and to the left of each joint probability distribution. Model diagrams are shown in Fig. 7. a) Hassenstein-Reichardt Correlator half-detector (‘half-HRC’). b) HRC. c) Rectified half-HRC. d) Rectified HRC.

Supplementary information

Supplementary Figs. 1–7, Supplementary Table 1, and Supplementary Notes 1–3

Reporting Summary

Supplementary Video 1

The stimuli used to probe opponency. A rightward drifting sinusoid grating is shown first (blue), followed by a leftward drifting sinusoid grating (orange). Last, the counterphase grating consists of the sum of the rightward and leftward gratings (purple).

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Badwan, B.A., Creamer, M.S., Zavatone-Veth, J.A. et al. Dynamic nonlinearities enable direction opponency in Drosophila elementary motion detectors. Nat Neurosci 22, 1318–1326 (2019). https://doi.org/10.1038/s41593-019-0443-y

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