Processing properties of ON and OFF pathways for Drosophila motion detection

Abstract

The algorithms and neural circuits that process spatio-temporal changes in luminance to extract visual motion cues have been the focus of intense research. An influential model, the Hassenstein-Reichardt correlator, relies on differential temporal filtering of two spatially separated input channels, delaying one input signal with respect to the other. Motion in a particular direction causes these delayed and non-delayed luminance signals to arrive simultaneously at a subsequent processing step in the brain; these signals are then nonlinearly amplified to produce a direction-selective response. Recent work in Drosophila has identified two parallel pathways that selectively respond to either moving light or dark edges. Each of these pathways requires two critical processing steps to be applied to incoming signals: differential delay between the spatial input channels, and distinct processing of brightness increment and decrement signals. Here we demonstrate, using in vivo patch-clamp recordings, that four medulla neurons implement these two processing steps. The neurons Mi1 and Tm3 respond selectively to brightness increments, with the response of Mi1 delayed relative to Tm3. Conversely, Tm1 and Tm2 respond selectively to brightness decrements, with the response of Tm1 delayed compared with Tm2. Remarkably, constraining Hassenstein-Reichardt correlator models using these measurements produces outputs consistent with previously measured properties of motion detectors, including temporal frequency tuning and specificity for light versus dark edges. We propose that Mi1 and Tm3 perform critical processing of the delayed and non-delayed input channels of the correlator responsible for the detection of light edges, while Tm1 and Tm2 play analogous roles in the detection of moving dark edges. Our data show that specific medulla neurons possess response properties that allow them to implement the algorithmic steps that precede the correlative operation in the Hassenstein-Reichardt correlator, revealing elements of the long-sought neural substrates of motion detection in the fly.

Extended Data Figure 1. Representative raw traces of responses to flashes of light of different duration from dark

a, Top: response of an Mi1 neuron to 200 ms, four consecutive 250 ms and 1 s full-field flashes of light from dark. Bottom: same as top for a Tm3 neuron. b, Same as a for a Tm1 neuron and a Tm2 neuron. c, Box plots illustrating the distribution of the OFF response as a percentage of the ON response for Mi1 (n =7) and Tm3 (n =10) and the ON response as a percentage of the OFF response for Tm1 (n =10) and Tm2 (n =11) averaged in Fig. 1. Black line, median; coloured line, average.

Extended Data Figure 2. Mi1, Tm3, Tm1 and Tm2 neurons encode stable information about luminance

a, Top left: averaged evoked responses (± s.e.m.) of Mi1 (n =7) in response to 5 s steps of light from dark to grey (0.5 intensity) to light to grey to dark. Top right: excerpts from the left trace where the pre-contrast change voltages have been matched. Bottom left and right: same as above for Tm3 (n =10). b, Tonic component (average difference in membrane potential between post- and pre-contrast change between 4 and 5 s after contrast change) as a percentage of the maximum peak response for brightness increments of the corresponding contrast difference. Error bars, s.e.m. c, d, Same as a and b for Tm1 (n =9) and Tm2 (n =7). The tonic component was measured as a percentage of the peak response for brightness decrements of the corresponding contrast difference. In all cases, expect for those marked with a cross, the distributions are significantly different from zero (P <0.05).

Extended Data Figure 3. Mi1, Tm3, Tm1 and Tm2 are not direction selective

a, Top: response of an Mi1 neuron to a white bar moving rightwards, upwards, leftwards and downwards at 100° s⁻¹ on a dark background. Bottom: same as top for a Tm3 neuron. b, Top: response of a Tm1 neuron to a black bar moving rightwards, upwards, leftwards and downwards at 100° s⁻¹ on a light background. Bottom: same as top for a Tm2 neuron. c, Average amplitude of the voltage response as a function of angle (0°, 90°, 180° and 270°) for Mi1 (n =2), Tm3 (n =2), Tm1 (n =2) and Tm2 (n =3) for a bar moving at 100° s⁻¹ (solid lines) and 400° s⁻¹ (dashed lines). The response amplitude was independent of the direction of motion in all cases.

Extended Data Figure 4. The response of Mi1, Tm3, Tm1 and Tm2 to a Gaussian noise stimulus is very reliable

a, Left: response of an Mi1 neuron to three consecutive 10 s presentations of an approximate Gaussian noise stimulus with 50% standard deviation and correlation time of 10 ms. Right: same as left for Tm3. b, Same as a for Tm1 (left) and Tm2 (right). c, Coherence of the measured responses in the four cell types. Deviations from 1 mean that variance in the output is not entirely accounted for by a linear transformation of the input. This can be caused by noise in the response unrelated to the input, or by the nonlinearities in the system response that we measured. The linear filter amplitude for each frequency is distinct from coherence, and those amplitudes as a function of frequency are plotted in Extended data Fig. 7a, b.

Extended Data Figure 5. Individual filters and nonlinearities from the Gaussian noise analysis of Mi1, Tm3, Tm1 and Tm2

a, Individual filters (in grey) overlaid on the average filter (± s.e.m.) for Mi1 neurons. b, Individual nonlinearities (in grey) overlaid on the averaged nonlinearity (±s.e.m.) for Mi1 neurons. c, d, Same as a and b for Tm3. e, f, Same as a and b for Tm1. g, h, Same as a and b for Tm2.

Extended Data Figure 6. Spatio-temporal analysis of Mi, Tm3, Tm1 and Tm2

a, Representative receptive fields of Mi1, Tm3, Tm1 and Tm2 neurons shown as a heat map of 256 pixels using the r value of linear prediction for each pixel intensity. b, Average temporal filters (± s.e.m.) extracted from the highest responding pixels for each neuron for Mi1 (n =4) and Tm3 (n =8) (see Methods). The peaks of the filters, with the average timing, are enlarged in the inset. c, Average nonlinearities over several neurons for both Mi1 and Tm3. To obtain each neuron’s nonlinearity, the neuron’s measured response was plotted against the linear prediction from the relevant pixels. Error bars, s.e.m. A line of slope 1 is shown in black. d, e, Equivalent to b and c for Tm1 (n =8) and Tm2 (n =7).

Extended Data Figure 7. Numerical and analytical HRC responses

a, b, We plot three terms in equation (2) of the Methods, and the total HRC response, using the empirical measurements for Tm1/Tm2 and Mi1/Tm3 as the twoinput arms for the correlator (f₂(t) and f₁(t), respectively). The analytical results computed here match the numerical ones shown in Fig. 4. Here and in all subsequent plots, we normalize the filter values so that they have a maximum of 1, and compute the relative HRC response from those normalized filters and the phase term. c, The same three components of equation (2) are plotted in the special case where f₁(t) =δ(t) and ${\mathrm{f}}_2(\mathrm{t})=\frac{1}{\mathrm{\tau }}{\mathrm{e}}^{-\mathrm{t}/\mathrm{\tau }}$. We plot the result with τ =150 ms, so that the peak response occurs at ~1 Hz. d, The same components of equation (2) are plotted in the case where both f₁(t) and f₂(t) are first-order low-pass filters, with time constants of 40 ms and 55 ms, respectively. e, False-colour plot of the temporal frequency optimum for various combinations of τ₁ and τ₂. Many combinations result in frequency optima near 1 Hz. f, The value of the relative HRC response at the optimal frequency in e is plotted for those same combinations of τ₁ and τ₂. To compute this, temporal filters have a maximum gain of 1, as in a–d. The responses become small primarily when the phase term becomes small. When the phase term is very small, the subtraction performed by the HRC is susceptible to noise, since it can be subtracting two larger numbers to yield the small difference. Therefore, filter combinations with very small differences seem less biologically plausible than those with larger phase terms. The phase terms for the two model HRCs in a and b are between 0.2 and 0.4 in the 1-Hz region, larger than for the toy model shown in d.

Extended Data Figure 8. 686-Gal4 labels Mi1 neurons and R13E12-Gal4 is specific to Tm3 neurons

a, Confocal image of a single Mi1 neuron obtained through a flip-out clone procedure with 686-Gal4. Mi1 neurons present processes at the level of M1 and M5 and terminate in the most proximal layers of the medulla. This line also sparsely labels Tm2 neurons, which were distinguishable both visually and functionally. b, Confocal image of twin-spot MARCM clones obtained using R13E12-Gal4. Tm3 neurons present processes at the medulla layers M1 and M5 and project to proximal layers of the medulla and superficial layers of the lobula.

Extended Data Figure 9. Evoked response of ‘tonic’ Mi1 neurons

a, Average evoked responses (± s.e.m.) of ‘tonic’ Mi1 (n =9) in response to 200 ms, four consecutive 250 ms and 1 s full-field flashes of light from dark. b, Average evoked responses (± s.e.m.) of ‘tonic’ Mi1 (n =7) in response to 5 s steps of light. c, Top: 2 s excerpt of the intensity signal from the 10 s full-field Gaussian noise stimulus. Correlation time is 10 ms. Bottom: average voltage response (± s.e.m.) of ‘tonic’ Mi1 (n =8) in response to the 2 s noise stimulus on top. The black trace corresponds to the average predicted linear response obtained by convolving the stimulus with the filters in d (± s.e.m.). d, Average temporal filters (± s.e.m.) extracted from the data in c that best predict the measured response of ‘tonic’ Mi1 as a function of contrast history. Individual filters are shown in grey. e, Nonlinearities for ‘tonic’ Mi1 cells. Actual responses are plotted against their linear predicted responses. Individual cell nonlinearities in grey; mean and s.e.m. are represented by the coloured line and patch. A line of slope 1 is shown in black. f, Average temporal filters (± s.e.m.) extracted from the highest-responding pixels for each ‘tonic’ Mi1 neuron in the spatio-temporal experiments. g, Averaged actual responses of ‘tonic’ Mi1 plotted against their averaged linear predicted responses in the spatio-temporal experiments. Error bars, s.e.m. A line of slope 1 is shown in black.

Figure 1. Motion detection and the fly optic lobe

A. A half Hassenstein-Reichardt correlator (HRC) sensitive to rightward motion. An object moving from left to right first activates input 1 and then input 2. The signal from input 1 is delayed (τ) and arrives at the correlation stage (M for multiplication) close in time to the signal from unit 2, nonlinearly enhancing the signal. For leftward motion, the signals are separated in time by the delay and no motion signal is generated. In the full correlator model, two mirror symmetric correlators are subtracted, producing responses that have opposite signs for opposite directions (see Figure 4A). B. Light edge (L1) and dark edge (L2) motion sensitive pathways in the Drosophila optic lobe. L1 and L2 lamina monopolar cells in the lamina provide inputs to two distinct motion sensitive pathways that selectively respond to moving light edges and dark edges, respectively. L1 and L3 also contribute to the pathway detecting moving dark edge (not shown). T4 and T5 in the lobula complex are the main inputs to LPTCs, and are themselves direction selective. T4 neurons respond selectively to moving light edges and T5 neurons respond to moving dark edges. Mi1 and Tm3 are the main postsynaptic targets of L1 while Tm1 and Tm2 are the main postsynaptic targets of L2. The axons of Mi1 and Tm3 contact T4 in the most proximal medulla layer, whereas Tm1 and Tm2 contact T5 dendrites in superficial lobula layers (modified from ref. ). C. In vivo electrophysiology set up: A window is cut in a dorsal region of the head cuticle of an immobilized live fly to expose the cell bodies of medulla neurons to a glass pipette used to perform the recordings. Grey-scale images are displayed on a screen positioned in front of the fly, using a digital light projector (DLP) coupled to a coherent fiber optic.

Figure 2. Mi1/Tm3 respond selectively to brightness increments while Tm1/Tm2 respond selectively to brightness decrements

A. Average evoked responses of Mi1 (N=7) and Tm3 (N=10) in the L1 pathway, in response to 200 ms, four consecutive 500 ms, and 1s full field flashes of light from dark. Thick lines indicate the mean and shaded region indicates ± SEM. B. Averaged evoked responses (+/− SEM) of Tm1 (N=10) and Tm2 (N=11), in the L2 pathway in response to the same stimuli.

Figure 3. Mi1/Tm3 and Tm1/Tm2 respond with different delays and nonlinearities to a Gaussian noise stimulus

A. Top: 2s excerpt of the intensity signal from a 10 s full-field Gaussian noise stimulus. Signal correlation time was 10 ms (see Methods). Middle: Average voltage response (+/− SEM) of Mi1 (N=7) and Tm3 (N=11) to the 2s noise stimulus on top. The black trace corresponds to the average predicted linear response (+/− SEM) obtained by convolving the stimulus with the filters in B. Bottom: Overlay of the Mi1 and Tm3 responses showing the high similarity in their response. B. Left: Average linear filters extracted from the data in panel A that best predict the measured response of Mi1 and Tm3 as a function of preceding light intensity changes (+/− SEM). The filters are comprised of a large positive lobe (arrow) and shallow negative lobe (see Extended data Figure 5). Right: Box plots of the distribution of the timing of the peak responses of the Mi1 and Tm3 neurons. There is, on average, an 18ms delay between the peak of Mi1 filters and Tm3 filters. Black line is the median, colored line is the average. C. Average actual responses of Mi1 and Tm3 plotted against their average linear predicted responses. Error bars represent +/− SEM. A line of slope 1 is shown in black. D–F. Same as above for Tm1 (N=15) and Tm2 (N=14). The filters are comprised of a large negative lobe (arrow) and a shallow positive lobe (Extended data Figure 5). The average delay between the peak of Tm1 and Tm2 filters is 13ms.

Figure 4. Modeling Mi1/Tm3 and Tm1/Tm2 as the delayed and non-delayed channels of light edges and dark edges correlators

A. Left: The average filters and nonlinearities from the receptive field stochastic data set (200 s noise presentation, 50 ms correlation time, Extended data Figure 6) were used to model Mi1 and Tm3 as the delayed and non-delayed channels of a correlator model in bottom left. Right: same as left with Tm1 and Tm2 as the delayed and non-delayed channels of correlator model. B. Computed normalized temporal frequency tuning curves obtained numerically for the Mi1/Tm3 model correlator (left) and the Tm1/Tm2 model correlator (right) using sine waves of different temporal frequencies. C. Computed normalized response of the Mi1/Tm3 model correlator (left) and Tm1/Tm2 model correlator (right) to light or dark edges of 100% contrast, moving at a range of speeds.