Excitatory and inhibitory neural dynamics jointly tune motion detection

Summary

Neurons integrate excitatory and inhibitory signals to produce their outputs, but the role of input timing in this integration remains poorly understood. Motion detection is a paradigmatic example of this integration, since theories of motion detection rely on different delays in visual signals. These delays allow circuits to compare scenes at different times to calculate the direction and speed of motion. Different motion detection circuits have different velocity sensitivity, but it remains untested how the response dynamics of individual cell types drives this tuning. Here, we sped up or slowed down specific neuron types in Drosophila’s motion detection circuit by manipulating ion channel expression. Altering the dynamics of individual neuron types upstream of motion detectors increased their sensitivity to fast or slow visual motion, exposing distinct roles for excitatory and inhibitory dynamics in tuning directional signals, including a role for the amacrine cell CT1. A circuit model constrained by functional data and anatomy qualitatively reproduced the observed tuning changes. Overall, these results reveal how excitatory and inhibitory dynamics together tune a canonical circuit computation.

In Brief:

Motion detection is thought to rely critically on the timing of signals in upstream neurons. Gonzalez-Suarez et al. manipulate the response timing of individual cell types in Drosophila’s early visual system to reveal how upstream response timing drives downstream sensitivity to stimulus velocity.

Introduction

When a neuron integrates synaptic inputs, the timing of those inputs is critical to the neuron’s output response. However, the roles played by the dynamics of excitatory and inhibitory neural inputs in neural computations remain poorly understood, in part because of difficulties in manipulating these dynamics. Previous studies have predominantly manipulated neural dynamics by using temperature and pharmacology^1–5, but these methods affect entire circuits, making it difficult to investigate how the dynamics of individual excitatory and inhibitory neuron types drive computation. In this study, we use the powerful genetic tools available in Drosophila to manipulate the response timing of individual excitatory and inhibitory visual neuron types to examine how these dynamics tune downstream computations.

Circuits that detect visual motion offer a robust testbed for understanding how the dynamics of excitatory and inhibitory inputs contribute to computations in downstream neurons. To detect motion, neurons must integrate visual information over both space and time. Indeed, dominant theories of visual motion detection all require adjacent visual signals to be processed with different delays to generate direction-selective (DS) responses^6–8 (Figure 1A). In both vertebrates and invertebrates, these different delays are thought to be implemented through the response dynamics of neurons upstream of motion-detecting cells^4,9–11. The response dynamics, or response timing, is defined as the shape of the neuron’s response to stimuli over time; that is, how the response rises and falls back to baseline in response to a stimulus. Across many animals and cells, different motion-detecting cells can have very different sensitivities to velocity^12–15, but it remains unclear how the dynamics of individual upstream excitatory and inhibitory neurons in these circuits interact to create and tune the downstream motion signals. Motion computation is a compelling framework for investigating the roles of neural dynamics because motion signals are highly interpretable in their selectivity for both direction and speed of motion.

Figure 1. Pure delay and a lowpass filter Barlow-Levick models predict different velocity sensitivity.

(A) A canonical, Barlow-Levick (BL) model detects motion using two inputs separated in space by an angle Δϕ: a fast, excitatory (i.e., exc.) input and a slow inhibitory (i.e., inh.)⁷. Nonlinear combination of the summed signals results in a direction-selective response.

(B) A BL model with a pure delay sums signals from a slow, inhibitory input and a fast, excitatory input before the sum is rectified.

(C) Three different pure delay filters with times τ_inh = 75, 100, and 125 ms.

(D) Mean response to a moving point of a pure delay BL model with spatial filters is plotted as a function of point velocity for the different inhibitory time constants (τ_inh). See Methods for details of these BL models.

(E) A BL model with two first order, lowpass input filters defined by τ_exc (fast) and τ_inh (slow). Signals are summed and rectified to produce a direction-selective response.

(F) The lowpass BL model described in (E) with τ_exc = 40 ms and τ_inh = 100 ms.

(G) Summed inputs of the lowpass BL model with lowpass filters described in (F) in response to a moving dot swept from 25°/s-250°/s in the preferred (top) and null (bottom) directions (PD and ND).

(H) We assessed the lowpass BL model while changing the excitatory time constant and maintaining the inhibitory time constant.

(I) Different τ_exc were 20 ms, 40 ms, and 60 ms, while τ_inh was held at 100 ms

(J) Mean responses of the model to periodic moving dots sweeping velocities in the PD (solid lines) and ND (dashed lines). Curve colors correspond to those in (I).

(K) We assessed the lowpass BL model as while changing the inhibitory time constant and maintaining the excitatory time constant.

(L) Different τ_inh were 75 ms, 100 ms, or 125 ms, while τ_exc was held at 40 ms.

(M) Mean responses of the model to periodic moving dots sweeping velocities in the PD (solid lines) and ND (dashed lines). Curve colors correspond to those in (L). See also Figure S1 for BL models including spatial filtering.

Drosophila’s motion detection circuits are anatomically and functionally well-characterized. In the fly eye, light intensity is first detected by photoreceptors. Two synapses later, the signals are split into ON and OFF pathways, which depolarize to light increments and decrements, respectively^16–18. Within each pathway, interneurons delay and rectify visual signals^4,19–21 before synapsing onto the elementary DS neurons of the ON and OFF pathways, T4 and T5¹². T4 and T5 neurons are classified into subtypes that respond preferentially to motion in one of four cardinal directions¹². Electron microscopy reconstruction shows that at least four types of interneurons, which receive information from three adjacent points in space, synapse onto T4 cells^22,23. These cells, with spatially displaced receptive fields, have distinct dynamical responses to stimuli, which are consistent with the delay and non-delay lines of classical models of direction selectivity^4,24. These excitatory and inhibitory spatiotemporal inputs are integrated by T4 to generate DS responses^24–29. Output signals from T4 and T5 cells are then summed over space to guide visually-evoked behaviors^12,30–32.

Anatomical and physiological studies have suggested different models to explain how T4 cells detect the direction and speed of motion^{4,22,24,26–29,33,34}, all of which depend on relative delays between signals at adjacent points in space (Figure 1A). In textbook versions of these models^6,7, the tuning of the motion detector to different velocities is fully determined by the relative delay between the responses of the two inputs (Figure 1A). Accordingly, changing the relative delay should predictably alter the tuning of DS signals.

Several lines of evidence suggest that relative delays alone are insufficient to account for downstream tuning and that linear filtering properties should be considered^4,11,19. However, to alter the tuning of motion detectors and the dynamics of their inputs, these studies used neuromodulatory manipulations^4,11. Such pharmacological manipulations act broadly and can alter many properties of neurons in the circuit³⁵. Thus, it remains untested how the velocity sensitivity of motion detectors is determined by the dynamics of individual upstream neuron types.

In this work, we manipulated the expression of specific membrane ion channels in four individual excitatory and inhibitory cell types in the fly motion detection circuit. These genetic manipulations of single cell types sped up or slowed down the dynamics of light responses in these neurons. Then, to test models of motion estimation, we asked how those manipulations of neural dynamics influence the tuning of downstream motion signals in T4 neurons. To do this, we manipulated ion channel expression in individual neuron types upstream of T4 while measuring the responses of T4 to different velocities of visual motion. This resulted in altered tuning curves, showing how the different manipulations changed the sensitivity of T4 neurons to different velocities. Last, we developed circuit models that are constrained by anatomy and data. These model responses are qualitatively consistent with our measurements of motion detector sensitivity. They showed that parallel, redundant excitatory and inhibitory inputs could qualitatively explain our experimental data. These results reveal how the timing of excitatory and inhibitory inputs generate motion signals and tune their sensitivity.

Results

Delays tune direction-selective signals in simple models

To gain intuition for how motion detectors are tuned to stimuli of different velocities, we examined Barlow-Levick (BL) models for motion detection⁷. BL models have a non-delayed, excitatory input and a delayed inhibitory input, followed by a nonlinear rectification, which together generate direction-selectivity (Figure 1A, see Methods). These models are thought to reflect several properties of motion detection in T4 and T5 neurons^29,36. They respond strongly to motion in a preferred direction (PD, rightward in these illustrations) and minimally to motion in the opposite direction, called the null direction (ND).

To understand how the response timing of inputs influences the velocity tuning of the detector, we examined how different forms of delays impacted velocity tuning. The simplest version of a delay is a pure delay. A pure delay simply shifts a signal to a later time, without changing the shape of the signal (Figure 1B). Thus, this pure delay BL model responds to a moving point of light by suppressing responses to ND motion. The peak ND suppression happens at velocities equal to the spatial distance between the receptors divided by the delay (Figure 1C–D).

Previous work has suggested that such pure delays are unrealistic. Instead, the dynamical properties of the inputs, typically modeled as a linear filter of the visual stimulus, are crucial for understanding the tuning of downstream motion detectors^4,11,19. Therefore, we examined a simple model for delays in the two arms: first-order, lowpass filters, defined by time constants τ_exc and τ_inh (Figure 1E–F). These filters delay and smear the signals in time. By looking at time traces of the summed inputs, before rectification, we gain intuition about how these filters help tune motion detection in this lowpass BL model (Figure 1G). In the case of PD motion, the excitatory input arrives first, while the inhibitory input follows with a delay. If the stimulus speed is fast enough, the inhibition follows the excitation closely, cutting off the excitation and reducing the integrated or mean response. This suppresses responses to fast, PD motion. In the case of ND motion, the inhibition precedes the excitation. If it arrives just before excitation (as it does with fast speeds), it suppresses the excitation completely. If the object moves more slowly, the excitation can produce a positive response.

The intuition above suggests that the sensitivity of this model to different velocities will depend on the lowpass filtering in each arm. To examine this dependence, we first examined different excitatory lowpass timescales (Figure 1H–I). We computed the mean response of each model to periodic dots moving at several velocities, in order to obtain a tuning curve for periodic stimuli, which will be used in later experiments. As expected, ND motion is suppressed, while PD responses are most suppressed at high speeds (Figure 1J). With these filters, the degree of suppression to different speeds depends both on the relative timing of the inputs after filtering and on the build-up of responses to the repeated stimuli (Figure S1). Interestingly, when we changed the excitatory filter time constant, faster and slower filters resulted in stronger or weaker responses to fast PD motion, respectively (Figure 1J). Similarly, when we manipulated the decay time constant of the inhibitory filter (Figure 1K–L), faster and slower filters resulted in stronger or weaker responses to fast PD motion, respectively (Figure 1M). Thus, this BL model with lowpass filters predicts that speeding up the excitatory or inhibitory input timing should shift the tuning of PD responses to faster velocities. These qualitative results hold with and without spatial filtering of inputs, and change only slightly when isolated, rather than periodic inputs, are used (Figure S1). With these predictions in mind, we set out to manipulate the timing of excitatory and inhibitory inputs to the neuron T4.

Measuring the response dynamics of medulla neurons using stochastic visual stimuli

To investigate the role of individual interneuron types in motion detection, we first measured the dynamic visual responses of cells that provide input to T4 cells. We targeted three ON-cell types with anatomically identified synapses onto T4: Mi1, Tm3, Mi4, and the ON-responsive terminals of CT1 (Figure 2A)²³. These neurons putatively correspond to the excitatory and inhibitory inputs to the motion detectors explored in Figure 1. Using in vivo two-photon microscopy, we recorded responses of these different cell types expressing the calcium indicator GCaMP6f³⁷ (Figure 2B), while their activity was driven by a stochastic, binary stimulus (Figure 2C). From these neural responses (Figure 2D), we used standard methods³⁸ to extract the linear filters, or kernels, that best predicted the neuron’s response to the preceding stimulus (Figures 2E)^4,39. These kernels are also equal to the linear prediction of the response to a flash of light at time zero. While this method does not capture all the features of temporal processing, including nonlinear changes in gain and dynamics^39–41, these kernels do quantify many dynamical response properties of these neurons. For instance, a kernel with a peak response that occurs after a short delay corresponds to a fast neural response to light. The kernel shape also determines how much signal is passed at different temporal frequencies, with narrowly peaked kernels transmitting more signal at high temporal frequencies. The kernels we extracted predicted each cell’s response to stochastic stimuli (Figure S1), and represent a rigorous low-order estimate of each cell’s response timing. Consistent with previous findings, Mi1 dynamics were slower than Tm3¹⁹, while both Mi1 and Tm3 responses were faster than Mi4^4,24 (Figure 2E). The response timing of CT1 terminals were also consistent with previous measurements (Figure 2E)⁴². Calcium indicators filter the true calcium concentration over time³⁷, limiting the resolution of our measurements. Thus, we used linear deconvolution to estimate the response kernels without the added indicator dynamics^4,37 (see Methods). The peak response of the deconvolved calcium kernels lies in between that of the raw calcium kernels and membrane voltage kernels we measured using the indicator ArcLight⁴³ (Figure S1).

Figure 2. Medulla neurons exhibit different filter dynamics.

(A) Circuit diagram highlighting neurons with strong anatomical connections to the direction-selective cell T4 ²³. Solid lines highlight functional connections ²⁴, while the dashed line refers to an anatomical connection without established function.

(B) Two-photon imaging was performed in head-fixed flies viewing stimuli presented on panoramic screens.

(C) A stochastic, binary, high-contrast stimulus was presented to flies to estimating neural linear filtering properties.

(D) Example response trace to the stimulus of an Mi1 neuron expressing GCaMP6f (hereafter Mi1 > GC6f), plotted as fractional change in fluorescence over time (ΔF/F).

(E) Linear kernels represent each neuron’s response dynamics by characterizing how they respond to preceding stimuli. Plotted filters correspond to Mi1 (Mi1 > GC6f, n = 68 flies), Tm3 (Tm3 > GC6f, n = 25 flies), Mi4 (Mi4 > GC6f, n = 15 flies), and CT1 (CT1 > GC6f, n = 17 flies). Linear kernels are normalized to their peak values to facilitate comparison of the shapes. Lines represent mean ± SEM. Neural response dynamics can be quantified by the filter’s half-rise time, peak time, and half-fall time. See also Figure S1 for comparisons between calcium, voltage, and deconvolved calcium kernels.

Manipulating endogenous ion channel expression alters neural dynamics

After measuring the wildtype kernels of Mi1, Tm3, Mi4, and CT1, we designed experiments to manipulate these cells by increasing or decreasing the expression of specific ion channels while co-expressing GCaMP6f to record the neuron’s response. We first tested how Mi1 dynamics were affected by knocking down several candidate ion channels, using either RNA interference (RNAi) or dominant-negative mutations (Figure S2). Based on these experiments, we chose to pursue manipulations using the channels slowpoke and cacophony because they (1) had the largest effect sizes, (2) are widely expressed in flies, and (3) could elicit opposing changes in Mi1 dynamics. We first manipulated the expression levels of slo⁴⁴, a voltage-gated, Ca²⁺-activated K⁺ channel and ortholog of BK-type channels in vertebrates^45,46. Slowpoke is widely expressed in Drosophila neurons, including many visual neurons^47,48. It has an established role in modulating neural excitability and membrane conductance^49–51, and has relatively slow dynamics⁵²—a property that makes it a candidate for helping induce the delays involved in Drosophila motion detection²⁵. However, the roles of slo in non-spiking neurons—like those in this study—have not been well-characterized. The RNAi knock-down of slo⁵³ slowed the kernel of Mi1 slightly, demonstrating that slowpoke is necessary for wildtype dynamics (Figures 3A–B). If reduced slo slows the kernel, we hypothesized that increased slo might speed it up. Indeed, when slo was over-expressed in Mi1, responses became faster, as quantified by faster kernel peak and fall times (Figures 3C–D). Thus, manipulations of slo expression in Mi1 bidirectionally altered its response timing.

Figure 3. Cell-type-specific genetic manipulations of excitatory neurons Mi1 and Tm3 alter their dynamics.

(A) Kernels of Mi1 expressing slo-RNAi (Mi1 > GC6f, n = 68; Mi1 > GC6f, slo-RNAi, n = 19). Lines are mean ± SEM.

(B) Half-rise (rise), peak, and half-fall (fall) times averaged across flies for the kernels in (A).

(C-D) As in (A-B), but with Mi1 over-expressing slowpoke (slo) (Mi1 > GC6f, slo, n = 16), compared to Mi1 native kernel kinetics (Mi1 > GC6f, n = 68).

(E-F) As in (A-B), but with Tm3 expressing slo-RNAi (Tm3 > GC6f, n = 25; Tm3 > GC6f, slo-RNAi, n = 19).

(G-H) As in (A-B), but with Tm3 over-expressing slo (Tm3 > GC6f, n = 25; Tm3 > GC6f, slo, n = 8). (* p<0.05, ** p<0.01, *** p<0.001 by Wilcoxon signed-rank tests across flies). See also Figure S1 for the linear model’s prediction of responses; Figure S2 for complete RNAi screen and additional controls; Figure S3 for axon terminal recordings, amplitude and dynamics comparisons in the deconvolved filters, and voltage recordings; and Figure S4 for un-normalized filters and additional controls.

To investigate whether the role of slo generalized to other neurons, we performed the identical RNAi knock-down and over-expression experiments in Tm3 neurons (Figures 3E–H). Interestingly, each manipulation had the opposite effect in Tm3 that it had in Mi1. Expressing slo-RNAi in Tm3 resulted in faster responses, significantly reducing the kernel fall time (Figures 3E–F), while over-expressing slo in Tm3 resulted in slower responses (Figures 3G–H). A second, distinct slo-RNAi construct⁵⁴ showed similarly strong effects on the response in Tm3, arguing against off-target effects for this strong phenotype (Figure S2). The opposing results in our experiments are consistent with other distinct processing properties of Mi1 and Tm3, including their differing adaptation to stimulus contrast³⁹ and their opposite responses to behavioral arousal³⁵. These experiments demonstrate that wildtype slo expression is required for both Mi1 and Tm3 wildtype dynamics, while the specific effect of manipulating slo expression appears to depend on the complement of channels expressed in the cell. In parallel experiments, when the bacterial voltage-gated Na⁺ channel NaChBac⁵⁵ was expressed in either Mi1 or Tm3 cells, there were also opposite changes in the response timing of the two cell types (Figure S2). The changes in Mi1 and Tm3 kernels were present in both dendrites and axon terminals, indicating that the manipulations impact signals throughout the cells (Figure S3). With these genetic perturbations, the relative magnitude of the effects in the deconvolved kernels were similar to those in the raw calcium indicator kernels (Figure S3).

To investigate whether these genetic manipulations also affected membrane potential response timing, we measured Mi1 and Tm3 voltage responses using Arclight⁴³ while using the manipulations that elicited the largest effects we observed with calcium indicators. Expressing slo-RNAi in Tm3 and NaChBac in Mi1 each sped up each cell’s membrane potential kernel, consistent with the calcium measurements (Figure S3). This suite of manipulations in Mi1 and Tm3 cells did not strongly affect calcium response nonlinearities or kernel amplitudes (Figure S4), so there is no obvious evidence that these genetic manipulations strongly alter basal physiological state. However, these experiments measure relative indicator fluorescence, which could obscure basal changes.

To test how widespread the effects of these cell-type-specific genetic manipulations are on the response kernels of other neurons in the circuit, we sped up Mi1 by expressing cac-RNAi while recording calcium signals in Tm3, which receives synaptic inputs from Mi1²³ (Figure S4). Under this manipulation of Mi1, we observed no significant change in Tm3’s response kernel shape, amplitude, or nonlinearity (Figure S4), suggesting that at least in some cases, altering one neuron’s kernel does not affect other T4 input neuron kernels.

Next, we set out to manipulate the dynamics of the inhibitory neurons Mi4 and CT1. Mi4 has been anatomically²³ and functionally²⁴ linked to T4, with other studies support its putative role as a delayed inhibitory input^4,29. On the other hand, the role of CT1, an amacrine cell, in motion detection remains unknown, despite its shared characteristics with Mi4: it releases the inhibitory neurotransmitter GABA²³, responds to local contrast increments⁴², and synapses onto T4 with an anatomy that parallels Mi4²². Due to the putative roles of Mi4 and CT1 as delayed inhibitory inputs, we sought to speed up their dynamics to determine how each cell type’s timing impacts T4 tuning.

Since slo over-expression and RNAi knock-down had opposite effects in Mi1 and Tm3, we used an alternative genetic manipulation that had the same effect on the dynamics of these two cell types. Expressing RNAi against cacophony (cac), the voltage-gated Ca²⁺ α1 channel subunit, sped up both Mi1 and Tm3 kernels (Figure S4). Using Arclight to measure membrane voltage, we observed that Tm3’s voltage kernels also became significantly faster when we expressed RNAi targeting cacophony (Figure S3). Similarly, when we used RNAi to knock-down cac in Mi4 and CT1, it made their calcium responses significantly faster (Figures 4A–B). Expressing cac-RNAi in CT1 sped up its kernels at terminals in both the medulla (Figures 4C–D) and the lobula (Figure S5). With this manipulation of a calcium channel, the calcium kernel amplitudes of both Mi4 and CT1 responses were decreased (Figure S4), consistent with a decrease in response amplitude reported when excising cacophony in Mi4⁵⁶. However, there was little change in the measured nonlinearities (Figure S4). These results suggest that cac expression is required to maintain Mi1, Tm3, Mi4, and CT1 wildtype calcium dynamics.

Figure 4. Cell-type-specific genetic manipulations of inhibitory neurons Mi4 and CT1 alter their dynamics.

(A) Kernels of Mi4 expressing an RNAi against cacophony (cac) (Mi4 > GC6f, n = 15; Mi4 > GC6f, cac-RNAi, n = 11). Lines are mean ± SEM.

(B) Half-rise (rise), peak, and half-fall (fall) times averaged across flies for the kernels in (A).

(C-D) As in (A-B), but with CT1 expressing cac-RNAi (CT1 > GC6f, n = 17; CT1 > GC6f, cac-RNAi, n = 11). (* p<0.05, ** p<0.01, *** p<0.001 by Wilcoxon signed-rank tests across flies). See also Figure S1 for the linear model’s prediction of responses; Figure S3 for amplitude and dynamics comparisons in the deconvolved filters; Figure S4 for un-normalized filters; and Figure S5 for recordings and manipulations of CT1’s lobula terminals.

Excitatory and inhibitory input dynamics regulate T4 tuning to motion velocity

While it is not surprising that manipulating membrane ion channel expression can alter response timing, these manipulations also enable us to interrogate how input dynamics drive downstream neural signals. We used these tools to investigate how T4 sensitivity to different stimulus velocities is determined by the response dynamics of its excitatory and inhibitory inputs. To do this, we sped up or slowed down the kernels of these inputs by expressing slo, slo-RNAi, or cac-RNAi, all while recording calcium responses in T4 cells (Figure 5–6). To measure the sensitivity of T4 to different velocities, we presented periodic, light bars that rotated about the fly at different velocities (Figure 5A), and then compared T4 responses between manipulated conditions and controls. We recorded responses in T4 axon terminals that respond to horizontal motion, and then combined responses across different PDs^25,33. As expected, wildtype T4 cells showed strong DS responses across the different velocities (Figure 5B). We plotted the tuning curve for each fly by averaging the responses over the 5 second presentation of each velocity (Figure 5D). These tuning curves peaked at around 32°/s. To summarize the tuning of these responses, we computed a response-weighted average that defines the curve’s center of mass on a log-velocity scale (Figure 5E, see Methods).

Figure 5. Genetic manipulations of the dynamics of excitatory inputs Mi1 and Tm3 alter T4 tuning.

(A) T4 tuning was probed using a stimulus with light 5°-wide bars with 30° spacing rotating rightward and leftward at speeds between 8 and 512°/s.

(B) Average time traces of T4 responses to light bars moving in the preferred direction (PD) and null direction (ND) at 16°/s, 64 °/s, and 256°/s. Both PD and ND responses are averaged over the 5 second stimulus presentation window (two controls are combined and averaged: T4T5 > GC6f; Mi1/+ and T4T5 > GC6f; slo/+, n = 47 flies).

(C) As in (B), but for flies over-expressing slowpoke (slo) in Mi1 (T4T5 > GC6f, Mi1 > slo, n = 9).

(D) Normalized tuning curves computed from the raw response traces in (B) and (C). PD responses are shown. T4 tuning curves of flies over-expressing slowpoke (slo) in Mi1 (T4T5 > GC6f, Mi1 > slo, n = 9) compared to two genetic controls (T4T5 > GC6f; Mi1/+, n = 36 and T4T5 > GC6f; slo/+, n = 11). Lines are mean ± SEM.

(E) The tuning curve’s log-velocity center of mass is a weighted average of the tuning curve shown in (D). Bars are mean ± SEM.

(F-I) As in (B-E), but for Mi1 expressing slo-RNAi (T4T5 > GC6f, Mi1 > slo-RNAi, n = 8) compared to two genetic controls (T4T5 > GC6f; Mi1/+, n = 36 and T4T5 > GC6f; slo-RNAi/+, n = 12).

(J-M) As in (B-E), but for Tm3 over-expressing slo (T4T5 > GC6f, Tm3 > slo, n = 7) compared to two genetic controls (T4T5 > GC6f; Tm3/+, n = 11 and T4T5 > GC6f; slo/+, n = 11).

(N-Q) As in (B-E), but for Tm3 expressing slo-RNAi (T4T5 > GC6f, Tm3 > slo-RNAi, n = 10) compared to two genetic controls (T4T5 > GC6f; Tm3/+, n = 11 and T4T5 > GC6f; slo-RNAi/+, n = 12). (* p<0.05, ** p<0.01, *** p<0.001 by Wilcoxon signed-rank tests across flies. When there are two controls (in D-E, H-I, L-M, P-Q), the reported significance is the larger of the two comparisons to the controls). See also Figure S5 for un-normalized T4 PD and ND tuning curves; and Figure S6 for tuning curves recorded with isolated moving bars, drifting sinusoidal contrast gratings, and drifting random checkerboard stimuli.

Figure 6. Genetic manipulations of the dynamics of inhibitory inputs Mi4 and CT1 alter T4 tuning.

(A) Mean time trace of T4 responses to light bars moving in the preferred direction (PD) and null direction (ND) at 16°/s, 64 °/s, and 256°/s. (Two controls are combined: T4T5 > GC6f; Mi4/+ and T4T5 > GC6f; cac-RNAi/+, n = 19 flies).

(B) As in (A), but for flies expressing cac-RNAi in Mi4 (T4T5 > GC6f, Mi4 > cac-RNAi, n = 8).

(C) T4 tuning curves are computed from the raw response traces in (A) and (B). Normalized PD responses are shown. Flies expressing cac-RNAi in Mi4 (T4T5 > GC6f, Mi4 > cac-RNAi, n = 8) are compared to two genetic controls (T4T5 > GC6f; Mi4/+, n = 12 and T4T5 > GC6f; cac-RNAi/+, n = 7). Lines are mean ± SEM.

(D) The tuning curve’s log-velocity center of mass is a weighted average of the tuning curve shown in (C). Bars are mean ± SEM.

(E-H) As in (A-D), but for CT1 expressing cac-RNAi (T4T5 > GC6f, CT1 > cac-RNAi, n = 7) compared to two genetic controls (T4T5 > GC6f; CT1/+, n = 11 and T4T5 > GC6f; cac-RNAi/+, n = 7). (* p<0.05, ** p<0.01, *** p<0.001 by Wilcoxon signed-rank tests across flies. When there are two controls (in C-D and G-H), the reported significance is the larger of the comparisons to the two controls). See also Figure S5 for un-normalized T4 PD and ND tuning curves and silencing controls of Mi4 and CT1; and Figure S6 for tuning curves recorded with isolated moving bars, drifting sinusoidal contrast gratings, and driving random checkerboard stimuli.

We first assessed the impact of Mi1 and Tm3 dynamics on T4 velocity tuning. If these two excitatory inputs serve as the non-delay inputs to T4²², then speeding them up should have two effects. First, it should extend the total delay between excitatory and inhibitory inputs. If the pure delay BL model has the dominant effect on T4 tuning, this should predictably increase the ND suppression at slow speeds (Figure 1B–D). Second, speeding up the kernel creates a faster decay. If the lowpass BL model has a dominant effect, this should predictably increase the sensitivity to faster velocities in the preferred direction (Figure 1H–J).

To evaluate these different predictions, we sped up Mi1 dynamics by over-expressing slo (Figures 3C–D), and measured T4 responses. With this manipulation, we observed an increase in T4 sensitivity to bars moving at high speeds and a shift of the curve’s center of mass to higher velocities (Figures 5C–E). This change was consistent with the lowpass BL model predictions. That is, making the Mi1 kernel decay faster increased T4 sensitivity to high velocities. Slowing Mi1 kernels by expressing slo-RNAi, caused a small, insignificant decrease in sensitivity to high velocities (Figures 5G–I), consistent with the small effect size in the Mi1 kernel. The downstream consequences of manipulating Tm3 dynamics paralleled those in Mi1. When Tm3 was slowed down by slo over-expression, T4 sensitivity to high velocities was reduced and the center of mass shifted to slower velocities (Figures 5K–M). Likewise, when Tm3 kernels were sped up by expressing slo-RNAi, T4 cells were significantly more sensitive to bars moving at high speeds (Figures 5O–Q). In some cases, genetic manipulation of Mi1 and Tm3 altered T4 response amplitudes to PD motion (Figure S5), but in all cases, T4 responses to motion in the ND remained near zero, regardless of the genetic manipulation (Figure S5). Therefore, we focused our comparisons on the PD curves. In sum, speeding up or slowing down Mi1 or Tm3—two excitatory inputs—impacts T4 in a consistent fashion and as qualitatively predicted by a lowpass BL model.

We next assessed how altering the dynamics of the inhibitory inputs Mi4 and CT1—putative delay lines—affects T4 velocity tuning (Figure 6). Making a delay line faster will have two effects on the circuit. First, it will decrease the relative delays between non-delayed and delayed inputs. If the pure delay model dominates direction-selective responses, then this change should increase suppression of ND stimuli at faster speeds (Figure 1B–D). Second, the faster delay line would have a faster decay. In the lowpass BL model, this manipulation increased relative responses to high PD velocities (Figure 1K–M).

When we sped up Mi4 and CT1 by expressing cac-RNAi, we observed a significant decrease in T4’s sensitivity to fast velocities moving in the PD (Figure 6), and no strong changes to responses to ND stimuli (Figure S5). Interestingly, these results contradict the predictions of both the pure delay and lowpass BL models. CT1 has been anatomically implicated in T4 motion detection²³ and it compartmentalizes signals that could potentially support local motion detection⁴². However, there has been no functional evidence for its involvement. Our results show that manipulating CT1 channel expression and response timing alters the tuning of T4.

Manipulating Mi4 or CT1 made their responses faster, but it also reduced their kernel amplitudes (Figure S4). Therefore, we wanted to test whether the effects we observed on tuning were similar to silencing. Surprisingly, silencing Mi4 or CT1 with tetanus toxin did not result in changes in T4 tuning (Figure S5). This suggests that manipulating dynamics can reveal roles not found using silencing experiments⁵, which could be more prone to compensatory mechanisms. In sum, these experiments show that speeding up Mi4 and CT1 responses significantly altered T4 velocity tuning in a similar fashion.

The periodic bar stimulus we used to measure T4 velocity sensitivity is not the only stimulus with which one could measure sensitivity. One could also measure sensitivity with isolated moving bars²⁹, with moving random checkerboard patterns²⁸, or with drifting sinusoidal gratings^12,26,30. These stimuli, as well as our original stimulus, have different spatiotemporal statistics and interrogate the tuning of T4 in response to solitary or spatially extended stimuli. To test the effects of stimulus protocol on qualitative changes in T4 velocity sensitivity, we tested two specific manipulations under these three, additional stimuli. We chose manipulations that had opposing effects on T4 tuning: expressing cac-RNAi in CT1, which decreased T4 sensitivity to fast velocities, and expressing slo in Mi1, which increased T4 sensitivity to fast velocities. The shifts observed in T4 tuning in response to isolated moving bars, moving stochastic patterns, and sinusoids were all qualitatively similar to the original measurements using periodic bars (Figure S6). The sensitivity to isolated moving bars was quite different from the others, peaking at slow speeds and exhibiting small responses to fast stimuli. The tuning phenotypes were smaller for this stimulus. Overall, these results suggest that the qualitative effects of these genetic manipulations are similar under a variety of stimuli.

A data-driven circuit model qualitatively reproduces T4 velocity tuning

To better understand how our findings constrain circuit models for motion detection, we compared our measurements to an anatomically-constrained circuit model that incorporated the measured temporal filtering properties of the input neurons (Figure 7)^24,28,34,57. This model consists of three, spatially-separated inputs that apply linear-nonlinear transformations to local visual signals³⁴. In this model, a central excitatory Mi1/Tm3-like ON input is flanked by an Mi9-like OFF inhibitory input on the ND side, and an Mi4-like ON inhibitory input on the PD side—all consistent with previous anatomical and functional data^4,23,24,29 (Figure 7B). Previous work has shown that this and related models can recapitulate many functional properties of T4 cells with minimal parameter or filter tuning, though it fails to capture short-timescale processing properties^28,34,58. We asked how this model responded to the periodic light bar stimulus used in T4 sensitivity measurements (Figures 5–6). To obtain data-driven kernels for the model’s inputs, we deconvolved calcium indicator dynamics from the measured kernels⁴ and generated smooth kernels by fitting them with a parametric model (Figure 7C and S6, see STAR Methods).

Figure 7. A circuit model requires parallel, delayed inhibitory inputs to reproduce experimental results.

(A) The experimental stimulus was used to simulate model responses.

(B) Anatomically constrained circuit model composed of three spatial inputs to T4: on the model’s null direction (ND) side, Mi9 is simulated as a delayed, OFF-responsive, inhibitory input; in the center, Mi1 and Tm3 share one spatial input and provide excitatory input; and on the model’s preferred direction (PD) side, Mi4 serves as a delayed, ON-responsive, inhibitory input (see Methods).

(C) Data-driven model kernels were produced by deconvolving indicator dynamics from measured kernels and then smoothing (see Methods).

(D) The data-driven wildtype kernels of each cell type were used to simulate the wildtype model’s response to the stimulus used in Figure 5–6 as it moved in PD and ND at different speeds.

(E-F) Kernels and tuning as in (C) and (D), but with kernels from wildtype Mi1, Mi1 over-expressing slowpoke (slo) (Mi1 > slo), and Mi1 expressing slo-RNAi (Mi1 > slo-RNAi).

(G-H) Kernels and tuning as in (C) and (D), but with kernels from wildtype Tm3, Tm3 over-expressing slo (Tm3 > slo), and Tm3 expressing slo-RNAi (Mi1 > slo-RNAi,).

(I-J) Kernels and tuning as in (C) and (D), but with kernels from wildtype Mi4 and Mi4 expressing cac-RNAi (Mi4 > cac-RNAi).

(K-L) Kernels and tuning as in (C) and (D), but with kernels from wildtype CT1 and CT1 expressing cac-RNAi (CT1 > cac-RNAi).

(M) As in (B), but for an extended synaptic model with two parallel, delayed inhibitory inputs representing Mi4 and CT1.

(N) The data-driven kernels from (C) were used to simulate the model’s response in the presence of a parallel, delayed inhibitory input, shown in (M).

(O) As in (N), but with the kernels in (E).

(P) As in (N), but with the kernels in (G).

(Q) As in (N), but with the kernels in (I).

(R) As in (N), but with the kernels in (K). See also Figure S6 for calcium, deconvolved, and smoothed filters for all genotypes tested; Figure S7 for manual identification of ROIs, sweep of deconvolution time constants, manipulations with synthetic filters and of filter gains, as well as simulations of Mi4 or CT1 silenced. See also Figure S7 for BL model with manipulations of kernel’s rising phase.

To test how the excitatory Mi1 and Tm3 dynamics might alter tuning of T4 neurons in this model, we set up Mi1 and Tm3 as parallel linear-nonlinear synaptic inputs to T4 with a shared, central spatial receptive field (Figure 7B), consistent with anatomical data²³. Using these data-driven filters, we computed the model’s sensitivity to our periodic light bar stimulus (Figure 7D). The model’s PD response center of mass was ~32°/s, while its ND response was ~1/4 the amplitude of its PD response, larger than the experimental ND responses (Figure 5–6 and S5). Next, we simulated the model’s response using the Mi1 kernels when Mi1 expressed slo or slo-RNAi (Figure 7E). In the model, the faster kernel of Mi1 > slo shifted the model’s sensitivity toward faster velocities, while the Mi1 > slo-RNAi kernel shifted the sensitivity to slower velocities (Figure 7F), qualitatively matching our experimental observations (Figure 5B–I). Similarly, the Tm3 > slo and Tm3 > slo-RNAi kernels (Figure 7G) shifted the model’s sensitivity to slower and faster velocities, respectively (Figure 7H), also in qualitative agreement with experiments (Figure 5J–Q). These simulations emphasize that the peak delay timing is not sufficient to qualitatively describe tuning changes; instead, they agree with the intuition from the lowpass BL model (Figure 1). When Mi1 and Tm3 become faster, one may also view them as passing more signal at high frequencies, which can explain the shift in tuning to higher velocities. This explanation is consistent with theoretical analyses of the Hassenstein-Reichardt correlator model^59,60, but these have never been directly tested by manipulating timing of individual inputs to a motion detector. In all, these simulations show that the changes in the kernels of Mi1 and Tm3 are sufficient to explain the qualitative tuning changes measured in T4, though the model predicts smaller changes than observed.

Next, we tested whether this model could explain our results when we manipulated the inhibitory Mi4 and CT1 input dynamics. When we substituted the Mi4 kernel with the Mi4 > cac-RNAi kernel (Figure 7I), the model’s direction preference reversed, so that the response to periodic light bars moving in the former ND was greater than the response to those in the former PD (Figure 7J). This change occurred because the manipulated Mi4 kernel responds faster than the Mi1/Tm3 kernels. This simulation result is not supported by our experimental findings (Figure 6 and S7). We also asked whether the model could predict changes in T4 tuning if CT1, rather than Mi4, acted as the model’s delayed inhibitory input (Figure 7L). Exchanging the CT1 kernel with the CT1 > cac-RNAi kernel (Figure 7K) also caused the model to reverse its direction preference (Figure 7L), similar to the Mi4 result and inconsistent with our T4 measurements of this manipulation (Figure 6).

These two failures of the initial model caused us to revise it. We created a new circuit model in which Mi4 and CT1 act as parallel, delayed, inhibitory inputs sharing the same spatial receptive field (Figure 7M), a proposal consistent with anatomy²³. Using data-driven kernels, this model architecture produced a velocity tuning curve that qualitatively resembled that of the previous model (Figure 7N). Similarly, adding the parallel, delayed inhibitory input did not change the model’s response to perturbations of the Mi1 or Tm3 inputs (using the kernels corresponding to wildtype, slo over-expression, and slo-RNAi expression) (Figure 7O–P). However, when we exchanged the Mi4 or CT1 wildtype kernels with the kernels for Mi4 > cac-RNAi (Figure 7I) or CT1 > cac-RNAi (Figure 7K), this model’s direction preference remained intact (Figure 7Q–R). In both cases, the model’s sensitivity shifted towards slower velocities (Figure 7Q–R). Both cases qualitatively matched the changes observed in T4 tuning (Figure 6A–D), though the observed changes were larger. Therefore, this revised circuit model can account for the direction of changes in T4 tuning when inhibitory Mi4 and CT1 dynamics are altered.

These qualitative results did not depend strongly on the details of the model. For instance, altering the deconvolution time constant used to generate the data-driven kernels did not alter the qualitative shifts in the model’s tuning (Figure S7). Tuning shifts remained consistent when we replaced the data-driven kernels with synthetic high- and lowpass filters (Figure S7). Our manipulations of Mi4 and CT1 both sped up the filters and also reduced their amplitudes (Figures 4A–D and S4), but simulations including both effects roughly matched those in which we altered only the filtering dynamics (Figure S7). In contrast, including only the reduction in amplitude in Mi4 or CT1 kernels, without changing the timing, resulted in T4 tuning changes in the opposite direction of our experiments (Figure S7). Silencing Mi4 or CT1 in the model caused the model sensitivity to shift to higher velocities by a similar degree to other manipulations (Figure S7); this did not match the results of our silencing experiments, in which we observed no large tuning changes (Figure S6). Thus, the model did not predict the qualitative results of the silencing experiments.

Both the data and the data-driven circuit model showed that our manipulations of the inhibitory delay lines, CT1 and Mi4, drove the sensitivity of T4 towards slower PD velocities (Figure 6–7). This is in contrast to the predictions made by the lowpass BL model, in which making the inhibitory input faster shifted the PD tuning to favor faster velocities (Figure 1K–M). In addition to altering the decay of the Mi4 and CT1 filters, our manipulations also substantially sped up the rising phase of the kernels. To test how this qualitative change in the shape of the inhibitory kernels could contribute to the changes in T4 velocity sensitivity, we created a BL model in which we manipulated the rise of the inhibitory kernel (Figure S7). In this model, when the kernel was made to rise faster, responses shifted to peak at slightly slower PD velocities (Figure S7N–P), qualitatively similar to circuit model and to the data. The simple BL models and our experimental results together suggest that PD tuning is dominated by the interactions of the initial phase of the inhibitory kernel with the excitatory kernel, including its decaying phase.

Discussion

Overall, this research provides causal evidence for how the dynamics of four input interneurons to T4—Mi1, Tm3, Mi4, and CT1—influence motion computation. First, we showed that manipulating ion channel expression can alter neural response timing (Figures 3–4). Specifically, we identified two membrane ion channels whose expression could be manipulated to alter the dynamics of various cell types. Next, we showed that manipulating the channel expression of single inputs alters T4 velocity tuning (Figure 5–6). Our experiments and models demonstrate that the response dynamics of excitatory and inhibitory neuron types jointly tune T4 sensitivity to different velocities. These experimental observations of T4 tuning under different input manipulations are not explained by models of motion detection that consider solely the delays of inputs. Instead, simple, dynamical models for motion detection provide intuition for how input timing affects downstream velocity selectivity (Figures 1, S7). These models manipulate the decay and the rise time of the filters and can qualitatively predict our experimental results. Finally, we showed that a data-constrained circuit model for T4 reproduces our findings qualitatively only when two delayed inhibitory inputs from Mi4 and CT1 are in parallel (Figure 7).

Ion channel expression regulates response dynamics

Networks of neurons regulate their processing dynamics in many ways, from conduction delays⁶¹ and synaptic dynamics⁶² to feedback and lateral circuit interactions⁶³. Our findings highlight how active membrane channel expression controls cellular response timing and, in turn, tunes circuit computations. In particular, we identified two ion channels—slowpoke and cacophony—that are critical to maintaining the native response timing of four input interneurons in the fly’s motion detection circuit (Figure 3–4 and S5). The four input interneurons we studied—Mi1, Tm3, Mi4, and CT1—impose additional delays in signals that can be sped up by manipulating ion channel expression (Figure 3–4). Ion channel expression has been shown to regulate neural dynamics in other Drosophila neurons^64,65, as well as in vertebrate motor control circuits, which can rely on axonal conductance properties to coordinate activity⁶¹. For neurons and circuits, regulating ion channel expression may provide a flexible way to control both dynamics and circuit computations.

The interneurons we manipulated are potentially under homeostatic control⁶⁶, yet our experiments successfully manipulated their response timing. This suggests that putative homeostatic regulation of response timing is imperfect in these cells. However, the possibility of homeostatic regulation warrants some caution in interpreting results: for instance, although the misexpression of certain genes creates phenotypes in response timing, those gene products are not necessarily the channels directly responsible for altering the neuron’s response timing, since many channels could change in abundance or function. The opposite, bidirectional effects of manipulating slo in Mi1 and Tm3 also make it probable that dynamics are controlled by a complex interplay of channels that are different between these two neurons. The differences observed in Mi1 and Tm3 responses to slo manipulations are consistent with experimental findings in vertebrates, where manipulating a potassium channel may either increase or decrease excitability, depending on the neuron type^67,68. One mRNA sequencing study found differential expression of type-T voltage-gated calcium channels in Mi1 and Tm3⁶⁹. We speculate that interactions with this channel, or homeostatic mechanisms related to this expression difference, could drive the opposing effects observed in these two neuron types.

Manipulating cellular expression patterns to alter neural response timing offers a circuit dissection tool that complements genetically encoded silencing methods, which have served as a powerful tool for understanding circuit function⁷⁰. Interestingly, these manipulations revealed roles for Mi4 and CT1 in tuning motion detection that silencing did not (Figure 6 and S6). It seems likely that by using genetic perturbations to alter neural properties, these manipulations act like activation experiments, which can circumvent problems of redundancy that might obscure silencing phenotypes. That is, these experiments alter neural activity as a function of on-going responses, and this changed activity is sufficient to affect the circuit in ways that silencing does not.

Using calcium indicators to measure dynamics in non-spiking cells

Neurons transform voltage depolarizations into calcium transients that result in synaptic release of neurotransmitters. Synaptic release is arguably the output of a cell; it serves as a locus of control for neural response timing⁷¹ and it can determine the timing of inputs to postsynaptic cells. In this study, however, we used calcium indicators to characterize neural responses and, for some genotypes, compared these calcium measurements to membrane voltage recordings (Figures S1, S3). How well do these calcium and voltage measurements capture the neuron’s response timing, given that synaptic release is the final output of a cell? First, our voltage kernels were faster than the calcium kernels, even after deconvolving the calcium indicator dynamics (Figure S1). It seems reasonable that calcium signals would be slower than the voltage signals that drive calcium influx. Second, in principle, it is possible that manipulating cacophony expression alters calcium, but not voltage, responses. Our results showed that cacophony manipulations could speed up both membrane voltage and calcium responses (Figure S3, S4). Third, in this circuit, it is especially difficult to measure the dynamics of neurotransmitter release for individual input neurons, since Mi1 and Tm3 are both cholinergic and Mi4 and CT1 are both GABAergic^23,72. However, electrophysiological data showed that the peak inhibition in T4 input happens ~150 ms after the stimulus²⁹. This peak response timing is similar to the dynamics of the deconvolved calcium kernels measured in CT1 and Mi4. In those same studies, the excitatory inputs excited T4 on a timescale of 80 ms, which is faster than the deconvolved calcium responses we measured²⁹. Thus, our deconvolved calcium kernels may better estimate the response timing of T4’s inhibitory inputs than its excitatory ones. Nonetheless, the changes in the excitatory response timing were consistent with the observed qualitative changes in T4 tuning.

Excitatory and inhibitory input dynamics jointly control velocity sensitivity

In this research, we developed a protocol to genetically manipulate individual inputs to T4 while simultaneously measuring the impact on T4 velocity tuning. Perturbing the dynamics of Mi1, Tm3, Mi4, and CT1 each changed T4 sensitivity to stimulus velocity (Figure 5–6). Thus, each of these neuron types individually contributes to tuning velocity sensitivity in T4, while the dynamics of both excitatory and inhibitory inputs jointly control the tuning of T4. A lowpass BL model highlights the importance of the interaction between the decay of the excitatory inputs and the rise of the inhibitory inputs (Figures 1, S7). Moreover, although prior work has suggested that the amacrine cell CT1 could be involved in T4 function^22,23,42, our results demonstrate that its responses tune T4 motion detection.

The tuning of motion detection by both excitatory and inhibitory dynamics may extend to motion detectors in mouse and other vertebrates. For instance, in mouse, both starburst amacrine cells and cortical DS cells receive excitatory inputs with differential delays^9,10,73. These delays appear critical to direction-selectivity and could be, in part, generated by differential expression of active ion channels. Moreover, starburst and cortical cells receive direct and indirect inhibition from neighboring cells, and our results suggest that the timing of this inhibition could tune the velocity sensitivity of these cells. Last, DS retinal ganglion cells receive excitatory inputs from bipolar cells and directional inhibition from starburst cells⁷⁴. Our results suggest that the dynamics of both the excitation and the inhibition control the sensitivity of these cells to velocity.

Manipulating single neuron type response dynamics to constrain circuit models

Our genetic manipulations of Mi1, Tm3, Mi4, and CT1 while recording T4 provide sensitive tests of models for motion detection in Drosophila. Our experimental and modeling results (Figure 5–7) suggest that the excitatory and inhibitory interneurons tested play redundant roles in T4 tuning. This redundancy is consistent with neural anatomy, in which these two pairs of neurons receive input from similar points in space²³. The redundancy is also consistent with the result that T4 largely maintains direction-selectivity even when its inputs are individually silenced²⁴. In addition, our experiments and models suggest that T4 sensitivity to different velocities depends on the filtering properties of individual input neurons relative to one another—a hitherto untested theoretical result^59,60. Prior work has incorporated linear filtering properties to obtain tuning curves that resemble the empirical ones^4,11,19, but the experiments here directly tested how different kernels interact.

While the circuit model produced qualitative results that resemble the data, it fell short in several quantitative predictions (Figure 7). First, the magnitude of the tuning curve shifts for different genetic manipulations tended to be much smaller in the model than in the T4 measurements (Figures 5–7). Second, the model responses to fast velocities were more suppressed compared to measured T4 responses (Figures 5–7). Third, the model ND responses were generally larger than the measured T4 ND responses (Figures 7, S6). Last, some manipulations generated negative responses in T4, which the model—by construction—cannot reproduce (Figures 5 and 6, see STAR Methods).

These discrepancies between the model and the data tell us about aspects of the model that do not accurately capture circuit function. First, there are significant differences between the model and the circuit. The fly’s motion detection circuit has feedback and lateral connections^23,75, while our circuit model considers it to be purely feedforward. Understanding how feedback and lateral interactions influence this circuit computation could help explain why T4 is more direction-selective than our anatomical model. Second, our circuit model used kernels that deconvolved calcium indicator kernels, but circuit function is ultimately determined by synaptic release kernels. The deconvolved calcium kernels may not accurately capture the dynamics of synaptic release. Similarly, the genetic perturbations could have other, unobserved physiological changes that influence synaptic release. Measurements with neurotransmitter indicators could help constrain the model’s response properties^76–78. Third, the circuit model assumes that manipulations only change single inputs in the circuit. Our data suggests that this may be true, since manipulating the timing of one neuron doesn’t always impact the timing of other input neurons (Figure S4). However, it is difficult to exclude that a narrow manipulation could have broader effects on inputs, and this could explain some differences between the model and data. Last, in constructing the circuit model, we assumed linear filtering of its inputs, which can generate a build-up of conductance with periodic inputs (Figure S1). Such a build-up of inhibition suppresses the model’s sensitivity to fast velocities, in contrast to relatively strong experimental responses. In the circuit, nonlinear mechanisms could prevent accumulation of inhibitory conductance. Overall, the circuit model has many parameters and extensions, so it is likely that it could be fitted to better match the data by changing input gains, thresholds, or nonlinearities. Such curve-fitting might not be particularly instructive about the actual circuit, however. Instead, by assessing the shortcomings of the circuit model, we can evaluate where future investigations could be targeted³⁴.

Previous work has shown that modulating channel expression can determine network dynamics⁷⁹, but this work shows how manipulating channel expression in single neuron types can influence neural computation. More generally, because neural circuits ubiquitously integrate excitatory and inhibitory inputs, our results show how the dynamical responses of neural inputs are critical to understanding circuit computations. Beyond vision and motion detection, input timing is central to many neural computations. For example, in auditory systems, interaural timing is crucial to localizing sounds^80–83, while in olfactory systems, the dynamics of odor responses facilitates odor discrimination^84,85. In rat pyramidal neurons, inhibitory inputs immediately following excitatory ones enforce short windows during which the cells integrate excitatory inputs⁸⁶. Similarly, motor control depends on the precise relative timing of neural signals^87,88. Investigating how the response timing of individual neurons in these systems drives circuit responses will test models for circuit function and could show how response timing is influenced by each neuron’s complement of membrane ion channels. Our results emphasize how the dynamics of responses in single excitatory and inhibitory neuron types interact to tailor neural computations in downstream circuits.

STAR Methods

Resource Availability

Lead Contact

Further information and requests for experimental data should be directed to and be fulfilled by the Lead Contact, Damon Clark (damon.clark@yale.edu).

Materials Availability

This study did not generate new unique reagents.

Data and Code Availability

All original modeling code has been deposited at GitHub and is publicly available using the following link: https://github.com/ClarkLabCode/TimingModels

Experimental Model and Subject Details

Fly Strains and Husbandry

Non-virgin female flies, grown on dextrose-based food, were used for all experiments. All flies were staged on CO₂ 12–24 hours after eclosion, and recordings were performed between 24 and 48 hours after staging. Both experimental and control flies used for imaging experiments were grown in incubators set to 25°C and on a 12-hour light/12-hour dark cycle. All genotypes used in the experiments are listed below, parental strains are listed in the Key Resources Table.

KEY RESOURCES TABLE.

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Experimental models: Organisms/strains
D. melanogaster Mil: +; +; R19F01-Gal4	[20];	BDSC_48852
D. melanogaster Mi4: +; R48A07-AD; R79H02-DBD	[24];	BDSC_86857
D. melanogaster Tm3: +; +; R13E12-Gal4	[19];	BDSC_48569
D. melanogaster GCaMP6f: +; UAS-GC6f; +	[37];	BDSC_42747
D. melanogaster T4T5: +; R42F06-LexA; +	[100]	BDSC_54203
D. melanogaster GCaMP6f: +; LexAOp-GC6f; +	[37]	BDSC_44277
D. melanogaster TNT: +; UAS-TNT; +	[101]	BDSC_28838
D. melanogaster slo-RNAi: +; UAS-slo-RNAi (TRiP)	[53]	BDSC_55405
D. melanogaster slo-RNAi v2: +; UAS-slo-RNAi	[54]	SCR_104421
D. melanogaster slo: w, UAS-slo; +; +	[102]	Gift from Dr. N. S. Atkinson, The University of Texas at Austin, Austin, TX, USA
D. melanogaster NaChBac: w; UAS-NaChBac	[55]	BDSC_9468
D. melanogaster cac-RNAi: yv; UAS-cac-RNAi	[53]	BDSC_27244
D. melanogaster GluClα1-RNAi: +; UAS-GluClα1-RNAi	[54]	SCR_105754
D. melanogaster UAS-Dcr-2: w; +; UAS-Dcr-2	[54]	BDSC_24651
D. melanogaster nAchRα1-RNAi: +; +; UAS-nAchRα1-RNAi	[53]	BDSC_28688
D. melanogaster para-RNAi: +; +; UAS-para-RNAi	[53]	BDSC_33923
D. melanogaster Sh-DN: w; UAS-Sh-DN	[103]	Gift from Dr. Haig Keshishian, Yale University, New Haven, CT, USA
D. melanogaster eag-DN: w; UAS-eag-DN	[104]	BDSC_8187
D. melanogaster Arclight: w; UAS-ArcLight/CyO	[43]	BDSC_51057
D. melanogaster CT1: w; R65E11-AD; R20C09-DBD	[23]	JRC_SS01001
D. melanogaster Mi9: w; R48A07-AD; VT046779-DBD	[24]	BDSC_86854
Software and algorithms
MATLAB 2018a	MathWorks	https://www.mathworks.com/
ScanImage	[94]
Psychtoolbox-3	[89, 90, 91]	http://psychtoolbox.org/
Custom modeling code	This paper	https://github.com/ClarkLabCode/TimingModels
Custom stimulus presentation and data acquisition code	This paper	Available upon request
Custom analysis code	This paper	Available upon request

Experimental Genotypes

Abbreviation	Genotype
Mil > GC6f	+; UAS-GCaMP6f/+; R19F01-Gal4/+
Mil > GC6f, slo	w, UAS-slo/+; UAS-GCaMP6f/+; R19F01-Gal4/+
Mil > GC6f, NaChBac	w/+; UAS-GCaMP6f/+; Rl9F0l-Gal4/UAS-NaChBac
Mil > GC6f, slo-RNAi	+; UAS-GCaMP6f/UAS-slo-RNAi; R19F01-Gal4/+
Mil > GC6f, GluClαl-RNAi	+; UAS-GCaMP6f/UAS-GluClα1-RNAi; Rl9F0l-Gal4/UAS-Dcr-2
Mil > GC6f, nAchRαl-RNAi	w/+; UAS-GCaMP6f/UAS-nAchRα1-RNAi; R19F01-Gal4/+
Mil > GC6f, para-RNAi	w/+; UAS-GCaMP6f/+; Rl9F0l-Gal4/para-RNAi
Mil > GC6f, Sh-DN	w/+; UAS-GCaMP6f/UAS-Sh-DN; R19F01-Gal4/+
Mil > GC6f, eag-DN	w/+; UAS-GCaMP6f/UAS-eag-DN; R19F01-Gal4/+
Tm3 > GC6f	+; UAS-GCaMP6f/+; R13E12-Gal4/+
Tm3 > GC6f, slo	w, UAS-slo/+; UAS-GCaMP6f/+; R13E12-Gal4/+
Tm3 > GC6f, NaChBac	w/+; UAS-GCaMP6f/+; Rl3El2-Gal4/UAS-NaChBac
Tm3 > GC6f, slo-RNAi	+; UAS-GCaMP6f/UAS-slo-RNAi; R13E12-Gal4/+
Mi4 > GC6f	w/+; UAS-GCaMP6f/R48A07-AD; R79H02-DBD/+
Mi4 > GC6f, cac-RNAi	w/+; UAS-GCaMP6f/R48A07-AD; R79H02-DBD/UAS-cac-RNAi
CT1 > GC6f	w/+; UAS-GCaMP6f/R65Ell-AD; R20C09-DBD/+
CT1 > GC6f, cac-RNAi	w/+; UAS-GCaMP6f/R65Ell-AD; R20C09-DBD/UAS-cac-RNAi
Tm3 > GC6f, slo-RNAi (v2)	+; UAS-GCaMP6f/UAS-slo-RNAi; R13E12-Gal4/+ (VDRC)
Mil > ArcLD	+; UAS-Arclight/+; R19F01-Gal4/+
Mil > ArcLD, NaChBac	w/+; UAS-Arclight/+; R19F01-Gal4/UAS-NaChBac
Tm3 > ArcLD	+; UAS-Arclight/+; R13E12-Gal4/+
Tm3 > ArcLD, slo-RNAi	+; UAS-Arclight/UAS-slo-RNAi; R19F01-Gal4/+
Mil > GC6f, cac-RNAi	w/+; UAS-GCaMP6f/+; R19F01 -Gal4/UAS-cac-RNAi
Tm3 > GC6f, cac-RNAi	w/+; UAS-GCaMP6f/+; R13E12-Gal4/UAS-cac-RNAi
T4T5 > GC6f, Mi1/+	+; LexAOp-GCaMP6f, R42F06-LexA/+; R19F01-Gal4/+
T4T5 > GC6f, slo/+	w, UAS-slo/+; LexAOp-GCaMP6f, R42F06-LexA/+; +
T4T5 > GC6f, Mi1 > slo	w, UAS-slo/+; LexAOp-GCaMP6f, R42F06-LexA/+; R19F01-Gal4/+
T4T5 > GC6f, slo-RNAi/+	+; LexAOp-GCaMP6f, R42F06-LexA/UAS-slo-RNAi; +
T4T5 > GC6f, Mi1 > slo-RNAi	+; LexAOp-GCaMP6f, R42F06-LexA/UAS-slo-RNAi; R19F01-Gal4/+
T4T5 > GC6f, Tm3/+	+; LexAOp-GCaMP6f, R42F06-LexA/+; R13E12-Gal4/+
T4T5 > GC6f, Tm3 > slo	w, UAS-slo/+; LexAOp-GCaMP6f, R42F06-LexA/+; R13E12-Gal4/+
T4T5 > GC6f, Tm3 > slo-RNAi	+; LexAOp-GCaMP6f, R42F06-LexA/UAS-slo-RNAi; R13E12-Gal4/+
T4T5 > GC6f, Mi4/+	w/+; LexAOp-GCaMP6f, R42F06-LexA/R48A07-AD; R79H02-DBD /+
T4T5 > GC6f, cac-RNAi/+	w/+; LexAOp-GCaMP6f, R42F06-LexA/+; UAS-cac-RNAi/+
T4T5 > GC6f, Mi4 > cac-RNAi	w/+; LexAOp-GCaMP6f, R42F06-LexA/R48A07-AD; R79H02-DBD/UAS-cac-RNAi
T4T5 > GC6f, CT1/+	w/+; LexAOp-GCaMP6f, R42F06-LexA/R65E11-AD; R20C09-DBD/+
T4T5 > GC6f, CT1 > cac-RNAi	w/+; LexAOp-GCaMP6f, R42F06-LexA/R65E11-AD; R20C09-DBD/UAS-cac-RNAi
T4T5 > GC6f, TNT/+	w/+; LexAOp-GCaMP6f, R42F06-LexA/UAS-TNT; +
T4T5 > GC6f, Mi4 > TNT	w/+; LexAOp-GCaMP6f, R42F06-LexA/R48A07-AD; R79H02-DBD/UAS-TNT
T4T5 > GC6f, CT1 > TNT	w/+; LexAOp-GCaMP6f, R42F06-LexA/R65E11-AD; R20C09-DBD/UAS-TNT
Mi9 > GC6f	w/+; UAS- GCaMP6f/R48A07-AD; VT046779-DBD/+
T4T5/+	+; R42F06-Gal4; +
TNT/+	w/+; UAS-TNT/+; +
T4T5 > TNT	w/+; R42F06-Gal4/UAS-TNT; +

Method Details

Visual stimuli

Stimuli for imaging experiments were generated using custom code written in MATLAB (The MathWorks, Natick, MA) and PsychToolBox ^89–91. Stimuli were projected with digital light projectors (Texas Instruments) onto panoramic screens surrounding the fly as described previously ⁹². Stimulus frames were presented at an update rate of 180 Hz, and stimuli were presented in green light with a mean intensity of ~70 cd/m². To minimize stimulus bleed-through onto microscope photomultiplier tubes (PMTs), the projector light was filtered with two 565/24 (center/FWHM) filters in series (Semrock, Rochester, NY, USA). All visual stimuli presented in the experiments are listed below.

Visual Stimuli

Name	Visual Stimulus Description	Figure(s)
Full Field Flicker with Contrast Sections (30 Hz for GCaMP6f kernel extraction)	Full-field flicker updated stochastically at 30 Hz, with 0.9 contrast and durations of 5 seconds. A 15s snippet of identical stimulus was repeated each minute during the stimulus.	2–4, S1–S6
Full Field Flicker with Contrast Sections (120 Hz for ArcLight Kernel Extractions)	Same stochastic stimulus as described above with one difference: the full-field flicker updated stochastically at 120 Hz rather than 30 Hz.	S1, S3
Periodic Light Bars Sweep (tuning measurements in T4)	Periodic light, 5° bars, on a dark background, spaced every 30° swept to the right or left at a randomly chosen velocity each epoch (8, 16, 32, 64, 128, 256, and 512°/s). Each velocity epoch lasted 5 seconds. The bars were stationary for 5 seconds in between epochs.	5–6, S5, S7
Rotating Sinewave Gratings (UAS-TNT control behavioral measurements)	25% contrast sinewaves with λ = 30° rotated right or left at randomly interleaved temporal frequencies (0.25, 0.375, 0.5, 0.75, 1, 1.5, 2, 3, 4, 6, 8, 12, 16, 24, and 32 Hz). Each temporal frequency epoch lasted 1 second. This was used in a behavioral experiment, following published methods 30.	S5
Random Checkerboard Gratings (tuning measurements in T4)	Random 1-dimensional 100% contrast light/dark checkerboards with 5° checks swept to the right or left at randomly chosen velocities in each epoch (8, 16, 32, 64, 128, 256, and 512°/s). Each velocity epoch lasted 5 seconds.	S6
Rotating Sinewave Gratings (tuning measurements in T4)	25% contrast sinewaves with λ = 32°, updating at 180 Hz rotated right or left at randomly chosen temporal frequencies each epoch (0.25, 0.5, 1, 2, 4, 8, and 16 Hz). Each temporal frequency epoch lasted 5 seconds.	S6
‘Isolated’ Light Bars Sweep (tuning measurements in T4)	Light, 5°-wide bars on a dark background swept to the right or left at randomly chosen velocities each epoch (8, 16, 32, 64, 128, 256, and 512°/s). The spatial periodicity was chosen so that bars passed each location at 1 Hz. For 8 and 16°/s speeds, the spatial period was 32°, so that bars passed each point at 0.25 and 0.5 Hz, respectively. Mean response was measured over 5 seconds, then divided by 5 for all velocity epochs except 8 and 16°/s, which were divided by 1.25 and 2.5 to obtain equivalent measurements per passing bar.	S6
Selection Probes
Moving Square Wave (ROI selection probe for T4)	Full-contrast square waves with 30° periods moved right, left, up, or down at 30°/s.	5–6, S5–S7
Moving Edges (ROI selection probe for T4)	Light edges moved left or right on a dark background at 30°/s and dark edges moved left or right on a light background at 30°/s.	5–6, S5–S7
Full Field Flash (ON-OFF, selection probe for Mi1, Tm3, Mi4, and CT1)	Alternating full-field light or dark with each luminance lasting 2 seconds.	2–4, S1–S6
Full Field Flash (ON-OFF, selection probe for ArcLD)	Same stimulus as described above, but with 250 ms presentations, rather than 2s.	S1, S3
Moving Bar (selection probe for Mi1, Tm3, Mi4, and CT1)	Light, 10°-wide bar moved right, left, up, and down at 30°/s on a dark background.	2–4, S1–S6

Two-Photon Imaging Protocol

Fluorescent activity of labelled neurons was recorded using two-photon scanning fluorescence microscopy. Flies were anesthetized on ice and mounted into holes in stainless steel shim holders. Using UV-cured epoxy, we fixed the anterior rim of their heads to the holder. We surgically removed the posterior cuticle and trachea of the right or left eye. The flies’ brains were covered by oxygenated sugar-saline solution⁹³. The metal holder was placed above a set of panoramic screens⁹² under a two-photon microscope (Scientifica, Clarksburg, NJ). The panoramic screens subtended 270° in azimuth and 69° in elevation. Fluorophores were excited with a Spectra-Physics MaiTai eHP laser set to 930 nm wavelength and with power at the sample less than or equal to ~30 mW. Using ScanImage⁹⁴, images were acquired at approximately 13 Hz. To prevent undesirable bleed-through from the visual stimulus, the input to the PMT was filtered with a 512/25 and a 514/30 (center/FWHM) filter in series (Semrock, Rochester, NY, USA). All data were processed and analyzed using custom MATLAB code.

Imaging Data Analysis: ROI Identification

For Mi1, Tm3, Mi4, and CT1 recordings, regions of interest (ROIs) were identified by hand to encompass one neuron per ROI. For Mi1 recordings, layers M1, M5, and M9/10 were analyzed, while for Tm3, layers M1, M4/5, and M9/10 were analyzed. For Mi4 recordings, layers M2/3/4/5 and M8/9/10 were analyzed²³. For CT1, terminals were recorded in the medulla M10 layer and in lobula layer L1. T4 axon terminals were recorded in the lobula plate, where we ran a watershed algorithm over the mean acquisition image to extract ROIs based on the baseline fluorescent intensity. For all, when low signal-to-noise ratio impeded identifying ROIs, we computed correlations in intensity over the movie between each pixel and its neighboring pixels, and used that ‘correlation image’ with watersheds to define the boundaries of ROIs.

Imaging Data Analysis: ROI Analysis

For each ROI, ΔF/F was computed with methods previously described²⁵. The baseline fluorescence F₀(t) for each ROI was computed by fitting a decaying exponential to the ROI’s time trace. When analyzing data where the stimuli contained interleaves (periods of mean gray between stimuli), only responses occurring during the interleave periods were fitted. Alternatively, with stimuli not containing interleaves, the complete time trace was fitted to calculate a baseline fluorescence. For most of the data acquired, background subtraction successfully eliminated low levels of bleed-through originating from the projector’s stimulus presentation. In cases of poor signal-to-noise recordings (particularly for the Arclight recordings and CT1 kernel extractions), custom MATLAB software used a linear model for bleed-through to subtract off contamination of the collected data. We calculated the fractional changes for each ROI trace as $\frac{\Delta F}{F}=\frac{F(t)-F_0(t)}{F_0(t)}$.

Imaging Data Analysis: ROI Selection

Responsive ROIs were selected as described previously³⁹. After extracting each ROI and computing its ΔF/F, we selected desirable ROIs based on their responses to a probe stimulus—a stimulus presented at the beginning and end of each recording and independent of the experimental stimulus. For recordings of Mi1, Tm3, Mi4, and CT1, selected ROIs responded to a full-field flashes with a response of appropriate polarity, or to the light bar moving in each of the four cardinal directions. For the full-field flash stimulus probe, we selected ROIs with preferential responses to full-field ON flashes if recordings came from cells with ON-center receptive fields (i.e., Mi1, Tm3, Mi4, and CT1 medulla terminals). Alternatively, for cells with OFF-center receptive fields (i.e., CT1 lobula terminals), we selected ROIs with a preferential response to full-field OFF flashes. For ROIs selected based on their responses to a moving light bar, we based selection on the ROI’s response to a minimum of two directions of the moving bar. This light moving bar stimulus probe was used for selection in a subset of Mi1, Tm3, and Mi4 recordings. In the genotype Tm3 > GC6f, the kernel of a single fly was a substantial outlier, with a fall time of 1.5 seconds. This fly was excluded from analysis throughout; including it did not affect the computed statistical significance values.

Selection of T4 ROIs was performed using previously described procedures^25,33. The stimulus probe for T4 recordings consisted of square waves moving right, left, up, or down, as well as light and dark edges moving rightward or leftward. The single edges were used to determine direction selectivity indices (DSIs) and edge selectivity indices (ESIs). We then selected T4 ROIs that met the specific response thresholds used previously (i.e., ESI > 0.3, DSI > 0.4 for the T4 progressive ROIs and DSI < −0.4 for T4 regressive ROIs).

Filter extraction

For recordings of Mi1, Tm3, Mi4, and CT1, linear filters were extracted to a binary, stochastic white noise stimulus of 0.9 contrast. We used ordinary least squares (OLS) regression to compute the linear filter that best predicted neural responses. Concretely, to compute the filter, we solved the equation Sk = r, where r is the response vector, and S is a matrix of stimulus contrasts that preceded each response. This equation used N pairs of stimulus-vectors and responses, as follows:

$$\left[\begin{array}{cccc}{s}_t& s_{t-1}& \cdots & s_{t-L}\\ s_{t+1}& s_t& & s_{t-L+1}\\ ⋮& & \ddots & \\ s_{t+N-1}& & & s_{t-L+N-1}\end{array}\right]\cdot \left[\begin{array}{c}{k}_0\\ k_1\\ ⋮\\ k_L\end{array}\right]=\left[\begin{array}{c}{r}_t\\ r_{t+1}\\ ⋮\\ r_{t+N-1}\end{array}\right]$$

The stimulus and response values at a specific time t are s_t and r_t, respectively. The filter is L + 1 elements long, and k_i gives the filter’s value at a specific time lag, i. We used standard methods in MATLAB to solve this over-determined ordinary least square equation to obtain the best fit kernel k. In the equations above, we included stimulus values that preceded each response to obtain (acausal) kernel elements.

For Arclight kernels (Figure S1, S3), we used a temporal super-resolution method that allowed us to extract the kernels with high resolution (~120 Hz) even while sampling responses at 13 frames per second⁹⁵.

Nonlinearities were computed by fitting each fly’s response to a linear-nonlinear (LN) model³⁹. In this model, the binary flickering stimulus was linearly filtered by the fitted kernel and then acted on by an instantaneous nonlinearity. To plot the nonlinearities, the linear prediction was plotted against the measured responses, with individual points binned by their linear prediction to determine a non-parametric nonlinearity. This nonlinearity represents the nonlinearity associated with the transformation of visual contrast to calcium²¹ and the nonlinearity associated with our calcium indicator³⁷. In our normalization of this LN model, if only the filter amplitude changes, then the plotted nonlinearities will lie on top of one another. These nonlinearities might be expected to change if, for instance, the basal calcium level in a cell changed under a manipulation.

To deconvolve linear calcium indicator dynamics from the filter, we assumed that the indicator acted as a first order low-pass filter with time constant of 250 ms³⁷, or different time constants in Figure S7. We then solved the same ordinary least squares equation above, except that we modeled the response as a first-order inhomogeneous recurrence relation with variable source:

$$r_t=\alpha r_{t-1}+\sum _{j=0}^L{k}_j{s}_{t-j}.$$

We chose the parameter $\alpha =\exp \left(-\frac{\mathrm{\Delta }t}{\tau }\right)=0.8$, where τ = 250 ms is the filter time constant and Δt = 70ms is our imaging measurement interval, which follows from comparing the formal solution to this recurrence to its analog in continuous time. This changed the equation above to read:

$$\left[\begin{array}{cccc}{s}_t& s_{t-1}& \cdots & s_{t-L}\\ s_{t+1}& s_t& & s_{t-L+1}\\ ⋮& & \ddots & \\ s_{t+N-1}& & & s_{t-L+N-1}\end{array}\right]\cdot \left[\begin{array}{c}{k}_0\\ k_1\\ ⋮\\ k_L\end{array}\right]=\left[\begin{array}{c}{r}_t-\alpha r_{t-1}\\ r_{t+1}-\alpha r_t\\ ⋮\\ r_{t+N-1}-\alpha r_{t+N-2}\end{array}\right]$$

We then used the same method to solve for this deconvolved k.

Behavioral analysis

Fly optomotor turning responses were measured and quantified using methods described in previous studies^25,92,96. Briefly, flies were briefly anesthetized on ice, glued to metal needles using UV-cured epoxy, and tethered so they could walk on air-supported balls. The flies were positioned in the center of panoramic screens that cover 270° of azimuth and 106° of vertical visual space⁹². Using the monochrome green light (peak 520 nm and mean luminance of ~100 cd m⁻²) of a Lightcrafter DLP (Texas Instruments, USA), we projected stimuli onto the screens creating a virtual cylinder around the fly. Turning response was quantified by measuring the rotation of the ball at 60 Hz using an optical mouse sensor. Flies were tested in a warm, temperature-controlled behavioral chamber (34–36°C), which resulted in strong behavior. Turning responses were averaged over the duration of the stimulus presentation and over trials to create fly averages. These were then averaged across multiple flies. Tuning curves were created following the same analysis procedure as in T4 imaging data.

Tuning curves and center of mass

To compute the T4 tuning curves, we recorded T4 responses to stimuli moving at a variety of speeds. Each stimulus lasted 5 seconds. For each ROI, we computed the mean response over the 5 second presentation and over all presentations of a specific speed. We then averaged ROIs within flies to generate each fly’s tuning curve. These were averaged across flies. Those average curves were normalized by setting each fly’s maximum response to equal 1 before averaging; the maximum was set to 1 again after averaging (Figure 5–6). Non-normalized versions were also computed (Figure S5).

These tuning curves were quantified with a single number representing the center of mass of the curve as a function of log-velocity. The center of mass was computed as:

$$\log M=\frac{{\sum }_{v}R(v)\log v}{{\sum }_{v}R(v)}$$

where R(v) was the mean ΔF/F response to a specific velocity v. R(v) was set to be 0 if the ΔF/F values were negative. Thus, the center of mass is a geometric mean of the velocities, weighted by the non-negative responses.

Numerical modeling

Toy Barlow-Levick (BL) models (Figures 1 and S1)

We constructed toy Barlow-Levick (BL) models to gain intuition about how input timing influences velocity tuning in simple motion detectors. These models filtered a moving point stimulus in space and in time before signals were summed and rectified to obtain the final result (Figure 1, S1, and S7). The periodic delta-function stimulus was $c(t,x)=C_0{\sum }_{n=-\infty }^{\infty }\delta (x-n\lambda -vt)$, where C₀ was set to be 1 second and the spatial period λ was set to be 30°. The spatial filters for the two inputs were centered at x = 0 and x = Δϕ, where the separation was 5°. The spatial filters were either delta functions or Gaussians with a full-width half-maximum of 5°. Both had unit area. In the pure delay model, the non-delay filter was f(t) = δ(t) while the delay filter was f(t) = δ(t − τ), where τ was the delay. In the lowpass model, the temporal kernels were of the form $f(t)=\frac{1}{\tau }{e}^{-t/\tau }$, where the normalization ensures that the gain of the filtering doesn’t change with changes in time constants. Time constants are provided in the figures or captions of Figures 1 and S1. When we tested kernels with different rising dynamics (Figure S7), we used an inhibitory kernel of the form

$$f(t)=p\left(\frac{t}{{\tau }_1^2}{e}^{-t/{\tau }_1}\right)+(1-p)\left(\frac{t}{{\tau }_2^2}{e}^{-t/{\tau }_2}\right),$$

where the normalization ensured that the gain of the filtering doesn’t change when p is adjusted (Figure S7). To make the different inhibitory kernel shapes, we used p = 0, 0.1, 0.2 in our simulations, with τ₁ = 15 ms and τ₂ = 100 ms. To make the excitatory kernel, we used p = 0 and τ₂ = 40 ms with the same functional form. After spatial and temporal filtering, we obtained an excitatory signal, S_exc(t), and an inhibitory signal, S_inh(t). The final model response was equal to R(S_exc − AS_inh). The relative weighting of excitatory and inhibitory signals, A, was chosen to be 6 for Figure 1 and S1 and to be 2 for Figure S7, which used different kernel shapes. Both weights yielded reasonably strong suppression of ND responses, also observed in T4^12,28,30. The function R(x) = max(x, 0), rectifies the output by setting all negative values to 0.

Circuit models for T4 neurons (Figures 7 and S7)

We constructed circuit models for T4 neurons following prior work³⁴. Here, we briefly summarize this circuit model, and describe two elaborations introduced in this work. The previously-introduced model³⁴ includes three inputs: a delayed ND-spatially-offset OFF inhibitory input representing Mi9, a centered ON excitatory input representing Mi1 and Tm3, and a delayed PD-spatially-offset ON inhibitory input representing Mi4. All inputs are modeled as linear-nonlinear (LN) transformations of the input contrast. Each input has a Gaussian spatial acceptance function with a full width at half maximum of 5.7 degrees^34,97; we denote the spatially filtered contrast signal by c(t, x) for brevity. For temporal filters f_Mi9, f_Mi1/Tm3, and f_Mi4, the three inputs to the model cell are then defined as rectified linear functions that mimic the polarity-selectivity of inputs to T4 cells:

$$g_{\text{Mi9}}(t,x)=R\left(-\left(f_{\text{Mi9}}*c\right)(t,x-\mathrm{\Delta })\right)$$

$$g_{\text{Mi}1/\text{Tm3}}(t,x)=R\left(+\left(f_{\text{Mi}1/\text{Tm3}}*c\right)(t,x)\right)$$

$$g_{\text{Mi}4}(t,x)=R\left(+\left(f_{\text{Mi}4}*c\right)(t,x+\mathrm{\Delta })\right),$$

where * denotes temporal convolution, R(x) = max{0, x} is the ramp function, and Δ = 5° is the spacing between neighboring inputs ^34,97. Using these inputs, we then define the conductances for excitatory and inhibitory currents:

$$g_{\text{exc}}={\gamma }_{\text{exc}}{g}_{\text{Mi}1/\text{Tm3}}$$

$$g_{\text{inh}}={\gamma }_{\text{inh}}\left(g_{\text{Mi9}}+g_{\text{Mi4}}\right),$$

where γ_exc and γ_inh are constant gain factors. We then define the membrane potential V_m of the model T4 cell as

$$V_{\text{m}}=\frac{g_{\text{inh}}{E}_{\text{inh}}+g_{\text{exc}}{E}_{\text{exc}}}{g_{\text{leak}}+g_{\text{inh}}+g_{\text{exc}}},$$

where E_inh and E_exc are the reversal potentials for inhibitory and excitatory currents, respectively, and g_leak is the leak conductance. Briefly, this nonlinearity follows from defining V_m such that the reversal potential for leak currents is 0 mV and then making a pseudo-steady-state approximation for the voltage in the limit of small membrane capacitance^29,34,98. Finally, we model the transformation from membrane voltage to calcium concentration by a positively rectifying half-quadratic function R²(x) ≡ (R(x))²:

$$C(t,x)=R^2\left(V_{\text{m}}(t,x)\right).$$

The gain factors γ_exc and γ_inh can then be represented in units of g_leak; as in prior work³⁴ we fix $\frac{{\gamma }_{\text{exc}}}{g_{\text{leak}}}=0.1$ and $\frac{{\gamma }_{\text{inh}}}{g_{\text{leak}}}=0.3$ throughout. We note that this choice also reflects a choice of scale of the temporal filters; we scale all temporal filters to have unit ℓ₂ norm after discretizing time in our simulations ³⁴. This choice of scale yields filters with units of inverse contrast.

In this work, we introduce two minimally elaborated versions of this model. First, as we perform simulations using measured, non-identical temporal filters for Mi1 and Tm3, we introduce an extension with separate inputs to represent these neurons,

$$g_{\text{Mi}1}(t,x)=R\left(+\left(f_{\text{Mi}1}*c\right)(t,x)\right)$$

$$g_{\text{Tm3}}(t,x)=R\left(+\left(f_{\text{Tm3}}*c\right)(t,x)\right),$$

which are then integrated as

$$g_{\text{exc}}={\gamma }_{\text{exc}}\frac{g_{\text{Mi}1}+g_{\text{Tm3}}}{2}.$$

Second, we introduce a variant that incorporates a second PD-spatially-offset delay line to represent CT1, with an additional input

$$g_{\text{CT}1}(t,x)=R\left(+\left(f_{\text{CT}1}*c\right)(t,x+\mathrm{\Delta })\right),$$

and the conductance of inhibitory currents modified to

$$g_{\text{inh}}={\gamma }_{\text{inh}}\left(g_{\text{Mi9}}+\frac{g_{\text{Mi}4}+g_{\text{CT}1}}{2}\right).$$

In both cases, we choose to introduce the new inputs such that the elaborated models reduce to the un-elaborated model when the relevant temporal filters are identical. We note that, with our stimulus design and chosen thresholds for the model, the Mi9-like input does not contribute to simulated model responses.

In Figure S7, we sweep the gain factor of the Mi4-like input to the model. Concretely, we fractionally rescale the value for the gain factor chosen in a prior version of the model³⁴ by a factor ranging between zero and four. To visualize the resulting tuning changes, we plot the center of mass of each tuning curve in log-velocity space. Previous work has shown that altering the gain factors of both flanking inhibitory inputs simultaneously affects how well the circuit model can recapitulate other functional properties of T4 cells, but has not considered how these parameters affect velocity tuning^28,34.

Synthetic filters

As in prior work ³⁴, we use an L₂-normalized second order lowpass filter $f(t)=2{\tau }^{-\frac{3}{2}}t\exp \left(-\frac{t}{\tau }\right)\mathrm{\Theta }(t)$ and its normalized distributional derivative $g(t)=2{\tau }^{-\frac{3}{2}}(\tau -t)\exp \left(-\frac{t}{\tau }\right)\mathrm{\Theta }(t)$, with rescaling to obtain unit ℓ₂ norms after discretization. The function Θ(t) is the Heaviside step function, which enforces causality.

Visual stimuli

In all simulations, we used 5-degree-wide drifting bar stimuli with a spatial period of 30 degrees, designed to mimic the stimuli used in experiments. We chose the background of these stimuli to have contrast zero, and the foreground bars to have contrast one. Therefore, the Mi9-like input of the model from³⁴ does not respond to these stimuli, as it is sensitive only to negative contrasts. This would change, however, if one chose non-zero rectification thresholds for the inputs, or equivalently a different baseline for the input stimulus. Previous work has shown that such modifications can noticeably change the response properties of circuit models similar to those studied here^57,58. We did not tune rectification thresholds in this work, as our objective was to characterize what features of our experimental data could be captured by a minimally extended version of the circuit model from³⁴.

Numerical methods

As in prior work³⁴, all simulations of the circuit model were performed using a spatial sampling interval of 0.5 degrees and a temporal sampling interval of 1/240 s. All simulations were performed using MATLAB 9.8 (R2020a) (The MathWorks, Natick, MA, USA).

Smoothing measured temporal filters using discrete Laguerre functions

We smoothed the measured, calcium-deconvolved filters by projecting them into a truncated basis set of discrete Laguerre functions^95,99. For a scale parameter α ∈ (0,1), the discrete Laguerre polynomials $p_j^{(\alpha )}[t]$ are the orthogonal polynomials on ${\mathbb{N}}_{\ge 0}$ for the discrete exponential weight, i.e., the polynomials satisfying ${\sum }_{t=0}^{\infty }{p}_j^{(\alpha )}[t]p_k^{(\alpha )}[t]{\alpha }^t={\delta }_{jk}$. The orthonormal discrete Laguerre functions ${\lambda }_j^{(\alpha )}[t]$ then follow by absorbing the weight, and are explicitly given as

$${\lambda }_j^{(\alpha )}[t]={\alpha }^{\frac{t-j}{2}}{(1-\alpha )}^{\frac{1}{2}}\sum _{k=0}^j{(-1)}^k\left(\begin{array}{l}t\hfill \\ k\hfill \end{array}\right)\left(\begin{array}{l}j\hfill \\ k\hfill \end{array}\right){\alpha }^{j-k}{(1-\alpha )}^k$$

for $t\in {\mathbb{N}}_{\ge 0}$ and $j\in {\mathbb{N}}_{\ge 0}$. These functions form a complete orthonormal basis for the space of square-summable functions on ${\mathbb{N}}_{\ge 0}$, and are a convenient basis for temporal kernels as they incorporate the expected temporal decay⁹⁹. As in prior work⁹⁵, we chose the five lowest-order functions. To obtain qualitatively reasonable smoothed filters, we set α = 0.2⁹⁹. After projecting the deconvolved filters into this subspace, we re-normalized them to have unit ℓ₂ norm. The resulting smoothed filters are plotted along with their deconvolved and raw counterparts in Figure S6.

Statistical analysis

For statistical purposes, individual flies were considered independent measurements. Each fly yielded multiple ROIs, and the ROIs’ responses were averaged together to generate a single response per fly. In extracting filters, all the filters extracted from a fly’s multiple ROI traces were averaged to obtain a single filter per fly. Then, each fly’s filter was normalized by its peak amplitude, and each filter’s characteristic rise, peak, and fall time were computed. To display normalized average filters, they were averaged across flies, before the average was scaled to have a maximum excursion of 1. Similarly, the dynamics bar plots are also the average across multiple flies. The solid filter line and shaded error bars indicate the mean ± SEM. Similar averaging was done for T4 recordings. After averaging ROI traces in time, a single tuning curve was obtained for the progressive and regressive layers of T4 and T5. Main text figures depict a tuning curve resulting from the combination of the progressive and regressive layers for T4. All tuning curves were normalized to their peak on a per-fly basis and the curve’s center of mass was computed on a per fly basis. In the figure legends, n values indicate the number of individual flies. Some control genotypes were tested continuously throughout the course of experiments, which were performed over several years. This is reflected in larger sample sizes for those genotypes. Throughout, non-parametric tests were used to assess statistical significance of the medians of distributions, as noted in the figure legends. Because data was graphically summarized by means and SEMs, the statistical significance based on medians does not always align with the graphical summary.

Highlights:

• Manipulating ion channel expression alters visual neuron response timing

• The altered timing changes the velocity sensitivity of downstream motion detectors

• Excitatory and inhibitory timing changes oppositely affect downstream sensitivity

• A circuit model with parallel input neurons qualitatively reproduces experiments