Nature Neuroscience: doi: /nn.4581

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2 Supplementary Figure 1 Anatomy and functional connectivity suggest that TB neurons are part of an excitatory feedforward pathway from the AOTU to the BU composed of parallel channels. a, Different channels of Fig. 1e. The signal from the pre-synaptic marker synaptotagmin expressed in a subset of TB neurons (SS02927 split Gal4) is seen only in the BU, consistent with these neurons being part of a feedforward pathway from the AOTU to the BU. b, An additional example of MCFO using SS02927 split-gal4 to label a subset of TB neurons. c, Examples of MCFO with sparse TB neuron labeling using R76B06-Gal4 as a driver line. A total of more than 60 flies with different labeling densities were examined. For examples of high-density labeling, see Supplementary Fig. 2a, b, e. For quantification of projection patterns, see Results and Online Methods. d, Average responses showing that optogenetic activation of TB neurons with CsChrimson (yellow bar) induces slow and multi-phasic GCaMP6f responses in ring neurons. Each trace represents a fly (4 repeats for each fly); the mean response is overlaid with a dark thick line. e, Variations of baseline activity in ring neurons, shown for different flies. Each trace represents a fly (6 flies, 4 repeats for each fly); the mean response across flies is overlaid with a dark thick line. Note that the activity does not return to baseline and that the elevation can sometimes persist for several seconds. F 0 is computed at the beginning of an experimental run, each of which comprised 4 repeats. Scale bars in a-c: 20 m.

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4 Supplementary Figure 2 Anatomical study showing a microglomerular organization of TB neuron outputs in the BU. a-b, Maximum intensity projection (MIP) and one cross-section (Section) of MCFO images of TB neurons (using R76B06-Gal4 driver line) in BU of one hemisphere in two example flies ((a) and (b), respectively). TB neuron axons are organized into distinct microglomeruli. Individual glomeruli appear to be innervated by single TB neurons (see (f) for an apparent exception). c-d, MCFO images of ring neurons (using R56H10-Gal4 driver line) in one BU. (c) and (d) are from two example flies; left panels show MIPs, and right panels show individual cross-sections. Ring neuron dendrites are also organized into distinct glomeruli. Based on their uniform labeling color, the majority of labeled glomeruli appear to be innervated by a single labeled ring neuron. However, some glomeruli showed labeling with more than one color even in single confocal sections, suggesting the presence of dendrites from more than one cell (see arrow in (c)). Note that ring neuron glomeruli appear hollow in the middle (more clearly seen in single sections), in contrast to the generally more compact structure of the TB neuron glomeruli. e-f, MIP of MCFO images of a population of TB neurons (using the R76B06-Gal4 driver line) in one hemisphere, including examples of dense (e) and sparse (f) labeling. The white arrowheads in (f) point to the terminals of an atypical TB neuron that appear to innervate three glomeruli in BU. The arrow in (e) points to a terminal with an unusually extended, perhaps multi-glomerular, shape. g-h, MIP of MCFO images of a population of ring neurons (using R56H10-Gal4 driver line) in one hemisphere, including examples of dense (g) and sparse (h) labeling. The white arrows in (h) point to the ring neuron that appears to branch and innervate several glomeruli in BU. i, MIP of immunostaining against GFP and DsRed in a transgenic fly expressing red and green GECIs in TB, ring, and MT neurons, where they overlap in the AOTU and BU.

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6 Supplementary Figure 3 Optimizing spectral separation in two-color two-photon imaging. a, Schematic of in vivo two-color two-photon imaging setup, with parameters of optical elements labeled. A 532 nm DPSS laser beam is split into two to drive two DMDs for visual stimulation. A narrow-band green channel filter (511/20) was used to isolate the GCaMP signal from contamination by the 532 nm visual stimulation light. A 641/75 filter was chosen for the red channel, as discussed in (b) and (c). We also found a non-coherent emission from the mode-locked laser that would severely contaminate the signal in the red channel. This emission can be filtered by a long-pass filter (715LP). b, Two-photon excitation and fluorescence emission spectra of jrgeco1a and GCaMP6f, (adapted from Dana H. et al., elife, 2016, Ref. 20). The green line is the 532 nm laser for visual stimulation. The emission spectra of GCaMP and RGECO overlap substantially, and GCaMP emission is relatively strong around the peak of RGECO emission. Filtering out GCaMP signal by using a more red-shifted and narrower bandpass filter would also decrease the SNR in the RGECO channel. The excitation spectra show that around 1000 nm, the brightness (and thus SNR) of RGECO increases monotonically with the increase of wavelength. Increasing the excitation wavelength thus compensates for the decrease of SNR in the RGECO channel from emission filtering, and by this means we achieved usable SNRs and spectral separation between GCaMP and RGECO. c, Labeled GCaMP and RGECO fluorescence emission spectra under non-optimized (first row) and optimized (second row) imaging conditions. Red and green channel PMT values in tissues only expressing GCaMP (middle column), and with both GCaMP and RGECO expressed and intermingled (right column), under the two imaging conditions. Each dot represents a single time point, and the dots are color-coded according to their glomeruli. Dots from the same glomeruli form a cluster. High levels of contamination lead to strong correlation between the two channels (upper middle). d, Exemplar traces of neural processes expressing only GCaMP nonetheless show strong bleed-through from the green channel into the red when imaged under sub-optimal conditions. Under 1000 nm excitation and 625/90 filtering, GCaMP signal contaminates the jrgeco1a channel, and F/F 0 values in the red channel match those of GCaMP6f, which can exceed the maximum F/F 0 available for jrgeco1a. By contrast, under 1020 nm excitation and with 641/75 filtering, no signal was seen in the red channel (e). Note that the red channel should not have any signal, since the imaged neural processes expressed only GCaMP. e, F/F 0 signals recorded in green and red channels in neurons expressing only GCaMP6f shows minimal bleed-through of signal from the green indicator into the red channel.

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8 Supplementary Figure 4 Contralateral suppression is the dominant effect in BU. a, Distribution of summated ring neuron responses to ipsilateral and contralateral bars, together with exemplar traces; each dot is a glomerulus. While the majority of the imaged glomeruli show contralateral suppression positive response to an ipsilateral bar and negative response to a contralateral bar (lower right quadrant with blue shade and exemplar traces thereof) there are also examples of contralateral enhancement (upper two quadrants). b-c, Distribution of summated TB and ring neuron responses to ipsilateral and contralateral bars in different GECI combinations, as in (a); each dot is a glomerulus. Ipsilateral excitation and contralateral inhibition is the dominant response pattern, regardless of cell type and GECI combination. Note that we did not image the entire BU; instead, we chose a similar depth that optimized coverage of the dorsal BU (see Online Methods for details, (TB) G _(Ring) R : 17 BUs from 10 flies; (TB) R _(Ring) G : 15 BUs from 12 flies). Right panel in (b) is the same as (a). We found that responses (% F/F 0 ) to bilateral stimuli are the linear combinations of responses to ipsilateral and contralateral stimuli, regardless of the GECI combinations used. For (TB) G _(Ring) R : R Bi ring = 0.83 * R Ipsi ring * R Contra ring -3.27, goodness of fit 2 = 0.90; R Bi TB= 0.89 * R Ipsi TB+ 0.16* R Contra TB-3.24, goodness of fit 2 = For (TB) R _(Ring) G : R Bi ring = 0.83 * R Ipsi ring * R Contra ring -5.74, goodness of fit 2 = 0.95; R Bi TB= 0.83* R Ipsi TB+ 0.34* R Contra TB-2.97, goodness of fit 2 = d, all selected glomeruli corresponding to Fig. 3e. e, all selected glomeruli corresponding to Fig. 4e, f.

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10 Supplementary Figure 5 Neuron-specific state-dependence. a, Averaged images of the BU across frames during an UP state (epoch of elevated calcium activity not specific to stimulus presentation) and a normal state, with glomerulus boundaries shown in dashed lines. Clear differences (white arrow) can be seen in ring neurons but not TB neurons in the highlighted glomerulus (thick solid white line). Typically, state-dependence was limited to specific neurons (for example, a ring neuron here) of specific glomeruli. b, Exemplar traces of TB and ring neurons; UP states in the ring neuron are highlighted within dashed boxes. Traces are taken from the highlighted glomerulus in (a). c, Exemplar traces of TB and ring neurons from the same BU at the same time as in (b) but in a different glomerulus than (b); no statedependence is seen.

11 Supplementary Figure 6 History dependence is strongest in bilateral stimuli.

12 a, Schematic of two-step stimulus sequence: a 1 s stimulus (either ipsilateral, contralateral, or bilateral bars) is followed by 1 s of darkness, and then a second stimulus (either an ipsilateral or contralateral bar) is presented for 1 s. Responses are grouped as X-Ipsi or X-Contra, where X designates the set of possible stimuli used in the first stimulus presentation (either ipsilateral, contralateral, or bilateral bars). b, Average responses (mean ± s.e.m.) to X-Ipsi and X-Contra stimuli in (a) in an exemplar BU glomerulus. c, Simulated responses generated by the circuit model in Fig. 6f-h capture the reduced history dependence (74%) in X-Ipsi compared to that in X-Bi (111%; Fig. 6h). While the model also predicts history dependence for X-Contra stimuli, rectification of the calcium signal prevents detection of history dependence in the data. d, Trans-synaptic scatter plot of history dependence (see Online Methods for details) for X-Ipsi and X-Contra stimulus conditions, shown for all (gray) and selected (black) glomeruli (corresponding to the analogous plots in Fig. 4f-g). See Supplementary Tables 2 and 5 for statistical results. e-f, Empirical cumulative distribution function of history dependence for X-Bi, X-Ipsi, and X-Contra conditions, shown for TB and ring neurons in all (solid line) and selected (dashed line) glomeruli in different GECI combinations. See Supplementary Tables 2 and 5 for statistical results.

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14 Supplementary Figure 7 History dependence only involves the most recent stimuli. a, Schematic of three-step stimulus sequence. A 1 s stimulus (either ipsilateral, or contralateral, or bilateral bars) is followed by 1 s of darkness, and then a second 1 s stimulus (either ipsilateral, or contralateral, or bilateral bars) is followed again by 1 s of darkness, and finally a third stimulus (bilateral bars) is presented for 1 s. b, Exemplar grouped glomeruli responses (mean ± s.e.m.) show no clear history dependence of the third response based on the first stimulus. Responses are grouped as X-Ipsi-Bi, X-Contra-Bi, and X-Bi-Bi, where X designates the set of possible stimuli used during the first stimulus presentation (either ipsilateral, contralateral, or bilateral bars). c, Simulated responses generated by the circuit model in Fig. 6f-h capture the lack of history dependence of the responses to the last stimulus ( Bi ) on stimuli presented two steps back ( X ). d-e, Trans-synaptic scatter plot of history dependence (see Online Methods for details) of three step sequence as in (a), shown for all (gray) and selected (black) glomeruli in different GECI combinations. The population average does not exhibit obvious history dependence in either GECI combination. See Supplementary Table 4 for statistical results. f-g, Cumulative distribution of history dependence of three step sequence as in (a), shown for all (solid lines) and selected (dashed lines) glomeruli in both GECI combinations. The population average does not exhibit obvious history dependence in either GECI combination. See Supplementary Table 4 for statistical results.

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16 Supplementary Figure 8 Activity during the dark period is correlated with history dependence in ring neurons. a, Schematic of the stimulus sequence. A 1 s stimulus (either ipsilateral, contralateral, or bilateral bars) is followed by a dark period of variable duration, and then a second stimulus (bilateral bars) is presented for 1 s. b, Ring-neuron-specific persistent activity (arrowheads) in exemplar BU glomerulus during dark periods of varying duration (mean ± s.e.m.). c, Zoomed-in traces from rectangle in (b). d, Simulated ring neuron responses generated by the circuit model in Fig. 6f-h capture the rank-ordered activity shown in (c) (shown for 5s period of darkness). e, Rank-ordered ring neuron responses to different stimulus sequences during the first stimulus (defined as the activity integrated over the period of the first stimulation) and during the dark period (defined as the activity integrated over the period beginning 1.5 s after the end of the first stimulus and ending at the beginning of the second stimulus) are reversed with respect to one another, irrespective of GECI combination. f, Rank-ordered ring neuron responses during dark period and during second stimulus presentation (defined as the activity integrated over the period of the second stimulation) are consistent in ring neurons, irrespective of GECI combination. g, The effect of stimulus history (see Online Methods for details) on ring neuron responses monotonically decreases as the duration of the dark period increases, irrespective of the GECI combination, while the effect on TB neuron responses fluctuates. ((TB) R _(Ring) G : 10 BUs from 8 flies; (TB) R _(Ring) G : 3 BUs from 3 flies).

17 Supplementary Figure 9 The properties of biphasic filters give rise to the observed suppression and history dependence in TB and ring neurons. a, Biphasic filters consist of leading ( and trailing ( ) phases of opposite sign, separated in time. Each phase of the filter is described by an amplitude and a latency. b, Pearson s correlation coefficient between model and data, shown for 38 TB neurons (dotted line) and 54 ring neurons (solid line). c, Amplitudes of ipsilateral (solid markers) and contralateral (open markers) filters fit to 30 pairs of TB neurons (left) and ring neurons (right). Bold markers correspond to the filters shown in bold in Fig. 5a. d, Peak latencies of ipsilateral (solid markers) and contralateral (open markers) filters fit to TB neurons (left) and ring neurons (right).

18 The presentation times of bar stimuli are shown shaded in gray. Bold markers correspond to the filters shown in bold in Fig. 5a. e, Contralateral suppression observed in the data, compared to leading amplitudes of biphasic filters (defined in (g)). f, History dependence observed in the data, compared to trailing amplitudes of biphasic filters (defined in (g)). g, Change in contralateral suppression (CS) and history dependence (HD) from TB to ring neurons, compared to the change in size of the contralateral filter (relative to the ipsilateral filter). See Supplementary Note for the quantification of the changes. h, Leading amplitudes of the biphasic filter give a simple estimate of contralateral suppression, while trailing amplitudes give a simple estimate of history dependence. As in Figs. 3 and 4, we measure the extent of contralateral suppression in terms of the integrated response to an ipsilateral stimulus (A Ipsi ; green) versus a bilateral stimulus (A Bi ; purple), and we measure the extent of history dependence in terms of the integrated response to a bilateral stimulus when preceded by a contralateral stimulus (A Bi Contra ; blue) versus an ipsilateral stimulus (A Bi Ipsi ; green).

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20 Supplementary Figure 10 Contralateral suppression does not depend on the location of the ipsilateral stimulus. a, Schematic showing excitatory field mapping with a single stimulus (left, designated as Single stimulus below) and excitatory field mapping in the presence of a contralateral stimulus (right, designated as With second stimulus below). b, Excitatory fields of paired TB and ring neurons. Note strong suppression in ring neurons but not in TB neurons. Dashed white lines indicate the cross section used in (d). c, Summated excitatory fields of TB and ring neurons across several glomeruli in one BU (24 glomeruli segmented in this example). Note strong suppression in ring neurons but not TB neurons. Dashed white lines indicate the cross section used in (e). d, Cross-section along the dashed white lines in (b), showing large-field suppression of the field in the presence of a contralateral stimulus. e, Cross-section along the dashed white lines in (c), showing large-field suppression of the field in the presence of a contralateral stimulus. f, Scatter plots of the ratio of summated F/F 0 over the area of the excitatory field mapped in the presence of a second stimulus versus that mapped with a single stimulus. This scatter plot shows post-synaptically enhanced contralateral suppression over different locations, irrespective of the GECI combination used. ((TB) G _(Ring) R : 9 BUs from 8 flies; (TB) R _(Ring) G : 2 BUs from 2 flies; P < 0.001, see Supplementary Table 6 for exact statistical results). g, Cumulative distribution of the ratio shown in (f). This distribution shows post-synaptically enhanced contralateral suppression over different locations, irrespective of GECI combination. ((TB) G _(Ring) R : 9 BUs from 8 flies; (TB) R _(Ring) G : 2 BUs from 2 flies; P < 0.001, see Supplementary Table 6 for exact statistical results).

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22 Supplementary Figure 11 Predicting responses to competing stimuli. a, Schematic showing a simulated stimulus condition in which a left and right bar are each presented for the same fixed duration (black arrows), but separated by a variable inter-stimulus-interval (ISI; defined as positive when the left bar precedes the right bar, and vice versa). After a variable delay (defined relative to the end of the second stimulus, whether a left or right bar), a pair of left and right bars are presented simultaneously. b, Two simulated neurons (left, upper, and right, lower) are each described by a pair of biphasic ipsilateral (black) and contralateral (gray) filters (see Supplementary Note). The overlap of each stimulus presentation with the corresponding filter (measured as the area under the ipsilateral filter swept out by each ipsilateral stimulus, and similarly the area under the contralateral filter swept out by each contralateral stimulus) determines whether its contribution to the overall response is excitatory (red) or inhibitory (blue). In this example, a left bar was presented less recently inside the left neuron s RF relative to the presentation of a right bar inside the right neuron s RF. c, The response of each neuron is determined by the total integrated area swept out by all stimuli. This area has a larger positive value for the left neuron (upper) than for the right neuron (lower). This response value can be computed for various combinations of ISI and delay, as shown in the triangular phase plots on the right. The black point marks the specific combination of ISI and delay exemplified in panel (b). d, The difference in response between the two neurons (computed by subtracting right from left) determines regions of parameter space for which the left neuron responds more strongly than the right (red regions), or the right neuron responds more strongly than the left (blue regions). e, The difference in response shown in (d) can be used to extract a consistent rule for determining which stimulus (left or right) will be selected when both stimuli are presented simultaneously. We measure this selection by determining which side (left or right) will produce a larger response to bilateral bars, based on the timing of left and right bars that were previously presented within the RF. For small delays, a larger response is evoked on the side where the stimulus was presented more recently inside the RF (cool colors), while for large delays, a larger response is evoked on the side where the stimulus was presented less recently inside the RF (warm colors). The dotted line indicates the transition between the two regimes. f, g, Monophasic filters produce a single regime in which responses are stronger for stimuli that have been presented more recently inside the RF (in contrast, biphasic filters produce two qualitatively different regimes). Note that on shorter timescales (brief stimuli presented with short ISI and short delays), a stronger response can be observed for stimuli that have been presented less recently inside the RF (see Supplementary Note).

23 Supplementary Table 1 Statistics for Fig. 3.

24 Statistical analysis of contralateral suppression (%) for all (a, corresponding to gray dots in Fig. 3e-f) and selected (b, corresponding to black dots in Fig. 3e-f) glomeruli under different GECI combinations (as labeled by the schematics). This analysis includes sample sizes, descriptive statistics (bootstrap mean and s.e.m.), and hypothesis tests (including the test used and the resulting p-value). Postsynaptic enhancement of contralateral suppression in ring neurons is significant under both GECI combinations in all (a) and selected (b) glomeruli. TB and ring neuron responses are not significantly different when recorded with different indicators (c).

25 Supplementary Table2 Statistics for Fig. 4.

26 Statistical analysis of history dependence (%) for all (a, corresponding to gray dots in Fig. 4e-f) and selected (b, corresponding to black dots in Fig. 4e-f) glomeruli under different GECI combinations (as labeled by the schematics). This analysis includes sample sizes, descriptive statistics (bootstrap mean and s.e.m.), and hypothesis tests (including the test used and the resulting p-value). Postsynaptic enhancement of history dependence in ring neurons is significant under both GECI combinations in all (a) and selected (b) glomeruli. TB and ring neuron responses are significantly different when recorded with different indicators (c).

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28 Supplementary Table3 Statistics for Supplementary Fig. 6. Statistical analysis of the history dependence of X-Ipsi (a-b, X = Ipsi, or Contra, or Bi) and X-Contra (c-d), in all and selected glomeruli, under different GECI combinations (as labeled by the schematics). This analysis includes sample sizes, descriptive statistics (bootstrap mean and s.e.m.), and hypothesis tests (including the test used and the resulting p-value). Most of the tests are not significant in selected glomeruli, except for X-Ipsi in (TB) G _(Ring) R flies (p = 8.87x10-4 ). Compared to the high significance found for the X-Bi condition in both GECI combinations in all and selected glomeruli (Supplementary Table 2), this indicates that history dependence is strongest in the X-Bi stimulus condition.

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30 Supplementary Table4 Statistics for Supplementary Fig. 7. Statistical analysis of the history dependence of X-Ipsi-Bi (a-b, X = Ipsi, or Contra, or Bi), X-Contra-Bi (c-d), and X-Bi-Bi (e-f), in all and selected glomeruli, under different GECI combinations (as labeled by the schematics). This analysis includes sample sizes, descriptive statistics (bootstrap mean and s.e.m.), and hypothesis tests (including the test used used and the resulting p-value). None of them is significant in selected glomeruli. This indicates that history dependence is limited to the stimulus immediately preceding the current one.

31 Supplementary Table5 Data table for Fig. 5. (a) Parameter values for fits of biphasic temporal filters to 38 TB neurons (upper table) and 54 ring neurons (lower table). Mean ± s.e.m. was estimated from 1000 bootstrap samples. See Online Methods for parameter definitions. (b) Parameter values for 30 pairs of TB neurons (upper table) and ring neurons (lower table). Mean ± s.e.m. was estimated from 1000 bootstrap samples.

32 Supplementary Table6 Statistics for Supplementary Fig. 10. Statistical analysis of the ratio of summated F/F0 over the area of the excitatory field in the presence of a second stimulus (see Supplementary Fig. 10a right panel) versus that mapped with just a single stimulus (see Supplementary Fig. 10a left panel), under different GECI combinations (as labeled by the schematics). This analysis includes sample sizes, descriptive statistics (bootstrap mean and s.e.m.), and hypothesis tests (including the test used and the resulting p-value). Contralateral suppression is significantly stronger in ring neurons, regardless of the GECI combinations.

33 Supplementary Table7 Transgenic flies used in this study. List of the transgenic flies used in this study, including genotypes and corresponding experiments (see Online Methods for details), Figures and Supplementary Figures. Landing sites are listed after symbol.

34 Supplementary Table8 Nomenclature. Abbreviations for terminology used in the manuscript.

35 Neural signatures of dynamic stimulus selection in Drosophila Yi Sun, Aljoscha Nern, Romain Franconville, Hod Dana, Eric R. Schreiter, Loren L. Looger, Karel Svoboda, Douglas S. Kim, Ann M. Hermundstad and Vivek Jayaraman Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, VA, USA Supplementary Note 1

36 Contents Fitting biphasic temporal filter 2 Linear biphasic filter model Fitting procedure Assessing goodness of fit Comparison of TB and ring filters Circuit model 4 Responses of TB neurons Responses of ring neurons Parameter values Model predictions 6 Fitting biphasic temporal filter Linear biphasic filter model We used linear biphasic filters to model the response of individual TB and ring neurons. We denote model responses by R (to distinguish them from measured responses, denoted r). The model response R(t S) to a given stimulus sequence S(t) was taken to be a sum of ipsilateral and contralateral components: R(t S) = R Ipsi (t S) + R Contra (t S) (1) We constructed each component by convolving a temporal response function, F (t), with the stimulus. Because the spatial location of stimuli was fixed to one of two values (given by the position of ipsilateral/contralateral bar stimuli), we simplified the spatial dependence of the stimulus into a single ipsilateral component, and a single contralateral component. Both components were taken to be binary; we used S Ipsi (t) = 1 to denote the presence of a stimulus on the ipsilateral side at time t, and S Ipsi (t) = 0 to denote darkness. In this formulation, the temporal filter F (t) fully captures the strength of the response to the presence of a stimulus. The response to an ipsilateral stimulus (or analogously, a contralateral stimulus) was given by: R Ipsi (t) = 0 dτ F Ipsi (τ)s Ipsi (t τ) (2) The temporal response function F (t) was modeled using a biphasic kernel of the following form [1]: ) (1) (αt)5 (2) (αt)7 F (t) = exp ( αt) (c c 5! 7! Fitting procedure We used separate sets of parameters to describe ipsilateral ( p Ipsi = [α Ipsi, c (1) Ipsi, c(2) Ipsi ]) and contralateral ( p Contra = [α Contra, c (1) Contra, c(2) Contra ]) filters. The full set of parameters p All = [ p Ipsi, p Contra ] was fit to trialaveraged responses to randomly-ordered ipsilateral, contralateral, and bilateral bars (described in Unilateral/bilateral stationary bars with delay in Online Methods). We first selected trials in which a given stimulus X [Ipsi, Contra, Bi] was followed by a bilateral (Bi) stimulus. We then averaged over all trials of a given type (Ipsi-Bi, Contra-Bi, and Bi-Bi), and we subtracted an average baseline response (estimated as the offset of the trial-averaged response at time t = 0, averaged across stimulus conditions). The resulting responses were used for fitting. (3) 2

37 Fitting was performed using MATLAB s fmincon routine to minimize an error function E( p All ). We constructed this error function with two terms: E( p All ) = E 1 ( p All ) + E 2 ( p All ) (4) Both terms of the error function incorporate the dynamics of the response, integrated over a maximum time window of 4.2T (where T = 1 s is the period of stimulation). The first term assigns a cost to the mean-squared-error between the observed ( r) and predicted ( R) responses: E 1 ( p All ) = X [Ipsi,Contra,Bi] 4.2T 0 dt ( R(t SX Bi ) r(t S X Bi ) ) 2 We found that this term alone was not sufficient to capture the history dependence observed in TB and ring neurons. We therefore added a second term that assigned a cost to the difference between Ipsi-Bi, Contra-Bi, and Bi-Bi responses during and following the second (Bi) portion of the stimulus presentation: (5) E 2 ( p All ) = X [Ipsi,Contra] ( 4.2T 2T dt ( R(t SX Bi ) R(t S Bi Bi ) ) ) 2 4.2T dt ( r(t S X Bi ) r(t S Bi Bi )) 2T (6) This second term is sensitive to the relative ordering of responses, and we found empirically that the addition of this term improved the fit to data. Fitting parameters were initialized to p All,0 = [5, 60, 60, 5, 12, 12] and were bounded between p All,Min = [3, 600, 600, 3, 600, 600] and p All,Max = [8, 600, 600, 8, 600, 600]. All parameters are given in units of s 1. Assessing goodness of fit We restricted our analyses to the 70 pairs of TB and ring neurons that met the selection criteria outlined in Glomeruli selection in Online Methods. We further selected those neurons that had sufficiently low noise in their responses. We measured noise in the mean-subtracted, trial-averaged responses ˆr. We defined noise as the average variability between successive time points relative to the average variability of the entire response: noise = X [Ipsi,Contra,Bi] 4.2T 0 dt (ˆr(t + 1 S X Bi ) ˆr(t S X Bi )) 2 4.2T 0 dt (ˆr(t S X Bi )) 2 (7) We selected those glomeruli whose total noise was less than 2.25 (an average noise of 0.75 on each stimulus condition). This criterion selected 58 TB neurons and 64 ring neurons that were used for fitting. We fit biphasic filters to each of the 58 TB neurons and 64 ring neurons. In some cases, we found that the fitting reached the bounds that we imposed on the parameter space, thereby producing responses with unrealistically short or long timescales. We removed these fits from further analysis. The remaining neurons (38 of 54 TB neurons (66%), and 54 of 64 ring neurons (84%)) were used for the analyses shown in Fig. 5. Parameter values for these fits are shown in Supplementary Table 5a. To assess goodness of fit for each neuron, we computed the Pearson s correlation coefficient between R(t S) and r(t S). We computed this correlation across all three stimulus conditions described above (Ipsi- Bi, Contra-Bi, and Bi-Bi). The distributions of correlation coefficients are shown in Supplementary Fig. 9b. Comparison of TB and ring filters To directly compare the temporal filters of TB versus ring neurons, we selected those pairs of neurons for which the fitting procedure converged in both cases. This procedure selected 30 pairs of TB and ring neurons that were used in the analyses in Fig. 5, Fig. 6i-l, Supplementary Fig. 9c-h, and Supplementary Fig. 11. Parameter values for these selected pairs are shown in Supplementary Table 5b. 3

38 To assess differences between the filters fit to TB versus ring neurons, we measured the size of the contralateral filter relative to the ipsilateral filter. We defined the size of each filter to be the total integrated area: size(f ) = 0 dτ F (τ) (8) We then compared the change in filter size (from TB to ring neurons) to the change in contralateral suppression and history dependence. For each given quantity γ (filter size, contralateral suppression, and history dependence), change was measured as the difference in the given quantity from TB to ring neurons, relative to the sum: The results are shown in Supplementary Fig. 9g. Circuit model change(γ) = γ ring γ T B γ ring + γ T B (9) We constructed a circuit model consisting of bilaterally-symmetric populations of TB and ring neurons. All populations consisted of N neurons. In the following discussion, we index individual neurons in the left (L) and right (R) hemisphere by i and j, respectively. For concreteness, we discuss the response of the ith neuron in the left hemisphere, denoted (i, L); all other neurons are described by analogous equations. Specific parameter values are listed at the end of the section. Responses of TB neurons The time-dependent response of each TB neuron to a stimulus S was modeled as a sum of ipsilateral and contralateral components: R (i,l) T B (t S) = R(i,L) T B,Ipsi (t S) + A(i,L) T B R(i,L) T B,Contra (t S) (10) where A (i,l) T B is a coefficient that weights the strength of the contralateral component relative to the ipsilateral component. The ipsilateral component was described by a spatiotemporally-separable RF (with spatial component G(x, y) and temporal component F (t)), convolved with a spatiotemporal stimulus S(x, y, t): R (i,l) T B,Ipsi (t S) = 0 dτ F (i,l) T B (τ) dx dy G (i,l) T B (x, y)s(x, y, t τ) (11) We modeled a bilateral neuron that pooled the responses of TB neurons on the contralateral side, to inhibit TB neurons on the ipsilateral side. The contralateral component of the ith TB neuron in the left hemisphere could therefore be written as a sum over ipsilateral responses of all TB neurons in the right hemisphere: R (i,l) T B,Contra (t S) = N j=1 R (j,r) T B,Ipsi (t S) (12) The spatiotemporal stimulus S(x, y, t) was taken to be the set of stimulus frames described in Unilateral/bilateral stationary bars with delay in Online Methods. The temporal filter of each TB neuron, F (i,l) T B (t), was modeled using a biphasic filter (Equation 3) parameterized by p (i,l) T B. We additionally included a temporal offset, t(i,l) T B, to adjust for baseline response. The spatial filter of each TB neuron, G (i,l) T B (x, y), was modeled as a Gabor filter: G (i,l) T B (x, y) = C exp ( (x(i,l) ) 2 2πσ x σ y 2σx 2 (y(i,l) ) 2 ) ( ) 2σy 2 cos kx (i,l) φ, (13) 4

39 where x (i,l) and y (i,l) represent a set of transformed coordinates measured relative to the center of the Gabor filter: ( x (i,l) = ( y (i,l) = ) x x (i,l) µ x x (i,l) µ ( sin ) cos θ (i,l)) ( ) + y y µ (i,l) ( θ (i,l)) ( + y y µ (i,l) ( cos ) sin θ (i,l)) (14) ( θ (i,l)) (15) Here, x (i,l) µ and y (i,l) µ define the center of the Gabor filter, and θ (i,l) defines the angular orientation. Within each hemisphere, we required that the excitatory portion of each Gabor filter overlap with the position of the bar stimulus, consistent with the selection process described in Glomeruli selection in Online Methods. There are many spatial arrangements that satisfy this condition and would thereby produce similar neural responses when convolved with the bar stimulus. For simplicity, we chose an idealized spatial arrangement, in which the filters were distributed in a ring about the stimulus location (described in more detail below). This arrangement is broadly consistent with the spatial distribution shown in Fig. 6e. Similar results could be achieved with a wide range of different spatial distributions, provided that the filters adequately cover the stimulus location and the pooled response (carried by the bilateral neuron) is effectively rectified. To achieve such a spatial organization, we arranged the Gabor filters in a ring of radius d, centered about the location of the stimulus bar in the corresponding visual field. We chose d to be equal to the height of the stimulus bar. The filter centers were distributed evenly around the ring at angles β (i,l) = 2πi/N: x (i,l) µ = x (L) bar + d cos (β (i,l)) (16) y (i,l) µ = y (L) bar + d sin (β (i,l)) (17) The angular orientation θ (i,l) of each filter was chosen to be tangential to the ring (θ (i,l) = β (i,l) + π/2), such that excitatory fields were localized within the ring. Responses of ring neurons We assumed that TB neurons made parallel, one-to-one connections with ring neurons. The time-dependent response of each ring neuron to a stimulus S was modeled as a sum of ipsilateral and contralateral components: R (i,l) ring (t S) = R(i,L) ring,ipsi (t S) + A(i,L) ring R(i,L) ring,contra (t S) (18) where A (i,l) ring weights the strength of the contralateral component relative to the ipsilateral component. The ipsilateral component was described by a temporal filter F (i,l) ring (t), convolved with the response inherited from the upstream TB neuron: where B (i,l) ring R (i,l) ring,ipsi (t S) = B(i,L) ring 0 dτ F (i,l) ring (τ)r(i,l) T B (t τ S) (19) weights the strength of the input from the upstream TB neuron. As with TB neurons, we modeled the temporal filter of each ring neuron, F (i,l) (i,l) ring (t), with a biphasic filter parameterized by p ring and temporally offset by t (i,l) ring. We modeled a second bilateral neuron that pooled the responses of ring neurons on the contralateral side, to inhibit ring neurons on the ipsilateral side. In analogy to Equation 12, the contralateral component of the ring neuron response is given by: R (i,l) ring,contra (t S) = N j=1 R (j,r) ring,ipsi (t S) (20) 5

40 Parameter values In parametrizing the spatial Gabor filters of TB neurons, we varied both the orientation of each filter and the location of its center relative to the stimulus. Filters were otherwise identical, with parameter values chosen to be: C = 30, k = 0.8/w s, σ x = w s, σ y = 1.5σ x, φ = π/2. All distances were measured relative to the width w s of a stimulus frame. All TB neurons were assumed to have identical temporal filters. The set of filters was parameterized by p T B = [5 s 1, 100 s 1, 67 s 1 ] and t T B = 0.2 s. Weighting coefficients were taken to be identical across all TB neurons and were chosen to be A T B = All ring neurons were assumed to have identical temporal filters. The set of filters was parameterized by p ring = [4 s 1, 100 s 1, 70 s 1 ] and t ring = 1.3 s. Weighting coefficients were taken to be identical across all ring neurons and were chosen to be A ring = 0.02 and B ring = Results were robust to parameter choices; qualitatively similar results could be achieved with a range of different parameter combinations, consistent with the variability found in the fits of the biphasic filters to data. Predicting responses to new stimuli To explore the implications of the bilateral circuit organization shown in Fig. 6g, we simulated the responses of a pair of identical, bilateral neurons to untested stimulus conditions. We described both neurons (labeled left and right ) by the same pair of ipsilateral and contralateral filters, and we convolved these filters with binary stimulus sequences (generated as described in Fitting of biphasic temporal filter ). Results are shown in Fig. 6 and Supplementary Fig. 11. Filters in Fig 6j, the right panel of Fig. 6k, and Supplementary Fig. 11 were taken from the fit to the ring neuron exemplified in the lower left panel of Fig. 5b; filters in the left panel of Fig. 6k were taken from the fit to its upstream partner. We considered a stimulus condition in which a left and right bar were each presented for a fixed duration, but separated in time. We then asked whether the left or right neuron would respond more strongly when left and right bars were presented simultaneously after a delay. We varied both the inter-stimulus-interval (ISI; defined as the time between the onset of each asynchronous bar), and the delay (defined as the time between the offset of the most recently presented asynchronous bar and the onset of the simultaneous bars). Each bar was presented for a fixed duration of 0.9 s (chosen for illustrative purposes). To quantify the response of each neuron, we first found the time of peak response to the simultaneous bars. We then used this same time point to compute the response when the simultaneous bars had been preceded by asynchronous bars. Supplementary Fig. 11b shows the response of each of the two neurons as a function of ISI and delay. The difference between the responses of the two neurons (Supplementary Fig. 11d) delineates a regime where a stronger response was produced on the side where the bar had been presented less recently (Fig. 6k, Supplementary Fig. 11e). Differences in response decayed significantly for delays greater than 2-3 s; we therefore did not simulate delays beyond 4 s. Supplementary Fig. 11f, g compares responses produced by monophasic filters, which were generated by inverting the sign of the second term in the expression for F (t) (see Equation 3). For stimulus durations above a certain value ( 0.5 s), monophasic filters produced a single regime in which responses were consistently stronger for stimuli presented more recently. For brief stimuli, we observed the emergence of a regime (for short ISI and short delay) in which both monophasic and biphasic filters produced stronger responses for stimuli presented less recently. References [1] Adelson, E. H. Bergen, J. R., Spatiotemporal Energy Models for the Perception of Motion. J Opt Soc Am A 2, (1985). 6