The computations performed by local neural populations, such as a cortical layer, are typically inferred from anatomical connectivity and observations of neural activity. Here we describe a method—influence mapping—that uses single-neuron perturbations to directly measure how cortical neurons reshape sensory representations. In layer 2/3 of the primary visual cortex (V1), we use two-photon optogenetics to trigger action potentials in a targeted neuron and calcium imaging to measure the effect on spiking in neighbouring neurons in awake mice viewing visual stimuli. Excitatory neurons on average suppressed other neurons and had a centre–surround influence profile over anatomical space. A neuron’s influence on its neighbour depended on their similarity in activity. Notably, neurons suppressed activity in similarly tuned neurons more than in dissimilarly tuned neurons. In addition, photostimulation reduced the population response, specifically to the targeted neuron’s preferred stimulus, by around 2%. Therefore, V1 layer 2/3 performed feature competition, in which a like-suppresses-like motif reduces redundancy in population activity and may assist with inference of the features that underlie sensory input. We anticipate that influence mapping can be extended to investigate computations in other neural populations.
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We thank J. Drugowitsch, M. Andermann, R. Born, O. Mazor, L. Orefice, and members of the Harvey laboratory for discussions; H. Nyitrai, L. Bickford, and P. Kaeser for help testing soma localization of opsins; and the Research Instrumentation Core and machine shop at Harvard Medical School (supported by grant P30 EY012196). This work was supported by a Burroughs-Wellcome Fund Career Award at the Scientific Interface, the Searle Scholars Program, the New York Stem Cell Foundation, NIH grants from the NIMH BRAINS program (R01 MH107620) and NINDS (R01 NS089521, R01 NS108410), an Armenise-Harvard Foundation Junior Faculty Grant, and an NSF Graduate Research Fellowship.
Nature thanks Adam Packer, Ikuko Smith and the other anonymous reviewer(s) for their contribution to the peer review of this work.
Extended data figures and tables
a, Left, GCaMP6s and densely expressed, soma-localized C1V1 in the same neurons. Right, Channelrhodopsin-2 tagged with mCherry, from a different mouse. Note that non-localized channels are prominent in the neuropil background compared with soma-localized channels. b, Photostimulation protocol schematic. Top, beam position as a function of time; samples of mirror trajectory plotted at 100 kHz. Bottom, four repeats of an identical sweep were used to photostimulate neurons. c, Photostimulation triggered average images, for a neuron (left) and control (right) site from the experiment in Fig. 1b. Arrows mark the locations of both sites. d, Cumulative density plots of photostimulated neuron responses for different lateral displacements of target location from the neuron’s centre. Same data as in Fig. 1f, but note log scale of x-axis. The 15–25-μm offset caused responses that were not present at greater distances. e, Fraction of neurons that could be photostimulated as a function of the threshold for this classification. At a threshold of 5 s.d. above shuffle, more than 96% of neurons (n = 518) could be photostimulated. Shuffle distributions were computed by bootstrap resampling of activity from trials in which the neuron was not targeted. f, Fit quality of the GP tuning model versus photostimulation magnitude. Each dot is a single targeted neuron (n = 518 neurons). Spearman correlation, c = 0.084, P = 0.055. g, Mean gratings response of a neuron versus photostimulation magnitude. Each dot is a single targeted neuron (n = 518 neurons). Spearman correlation, c = 0.11, P = 0.009. h, A convolutional neural network (CNN) was trained with human-labelled data to predict whether CNMF sources were identified as a cell body or an alternative source, including distinct neural processes, excessively blurry or out-of-plane cells, or artefactual sources (see Methods). Note that many non-soma sources exhibited similar calcium transient signals as cell body sources. Because there is no objective ground-truth for this classification, held-out datasets were hand labelled, and compared to CNN labelling. One example dataset is shown here. The large majority of sources were labelled identically, but there were borderline cases for which labels differed; many cases appear to result from either human error in labelling, owing to finite human time and inconsistencies in making borderline judgments, or an overly conservative CNN criteria for cell classification. Neither of these errors are expected to affect the results presented here.
a, Log-odds excited metric. This metric uses a non-parametric bootstrap procedure to estimate the chance of observing average responses to photostimulation of a target from random sampling of a neuron’s activity (see Methods). An influence value of 0.1 corresponds to a log-odds of ~1.259, or a probability of being excited above shuffles of ~0.557. This metric adapts to the varyingly sparse, heavy-tailed, and skewed response distributions of each neuron’s activity, and so complements the ΔActivity measure. Key analyses from Figs. 2, 3 were repeated using this log-odds metric. b, Calculation of influence using the activity of a non-targeted neuron. Examples are shown for two pairs of neurons. Left, deconvolved activity of a non-targeted neuron on trials photostimulating a different neuron (red). Black lines indicate 5% and 95% bounds from resampling all trials. Data were smoothed with a 67-ms s.d. Gaussian filter for display only. Right, mean deconvolved activity for non-targeted neuron averaged over 0.367 s following photostimulation of target (red). Probabilities for obtaining a given deconvolved activity from the shuffle distribution of the non-targeted neuron are shown (black). c, Influence bias (average of signed influence values) as a function of distance between the targeted site and non-targeted neurons., plotted for both neuron and control photostimulation targets. Mean ± s.e.m. Same pairs as in Fig. 2g, n = 153,689 neuron site pairs, 90,705 control site pairs. d, Influence magnitude measured as the absolute value of influence values for all pairs following neuron or control site photostimulation. The non-zero value for control sites is expected because of noise due to random sampling of neural activity and potential off-target effects. Mean ± s.e.m. n = 153,689 neuron site pairs, 90,705 control site pairs. Neuron versus control: P = 2.31 × 10−5, Mann–Whitney U-test. e, Influence bias for a single target was the mean of influence values for the targeted neuron across all non-targeted neurons. Mean ± s.e.m. across targets. n = 518 neuron targets, 295 control targets. P = 7.40 × 10−4, Mann–Whitney U-test. f, Influence dispersion for a single target was the s.d. of influence values for the targeted neuron across all non-targeted neurons. Mean ± s.e.m. across targets. n = 518 neuron targets, 295 control targets. P = 2.3 × 10−6, Mann–Whitney U-test. g, Mean influence for all values for a single target was calculated. The s.d. of these values for neuron sites and control sites is plotted. The similar values indicate that it is unlikely that some neurons tended to have much larger positive or negative influence than expected based on control sites. n = 518 neuron sites, 295 control sites. P = 0.88, two-sample F-test. h, Running average of influence with noise correlation, for nearby (black) or distant (grey) pairs, with bin half-width of 20% (percentile bins). i, Running average of influence with signal correlation, with bin half-width of 15% (percentile bins). j, Running average of influence with difference in preferred orientation, with bin half-width of 12.5°. k, Coefficient estimates for linear regression of influence values. Plots show bootstrap distribution with median estimate as grey line, 25–75% interval as box, 1–99% interval as whiskers. Left, coefficients for piece-wise linear distance predictors from the model. Significance estimated by bootstrap: 25–100 μm, offset P = 0.0006, slope P < 1 × 10−4; 100–300 μm, offset P < 1 × 10−4, slope P < 1 × 10−4; > 300 μm, offset P = 0.68, slope P = 0.056. Right: coefficients for activity predictors from the same model. Signal correlation, P = 0.0002; signal–distance interaction, P = 0.96; noise correlation P = 0.0010; noise–distance interaction, P = 0.0024; signal–noise interaction P = 0.14; n = 64,485 pairs. l, Coefficient estimates from separate models in which the specified tuning correlation replaced signal correlation in the influence regression model of k, same bootstrap and boxplot conventions. Each model used only pairs in which targeted and non-targeted neurons exhibited tuning. Direction, P = 0.21, n = 36,565 pairs; orientation, P = 0.0026, n = 36,565; spatial frequency, P = 0.30, n = 47,810; temporal frequency, P = 0.011, n = 26,526; running speed, P = 0.11, n = 46,634.
a, Comparison of influence bias (mean ΔActivity) between neuron and control site photostimulation, after exclusion of pairs with individually significant influence values. The significance of each individual pair’s influence was determined with a non-parametric bootstrap (Extended Data Fig. 2, Methods), and a P value threshold for significance was chosen to restrict the fraction of false positives to less than 5% or 25% (pFDR, Methods). For 0%, n = 153,689 neuron and 90,705 control pairs. 225 neuron and 26 control pairs were excluded for 5% pFDR, 638 neuron and 50 control pairs were excluded for 25% pFDR. Influence following neuron photostimulation was significantly negative for all thresholds; Mann–Whitney U-test, 0% P = 8.90 × 10−16, 5% P = 7.24 × 10−15, 25% P = 5.72 × 10−12. b, As in a but for influence dispersion (s.d. of ΔActivity). Influence dispersion was greater following neuron than control photostimulation for all thresholds; two-sample F-test, 0% P = 6.84 × 10−39, 5% P = 6.04 × 10−20, 25% P = 2.63 × 10−14. c, As in a, b, but for influence bias as a function of distance. A quantitatively similar centre–surround pattern was observed for all thresholds. d, Average influence values for a non-targeted neuron (over all photostimulated neurons) versus that neuron’s average deconvolved activity during non-photostimulated trials in influence mapping blocks. Each dot is a single non-targeted neuron. n = 8,552 neurons. Spearman correlation, c = −0.00003, P = 0.99. e, As in d, but for mean trace correlation during tuning measurement blocks. c = 0.0068, P = 0.53. f, As in d, but for trace correlation strength. c = 0.0099, P = 0.36. g, As in d, but for gratings response. c = 0.0092, P = 0.38. h, As in d, but for GP tuning model fit quality. c = 0.011, P = 0.29. i, Mean influence for all values for a single-target was calculated. The s.d. of these values for neuron sites and control sites is plotted. The similar values indicate that it is unlikely that some neurons tended to have much larger positive or negative influence than expected based on random sampling of the group mean (which was lower for neuron than control sites, see Fig. 2). Data shown as mean ± s.e.m. across targets. n = 518 neuron targets, 295 control targets, P = 0.72, two-sample F-test. j, Running average of influence with pairwise distance using bin half-width of 30 μm. Shading corresponds to mean ± s.e.m. calculated by bootstrap. Data are divided into influence from photostimulation sites with stronger versus weaker direct photostimulation responses in the targeted neuron, using a median split of photostimulation significance, as well as for control site photostimulation. Mean photostimulation response was 0.36 ΔF/F and 0.85 ΔF/F for weak and strong groups, respectively. Note that the weak distance-dependence observed for control site photostimulation is consistent with greatly reduced, but non-zero, neural excitation when targeting control sites. This may result from a number of factors including suboptimal resolution and brain movement in vivo, and indicates the necessity of control site photostimulation.
a, GP model fit quality (Pearson correlation with held-out data). Each neuron plotted at its relative position in an individual experiment’s FOV. Neurons at all positions were similarly well fit. b, 2D histogram of GP model fit quality (‘test accuracy’) and prediction quality on not-held-out data (‘train accuracy’). Major overfitting was not observed. c, Depth of modulation (see Methods) for each individual tuning dimension, for all neurons that passed model fit criteria. Dimensions exhibited qualitatively distinct distributions. Left, many neurons had almost no drift direction modulation, with many others exhibiting extremely pronounced modulation (>10). Right, almost all neurons exhibited moderate modulation (~5) by running speed. d, z-scored tuning curves for each individual tuning dimension, for all neurons that passed model fit criteria and had significant modulation (>2) for the plotted dimension. Tuning was qualitatively different for different dimensions. Spatial frequency tuning was distributed evenly over our stimulus set and generally bandpass. Running speed tuning was distributed more tightly into a few neurons that preferred stillness, versus many that broadly preferred running. e, Significance of tuning for each dimension as determined by GP regression.
a, Model fit qualities for an example session, assessed on left-out data. Each dot is a single neuron, n = 358 neurons. GP model fit qualities were higher than those from the parametric tuning model, mean difference of 0.11, P = 5.02 × 10−60, Mann–Whitney U-test. b, Estimated preferred orientations of neurons were similar between models. Pearson correlation c = 0.88, calculated using only neurons significantly tuned to orientation. c, Estimated spatial frequency preferences of neurons were similar between models; c = 0.95 calculated using only neurons significantly tuned to spatial frequency. d, Signal correlations calculated from the two models were similar; c = 0.80. e, Noise correlations calculated from the two models were similar; c = 0.94.
a, Probability density functions estimated by kernel smoothing for distance (left) and signal correlation (right), for all data used in influence regression (n = 64,485 pairs). Separate densities were estimated for pairs that exhibited varying trace correlation (left) or noise correlation (right). Pairs with high trace correlations occurred at all distances, but more often for nearby neurons. Similarly, signal correlations for pairs with high versus low noise correlations were distinct but overlapping distributions. This highlights the importance and feasibility of using influence regression to disambiguate the contributions of distance, signal, and noise correlation. b, 2D probability density functions for pairs of similarity metrics, estimated using kernel smoothing, for all data used in influence regression. Spearman correlation values for each pair of similarity metrics are overlaid. All correlations were significant with P < 1 × 10−60, n = 64,845 pairs. c, Running average of influence data (black) and predictions (coloured lines) from influence regression model, using a bin half-width of 15% (percentile bins). Black lines and shading show mean ± s.e.m. of data by bootstrap. Signal correlation is plotted against mean influence, for the subset of pairs more than 300 µm apart. Model predictions are computed using a full influence regression model (blue), or using subsets of coefficients from the same model (distance, red; signal, green; noise, purple). The full model prediction is equal to the sum of the three components. The running average analysis here accurately reflects the signal component of the influence regression model, plus a tonic offset from the distance component. d, Running average as in c, but for noise correlation and pairs at all distances. Note that signal and noise interaction coefficients with distance are included in signal and noise components, respectively. The running average analysis here confusingly indicates a flat slope of noise correlation and influence. Our model predicts this relationship because pairs with higher noise correlations were located at shorter distances, and also had increased signal correlations, and these effects together cancelled out increases in influence due to noise correlation. e, Running average as in c, but for model-free correlations of single-trial responses, and for pairs separated by less than 125 µm. At short distances, the positive effect of noise correlations dominated the negative effect of signal correlations. f, Running average as in c, but for model-free correlations of single-trial responses, and for pairs separated by more than 125 µm. At long distances, the negative effect of signal correlations dominated the positive effect of noise correlations.
Extended Data Fig. 7 Results of influence regression are robust to potential artefacts from data processing and off-target photostimulation.
a, Analysis of influence effects directly in ΔF/F traces. ΔFluorescence was calculated as for ΔActivity, but using ΔF/F traces rather than trial-averaged deconvolved activity. ΔFluorescence was significantly negative in the 1 s following neuron photostimulation relative to control; n = 153,689 neuron site pairs and 90,705 control site pairs. Neuron versus control site: P = 6.79 × 10−15, Mann–Whitney U-test. Data in all plots shown as mean ± s.e.m. calculated by bootstrap. b, ΔFluorescence in non-targeted neurons following photostimulation of neurons at varying distances. n = 1,822 near pairs, 35,541 mid-range pairs, 35,882 far pairs. Near versus mid-range: P = 7.62 × 10−19; near versus far: P = 5.0 × 10−6; mid-range versus far: P = 1.21 × 10−47; Mann–Whitney U-test. c, As in b, but without neuropil subtraction, or any source de-mixing from CNMF; traces were extracted by projecting raw movies onto neuron ROIs. n = 1,822 near pairs, 35,541 mid-range pairs, 35,882 far pairs. Near versus mid-range: P = 5.96 × 10−28; near versus far: P = 5.21 × 10−38; mid-range versus far: P = 4.15 × 10−13; Mann–Whitney U-test. This indicates that distance-dependent influence effects were not an artefact of source extraction algorithms. d, The influence regression from Fig. 3d was applied to ΔFluorescence traces. This regression resulted in beta coefficients for traces at each time frame relative to photostimulation onset, which are plotted over time. Coefficients for slopes for the three distance bins are plotted. The same size and ordering of effects is apparent as when using deconvolved data and the ΔActivity metric (compare to Fig. 3). Mean ± s.e.m. calculated using 10,000 coefficient estimates by bootstrap resampling. All coefficients were significantly different from zero, averaged over 0–1,000 ms from photostimulation onset, with P < 1 × 10−4 by bootstrap. e, As in a but for signal and noise correlation coefficients. Averaged over 0–1,000 ms from photostimulation onset, signal correlation coefficients were significantly less than zero with P = 0.0008 and noise correlation was greater than zero with P = 0.0154, estimated by bootstrap. f, Similar to regression analysis in Fig. 3d, e, but as a test of potential off-target effects. Instead of using only the photostimulated neuron’s activity and tuning properties to calculate correlations with the non-targeted neuron, properties of multiple nearby neurons were used, to test whether off-target photostimulation of nearby cells could underlie the observed effects (see Methods). This is equivalent to influence regression using identical influence values and distance predictors as in Fig. 3e, but changing all activity predictors. Only distance effects were apparent, as expected, whereas activity-related effects were absent. This suggests that the properties of the individually targeted neuron were responsible for the influence relationships we observed. Plots show bootstrap distribution with median estimate as grey line, 25–75% interval as box, 1–99% interval as whiskers. Left, coefficients for piece-wise linear distance predictors from the model. Significance estimated by bootstrap: 25–100 μm, offset P = 0.0982, slope P < 1 × 10−4; 100–300 μm, offset P < 1 × 10−4, slope P < 1 × 10−4; >300 μm, offset P = 0.0018, slope P = 0.0316. Right, coefficients for activity predictors from the same model. Signal correlation, P = 0.9370; signal × distance interaction, P = 0.4072; noise correlation P = 0.8772; noise × distance interaction, P = 0.5138; signal × noise interaction P = 0.5260; n = 64,485 pairs.
a, The orientation information content of all neurons during influence mapping blocks, calculated using the same binning approach used for population decoding. Information is colour coded, and plotted as a function of a neuron’s directional modulation and preferred spatial frequencies estimated during tuning measurement blocks. This demonstrates that tuning estimated in tuning and influence measurement blocks were concurrent (gratings during influence mapping were always 0.04 cycles per degree), but that responses to full-field, low-contrast gratings in influence measurement blocks were sparse. b, Schema indicating the orthogonalization procedure used for population analysis. In brief, because average responses to each grating orientation were not entirely orthogonal, and because photostimulation evoked highly significant changes in response gain in our dataset, we wished to isolate potential changes along alternative population activity dimensions independent of gain changes. To accomplish this, we orthogonalized projections along non-gain dimensions relative to the gain projection observed on individual trials. This ensured that changes in response gain could not trivially produce changes along non-gain population dimensions.
a, Diagram of rate-network model, in which each neuron i receives feedforward input ui driven by the orientation of a visual stimulus and has functional connection wi,j with neuron j. Neurons were modelled as rectified-linear units. b, Influence regression coefficients for the rate-network model. Signal and noise correlations were estimated from noisy simulated trials and regressed against functional connections (W), similar to Fig. 3d, e. To be consistent with experimental data, random trial-to-trial fluctuations in gain as well as single-neuron-specific noise were added to simulations (see Methods), such that all networks exhibited a positive correlation between signal and noise correlations. However results were similar without simulated gain fluctuations. c, Model neuron responses following presentation of a 90° stimulus. Feedforward inputs were identical for all networks. Colours are the same as in a. Dashed line indicates orientation of the visual stimulus. d, Model neuron responses following presentation of a linear sum of 60° and 120° stimuli. Grey lines are the average response of each network to the two stimuli presented individually. Note that neurons that preferred 70° and 110° receive the maximum feedforward input. e, Model neuron responses to a visual stimulus (90°) with simulated photostimulation of a neuron. Responses (in non-stimulated neurons) are shown when the ‘photostimulated’ neuron had preference for similar (top, 80°) or dissimilar (bottom, 10°) orientations relative to the visual stimulus, colour coded by network type. Responses are normalized to activity without simulated photostimulation. f, Model network responses to visual stimuli with simultaneous ‘photostimulation’, as a function of difference in orientation between visual stimulus and ‘photostimulated’ neuron’s preference. The response gain dimension was calculated as the normalized response to the visual stimulus in the absence of ‘photostimulation’. g, Analytical solution for the linear aspect of network dynamics (see Methods for derivation). This indicates that the network performs a comparison between inputs y and an internal estimate ynet, which when s is negative corresponds to dynamical explaining away of network inputs.
Extended Data Fig. 10 Interaction of trace correlation with influence regression model coefficients.
a, Further characterization of the effects of trace correlation on feature competition versus amplification (compare to Fig. 5d). Influence regression (as in Fig. 3d) was performed after including an interaction of each predictor with the magnitude of trace correlation. Coefficient estimates for each interaction plotted with uncertainty from bootstrap: grey line, median; box, 25–75% interval; whiskers, 1–99% interval. This analysis used no manually specified division between ‘strong’ and ‘weak’ correlations, and considered whether trace correlation changed the relationship between influence and any predictors in the influence regression. Signal correlation exhibited a highly significant positive interaction, indicating a transition from competition (negative slope) to amplification (positive slope) as the magnitude of trace correlation increased; n = 64,845 pairs, P = 0.0002 (bootstrap). Interactions with all other activity predictors were not significant (P > 0.444). Interactions with the slopes of distance predictors were not significant (P > 0.2716). There were weak interactions with offsets for near (P = 0.0486) and mid (P = 0.0076) distance bins, but not for far (P = 0.4738). These results indicate that the magnitude of trace correlation had a substantial effect on the relationship between signal correlation and influence.
Photostimulation-triggered average movies for three neuron sites. Three movies are shown sequentially, each showing 1-second before through 3-seconds after photostimulation of a neuron. On left is averaged fluorescence data, on right is dF/F. Each neuron responds when targeted, but not to stimulation of a nearby neuron
Photostimulation-triggered average movie for one neuron target from the experiment shown in Fig. 1b. The entire FOV is shown, on left as averaged fluorescence data, on right as dF/F relative to pre-stimulation data
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