Neuronal computations underlying higher brain functions depend on synaptic interactions among specific neurons. A mechanistic understanding of such computations requires wiring diagrams of neuronal networks. In this study, we examined how the olfactory bulb (OB) performs ‘whitening’, a fundamental computation that decorrelates activity patterns and supports their classification by memory networks. We measured odor-evoked activity in the OB of a zebrafish larva and subsequently reconstructed the complete wiring diagram by volumetric electron microscopy. The resulting functional connectome revealed an over-representation of multisynaptic connectivity motifs that mediate reciprocal inhibition between neurons with similar tuning. This connectivity suppressed redundant responses and was necessary and sufficient to reproduce whitening in simulations. Whitening of odor representations is therefore mediated by higher-order structure in the wiring diagram that is adapted to natural input patterns.
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Image data are available under https://doi.org/10.7281/T1MS3QN7 and can be accessed through the NeuroData web services (http://neurodata.io/wanner16)25. They can also be viewed interactively using PyKNOSSOS (https://github.com/adwanner/PyKNOSSOS)25. The skeleton reconstructions and soma outlines of the 1,022 neurons can be downloaded from https://doi.org/10.5281/zenodo.58985 as previously described25. All other data that support the findings of this study are available from the corresponding author upon reasonable request.
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We thank B. Hu, A. Lüthi, P. Rupprecht and N. Temiz for comments on the manuscript and the Friedrich group for valuable discussions. C. Genoud made outstanding contributions to the acquisition of electron microscopy data. We thank J. Li, D. Robson, F. Engert and A. Schier (Harvard University) for elavl3:GCaMP5 fish. This work was supported by the Novartis Research Foundation, the Human Frontiers Science Program (rgp0015/2010 to R.W.F.) and the Swiss National Science Foundation (CRSII3_130470/1, 310030B_152833 to R.W.F.).
A.A.W. is the founder and owner of ariadne-service gmbh (https://ariadne.ai).
Peer review information Nature Neuroscience thanks D. F. Albeanu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
a, Distribution of the fraction of synaptic inputs onto INs that originated from sensory axons. The average fraction of synaptic inputs onto INs that came from sensory neurons was 5.9 ± 4.6% (mean ± s.d.). This is an upper-bound estimate because structures in EM images were classified as sensory synapses even when they were small and when synaptic features such as postsynaptic densities and vesicle clusters were ambiguous. No obvious synaptic connections were observed from OB neurons onto axon terminals of sensory neurons. b, Displacement of regions of interest (ROIs) during manual proofreading. ROIs representing somata were mapped from the EM dataset to optical image planes in each trial by an affine transformation that was determined by an iterative landmark-based procedure (Methods). Subsequently, the position of each ROI was adjusted manually on the optical image (n = 7,280 ROIs; six image planes with 11 trials each). The mean displacement (± s.d.) during manual adjustment (proofreading) was small (593 ± 833 nm), implying that automated mapping was highly reliable.
a, Raw calcium signals (ΔF/F) evoked by eight odors in neurons that were present in all trials and included in simulations (208 MCs and 68 INs; average of two trials). Gray bars indicate odor stimulation. b, Raw calcium signals (ΔF/F) evoked by eight odors and E3 medium in neurons that were present in all trials and included in simulations (176 MCs and 50 INs; average of two trials; sorted by response to E3 medium). c, Correlation matrices of MC activity patterns at t1 and t2 after excluding 10 MCs with highest responses to E3 medium (all MCs in b except for the first 10; n = 166 MCs in total). Calcium signals were deconvolved to estimate firing rate changes as in Fig. 2. As observed in the full dataset (Fig. 2e), MC activity patterns evoked by similar odors were correlated at t1 and became decorrelated at t2. The main results were therefore not affected by possible responses to E3 medium.
a, Pearson correlation matrices showing similarities of activity patterns across odors and trials at t1 and t2 (average over 100 repetitions). In each repetition, two activity patterns (trials) were generated for each odor by randomly assigning the first or second response of each neuron to each trial. Note the high correlations between activity patterns representing the same odor in different trials, particularly at t2. b, Success rates of odor identification by template matching. For each odor, the vector representing the odor in one trial (test vector) was correlated to vectors representing all odors in the other trial (templates) and assigned to the odor represented by the template with the highest correlation. Dots show the mean fraction of correct identifications, error bars show s.d., boxes show median, 25th percentile and 75th percentile (n = 100 repetitions each). Dashed gray line shows chance level. Top: identification based on patterns averaged over time windows t1 and t2 (see text). Bottom: identification based on single frames within t1 and t2. Left: tests and templates included all MCs. Center, right: the 10 or 100 MCs with the highest contribution to the initial pattern correlation (highest ri,t1) were omitted for each odor pair. Omitting the 10 MCs with the highest ri,t1 (cohorts) had almost no consequence on odor identification, confirming that information about precise odor identity is conveyed predominantly by other MCs.
a, Mean Pearson correlation between IN activity patterns (blue) and the corresponding MC activity patterns (black) evoked by different bile acid inputs in simulations (n = 6 bile acid pairs each). Correlations between IN activity patterns remain higher than correlations between MC activity patterns. b, Mean Pearson correlation between simulated MC activity patterns evoked by inputs representing different odors (blue; all bile acid pairs) and between activity patterns evoked by inputs representing the same odors in trials with input noise (purple; all bile acids). Shading shows s.d.. Noise was modeled based on conservative estimates of the number and firing rates of olfactory sensory neurons in zebrafish larvae (Methods). Three noisy trials were simulated for each odor, resulting in n = 12 correlations between same-odor trials and n = 54 correlations between different-odor trials. Patterns evoked by different inputs were decorrelated whereas noisy versions of the same inputs were not decorrelated.
a, Schematic: simple algebraic approach to approximate transformations of MC activity patterns by feedback inhibition. Input activity patterns (MC activity at t1) were multiplied by the feed-forward connectivity matrix WMC→IN, normalized and thresholded. Normalization and thresholding are basic operations performed by the neuronal circuits of the OB10 and by individual neurons, respectively. The resulting IN activity patterns were multiplied with the feedback connectivity matrix WMC←IN, resulting in odor-specific patterns of feedback inhibition onto MCs. Feedback inhibition was either subtracted from the MC activation patterns (subtractive inhibition), or MC activation patterns were divided by the feedback inhibition patterns (divisive inhibition), followed by thresholding. Scaling factors and thresholds were adjusted so that effects on the mean activity were small. b, Mean activity, Pearson pattern correlation and s.d. of pattern variance at t2 after algebraic transformations of input patterns as described in a (“Experiment”: experimental results). Horizontal black lines show mean experimental values at t1; activity and s.d. of pattern variance is normalized to the experimental value at t1. Dots show means, error bars show s.d., filled bars show difference to corresponding values at t1. Box plots show median, 25% percentile, and 75th percentile. For experimental results and simulations using the reconstructed wiring diagram, variability was measured across odor pairs (correlation; bile acids only; n = 6) or individual odors (s.d. of variance; n = 8). Significance tests compare values at t2 to experimental values at t1 (correlation: two-sided Wilcoxon rank-sum test; s.d. of variance: F-test with df1 = df2 = 7 degrees of freedom). For results obtained with randomized wiring diagrams (W random), variability was measured across n = 50 permutations of the wiring diagram. Significance tests compare repetitions to the mean value observed experimentally at t1 (two-sided Wilcoxon rank-sum test). *, p < 0.05; **, p < 0.01; ***, p < 0.001; n.s., not significant. In “targeted suppression”, the activity of the 10 MCs that contributed most strongly to the pattern correlation at t1 for each odor pair (“functional cohort”) was set to the population mean. No other manipulations or algebraic operations were performed. P-values: activity: 0.57, 0.57, 0.25, 0.23 0.17; Pearson correlation: 0.03, 0.04, 0.98, 0.04, 0.008; s.d. of variance: 0.003, 10−23, 10−26, 10−21, 10−16.
Z-scores quantify the over-representation of motifs among MC pairs with signal correlations greater than a threshold between -0.8 and 0.8. For each motif, color-coded bars show z-scores for different signal correlation thresholds. Z-scores were determined by comparison against 10,000 shufflings of the tuning correlation matrix as in Fig. 4d.
a, IN-MC-IN triplets included in the analysis. Connections between INs were analyzed separately (see below and main text) to facilitate the comparison to MC-IN-MC triplets (Fig. 4). b, Left: number of IN-MC-IN motifs found in the wiring diagram (considering only INs with activity measurements and at least one MC→IN and MC←IN connection; n = 66). Right: z-score quantifying over- or under-representation of motifs as compared to 10,000 independent randomizations. c, Top: disynaptic connections between responsive INs as a function of tuning similarity (Pearson correlation), normalized to the mean (n = 992 neuron pairs; neurons were included only when their activity exceeded a threshold; see Methods; number of neuron pairs per bin: 192, 218, 178, 228, 176). Dots and error bars show mean ± s.e.m. when tuning curves were determined using all eight odor stimuli. Box plots show median, 25th percentile and 75th percentile across results when tuning curves were determined by all possible combinations of four odors. Bottom: result of the same analysis including only reciprocal connections (motif 4; n = 992 neuron pairs). d, Left: Pearson correlations between the mean tuning curves of MC inputs to INs (n = 57 INs). INs were ordered by optimal leaf ordering for hierarchical clustering. Right: Pearson correlations between the mean tuning curves of the MC targets of INs (same ordering of INs). INs were included in the analysis when their activity was measured, when they received input from at least 1 MC and 1 IN for which activity measurements were available, and when they targeted at least 1 MC and 1 IN for which activity measurements were available. e, X-axis: Pearson correlation between the tuning curves of each IN and the mean tuning curves of MC inputs to the same IN (rIN-inputs). Y-axis: Pearson correlation between the tuning curves of each IN and the mean tuning curves of its MC targets (rIN-targets). r, correlation coefficient; ***, p = 10-8 (two-tailed t-test, n = 63 INs). INs were included in the analysis when their activity was measured, when they received input from at least 1 MC for which activity measurements were available, and when they targeted at least 1 MC for which activity measurements were available. f, Black: number of maximal IN cliques in the wiring diagram as a function of clique size. Gray curve shows expectation based on randomized wiring diagrams (10,000 permutations). A maximal clique is a complete set of INs that are all reciprocally connected to each other. Top and bottom plots show distributions for cliques without a MC and cliques with one reciprocally connected MC, respectively. Maximal cliques with more than one MC do not exist because the wiring diagram contained no connections between MCs. g, Left: Mean Pearson correlation of tuning curves between neurons in maximal cliques as a function of clique size (n = 414; number per bin: 3, 19, 22, 44, 96, 99, 75, 29, 24, 3). Dots and error bars show mean ± s.e.m.; box plots show median, 25th percentile and 75th percentile. Gray curve shows mean after shuffling of tuning correlation matrix (right). Right: same analysis after shuffling of tuning correlation matrix (1,000 repetitions; n = 414,000; number per bin: 3,000, 19,000, 22,000, 44,000, 96,000, 99,000, 75,000, 29,000, 24,000, 3,000). Black curve shows mean of original data (left).
a, Schematic: effect of contrast enhancement on the correlation between displaced Gaussian patterns. The X-axis represents neurons while the Y-axis represents their activity. Blue and orange bars represent overlapping activity patterns evoked by two different stimuli. The similarity of activity patterns is quantified by the Pearson correlation coefficient, r. Note that many neurons respond to both stimuli but neurons showing maximal responses differ between stimuli. Hence, strongly active neurons convey stimulus-specific information. Contrast enhancement therefore decorrelates patterns because it emphasizes strongly active neurons and suppresses weakly active neurons. b, Effect of contrast enhancement on the Pearson correlation between activity pattern that overlap in strongly active neurons. Activity patterns have the same Pearson correlation as in a but their shape is slightly different: maximal responses to the two stimuli occur in the same neuron, and tails of moderately or weakly active neurons extend in opposite directions. Hence, stimulus-specific information is conveyed primarily by moderately or weakly active neurons while strong responses are non-specific. As a consequence, contrast enhancement fails to decorrelate these patterns. c, Patterns that overlap in strongly active neurons (same as in b; r: Pearson correlation) are decorrelated by selective inhibition of strongly active neurons, which results in contrast reduction. Decorrelation occurs because the relative contribution of moderately or weakly active neurons is enhanced as the activity of strongly active neurons is suppressed. Selective inhibition of strongly active units is generated by reciprocal inhibition that is stronger or denser within cohorts of co-tuned neurons. Inhibitory feedback gain is therefore higher than the average inhibitory feedback gain within a co-tuned cohort when the stimulus feature that activates the cohort is present (feature suppression).
a, Composition of functional MC cohorts. For each pair of bile acid odors (X-axis), a functional MC cohort was defined as the 10 MCs that contribute most to the correlation between odor-evoked activity patterns at t1 (highest ri,t1). Gray pixels denote membership of each MC (Y-axis) in each cohort. Cohorts for different odor pairs overlapped substantially. Consistent with this observation, the mean Pearson correlation between tuning curves of MCs at t1 was significantly higher within cohorts (r = 0.56 ± 0.40; mean ± s.d.) than across all MCs (r = 0.01 ± 0.38; p = 10-84; two-sided Wilcoxon rank-sum test). Furthermore, we analyzed the mean tuning correlation at t1 among the 16 MCs that were not part of cohorts themselves but provided the highest number of disynaptic input connections to neurons inside cohorts (r = 0.23 ± 0.52; mean ± s.d.). This tuning correlation was lower than the tuning correlation within the cohort but still significantly higher than the mean tuning correlation across all MCs (p = 10-40; two-sided Wilcoxon rank-sum test). Similarly, the mean tuning correlation at t1 among the 16 MCs that received the most disynaptic output connections from neurons inside cohorts (r = 0.17 ± 0.53; mean ± s.d.) was lower than the tuning correlation within the cohort but significantly higher than the mean tuning correlation across all MCs (p = 10-17; two-sided Wilcoxon rank-sum test). b, Black: frequency of each MC-IN-MC triplet motif in MC cohorts (n = 6 cohorts for each motif). Dots show means, error bars show s.d., box plots show median, 25% percentile, and 75th percentile. Gray: frequency of MC-IN-MC triplet motifs among randomly selected MC subsets of the same size (n = 10 MCs; n = 600 repetitions for each motif). Frequency of occurrence is normalized to the mean frequency in random subsets for each motif. **, p < 0.01; ***, p < 0.001 (two-sided Wilcoxon rank-sum test). P-values: 0.002, 10-5, 0.0008, 0.0001. We also observed that the 10 INs receiving the largest number of MC inputs from each cohort were 1.7 times more likely to make direct connections than random subsets of INs (p = 0.007; two-sided Wilcoxon rank-sum test). c, Blue: mean activity of the 10 MCs in the functional cohort defined by responses to TCA and GCDCA (example odors in Fig. 5b). Green: mean activity of the 10 INs that were included in activity measurements and provided the highest synaptic input to the MC cohort. As expected, IN activity increased while MC activity decreased during odor application.
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Wanner, A.A., Friedrich, R.W. Whitening of odor representations by the wiring diagram of the olfactory bulb. Nat Neurosci (2020). https://doi.org/10.1038/s41593-019-0576-z