Synaptic density comparisons across species.

A, Schematic of the quantities used throughout this study. Namely, dendritic length (L; black), volume (V ; dashed blue ellipse), and number of synapses (n; green). Inset zooming in dendrite cable in red highlights that the dendritic synaptic density is constant regardless of cell size or complexity. Axon is depicted in gray and soma as the circular gray structure connecting dendrites and axons. B, Log–log plot showing the relationship between total dendritic length and the number of synapses per neuron across four species: Drosophila larva (blue), adult Drosophila (orange), zebrafish (yellow), and mouse (purple). Each dot represents a single reconstructed neuron (NTotal = 2486, ND.Larva = 233, ND.Adult = 60, NZebrafish = 709, NMouse = 1484; see Table 1, 2 and Methods 3.5). A linear fit (dashed line) across all data reveals a strong scaling relationship (r2 = 0.96; slope = 1.07), closely matching the unity line (; slope = 1). C, Swarm plot of synaptic densities across species. Each data point is one neuron, with the colour corresponding to species. Horizontal black line indicates mean values per species; error bars, standard deviation. Red diamond shape indicates mean values of corresponding species from [44]. Pair-wise statistical analysis using permutation tests (10000 permutations), “n.s.” non significant.

Details of species, brain regions and cell-types used in this study originated from electronic (EM) and light (LM) microscopy.

The table provides a comprehensive overview of the cell-types investigated across various species, including Drosophila (both larval and adult stages), zebrafish, mouse, rat and human. For each cell-type, the corresponding species, sample size, sex, and age are listed. Sex is Female (F), Male (M). Age is hours after egg laying (AEL), hours after pupating, post embryonic days (Pdays), or human subjects age years (y). Star sign denotes datasets from which estimations of synaptic density were retrieved, but anatomical data were not available. References for the data sources are provided.

Quantitative summary of synaptic properties across different species.

This table provides a quantitative summary of synaptic properties across various species, detailing synaptic density, inter-synaptic distance, and spatial location. The values are presented as mean ± standard deviation (SD). Spatial location, indicating variability in synapse positioning. The location ranges between [0 − 1], with value 0 meaning the most proximal, 0.5 is uniformly distributed at random, and 1 the most distal (see Methods 3.5). Star sign denotes corrected values (uncorrected zebrafish synaptic density ; uncorrected zebrafish inter-synaptic distance ; see Methods 3.5)

Synaptic density comparisons across Drosophila mutants.

A, Schematic of EM volumes used in the comparative dendritic synaptic density analysis. Left scheme, wild-type: depicts the larval Drosophila brain and ventral nerve cord (grey) with a central dashed line indicating the body’s axis of left-right symmetry. The mechanosensory axon is shown in red, connecting to dendritic trees (black). The inset highlights synaptic density. Central scheme, FraRobo mutant: similar to WT scheme, but with the mechanosensory axon (red) shifted from its typical location. Right scheme, TNT mutant: illustrates synaptic transmission supression in the mechanosensory axons B, Bar plot of synaptic densities across wild-type D. larvae mechanosensory neurons and mutants. On each plot, coloured bars corresponds to mean values, respectively per EM volume. Error bars indicate standard deviation (NWT = 14, NTNT = 12, NFraRobo = 14; see Methods 3.5). Pair-wise statistical analysis using permutation tests (10000 permutations), ∗ ∗ ∗ indicates p < 0.001.

Quantitative summary of number of neurons per dataset used in this study.

This table provides a detailed overview of the datasets used in the study, specifying the number of neurons used to compute synapse density, scaling law based on wiring minimisation, synapse location, synapse size, radius, model simulations, and the total count of neurons per dataset. † Indicates the total number of cells used to calculate the postsynaptic reconstruction correlation with synaptic density (Figure S1 D).

Dendritic structure scaling relationships and synaptic density across species.

A, Schematic illustrating the impact on synaptic density by varying the number of synapses (green) while keeping dendritic length (black) and volume (blue dashed ellipse) constant. B, Shown is the relation between total dendrite length of real dendrites (LReal) and the predicted length (LPredicted) computed using the scaling law for all morphologies of all datasets besides human data (N = 2486; log-transformed data; see Table 1, 2). Predicted dendritic length from scaling equation closely matches observed length across all species, with data falling along the unity line (dashed line;; slope = 1; fit using linear regression.). Each datapoint is one neuron, with the colour corresponding to species, similar to Figure 1B. C, Sensitivity analysis of synaptic density and wiring optimisation. The root mean square error (RMSE) between LPredicted and LReal is plotted as a function of synaptic density. This analysis systematically varies the synaptic density across all morphologies to evaluate wiring prediction error. This analysis reveals an inflection point around . The red star denotes the empirically observed mean synaptic density across datasets.

Impact of synaptic size packing on dendritic synaptic density in mouse cells

A, The schematic illustrates how different synapse packing arrangements affect synaptic density, without changing the total synaptic volume (shown in green). This effect is observed as synapses are dispersed along a dendritic arbour (black) in the form of numerous smaller synapses or a reduced number of larger synapses. B, Schematic (top) and plot (bottom) illustrating how synapse size distribution affects estimated dendritic synaptic density. In the schematic, synapses are sorted by size (green shapes) and grouped into cumulative intervals (lower black bars), starting either from the smallest or largest synapses. For each interval, the total synaptic volume (total V) is converted into a number of synapses using the mean size within that interval (inter. mean (V)). For example, in the top right (blue), total volume is redistributed using smaller synapses, resulting in a higher estimated synapse count and density. In the plot below, the x-axis represents cumulative intervals as percentages, computed in 5% steps starting either from the largest 5% of synapses or the smallest 5%, continuing until all observed synapses are included (100%). The y-axis represents the overall mean synaptic density corresponding to these intervals. Different colours indicate distinct starting points for interval calculation. Error bars indicate standard deviation. C, Correlation plot of mean dendritic synapse size (normalised data; N = 1446 from [46, 47]; see Methods 3.5) against dendrite synaptic density in mouse cells (correlation coefficient of r = −0.29, p < 0.001). Data points represent individual cells, colours as before. The data are fit with a line of slope −0.4 ± 0.04 (orange dashed line) to assess the relationship between synapse size and synaptic density. Statistical significance was assessed using permutation test (10000 permutations), with Bonferroni correction applied across all interval comparisons to control for multiple testing; “n.s.” denotes non significant. Orange dashed line was fit using linear regression.

Radius-synaptic density correlation stabilizes voltage response in steady-state biophysical models.

A, Correlation plot of normalised dendrite radius (N = 1484; see Methods 3.5) against synaptic density in mouse cells. The correlation coefficient is r = 0.67 (p < 0.001). Data points represent individual cells, and colours match prior panels. The data are fit with a line of slope 1.81 ± 0.05 (orange dashed line), to assess the relationship between dendritic radius and synaptic density. B, Correlation plot of normalised dendrite radius (N = 1446; see Methods 3.5) against normalised synaptic size in mouse cells. The correlation coefficient is r = 0.08 (p < 0.01). Data points represent individual cells, and colours match prior panels. The data are fit with a line of slope 0.16 ± 0.05 (orange line), to assess the relationship between dendritic radius and synaptic size. C, Shown are a random subset of neuronal morphologies used to constrain the biophysical models. Right, schematic of the proposed compensatory mechanism maintaining neuronal excitability in mouse data. Top: a thicker dendrite adjusts synaptic density to offset higher input conductance, due to the increased membrane surface area. Bottom: the opposite for a thinner dendrite. Scale bar 100μm D, Average voltage responses of modelled morphologies (N = 1186) plotted against normalised length under three conditions: mangenta, real diameters and synaptic densities; light purple, real synaptic densities but average fixed diameters across all morphologies; yellow, real diameters but average fixed synaptic densities. Corresponding nRMSE values are provided for each condition. Shaded areas represent standard error of the mean (SEM). Black line show predictions from the dendritic constancy equation. Target voltage was set to Vsyn = 11mV, to match spike threshold of mouse pyramidal neurons following [29]. Correlation coefficients (r) are calculated using Pearson correlation; p values are obtained from permutation tests (10000 permutations), and linear regression lines are fit where applicable.

Details of species, brain regions and quantification of postsynaptic density area.

The table summarizes the postsynaptic density (PSD) characteristics for various species, including Drosophila (larva and adult), rat, mouse, and human. For each species, the specific brain region studied, sample size, and mean area of the PSD in square nanometres (nm2) are provided. For human data, “AS” denotes asymmetrical synapse, and “SS” symmetrical synapse. References for the data sources are included.

Relationship between dendritic radius and synaptic size across species

A, Schematic of the hypothesised compensatory relationship for maintaining neuronal excitability across species. As dendrites (black) increase in size, synapses (green) also increase in size to offset higher input conductance and stabilise the voltage response. B, Correlation plot between the mean radius of dendrites (N = 3309; Table 3; Methods 3.5) and the size of synapses (N = 10286; Table 4; Methods 3.5), measured by the area of postsynaptic densities (PSDs), across different species (correlation coefficient of r = 0.88, p = 0.018). Each color represents a different species. For human data, “AS” is asymmetric synapses (larger PSD value) and “SS” is symmetric synapse (smaller PSD value). The data are fit with a line of slope 321.25 ± 87.82 (black dashed line) to assess the relationship between dendritic radius and synaptic size (PSD). C, Normalised voltage responses plotted against dendritic radius (range = 100–500nm) under three conditions. The dashed line represents the initial voltage response at the beginning of the range, which was used to normalise all other responses. We quantified deviations from the initial response using nRMSE. Blue: dendritic radius, input current, and synaptic conductance scale linearly. Red: input current and synaptic conductance scale, but radius remains fixed at 100 nm. Green: radius scales while input current and synaptic conductance remain constant. Correlation coefficients (r) were obtained using Pearson correlation, and p values obtained from a permutation test (10000 permutations); lines were fit using linear regression.

Synaptic density corrections and correlation analysis with postsynaptic reconstruction completeness level.

A, Same as Figure 1C. B, Similar swarm plot of synaptic densities across species as in A, but with uncorrected zebrafish density values (see Methods 3.5). C Zebrafish synaptic density estimates following terminal-branch corrections. Observed synaptic densities (Obs.) were recalculated after adding 1, 2, or 3 synapses per terminal branch. Each point represents the mean synaptic density across zebrafish neurons, and error bars indicate the standard deviation. D, Correlation plot showing dendritic synaptic density as a function of postsynaptic completion rate in the adult fly Hemibrain connectome (ρ = 0.61, p < 0.001; Table 1, 2; see 3.5) [41, 77]. Different colours indicate different cell types in the adult fly brain. Error bars indicate the standard deviation. The data are fitted with an exponential fit (black dashed line) to assess the relationship between reconstruction completion rate and synaptic density. The correlation coefficient (r) was obtained by Spearman’s rank correlation, and p values were obtained from a permutation test (10000 permutations).

Comparative analysis of dendritic morphometrics in WT, FraRobo, and TNT EM volumes

A, Box plot showing the distribution of dendritic length across wild type (WT; N = 14), FraRobo (N = 14), and TNT (N = 12) mutants. B-D, same as A, but for dendritic volume, number of branch points, and mean branch order measurements. The red plus symbols indicate outliers within the data set for each condition. Outliers were defined based on the interquartile range. Horizontal lines above the plots denote statistical comparisons, with “n.s.” indicating a lack of statistical significance (p > 0.05), with p values obtained from permutation tests (10000 permutations).

Scaling relationships plotted across individual species.

The data is the same as in Figure 3C. A, Shown is the relation between total dendrite length of real dendrites (LReal) and the predicted length (LPredicted) computed using the scaling law for all Drosophila larva morphologies (N = 233; r = 0.95, p < 0.001; log-transformed data; Table 1). B-D, same as in A but for adult Drosophila (N = 60; r = 0.94, p < 0.001); larval zebrafish (N = 709; r = 0.9, p < 0.001); and mouse (N = 1484; r = 0.64, p < 0.001). Correlation coefficients (r) were obtained by Pearson correlation, and p values were obtained from a permutation tests (10000 permutations).

Illustrative dendrite-axon split algorithm for adult Drosophila and zebrafish datasets.

A, Dendrite-axon split in adult Drosophila Kenyon-cell. The figure shows the four-step process: starting with the reconstructed morphology, then illustrating the separated compartments using K-means, highlighting the dendritic (pink) and axonal (black) and main trunk (green), and finally presenting the dendritic tree after main branch removal, with the soma marked (yellow dot). B, Dendrite-axon split of larval zebrafish mitral cell. The three-step process starts with representative morphology, then shows separated compartments (dendritic in pink and axonal in black) using K-means, and finally highlights the dendritic compartment (pink) and the soma proxy location (yellow). Scale bars: 10 μm.

Simulations show that observed dendrite length–volume scaling is not imposed by decomposition method in MICrONS mm3 dataset.

A, Relationship between dendrite length and dendrite volume for three groups (N = 1183): wild-type mouse neurons (purple; MICrONS mm3 dataset), tortuous morphologies (light purple), and randomly reconnected morphologies (dark gray). The dashed line indicates the unity line (slope = 1). (Right) Zoom-in of the region within the gray rectangle to highlight differences among groups. All correlations are statistically significant (p < 0.001). Correlation coefficients (r) were obtained using Pearson correlation, and p values obtained from a permutation test (10000 permutations)