In 1986, electron microscopy was used to reconstruct by hand the entire nervous system of a roundworm, the nematode Caenorhabditis elegans1. Since this landmark study, high-throughput electron-microscopic techniques have enabled reconstructions of much larger mammalian brain circuits at synaptic resolution2,3. Nevertheless, it remains unknown how the structure of a synapse relates to its physiological transmission strength—a key limitation for inferring brain function from neuronal wiring diagrams. Here we combine slice electrophysiology of synaptically connected pyramidal neurons in the mouse somatosensory cortex with correlated light microscopy and high-resolution electron microscopy of all putative synaptic contacts between the recorded neurons. We find a linear relationship between synapse size and strength, providing the missing link in assigning physiological weights to synapses reconstructed from electron microscopy. Quantal analysis also reveals that synapses contain at least 2.7 neurotransmitter-release sites on average. This challenges existing release models and provides further evidence that neocortical synapses operate with multivesicular release4,5,6, suggesting that they are more complex computational devices than thought, and therefore expanding the computational power of the canonical cortical microcircuitry.
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A preprint of this study was published on bioRxiv (https://doi.org/10.1101/2019.12.13.875971). Source data underlying all graphical representations are provided with the paper. Further data generated here are available from corresponding author upon request. Source data are provided with this paper.
Custom-written code is available on GitHub (https://github.com/gschuhknecht/SynapseStructureFunction).
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We thank O. Ohana for training and sharing expertise in patch-clamp recordings; S. Solinas for assistance with NEURON simulations; S. Soldado-Magraner, A. Huber and J. C. Anderson for constant support; and M. Buchholz and F. Engert for comments on the manuscript. As members of the Institute of Neuroinformatics, we are signatories of the Basel Declaration. This work was supported by the Swiss Society for Neuroscience and the Neuroscience Center Zurich (to G.F.P.S.) and by funding from the University of Zurich (to K.A.C.M.).
The authors declare no competing interests.
Peer review information Nature thanks Tianyi Mao, Andreas Tolias 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.
Extended data figures and tables
Extended Data Fig. 1 Complete light-microscopic reconstruction of presynaptic axons and postsynaptic dendrites of connected neurons preserved in the 300-μm slice.
a, Full 3D light-microscopy reconstruction of a recurrently connected pair; an axon of the blue cell formed one synapse with a dendrite of the black cell; axons of the black cell formed two synapses with dendrites of the blue cell and three non-synaptic contacts; arrows show regions of interest illustrated in subsequent panels; cortical surface indicated. b, Side-projection of the same reconstruction, showing how the acute slice was resliced into four sections (indicated); regions of interest are highlighted as in a. c, Alignment of sections 1 and 2. All neurites that were cut during reslicing (arrowheads) could be aligned between sections. Note that the soma of the black neuron was cut during reslicing (arrows), with the subsequent alignment (right) indicating that there was virtually no tissue loss during reslicing. d, e, Neurites terminating at the top of section 1 (that is, cut during acute slice preparation for electrophysiology). Note that neurites that were cut during acute slice preparation ended in typical biocytin-filled blebs at the cut surface (arrowheads). d, The axon of the blue neuron terminates at the surface of section 1 (arrowhead, membrane bleb at slice surface). e, Dendrite of the black neuron terminating at the surface of section 1 (arrowhead, membrane bleb at slice surface). f, g, For experiments to be included in the final data set, neurites that terminated within sections needed to end in well labelled terminals; when neurites showed signs of incomplete biocytin filling, as in h, i (for example, ‘fading out’ within sections), experiments were discarded. f, Axon of black cell terminating in well labelled bouton in the middle of section. g, Dendrite of the blue cell terminating in the middle of the section in a number of dendritic spines emerging from the dendritic shaft. h, i, Examples of incompletely labelled neurites in an experiment that was discarded (a different experiment to that shown in a–g). h, In incompletely labelled dendrite segments (arrowheads), dendritic shafts appeared faint and spines were not filled; arrow, dendritic labelling fading completely, rendering dendrite untraceable. Panels show different dendrites in the same experiment. i, The biocytin label fades in an axon (arrowheads), while interspersed boutons are densely labelled; arrow, axonal label fading completely, rendering the axon untraceable.
Extended Data Fig. 2 Tilt-series and colour-inverted micrographs facilitate reconstruction of synaptic ultrastructure in biocytin-filled dendritic spines.
a–c, Identification and reconstruction of synaptic ultrastructure following slice recordings (synapse 1 in Fig. 1). a, Tilted and inverted micrographs for three cross-sections through a synaptic contact. Left column, synaptic specializations were often ambiguous in untilted micrographs. Centre left column, collage of micrographs from sections that were physically tilted inside the electron microscope (tilt angle indicated) facilitated the detection of synaptic specializations. Centre right, tilted micrographs from the centre left column were colour-inverted, highlighting subtle contrast differences and aiding identification of the PSD (arrows omitted for clarity, except arrowheads indicating the PSD). Right column, reconstruction of presynaptic and postsynaptic morphologies with aid from tilted and inverted micrographs. b, En-face representation (2D projection) of the reconstructed PSD from a. c, 3D electron-microscopic reconstruction of the complete synaptic contact shown in a, b, with the same colour scheme as in a; black, dendritic spine head. d–f, Identification and reconstruction of synaptic ultrastructure for a different synapse (synapse from a different experiment to that shown in a–c); panel layout analogous to that in a–c. d, Left column, untilted micrographs did not permit clear identification of the synaptic cleft and PSD. Centre left column, tilted micrographs revealed the synaptic cleft and PSD. Centre right column, inversion of tilted micrographs facilitated identification of the PSD (arrows omitted for clarity, except for arrowheads indicating the PSD). Right column, reconstruction of presynaptic and postsynaptic morphologies with help from tilted and inverted micrographs. e, En-face representation (2D projection) of the reconstructed PSD from d. f, 3D electron-microscopic reconstruction of the complete synaptic contact shown in e, f; same colour scheme as in d.
Extended Data Fig. 3 Overview across the ten connected neuron pairs, showing important anatomical features of recovered synapses and corresponding EPSPs.
a–c, Catalogue showing distances of recorded synapses on dendrites, reconstructed PSDs, and recorded EPSP waveforms. Experiments sorted by decreasing mean EPSP amplitude. a, Dendritic distances from the identified synapses to the soma. The collapsed dendritic tree is represented schematically ranging from the soma (bottom) to a distance of 250 μm (top, cut off); dendritic distances at which respective synapses were found are indicated by spine locations (grey balls and sticks). No distinction was made between apical and basal dendrites; all synapses were formed on dendritic spines, except the proximal synapse in experiment 10, which was formed on a dendritic shaft (indicated). b, Morphologies of reconstructed PSDs. En-face representations (2D projections) of PSDs highlight the ranges of identified sizes and shapes. PSDs were positioned next to spines according to their respective dendritic distances as indicated in a. See scale bar at bottom right; asterisks indicate PSDs with complex morphologies. c, Waveforms of evoked EPSP recordings. Black, average waveform of EPSP recordings during stable epochs for each connection; grey, ten randomly selected single-trial EPSP waveforms taken during stable epochs of recording. d, EPSP rise times correlate with mean dendritic distances of identified synapses to soma. Shown are the correlation coefficient (r) and P value from a two-tailed, non-parametric Spearman correlation; line was fit using linear regression.
a, b, Bootstrap resampling from experimentally recorded EPSP distributions shows that the synaptic size–strength correlation is very robust when 100 EPSPs are averaged per experiment. a, Relationship between resampled mean EPSP amplitudes and cPSD area for the ten connected pairs. Black error bars indicate the range of mean EPSP amplitudes that resulted from a total of 10,000 resampling runs; grand means of resampled mean EPSP amplitudes (black dots) were fit with a line (dashed black) of slope 7.96 ± 2.44. Grey dots show experimentally measured EPSPs during stable recordings; the grey line shows the fit to experimentally measured mean EPSP amplitudes (both as in Fig. 3c). b, Histogram of P values for 10,000 correlations between resampled mean EPSP amplitudes and cPSD area. c–f, The synaptic size–strength correlation is weak on a trial-to-trial basis. c–e, Three example plots showing relationships between cPSD area and only a single evoked EPSP amplitude for each connected pair, which was randomly selected from stable recordings. Green, significant correlation; red, no significant correlation; grey dots and lines as in Fig. 3c. f, Histogram of P values for 10,000 correlations between randomly chosen single-trial EPSPs and cPSD area, such as the examples in c–e. Shown are correlation coefficients (r) and P values from two-tailed, non-parametric Spearman correlations.
The model was used to reproduce results obtained from combined dendritic and somatic patch-clamp recordings in barrel cortex L2/3 (ref. 25) and L5 pyramidal cells (ref. 26). Without further tuning, electrical coupling in the model was in excellent agreement with experimental data for depolarizing current injections, confirming that the model captured the electrical behaviour necessary to realistically simulate the transfer of excitatory synaptic currents from dendrites to soma. Note that transfer resistance (the steady-state form of transfer impedance) is symmetrical, that is, of the same magnitude in both somatodendritic and dendrosomatic directions. a–c, Dendritic voltage responses to somatic current injections in the model cell are in good agreement with experimental data from L2/3 pyramidal cells (see Fig. 1a, b in ref. 25). a, Compartmental model with simulated somatic and dendritic recording sites indicated; the distance from the dendritic recording site to the soma was chosen to match ref. 25. b, Bottom, current steps injected at soma; middle, somatic voltage responses to somatic current injections; top, voltage traces at the dendritic recording site shown in a in response to somatic current injections were in good agreement with experimental traces from ref. 25. c, Current–voltage relationships at soma (grey) and dendritic recording site (blue) of the model cell. The model’s linear current–voltage responses for depolarizing subthreshold current injections (which constitute the relevant factor for simulating the propagation of excitatory synaptic currents in dendrites) were in excellent agreement with dendritic recordings in L2/3 pyramidal neurons25. d–f, Comparison of somatodendritic transfer resistance in the model with experimental data obtained using dendritic recordings in L5 pyramidal cells (see Fig. 1d in ref. 26). d, Transfer resistance was measured between 338 dendritic locations (blue circles) and the soma of the model. e, Transfer resistance in the model cell as a function of dendritic distance to soma; grey bar, distance range that corresponds to the dendritic recordings in ref. 26. f, Transfer resistances for dendritic locations at 100–130 μm from the soma were in excellent agreement with the experimental measurements of ref. 26.
a, Relationship between cPSD area and estimated cIsyn; data were fit with a line of slope 1.04 ± 0.27. b, Comparison of estimated Isyn for PSDs with simple morphologies and complex morphologies (asterisks in Extended Data Fig. 3); means ± s.d. indicated; P value obtained by non-parametric Mann–Whitney test. c, Relationship between estimated Isyn and corresponding dendritic spine volume; data were fit with a line of slope 0.77 ± 0.32. d, Relationship between estimated Isyn and the length of the corresponding dendritic spine necks. Lines were fit using linear regression; 95% confidence intervals for estimated Isyn are indicated with error bars in a, c, d. a, c, d, Shown are the correlation coefficients (r) and P values of two-tailed, non-parametric Spearman correlations.
a, For connections comprising a single synapse, Isyn can be estimated using Ohm’s Law from the experimentally recorded somatic EPSP amplitude and the simulated distance-dependent transfer impedance. b, When two synapses (A and B) were identified in electron microscopy, we assumed that the ratio of IsynA to IsynB followed the ratio of PSDA to PSDB, and that synaptic potentials sum linearly at the soma.
a–c, Relationship between PSD area and Isyn, estimated using four different parameter combinations in the compartmental model. The white circles and dashed lines show Isyn estimated from the default model used throughout this paper (as in Fig. 3f); for clarity, data points are shifted slightly horizontally. a, b, Estimates of Isyn were remarkably robust to changes in Ri and Rm. Parameters were tuned such that the model cell reproduced our somatically recorded current–voltage responses. Thus, changing Ri required Rm to be adjusted in the opposite direction. This appeared to have little net effect on the transfer impedance, which was then used to estimate Isyn. c, Lowering Cm resulted in lower estimates of Isyn. We chose a value for Cm of 1 μF cm−2 because of its widespread use in previous L2/3 models; we note, however, that Cm values below 2 μF cm−2 resulted in unrealistically short membrane time constants when compared with our in vitro recordings from the neuron that was later reconstructed for the model cell (data not shown). Models with Cm values of 2 μF cm−2 reproduce our experimental current–voltage responses markedly better and thus provide more realistic fits. Thus, the plot does not resemble an accurate estimate of Isyn, but rather a minimum bound for Isyn as a function of parameter tuning. d, Table summarizing model parameter combinations and non-parametric Spearman correlation coefficients (r), P values of correlations, and slopes of linear regressions for the four resulting PSD–Isyn relationships; varied parameters are indicated with bold font. The specific combinations of model parameters were chosen because they conformed with experimental measurements or were used in previous models of L2/3 neurons (see Methods). Note that all tested models resulted in statistically significant PSD–Isyn relationships.
Extended Data Fig. 9 Quantal analysis using SMAQ provides similar results and uncertainty compared with the method of fitting binomial models to peaky histograms.
a–e, EPSP amplitude histograms from five experiments contained equally spaced peaks (suggesting discrete multiples of quantal size) but failed our anatomical quality criteria and were excluded from structure–function analyses. These histograms could be fit successfully with a simple quantal binomial model to extract quantal parameters (black lines overlaid on histograms). In addition, quantal parameters were estimated using SMAQ. The insets compare the quantal parameters found by fitting peaky histograms and by SMAQ. N, number of release sites; P, release probability; Q, quantal size; n, number of entries per histogram. f, Comparison of solutions for quantal parameters and associated 95% confidence intervals given by the method of fitting peaky histograms (black) and SMAQ (blue) across the five experiments shown in a–e. Dark blue, Bayesian-inspired confidence intervals for SMAQ; light blue, confidence intervals for SMAQ derived from the same bootstrap resampling algorithm used to derive confidence intervals for the method of fitting peaky histograms (black). Solutions provided by the two methods were compared with the non-parametric Wilcoxon matched-pairs test (two-tailed P values shown in bold). For all three quantal parameters, solutions given by the two methods were not significantly different (see text).
a, SMAQ solutions for release probability (left-hand y-axis) and quantal size (right-hand y-axis) with corresponding 95% confidence intervals for the ten connected pairs. Pairs are sorted by decreasing number of release sites, as in Fig. 4c. b, Histograms of SMAQ solutions for release probability and quantal size, plotted on the same y-axes as in a.
Supplementary Discussion: Discussion of previous experimental and modeling work in rodent barrel cortex and our own data highlighting that dendritic trees of L2/3 pyramidal neurons behave as passive, linear structures under the experimental paradigm used in our study – thus justifying the use of a passive compartmental model.
Series of consecutive cross-sections through synapse shown in Fig. 1f and Extended Data Fig. 2a. The video shows micrographs of all consecutive sections through the synaptic contact (left panel), collages of optimal tilt angles for all micrographs containing synaptic specializations (centre left panel), color-inverted images of these tilted micrographs (centre right panel) and our reconstruction (right panel). The video contains all information used by the authors to identify and reconstruct PSDs.
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Holler, S., Köstinger, G., Martin, K.A.C. et al. Structure and function of a neocortical synapse. Nature 591, 111–116 (2021). https://doi.org/10.1038/s41586-020-03134-2
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