SUMMARY
The balance between excitatory and inhibitory (E and I) synaptic inputs is thought to be critical for information processing in neural circuits. However, little is known about the principles of spatial organization of E and I synapses across the entire dendritic tree of mammalian neurons. We developed a new, open-source, reconstruction platform for mapping the size and spatial distribution of E and I synapses received by individual, genetically-labeled, layer 2/3 cortical pyramidal neurons (PNs) in vivo. We mapped over 90,000 E and I synapses across twelve L2/3 PNs and uncovered structured organization of E and I synapses across dendritic domains as well as within individual dendritic segments in these cells. Despite significant, domain-specific, variations in the absolute density of E and I synapses, their ratio is strikingly balanced locally across dendritic segments. Computational modeling indicates that this spatially-precise E/I balance dampens dendritic voltage fluctuations and strongly impacts neuronal firing output.
INTRODUCTION
The spatial organization of synapses throughout the dendritic tree is a critical determinant of their integration properties and dictates the somatic firing patterns of individual neuronal subtypes (1-4). Within dendritic branches, clustered potentiation of excitatory and inhibitory (E and I) synaptic inputs underlie both circuit development and experience-dependent plasticity (5-9). Recently there has been substantial progress toward mapping neuronal connectivity at multiple scales (10-13). However, significant roadblocks remain in identifying basic principles of synaptic organization for individual neuronal subtypes (14-17), leaving important questions unanswered: Are there multiple spatial scales of E and I organization within neurons? Are there hotspots of enhanced synaptic connectivity? Is there a structural correlate of E/I balance within specific dendritic domains or individual dendritic segments? Finally, how does E and I synaptic organization characterizing a given neuronal subtype influence the dendritic and somatic firing properties of these neurons?
Comparing the distributions of excitatory and inhibitory synapses within the same neuron is particularly important to determine the cellular logic of synaptic organization. At the circuit level, a precise balance of excitation and inhibition is critical for calibrating both global and fine-scale levels of activity throughout development and during adult function (18-20). In both auditory and somatosensory cortex, the co-tuning of E and I conductances is set by experience-dependent refinement of intracortical inhibition (21, 22). An anatomical basis for E/I balance within individual neurons has also been observed in visual cortex and CA1, where excitatory inputs onto pyramidal neurons are continuously offset by somatic inhibition (23, 24). A conserved ratio of the numbers of E/I synapses was observed throughout the dendrites of cultured hippocampal neurons, suggesting that the spatial distribution of synapses might also contribute to E/I balance (2). However, this finding has not been extended to neurons in vivo. Activation of NMDA-type glutamate receptors leads to input-specific long term potentiation of dendritic inhibition mediated by somatostatin-expressing interneurons, linking excitation and inhibition within individual dendritic segments (25).
Here we have developed an adaptable, open-source platform for imaging and mapping E and I synapses across the entire dendritic arbor of individual neurons. We created whole-cell reconstructions of individual, optically-isolated pyramidal neurons (PNs) containing information about the size, shape, and continuous position of all E and I synapses across their entire dendritic arbors: the first dataset of its kind for any neuronal subtype. We focused our study on layer 2/3 (L2/3) PNs of the adult mouse primary somatosensory cortex, where substantial prior knowledge of the synaptic microstructure and connectivity allowed validation of our platform and some of our findings (26-31) as well as identification of new principles of E and I synaptic organization.
RESULTS
Synapse Detector: a Platform to Create Whole-Neuron Structural Inputs Maps
To obtain optically isolated, single L2/3 PNs for these synaptic reconstructions, we co-electroporated Cre-dependent Flex-tdTomato with low levels of Cre recombinase for extremely sparse in utero electroporation ((32, 33); Fig. 1A and Movie S1). We also labeled inhibitory synapses received by individual PNs by co-electroporating the inhibitory postsynaptic scaffolding protein Gephyrin tagged with EGFP, a strategy previously shown to reliably label all GABAergic and glycinergic inputs without affecting their development (9, 34). We achieved single-synapse resolution using confocal microscopy by imaging neurons across 2-3 serial 150 μm vibratome sections with a 100x 1.49 NA objective lens (Fig. 1B and 1D and Movie S2).
This new Synapse Detector toolkit within Vaa3D generates synaptic maps by taking image data and a trace of the dendritic tree as input to automatically isolate E and I synapses within a user-defined radius of each dendrite. Within this toolkit, excitatory synapses (dendritic spines) are classified with a Spine Detector module that identifies regions of fluorescence surrounding the dendritic trace (Fig. 1D top and middle panels and Movies S3-S5). Inhibitory synapses are identified using an IS Detector program that identifies EGFP-Gephyrin puncta that co-localize with the cytosolic Flex-tdTomato (Fig. 1D bottom panel and Movies S6 and S7). Together these software platforms measure E and I synapse position in 3D along the dendritic tree, as well as morphological features of E and I synapses such as their volume, spine neck length, position of I synapses along dendritic shaft or on spine heads (so called dually innervated spines, (9, 27, 35)). During reconstruction, Synapse Detector’s editing features allow the user to edit the volume of each identified synapse and eliminate false positives (Fig. S1). Synapse Detector has a minimal false negative rate compared to manual reconstructions and generates consistent annotation results among multiple users (Fig. S3). Following reconstruction and manual annotation, synaptic features are associated with nodes providing their geometric position in 3D along the dendritic tree. In the final step, neuron trace fragments containing information about individual synapse position and size from serial tissue sections are stitched together into a final input map with the Vaa3D Neuron Stitcher program that can be used to analyze the morphology of all synapses as a function of their continuous distance from the soma along the dendritic arborization (36).
We used this new Vaa3D reconstruction pipeline to map all E and I synapses across 10 PNs from L2/3 primary somatosensory cortex (as well as excitatory synapses from 2 additional PNs; Fig. 2). These neurons contained on average 6773±212 dendritic spines (range: 5558-8115) and 939±101 inhibitory synapses (range: 595-1556; Fig. 2C). On average, the total length of these dendritic trees was 4579±103 µm and these neurons displayed overall E and I synaptic densities consistent with previous reports (1.48±0.04 spines/µm and 0.20±0.02 inhibitory synapses/µm respectively) ((9, 35, 37); Fig. 2C). We also found that 26%±2% of inhibitory synapses targeted dendritic spines in L2/3 PNs (Fig. 2C). This fraction of spines dually innervated by an E and I synapse is comparable with previously observed values in these neurons (9, 27, 35).
Features of E and I synaptic organization across the entire dendritic tree of layer 2/3 PNs
To analyze synaptic distribution across the entire dendrites of the reconstructed L2/3 PNs, we subdivided dendritic arbors into three distinct domains: apical tuft, apical oblique, and basal dendrites (38). Within these domains, we distinguished among segment types by their relative branch order: primary, intermediate, and terminal ((38); Fig. 3A). This categorization is functionally relevant as different branch orders have distinct passive conductance properties resulting from their relative size and distance to the soma (38, 39). Primary dendrites have relatively low input impedance due to their large size, while terminal dendrites have higher input impedance due to their smaller diameter and sealed end. In addition to the domain classification used here, we developed a Subtree Labeling program as part of the Spine Detector toolkit that enables user-directed annotation of regions of interest throughout the neuron trace to assess experiment-specific questions about domain-level synaptic organization (Fig. S2E and see Material and Methods).
This division of the dendritic tree into specific domains and branch types allowed us to characterize the profile of synaptic distribution across L2/3 PNs. Similar to previous observations in CA1 PNs, E and I synaptic distribution appear to be inversely correlated at the domain level with relatively low spine density proximal to the soma, suggesting that this may be a general feature of synaptic organization across PN subtypes ((40, 41); Fig. 3B). In contrast to previous studies however, our complete reconstructions enable whole-cell mapping of relative E and I synaptic distribution (Fig. 2C, S4 and S5). Maps of E and I synaptic distribution in the same neuron demonstrate an almost complete absence of spines along primary dendrites accompanied by the highest density of inhibitory synapses (Fig. 3C).
L2/3 PNs receive direct thalamic input from both the ventral posteromedial nucleus (VPM) and the posterior medial nucleus (POm) terminating mainly onto their apical tufts (L1) and basal dendrites (L3) respectively (28, 42). The vast majority of neocortical spines that are dually innervated by an inhibitory synapse receive excitatory inputs from corticothalamic axons, suggesting that distal tuft and basal dendrites should have a relatively high proportion of dually innervated spines (27). Our unbiased mapping of the location of IS located on spine heads demonstrates that apical tuft and basal terminal dendrites of L2/3 PNs display a significantly higher proportion of dually innervated spines than primary and intermediate dendrites (Fig. 3D-E), validating the spatial resolution of our labeling, imaging, and reconstruction approaches.
Because spine head volume is linearly proportional to excitatory synaptic strength (e.g. size of the post-synaptic density and density of glutamatergic AMPA receptors), it is also possible to use Synapse Detector to map the distribution of relative synaptic strengths (3, 43, 44). We classified “large” synapses as greater than the highest 20th percentile of synaptic volume for each neuron, closely corresponding to the persistent 160% increase in volume reported for synapses following structural forms of long-term potentiation (5, 45, 46). Interestingly, while there is no specific trend for the distribution of large spines across dendritic domains, large inhibitory synapses appear to be clustered around the apical intermediate dendritic segments (Figures 3F and 3G), a feature never detected before.
E and I synaptic distribution is structured and locally balanced in dendritic segments
Active dendritic conductances evoked by clustered synaptic inputs can produce nonlinear depolarization and change the probability of somatic firing (47). Local increases in excitatory synaptic density in a subset of segments within the same dendritic domain could reflect clustered spine stabilization following branch-specific synaptic potentiation (5, 47). Therefore, we tested if L2/3 PNs exhibit local changes in the relative distribution of E and I synapses across segments within each dendritic domain (Fig. 4). To assess the extent of this potential weighted synaptic distribution, we compared the experimentally observed variation in synaptic density between segments within each dendritic domain to randomly shuffled densities for each neuron reconstructed. This was done by randomly redistributing synaptic density values across segments of the same domain (see Supplementary Material). Neurons in which synaptic distribution is significantly weighted toward a subset of dendritic segments would therefore display greater domain-specific variation in synaptic density than correspondingly randomized versions. Excitatory synaptic (spine) distribution is significantly weighted toward a subpopulation of dendritic segments across almost the entire dendritic tree (Fig. 4A and 4D). Interestingly, inhibitory synaptic distribution is significantly non-random and clustered only in apical and basal terminal domains, raising the intriguing possibility that E and I synapses are weighted toward the same dendritic segments (Fig. 4B and 4D).
Co-regulation of E and I synaptic inputs, generally referred to as E/I balance, is a critical mechanism for calibrating both global and fine-scale levels of neuronal activity (23, 48, 49). While several studies have demonstrated mechanistic links between E and I synaptic potentiation, whether it results in local, fine-scale balance between E and I synaptic distribution within dendritic segments remains an open question (25, 46, 50). Remarkably, we find that E and I synaptic density strongly co-varied in terminal segments throughout the dendritic tree of layer 2/3 PNs (Figure 5). This structural E/I balance appears to increase as a function of distance from the soma, with segments distal to the soma showing remarkable correlation between E and I synaptic density (Figure 5). Taken together, these results demonstrate that in L2/3 PNs: (1) both E and I synaptic density varies more than by chance between dendritic segments among a given dendritic domain and (2) that despite this variability in E and I synapse density between segments of a given dendritic domain, the ratio between E and I synaptic density is tightly controlled locally within these segments.
Functional implications of global and domain-specific E/I balance
To better understand the functional implications of the local E/I balance we found experimentally (Figure 5), we performed computational modeling of the 10 individual L2/3 PNs reconstructed (shown in Fig.S4 and S5), including their 3D reconstructed morphology and the dendritic location of their E and I synapses. Passive and active membrane properties of these cells were based on previously published biological values (see Material and Methods). All excitatory synapses were activated randomly at an average rate of 1.75 HZ while inhibitory synapses were activated at 10 Hz so that the firing rate of the modeled cells matched ranges found in vivo (31). These models also replicated several active and passive dendritic properties observed in L2/3 PNs, including back-propagating action potentials, the somatic input resistance, and membrane time constants (Figure 6 and see Material and Methods).
To test the significance of the synaptic distribution we observed in these 10 L2/3 PNs, we manipulated the variance (here measured as standard deviation, SD) of the domain-specific E/I ratio while keeping the total number of synapses within each domain constant (thus keeping the global E/I ratio fixed for the modeled cell). This created a range of E/I ratio SD values, ranging from very tight E/I ratio variance, where each segment within a given domain has a similar ratio of E and I synapses (Fig. 7A, the balanced case, left), to the extreme case, in which each branch in a given domain had either only excitatory or only inhibitory synapses (Fig. 7B, the unbalanced case, left). Manipulation of the variance of segment-specific E/I ratio had a strong effects on predicted dendritic voltage dynamics (Fig. 7A-B, right): variation in dendritic voltage (including active dendritic spiking and back propagating action potentials (Material and Methods in Fig. 7A-7B) in balanced segments is dampened and overall more hyperpolarized (Figure 7A, right) compared to the unbalanced E and I cases (Fig. 7B, right). In the case of minimal variance of local E/I ratio per segment, the voltage distribution was narrower and very similar to that predicted from the biologically-observed E/I ratio (compare blue to green lines in Fig.7C). We found that terminal domains which, experimentally, had a near-balanced E/I ratio (Fig. 5) were highly sensitive to increasing the E/I ratio variance: gradually increasing the variance of E/I ratio among segments resulted in a gradual increase of the mean dendritic voltage time-integral (Fig. 7D). This was not the case for intermediate domains with biologically unbalanced E/I ratio, where the change in variance of E/I ratio between segments had minimal effect on the dendritic voltage time-integral (Fig. 7G and see Material and Methods). This is likely due to the small contribution of intermediate synapses to the voltage perturbations in those domains, possibly as a result of their small relative number: indeed, if we perform our simulations after removing the synapses in intermediate domains, of the voltage integral was reduced by less than 1%, compared to 10-30% in the terminal domains (Fig. S7A).
The somatic firing rate in the 10 modeled cells was also strongly affected by the domain-specific E/I SD value (keeping the global E/I balance fixed per cell). Indeed, when testing the combined effect of differences in the global E/I ratio for different modeled cells together with the effect of the domain-specific E/I SD, we found a high correlation (R2 = 0.7, dashed line) between somatic firing rate and global E/I ratio (Figure 7F). Not surprisingly, cells with larger relative number of excitatory synapses fire at higher rates. Strikingly, in all modeled cells, the output firing rate increases as much as twofold per cell when the domain specific E/I ratio SD was increased, suggesting that the local E/I ratio (in addition to the global E/I ratio) must be considered for understanding how synaptic activity shapes the neuron’s output. Our experimentally-based modeling demonstrates that in L2/3 PNs, E/I ratio is optimally-balanced in key dendritic domains; this domain-specific, local E/I balance at the level of dendritic segments constrains dendritic voltage fluctuations, and controls to a significant extent the firing rate of these neurons (Figures 7F and S6).
DISCUSSION
Mapping the spatial organization of synapses across the entire dendritic arbor of individual neurons is crucial for bridging the gap between our understanding of the molecular determinants of synaptic development and the principles of neural circuit connectivity. Here, we developed an adaptable, open-source toolkit for mapping the morphology and spatial distribution of all E and I synapses across complete neurons. This method has several key benefits for mapping subcellular synaptic morphology and distribution. As part of the Vaa3D image annotation platform, Synapse Detector is fully integrated into Vaa3D automatic pipeline for image segmentation, 3D image stitching, and surface reconstruction (36, 51, 52). Synapse Detector is compatible with any fluorescent imaging method including high resolution confocal microscopy. Most importantly, Synapse Detector provides a generalizable toolkit for quantifying and mapping features of subcellular fluorescent marker distribution.
The synaptic mapping pipeline developed here enabled the reconstruction of 12 L2/3 PNs, including the location and morphology of over 90,000 E and I synapses. Previous anatomical studies of the synaptic morphology and connectivity of this cell type allowed validation of our platform and observed results (26-31). Our 3D reconstruction method for dendritic spines closely matched estimates from manual reconstructions of L2/3 PN spine density and morphology generated by tracing synapses from serial focal planes (26). We also observed inhibitory synaptic distributions consistent with previous observations, as well as a common proportion of inhibitory synapses targeted to spines (9, 34, 35). Strikingly, the distribution of specific synaptic features characterizing mouse L2/3 PNs recapitulates known motifs of circuit connectivity: in L2/3 PNs, dually innervated spines almost exclusively correspond to dendritic spines receiving thalamic inputs, and these synapses were significantly enriched in the L1 apical tufts and deep L3 basal dendrites, the two layers targeted by thalamic afferents from POm and VPL that innervate S1 (27, 28).
Analyzing the distribution of E and I synapses across complete dendritic arbors has revealed several scales of structured organization within L2/3 PNs. E and I synaptic distribution also varies significantly across dendritic domains, with fewer spines located in proximal than along distal dendritic segments, similar to what has been observed in CA1 PNs, potentially suggesting a shared principle for synaptic organization between these PN subtypes (40, 41).
Crucially, within-neuron comparisons of observed and randomized synaptic locations enabled the identification of structured distribution of E and I synapses to a restricted subset of dendritic segments within each domain. The formation of hotspots of synaptic density is consistent with known cellular mechanisms promoting spatially clustered synaptic stabilization and potentiation at the scale of single dendritic segments (47, 53). Active properties of dendrites critical for initiating clustered potentiation are engaged in somatosensory and visual cortical PNs during sensory processing, raising the tantalizing possibility that these hotspots of synaptic density might represent a structural signature of salient feature storage within neuronal dendrites (8, 54-56).
A novel feature of structured synaptic distribution that emerged from our study is the strong, branch-specific, and local balance between E and I synaptic density across terminal dendritic segments. This suggests a far stronger association between E and I synaptic distribution than previous observations in vitro that the total number of E and I synapses are correlated across dendrites (2). Indeed, while a conserved ratio of the number of E and I inputs across dendrites can be largely explained by longer dendrites receiving more inputs, our data strongly suggest that molecular mechanisms co-regulating the balance between E and I synaptic density must be acting at the scale of short dendritic segments. This spatial pattern closely matches the dendritic targeting of somatostatin-expressing interneurons, whose synapses onto L2/3 PNs were recently demonstrated to undergo NMDAR-dependent long term potentiation (25, 57, 58). While the study of E/I balance at the level of single neurons has largely been restricted to feedforward inhibition mediated by perisomatic-targeting basket interneurons, our whole-neuron synaptic input maps suggest that a precise balance between excitation and inhibition is critical for dendritic integration as well (23, 59).
This novel principle of local E/I balance within dendritic segments has significant implications for dendritic integration. Indeed, our simulations show that disrupting the biologically-observed dendritic E/I balance in terminal dendrites dramatically enhances local dendritic voltage fluctuations and the initiation of local dendritic non-linearities, resulting in increased firing at the soma. Our first-ever complete mapping of E and I synapses over the whole dendritic tree of a subtype of PNs, combined with detailed simulations, suggest that the fine-tuned spatial balance of E and I synapses we observed strongly impacts local dendritic computation as well as the global input/output dynamics of cortical neurons within a network. Finally, we provide here the open-source synaptic reconstruction tools we have developed as well as our complete data set of 12 pyramidal neuron input maps containing information about the size, shape, and placement of over 90,000 E and I synapses publicly available upon acceptance.
MATERIALS AND METHODS
Principles of excitatory and inhibitory synaptic organization constrain dendritic spiking in pyramidal neurons
Iascone and Li et al.
This PDF file includes
Key Resources Table Figures S1 to S7 Methods
Synapse Detector User’s Guide References
Other Supplementary Material includes Movies S1 to S7 and 12 L2/3 PN synaptic maps
KEY RESOURCES TABLE
METHODS
Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Franck Polleux (fp2304{at}columbia.edu).
DATA ACQUISITION
Mice
All animals were handled according to protocols approved by the Institutional Animal Care and Use Committee at Columbia University, New York. Postnatal day 42 CD-1 IGS mice (strain code: 022; Charles River) were used for all experiments. Timed-pregnant female mice were maintained in a 12 hour light/dark cycle and obtained by overnight breeding with males of the same strain. For timed-pregnant mating, noon after mating is considered E0.5.
Constructs
The tdTomato reporter insert was subcloned into the pAAV-Ef1a-DIO eNpHR 3.0-EYFP plasmid (Addgene plasmid # 26966) between the AscI and NheI cloning sites. EGFP-GPHN (clone P1) was obtained from
H. Cline (TSRI, La Jolla, USA) and subcloned into pCAG downstream of a CMV-enhancer/chicken-β-actin (CAG) promoter, by replacing EGFP between the XmaI and NotI cloning sites.
In utero electroporation
In utero cortical electroporation was performed at E15.5 on timed pregnant CD1 females. The previously described protocol for in utero cortical electroporation (61) was modified as follows. Endotoxin-free DNA was injected using a glass pipette into one ventricle of the mouse embryos. The volume of injected DNA was adjusted depending on the experiments. Electroporation was performed at E15.5 using a square wave electroporator (ECM 830, BTX) and gold paddles. The electroporation settings were: 5 pulses of 45 V for 50 ms with 500 ms intervals. Plasmids were used at the following concentrations: Flex-tdTomato reporter plasmid: 1 µg/µl; EGFP-GPHN 0.5 µg/µl; NLS-Cre recombinase: 0.0002 µg/µl.
Tissue preparation
Animals at the indicated age were anaesthetized with isofluorane before intracardiac perfusion with PBS and 4% PFA (Electron Microscopy Sciences). 130 μm coronal brain sections were obtained using a vibrating microtome (Leica VT1200S). Sections were mounted on slides and briefly dehydrated at room temperature to reduce section thickness before being coverslipped in Fluoromount-G (SouthernBiotech).
Confocal imaging
Confocal images of electroporated neurons in slices were acquired in 1024×1024 mode using an A1R laser scanning 11 confocal microscope controlled by the Nikon software NIS-Elements (Nikon Corporation, Melville, NY). We used a 100X H-TIRF, NA 1.49 (Nikon) objective lens to acquire image volumes of neuron fragments. Z-stacks of images were acquired with spacing of 100 nm. To counteract possible interference from light diffraction through the tissue, laser power was linearly increased as a function of depth within each tissue section to normalize the mean fluorescent intensity of pixels from image planes throughout the stack (Figure S2A). Dendritic spines and inhibitory synapses were quantified based on tdTomato fluorescence and EGFP-GPHN puncta fluorescence respectively. All quantifications were performed in L2/3 somatosensory cortex in sections of comparable rostro-caudal position.
Heat map generation
We query the synaptic annotations for individual neurons to return a subset of the synapses satisfying the query. Some examples are “all inhibitory synapses,” “large spines,” and “all inhibitory synapses on spines.” We classified “large” synapses as greater than the 20th percentile of synaptic volume for each neuron, closely corresponding to the persistent 160% increase in volume reported for synapses following structural forms of long-term potentiation (5, 45, 46). We calculate the path distances between these nodes and the soma, which is the 3D distance on the dendritic arbor from the soma to the node of interest. We calculate the distances between consecutive nodes that are in “ancestor-descendent” relationships on the neuronal arbor by obtaining the absolute value of the difference between their path distances.
To calculate the density of the synapses of interest at any given point on the dendritic arbor (the heat map), we count the synapses of interest that are within W µm of that point in terms of the path distance on the dendritic arbor, and convert these counts into color codes. Smaller W values increase the resolution of the heat map. On the other hand, when W is too small, the heat map will display high frequency noise. Therefore, we set the W values adaptively for each dendritic arbor as where |S| denotes the number of synapses of interest, and L denotes the total dendritic length of the arbor so that the unit of λ is μm-1. When mapping local counts to colors in the heat maps, we typically saturate the range of counts between the 2nd and 98th percentiles of the values to utilize the dynamic range of the colors more effectively.
E/I balance heat map generation
The excitatory and inhibitory heat map values for individual neurons are scaled and shifted to lie in the [0, 1] interval. The absolute value of the difference, which again lies in the [0, 1] interval, is displayed.
Within-domain randomization for structural organization analysis
For each neuron, we first find all the nodes of the arbor trace in the domain of interest. The nodes that carry synapses on them have extra annotations reflecting the size and type of the synapses. Then, we reassign the size-and-type annotations to those nodes uniformly at random, thus leaving the structure of the arbor unchanged.
Branch-level synaptic rate correlation analysis
For each relevant branch (i.e., primary, intermediate, terminal) in each neuron, we count the synapses of interest and divide by the path length of that branch to obtain the density estimate. We calculate the correlation coefficient and the p-value pair for each plot using the corrcoef command in MATLAB.
Analysis software
The software used to generate the heat maps, the rate plots, and the within-domain randomization results is available at https://github.com/uygarsumbul/spines.
Quantification and statistical analysis of synaptic distribution data
Data is shown as the mean ± SEM, unless otherwise stated. T-tests was used to compare the mean of two groups with corrections for multiple comparisons: discovery determined using the Two-stage linear step-up procedure of Benjamini, Krieger and Yekutieli, with Q = 1%. A one-way ANOVA was used when more than two groups existed. Significance for all experiments was placed at p < 0.05. Statistical tests were carried out with GraphPad Prism.
Modeling
Reconstructed morphological data, synaptic attributes and spatial distribution of E and I synapses were taken from Vaa3D reconstructions. Modeling and simulation was performed using NEURON simulator, accessed using a python script (62). Specific membrane resistance and capacitance, and axial resistance were 12,000 Ωcm2, 1 µF/cm2, 150 Ωcm, respectively. These values were chosen such that the somatic input resistance and time constant will be within known biological ranges for these neurons (92 ± 15MΩ and 12 ms, respectively (63)). Active membrane ion channels were taken from the Blue Brain Project models of L2/3 PNs (64) and tuned to produce similar results to that found in vivo for L2/3 PNs (60). The activation of excitatory and inhibitory synapses was randomly sampled from a Poisson distribution with an average of 1.75 Hz and 10 Hz for the E and I synapses, respectively. This generated a mean somatic firing rate for the 10 modeled cells of 4.6 ± 3.6 Hz, similar to that found experimentally (31). The synaptic peak conductance for the Esynapses was 0.4 nS (for α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) component as well as for the N-methyl-D-aspartate (NMDA) components) and 1 nS for the γ-Aminobutyric acid (GABAA) synapses. The rise time constants for the conductances of these synapses was 0.2 ms, 2.04 ms and 0.18 ms, respectively and the respective decay time was 1.7 ms, 75.2 ms and 1.7 ms. The reversal potential values are 0 mV, 0 mV, and −80 mV, respectively. Dendritic voltage traces were recorded from the center of the respective dendritic branch.
Fitting model to in vitro experiment results
To ensure that our model captures important aspects of dendritic nonlinearities and voltage attenuation, we tuned the Na+ and Ih membrane conductances to replicate two experiments as in Waters et al, 2003. In order to replicate the attenuation of the back-propagating action potential along the apical trunk in L2/3 PN as in Figure 6C, a step depolarization current of 200 pA for 200 ms was injected to the modelled soma, invoking a somatic action potential, and recorded the amplitude at 10 µm intervals along the apical trunk (Figure 6D). To replicate the contribution of Na+ channels to the backpropagation of action potentials (Figure 6E), we have injected 200 pA for 200 ms to the soma, invoking an action potential, and recorded the voltage both at the soma and 80 µm from the soma on the apical trunk. Then, we simulated the application of TTX by removing the Na+ channels from the model, voltage clamping the soma to the voltage trace created by the action potential, and recording the amplitude of the passively propagated action potential 80 µm from the soma on the apical trunk (Figure 6F). The model (Figures 6D and 6F) was able to replicate the experimental results (Figures 6C and 6E) of both the attenuation and the dependency on Na+ channels of the back-propagating action potential.
As found experimentally (31), our L23 PN models produced a range of firing rates; some cells fire at high rate (10 Hz, red circle in Figures 6G-6I recorded) and some fire at low rate (3 Hz, blue circle in Figures 6G-6I). This variance in somatic firing rate persisted despite that fact that all models have the same passive and active properties and E and I input frequencies. We found that the global E/I balance per cell (Figure 6G) was a strong indicator of the output firing rate (Figure 7F). Additionally, we found that the somatic firing rate is correlated with the size of the cell, the larger the surface area of the cell, the lower is its firing rate (Figure 6H). This is due to the interesting experimental finding that larger cells have lower global E/I ratio and, consequently, that their firing rate is lower (Figure 6I).
Changing E/I ratio variance across dendritic domains
To study the influence of the ratio of excitatory and inhibitory synapses in a given dendritic branch, we iteratively increased or decreased the variance of E/I ratios over all branches belonging to a given domain. To change the E/I ratio variance, we randomly distributed the location of synapses between branches, while keeping the total number of synapses in the domain fixed (as found experimentally for the respective modeled cell). This process was repeated ten times, each time with a different initial distribution of the synapses. In Figures 7D and 7E and Figure S6 the voltage time integral (in a time window of 3000 sec) was computed at the center of each branch in a particular domain, for different E/I SD, averaged over all branches in that domain. The same was performed for the somatic firing rates (Figure 7F) for different E/I SD in the basal terminal domain.
Contribution of synapses in a domain to voltage in that domain
To measure the contribution of synapses located in a specific domain to the depolarization in that domain, we simulated each of the modeled cell with excitatory and inhibitory synapses as described above, and calculated the mean voltage time-integral in each domain. We then calculated the respective mean voltage time-integral when all synapses in that domain were not active and compared the two cases (Figure S7A).
SOFTWARE DEVELOPMENT
Computational pipeline overview
Information for dendritic spine placement and morphology was acquired from large-volume high-resolution image stacks of thick brain tissue. There are two possible strategies for quantifying the spatial distribution of excitatory and inhibitory (E and I) synapses of an entire neuron:
Stitch image volumes together prior to analysis.
Analyze each image volume independently and align the spatial information recorded from each image to create a complete neuron representation.
The first strategy, which involves all the image stacks into a terabyte volume and then perform neuron tracing, synapse segmentation and spatial analysis globally on the combined volume. The downside of the approach is a big data problem of manipulating, storing and analyzing the giant volume. Additionally, this approach is computationally wasteful because only a fraction of the stitched volume contains relevant structure. To avoid this big data problem, we pursued the alternative strategy of performing dendrite tracing and synapse segmentation on each image stack individually and associating morphological information of each synapse to a specific node of the trace (thereby encoding the location of every synapse within the spatial context of the neuron). To create representations of complete neurons across serial vibratome sections, dendrite traces containing synaptic information were aligned and stitched together. In comparison with the terabyte combined volume generated by the first reconstruction strategy, the resulting reconstructions are 4-6 megabytes in size.
Our pipeline for whole-neuron synaptic reconstruction consists of two parts. In the first part, we extract E and I synaptic information for an individual image across a tissue section (Figure S1A). For each image stack, we trace the dendritic arbor of the neuron fragment using automatic tracing methods followed by manual corrections. Then both Spine Detector and IS Detector take the neuron skeleton and the image stack as input to automatically isolate spines and inhibitory synapses within a user-defined radius of each dendrite. Spine Detector generates a table that records the local information of dendritic spines including the distance between each synapse and the dendrite, volume, and the nearest tree node. IS Detector generates a table that records the local information of inhibitory synapses including volume, whether the inhibitory synapse is located on a spine or the dendrite, and the nearest tree node. These morphological characteristics of synapses impact their neurotransmitter content and integration properties (43, 65-67).
In the second part of our reconstruction pipeline, we map E and I synaptic morphology across multiple images for whole-neuron spatial distribution analysis (Figure S1B). First, the dendritic spine information and inhibitory synaptic information from each image are mapped to the closest tree node of their corresponding dendrite trace. Next, the traces containing local synaptic information from each image stack are aligned and stitched together to generate a whole-neuron synaptic reconstruction. Notably, the association between synapses and their respective tree nodes remains unchanged during the assembly. After obtaining the single reconstruction trace of the whole neuron, we subtype the dendritic arbor in terms of identity and morphology so that we can analyze the synaptic features within domain and segment levels.
Neuron reconstruction
Digital reconstructions, or traces, are an effective representation of neuronal topology and geometry. The traces are usually described using a tree graph and consist of 3-D point coordinates, diameters, and connectivity between points. This succinct representation enables an extensive quantitative analyses of the geometrical organization of the neurons they represent including total length, branching angles, distribution statistics and cumulative distance from the soma (68). Numerous automated tracing methods have been developed (69-71). In this paper, the initial reconstructions are obtained using the automatic tracing methods built in the open source 3D visualization and analysis tool Vaa3D (52). Then, experts manually proofread the traces and make adjustments with the built-in proof-editing tools. Notably our synapse analysis pipeline works for traces generated by all tracing methods. Accurate reconstructions are important to improve the performance of automatic synapse detection.
Automatic spine detection
To automatically identify potential spines, Spine Detector segments candidate spine-associated voxels whose fluorescence is greater than a linearly interpolated local threshold between nodes along the closest dendritic segment (72). Spine detection is performed within a user-defined region around the dendrite and intensity threshold such that all voxels within the user-defined region and above the threshold are identified possible spine voxels. Spine Detector takes both the image and the dendritic trace as input and clusters adjacent voxels in the cell-fill channel based on their distance from the dendrite surface. Touching spines are separated based on voxel intensities. Because the dendrite traces represent the dendrites with a series of overlapping nodes (73), information about the volume and distance from the dendrite of each spine can be associated with its nearest node to assign a location within the spatial context of the dendritic arbor.
Voxel clustering for enhanced detection
In contrast to previous approaches that estimate spine volume from the spine tip backward toward the dendrite (72), Spine Detector identifies potential spine voxels at the dendrite shaft and estimates their volume by iteratively adding layers of connected voxels toward the spine tips. To quickly estimate the minimum distance between each voxel and the nearest dendrite surface, Spine Detector uses the radius of each node across the neuron trace as a representation of the dendrite surface and performs a distance transform on the image (Figures S2C and S2D). The initial seeds of potential spines are the voxels the shortest distance from the dendrite surface. In each iteration, potential spines are identified and grown by adding new layers of connected neighbor-voxels until a spine edge is detected. This is achieved by establishing a floor value to the distance between the initial seeds and the dendrite surface and repeatedly adding layers of connected neighbor-voxels equal to the floor value of the previous layer. At the end of each iteration, Spine Detector determines whether the number of voxels have exceeded the user-defined spine size and whether the maximum layer width has exceeded the user-defined layer width. If the most recently added layer did not meet these criteria, all previous layers are discarded and the voxels in that layer serve as the seed for the next layer. The iteration stops when all qualified voxels are assessed. Spine candidates are rejected based on user-supplied parameters for minimum voxel count and minimum spine length, allowing users to reconstruct images acquired at different magnifications. Notably, spines can be detected with this methodology regardless of the resolution of the spine neck.
Intensity-based segmentation of adjacent spines
Limited image resolution, inaccurate thresholding, and physical proximity can all give rise to adjacent spines incorrectly categorized as a single synapse. Based on the observation that spine voxel intensities are naturally brighter at the center than the edges, we adopted an adapted watershed algorithm to separate spines within close spatial proximity (74). First an initial threshold is set at a relatively high fluorescence intensity so that only the center-voxels of spines are identified (Figure S2E). With the successively decreasing fluorescence toward the spine border, the spine boundary grows in size. When two potential spine boundaries meet they each become defined to separate adjacent spines. The merger of two spine volumes is only considered when both spines are relatively small (lower than 1% of the average volume).
Inhibitory synapse detection
We labeled inhibitory synapses using the scaffolding protein Gephyrin tagged with a fluorescent protein as a marker (9). Because these synapses can only occur on the dendrites or the spines of neurons of interest, we use the image from the cell-fill channel containing the dendrites and the spines as a mask image to extract the relevant region for the inhibitory synaptic marker. Then, signal beyond user-input parameters for minimum/maximum voxel count and distance from the trace is excluded and potential inhibitory synapses from the resulting image are identified based on a user-input intensity threshold. Users have the ability to accept or reject potential inhibitory synapses, adjust their volume, and assign them as dendrite-targeting or spine-targeting.
Stitching neuron traces across serial 3D image sections
To assemble the neuron reconstructions traced across multiple image stacks we used Neuron Stitcher (36), a software suite for stitching non-overlapping neuron fragments in serial 3D image sections. The software identifies severed neurite traces at the section planes, known as ‘border tips’, and then uses a triangle matching algorithm to align traces created from neurons spanning serial tissue sections. Once the initial border tip matches are identified, the alignment is estimated in the form of an affine transformation and the border tips are connected to form a complete neuron trace.
Neurite subtyping
To better understand the synaptic distribution within domain and segment levels, we developed the Subtree Labeling program as a plug-in of Vaa3D to subtype neurites for further analysis. Using this program it is possible to assign a neurite segment into multiple categories: axon, soma, apical trunk, apical tufts, apical oblique dendrites, and basal dendrites. The user interface allows the user to select the starting vertex for each branch and to assign neurite type. The program first finds the tree node for soma and sorts the tree with the soma node as the tree root. Then, all the child vertices of the starting vertex are assigned the same branch type as each manually annotated starting vertex.
USER’S GUIDE
Synapse Detector Interactive User Interface
To broaden the utility of SynapseDetector to work with a variety of different data acquisition processes, we designed an interactive interface to (1) allow visual evaluation of detection results and accept or reject putative synapses; and (2) enable manual correction of synaptic volume through addition or subtraction of associated pixels. The software was implemented in C/C++ as a plugin of Vaa3D, which is a publicly available open source platform with a user-friendly interface for 3D+ image analysis and visualization. In the following sections, we will introduce how to use the tools. For detailed directions how to create neuron traces using Vaa3D, see the recently published protocol (52).
Main website: http://vaa3d.org/
Documentation: http://code.google.com/p/vaa3d/
Help/DiscussionForum: http://www.nitrc.org/forum/forum.php?forum_id=1553
Bug tracking and requesting new features: http://www.nitrc.org/tracker/?group_id=379
Sorting dendrite traces for reconstruction
A dendrite trace (swc file) is composed of a series of connected nodes with varying radii. This plugin connects nodes that were not linked during manual trace editing, which is critical for proper segment classification. This plugin allows the user to designate the soma as the “root node,” the first node in the tree from which the distance to all daughter nodes can be determined to analyze synaptic distribution.
In Vaa3D, drag a neuron trace into the 3D viewer.
Use ‘Cmd/Ctrl+L’ to toggle between the line (skeleton) display mode and the surface mesh display mode of the neuron. In line display mode it is possible to visualize root nodes contained within the trace.
If the trace contains a soma, hover cursor over soma to identify the node number that will be designated as the root node.
In Vaa3D, go to the ‘Plug-in’ main window menu and click ‘neuron_utilities’, then click on ‘sort_neuron_swc’, and finally click on ‘sort_swc’.
Select the trace in the ‘Open from 3D Viewer’ tab.
If the trace contains a soma, specify the root node number as the soma node number. If the trace does not contain a soma, click ‘cancel’.
Specify a voxel threshold for adjacent segments to be connected. To connect all segments click ‘cancel’. Save the sorted neuron trace.
Resampling dendrite traces for reconstruction
To maximize the spatial resolution of synaptic distribution analysis, it is recommended to resample the associated neuron trace to contain the highest possible number of tree nodes.
In Vaa3D, go to the ‘Plug-in’ main window menu and click ‘neuron_utilities’, then click on ‘resample_swc’, and finally click on ‘resample’.
Select the trace and specify a step length of 1. Click ‘ok’ and save the resampled neuron trace.
Using Crop Image Trace to analyze large image volumes
This new tool allows the user to analyze image volumes with Synapse Detector that would normally be too large by cropping a region of interest based on XYZ pixel coordinates and aligning an associated neuron trace to the resulting image volume. In practice, image volumes greater than 2000 x 2000 pixels in X and Y and 500 pixels in Z are difficult to reconstruct without cropping.
In Vaa3D, use ‘Cmd/Ctrl+O’ to open the appropriate image file.
In the tri-view window, click ‘see in 3D’ and then click ‘entire image’ to visualize the image file.
Drag and drop the neuron trace corresponding to the image file into the 3D view window.
Go to the ‘Plug-in’ main window menu and click ‘image_geometry’,andthen‘crop_image_tace’, and finally click on ‘crop’.
Select an appropriate output directory, and specify the XYZ coordinates to crop the image (the number of pixels in X, Y, and Z that compose each image can be viewed in the tri-view window and 3D viewer), and specify the color channels to include in the new image. Click on ‘run and save’.
Synapse annotation with Synapse Detector
This new tool semi-automatedly identifies dendritic spines (Spine Detector) or inhibitory synapses (IS Detector) and quantifies their morphology and spatial distribution. Synapses can be manually accepted or rejected, as well as edited by dilating or eroding pixels. IS Detector also allows the user to designate inhibitory synapse location on either a spine or the dendritic shaft.
Spine Detector user interface
In Vaa3D, go to the ‘Plug-in’ main window menu, click ‘synapse_detector’, and click on ‘SpineDetector_NewProject’. Users can also continue an existing project by clicking ‘SpineDetector_ExisitingProject’.
Load the image volume (v3dpbd or v3draw), associated trace file (swc), and designate an output destination for the sorted reconstruction. Select the color channel of the cell-fill.
Specify the threshold for background signal in the image and volume parameters for potential spines. Pixel to micron conversion can be calculated from the imaging magnification and is usually stored within the image properties. Click ‘Run’.
Click ‘Proofread by segment’ to edit spines along a dendrite segment (recommended) or ‘Proofread by spine’ to edit each spine individually.
Accept/reject potential spines and proofread spine morphology by dilating/eroding volume. The highlighted regions indicate the potential spines (Figure S1C). It is recommended to look at the segment at different angles and toggle between views with the spine annotation channel on and off in the 3D viewer.
Click ‘Save current result’ to save intermediate results during proofreading. Spine Detector will generate 4 files in the output folder: a text file ‘project.txt’ (includes all info needed to reload the last saved reconstruction project), a marker file indicating the positions of accepted/rejected spines, a csv file (table of accepted spine information), and an image file of accepted spines.
Click ‘Finish proofreading’ to save final results after proofreading. After proofreading is completed, Spine Detector generates 2 image files (edited spine reconstruction and isolated spine annotations), a marker file of spine positions, and a csv file containing spine morphology data (all data measured in pixels).
IS Detector user interface
In Vaa3D, go to the ‘Plug-in’ main window menu, click ‘synapse_detector’, and click on ‘IS_Detector_NewProject’. Users can also click on ‘IS_Detector_ExisitingProject’ to reload a previously saved project.
Load the image volume (v3dpbd or v3draw), associated trace file (swc), and designate an output destination for the sorted reconstruction. Select the color channel of the cell-fill and the color channel of the inhibitory synaptic marker (or other punctate intracellular marker).
Specify the threshold for background signal in both image channels and volume parameters for potential inhibitory synapses. Pixel to micron conversion can be calculated from the imaging magnification and is usually stored within the image properties. Click ‘Run’, and then click ‘Proofread by segment’.
Accept/reject potential inhibitory synapses and proofread morphology by dilating/eroding volume and specifying synapse location on spine/dendrite. The highlighted regions indicate the potential inhibitory synapses (Figure S1D). It is recommended to adjust the lookup table thresholds for synaptic visualization by clicking the ‘Vol Colormap’ button on the right-side control pane of the 3D viewer.
Click ‘Save current result’ to save intermediate results during proofreading. Spine Detector will generate 2 files in the output folder: a text file (includes all info needed to reload the last saved reconstruction project) and a csv file (table of accepted spine information).
Click ‘Finish proofreading’ to save final results after proofreading. After proofreading is completed, Spine Detector generates 2 image files (unedited and edited inhibitory synapses), a marker file of synaptic positions, and a csv file containing synaptic morphology data (all data measured in pixels).
Embedding synaptic data within the neuron trace
After spines and inhibitory synapses have been annotated throughout the image volume, synaptic information stored in tables can be associated with their corresponding nodes throughout the neuron trace using the Synapse Detector Combiner.
In Vaa3D, go to the ‘Plug-in’ main window menu click ‘synapse_detector’, and click on ‘Combiner’.
Load the spine and inhibitory synapse tables that correspond to the neuron trace. If the image volume was cropped before reconstruction the trace will be associated with tables from each cropped region. Click ‘Run’, and save the neuron reconstruction.
Assembling reconstruction fragments with Neuron Stitcher
For detailed directions how to stitch neuron traces using Neuron Stitcher, see the recently published protocol (36). To preserve synaptic information within the reconstruction, assemble reconstruction fragments to produce an eswc trace.
Annotating reconstruction traces with Subtree Labeling
This new tool creates an enhanced neuron skeleton that contains information about dendrite identity, branch order, and cumulative dendritic distance from the soma. The user interface allows the user to select the starting vertex for each branch and to assign neurite type. Child vertices of each starting vertex are assigned the same branch type as each manually annotated starting vertex. To label neuron reconstructions stitched from multiple fragments throughout the entire dendritic arbor, these traces must first be sorted with the Neuron Connector plugin to preserve the eswc file type.
In Vaa3D, go to the ‘Plug-in’ main window menu,click‘neuron_utilities’and‘neuron_connector’,andselect‘connect_neuron_swc’.
Load the input trace file and designate an output destination for the sorted reconstruction.
Set the ‘connection configuration’ to ‘connect all, shortest distance and click ‘Connect’.
After sorting the reconstruction, drag it into the 3D viewer.
Use ‘Cmd/Ctrl+L’ to toggle between the line (skeleton) display mode and the surface mesh display mode of the neuron. In line display mode it is possible to visualize root nodes contained within the trace.
Right-click at the soma to and click ‘create marker from the nearest neuron-node’ to create a marker at the root node. Create markers between the root node and dendrite terminals according to experiment-specific labeling schemes (Figure S1E).
In Vaa3D, go to the ‘Plug-in’ main window menu, click ‘neuron_utilities’, and then ‘subtree_labeling’.
Select ‘Refresh markers’ to ensure all markers were selected. Assign dendrite labels to each marker. It is possible to add new markers and click ‘Refresh markers’ to add them to the list of labeled markers. Markers will be labeled in descending order starting with marker 1, so it is recommended to place makers from the root node outward according to the labeling scheme.
Click ‘run labeling’. Review the neuron trace in the 3D viewer to verify segments were properly labeled and click ‘save’ within the Subtree Labeling interface window.
ACKNOWLEDGEMENTS
We thank Attila Losonczy, Wes Grueber, Inbal Israeli, Larry Abbott and members of the Polleux lab for fruitful discussions. This work was supported by grants from the NIH (RO1 NS067557 to F.P. and F31 NS101820 to D.M.I.), the NSF (1564736 to Y.L.), ARO MURI (W911NF-12-1-0594 to U.S.), and DoI/IBC IARPA (D16PC00008 to U.S.). I.S. was supported by grant agreement no. 604102 ‘Human Brain Project’ and by a grant from the Gatsby Charitable Foundation. Contributions: D.M.I. and F.P. designed the study. D.M.I. developed the labeling/imaging protocol and performed cloning, animal surgery, and imaging. Y.L. and H.P. developed the Synapse Detector and Subtree Labeling programs with assistance from D.M.I. for user interface design. U.S. developed the anatomical synaptic distribution analysis with assistance from D.M.I. and generated neuron heat maps. M.D. and I.S. performed computational modeling experiments in coordination with D.M.I. and F.P. H.C. developed the trace stitching program. D.M.I., V.A., and F.G. generated neuron reconstructions using Synapse Detector. D.M.I., Y.L., U.S., M.D., I.S., H.P., and F.P. wrote the paper.