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Morphology of spiny and basket cells analysed in study. (A) Spiny cell axons (blue lines) and dendritic (red lines) arbors of each neuron shown in coronal plane against approximate laminar boundaries (n = 10). (B) Basket cell axons (blue lines) and dendritic (red lines) arbors of each neuron shown in coronal plane aligned with approximate laminar boundaries (n = 9). Cell identifiers matched with results given in Table S1. For clarity, axonal boutons are not shown. (Anatomical axes: A, anterior; D, dorsal; M, medial).
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The brain contains a complex network of axons rapidly communicating information between billions of synaptically connected neurons. The morphology of individual axons, therefore, defines the course of information flow within the brain. More than a century ago, Ramón y Cajal proposed that conservation laws to save material (wire) length and limit co...
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Despite recent interest in reconstructing neuronal networks, complete wiring diagrams on the level of individual synapses remain scarce and the insights into function they can provide remain unclear. Even for Caenorhabditis elegans, whose neuronal network is relatively small and stereotypical from animal to animal, published wiring diagrams are nei...
Citations
... Other reconstructed layer 3 pyramidal neurons in cat cortex (cited in http://neuromorpho.org/) all matched the canonical form used by Binzegger et al. (2004): in the deep layers, their axons arborized mainly in layer 5 and may have continued through layer 6 with a non-branching axon to reach the white matter (Hirsch et al. 2002;Martinez et al. 2005;Volgushev et al. 2006;Budd et al. 2010). (Note that the neuron reconstructed by Stepanyants et al. (2008) is actually listed in the neuromorpho database, but linked to a different publication: http://neuromorpho.org/neuron_info. ...
The cat primary visual cortex (V1) is a cortical area for which we have one of the most detailed estimates of the connection ‘weights’ (expressed as number of synapses) between different neural populations in different layers (Binzegger et al in J Neurosci 24:8441–8453, 2004). Nevertheless, the majority of excitatory input sources to layer 6, the deepest layer in a local translaminar excitatory feedforward loop, was not accounted for by the known neuron types used to generate the quantitative Binzegger diagram. We aimed to fill this gap by using a retrograde tracer that would label neural cell bodies in and outside V1 that directly connect to layer 6 of V1. We found that more than 80% of labeled neurons projecting to layer 6 were within V1 itself. Our data indicate that a substantial fraction of the missing input is provided by a previously unidentified population of layer 3/4 border neurons, laterally distributed and connecting more strongly to layer 6 than the typical superficial layer pyramidal neurons considered by Binzegger et al. (Binzegger et al in J Neurosci 24:8441–8453, 2004). This layer 3/4 to layer 6 connection may be a parallel route to the layer 3 – layer 5 – layer 6 feedforward pathway, be associated with the fast-conducting, movement-related Y pathway and provide convergent input from distant (5–10 degrees) regions of the visual field.
... Once target points (target points are successively connected to the dendritic tree according to optimal wiring principles weighted by bf) are distributed within a cell-type specific dendritic density field, they can be connected to a tree structure according to these optimised wiring costs in e.g. fly [47] or mouse [48] dendrites as well as in some axons [49]. Given the general applicability of the method, here we investigate whether such morphological modelling can also be used to better understand and implement dendrite repair. ...
Investigating and modelling the functionality of human neurons remains challenging due to the technical limitations, resulting in scarce and incomplete 3D anatomical reconstructions. Here we used a morphological modelling approach based on optimal wiring to repair the parts of a dendritic morphology that were lost due to incomplete tissue samples. In Drosophila , where dendritic regrowth has been studied experimentally using laser ablation, we found that modelling the regrowth reproduced a bimodal distribution between regeneration of cut branches and invasion by neighbouring branches. Interestingly, our repair model followed growth rules similar to those for the generation of a new dendritic tree. To generalise the repair algorithm from Drosophila to mammalian neurons, we artificially sectioned reconstructed dendrites from mouse and human hippocampal pyramidal cell morphologies, and showed that the regrown dendrites were morphologically similar to the original ones. Furthermore, we were able to restore their electrophysiological functionality, as evidenced by the recovery of their firing behaviour. Importantly, we show that such repairs also apply to other neuron types including hippocampal granule cells and cerebellar Purkinje cells. We then extrapolated the repair to incomplete human CA1 pyramidal neurons, where the anatomical boundaries of the particular brain areas innervated by the neurons in question were known. Interestingly, the repair of incomplete human dendrites helped to simulate the recently observed increased synaptic thresholds for dendritic NMDA spikes in human versus mouse dendrites. To make the repair tool available to the neuroscience community, we have developed an intuitive and simple graphical user interface (GUI), which is available in the TREES toolbox ( www.treestoolbox.org ).
... To determine whether the average spacing between points varies non-uniformly between supposed fibers of passage and putative synapse-bearing axons, we separated the axonal branches in each presubiculum neuron based on Strahler (centripetal) order, namely order 1-3 (terminal, pre-terminal, and pre-pre-terminal branches) from order 4-6 (those more than 2 bifurcations away from an ending). This choice is justified by converging experimental evidence that cortical axons make most presynaptic contacts at Strahler orders 1-3, while boutons are substantially sparser at orders 4-6 45,46 . This is also consistent with the strongly non-uniform distribution of average branch length in the dataset investigated in this study, indicating more likely fibers of passage at Strahler order 4-6 (964.4 ± 1037.1 µm) than at Strahler order 1-3 (144.7 ± 80.2 µm; one-tail t-test p = 4.8 × 10 −11 ; t-value = −7.35; ...
We present a quantitative strategy to identify all projection neuron types from a given region with statistically different patterns of anatomical targeting. We first validate the technique with mouse primary motor cortex layer 6 data, yielding two clusters consistent with cortico-thalamic and intra-telencephalic neurons. We next analyze the presubiculum, a less-explored region, identifying five classes of projecting neurons with unique patterns of divergence, convergence, and specificity. We report several findings: individual classes target multiple subregions along defined functions; all hypothalamic regions are exclusively targeted by the same class also invading midbrain and agranular retrosplenial cortex; Cornu Ammonis receives input from a single class of presubicular axons also projecting to granular retrosplenial cortex; path distances from the presubiculum to the same targets differ significantly between classes, as do the path distances to distinct targets within most classes; the identified classes have highly non-uniform abundances; and presubicular somata are topographically segregated among classes. This study thus demonstrates that statistically distinct projections shed light on the functional organization of their circuit.
... Once target points are distributed within a 88 cell-type specific dendritic density field, they can be connected to a tree structure according 89 to these optimised wiring costs in e.g. fly (Cuntz et al., 2008) or mouse (Cuntz, 2012) as well 90 as in some axons (Budd et al., 2010). Given the general applicability of the method, here we 91 investigate whether such morphological modelling can also be used to better understand and 92 implement dendrite repair. ...
Investigating and modelling the functionality of human neurons remains challenging due to the technical limitations, resulting in scarce and incomplete 3D anatomical reconstructions. Here we used a morphological modelling approach based on optimal wiring to repair the parts of a dendritic morphology that were lost due to incomplete tissue samples. In Drosophila , where dendritic regrowth has been studied experimentally using laser ablation, we found that modelling the regrowth reproduced a bimodal distribution between regeneration of cut branches and invasion by neighbouring branches. Interestingly, our repair model followed growth rules similar to those for the generation of a new dendritic tree. To generalise the repair algorithm from Drosophila to mammalian neurons, we artificially sectioned reconstructed dendrites from mouse and human hippocampal pyramidal cell morphologies, and showed that the regrown dendrites were morphologically similar to the original ones. Furthermore, we were able to restore their electrophysiological functionality, as evidenced by the recovery of their firing behaviour. Importantly, we show that such repairs also apply to other neuron types including hippocampal granule cells and cerebellar Purkinje cells. We then extrapolated the repair to incomplete human CA1 pyramidal neurons, where the anatomical boundaries of the particular brain areas innervated by the neurons in question were known. Interestingly, the repair of incomplete human dendrites helped to simulate the recently observed increased synaptic thresholds for dendritic NMDA spikes in human versus mouse dendrites. To make the repair tool available to the neuroscience community, we have developed an intuitive and simple graphical user interface (GUI), which is available in the TREES Toolbox ( www.treestoolbox.org ).
In brief
We use morphological modelling inspired by the regeneration of various artificially cut neuron types and repair incomplete human and nonhuman neuronal dendritic reconstructions.
Author summary
Reconstructing neuronal dendrites by drawing their 3D branching structures in the computer has proven to be crucial for interpreting the flow of electrical signals and therefore the computations that dendrites implement on their inputs. These reconstructions are tedious and prone to disruptive limitations imposed by experimental procedures. In recent years, complementary computational procedures have emerged that reproduce the fine details of morphology in theoretical models. These models allow, for example, to populate large-scale neural networks and to study structure-function relationships. In this work we use a morphological model based on optimised wiring for signal conduction and material cost to repair faulty reconstructions, in particular those of human hippocampal dendrites, which are rare and precious but often cut due to technical limitations. Interestingly, we find that our synthetic repair mechanism reproduces the two distinct modes of repair observed in real dendrites: regeneration from the severed branch and invasion from neighbouring branches. Our model therefore provides both a useful tool for single-cell electrophysiological simulations and a useful theoretical concept for studying the biology of dendrite repair.
Highlights
Optimal wiring-based growth algorithm replicates regrowth of artificially cut dendrites
The growth algorithm repairs cut dendrites in incomplete reconstructions
The algorithm works for diverse neuron types in multiple species
The repair of morphology restores original electrophysiology
The repair of morphology supports simulations of high synaptic thresholds for NMDA spikes in human dendrites
The repair tool with user interface is available in the TREES Toolbox
... Axon distribution and trajectory are widely accepted criteria of neuronal classification schemes in several CNS regions, such as the cerebral cortex (DeFelipe et al., 2013;Markram et al., 2015) or hippocampus (Klausberger & Somogyi, 2008;Pelkey et al., 2017). Identification of axonal termination fields and their target domains, based on detailed axonal reconstructions, largely advanced our understanding of the function of microcircuits in several brain regions (Budd et al., 2010;Karube & Kisvarday, 2011;Maccaferri et al., 2000). Furthermore, high-resolution spatial maps and quantitative data derived from single-axon reconstructions provided a novel perspective on several aspects of cortical connectivity (Rockland, 2020). ...
Our knowledge about the detailed wiring of neuronal circuits in the spinal dorsal horn (DH), where initial sensory processing takes place, is still very sparse. While a substantial amount of data is available on the somatodendritic morphology of DH neurons, the laminar and segmental distribution patterns and consequential function of individual axons are much less characterized. In the present study, we fully reconstructed the axonal and dendritic processes of 10 projection neurons (PNs) and 15 interneurons (INs) in lamina I of the rat, to reveal quantitative differences in their distribution. We also performed whole‐cell patch‐clamp recordings to test the predicted function of certain axon collaterals. In line with our earlier qualitative description, we found that lamina I INs in the lateral aspect of the superficial DH send axon collaterals toward the medial part and occupy mostly laminae I–III, providing anatomical basis for a lateromedial flow of information within the DH. Local axon collaterals of PNs were more extensively distributed including dorsal commissural axon collaterals that might refer to those reported earlier linking the lateral aspect of the left and right DHs. PN collaterals dominated the dorsolateral funiculus and laminae IV–VI, suggesting propriospinal and ventral connections. Indeed, patch‐clamp recordings confirmed the existence of a dorsoventral excitatory drive upon activation of neurokinin‐1 receptors that, although being expressed in various lamina I neurons, are specifically enriched in PNs. In summary, lamina I PNs and INs have almost identical dendritic input fields, while their segmental axon collateral distribution patterns are distinct. INs, whose somata reside in lamina I, establish local connections, may show asymmetry, and contribute to bridging the medial and lateral halves of the DH. PNs, on the other hand, preferably relay their integrated dendritic input to deeper laminae of the spinal gray matter where it might be linked to other ascending pathways or the premotor network, resulting in a putative direct contribution to the nociceptive withdrawal reflex. Quantitative analyses of spinal lamina I projection neurons (PNs) and interneurons (INs) revealed almost identical dendritic patterns but local axon collateral distribution patterns that are distinct. INs mostly establish connections within the superficial dorsal horn and may bridge its medial and lateral halves. PNs also relay their input locally, to deeper laminae of the spinal gray matter and may link other ascending systems and participate directly in the nociceptive withdrawal reflex.
... [72]), these studies indicate that dendrite morphology is well constrained by optimal wiring alone (if defined as optimal dendritic structure for minimizing the cable length and the conduction time [68,70]). Similar observations have been made for axonal connections [43,[73][74][75][76] (but see also [77]). Therefore, in this article we focus mostly on the conductance space and do not discuss the morphological space of population neuronal models and its impact on the variability and robustness of electrophysiological behaviour (for this topic see e.g. ...
Neurons encounter unavoidable evolutionary trade-offs between multiple tasks. They must consume as little energy as possible while effectively fulfilling their functions. Cells displaying the best performance for such multi-task trade-offs are said to be Pareto optimal, with their ion channel configurations underpinning their functionality. Ion channel degeneracy, however, implies that multiple ion channel configurations can lead to functionally similar behaviour. Therefore, instead of a single model, neuroscientists often use populations of models with distinct combinations of ionic conductances. This approach is called population (database or ensemble) modelling. It remains unclear, which ion channel parameters in the vast population of functional models are more likely to be found in the brain. Here we argue that Pareto optimality can serve as a guiding principle for addressing this issue by helping to identify the subpopulations of conductance-based models that perform best for the trade-off between economy and functionality. In this way, the high-dimensional parameter space of neuronal models might be reduced to geometrically simple low-dimensional manifolds, potentially explaining experimentally observed ion channel correlations. Conversely, Pareto inference might also help deduce neuronal functions from high-dimensional Patch-seq data. In summary, Pareto optimality is a promising framework for improving population modelling of neurons and their circuits.
... Our analyses indicate that the tortuosity of bouton-forming axonal segments of pyramidal cells is an invariable property and, therefore, neurons save material and use other strategies in finding their specific targets (Anderson et al., 2002;Budd et al., 2010). We found that all variables related to bouton placement differed significantly between patch and no-patch axons. ...
Axonal patches are known as the major sites of synaptic connections in the cerebral cortex of higher order mammals. However, the functional role of these patches is highly debated. Patches are formed by populations of nearby neurons in a topographic manner and are recognized as the termination fields of long-distance lateral connections within and between cortical areas. In addition, axons form numerous boutons that lie outside the patches, whose function is also unknown. To better understand the functional roles of these two distinct populations of boutons, we compared individual and collective morphological features of axons within and outside the patches of intra-areal, feedforward, and feedback pathways by way of tract tracing in the somatosensory cortex of New World monkeys. We found that, with the exception of tortuosity, which is an invariant property, bouton spacing and axonal convergence properties differ significantly between axons within patch and no-patch domains. Principal component analyses corroborated the clustering of axons according to patch formation without any additional effect by the type of pathway or laminar distribution. Stepwise logistic regression identified convergence and bouton density as the best predictors of patch formation. These findings support that patches are specific sites of axonal convergence that promote the synchronous activity of neuronal populations. On the other hand, no-patch domains could form a neuroanatomical substrate to diversify the responses of cortical neurons.
... Thus, although many open questions about the relationship between morphology and biophysics in neuronal models remain (see e.g., Stiefel and Torben-Nielsen, 2014), these studies indicate that dendrite morphology is well constrained by optimal wiring alone. Similar observations have been made for axonal connections (Chen et al., 2006;Budd et al., 2010;Avena-Koenigsberger et al., 2014;Ollé-Vila et al., 2020;Ma et al., 2021; but see also Stiefel et al., 2013). Therefore, in this article we focus mostly on the conductance space and do not discuss the morphological space of population neuronal models and its impact on the variability and robustness of electrophysiological behavior (for this topic see e.g., Beining et al., 2017;Cuntz et al., 2021) or their potential interactions. ...
Nerve cells encounter unavoidable evolutionary trade-offs between multiple tasks. They must consume as little energy as possible (be energy-efficient or economical) but at the same time fulfil their functions (be functionally effective). Neurons displaying best performance for such multi-task trade-offs are said to be Pareto optimal. However, it is not understood how ion channel parameters contribute to the Pareto optimal performance of neurons. Ion channel degeneracy implies that multiple combinations of ion channel parameters can lead to functionally similar neuronal behavior. Therefore, to simulate functional behavior, instead of a single model, neuroscientists often use populations of valid models with distinct ion conductance configurations. This approach is called population (also database or ensemble) modeling. It remains unclear, which ion channel parameters in a vast population of functional models are more likely to be found in the brain. Here we propose that Pareto optimality can serve as a guiding principle for addressing this issue. The Pareto optimum concept can help identify the subpopulations of conductance-based models with ion channel configurations that perform best for the trade-off between economy and functional effectiveness. In this way, the high-dimensional parameter space of neuronal models might be reduced to geometrically simple low-dimensional manifolds. Therefore, Pareto optimality is a promising framework for improving population modeling of neurons and their circuits. We also discuss how Pareto inference might help deduce neuronal functions from high-dimensional Patch-seq data. Furthermore, we hypothesize that Pareto optimality might contribute to our understanding of observed ion channel correlations in neurons.
... Following the quantification of the geometrical features of neurons, astrocytes, and the vasculature, it was apparent that there was a systematic order-of-magnitude difference between them. The data suggested there is a hierarchy in cortical composition, the origin of which has been theorized in terms of length (Klyachko and Stevens 2003;Wen et al. 2009), conduction delay (Budd et al. 2010), volume or/and spine economy (Karbowski 2015) minimization. Most importantly, we showed here that an in silico circuit of the NGV architecture can indeed be used to investigate questions concerning the intricacies of cortical composition and their relation to computational capacity. ...
... Also, the lower average density of the P14 rat neuropil combined with the partially ramified morphologies resulted in a volume occupancy that was 6% lower than reported values for adult animals. The data suggested there is a hierarchy in cortical composition, the origin of which has been theorized in terms of length (Klyachko and Stevens 2003;Wen et al. 2009), conduction delay (Budd et al. 2010), volume or/and spine economy (Karbowski 2015) minimization. Finally, we showed that an in silico circuit of the NGV architecture could indeed be used to simultaneously quantify both compositional (densities, wiring, surface areas, and volume) and organizational (connectivities, distance distributions, correlations) aspects of its entities, as well as to investigate questions concerning the intricacies of cortical composition and their relation to computational capacity. ...
Astrocytes connect the vasculature to neurons mediating the supply of nutrients and biochemicals. They are involved in a growing number of physiological and pathophysiological processes that result from biophysical, physiological, and molecular interactions in this neuro-glia-vascular ensemble (NGV). The lack of a detailed cytoarchitecture severely restricts the understanding of how they support brain function. To address this problem, we used data from multiple sources to create a data-driven digital reconstruction of the NGV at micrometer anatomical resolution. We reconstructed 0.2 mm3 of the rat somatosensory cortex with 16 000 morphologically detailed neurons, 2500 protoplasmic astrocytes, and its microvasculature. The consistency of the reconstruction with a wide array of experimental measurements allows novel predictions of the NGV organization, allowing the anatomical reconstruction of overlapping astrocytic microdomains and the quantification of endfeet connecting each astrocyte to the vasculature, as well as the extent to which they cover the latter. Structural analysis showed that astrocytes optimize their positions to provide uniform vascular coverage for trophic support and signaling. However, this optimal organization rapidly declines as their density increases. The NGV digital reconstruction is a resource that will enable a better understanding of the anatomical principles and geometric constraints, which govern how astrocytes support brain function.
... Furthermore, our algorithm can be further extended, improved, and possibly integrated with already in-use techniques to overcome important limitations such as the detection of inhibitory connections and the inference of effective connectivity in the bursting regime. Importantly, spatiotemporal information is implicitly contained in the estimated connectivity and delay map; we expect therefore that, when used in combination with novel computational methodologies (Budd et al., 2010;Puppo et al., 2018;Silva, 2019), our method will help reveal more fundamental network properties crucial to the understanding of the relationships between network topology, dynamic signaling, and network functions in healthy and disease models. ...
Despite advancements in the development of cell-based in-vitro neuronal network models, the lack of appropriate computational tools limits their analyses. Methods aimed at deciphering the effective connections between neurons from extracellular spike recordings would increase utility of in vitro local neural circuits, especially for studies of human neural development and disease based on induced pluripotent stem cells (hiPSC). Current techniques allow statistical inference of functional couplings in the network but are fundamentally unable to correctly identify indirect and apparent connections between neurons, generating redundant maps with limited ability to model the causal dynamics of the network. In this paper, we describe a novel mathematically rigorous, model-free method to map effective—direct and causal—connectivity of neuronal networks from multi-electrode array data. The inference algorithm uses a combination of statistical and deterministic indicators which, first, enables identification of all existing functional links in the network and then reconstructs the directed and causal connection diagram via a super-selective rule enabling highly accurate classification of direct, indirect, and apparent links. Our method can be generally applied to the functional characterization of any in vitro neuronal networks. Here, we show that, given its accuracy, it can offer important insights into the functional development of in vitro hiPSC-derived neuronal cultures.
