Statistical connectivity provides a sufficient foundation for specific functional connectivity in neocortical neural microcircuits

Fractal Resonance: Can Fractal Geometry Be Used to Optimize the Connectivity of Neurons to Artificial Implants?

In parallel to medical applications, exploring how neurons interact with the artificial interface of implants in the human body can be used to learn about their fundamental behavior. For both fundamental and applied research, it is important to determine the conditions that encourage neurons to maintain their natural behavior during these interactions. Whereas previous biocompatibility studies have focused on the material properties of the neuron-implant interface, here we discuss the concept of fractal resonance - the possibility that favorable connectivity properties might emerge by matching the fractal geometry of the implant surface to that of the neurons.To investigate fractal resonance, we first determine the degree to which neurons are fractal and the impact of this fractality on their functionality. By analyzing three-dimensional images of rat hippocampal neurons, we find that the way their dendrites fork and weave through space is important for generating their fractal-like behavior. By modeling variations in neuron connectivity along with the associated energetic and material costs, we highlight how the neurons' fractal dimension optimizes these constraints. To simulate neuron interactions with implant interfaces, we distort the neuron models away from their natural form by modifying the dendrites' fork and weaving patterns. We find that small deviations can induce large changes in fractal dimension, causing the balance between connectivity and cost to deteriorate rapidly. We propose that implant surfaces should be patterned to match the fractal dimension of the neurons, allowing them to maintain their natural functionality as they interact with the implant.

Controlling morpho-electrophysiological variability of neurons with detailed biophysical models

Variability, which is known to be a universal feature among biological units such as neuronal cells, holds significant importance, as, for example, it enables a robust encoding of a high volume of information in neuronal circuits and prevents hypersynchronizations. While most computational studies on electrophysiological variability in neuronal circuits were done with single-compartment neuron models, we instead focus on the variability of detailed biophysical models of neuron multi-compartmental morphologies. We leverage a Markov chain Monte Carlo method to generate populations of electrical models reproducing the variability of experimental recordings while being compatible with a set of morphologies to faithfully represent specifi morpho-electrical type. We demonstrate our approach on layer 5 pyramidal cells and study the morpho-electrical variability and in particular, find that morphological variability alone is insufficient to reproduce electrical variability. Overall, this approach provides a strong statistical basis to create detailed models of neurons with controlled variability.

Integrating EM and Patch-seq data: Synaptic connectivity and target specificity of predicted Sst transcriptomic types

Neural circuit function is shaped both by the cell types that comprise the circuit and the connections between those cell types ¹ . Neural cell types have previously been defined by morphology ^{2, 3} , electrophysiology ^{4, 5} , transcriptomic expression ^6-8 , connectivity ^9-13 , or even a combination of such modalities ^14-16 . More recently, the Patch-seq technique has enabled the characterization of morphology (M), electrophysiology (E), and transcriptomic (T) properties from individual cells ^17-20 . Using this technique, these properties were integrated to define 28, inhibitory multimodal, MET-types in mouse primary visual cortex ²¹ . It is unknown how these MET-types connect within the broader cortical circuitry however. Here we show that we can predict the MET-type identity of inhibitory cells within a large-scale electron microscopy (EM) dataset and these MET-types have distinct ultrastructural features and synapse connectivity patterns. We found that EM Martinotti cells, a well defined morphological cell type ^{22, 23} known to be Somatostatin positive (Sst+) ^{24, 25} , were successfully predicted to belong to Sst+ MET-types. Each identified MET-type had distinct axon myelination patterns and synapsed onto specific excitatory targets. Our results demonstrate that morphological features can be used to link cell type identities across imaging modalities, which enables further comparison of connectivity in relation to transcriptomic or electrophysiological properties. Furthermore, our results show that MET-types have distinct connectivity patterns, supporting the use of MET-types and connectivity to meaningfully define cell types.

Thalamic control of sensory processing and spindles in a biophysical somatosensory thalamoreticular circuit model of wakefulness and sleep

Thalamoreticular circuitry plays a key role in arousal, attention, cognition, and sleep spindles, and is linked to several brain disorders. A detailed computational model of mouse somatosensory thalamus and thalamic reticular nucleus has been developed to capture the properties of over 14,000 neurons connected by 6 million synapses. The model recreates the biological connectivity of these neurons, and simulations of the model reproduce multiple experimental findings in different brain states. The model shows that inhibitory rebound produces frequency-selective enhancement of thalamic responses during wakefulness. We find that thalamic interactions are responsible for the characteristic waxing and waning of spindle oscillations. In addition, we find that changes in thalamic excitability control spindle frequency and their incidence. The model is made openly available to provide a new tool for studying the function and dysfunction of the thalamoreticular circuitry in various brain states.

Towards a mesoscale physical modeling framework for stereotactic-EEG recordings

Objective.Stereotactic-electroencephalography (SEEG) and scalp EEG recordings can be modeled using mesoscale neural mass population models (NMMs). However, the relationship between those mathematical models and the physics of the measurements is unclear. In addition, it is challenging to represent SEEG data by combining NMMs and volume conductor models due to the intermediate spatial scale represented by these measurements.Approach.We provide a framework combining the multi-compartmental modeling formalism and a detailed geometrical model to simulate the transmembrane currents that appear in layer 3, 5 and 6 pyramidal cells due to a synaptic input. With this approach, it is possible to realistically simulate the current source density (CSD) depth profile inside a cortical patch due to inputs localized into a single cortical layer and the induced voltage measured by two SEEG contacts using a volume conductor model. Based on this approach, we built a framework to connect the activity of a NMM with a volume conductor model and we simulated an example of SEEG signal as a proof of concept.Main results.CSD depends strongly on the distribution of the synaptic inputs onto the different cortical layers and the equivalent current dipole strengths display substantial differences (of up to a factor of four in magnitude in our example). Thus, the inputs coming from different neural populations do not contribute equally to the electrophysiological recordings. A direct consequence of this is that the raw output of NMMs is not a good proxy for electrical recordings. We also show that the simplest CSD model that can accurately reproduce SEEG measurements can be constructed from discrete monopolar sources (one per cortical layer).Significance.Our results highlight the importance of including a physical model in NMMs to represent measurements. We provide a framework connecting microscale neuron models with the neural mass formalism and with physical models of the measurement process that can improve the accuracy of predicted electrophysiological recordings.

Neural Assemblies as Precursors for Brain Function

This concept paper gives a narrative about intelligence from insects to the human brain, showing where evolution may have been influenced by the structures in these simpler organisms. The ideas also come from the author’s own cognitive model, where a number of algorithms have been developed over time and the precursor structures should be codable to some level. Through developing and trying to implement the design, ideas like separating the data from the function have become architecturally appropriate and there have been several opportunities to make the system more orthogonal. Similarly for the human brain, neural structures may work in-sync with the neural functions, or may be slightly separate from them. Each section discusses one of the neural assemblies with a potential functional result, that cover ideas such as timing or scheduling, structural intelligence and neural binding. Another aspect of self-representation or expression is interesting and may help the brain to realise higher-level functionality based on these lower-level processes.

The quest for multiscale brain modeling

Addressing the multiscale organization of the brain, which is fundamental to the dynamic repertoire of the organ, remains challenging. In principle, it should be possible to model neurons and synapses in detail and then connect them into large neuronal assemblies to explain the relationship between microscopic phenomena, large-scale brain functions, and behavior. It is more difficult to infer neuronal functions from ensemble measurements such as those currently obtained with brain activity recordings. In this article we consider theories and strategies for combining bottom-up models, generated from principles of neuronal biophysics, with top-down models based on ensemble representations of network activity and on functional principles. These integrative approaches are hoped to provide effective multiscale simulations in virtual brains and neurorobots, and pave the way to future applications in medicine and information technologies.

Computational Concepts for Reconstructing and Simulating Brain Tissue

It has previously been shown that it is possible to derive a new class of biophysically detailed brain tissue models when one computationally analyzes and exploits the interdependencies or the multi-modal and multi-scale organization of the brain. These reconstructions, sometimes referred to as digital twins, enable a spectrum of scientific investigations. Building such models has become possible because of increase in quantitative data but also advances in computational capabilities, algorithmic and methodological innovations. This chapter presents the computational science concepts that provide the foundation to the data-driven approach to reconstructing and simulating brain tissue as developed by the EPFL Blue Brain Project, which was originally applied to neocortical microcircuitry and extended to other brain regions. Accordingly, the chapter covers aspects such as a knowledge graph-based data organization and the importance of the concept of a dataset release. We illustrate algorithmic advances in finding suitable parameters for electrical models of neurons or how spatial constraints can be exploited for predicting synaptic connections. Furthermore, we explain how in silico experimentation with such models necessitates specific addressing schemes or requires strategies for an efficient simulation. The entire data-driven approach relies on the systematic validation of the model. We conclude by discussing complementary strategies that not only enable judging the fidelity of the model but also form the basis for its systematic refinements.

Statistical Perspective on Functional and Causal Neural Connectomics: A Comparative Study

Representation of brain network interactions is fundamental to the translation of neural structure to brain function. As such, methodologies for mapping neural interactions into structural models, i.e., inference of functional connectome from neural recordings, are key for the study of brain networks. While multiple approaches have been proposed for functional connectomics based on statistical associations between neural activity, association does not necessarily incorporate causation. Additional approaches have been proposed to incorporate aspects of causality to turn functional connectomes into causal functional connectomes, however, these methodologies typically focus on specific aspects of causality. This warrants a systematic statistical framework for causal functional connectomics that defines the foundations of common aspects of causality. Such a framework can assist in contrasting existing approaches and to guide development of further causal methodologies. In this work, we develop such a statistical guide. In particular, we consolidate the notions of associations and representations of neural interaction, i.e., types of neural connectomics, and then describe causal modeling in the statistics literature. We particularly focus on the introduction of directed Markov graphical models as a framework through which we define the Directed Markov Property—an essential criterion for examining the causality of proposed functional connectomes. We demonstrate how based on these notions, a comparative study of several existing approaches for finding causal functional connectivity from neural activity can be conducted. We proceed by providing an outlook ahead regarding the additional properties that future approaches could include to thoroughly address causality.

Advanced Technologies for Local Neural Circuits in the Cerebral Cortex

The neural network in the brain can be viewed as an integrated system assembled from a large number of local neural circuits specialized for particular brain functions. Activities of neurons in local neural circuits are thought to be organized both spatially and temporally under the rules optimized for their roles in information processing. It is well perceived that different areas of the mammalian neocortex have specific cognitive functions and distinct computational properties. However, the organizational principles of the local neural circuits in different cortical regions have not yet been clarified. Therefore, new research principles and related neuro-technologies that enable efficient and precise recording of large-scale neuronal activities and synaptic connections are necessary. Innovative technologies for structural analysis, including tissue clearing and expansion microscopy, have enabled super resolution imaging of the neural circuits containing thousands of neurons at a single synapse resolution. The imaging resolution and volume achieved by new technologies are beyond the limits of conventional light or electron microscopic methods. Progress in genome editing and related technologies has made it possible to label and manipulate specific cell types and discriminate activities of multiple cell types. These technologies will provide a breakthrough for multiscale analysis of the structure and function of local neural circuits. This review summarizes the basic concepts and practical applications of the emerging technologies and new insight into local neural circuits obtained by these technologies.

Mechanisms Underlying Target Selectivity for Cell Types and Subcellular Domains in Developing Neocortical Circuits

The cerebral cortex contains numerous neuronal cell types, distinguished by their molecular identity as well as their electrophysiological and morphological properties. Cortical function is reliant on stereotyped patterns of synaptic connectivity and synaptic function among these neuron types, but how these patterns are established during development remains poorly understood. Selective targeting not only of different cell types but also of distinct postsynaptic neuronal domains occurs in many brain circuits and is directed by multiple mechanisms. These mechanisms include the regulation of axonal and dendritic guidance and fine-scale morphogenesis of pre- and postsynaptic processes, lineage relationships, activity dependent mechanisms and intercellular molecular determinants such as transmembrane and secreted molecules, many of which have also been implicated in neurodevelopmental disorders. However, many studies of synaptic targeting have focused on circuits in which neuronal processes target different lamina, such that cell-type-biased connectivity may be confounded with mechanisms of laminar specificity. In the cerebral cortex, each cortical layer contains cell bodies and processes from intermingled neuronal cell types, an arrangement that presents a challenge for the development of target-selective synapse formation. Here, we address progress and future directions in the study of cell-type-biased synaptic targeting in the cerebral cortex. We highlight challenges to identifying developmental mechanisms generating stereotyped patterns of intracortical connectivity, recent developments in uncovering the determinants of synaptic target selection during cortical synapse formation, and current gaps in the understanding of cortical synapse specificity.

Self-Organized Structuring of Recurrent Neuronal Networks for Reliable Information Transmission

Simple Summary

Information processing in the brain takes places at multiple stages, each of which is a local network of neurons. The long-range connections between these network stages are sparse and do not change over time. Thus, within each stage information arrives at a sparse subset of input neurons and must be routed to a sparse subset of output neurons. In this theoretical work, we investigate how networks achieve this routing in a self-organized manner without losing information. We show that biologically inspired self-organization entails that input information is distributed to all neurons in the network by strengthening many synapses in the local networks. Thus, after successful self-organization, input information can be read out and decoded from a small number of outputs. We also show that this way of self-organization can still be more energy efficient than creating more long-range in- and output connections.

Abstract

Our brains process information using a layered hierarchical network architecture, with abundant connections within each layer and sparse long-range connections between layers. As these long-range connections are mostly unchanged after development, each layer has to locally self-organize in response to new inputs to enable information routing between the sparse in- and output connections. Here we demonstrate that this can be achieved by a well-established model of cortical self-organization based on a well-orchestrated interplay between several plasticity processes. After this self-organization, stimuli conveyed by sparse inputs can be rapidly read out from a layer using only very few long-range connections. To achieve this information routing, the neurons that are stimulated form feed-forward projections into the unstimulated parts of the same layer and get more neurons to represent the stimulus. Hereby, the plasticity processes ensure that each neuron only receives projections from and responds to only one stimulus such that the network is partitioned into parts with different preferred stimuli. Along this line, we show that the relation between the network activity and connectivity self-organizes into a biologically plausible regime. Finally, we argue how the emerging connectivity may minimize the metabolic cost for maintaining a network structure that rapidly transmits stimulus information despite sparse input and output connectivity.

Progress towards a cellularly resolved mouse mesoconnectome is empowered by data fusion and new neuroanatomy techniques

Over the past decade there has been a rapid improvement in techniques for obtaining large-scale cellular level data related to the mouse brain connectome. However, a detailed mapping of cell-type-specific projection patterns is lacking, which would, for instance, allow us to study the role of circuit motifs in cognitive processes. In this work, we review advanced neuroanatomical and data fusion techniques within the context of a proposed Multimodal Connectomic Integration Framework for augmenting the cellularly resolved mouse mesoconnectome. First, we emphasize the importance of registering data modalities to a common reference atlas. We then review a number of novel experimental techniques that can provide data for characterizing cell-types in the mouse brain. Furthermore, we examine a number of data integration strategies, which involve fine-grained cell-type classification, spatial inference of cell densities, latent variable models for the mesoconnectome and multi-modal factorisation. Finally, we discuss a number of use cases which depend on connectome augmentation techniques, such as model simulations of functional connectivity and generating mechanistic hypotheses for animal disease models.

Rodent somatosensory thalamocortical circuitry: Neurons, synapses, and connectivity

As our understanding of the thalamocortical system deepens, the questions we face become more complex. Their investigation requires the adoption of novel experimental approaches complemented with increasingly sophisticated computational modeling. In this review, we take stock of current data and knowledge about the circuitry of the somatosensory thalamocortical loop in rodents, discussing common principles across modalities and species whenever appropriate. We review the different levels of organization, including the cells, synapses, neuroanatomy, and network connectivity. We provide a complete overview of this system that should be accessible for newcomers to this field while nevertheless being comprehensive enough to serve as a reference for seasoned neuroscientists and computational modelers studying the thalamocortical system. We further highlight key gaps in data and knowledge that constitute pressing targets for future experimental work. Filling these gaps would provide invaluable information for systematically unveiling how this system supports behavioral and cognitive processes.

How neurons exploit fractal geometry to optimize their network connectivity

We investigate the degree to which neurons are fractal, the origin of this fractality, and its impact on functionality. By analyzing three-dimensional images of rat neurons, we show the way their dendrites fork and weave through space is unexpectedly important for generating fractal-like behavior well-described by an ‘effective’ fractal dimension D. This discovery motivated us to create distorted neuron models by modifying the dendritic patterns, so generating neurons across wide ranges of D extending beyond their natural values. By charting the D-dependent variations in inter-neuron connectivity along with the associated costs, we propose that their D values reflect a network cooperation that optimizes these constraints. We discuss the implications for healthy and pathological neurons, and for connecting neurons to medical implants. Our automated approach also facilitates insights relating form and function, applicable to individual neurons and their networks, providing a crucial tool for addressing massive data collection projects (e.g. connectomes).

Excess Neuronal Branching Allows for Local Innervation of Specific Dendritic Compartments in Mature Cortex

The connectivity of cortical microcircuits is a major determinant of brain function; defining how activity propagates between different cell types is key to scaling our understanding of individual neuronal behavior to encompass functional networks. Furthermore, the integration of synaptic currents within a dendrite depends on the spatial organization of inputs, both excitatory and inhibitory. We identify a simple equation to estimate the number of potential anatomical contacts between neurons; finding a linear increase in potential connectivity with cable length and maximum spine length, and a decrease with overlapping volume. This enables us to predict the mean number of candidate synapses for reconstructed cells, including those realistically arranged. We identify an excess of potential local connections in mature cortical data, with densities of neurite higher than is necessary to reliably ensure the possible implementation of any given axo-dendritic connection. We show that the number of local potential contacts allows specific innervation of distinct dendritic compartments.

Dissecting Sholl Analysis into Its Functional Components

Sholl analysis has been an important technique in dendritic anatomy for more than 60 years. The Sholl intersection profile is obtained by counting the number of dendritic branches at a given distance from the soma and is a key measure of dendritic complexity; it has applications from evaluating the changes in structure induced by pathologies to estimating the expected number of anatomical synaptic contacts. We find that the Sholl intersection profiles of most neurons can be reproduced from three basic, functional measures: the domain spanned by the dendritic arbor, the total length of the dendrite, and the angular distribution of how far dendritic segments deviate from a direct path to the soma (i.e., the root angle distribution). The first two measures are determined by axon location and hence microcircuit structure; the third arises from optimal wiring and represents a branching statistic estimating the need for conduction speed in a neuron.

Fluorescence-Based Quantitative Synapse Analysis for Cell Type-Specific Connectomics

Anatomical methods for determining cell type-specific connectivity are essential to inspire and constrain our understanding of neural circuit function. We developed genetically-encoded reagents for fluorescence-synapse labeling and connectivity analysis in brain tissue, using a fluorogen-activating protein (FAP)-coupled or YFP-coupled, postsynaptically-localized neuroligin-1 (NL-1) targeting sequence (FAP/YFPpost). FAPpost expression did not alter mEPSC or mIPSC properties. Sparse AAV-mediated expression of FAP/YFPpost with the cell-filling, red fluorophore dTomato (dTom) enabled high-throughput, compartment-specific detection of putative synapses across diverse neuron types in mouse somatosensory cortex. We took advantage of the bright, far-red emission of FAPpost puncta for multichannel fluorescence alignment of dendrites, FAPpost puncta, and presynaptic neurites in transgenic mice with saturated labeling of parvalbumin (PV), somatostatin (SST), or vasoactive intestinal peptide (VIP)-expressing neurons using Cre-reporter driven expression of YFP. Subtype-specific inhibitory connectivity onto layer 2/3 (L2/3) neocortical pyramidal (Pyr) neurons was assessed using automated puncta detection and neurite apposition. Quantitative and compartment-specific comparisons show that PV inputs are the predominant source of inhibition at both the soma and the dendrites and were particularly concentrated at the primary apical dendrite. SST inputs were interleaved with PV inputs at all secondary-order and higher-order dendritic branches. These fluorescence-based synapse labeling reagents can facilitate large-scale and cell-type specific quantitation of changes in synaptic connectivity across development, learning, and disease states.

Decay of connection probabilities with distance in 2D and 3D neuronal networks

We study connectivity in a model of a growing neuronal network in dimensions 2 and 3. Although the axon-to-dendrite proximity is an insufficient condition for establishing a functional synapse, it is still a necessary one. Therefore we study connection probabilities at short distances between the randomly grown axon trees and somas as probabilities of potential connections between the corresponding neurons. Our results show that, contrary to a common belief, these probabilities do not necessarily decay polynomially or exponentially in distance, but there are regimes of parameter values when the probability of proximity is not sensitive to the distance. In particular, in 3 dimensions the Euclidean distance between the neuronal cell body centers of neurons seems to play a very subtle role, as the probabilities of connections are practically constant within a certain finite range of distance. The model has a sufficient number of parameters to assess networks of neurons of different types. Our results give a firm basis for further modelling of the neuronal connectivity taking into account some realistic bouton distributions for establishing synaptic connections.

A Brief History of Simulation Neuroscience

Our knowledge of the brain has evolved over millennia in philosophical, experimental and theoretical phases. We suggest that the next phase is simulation neuroscience. The main drivers of simulation neuroscience are big data generated at multiple levels of brain organization and the need to integrate these data to trace the causal chain of interactions within and across all these levels. Simulation neuroscience is currently the only methodology for systematically approaching the multiscale brain. In this review, we attempt to reconstruct the deep historical paths leading to simulation neuroscience, from the first observations of the nerve cell to modern efforts to digitally reconstruct and simulate the brain. Neuroscience began with the identification of the neuron as the fundamental unit of brain structure and function and has evolved towards understanding the role of each cell type in the brain, how brain cells are connected to each other, and how the seemingly infinite networks they form give rise to the vast diversity of brain functions. Neuronal mapping is evolving from subjective descriptions of cell types towards objective classes, subclasses and types. Connectivity mapping is evolving from loose topographic maps between brain regions towards dense anatomical and physiological maps of connections between individual genetically distinct neurons. Functional mapping is evolving from psychological and behavioral stereotypes towards a map of behaviors emerging from structural and functional connectomes. We show how industrialization of neuroscience and the resulting large disconnected datasets are generating demand for integrative neuroscience, how the scale of neuronal and connectivity maps is driving digital atlasing and digital reconstruction to piece together the multiple levels of brain organization, and how the complexity of the interactions between molecules, neurons, microcircuits and brain regions is driving brain simulation to understand the interactions in the multiscale brain.

A regularity index for dendrites - local statistics of a neuron's input space

Neurons collect their inputs from other neurons by sending out arborized dendritic structures. However, the relationship between the shape of dendrites and the precise organization of synaptic inputs in the neural tissue remains unclear. Inputs could be distributed in tight clusters, entirely randomly or else in a regular grid-like manner. Here, we analyze dendritic branching structures using a regularity index R, based on average nearest neighbor distances between branch and termination points, characterizing their spatial distribution. We find that the distributions of these points depend strongly on cell types, indicating possible fundamental differences in synaptic input organization. Moreover, R is independent of cell size and we find that it is only weakly correlated with other branching statistics, suggesting that it might reflect features of dendritic morphology that are not captured by commonly studied branching statistics. We then use morphological models based on optimal wiring principles to study the relation between input distributions and dendritic branching structures. Using our models, we find that branch point distributions correlate more closely with the input distributions while termination points in dendrites are generally spread out more randomly with a close to uniform distribution. We validate these model predictions with connectome data. Finally, we find that in spatial input distributions with increasing regularity, characteristic scaling relationships between branching features are altered significantly. In summary, we conclude that local statistics of input distributions and dendrite morphology depend on each other leading to potentially cell type specific branching features.

Dendritic tree structures of nerve cells are built to optimally collect inputs from other cells in the circuit. By looking at how regularly the branch and termination points of dendrites are distributed, we find characteristic differences between cell types that correlate little with other traditional branching statistics and affect their scaling properties. Using computational models based on optimal wiring principles, we then show that termination points of dendrites generally spread more randomly than the inputs that they receive while branch points follow more closely the underlying input organization. Existing connectome data validate these predictions indicating the importance of our findings for large scale neural circuit analysis.

Segregated Excitatory-Inhibitory Recurrent Subnetworks in Layer 5 of the Rat Frontal Cortex

A prominent feature of neocortical pyramidal cells (PCs) is their numerous projections to diverse brain areas. In layer 5 (L5) of the rat frontal cortex, there are 2 major subtypes of PCs that differ in their long-range axonal projections, corticopontine (CPn) cells and crossed corticostriatal (CCS) cells. The outputs of these L5 PCs can be regulated by feedback inhibition from neighboring cortical GABAergic cells. Two major subtypes of GABAergic cells are parvalbumin (PV)-positive and somatostatin (SOM)-positive cells. PV cells have a fast-spiking (FS) firing pattern, while SOM cells have a low threshold spike (LTS) and regular spiking. In this study, we found that the 2 PC subtypes in L5 selectively make recurrent connections with LTS cells. The connection patterns correlated with the morphological and physiological diversity of LTS cells. LTS cells with high input resistance (Ri) exhibited more compact dendrites and more rebound spikes than LTS cells with low Ri, which had vertically elongated dendrites. LTS subgroups differently inhibited the PC subtypes, although FS cells made nonselective connections with both projection subtypes. These results demonstrate a novel recurrent network of inhibitory and projection-specific excitatory neurons within the neocortex.

Morphological Diversity Strongly Constrains Synaptic Connectivity and Plasticity

Synaptic connectivity between neurons is naturally constrained by the anatomical overlap of neuronal arbors, the space on the axon available for synapses, and by physiological mechanisms that form synapses at a subset of potential synapse locations. What is not known is how these constraints impact emergent connectivity in a circuit with diverse morphologies. We investigated the role of morphological diversity within and across neuronal types on emergent connectivity in a model of neocortical microcircuitry. We found that the average overlap between the dendritic and axonal arbors of different types of neurons determines neuron-type specific patterns of distance-dependent connectivity, severely constraining the space of possible connectomes. However, higher order connectivity motifs depend on the diverse branching patterns of individual arbors of neurons belonging to the same type. Morphological diversity across neuronal types, therefore, imposes a specific structure on first order connectivity, and morphological diversity within neuronal types imposes a higher order structure of connectivity. We estimate that the morphological constraints resulting from diversity within and across neuron types together lead to a 10-fold reduction of the entropy of possible connectivity configurations, revealing an upper bound on the space explored by structural plasticity.

What Is the Evidence for Inter-laminar Integration in a Prefrontal Cortical Minicolumn?

The objective of this perspective article is to examine columnar inter-laminar integration during the executive control of behavior. The integration hypothesis posits that perceptual and behavioral signals are integrated within the prefrontal cortical inter-laminar microcircuits. Inter-laminar minicolumnar activity previously recorded from the dorsolateral prefrontal cortex (dlPFC) of nonhuman primates, trained in a visual delay match-to-sample (DMS) task, was re-assessed from an integrative perspective. Biomorphic multielectrode arrays (MEAs) played a unique role in the in vivo recording of columnar cell firing in the dlPFC layers 2/3 and 5/6. Several integrative aspects stem from these experiments: 1. Functional integration of perceptual and behavioral signals across cortical layers during executive control. The integrative effect of dlPFC minicolumns was shown by: (i) increased correlated firing on correct vs. error trials; (ii) decreased correlated firing when the number of non-matching images increased; and (iii) similar spatial firing preference across cortical-striatal cells during spatial-trials, and less on object-trials. 2. Causal relations to integration of cognitive signals by the minicolumnar turbo-engines. The inter-laminar integration between the perceptual and executive circuits was facilitated by stimulating the infra-granular layers with firing patterns obtained from supra-granular layers that enhanced spatial preference of percent correct performance on spatial trials. 3. Integration across hierarchical levels of the brain. The integration of intention signals (visual spatial, direction) with movement preparation (timing, velocity) in striatum and with the motor command and posture in midbrain is also discussed. These findings provide evidence for inter-laminar integration of executive control signals within brain's prefrontal cortical microcircuits.

Specific excitatory connectivity for feature integration in mouse primary visual cortex

Local excitatory connections in mouse primary visual cortex (V1) are stronger and more prevalent between neurons that share similar functional response features. However, the details of how functional rules for local connectivity shape neuronal responses in V1 remain unknown. We hypothesised that complex responses to visual stimuli may arise as a consequence of rules for selective excitatory connectivity within the local network in the superficial layers of mouse V1. In mouse V1 many neurons respond to overlapping grating stimuli (plaid stimuli) with highly selective and facilitatory responses, which are not simply predicted by responses to single gratings presented alone. This complexity is surprising, since excitatory neurons in V1 are considered to be mainly tuned to single preferred orientations. Here we examined the consequences for visual processing of two alternative connectivity schemes: in the first case, local connections are aligned with visual properties inherited from feedforward input (a 'like-to-like' scheme specifically connecting neurons that share similar preferred orientations); in the second case, local connections group neurons into excitatory subnetworks that combine and amplify multiple feedforward visual properties (a 'feature binding' scheme). By comparing predictions from large scale computational models with in vivo recordings of visual representations in mouse V1, we found that responses to plaid stimuli were best explained by assuming feature binding connectivity. Unlike under the like-to-like scheme, selective amplification within feature-binding excitatory subnetworks replicated experimentally observed facilitatory responses to plaid stimuli; explained selective plaid responses not predicted by grating selectivity; and was consistent with broad anatomical selectivity observed in mouse V1. Our results show that visual feature binding can occur through local recurrent mechanisms without requiring feedforward convergence, and that such a mechanism is consistent with visual responses and cortical anatomy in mouse V1.

On the Structure of Cortical Microcircuits Inferred from Small Sample Sizes

The structure in cortical microcircuits deviates from what would be expected in a purely random network, which has been seen as evidence of clustering. To address this issue, we sought to reproduce the nonrandom features of cortical circuits by considering several distinct classes of network topology, including clustered networks, networks with distance-dependent connectivity, and those with broad degree distributions. To our surprise, we found that all of these qualitatively distinct topologies could account equally well for all reported nonrandom features despite being easily distinguishable from one another at the network level. This apparent paradox was a consequence of estimating network properties given only small sample sizes. In other words, networks that differ markedly in their global structure can look quite similar locally. This makes inferring network structure from small sample sizes, a necessity given the technical difficulty inherent in simultaneous intracellular recordings, problematic. We found that a network statistic called the sample degree correlation (SDC) overcomes this difficulty. The SDC depends only on parameters that can be estimated reliably given small sample sizes and is an accurate fingerprint of every topological family. We applied the SDC criterion to data from rat visual and somatosensory cortex and discovered that the connectivity was not consistent with any of these main topological classes. However, we were able to fit the experimental data with a more general network class, of which all previous topologies were special cases. The resulting network topology could be interpreted as a combination of physical spatial dependence and nonspatial, hierarchical clustering.SIGNIFICANCE STATEMENT The connectivity of cortical microcircuits exhibits features that are inconsistent with a simple random network. Here, we show that several classes of network models can account for this nonrandom structure despite qualitative differences in their global properties. This apparent paradox is a consequence of the small numbers of simultaneously recorded neurons in experiment: when inferred via small sample sizes, many networks may be indistinguishable despite being globally distinct. We develop a connectivity measure that successfully classifies networks even when estimated locally with a few neurons at a time. We show that data from rat cortex is consistent with a network in which the likelihood of a connection between neurons depends on spatial distance and on nonspatial, asymmetric clustering.

Genetic evidence for role of integration of fast and slow neurotransmission in schizophrenia

The most recent genome-wide association studies (GWAS) of schizophrenia (SCZ) identified hundreds of risk variants potentially implicated in the disease. Further, novel statistical methodology designed for polygenic architecture revealed more potential risk variants. This can provide a link between individual genetic factors and the mechanistic underpinnings of SCZ. Intriguingly, a large number of genes coding for ionotropic and metabotropic receptors for various neurotransmitters-glutamate, γ-aminobutyric acid (GABA), dopamine, serotonin, acetylcholine and opioids-and numerous ion channels were associated with SCZ. Here, we review these findings from the standpoint of classical neurobiological knowledge of neuronal synaptic transmission and regulation of electrical excitability. We show that a substantial proportion of the identified genes are involved in intracellular cascades known to integrate 'slow' (G-protein-coupled receptors) and 'fast' (ionotropic receptors) neurotransmission converging on the protein DARPP-32. Inspection of the Human Brain Transcriptome Project database confirms that that these genes are indeed expressed in the brain, with the expression profile following specific developmental trajectories, underscoring their relevance to brain organization and function. These findings extend the existing pathophysiology hypothesis by suggesting a unifying role of dysregulation in neuronal excitability and synaptic integration in SCZ. This emergent model supports the concept of SCZ as an 'associative' disorder-a breakdown in the communication across different slow and fast neurotransmitter systems through intracellular signaling pathways-and may unify a number of currently competing hypotheses of SCZ pathophysiology.

Brain Computation Is Organized via Power-of-Two-Based Permutation Logic

There is considerable scientific interest in understanding how cell assemblies—the long-presumed computational motif—are organized so that the brain can generate intelligent cognition and flexible behavior. The Theory of Connectivity proposes that the origin of intelligence is rooted in a power-of-two-based permutation logic (N = 2ⁱ–1), producing specific-to-general cell-assembly architecture capable of generating specific perceptions and memories, as well as generalized knowledge and flexible actions. We show that this power-of-two-based permutation logic is widely used in cortical and subcortical circuits across animal species and is conserved for the processing of a variety of cognitive modalities including appetitive, emotional and social information. However, modulatory neurons, such as dopaminergic (DA) neurons, use a simpler logic despite their distinct subtypes. Interestingly, this specific-to-general permutation logic remained largely intact although NMDA receptors—the synaptic switch for learning and memory—were deleted throughout adulthood, suggesting that the logic is developmentally pre-configured. Moreover, this computational logic is implemented in the cortex via combining a random-connectivity strategy in superficial layers 2/3 with nonrandom organizations in deep layers 5/6. This randomness of layers 2/3 cliques—which preferentially encode specific and low-combinatorial features and project inter-cortically—is ideal for maximizing cross-modality novel pattern-extraction, pattern-discrimination and pattern-categorization using sparse code, consequently explaining why it requires hippocampal offline-consolidation. In contrast, the nonrandomness in layers 5/6—which consists of few specific cliques but a higher portion of more general cliques projecting mostly to subcortical systems—is ideal for feedback-control of motivation, emotion, consciousness and behaviors. These observations suggest that the brain’s basic computational algorithm is indeed organized by the power-of-two-based permutation logic. This simple mathematical logic can account for brain computation across the entire evolutionary spectrum, ranging from the simplest neural networks to the most complex.

Connectomic Analysis of Brain Networks: Novel Techniques and Future Directions

Brain networks, localized or brain-wide, exist only at the cellular level, i.e., between specific pre- and post-synaptic neurons, which are connected through functionally diverse synapses located at specific points of their cell membranes. "Connectomics" is the emerging subfield of neuroanatomy explicitly aimed at elucidating the wiring of brain networks with cellular resolution and a quantified accuracy. Such data are indispensable for realistic modeling of brain circuitry and function. A connectomic analysis, therefore, needs to identify and measure the soma, dendrites, axonal path, and branching patterns together with the synapses and gap junctions of the neurons involved in any given brain circuit or network. However, because of the submicron caliber, 3D complexity, and high packing density of most such structures, as well as the fact that axons frequently extend over long distances to make synapses in remote brain regions, creating connectomic maps is technically challenging and requires multi-scale approaches, Such approaches involve the combination of the most sensitive cell labeling and analysis methods available, as well as the development of new ones able to resolve individual cells and synapses with increasing high-throughput. In this review, we provide an overview of recently introduced high-resolution methods, which researchers wanting to enter the field of connectomics may consider. It includes several molecular labeling tools, some of which specifically label synapses, and covers a number of novel imaging tools such as brain clearing protocols and microscopy approaches. Apart from describing the tools, we also provide an assessment of their qualities. The criteria we use assess the qualities that tools need in order to contribute to deciphering the key levels of circuit organization. We conclude with a brief future outlook for neuroanatomic research, computational methods, and network modeling, where we also point out several outstanding issues like structure-function relations and the complexity of neural models.

Morphological Neuron Classification Using Machine Learning

Classification and quantitative characterization of neuronal morphologies from histological neuronal reconstruction is challenging since it is still unclear how to delineate a neuronal cell class and which are the best features to define them by. The morphological neuron characterization represents a primary source to address anatomical comparisons, morphometric analysis of cells, or brain modeling. The objectives of this paper are (i) to develop and integrate a pipeline that goes from morphological feature extraction to classification and (ii) to assess and compare the accuracy of machine learning algorithms to classify neuron morphologies. The algorithms were trained on 430 digitally reconstructed neurons subjectively classified into layers and/or m-types using young and/or adult development state population of the somatosensory cortex in rats. For supervised algorithms, linear discriminant analysis provided better classification results in comparison with others. For unsupervised algorithms, the affinity propagation and the Ward algorithms provided slightly better results.

Relative Contributions of Specific Activity Histories and Spontaneous Processes to Size Remodeling of Glutamatergic Synapses

The idea that synaptic properties are defined by specific pre- and postsynaptic activity histories is one of the oldest and most influential tenets of contemporary neuroscience. Recent studies also indicate, however, that synaptic properties often change spontaneously, even in the absence of specific activity patterns or any activity whatsoever. What, then, are the relative contributions of activity history-dependent and activity history-independent processes to changes synapses undergo? To compare the relative contributions of these processes, we imaged, in spontaneously active networks of cortical neurons, glutamatergic synapses formed between the same axons and neurons or dendrites under the assumption that their similar activity histories should result in similar size changes over timescales of days. The size covariance of such commonly innervated (CI) synapses was then compared to that of synapses formed by different axons (non-CI synapses) that differed in their activity histories. We found that the size covariance of CI synapses was greater than that of non-CI synapses; yet overall size covariance of CI synapses was rather modest. Moreover, momentary and time-averaged sizes of CI synapses correlated rather poorly, in perfect agreement with published electron microscopy-based measurements of mouse cortex synapses. A conservative estimate suggested that ~40% of the observed size remodeling was attributable to specific activity histories, whereas ~10% and ~50% were attributable to cell-wide and spontaneous, synapse-autonomous processes, respectively. These findings demonstrate that histories of naturally occurring activity patterns can direct glutamatergic synapse remodeling but also suggest that the contributions of spontaneous, possibly stochastic, processes are at least as great.

Cell-Autonomous Regulation of Dendritic Spine Density by PirB

Synapse density on cortical pyramidal neurons is modulated by experience. This process is highest during developmental critical periods, when mechanisms of synaptic plasticity are fully engaged. In mouse visual cortex, the critical period for ocular dominance (OD) plasticity coincides with the developmental pruning of synapses. At this time, mice lacking paired Ig-like receptor B (PirB) have excess numbers of dendritic spines on L5 neurons; these spines persist and are thought to underlie the juvenile-like OD plasticity observed in adulthood. Here we examine whether PirB is required specifically in excitatory neurons to exert its effect on dendritic spine and synapse density during the critical period. In mice with a conditional allele of PirB (PirB^fl/fl), PirB was deleted only from L2/3 cortical pyramidal neurons in vivo by timed in utero electroporation of Cre recombinase. Sparse mosaic expression of Cre produced neurons lacking PirB in a sea of wild-type neurons and glia. These neurons had significantly elevated dendritic spine density, as well as increased frequency of miniature EPSCs, suggesting that they receive a greater number of synaptic inputs relative to Cre^– neighbors. The effect of cell-specific PirB deletion on dendritic spine density was not accompanied by changes in dendritic branching complexity or axonal bouton density. Together, results imply a neuron-specific, cell-autonomous action of PirB on synaptic density in L2/3 pyramidal cells of visual cortex. Moreover, they are consistent with the idea that PirB functions normally to corepress spine density and synaptic plasticity, thereby maintaining headroom for cells to encode ongoing experience-dependent structural change throughout life.

Processing Time Reduction: an Application in Living Human High-Resolution Diffusion Magnetic Resonance Imaging Data

High Angular Resolution Diffusion Imaging (HARDI) is a type of brain imaging that collects a very large amount of data, and if many subjects are considered then it amounts to a big data framework (e.g., the human connectome project has 20 Terabytes of data). HARDI is also becoming increasingly relevant for clinical settings (e.g., detecting early cerebral ischemic changes in acute stroke, and in pre-clinical assessment of white matter-WM anatomy using tractography). Thus, this method is becoming a routine assessment in clinical settings. In such settings, the computation time is critical, and finding forms of reducing the processing time in high computation processes such as Diffusion Spectrum Imaging (DSI), a form of HARDI data, is very relevant to increase data-processing speed. Here we analyze a method for reducing the computation time of the dMRI-based axonal orientation distribution function h by using Monte Carlo sampling-based methods for voxel selection. Results evidenced a robust reduction in required data sampling of about 50 % without losing signal's quality. Moreover, we show that the convergence to the correct value in this type of Monte Carlo HARDI/DSI data-processing has a linear improvement in data-processing speed of the ODF determination. Although further improvements are needed, our results represent a promissory step for future processing time reduction in big data.

Neural networks within multi-core optic fibers

Hardware implementation of artificial neural networks facilitates real-time parallel processing of massive data sets. Optical neural networks offer low-volume 3D connectivity together with large bandwidth and minimal heat production in contrast to electronic implementation. Here, we present a conceptual design for in-fiber optical neural networks. Neurons and synapses are realized as individual silica cores in a multi-core fiber. Optical signals are transferred transversely between cores by means of optical coupling. Pump driven amplification in erbium-doped cores mimics synaptic interactions. We simulated three-layered feed-forward neural networks and explored their capabilities. Simulations suggest that networks can differentiate between given inputs depending on specific configurations of amplification; this implies classification and learning capabilities. Finally, we tested experimentally our basic neuronal elements using fibers, couplers, and amplifiers, and demonstrated that this configuration implements a neuron-like function. Therefore, devices similar to our proposed multi-core fiber could potentially serve as building blocks for future large-scale small-volume optical artificial neural networks.

Somatostatin-expressing neurons in cortical networks

Somatostatin-expressing GABAergic neurons constitute a major class of inhibitory neurons in the mammalian cortex and are characterized by dense wiring into the local network and high basal firing activity that persists in the absence of synaptic input. This firing provides both GABA type A receptor (GABAAR)- and GABABR-mediated inhibition that operates at fast and slow timescales. The activity of somatostatin-expressing neurons is regulated by brain state, during learning and in rewarded behaviour. Here, we review recent advances in our understanding of how this class of cells can control network activity, with specific reference to how this is constrained by their anatomical and electrophysiological properties.

A Detailed Data-Driven Network Model of Prefrontal Cortex Reproduces Key Features of In Vivo Activity

The prefrontal cortex is centrally involved in a wide range of cognitive functions and their impairment in psychiatric disorders. Yet, the computational principles that govern the dynamics of prefrontal neural networks, and link their physiological, biochemical and anatomical properties to cognitive functions, are not well understood. Computational models can help to bridge the gap between these different levels of description, provided they are sufficiently constrained by experimental data and capable of predicting key properties of the intact cortex. Here, we present a detailed network model of the prefrontal cortex, based on a simple computationally efficient single neuron model (simpAdEx), with all parameters derived from in vitro electrophysiological and anatomical data. Without additional tuning, this model could be shown to quantitatively reproduce a wide range of measures from in vivo electrophysiological recordings, to a degree where simulated and experimentally observed activities were statistically indistinguishable. These measures include spike train statistics, membrane potential fluctuations, local field potentials, and the transmission of transient stimulus information across layers. We further demonstrate that model predictions are robust against moderate changes in key parameters, and that synaptic heterogeneity is a crucial ingredient to the quantitative reproduction of in vivo-like electrophysiological behavior. Thus, we have produced a physiologically highly valid, in a quantitative sense, yet computationally efficient PFC network model, which helped to identify key properties underlying spike time dynamics as observed in vivo, and can be harvested for in-depth investigation of the links between physiology and cognition.

Computational network models are an important tool for linking physiological and neuro-dynamical processes to cognition. However, harvesting network models for this purpose may less depend on how much biophysical detail is included, but more on how well the model can capture the functional network physiology. Here, we present the first network model of the prefrontal cortex which has not only its single neuron properties and anatomical layout tightly constrained by experimental data, but is also able to quantitatively reproduce a large range of spiking, field potential, and membrane voltage statistics obtained from in vivo data, without need of specific parameter tuning. It thus represents a novel computational tool for addressing questions about the neuro-dynamics of cognition in health and disease.

The future of human cerebral cartography: a novel approach

Cerebral cartography can be understood in a limited, static, neuroanatomical sense. Temporal information from electrical recordings contributes information on regional interactions adding a functional dimension. Selective tagging and imaging of molecules adds biochemical contributions. Cartographic detail can also be correlated with normal or abnormal psychological or behavioural data. Modern cerebral cartography is assimilating all these elements. Cartographers continue to collect ever more precise data in the hope that general principles of organization will emerge. However, even detailed cartographic data cannot generate knowledge without a multi-scale framework making it possible to relate individual observations and discoveries. We propose that, in the next quarter century, advances in cartography will result in progressively more accurate drafts of a data-led, multi-scale model of human brain structure and function. These blueprints will result from analysis of large volumes of neuroscientific and clinical data, by a process of reconstruction, modelling and simulation. This strategy will capitalize on remarkable recent developments in informatics and computer science and on the existence of much existing, addressable data and prior, though fragmented, knowledge. The models will instantiate principles that govern how the brain is organized at different levels and how different spatio-temporal scales relate to each other in an organ-centred context.

Saturated Reconstruction of a Volume of Neocortex

We describe automated technologies to probe the structure of neural tissue at nanometer resolution and use them to generate a saturated reconstruction of a sub-volume of mouse neocortex in which all cellular objects (axons, dendrites, and glia) and many sub-cellular components (synapses, synaptic vesicles, spines, spine apparati, postsynaptic densities, and mitochondria) are rendered and itemized in a database. We explore these data to study physical properties of brain tissue. For example, by tracing the trajectories of all excitatory axons and noting their juxtapositions, both synaptic and non-synaptic, with every dendritic spine we refute the idea that physical proximity is sufficient to predict synaptic connectivity (the so-called Peters' rule). This online minable database provides general access to the intrinsic complexity of the neocortex and enables further data-driven inquiries.

An algorithm to predict the connectome of neural microcircuits

Experimentally mapping synaptic connections, in terms of the numbers and locations of their synapses and estimating connection probabilities, is still not a tractable task, even for small volumes of tissue. In fact, the six layers of the neocortex contain thousands of unique types of synaptic connections between the many different types of neurons, of which only a handful have been characterized experimentally. Here we present a theoretical framework and a data-driven algorithmic strategy to digitally reconstruct the complete synaptic connectivity between the different types of neurons in a small well-defined volume of tissue—the micro-scale connectome of a neural microcircuit. By enforcing a set of established principles of synaptic connectivity, and leveraging interdependencies between fundamental properties of neural microcircuits to constrain the reconstructed connectivity, the algorithm yields three parameters per connection type that predict the anatomy of all types of biologically viable synaptic connections. The predictions reproduce a spectrum of experimental data on synaptic connectivity not used by the algorithm. We conclude that an algorithmic approach to the connectome can serve as a tool to accelerate experimental mapping, indicating the minimal dataset required to make useful predictions, identifying the datasets required to improve their accuracy, testing the feasibility of experimental measurements, and making it possible to test hypotheses of synaptic connectivity.

The anatomical problem posed by brain complexity and size: a potential solution

Over the years the field of neuroanatomy has evolved considerably but unraveling the extraordinary structural and functional complexity of the brain seems to be an unattainable goal, partly due to the fact that it is only possible to obtain an imprecise connection matrix of the brain. The reasons why reaching such a goal appears almost impossible to date is discussed here, together with suggestions of how we could overcome this anatomical problem by establishing new methodologies to study the brain and by promoting interdisciplinary collaboration. Generating a realistic computational model seems to be the solution rather than attempting to fully reconstruct the whole brain or a particular brain region.

The effects of neuron morphology on graph theoretic measures of network connectivity: the analysis of a two-level statistical model

We developed a two-level statistical model that addresses the question of how properties of neurite morphology shape the large-scale network connectivity. We adopted a low-dimensional statistical description of neurites. From the neurite model description we derived the expected number of synapses, node degree, and the effective radius, the maximal distance between two neurons expected to form at least one synapse. We related these quantities to the network connectivity described using standard measures from graph theory, such as motif counts, clustering coefficient, minimal path length, and small-world coefficient. These measures are used in a neuroscience context to study phenomena from synaptic connectivity in the small neuronal networks to large scale functional connectivity in the cortex. For these measures we provide analytical solutions that clearly relate different model properties. Neurites that sparsely cover space lead to a small effective radius. If the effective radius is small compared to the overall neuron size the obtained networks share similarities with the uniform random networks as each neuron connects to a small number of distant neurons. Large neurites with densely packed branches lead to a large effective radius. If this effective radius is large compared to the neuron size, the obtained networks have many local connections. In between these extremes, the networks maximize the variability of connection repertoires. The presented approach connects the properties of neuron morphology with large scale network properties without requiring heavy simulations with many model parameters. The two-steps procedure provides an easier interpretation of the role of each modeled parameter. The model is flexible and each of its components can be further expanded. We identified a range of model parameters that maximizes variability in network connectivity, the property that might affect network capacity to exhibit different dynamical regimes.

Automatic discovery of cell types and microcircuitry from neural connectomics

Neural connectomics has begun producing massive amounts of data, necessitating new analysis methods to discover the biological and computational structure. It has long been assumed that discovering neuron types and their relation to microcircuitry is crucial to understanding neural function. Here we developed a non-parametric Bayesian technique that identifies neuron types and microcircuitry patterns in connectomics data. It combines the information traditionally used by biologists in a principled and probabilistically coherent manner, including connectivity, cell body location, and the spatial distribution of synapses. We show that the approach recovers known neuron types in the retina and enables predictions of connectivity, better than simpler algorithms. It also can reveal interesting structure in the nervous system of Caenorhabditis elegans and an old man-made microprocessor. Our approach extracts structural meaning from connectomics, enabling new approaches of automatically deriving anatomical insights from these emerging datasets.

Developmental time windows for axon growth influence neuronal network topology

Early brain connectivity development consists of multiple stages: birth of neurons, their migration and the subsequent growth of axons and dendrites. Each stage occurs within a certain period of time depending on types of neurons and cortical layers. Forming synapses between neurons either by growing axons starting at similar times for all neurons (much-overlapped time windows) or at different time points (less-overlapped) may affect the topological and spatial properties of neuronal networks. Here, we explore the extreme cases of axon formation during early development, either starting at the same time for all neurons (parallel, i.e., maximally overlapped time windows) or occurring for each neuron separately one neuron after another (serial, i.e., no overlaps in time windows). For both cases, the number of potential and established synapses remained comparable. Topological and spatial properties, however, differed: Neurons that started axon growth early on in serial growth achieved higher out-degrees, higher local efficiency and longer axon lengths while neurons demonstrated more homogeneous connectivity patterns for parallel growth. Second, connection probability decreased more rapidly with distance between neurons for parallel growth than for serial growth. Third, bidirectional connections were more numerous for parallel growth. Finally, we tested our predictions with C. elegans data. Together, this indicates that time windows for axon growth influence the topological and spatial properties of neuronal networks opening up the possibility to a posteriori estimate developmental mechanisms based on network properties of a developed network.

Generation of dense statistical connectomes from sparse morphological data

Sensory-evoked signal flow, at cellular and network levels, is primarily determined by the synaptic wiring of the underlying neuronal circuitry. Measurements of synaptic innervation, connection probabilities and subcellular organization of synaptic inputs are thus among the most active fields of research in contemporary neuroscience. Methods to measure these quantities range from electrophysiological recordings over reconstructions of dendrite-axon overlap at light-microscopic levels to dense circuit reconstructions of small volumes at electron-microscopic resolution. However, quantitative and complete measurements at subcellular resolution and mesoscopic scales to obtain all local and long-range synaptic in/outputs for any neuron within an entire brain region are beyond present methodological limits. Here, we present a novel concept, implemented within an interactive software environment called NeuroNet, which allows (i) integration of sparsely sampled (sub)cellular morphological data into an accurate anatomical reference frame of the brain region(s) of interest, (ii) up-scaling to generate an average dense model of the neuronal circuitry within the respective brain region(s) and (iii) statistical measurements of synaptic innervation between all neurons within the model. We illustrate our approach by generating a dense average model of the entire rat vibrissal cortex, providing the required anatomical data, and illustrate how to measure synaptic innervation statistically. Comparing our results with data from paired recordings in vitro and in vivo, as well as with reconstructions of synaptic contact sites at light- and electron-microscopic levels, we find that our in silico measurements are in line with previous results.