On the Structure of Cortical Microcircuits Inferred from Small Sample Sizes

Directed and acyclic synaptic connectivity in the human layer 2-3 cortical microcircuit

The computational capabilities of neuronal networks are fundamentally constrained by their specific connectivity. Previous studies of cortical connectivity have mostly been carried out in rodents; whether the principles established therein also apply to the evolutionarily expanded human cortex is unclear. We studied network properties within the human temporal cortex using samples obtained from brain surgery. We analyzed multineuron patch-clamp recordings in layer 2-3 pyramidal neurons and identified substantial differences compared with rodents. Reciprocity showed random distribution, synaptic strength was independent from connection probability, and connectivity of the supragranular temporal cortex followed a directed and mostly acyclic graph topology. Application of these principles in neuronal models increased dimensionality of network dynamics, suggesting a critical role for cortical computation.

Correlated Somatosensory Input in Parvalbumin/Pyramidal Cells in Mouse Motor Cortex

In mammalian cortex, feedforward excitatory connections recruit feedforward inhibition. This is often carried by parvalbumin (PV+) interneurons, which may densely connect to local pyramidal (Pyr) neurons. Whether this inhibition affects all local excitatory cells indiscriminately or is targeted to specific subnetworks is unknown. Here, we test how feedforward inhibition is recruited by using two-channel circuit mapping to excite cortical and thalamic inputs to PV+ interneurons and Pyr neurons to mouse primary vibrissal motor cortex (M1). Single Pyr and PV+ neurons receive input from both cortex and thalamus. Connected pairs of PV+ interneurons and excitatory Pyr neurons receive correlated cortical and thalamic inputs. While PV+ interneurons are more likely to form local connections to Pyr neurons, Pyr neurons are much more likely to form reciprocal connections with PV+ interneurons that inhibit them. This suggests that Pyr and PV ensembles may be organized based on their local and long-range connections, an organization that supports the idea of local subnetworks for signal transduction and processing. Excitatory inputs to M1 can thus target inhibitory networks in a specific pattern which permits recruitment of feedforward inhibition to specific subnetworks within the cortical column.

Relating local connectivity and global dynamics in recurrent excitatory-inhibitory networks

How the connectivity of cortical networks determines the neural dynamics and the resulting computations is one of the key questions in neuroscience. Previous works have pursued two complementary approaches to quantify the structure in connectivity. One approach starts from the perspective of biological experiments where only the local statistics of connectivity motifs between small groups of neurons are accessible. Another approach is based instead on the perspective of artificial neural networks where the global connectivity matrix is known, and in particular its low-rank structure can be used to determine the resulting low-dimensional dynamics. A direct relationship between these two approaches is however currently missing. Specifically, it remains to be clarified how local connectivity statistics and the global low-rank connectivity structure are inter-related and shape the low-dimensional activity. To bridge this gap, here we develop a method for mapping local connectivity statistics onto an approximate global low-rank structure. Our method rests on approximating the global connectivity matrix using dominant eigenvectors, which we compute using perturbation theory for random matrices. We demonstrate that multi-population networks defined from local connectivity statistics for which the central limit theorem holds can be approximated by low-rank connectivity with Gaussian-mixture statistics. We specifically apply this method to excitatory-inhibitory networks with reciprocal motifs, and show that it yields reliable predictions for both the low-dimensional dynamics, and statistics of population activity. Importantly, it analytically accounts for the activity heterogeneity of individual neurons in specific realizations of local connectivity. Altogether, our approach allows us to disentangle the effects of mean connectivity and reciprocal motifs on the global recurrent feedback, and provides an intuitive picture of how local connectivity shapes global network dynamics.

Reconstruction of neocortex: Organelles, compartments, cells, circuits, and activity

We assembled a semi-automated reconstruction of L2/3 mouse primary visual cortex from ∼250 × 140 × 90 μm3 of electron microscopic images, including pyramidal and non-pyramidal neurons, astrocytes, microglia, oligodendrocytes and precursors, pericytes, vasculature, nuclei, mitochondria, and synapses. Visual responses of a subset of pyramidal cells are included. The data are publicly available, along with tools for programmatic and three-dimensional interactive access. Brief vignettes illustrate the breadth of potential applications relating structure to function in cortical circuits and neuronal cell biology. Mitochondria and synapse organization are characterized as a function of path length from the soma. Pyramidal connectivity motif frequencies are predicted accurately using a configuration model of random graphs. Pyramidal cells receiving more connections from nearby cells exhibit stronger and more reliable visual responses. Sample code shows data access and analysis.

Regional Neurodegeneration in vitro: The Protective Role of Neural Activity

Traumatic brain injury is a devastating public health problem, the eighth leading cause of death across the world. To improve our understanding of how injury at the cellular scale affects neural circuit function, we developed a protocol to precisely injure individual neurons within an in vitro neural network. We used high speed calcium imaging to estimate alterations in neural activity and connectivity that occur followed targeted microtrauma. Our studies show that mechanically injured neurons inactivate following microtrauma and eventually re-integrate into the network. Single neuron re-integration is dependent on its activity prior to injury and initial connections in the network: more active and integrated neurons are more resistant to microtrauma and more likely to re-integrate into the network. Micromechanical injury leads to neuronal death 6 h post-injury in a subset of both injured and uninjured neurons. Interestingly, neural activity and network participation after injury were associated with survival in linear discriminate analysis (77.3% correct prediction, Wilks' Lambda = 0.838). Based on this observation, we modulated neuronal activity to rescue neurons after microtrauma. Inhibition of neuronal activity provided much greater survivability than did activation of neurons (ANOVA, p < 0.01 with post-hoc Tukey HSD, p < 0.01). Rescue of neurons by blocking activity in the post-acute period is partially mediated by mitochondrial energetics, as we observed silencing neurons after micromechanical injury led to a significant reduction in mitochondrial calcium accumulation. Overall, the present study provides deeper insight into the propagation of injury within networks, demonstrating that together the initial activity, network structure, and post-injury activity levels contribute to the progressive changes in a neural circuit after mechanical trauma.

Dynamics of Structured Networks of Winfree Oscillators

Winfree oscillators are phase oscillator models of neurons, characterized by their phase response curve and pulsatile interaction function. We use the Ott/Antonsen ansatz to study large heterogeneous networks of Winfree oscillators, deriving low-dimensional differential equations which describe the evolution of the expected state of networks of oscillators. We consider the effects of correlations between an oscillator's in-degree and out-degree, and between the in- and out-degrees of an “upstream” and a “downstream” oscillator (degree assortativity). We also consider correlated heterogeneity, where some property of an oscillator is correlated with a structural property such as degree. We finally consider networks with parameter assortativity, coupling oscillators according to their intrinsic frequencies. The results show how different types of network structure influence its overall dynamics.

Columnar grouping preserves synchronization in neuronal networks with distance-dependent time delays

Neuronal connectivity at the cellular level in the cerebral cortex is far from random, with characteristics that point to a hierarchical design with intricately connected neuronal clusters. Here we investigate computationally the effects of varying neuronal cluster connectivity on network synchronization for two different spatial distributions of clusters: one where clusters are arranged in columns in a grid and the other where neurons from different clusters are spatially intermixed. We characterize each case by measuring the degree of neuronal spiking synchrony as a function of the number of connections per neuron and the degree of intercluster connectivity. We find that in both cases as the number of connections per neuron increases, there is an asynchronous to synchronous transition dependent only on intrinsic parameters of the biophysical model. We also observe in both cases that with very low intercluster connectivity clusters have independent firing dynamics yielding a low degree of synchrony. More importantly, we find that for a high number of connections per neuron but intermediate intercluster connectivity, the two spatial distributions of clusters differ in their response where the clusters in a grid have a higher degree of synchrony than the clusters that are intermixed.

Cyclic transitions between higher order motifs underlie sustained asynchronous spiking in sparse recurrent networks

A basic—yet nontrivial—function which neocortical circuitry must satisfy is the ability to maintain stable spiking activity over time. Stable neocortical activity is asynchronous, critical, and low rate, and these features of spiking dynamics contribute to efficient computation and optimal information propagation. However, it remains unclear how neocortex maintains this asynchronous spiking regime. Here we algorithmically construct spiking neural network models, each composed of 5000 neurons. Network construction synthesized topological statistics from neocortex with a set of objective functions identifying naturalistic low-rate, asynchronous, and critical activity. We find that simulations run on the same topology exhibit sustained asynchronous activity under certain sets of initial membrane voltages but truncated activity under others. Synchrony, rate, and criticality do not provide a full explanation of this dichotomy. Consequently, in order to achieve mechanistic understanding of sustained asynchronous activity, we summarized activity as functional graphs where edges between units are defined by pairwise spike dependencies. We then analyzed the intersection between functional edges and synaptic connectivity- i.e. recruitment networks. Higher-order patterns, such as triplet or triangle motifs, have been tied to cooperativity and integration. We find, over time in each sustained simulation, low-variance periodic transitions between isomorphic triangle motifs in the recruitment networks. We quantify the phenomenon as a Markov process and discover that if the network fails to engage this stereotyped regime of motif dominance “cycling”, spiking activity truncates early. Cycling of motif dominance generalized across manipulations of synaptic weights and topologies, demonstrating the robustness of this regime for maintenance of network activity. Our results point to the crucial role of excitatory higher-order patterns in sustaining asynchronous activity in sparse recurrent networks. They also provide a possible explanation why such connectivity and activity patterns have been prominently reported in neocortex.

Neocortical spiking activity tends to be low-rate and non-rhythmic, and to operate near the critical point of a phase transition. It remains unclear how this kind of spiking activity can be maintained within a neuronal network. Neurons are leaky and individual synaptic connections are sparse and weak, making the maintenance of an asynchronous regime a nontrivial problem. Higher order patterns involving more than two units abound in neocortex, and several lines of evidence suggest that they may be instrumental for brain function. For example, stable activity in vivo displays elevated clustering dominated by specific three-node (triplet) motifs. In this study we demonstrate a link between the maintenance of asynchronous activity and triplet motifs. We algorithmically build spiking neural network models to mimic the topology of neocortex and the spiking statistics that characterize wakefulness. We show that higher order coordination of synapses is always present during sustained asynchronous activity. Coordination takes the form of transitions in time between specific triangle motifs. These motifs summarize the way spikes traverse the underlying synaptic topology. The results of our model are consistent with numerous experimental observations, and their generalizability to other weakly and sparsely connected networks is predicted.

Firing rate homeostasis counteracts changes in stability of recurrent neural networks caused by synapse loss in Alzheimer's disease

The impairment of cognitive function in Alzheimer's disease is clearly correlated to synapse loss. However, the mechanisms underlying this correlation are only poorly understood. Here, we investigate how the loss of excitatory synapses in sparsely connected random networks of spiking excitatory and inhibitory neurons alters their dynamical characteristics. Beyond the effects on the activity statistics, we find that the loss of excitatory synapses on excitatory neurons reduces the network's sensitivity to small perturbations. This decrease in sensitivity can be considered as an indication of a reduction of computational capacity. A full recovery of the network's dynamical characteristics and sensitivity can be achieved by firing rate homeostasis, here implemented by an up-scaling of the remaining excitatory-excitatory synapses. Mean-field analysis reveals that the stability of the linearised network dynamics is, in good approximation, uniquely determined by the firing rate, and thereby explains why firing rate homeostasis preserves not only the firing rate but also the network's sensitivity to small perturbations.

The effects of within-neuron degree correlations in networks of spiking neurons

We consider the effects of correlations between the in- and out-degrees of individual neurons on the dynamics of a network of neurons. By using theta neurons, we can derive a set of coupled differential equations for the expected dynamics of neurons with the same in-degree. A Gaussian copula is used to introduce correlations between a neuron's in- and out-degree, and numerical bifurcation analysis is used determine the effects of these correlations on the network's dynamics. For excitatory coupling, we find that inducing positive correlations has a similar effect to increasing the coupling strength between neurons, while for inhibitory coupling it has the opposite effect. We also determine the propensity of various two- and three-neuron motifs to occur as correlations are varied and give a plausible explanation for the observed changes in dynamics.

High-throughput microcircuit analysis of individual human brains through next-generation multineuron patch-clamp

Comparing neuronal microcircuits across different brain regions, species and individuals can reveal common and divergent principles of network computation. Simultaneous patch-clamp recordings from multiple neurons offer the highest temporal and subthreshold resolution to analyse local synaptic connectivity. However, its establishment is technically complex and the experimental performance is limited by high failure rates, long experimental times and small sample sizes. We introduce an in vitro multipatch setup with an automated pipette pressure and cleaning system facilitating recordings of up to 10 neurons simultaneously and sequential patching of additional neurons. We present hardware and software solutions that increase the usability, speed and data throughput of multipatch experiments which allowed probing of 150 synaptic connections between 17 neurons in one human cortical slice and screening of over 600 connections in tissue from a single patient. This method will facilitate the systematic analysis of microcircuits and allow unprecedented assessment of inter-individual variability.

Firing rate distributions in spiking networks with heterogeneous connectivity

Mean-field theory for networks of spiking neurons based on the so-called diffusion approximation has been used to calculate certain measures of neuronal activity which can be compared with experimental data. This includes the distribution of firing rates across the network. However, the theory in its current form applies only to networks in which there is relatively little heterogeneity in the number of incoming and outgoing connections per neuron. Here we extend this theory to include networks with arbitrary degree distributions. Furthermore, the theory takes into account correlations in the in-degree and out-degree of neurons, which would arise, e.g., in the case of networks with hublike neurons. Finally, we show that networks with broad and positively correlated degrees can generate a large-amplitude sustained response to transient stimuli which does not occur in more homogeneous networks.

Robust Associative Learning Is Sufficient to Explain the Structural and Dynamical Properties of Local Cortical Circuits

The ability of neural networks to associate successive states of network activity lies at the basis of many cognitive functions. Hence, we hypothesized that many ubiquitous structural and dynamical properties of local cortical networks result from associative learning. To test this hypothesis, we trained recurrent networks of excitatory and inhibitory neurons on memories composed of varying numbers of associations and compared the resulting network properties with those observed experimentally. We show that, when the network is robustly loaded with near-maximum amount of associations it can support, it develops properties that are consistent with the observed probabilities of excitatory and inhibitory connections, shapes of connection weight distributions, overexpression of specific 2- and 3-neuron motifs, distributions of connection numbers in clusters of 3-8 neurons, sustained, irregular, and asynchronous firing activity, and balance of excitation and inhibition. In addition, memories loaded into the network can be retrieved, even in the presence of noise that is comparable with the baseline variations in the postsynaptic potential. The confluence of these results suggests that many structural and dynamical properties of local cortical networks are simply a byproduct of associative learning. We predict that overexpression of excitatory-excitatory bidirectional connections observed in many cortical systems must be accompanied with underexpression of bidirectionally connected inhibitory-excitatory neuron pairs.SIGNIFICANCE STATEMENT Many structural and dynamical properties of local cortical networks are ubiquitously present across areas and species. Because synaptic connectivity is shaped by experience, we wondered whether continual learning, rather than genetic control, is responsible for producing such features. To answer this question, we developed a biologically constrained recurrent network of excitatory and inhibitory neurons capable of learning predefined sequences of network states. Embedding such associative memories into the network revealed that, when individual neurons are robustly loaded with a near-maximum amount of memories they can support, the network develops many properties that are consistent with experimental observations. Our findings suggest that basic structural and dynamical properties of local networks in the brain are simply a byproduct of learning and memory storage.

Rich-club connectivity, diverse population coupling, and dynamical activity patterns emerging from local cortical circuits

Experimental studies have begun revealing essential properties of the structural connectivity and the spatiotemporal activity dynamics of cortical circuits. To integrate these properties from anatomy and physiology, and to elucidate the links between them, we develop a novel cortical circuit model that captures a range of realistic features of synaptic connectivity. We show that the model accounts for the emergence of higher-order connectivity structures, including highly connected hub neurons that form an interconnected rich-club. The circuit model exhibits a rich repertoire of dynamical activity states, ranging from asynchronous to localized and global propagating wave states. We find that around the transition between asynchronous and localized propagating wave states, our model quantitatively reproduces a variety of major empirical findings regarding neural spatiotemporal dynamics, which otherwise remain disjointed in existing studies. These dynamics include diverse coupling (correlation) between spiking activity of individual neurons and the population, dynamical wave patterns with variable speeds and precise temporal structures of neural spikes. We further illustrate how these neural dynamics are related to the connectivity properties by analysing structural contributions to variable spiking dynamics and by showing that the rich-club structure is related to the diverse population coupling. These findings establish an integrated account of structural connectivity and activity dynamics of local cortical circuits, and provide new insights into understanding their working mechanisms.

To integrate essential anatomical and physiological properties of local cortical circuits and to elucidate mechanistic links between them, we develop a novel circuit model capturing key synaptic connectivity features. We show that the model explains the emergence of a range of connectivity patterns such as rich-club connectivity, and gives rise to a rich repertoire of cortical states. We identify both the anatomical and physiological mechanisms underlying the transition of these cortical states, and show that our model reconciles an otherwise disparate set of key physiological findings on neural activity dynamics. We further illustrate how these neural dynamics are related to the connectivity properties by analysing structural contributions to variable spiking dynamics and by showing that the rich-club structure is related to diverse neural population correlations as observed recently. Our model thus provides a framework for integrating and explaining a variety of neural connectivity properties and spatiotemporal activity dynamics observed in experimental studies, and provides novel experimentally testable predictions.

Introducing chaotic codes for the modulation of code modulated visual evoked potentials (c-VEP) in normal adults for visual fatigue reduction

Code modulated Visual Evoked Potentials (c-VEP) based BCI studies usually employ m-sequences as a modulating codes for their broadband spectrum and correlation property. However, subjective fatigue of the presented codes has been a problem. In this study, we introduce chaotic codes containing broadband spectrum and similar correlation property. We examined whether the introduced chaotic codes could be decoded from EEG signals and also compared the subjective fatigue level with m-sequence codes in normal subjects. We generated chaotic code from one-dimensional logistic map and used it with conventional 31-bit m-sequence code. In a c-VEP based study in normal subjects (n = 44, 21 females) we presented these codes visually and recorded EEG signals from the corresponding codes for their four lagged versions. Canonical correlation analysis (CCA) and spatiotemporal beamforming (STB) methods were used for target identification and comparison of responses. Additionally, we compared the subjective self-declared fatigue using VAS caused by presented m-sequence and chaotic codes. The introduced chaotic code was decoded from EEG responses with CCA and STB methods. The maximum total accuracy values of 93.6 ± 11.9% and 94 ± 14.4% were achieved with STB method for chaotic and m-sequence codes for all subjects respectively. The achieved accuracies in all subjects were not significantly different in m-sequence and chaotic codes. There was significant reduction in subjective fatigue caused by chaotic codes compared to the m-sequence codes. Both m-sequence and chaotic codes were similar in their accuracies as evaluated by CCA and STB methods. The chaotic codes significantly reduced subjective fatigue compared to the m-sequence codes.

Ensemble stacking mitigates biases in inference of synaptic connectivity

A promising alternative to directly measuring the anatomical connections in a neuronal population is inferring the connections from the activity. We employ simulated spiking neuronal networks to compare and contrast commonly used inference methods that identify likely excitatory synaptic connections using statistical regularities in spike timing. We find that simple adjustments to standard algorithms improve inference accuracy: A signing procedure improves the power of unsigned mutual-information-based approaches and a correction that accounts for differences in mean and variance of background timing relationships, such as those expected to be induced by heterogeneous firing rates, increases the sensitivity of frequency-based methods. We also find that different inference methods reveal distinct subsets of the synaptic network and each method exhibits different biases in the accurate detection of reciprocity and local clustering. To correct for errors and biases specific to single inference algorithms, we combine methods into an ensemble. Ensemble predictions, generated as a linear combination of multiple inference algorithms, are more sensitive than the best individual measures alone, and are more faithful to ground-truth statistics of connectivity, mitigating biases specific to single inference methods. These weightings generalize across simulated datasets, emphasizing the potential for the broad utility of ensemble-based approaches.