Beyond the cortical column: abundance and physiology of horizontal connections imply a strong role for inputs from the surround

Dendrites and efficiency: Optimizing performance and resource utilization

The brain is a highly efficient system that has evolved to optimize performance under limited resources. In this review, we highlight recent theoretical and experimental studies that support the view that dendrites make information processing and storage in the brain more efficient. This is achieved through the dynamic modulation of integration versus segregation of inputs and activity within a neuron. We argue that under conditions of limited energy and space, dendrites help biological networks to implement complex functions such as processing natural stimuli on behavioral timescales, performing the inference process on those stimuli in a context-specific manner, and storing the information in overlapping populations of neurons. A global picture starts to emerge, in which dendrites help the brain achieve efficiency through a combination of optimization strategies that balance the tradeoff between performance and resource utilization.

Layer 1 of somatosensory cortex: an important site for input to a tiny cortical compartment

Neocortical layer 1 has been proposed to be at the center for top-down and bottom-up integration. It is a locus for interactions between long-range inputs, layer 1 interneurons, and apical tuft dendrites of pyramidal neurons. While input to layer 1 has been studied intensively, the level and effect of input to this layer has still not been completely characterized. Here we examined the input to layer 1 of mouse somatosensory cortex with retrograde tracing and optogenetics. Our assays reveal that local input to layer 1 is predominantly from layers 2/3 and 5 pyramidal neurons and interneurons, and that subtypes of local layers 5 and 6b neurons project to layer 1 with different probabilities. Long-range input from sensory-motor cortices to layer 1 of somatosensory cortex arose predominantly from layers 2/3 neurons. Our optogenetic experiments showed that intra-telencephalic layer 5 pyramidal neurons drive layer 1 interneurons but have no effect locally on layer 5 apical tuft dendrites. Dual retrograde tracing revealed that a fraction of local and long-range neurons was both presynaptic to layer 5 neurons and projected to layer 1. Our work highlights the prominent role of local inputs to layer 1 and shows the potential for complex interactions between long-range and local inputs, which are both in position to modify the output of somatosensory cortex.

Efficient parameter calibration and real-time simulation of large-scale spiking neural networks with GeNN and NEST

Spiking neural networks (SNNs) represent the state-of-the-art approach to the biologically realistic modeling of nervous system function. The systematic calibration for multiple free model parameters is necessary to achieve robust network function and demands high computing power and large memory resources. Special requirements arise from closed-loop model simulation in virtual environments and from real-time simulation in robotic application. Here, we compare two complementary approaches to efficient large-scale and real-time SNN simulation. The widely used NEural Simulation Tool (NEST) parallelizes simulation across multiple CPU cores. The GPU-enhanced Neural Network (GeNN) simulator uses the highly parallel GPU-based architecture to gain simulation speed. We quantify fixed and variable simulation costs on single machines with different hardware configurations. As a benchmark model, we use a spiking cortical attractor network with a topology of densely connected excitatory and inhibitory neuron clusters with homogeneous or distributed synaptic time constants and in comparison to the random balanced network. We show that simulation time scales linearly with the simulated biological model time and, for large networks, approximately linearly with the model size as dominated by the number of synaptic connections. Additional fixed costs with GeNN are almost independent of model size, while fixed costs with NEST increase linearly with model size. We demonstrate how GeNN can be used for simulating networks with up to 3.5 · 10⁶ neurons (> 3 · 10¹²synapses) on a high-end GPU, and up to 250, 000 neurons (25 · 10⁹ synapses) on a low-cost GPU. Real-time simulation was achieved for networks with 100, 000 neurons. Network calibration and parameter grid search can be efficiently achieved using batch processing. We discuss the advantages and disadvantages of both approaches for different use cases.

Modular Organization of Signal Transmission in Primate Somatosensory Cortex

Axonal patches are known as the major sites of synaptic connections in the cerebral cortex of higher order mammals. However, the functional role of these patches is highly debated. Patches are formed by populations of nearby neurons in a topographic manner and are recognized as the termination fields of long-distance lateral connections within and between cortical areas. In addition, axons form numerous boutons that lie outside the patches, whose function is also unknown. To better understand the functional roles of these two distinct populations of boutons, we compared individual and collective morphological features of axons within and outside the patches of intra-areal, feedforward, and feedback pathways by way of tract tracing in the somatosensory cortex of New World monkeys. We found that, with the exception of tortuosity, which is an invariant property, bouton spacing and axonal convergence properties differ significantly between axons within patch and no-patch domains. Principal component analyses corroborated the clustering of axons according to patch formation without any additional effect by the type of pathway or laminar distribution. Stepwise logistic regression identified convergence and bouton density as the best predictors of patch formation. These findings support that patches are specific sites of axonal convergence that promote the synchronous activity of neuronal populations. On the other hand, no-patch domains could form a neuroanatomical substrate to diversify the responses of cortical neurons.

Classical-Contextual Interactions in V1 May Rely on Dendritic Computations

A signature feature of the neocortex is the dense network of horizontal connections (HCs) through which pyramidal neurons (PNs) exchange "contextual" information. In primary visual cortex (V1), HCs are thought to facilitate boundary detection, a crucial operation for object recognition, but how HCs modulate PN responses to boundary cues within their classical receptive fields (CRF) remains unknown. We began by "asking" natural images, through a structured data collection and ground truth labeling process, what function a V1 cell should use to compute boundary probability from aligned edge cues within and outside its CRF. The "answer" was an asymmetric 2-D sigmoidal function, whose nonlinear form provides the first normative account for the "multiplicative" center-flanker interactions previously reported in V1 neurons (Kapadia et al., 1995, 2000; Polat et al., 1998). Using a detailed compartmental model, we then show that this boundary-detecting classical-contextual interaction function can be computed by NMDAR-dependent spatial synaptic interactions within PN dendrites - the site where classical and contextual inputs first converge in the cortex. In additional simulations, we show that local interneuron circuitry activated by HCs can powerfully leverage the nonlinear spatial computing capabilities of PN dendrites, providing the cortex with a highly flexible substrate for integration of classical and contextual information.

Focal lesions induce large-scale percolation of sleep-like intracerebral activity in awake humans

Focal cortical lesions are known to result in large-scale functional alterations involving distant areas; however, little is known about the electrophysiological mechanisms underlying these network effects. Here, we addressed this issue by analysing the short and long distance intracranial effects of controlled structural lesions in humans. The changes in Stereo-Electroencephalographic (SEEG) activity after Radiofrequency-Thermocoagulation (RFTC) recorded in 21 epileptic subjects were assessed with respect to baseline resting wakefulness and sleep activity. In addition, Cortico-Cortical Evoked Potentials (CCEPs) recorded before the lesion were employed to interpret these changes with respect to individual long-range connectivity patterns. We found that small structural ablations lead to the generation and large-scale propagation of sleep-like slow waves within the awake brain. These slow waves match those recorded in the same subjects during sleep, are prevalent in perilesional areas, but can percolate up to distances of 60 mm through specific long-range connections, as predicted by CCEPs. Given the known impact of slow waves on information processing and cortical plasticity, demonstrating their intrusion and percolation within the awake brain add key elements to our understanding of network dysfunction after cortical injuries.

Scale-Free Dynamics in Animal Groups and Brain Networks

Collective phenomena fascinate by the emergence of order in systems composed of a myriad of small entities. They are ubiquitous in nature and can be found over a vast range of scales in physical and biological systems. Their key feature is the seemingly effortless emergence of adaptive collective behavior that cannot be trivially explained by the properties of the system's individual components. This perspective focuses on recent insights into the similarities of correlations for two apparently disparate phenomena: flocking in animal groups and neuronal ensemble activity in the brain. We first will summarize findings on the spontaneous organization in bird flocks and macro-scale human brain activity utilizing correlation functions and insights from critical dynamics. We then will discuss recent experimental findings that apply these approaches to the collective response of neurons to visual and motor processing, i.e., to local perturbations of neuronal networks at the meso- and microscale. We show how scale-free correlation functions capture the collective organization of neuronal avalanches in evoked neuronal populations in nonhuman primates and between neurons during visual processing in rodents. These experimental findings suggest that the coherent collective neural activity observed at scales much larger than the length of the direct neuronal interactions is demonstrative of a phase transition and we discuss the experimental support for either discontinuous or continuous phase transitions. We conclude that at or near a phase-transition neuronal information can propagate in the brain with similar efficiency as proposed to occur in the collective adaptive response observed in some animal groups.

Robustness of connectome harmonics to local gray matter and long-range white matter connectivity changes

Recently, it has been proposed that the harmonic patterns emerging from the brain's structural connectivity underlie the resting state networks of the human brain. These harmonic patterns, termed connectome harmonics, are estimated as the Laplace eigenfunctions of the combined gray and white matters connectivity matrices and yield a connectome-specific extension of the well-known Fourier basis. However, it remains unclear how topological properties of the combined connectomes constrain the precise shape of the connectome harmonics and their relationships to the resting state networks. Here, we systematically study how alterations of the local and long-range connectivity matrices affect the spatial patterns of connectome harmonics. Specifically, the proportion of local gray matter homogeneous connectivity versus long-range white-matter heterogeneous connectivity is varied by means of weight-based matrix thresholding, distance-based matrix trimming, and several types of matrix randomizations. We demonstrate that the proportion of local gray matter connections plays a crucial role for the emergence of wide-spread, functionally meaningful, and originally published connectome harmonic patterns. This finding is robust for several different cortical surface templates, mesh resolutions, or widths of the local diffusion kernel. Finally, using the connectome harmonic framework, we also provide a proof-of-concept for how targeted structural changes such as the atrophy of inter-hemispheric callosal fibers and gray matter alterations may predict functional deficits associated with neurodegenerative conditions.

Two-Photon Voltage Imaging of Spontaneous Activity from Multiple Neurons Reveals Network Activity in Brain Tissue

Recording the electrical activity of multiple neurons simultaneously would greatly facilitate studies on the function of neuronal circuits. The combination of the fast scanning by random-access multiphoton microscopy (RAMP) and the latest two-photon-compatible high-performance fluorescent genetically encoded voltage indicators (GEVIs) has enabled action potential detection in deep layers in in vivo brain. However, neuron connectivity analysis on optically recorded action potentials from multiple neurons in brain tissue has yet to be achieved. With high expression of a two-photon-compatible GEVI, ASAP3, via in utero electroporation and RAMP, we achieved voltage recording of spontaneous activities from multiple neurons in brain slice. We provide evidence for the developmental changes in intralaminar horizontal connections in somatosensory cortex layer 2/3 with a greater sensitivity than calcium imaging. This method thus enables investigation of neuronal network connectivity at the cellular resolution in brain tissue.

Facilitating the propagation of spiking activity in feedforward networks by including feedback

Transient oscillations in network activity upon sensory stimulation have been reported in different sensory areas of the brain. These evoked oscillations are the generic response of networks of excitatory and inhibitory neurons (EI-networks) to a transient external input. Recently, it has been shown that this resonance property of EI-networks can be exploited for communication in modular neuronal networks by enabling the transmission of sequences of synchronous spike volleys (’pulse packets’), despite the sparse and weak connectivity between the modules. The condition for successful transmission is that the pulse packet (PP) intervals match the period of the modules’ resonance frequency. Hence, the mechanism was termed communication through resonance (CTR). This mechanism has three severe constraints, though. First, it needs periodic trains of PPs, whereas single PPs fail to propagate. Second, the inter-PP interval needs to match the network resonance. Third, transmission is very slow, because in each module, the network resonance needs to build up over multiple oscillation cycles. Here, we show that, by adding appropriate feedback connections to the network, the CTR mechanism can be improved and the aforementioned constraints relaxed. Specifically, we show that adding feedback connections between two upstream modules, called the resonance pair, in an otherwise feedforward modular network can support successful propagation of a single PP throughout the entire network. The key condition for successful transmission is that the sum of the forward and backward delays in the resonance pair matches the resonance frequency of the network modules. The transmission is much faster, by more than a factor of two, than in the original CTR mechanism. Moreover, it distinctly lowers the threshold for successful communication by synchronous spiking in modular networks of weakly coupled networks. Thus, our results suggest a new functional role of bidirectional connectivity for the communication in cortical area networks.

The cortex is organized as a modular system, with the modules (cortical areas) communicating via weak long-range connections. It has been suggested that the intrinsic resonance properties of population activities in these areas might contribute to enabling successful communication. A module’s intrinsic resonance appears in the damped oscillatory response to an incoming spike volley, enabling successful communication during the peaks of the oscillation. Such communication can be exploited in feedforward networks, provided the participating networks have similar resonance frequencies. This, however, is not necessarily true for cortical networks. Moreover, the communication is slow, as it takes several oscillation cycles to build up the response in the downstream network. Also, only periodic trains of spikes volleys (and not single volleys) with matching intervals can propagate. Here, we present a novel mechanism that alleviates these shortcomings and enables propagation of synchronous spiking across weakly connected networks with not necessarily identical resonance frequencies. In this framework, an individual spike volley can propagate by local amplification through reverberation in a loop between two successive networks, connected by feedforward and feedback connections: the resonance pair. This overcomes the need for activity build-up in downstream networks, causing the volley to propagate distinctly faster and more reliably.

A New Rehabilitative Mechanism in Primary Motor Cortex After Peripheral Trauma

Homuncular organization, i.e., the neuronal representation of the human body within the primary motor cortex, is one of the most fundamental principles of the human brain. Despite this, in rare peripheral nerve surgery patients, the transformation of a monofunctional (diaphragm activation) into a bifunctional motor area (diaphragm and arm activation is controlled by the same cortical area) has previously been demonstrated. The mechanisms behind this transformation are not fully known. To investigate this transformation of a monofunctional area we investigate functional connectivity changes in a unique and highly instructive pathophysiological patient model. These patients suffer from complete brachial plexus avulsion with arm paralysis and had been treated with reconnection of the end of the musculocutaneous nerve to the side of a fully functional phrenic nerve to regain function. Task-based functional connectivity between the arm representations and the diaphragm (phrenic nerve) representations were examined in six patients and 12 aged matched healthy controls at ultra-high field MRI while they either performed or tried isolated elbow flexion or conducted forced abdominal inspiration. Functional connectivity values are considerably increased between the diseased arm and the bilateral diaphragm areas while trying strong muscle tension in the diseased arm as compared to the healthy arm. This effect was not found as compared to the healthy arm in the patient group. This connectivity was stronger between ipsilateral than between corresponding contralateral brain regions. No corresponding differences were found in healthy subjects. Our data suggests that the increased functional connectivity between the deprived arm area and the diaphragm area drives biceps muscle function. From this findings we infer that this new rehabilitative mechanism in the primary motor cortex may establish new intrahemispheric connections within the brain and the motor cortex in particular to reroute the output of a completely denervated motor area. This study extend current knowledge about neuroplasticity within the motor cortex.

Gradient theories of brain activation: A novel application to studying the parental brain

PURPOSE OF REVIEW

Parental brain research primarily employs general-linear-model-based (GLM-based) analyses to assess blood-oxygenation-level-dependent responses to infant auditory and visual cues, reporting common responses in shared cortical and subcortical structures. However, this approach does not reveal intermixed neural substrates related to different sensory modalities. We consider this notion in studying the parental brain.

RECENT FINDINGS

Spatial independent component analysis (sICA) has been used to separate mixed source signals from overlapping functional networks. We explore relative differences between GLM-based analysis and sICA as applied to an fMRI dataset acquired from women while they listened to infant cries or viewed infant sad faces.

SUMMARY

There is growing appreciation for the value of moving beyond GLM-based analyses to consider brain functional organization as continuous, distributive, and overlapping gradients of neural substrates related to different sensory modalities. Preliminary findings suggest sICA can be applied to the study of the parental brain.

Perturbing low dimensional activity manifolds in spiking neuronal networks

Several recent studies have shown that neural activity in vivo tends to be constrained to a low-dimensional manifold. Such activity does not arise in simulated neural networks with homogeneous connectivity and it has been suggested that it is indicative of some other connectivity pattern in neuronal networks. In particular, this connectivity pattern appears to be constraining learning so that only neural activity patterns falling within the intrinsic manifold can be learned and elicited. Here, we use three different models of spiking neural networks (echo-state networks, the Neural Engineering Framework and Efficient Coding) to demonstrate how the intrinsic manifold can be made a direct consequence of the circuit connectivity. Using this relationship between the circuit connectivity and the intrinsic manifold, we show that learning of patterns outside the intrinsic manifold corresponds to much larger changes in synaptic weights than learning of patterns within the intrinsic manifold. Assuming larger changes to synaptic weights requires extensive learning, this observation provides an explanation of why learning is easier when it does not require the neural activity to leave its intrinsic manifold.

Excitable neuronal assemblies with adaptation as a building block of brain circuits for velocity-controlled signal propagation

The time scale of neuronal network dynamics is determined by synaptic interactions and neuronal signal integration, both of which occur on the time scale of milliseconds. Yet many behaviors like the generation of movements or vocalizations of sounds occur on the much slower time scale of seconds. Here we ask the question of how neuronal networks of the brain can support reliable behavior on this time scale. We argue that excitable neuronal assemblies with spike-frequency adaptation may serve as building blocks that can flexibly adjust the speed of execution of neural circuit function. We show in simulations that a chain of neuronal assemblies can propagate signals reliably, similar to the well-known synfire chain, but with the crucial difference that the propagation speed is slower and tunable to the behaviorally relevant range. Moreover we study a grid of excitable neuronal assemblies as a simplified model of the somatosensory barrel cortex of the mouse and demonstrate that various patterns of experimentally observed spatial activity propagation can be explained.

Models of activity propagation in cortical networks have often been based on feedforward structures. Here we propose a model of activity propagation, called excitation chain, which does not need such a feedforward structure. The model is composed of excitable neural assemblies with spike-frequency adaptation, connected bidirectionally in a row or a grid. This prototypical neural circuit can propagate activity forwards, backwards or in both directions. Furthermore, the propagation speed is slow enough to trigger the generation of behaviors on the time scale of hundreds of milliseconds. A two-dimensional variant of the model is able to generate different activity propagation patterns, similar to spontaneous activity and stimulus-evoked responses in anesthetized mouse barrel cortex. We propose the excitation chain model as a basic component that can be employed in various ways to create spiking neural circuit models that generate signals on behavioral time scales. In contrast to abstract models of excitable media, our model makes an explicit link to the time scale of neuronal spikes.

Cortical Reorganization of Sensorimotor Systems and the Role of Intracortical Circuits After Spinal Cord Injury

The plasticity of sensorimotor systems in mammals underlies the capacity for motor learning as well as the ability to relearn following injury. Spinal cord injury, which both deprives afferent input and interrupts efferent output, results in a disruption of cortical somatotopy. While changes in corticospinal axons proximal to the lesion are proposed to support the reorganization of cortical motor maps after spinal cord injury, intracortical horizontal connections are also likely to be critical substrates for rehabilitation-mediated recovery. Intrinsic connections have been shown to dictate the reorganization of cortical maps that occurs in response to skilled motor learning as well as after peripheral injury. Cortical networks incorporate changes in motor and sensory circuits at subcortical or spinal levels to induce map remodeling in the neocortex. This review focuses on the reorganization of cortical networks observed after injury and posits a role of intracortical circuits in recovery.

Winnerless competition in clustered balanced networks: inhibitory assemblies do the trick

Balanced networks are a frequently employed basic model for neuronal networks in the mammalian neocortex. Large numbers of excitatory and inhibitory neurons are recurrently connected so that the numerous positive and negative inputs that each neuron receives cancel out on average. Neuronal firing is therefore driven by fluctuations in the input and resembles the irregular and asynchronous activity observed in cortical in vivo data. Recently, the balanced network model has been extended to accommodate clusters of strongly interconnected excitatory neurons in order to explain persistent activity in working memory-related tasks. This clustered topology introduces multistability and winnerless competition between attractors and can capture the high trial-to-trial variability and its reduction during stimulation that has been found experimentally. In this prospect article, we review the mean field description of balanced networks of binary neurons and apply the theory to clustered networks. We show that the stable fixed points of networks with clustered excitatory connectivity tend quickly towards firing rate saturation, which is generally inconsistent with experimental data. To remedy this shortcoming, we then present a novel perspective on networks with locally balanced clusters of both excitatory and inhibitory neuron populations. This approach allows for true multistability and moderate firing rates in activated clusters over a wide range of parameters. Our findings are supported by mean field theory and numerical network simulations. Finally, we discuss possible applications of the concept of joint excitatory and inhibitory clustering in future cortical network modelling studies.

Self-Consistent Scheme for Spike-Train Power Spectra in Heterogeneous Sparse Networks

Recurrent networks of spiking neurons can be in an asynchronous state characterized by low or absent cross-correlations and spike statistics which resemble those of cortical neurons. Although spatial correlations are negligible in this state, neurons can show pronounced temporal correlations in their spike trains that can be quantified by the autocorrelation function or the spike-train power spectrum. Depending on cellular and network parameters, correlations display diverse patterns (ranging from simple refractory-period effects and stochastic oscillations to slow fluctuations) and it is generally not well-understood how these dependencies come about. Previous work has explored how the single-cell correlations in a homogeneous network (excitatory and inhibitory integrate-and-fire neurons with nearly balanced mean recurrent input) can be determined numerically from an iterative single-neuron simulation. Such a scheme is based on the fact that every neuron is driven by the network noise (i.e., the input currents from all its presynaptic partners) but also contributes to the network noise, leading to a self-consistency condition for the input and output spectra. Here we first extend this scheme to homogeneous networks with strong recurrent inhibition and a synaptic filter, in which instabilities of the previous scheme are avoided by an averaging procedure. We then extend the scheme to heterogeneous networks in which (i) different neural subpopulations (e.g., excitatory and inhibitory neurons) have different cellular or connectivity parameters; (ii) the number and strength of the input connections are random (Erdős-Rényi topology) and thus different among neurons. In all heterogeneous cases, neurons are lumped in different classes each of which is represented by a single neuron in the iterative scheme; in addition, we make a Gaussian approximation of the input current to the neuron. These approximations seem to be justified over a broad range of parameters as indicated by comparison with simulation results of large recurrent networks. Our method can help to elucidate how network heterogeneity shapes the asynchronous state in recurrent neural networks.

Assessing the Role of Inhibition in Stabilizing Neocortical Networks Requires Large-Scale Perturbation of the Inhibitory Population

Neurons within cortical microcircuits are interconnected with recurrent excitatory synaptic connections that are thought to amplify signals (Douglas and Martin, 2007), form selective subnetworks (Ko et al., 2011), and aid feature discrimination. Strong inhibition (Haider et al., 2013) counterbalances excitation, enabling sensory features to be sharpened and represented by sparse codes (Willmore et al., 2011). This balance between excitation and inhibition makes it difficult to assess the strength, or gain, of recurrent excitatory connections within cortical networks, which is key to understanding their operational regime and the computations that they perform. Networks that combine an unstable high-gain excitatory population with stabilizing inhibitory feedback are known as inhibition-stabilized networks (ISNs) (Tsodyks et al., 1997). Theoretical studies using reduced network models predict that ISNs produce paradoxical responses to perturbation, but experimental perturbations failed to find evidence for ISNs in cortex (Atallah et al., 2012). Here, we reexamined this question by investigating how cortical network models consisting of many neurons behave after perturbations and found that results obtained from reduced network models fail to predict responses to perturbations in more realistic networks. Our models predict that a large proportion of the inhibitory network must be perturbed to reliably detect an ISN regime robustly in cortex. We propose that wide-field optogenetic suppression of inhibition under promoters targeting a large fraction of inhibitory neurons may provide a perturbation of sufficient strength to reveal the operating regime of cortex. Our results suggest that detailed computational models of optogenetic perturbations are necessary to interpret the results of experimental paradigms.SIGNIFICANCE STATEMENT Many useful computational mechanisms proposed for cortex require local excitatory recurrence to be very strong, such that local inhibitory feedback is necessary to avoid epileptiform runaway activity (an "inhibition-stabilized network" or "ISN" regime). However, recent experimental results suggest that this regime may not exist in cortex. We simulated activity perturbations in cortical networks of increasing realism and found that, to detect ISN-like properties in cortex, large proportions of the inhibitory population must be perturbed. Current experimental methods for inhibitory perturbation are unlikely to satisfy this requirement, implying that existing experimental observations are inconclusive about the computational regime of cortex. Our results suggest that new experimental designs targeting a majority of inhibitory neurons may be able to resolve this question.

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.

A quantitative theory of gamma synchronization in macaque V1

Gamma-band synchronization coordinates brief periods of excitability in oscillating neuronal populations to optimize information transmission during sensation and cognition. Commonly, a stable, shared frequency over time is considered a condition for functional neural synchronization. Here, we demonstrate the opposite: instantaneous frequency modulations are critical to regulate phase relations and synchronization. In monkey visual area V1, nearby local populations driven by different visual stimulation showed different gamma frequencies. When similar enough, these frequencies continually attracted and repulsed each other, which enabled preferred phase relations to be maintained in periods of minimized frequency difference. Crucially, the precise dynamics of frequencies and phases across a wide range of stimulus conditions was predicted from a physics theory that describes how weakly coupled oscillators influence each other's phase relations. Hence, the fundamental mathematical principle of synchronization through instantaneous frequency modulations applies to gamma in V1 and is likely generalizable to other brain regions and rhythms.

A biological blueprint for the axons of superficial layer pyramidal cells in cat primary visual cortex

Pyramidal cells in the superficial layers of neocortex of higher mammals form a lateral network of axon clusters known as the 'daisy' network. The role of these axon clusters remains speculative and we still lack a comprehensive quantitative description of the single neurons forming the daisy or their heterogeneity. We filled intracellularly 50 superficial layer pyramidal neurons in the cat primary visual cortex and reconstructed the axonal tree and their synaptic boutons in 3D. Individual bouton clusters were identified using an objective mean-shift algorithm. By parameterizing the morphology of these 50 axonal trees and the 217 bouton clusters they formed, we were able to extract one set of relatively constant parameters and another set of variable parameters. Both sets combined allowed us to outline a comprehensive biological blueprint of superficial layer pyramidal neurons. Overall, our detailed analysis supports the hypothesis that pyramidal neurons use their lateral clusters to combine differential contextual cues, required for context-dependent processing of natural scenes.

Large-scale functional network overlap is a general property of brain functional organization: Reconciling inconsistent fMRI findings from general-linear-model-based analyses

Functional magnetic resonance imaging (fMRI) studies regularly use univariate general-linear-model-based analyses (GLM). Their findings are often inconsistent across different studies, perhaps because of several fundamental brain properties including functional heterogeneity, balanced excitation and inhibition (E/I), and sparseness of neuronal activities. These properties stipulate heterogeneous neuronal activities in the same voxels and likely limit the sensitivity and specificity of GLM. This paper selectively reviews findings of histological and electrophysiological studies and fMRI spatial independent component analysis (sICA) and reports new findings by applying sICA to two existing datasets. The extant and new findings consistently demonstrate several novel features of brain functional organization not revealed by GLM. They include overlap of large-scale functional networks (FNs) and their concurrent opposite modulations, and no significant modulations in activity of most FNs across the whole brain during any task conditions. These novel features of brain functional organization are highly consistent with the brain's properties of functional heterogeneity, balanced E/I, and sparseness of neuronal activity, and may help reconcile inconsistent GLM findings.

Reduced functional connectivity within the primary motor cortex of patients with brachial plexus injury

This study aims at the effects of traumatic brachial plexus lesion with root avulsions (BPA) upon the organization of the primary motor cortex (M1). Nine right-handed patients with a right BPA in whom an intercostal to musculocutaneous (ICN-MC) nerve transfer was performed had post-operative resting state fMRI scanning. The analysis of empirical functional correlations between neighboring voxels revealed faster correlation decay as a function of distance in the M1 region corresponding to the arm in BPA patients as compared to the control group. No differences between the two groups were found in the face area. We also investigated whether such larger decay in patients could be attributed to a gray matter diminution in M1. Structural imaging analysis showed no difference in gray matter density between groups. Our findings suggest that the faster decay in neighboring functional correlations without significant gray matter diminution in BPA patients could be related to a reduced activity in intrinsic horizontal connections in M1 responsible for upper limb motor synergies.

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.

Push-Pull Receptive Field Organization and Synaptic Depression: Mechanisms for Reliably Encoding Naturalistic Stimuli in V1

Neurons in the primary visual cortex are known for responding vigorously but with high variability to classical stimuli such as drifting bars or gratings. By contrast, natural scenes are encoded more efficiently by sparse and temporal precise spiking responses. We used a conductance-based model of the visual system in higher mammals to investigate how two specific features of the thalamo-cortical pathway, namely push-pull receptive field organization and fast synaptic depression, can contribute to this contextual reshaping of V1 responses. By comparing cortical dynamics evoked respectively by natural vs. artificial stimuli in a comprehensive parametric space analysis, we demonstrate that the reliability and sparseness of the spiking responses during natural vision is not a mere consequence of the increased bandwidth in the sensory input spectrum. Rather, it results from the combined impacts of fast synaptic depression and push-pull inhibition, the later acting for natural scenes as a form of “effective” feed-forward inhibition as demonstrated in other sensory systems. Thus, the combination of feedforward-like inhibition with fast thalamo-cortical synaptic depression by simple cells receiving a direct structured input from thalamus composes a generic computational mechanism for generating a sparse and reliable encoding of natural sensory events.

Mechanisms of Self-Sustained Oscillatory States in Hierarchical Modular Networks with Mixtures of Electrophysiological Cell Types

In a network with a mixture of different electrophysiological types of neurons linked by excitatory and inhibitory connections, temporal evolution leads through repeated epochs of intensive global activity separated by intervals with low activity level. This behavior mimics “up” and “down” states, experimentally observed in cortical tissues in absence of external stimuli. We interpret global dynamical features in terms of individual dynamics of the neurons. In particular, we observe that the crucial role both in interruption and in resumption of global activity is played by distributions of the membrane recovery variable within the network. We also demonstrate that the behavior of neurons is more influenced by their presynaptic environment in the network than by their formal types, assigned in accordance with their response to constant current.

Functional congruity in local auditory cortical microcircuits

Functional columns of primary auditory cortex (AI) are arranged in layers, each composed of highly connected fine-scale networks. The basic response properties and interactions within these local subnetworks have only begun to be assessed. We examined the functional diversity of neurons within the laminar microarchitecture of cat AI to determine the relationship of spectrotemporal processing between neighboring neurons. Neuronal activity was recorded across the cortical layers while presenting a dynamically modulated broadband noise. Spectrotemporal receptive fields (STRFs) and their nonlinear input/output functions (nonlinearities) were constructed for each neuron and compared for pairs of neurons simultaneously recorded at the same contact site. Properties of these local neuron pairs showed greater similarity than non-paired neurons within the same column for all considered parameters including firing rate, envelope-phase precision, preferred spectral and temporal modulation frequency, as well as for the threshold and transition of the response nonlinearity. This higher functional similarity of paired versus non-paired neurons was most apparent in infragranular neuron pairs, and less for local supragranular and granular pairs. The functional similarity of local paired neurons for firing rate, best temporal modulation frequency and two nonlinearity aspects was laminar dependent, with infragranular local pair-wise differences larger than for granular or supragranular layers. Synchronous spiking events between pairs of neurons revealed that simultaneous 'Bicellular' spikes, in addition to carrying higher stimulus information than non-synchronized spikes, encoded faster modulation frequencies. Bicellular functional differences to the best matched of the paired neurons could be substantial. Bicellular nonlinearities showed that synchronous spikes act to transmit stimulus information with higher fidelity and precision than non-synchronous spikes of the individual neurons, thus, likely enhancing stimulus feature selectivity in their target neurons. Overall, the well-correlated and temporally precise processing within local subnetworks of cat AI showed laminar-dependent functional diversity in spectrotemporal processing, despite high intra-columnar congruity in frequency preference.

A framework for the first-person internal sensation of visual perception in mammals and a comparable circuitry for olfactory perception in Drosophila

Perception is a first-person internal sensation induced within the nervous system at the time of arrival of sensory stimuli from objects in the environment. Lack of access to the first-person properties has limited viewing perception as an emergent property and it is currently being studied using third-person observed findings from various levels. One feasible approach to understand its mechanism is to build a hypothesis for the specific conditions and required circuit features of the nodal points where the mechanistic operation of perception take place for one type of sensation in one species and to verify it for the presence of comparable circuit properties for perceiving a different sensation in a different species. The present work explains visual perception in mammalian nervous system from a first-person frame of reference and provides explanations for the homogeneity of perception of visual stimuli above flicker fusion frequency, the perception of objects at locations different from their actual position, the smooth pursuit and saccadic eye movements, the perception of object borders, and perception of pressure phosphenes. Using results from temporal resolution studies and the known details of visual cortical circuitry, explanations are provided for (a) the perception of rapidly changing visual stimuli, (b) how the perception of objects occurs in the correct orientation even though, according to the third-person view, activity from the visual stimulus reaches the cortices in an inverted manner and (c) the functional significance of well-conserved columnar organization of the visual cortex. A comparable circuitry detected in a different nervous system in a remote species-the olfactory circuitry of the fruit fly Drosophila melanogaster-provides an opportunity to explore circuit functions using genetic manipulations, which, along with high-resolution microscopic techniques and lipid membrane interaction studies, will be able to verify the structure-function details of the presented mechanism of perception.

Dopaminergic impact on local and global cortical circuit processing during learning

We have learned to detect, predict and behaviorally respond to important changes in our environment on short and longer time scales. Therefore, brains of humans and higher animals build upon a perceptual and semantic salience stored in their memories mainly generated by associative reinforcement learning. Functionally, the brain needs to extract and amplify a small number of features of sensory input with behavioral relevance to a particular situation in order to guide behavior. In this review, I argue that dopamine action, particularly in sensory cortex, orchestrates layer-dependent local and long-range cortical circuits integrating sensory associated bottom-up and semantically relevant top-down information, respectively. Available evidence reveals that dopamine thereby controls both the selection of perceptually or semantically salient signals as well as feedback processing from higher-order areas in the brain. Sensory cortical dopamine thereby governs the integration of selected sensory information within a behavioral context. This review proposes that dopamine enfolds this function by temporally distinct actions on particular layer-dependent local and global cortical circuits underlying the integration of sensory, and non-sensory cognitive and behavioral variables.

Long-range recruitment of Martinotti cells causes surround suppression and promotes saliency in an attractor network model

Although the importance of long-range connections for cortical information processing has been acknowledged for a long time, most studies focused on the long-range interactions between excitatory cortical neurons. Inhibitory interneurons play an important role in cortical computation and have thus far been studied mainly with respect to their local synaptic interactions within the cortical microcircuitry. A recent study showed that long-range excitatory connections onto Martinotti cells (MC) mediate surround suppression. Here we have extended our previously reported attractor network of pyramidal cells (PC) and MC by introducing long-range connections targeting MC. We have demonstrated how the network with Martinotti cell-mediated long-range inhibition gives rise to surround suppression and also promotes saliency of locations at which simple non-uniformities in the stimulus field are introduced. Furthermore, our analysis suggests that the presynaptic dynamics of MC is only ancillary to its orientation tuning property in enabling the network with saliency detection. Lastly, we have also implemented a disinhibitory pathway mediated by another interneuron type (VIP interneurons), which inhibits MC and abolishes surround suppression.

Long, intrinsic horizontal axons radiating through and beyond rat barrel cortex have spatial distributions similar to horizontal spreads of activity evoked by whisker stimulation

Stimulation of a single whisker evokes a peak of activity that is centered over the associated barrel in rat primary somatosensory cortex, and yet the evoked local field potential and the intrinsic signal optical imaging response spread symmetrically away from this barrel for over 3.5 mm to cross cytoarchitectonic borders into other "unimodal" sensory cortical areas. To determine whether long horizontal axons have the spatial distribution necessary to underlie this activity spread, we injected adeno-associated viral vectors into barrel cortex and characterized labeled axons extending from the injection site in transverse sections of flattened cortex. Combined qualitative and quantitative analyses revealed labeled axons radiating diffusely in all directions for over 3.5 mm from supragranular injection sites, with density declining over distance. The projection pattern was similar at four different cortical depths, including infragranular laminae. Infragranular vector injections produced patterns similar to the supragranular injections. Long horizontal axons were detected both using a vector with a permissive cytomegalovirus promoter to label all neuronal subtypes and using a calcium/calmodulin-dependent protein kinase II α vector to restrict labeling to excitatory cortical pyramidal neurons. Individual axons were successfully reconstructed from series of supragranular sections, indicating that they traversed gray matter only. Reconstructed axons extended from the injection site, left the barrel field, branched, and sometimes crossed into other sensory cortices identified by cytochrome oxidase staining. Thus, radiations of long horizontal axons indeed have the spatial characteristics necessary to explain horizontal activity spreads. These axons may contribute to multimodal cortical responses and various forms of cortical neural plasticity.

Role of input correlations in shaping the variability and noise correlations of evoked activity in the neocortex

Recent analysis of evoked activity recorded across different brain regions and tasks revealed a marked decrease in noise correlations and trial-by-trial variability. Given the importance of correlations and variability for information processing within the rate coding paradigm, several mechanisms have been proposed to explain the reduction in these quantities despite an increase in firing rates. These models suggest that anatomical clusters and/or tightly balanced excitation-inhibition can generate intrinsic network dynamics that may exhibit a reduction in noise correlations and trial-by-trial variability when perturbed by an external input. Such mechanisms based on the recurrent feedback crucially ignore the contribution of feedforward input to the statistics of the evoked activity. Therefore, we investigated how statistical properties of the feedforward input shape the statistics of the evoked activity. Specifically, we focused on the effect of input correlation structure on the noise correlations and trial-by-trial variability. We show that the ability of neurons to transfer the input firing rate, correlation, and variability to the output depends on the correlations within the presynaptic pool of a neuron, and that an input with even weak within-correlations can be sufficient to reduce noise correlations and trial-by-trial variability, without requiring any specific recurrent connectivity structure. In general, depending on the ongoing activity state, feedforward input could either increase or decrease noise correlation and trial-by-trial variability. Thus, we propose that evoked activity statistics are jointly determined by the feedforward and feedback inputs.

Reconstruction of recurrent synaptic connectivity of thousands of neurons from simulated spiking activity

Dynamics and function of neuronal networks are determined by their synaptic connectivity. Current experimental methods to analyze synaptic network structure on the cellular level, however, cover only small fractions of functional neuronal circuits, typically without a simultaneous record of neuronal spiking activity. Here we present a method for the reconstruction of large recurrent neuronal networks from thousands of parallel spike train recordings. We employ maximum likelihood estimation of a generalized linear model of the spiking activity in continuous time. For this model the point process likelihood is concave, such that a global optimum of the parameters can be obtained by gradient ascent. Previous methods, including those of the same class, did not allow recurrent networks of that order of magnitude to be reconstructed due to prohibitive computational cost and numerical instabilities. We describe a minimal model that is optimized for large networks and an efficient scheme for its parallelized numerical optimization on generic computing clusters. For a simulated balanced random network of 1000 neurons, synaptic connectivity is recovered with a misclassification error rate of less than 1 % under ideal conditions. We show that the error rate remains low in a series of example cases under progressively less ideal conditions. Finally, we successfully reconstruct the connectivity of a hidden synfire chain that is embedded in a random network, which requires clustering of the network connectivity to reveal the synfire groups. Our results demonstrate how synaptic connectivity could potentially be inferred from large-scale parallel spike train recordings.

Eigenspectrum bounds for semirandom matrices with modular and spatial structure for neural networks

The eigenvalue spectrum of the matrix of directed weights defining a neural network model is informative of several stability and dynamical properties of network activity. Existing results for eigenspectra of sparse asymmetric random matrices neglect spatial or other constraints in determining entries in these matrices, and so are of partial applicability to cortical-like architectures. Here we examine a parameterized class of networks that are defined by sparse connectivity, with connection weighting modulated by physical proximity (i.e., asymmetric Euclidean random matrices), modular network partitioning, and functional specificity within the excitatory population. We present a set of analytical constraints that apply to the eigenvalue spectra of associated weight matrices, highlighting the relationship between connectivity rules and classes of network dynamics.

Long-range intralaminar noise correlations in the barrel cortex

Identifying the properties of correlations in the firing of neocortical neurons is central to our understanding of cortical information processing. It has been generally assumed, by virtue of the columnar organization of the neocortex, that the firing of neurons residing in a certain vertical domain is highly correlated. On the other hand, firing correlations between neurons steeply decline with horizontal distance. Technical difficulties in sampling neurons with sufficient spatial information have precluded the critical evaluation of these notions. We used 128-channel "silicon probes" to examine the spike-count noise correlations during spontaneous activity between multiple neurons with identified laminar position and over large horizontal distances in the anesthetized rat barrel cortex. Eigen decomposition of correlation coefficient matrices revealed that the laminar position of a neuron is a significant determinant of these correlations, such that the fluctuations of layer 5B/6 neurons are in opposite direction to those of layers 5A and 4. Moreover, we found that within each experiment, the distribution of horizontal, intralaminar spike-count correlation coefficients, up to a distance of ∼1.5 mm, is practically identical to the distribution of vertical correlations. Taken together, these data reveal that the neuron's laminar position crucially affects its role in cortical processing. Moreover, our analyses reveal that this laminar effect extends over several functional columns. We propose that within the cortex the influence of the horizontal elements exists in a dynamic balance with the influence of the vertical domain and this balance is modulated with brain states to shape the network's behavior.

Columnar architecture improves noise robustness in a model cortical network

Cortical columnar architecture was discovered decades ago yet there is no agreed upon explanation for its function. Indeed, some have suggested that it has no function, it is simply an epiphenomenon of developmental processes. To investigate this problem we have constructed a computer model of one square millimeter of layer 2/3 of the primary visual cortex (V1) of the cat. Model cells are connected according to data from recent paired cell studies, in particular the connection probability between pyramidal cells is inversely proportional both to the distance separating the cells and to the distance between the preferred parameters (features) of the cells. We find that these constraints, together with a columnar architecture, produce more tightly clustered populations of cells when compared to the random architecture seen in, for example, rodents. This causes the columnar network to converge more quickly and accurately on the pattern representing a particular stimulus in the presence of noise, suggesting that columnar connectivity functions to improve pattern recognition in cortical circuits. The model also suggests that synaptic failure, a phenomenon exhibited by weak synapses, may conserve metabolic resources by reducing transmitter release at these connections that do not contribute to network function.

A formalism for evaluating analytically the cross-correlation structure of a firing-rate network model

We introduce a new formalism for evaluating analytically the cross-correlation structure of a finite-size firing-rate network with recurrent connections. The analysis performs a first-order perturbative expansion of neural activity equations that include three different sources of randomness: the background noise of the membrane potentials, their initial conditions, and the distribution of the recurrent synaptic weights. This allows the analytical quantification of the relationship between anatomical and functional connectivity, i.e. of how the synaptic connections determine the statistical dependencies at any order among different neurons. The technique we develop is general, but for simplicity and clarity we demonstrate its efficacy by applying it to the case of synaptic connections described by regular graphs. The analytical equations so obtained reveal previously unknown behaviors of recurrent firing-rate networks, especially on how correlations are modified by the external input, by the finite size of the network, by the density of the anatomical connections and by correlation in sources of randomness. In particular, we show that a strong input can make the neurons almost independent, suggesting that functional connectivity does not depend only on the static anatomical connectivity, but also on the external inputs. Moreover we prove that in general it is not possible to find a mean-field description à la Sznitman of the network, if the anatomical connections are too sparse or our three sources of variability are correlated. To conclude, we show a very counterintuitive phenomenon, which we call stochastic synchronization, through which neurons become almost perfectly correlated even if the sources of randomness are independent. Due to its ability to quantify how activity of individual neurons and the correlation among them depends upon external inputs, the formalism introduced here can serve as a basis for exploring analytically the computational capability of population codes expressed by recurrent neural networks.

Natural grouping of neural responses reveals spatially segregated clusters in prearcuate cortex

A fundamental challenge in studying the frontal lobe is to parcellate this cortex into "natural" functional modules despite the absence of topographic maps, which are so helpful in primary sensory areas. Here we show that unsupervised clustering algorithms, applied to 96-channel array recordings from prearcuate gyrus, reveal spatially segregated subnetworks that remain stable across behavioral contexts. Looking for natural groupings of neurons based on response similarities, we discovered that the recorded area includes at least two spatially segregated subnetworks that differentially represent behavioral choice and reaction time. Importantly, these subnetworks are detectable during different behavioral states and, surprisingly, are defined better by "common noise" than task-evoked responses. Our parcellation process works well on "spontaneous" neural activity, and thus bears strong resemblance to the identification of "resting-state" networks in fMRI data sets. Our results demonstrate a powerful new tool for identifying cortical subnetworks by objective classification of simultaneously recorded electrophysiological activity.

Input-dependent frequency modulation of cortical gamma oscillations shapes spatial synchronization and enables phase coding

Fine-scale temporal organization of cortical activity in the gamma range (∼25-80Hz) may play a significant role in information processing, for example by neural grouping ('binding') and phase coding. Recent experimental studies have shown that the precise frequency of gamma oscillations varies with input drive (e.g. visual contrast) and that it can differ among nearby cortical locations. This has challenged theories assuming widespread gamma synchronization at a fixed common frequency. In the present study, we investigated which principles govern gamma synchronization in the presence of input-dependent frequency modulations and whether they are detrimental for meaningful input-dependent gamma-mediated temporal organization. To this aim, we constructed a biophysically realistic excitatory-inhibitory network able to express different oscillation frequencies at nearby spatial locations. Similarly to cortical networks, the model was topographically organized with spatially local connectivity and spatially-varying input drive. We analyzed gamma synchronization with respect to phase-locking, phase-relations and frequency differences, and quantified the stimulus-related information represented by gamma phase and frequency. By stepwise simplification of our models, we found that the gamma-mediated temporal organization could be reduced to basic synchronization principles of weakly coupled oscillators, where input drive determines the intrinsic (natural) frequency of oscillators. The gamma phase-locking, the precise phase relation and the emergent (measurable) frequencies were determined by two principal factors: the detuning (intrinsic frequency difference, i.e. local input difference) and the coupling strength. In addition to frequency coding, gamma phase contained complementary stimulus information. Crucially, the phase code reflected input differences, but not the absolute input level. This property of relative input-to-phase conversion, contrasting with latency codes or slower oscillation phase codes, may resolve conflicting experimental observations on gamma phase coding. Our modeling results offer clear testable experimental predictions. We conclude that input-dependency of gamma frequencies could be essential rather than detrimental for meaningful gamma-mediated temporal organization of cortical activity.

Strength and duration of perisomatic GABAergic inhibition depend on distance between synaptically connected cells

GABAergic perisoma-inhibiting fast-spiking interneurons (PIIs) effectively control the activity of large neuron populations by their wide axonal arborizations. It is generally assumed that the output of one PII to its target cells is strong and rapid. Here, we show that, unexpectedly, both strength and time course of PII-mediated perisomatic inhibition change with distance between synaptically connected partners in the rodent hippocampus. Synaptic signals become weaker due to lower contact numbers and decay more slowly with distance, very likely resulting from changes in GABAA receptor subunit composition. When distance-dependent synaptic inhibition is introduced to a rhythmically active neuronal network model, randomly driven principal cell assemblies are strongly synchronized by the PIIs, leading to higher precision in principal cell spike times than in a network with uniform synaptic inhibition.

Physiology and Impact of Horizontal Connections in Rat Neocortex

Cortical information processing at the cellular level has predominantly been studied in local networks, which are dominated by strong vertical connectivity between layers. However, recent studies suggest that the bulk of axons targeting pyramidal neurons most likely originate from outside this local range, emphasizing the importance of horizontal connections. We mapped a subset of these connections to L5B pyramidal neurons in rat somatosensory cortex with photostimulation, identifying intact projections up to a lateral distance of 2 mm. Our estimates of the spatial distribution of cells presynaptic to L5B pyramids support the idea that the majority is located outside the local volume. The synaptic physiology of horizontal connections does not differ markedly from that of local connections, whereas the layer and cell-type-dependent pattern of innervation does. Apart from L2/3, L6A provides a strong source of horizontal connections. Implementing our data into a spiking neuronal network model shows that more horizontal connections promote robust asynchronous ongoing activity states and reduce noise correlations in stimulus-induced activity.

Möbius-strip-like columnar functional connections are revealed in somato-sensory receptive field centroids

Receptive fields of neurons in the forelimb region of areas 3b and 1 of primary somatosensory cortex, in cats and monkeys, were mapped using extracellular recordings obtained sequentially from nearly radial penetrations. Locations of the field centroids indicated the presence of a functional system in which cortical homotypic representations of the limb surfaces are entwined in three-dimensional Möbius-strip-like patterns of synaptic connections. Boundaries of somatosensory receptive field in nested groups irregularly overlie the centroid order, and are interpreted as arising from the superposition of learned connections upon the embryonic order. Since the theory of embryonic synaptic self-organization used to model these results was devised and earlier used to explain findings in primary visual cortex, the present findings suggest the theory may be of general application throughout cortex and may reveal a modular functional synaptic system, which, only in some parts of the cortex, and in some species, is manifest as anatomical ordering into columns.

Time-sensitive reorganization of the somatosensory cortex poststroke depends on interaction between Hebbian and homeoplasticity: a simulation study

Together with Hebbian plasticity, homeoplasticity presumably plays a significant, yet unclear, role in recovery postlesion. Here, we undertake a simulation study addressing the role of homeoplasticity and rehabilitation timing poststroke. We first hypothesize that homeoplasticity is essential for recovery and second that rehabilitation training delivered too early, before homeoplasticity has compensated for activity disturbances postlesion, is less effective for recovery than training delivered after a delay. We developed a neural network model of the sensory cortex driven by muscle spindle inputs arising from a six-muscle arm. All synapses underwent Hebbian plasticity, while homeoplasticity adjusted cell excitability to maintain a desired firing distribution. After initial training, the network was lesioned, leading to areas of hyper- and hypoactivity due to the loss of lateral synaptic connections. The network was then retrained through rehabilitative arm movements. We found that network recovery was unsuccessful in the absence of homeoplasticity, as measured by reestablishment of lesion-affected inputs. We also found that a delay preceding rehabilitation led to faster network recovery during the rehabilitation training than no delay. Our simulation results thus suggest that homeoplastic restoration of prelesion activity patterns is essential to functional network recovery via Hebbian plasticity.

Emergence of bursting activity in connected neuronal sub-populations

Uniform and modular primary hippocampal cultures from embryonic rats were grown on commercially available micro-electrode arrays to investigate network activity with respect to development and integration of different neuronal populations. Modular networks consisting of two confined active and inter-connected sub-populations of neurons were realized by means of bi-compartmental polydimethylsiloxane structures. Spontaneous activity in both uniform and modular cultures was periodically monitored, from three up to eight weeks after plating. Compared to uniform cultures and despite lower cellular density, modular networks interestingly showed higher firing rates at earlier developmental stages, and network-wide firing and bursting statistics were less variable over time. Although globally less correlated than uniform cultures, modular networks exhibited also higher intra-cluster than inter-cluster correlations, thus demonstrating that segregation and integration of activity coexisted in this simple yet powerful in vitro model. Finally, the peculiar synchronized bursting activity shown by confined modular networks preferentially propagated within one of the two compartments (‘dominant’), even in cases of perfect balance of firing rate between the two sub-populations. This dominance was generally maintained during the entire monitored developmental frame, thus suggesting that the implementation of this hierarchy arose from early network development.

Spatial consistency of neural firing regulates long-range local field potential synchronization: a computational study

Local field potentials (LFPs) are thought to integrate neuronal processes within the range of a few millimeters of radius, which corresponds to the scale of multiple columns. In this study, the model of LFP in the visual cortex proposed by Mazzoni et al. (2008) was adapted to organize a network of two cortical areas, in which pyramidal neurons were divided into two sub-population modeling columns with spatially organized connections to neurons in other areas. Using the model enabled the relationship between neural firing and LFP to be evaluated, in addition to the LFP coherence between the two areas. Results showed that: (1) neurons in a particular sub-population generated the LFP in the area; (2) the spatial consistency of neural firing in the two areas was strongly correlated with LFP coherence; and (3) this consistency was capable of regulating LFP coherence in a lower frequency band, which was originally introduced to neurons in a particular sub-population. These results were derived from a winner-take-all operation in the columnar structure; thus, they are expected to be common in the cortex. It is suggested that the spatial consistency of neural firing is essential for regulating long-range LFP synchronization, which would facilitate neuronal integration processes over multiple cortical areas.

Multiple Tests Based on a Gaussian Approximation of the Unitary Events Method with Delayed Coincidence Count

The unitary events (UE) method is one of the most popular and efficient methods used over the past decade to detect patterns of coincident joint spike activity among simultaneously recorded neurons. The detection of coincidences is usually based on binned coincidence count (Grün, 1996 ), which is known to be subject to loss in synchrony detection (Grün, Diesmann, Grammont, Riehle, & Aertsen, 1999 ). This defect has been corrected by the multiple shift coincidence count (Grün et al., 1999 ). The statistical properties of this count have not been further investigated until this work, the formula being more difficult to deal with than the original binned count. First, we propose a new notion of coincidence count, the delayed coincidence count, which is equal to the multiple shift coincidence count when discretized point processes are involved as models for the spike trains. Moreover, it generalizes this notion to nondiscretized point processes, allowing us to propose a new gaussian approximation of the count. Since unknown parameters are involved in the approximation, we perform a plug-in step, where unknown parameters are replaced by estimated ones, leading to a modification of the approximating distribution. Finally the method takes the multiplicity of the tests into account via a Benjamini and Hochberg approach (Benjamini & Hochberg, 1995 ), to guarantee a prescribed control of the false discovery rate. We compare our new method, MTGAUE (multiple tests based on a gaussian approximation of the unitary events) and the UE method proposed in Grün et al. ( 1999 ) over various simulations, showing that MTGAUE extends the validity of the previous method. In particular, MTGAUE is able to detect both profusion and lack of coincidences with respect to the independence case and is robust to changes in the underlying model. Furthermore MTGAUE is applied on real data.

Phase-coherence transitions and communication in the gamma range between delay-coupled neuronal populations

Synchronization between neuronal populations plays an important role in information transmission between brain areas. In particular, collective oscillations emerging from the synchronized activity of thousands of neurons can increase the functional connectivity between neural assemblies by coherently coordinating their phases. This synchrony of neuronal activity can take place within a cortical patch or between different cortical regions. While short-range interactions between neurons involve just a few milliseconds, communication through long-range projections between different regions could take up to tens of milliseconds. How these heterogeneous transmission delays affect communication between neuronal populations is not well known. To address this question, we have studied the dynamics of two bidirectionally delayed-coupled neuronal populations using conductance-based spiking models, examining how different synaptic delays give rise to in-phase/anti-phase transitions at particular frequencies within the gamma range, and how this behavior is related to the phase coherence between the two populations at different frequencies. We have used spectral analysis and information theory to quantify the information exchanged between the two networks. For different transmission delays between the two coupled populations, we analyze how the local field potential and multi-unit activity calculated from one population convey information in response to a set of external inputs applied to the other population. The results confirm that zero-lag synchronization maximizes information transmission, although out-of-phase synchronization allows for efficient communication provided the coupling delay, the phase lag between the populations, and the frequency of the oscillations are properly matched.

Anatomical constraints on lateral competition in columnar cortical architectures

Competition is a well-studied and powerful mechanism for information processing in neuronal networks, providing noise rejection, signal restoration, decision making and associative memory properties, with relatively simple requirements for network architecture. Models based on competitive interactions have been used to describe the shaping of functional properties in visual cortex, as well as the development of functional maps in columnar cortex. These models require competition within a cortical area to occur on a wider spatial scale than cooperation, usually implemented by lateral inhibitory connections having a longer range than local excitatory connections. However, measurements of cortical anatomy reveal that the spatial extent of inhibition is in fact more restricted than that of excitation. Relatively few models reflect this, and it is unknown whether lateral competition can occur in cortical-like networks that have a realistic spatial relationship between excitation and inhibition. Here we analyze simple models for cortical columns and perform simulations of larger models to show how the spatial scales of excitation and inhibition can interact to produce competition through disynaptic inhibition. Our findings give strong support to the direct coupling effect-that the presence of competition across the cortical surface is predicted well by the anatomy of direct excitatory and inhibitory coupling and that multisynaptic network effects are negligible. This implies that for networks with short-range inhibition and longer-range excitation, the spatial extent of competition is even narrower than the range of inhibitory connections. Our results suggest the presence of network mechanisms that focus on intra-rather than intercolumn competition in neocortex, highlighting the need for both new models and direct experimental characterizations of lateral inhibition and competition in columnar cortex.