The number of synaptic inputs and the synchrony of large, sparse neuronal networks

Biophysical modulation and robustness of itinerant complexity in neuronal networks

Transient synchronization of bursting activity in neuronal networks, which occurs in patterns of metastable itinerant phase relationships between neurons, is a notable feature of network dynamics observed in vivo. However, the mechanisms that contribute to this dynamical complexity in neuronal circuits are not well understood. Local circuits in cortical regions consist of populations of neurons with diverse intrinsic oscillatory features. In this study, we numerically show that the phenomenon of transient synchronization, also referred to as metastability, can emerge in an inhibitory neuronal population when the neurons' intrinsic fast-spiking dynamics are appropriately modulated by slower inputs from an excitatory neuronal population. Using a compact model of a mesoscopic-scale network consisting of excitatory pyramidal and inhibitory fast-spiking neurons, our work demonstrates a relationship between the frequency of pyramidal population oscillations and the features of emergent metastability in the inhibitory population. In addition, we introduce a method to characterize collective transitions in metastable networks. Finally, we discuss potential applications of this study in mechanistically understanding cortical network dynamics.

Amacrine cells differentially balance zebrafish color circuits in the central and peripheral retina

The vertebrate inner retina is driven by photoreceptors whose outputs are already pre-processed; in zebrafish, outer retinal circuits split "color" from "grayscale" information across four cone-photoreceptor types. It remains unclear how the inner retina processes incoming spectral information while also combining cone signals to shape grayscale functions. We address this question by imaging the light-driven responses of amacrine cells (ACs) and bipolar cells (BCs) in larval zebrafish in the presence and pharmacological absence of inner retinal inhibition. We find that ACs enhance opponency in some bipolar cells while at the same time suppressing pre-existing opponency in others, so that, depending on the retinal region, the net change in the number of color-opponent units is essentially zero. To achieve this "dynamic balance," ACs counteract intrinsic color opponency of BCs via the On channel. Consistent with these observations, Off-stratifying ACs are exclusively achromatic, while all color-opponent ACs stratify in the On sublamina.

Computational modeling predicts regulation of central pattern generator oscillations by size and density of the underlying heterogenous network

Central pattern generators are characterized by a heterogeneous cellular composition, with different cell types playing distinct roles in the production and transmission of rhythmic signals. However, little is known about the functional implications of individual variation in the relative distributions of cells and their connectivity patterns. Here, we addressed this question through a combination of morphological data analysis and computational modeling, using the pacemaker nucleus of the weakly electric fish Apteronotus leptorhynchus as case study. A neural network comprised of 60-110 interconnected pacemaker cells and 15-30 relay cells conveying its output to electromotoneurons in the spinal cord, this nucleus continuously generates neural signals at frequencies of up to 1 kHz with high temporal precision. We systematically explored the impact of network size and density on oscillation frequencies and their variation within and across cells. To accurately determine effect sizes, we minimized the likelihood of complex dynamics using a simplified setup precluding differential delays. To identify natural constraints, parameter ranges were extended beyond experimentally recorded numbers of cells and connections. Simulations revealed that pacemaker cells have higher frequencies and lower within-population variability than relay cells. Within-cell precision and between-cells frequency synchronization increased with the number of pacemaker cells and of connections of either type, and decreased with relay cell count in both populations. Network-level frequency-synchronized oscillations occurred in roughly half of simulations, with maximized likelihood and firing precision within biologically observed parameter ranges. These findings suggest the structure of the biological pacemaker nucleus is optimized for generating synchronized sustained oscillations.

Theory of hierarchically organized neuronal oscillator dynamics that mediate rodent rhythmic whisking

Rodents explore their environment through coordinated orofacial motor actions, including whisking. Whisking can free-run via an oscillator of inhibitory neurons in the medulla and can be paced by breathing. Yet, the mechanics of the whisking oscillator and its interaction with breathing remain to be understood. We formulate and solve a hierarchical model of the whisking circuit. The first whisk within a breathing cycle is generated by inhalation, which resets a vibrissa oscillator circuit, while subsequent whisks are derived from the oscillator circuit. Our model posits, consistent with experiment, that there are two subpopulations of oscillator neurons. Stronger connections between the subpopulations support rhythmicity, while connections within each subpopulation induce variable spike timing that enhances the dynamic range of rhythm generation. Calculated cycle-to-cycle changes in whisking are consistent with experiment. Our model provides a computational framework to support longstanding observations of concurrent autonomous and driven rhythmic motor actions that comprise behaviors.

Amyloid beta induces Fmr1 ‐dependent translational suppression and hyposynchrony of neural activity via phosphorylation of eIF2α and eEF2

Alzheimer's disease (AD) is the most common cause of dementia, with the accumulation of amyloid beta peptide (Aβ) being one of the main causes of the disease. Fragile X mental retardation protein (FMRP), encoded by fragile X mental retardation 1 (Fmr1), is an RNA‐binding protein that represses translation of its bound mRNAs or exerts other indirect mechanisms that result in translational suppression. Because the accumulation of Aβ has been shown to cause translational suppression resulting from the elevated cellular stress response, in this study we asked whether and how Fmr1 is involved in Aβ‐induced translational regulation. Our data first showed that the application of synthetic Aβ peptide induces the expression of Fmr1 in cultured primary neurons. We followed by showing that Fmr1 is required for Aβ‐induced translational suppression, hyposynchrony of neuronal firing activity, and loss of excitatory synapses. Mechanistically, we revealed that Fmr1 functions to repress the expression of phosphatases including protein phosphatase 2A (PP2A) and protein phosphatase 1 (PP1), leading to elevated phosphorylation of eukaryotic initiation factor 2‐α (eIF2α) and eukaryotic elongation factor 2 (eEF2), and subsequent translational suppression. Finally, our data suggest that such translational suppression is critical to Aβ‐induced hyposynchrony of firing activity, but not the loss of synapses. Altogether, our study uncovers a novel mechanism by which Aβ triggers translational suppression and we reveal the participation of Fmr1 in altered neural plasticity associated with Aβ pathology. Our study may also provide information for a better understanding of Aβ‐induced cellular stress responses in AD.

Sparse balance: Excitatory-inhibitory networks with small bias currents and broadly distributed synaptic weights

Cortical circuits generate excitatory currents that must be cancelled by strong inhibition to assure stability. The resulting excitatory-inhibitory (E-I) balance can generate spontaneous irregular activity but, in standard balanced E-I models, this requires that an extremely strong feedforward bias current be included along with the recurrent excitation and inhibition. The absence of experimental evidence for such large bias currents inspired us to examine an alternative regime that exhibits asynchronous activity without requiring unrealistically large feedforward input. In these networks, irregular spontaneous activity is supported by a continually changing sparse set of neurons. To support this activity, synaptic strengths must be drawn from high-variance distributions. Unlike standard balanced networks, these sparse balance networks exhibit robust nonlinear responses to uniform inputs and non-Gaussian input statistics. Interestingly, the speed, not the size, of synaptic fluctuations dictates the degree of sparsity in the model. In addition to simulations, we provide a mean-field analysis to illustrate the properties of these networks.

A class of models in computational neuroscience that have been successful at describing a variety of effects in the neocortex involve a tight balance between excitatory, inhibitory and unrealistically large external input, without which the model cannot produce robust patterns of activity. In this work, we explore what happens when these inputs are smaller in size, and we provide an alternative solution for recovering robust network activity. This solution relies on broadly distributed synaptic strengths and, interestingly, gives rise to sparse subsets of neurons firing at any given time. Unlike the conventional models, the networks exhibit nonlinear responses to uniform external input.

Role of phase-dependent influence function in the Winfree model of coupled oscillators

We consider a globally coupled Winfree model comprised of a phase-dependent influence function and sensitive function, and unravel the impact of offset and integer parameters, characterizing the shape of the influence function, on the phase diagram of the Winfree model. The decreasing value of the offset parameter decreases the degree of positive phase shift among the oscillators by promoting the negative phase shift, which indeed favors the onset of multistability among the synchronous oscillatory state and asynchronous stable steady states in a large region of the phase diagram. Further, large integer parameters lead to brief pulses of the influence function, which again enhances the effect of the offset parameter. There is an explosive transition to a synchronous oscillatory state from an asynchronous steady state via a Hopf bifurcation. Dynamical transitions and multistability emerge through saddle-node, pitchfork, and homoclinic bifurcations in the phase diagram. We deduce two ordinary differential equations corresponding to the two macroscopic variables from the population of globally coupled Winfree oscillators using the Ott-Antonsen ansatz. We also deduce various bifurcation curves analytically from the reduced low-dimensional macroscopic variables for the exactly solvable case. The analytical curves exactly match the simulation boundaries in the phase diagram.

Structured patterns of activity in pulse-coupled oscillator networks with varied connectivity

Identifying coordinated activity within complex systems is essential to linking their structure and function. We study collective activity in networks of pulse-coupled oscillators that have variable network connectivity and integrate-and-fire dynamics. Starting from random initial conditions, we see the emergence of three broad classes of behaviors that differ in their collective spiking statistics. In the first class (“temporally-irregular”), all nodes have variable inter-spike intervals, and the resulting firing patterns are irregular. In the second (“temporally-regular”), the network generates a coherent, repeating pattern of activity in which all nodes fire with the same constant inter-spike interval. In the third (“chimeric”), subgroups of coherently-firing nodes coexist with temporally-irregular nodes. Chimera states have previously been observed in networks of oscillators; here, we find that the notions of temporally-regular and chimeric states encompass a much richer set of dynamical patterns than has yet been described. We also find that degree heterogeneity and connection density have a strong effect on the resulting state: in binomial random networks, high degree variance and intermediate connection density tend to produce temporally-irregular dynamics, while low degree variance and high connection density tend to produce temporally-regular dynamics. Chimera states arise with more frequency in networks with intermediate degree variance and either high or low connection densities. Finally, we demonstrate that a normalized compression distance, computed via the Lempel-Ziv complexity of nodal spike trains, can be used to distinguish these three classes of behavior even when the phase relationship between nodes is arbitrary.

Growth rules for the repair of Asynchronous Irregular neuronal networks after peripheral lesions

Several homeostatic mechanisms enable the brain to maintain desired levels of neuronal activity. One of these, homeostatic structural plasticity, has been reported to restore activity in networks disrupted by peripheral lesions by altering their neuronal connectivity. While multiple lesion experiments have studied the changes in neurite morphology that underlie modifications of synapses in these networks, the underlying mechanisms that drive these changes are yet to be explained. Evidence suggests that neuronal activity modulates neurite morphology and may stimulate neurites to selective sprout or retract to restore network activity levels. We developed a new spiking network model of peripheral lesioning and accurately reproduced the characteristics of network repair after deafferentation that are reported in experiments to study the activity dependent growth regimes of neurites. To ensure that our simulations closely resemble the behaviour of networks in the brain, we model deafferentation in a biologically realistic balanced network model that exhibits low frequency Asynchronous Irregular (AI) activity as observed in cerebral cortex. Our simulation results indicate that the re-establishment of activity in neurons both within and outside the deprived region, the Lesion Projection Zone (LPZ), requires opposite activity dependent growth rules for excitatory and inhibitory post-synaptic elements. Analysis of these growth regimes indicates that they also contribute to the maintenance of activity levels in individual neurons. Furthermore, in our model, the directional formation of synapses that is observed in experiments requires that pre-synaptic excitatory and inhibitory elements also follow opposite growth rules. Lastly, we observe that our proposed structural plasticity growth rules and the inhibitory synaptic plasticity mechanism that also balances our AI network both contribute to the restoration of the network to pre-deafferentation stable activity levels.

An accumulating body of evidence suggests that our brain can compensate for peripheral lesions by adaptive rewiring of its neuronal circuitry. The underlying process, structural plasticity, can modify the connectivity of neuronal networks in the brain, thus affecting their function. To better understand the mechanisms of structural plasticity in the brain, we have developed a novel model of peripheral lesions and the resulting activity-dependent rewiring in a simplified balanced cortical network model that exhibits biologically realistic Asynchronous Irregular (AI) activity. In order to accurately reproduce the directionality and course of network rewiring after injury that is observed in peripheral lesion experiments, we derive activity dependent growth rules for different synaptic elements: dendritic and axonal contacts. Our simulation results suggest that excitatory and inhibitory synaptic elements have to react to changes in neuronal activity in opposite ways. We show that these rules result in a homeostatic stabilisation of activity in individual neurons. In our simulations, both synaptic and structural plasticity mechanisms contribute to network repair. Furthermore, our simulations indicate that while activity is restored in neurons deprived by the peripheral lesion, the temporal firing characteristics of the network may not be retained by the rewiring process.

Spike-phase coupling as an order parameter in a leaky integrate-and-fire model

It is known that the leaky integrate-and-fire neural model shows a transition from irregular to synchronous firing by increasing the coupling between the neurons. However, a quantitative characterization of this order-disorder transition, that is, the determination of the order of transition and also the critical exponents in the case of continuous transition, is not entirely known. In this work, we consider a network of N excitatory neurons with local connections, residing on a square lattice with periodic boundary conditions. The cooperation between neurons K plays the role of the control parameter that generates criticality when the critical cooperation strength K_{c} is adopted. We introduce the population-averaged voltage (PAV) as a representative value of the network's cooperative activity. Then, we show that the coupling between the timing of spikes and the phase of temporal fluctuations of PAV defined as m resorts to identify a Kuramoto order parameter. By increasing K, we find a continuous transition from irregular spiking to a phase-locked state at the critical point K_{c}. We deploy the finite-size scaling analysis to calculate the critical exponents of this transition. To explore the formal indicator of criticality, we study the neuronal avalanches profile at this critical point and find a scaling behavior with the exponents in a fair agreement with the experimental values both in vivo and in vitro.

Synaptic inhibition in the neocortex: Orchestration and computation through canonical circuits and variations on the theme

The neocortex plays a crucial role in all basic and abstract cognitive functions. Conscious mental processes are achieved through a correct flow of information within and across neocortical networks, whose particular activity state results from a tight balance between excitation and inhibition. The proper equilibrium between these indissoluble forces is operated with multiscale organization: along the dendro-somatic axis of single neurons and at the network level. Fast synaptic inhibition is assured by a multitude of inhibitory interneurons. During cortical activities, these cells operate a finely tuned division of labor that is epitomized by their detailed connectivity scheme. Recent results combining the use of mouse genetics, cutting-edge optical and neurophysiological approaches have highlighted the role of fast synaptic inhibition in driving cognition-related activity through a canonical cortical circuit, involving several major interneuron subtypes and principal neurons. Here we detail the organization of this cortical blueprint and we highlight the crucial role played by different neuron types in fundamental cortical computations. In addition, we argue that this canonical circuit is prone to many variations on the theme, depending on the resolution of the classification of neuronal types, and the cortical area investigated. Finally, we discuss how specific alterations of distinct inhibitory circuits can underlie several devastating brain diseases.

Itinerant complexity in networks of intrinsically bursting neurons

Active neurons can be broadly classified by their intrinsic oscillation patterns into two classes characterized by spiking or bursting. Here, we show that networks of identical bursting neurons with inhibitory pulsatory coupling exhibit itinerant dynamics. Using the relative phases of bursts between neurons, we numerically demonstrate that the network exhibits endogenous transitions between multiple modes of transient synchrony. This is true even for bursts consisting of two spikes. In contrast, our simulations reveal that networks of identical singlet-spiking neurons do not exhibit such complexity. These results suggest a role for bursting dynamics in realizing itinerant complexity in neural circuits.

Enabling Large-Scale Simulations With the GENESIS Neuronal Simulator

In this paper, we evaluate the computational performance of the GEneral NEural SImulation System (GENESIS) for large scale simulations of neural networks. While many benchmark studies have been performed for large scale simulations with leaky integrate-and-fire neurons or neuronal models with only a few compartments, this work focuses on higher fidelity neuronal models represented by 50–74 compartments per neuron. After making some modifications to the source code for GENESIS and its parallel implementation, PGENESIS, particularly to improve memory usage, we find that PGENESIS is able to efficiently scale on supercomputing resources to network sizes as large as 9 × 10⁶ neurons with 18 × 10⁹ synapses and 2.2 × 10⁶ neurons with 45 × 10⁹ synapses. The modifications to GENESIS that enabled these large scale simulations have been incorporated into the May 2019 Official Release of PGENESIS 2.4 available for download from the GENESIS web site (genesis-sim.org).

Synchronization of Electrically Coupled Resonate-and-Fire Neurons

Electrical coupling between neurons is broadly present across brain areas and is typically assumed to synchronize network activity. However, intrinsic properties of the coupled cells can complicate this simple picture. Many cell types with electrical coupling show a diversity of post-spike subthreshold fluctuations, often linked to subthreshold resonance, which are transmitted through electrical synapses in addition to action potentials. Using the theory of weakly coupled oscillators, we explore the effect of both subthreshold and spike-mediated coupling on synchrony in small networks of electrically coupled resonate-and-fire neurons, a hybrid neuron model with damped subthreshold oscillations and a range of post-spike voltage dynamics. We calculate the phase response curve using an extension of the adjoint method that accounts for the discontinuous post-spike reset rule. We find that both spikes and subthreshold fluctuations can jointly promote synchronization. The subthreshold contribution is strongest when the voltage exhibits a significant post-spike elevation in voltage, or plateau potential. Additionally, we show that the geometry of trajectories approaching the spiking threshold causes a "reset-induced shear" effect that can oppose synchrony in the presence of network asymmetry, despite having no effect on the phase-locking of symmetrically coupled pairs.

Reduced Prefrontal Synaptic Connectivity and Disturbed Oscillatory Population Dynamics in the CNTNAP2 Model of Autism

Loss-of-function mutations in CNTNAP2 cause a syndromic form of autism spectrum disorder in humans and produce social deficits, repetitive behaviors, and seizures in mice. However, the functional effects of these mutations at cellular and circuit levels remain elusive. Using laser-scanning photostimulation, whole-cell recordings, and electron microscopy, we found a dramatic decrease in excitatory and inhibitory synaptic inputs onto L2/3 pyramidal neurons of the medial prefrontal cortex (mPFC) of Cntnap2 knockout (KO) mice, concurrent with reduced spines and synapses, despite normal dendritic complexity and intrinsic excitability. Moreover, recording of mPFC local field potentials (LFPs) and unit spiking in vivo revealed increased activity in inhibitory neurons, reduced phase-locking to delta and theta oscillations, and delayed phase preference during locomotion. Excitatory neurons showed similar phase modulation changes at delta frequencies. Finally, pairwise correlations increased during immobility in KO mice. Thus, reduced synaptic inputs can yield perturbed temporal coordination of neuronal firing in cortical ensembles.

Neural activity of heterogeneous inhibitory spiking networks with delay

We study a network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses. For globally coupled systems the increase of the inhibitory coupling reduces the number of firing neurons by following a winner-takes-all mechanism. For sufficiently large transmission delay we observe the emergence of collective oscillations in the system beyond a critical coupling value. Heterogeneity promotes neural inactivation and asynchronous dynamics and its effect can be counteracted by considering longer time delays. In sparse networks, inhibition has the counterintuitive effect of promoting neural reactivation of silent neurons for sufficiently large coupling. In this regime, current fluctuations are on one side responsible for neural firing of subthreshold neurons and on the other side for their desynchronization. Therefore, collective oscillations are present only in a limited range of coupling values, which remains finite in the thermodynamic limit. Out of this range the dynamics is asynchronous and for very large inhibition neurons display a bursting behavior alternating periods of silence with periods where they fire freely in absence of any inhibition.

Various synchronous states due to coupling strength inhomogeneity and coupling functions in systems of coupled identical oscillators

We study the effects of coupling strength inhomogeneity and coupling functions on locking behaviors of coupled identical oscillators, some of which are relatively weakly coupled to others while some are relatively strongly coupled. Through the stability analysis and numerical simulations, we show that several categories of fully locked or partially locked states can emerge and obtain the conditions for these categories. In this system with coupling strength inhomogeneity, locked and drifting subpopulations are determined by the coupling strength distribution and the shape of the coupling functions. Even the strongly coupled oscillators can drift while weakly coupled oscillators can be locked. The simulation results with Gaussian and power-law distributions for coupling strengths are compared and discussed.

Constraints of Metabolic Energy on the Number of Synaptic Connections of Neurons and the Density of Neuronal Networks

Neuronal networks in the brain are the structural basis of human cognitive function, and the plasticity of neuronal networks is thought to be the principal neural mechanism underlying learning and memory. Dominated by the Hebbian theory, researchers have devoted extensive effort to studying the changes in synaptic connections between neurons. However, understanding the network topology of all synaptic connections has been neglected over the past decades. Furthermore, increasing studies indicate that synaptic activities are tightly coupled with metabolic energy, and metabolic energy is a unifying principle governing neuronal activities. Therefore, the network topology of all synaptic connections may also be governed by metabolic energy. Here, by implementing a computational model, we investigate the general synaptic organization rules for neurons and neuronal networks from the perspective of energy metabolism. We find that to maintain the energy balance of individual neurons in the proposed model, the number of synaptic connections is inversely proportional to the average of the synaptic weights. This strategy may be adopted by neurons to ensure that the ability of neurons to transmit signals matches their own energy metabolism. In addition, we find that the density of neuronal networks is also an important factor in the energy balance of neuronal networks. An abnormal increase or decrease in the network density could lead to failure of energy metabolism in the neuronal network. These rules may change our view of neuronal networks in the brain and have guiding significance for the design of neuronal network models.

Transition from Asynchronous to Oscillatory Dynamics in Balanced Spiking Networks with Instantaneous Synapses

We report a transition from asynchronous to oscillatory behavior in balanced inhibitory networks for class I and II neurons with instantaneous synapses. Collective oscillations emerge for sufficiently connected networks. Their origin is understood in terms of a recently developed mean-field model, whose stable solution is a focus. Microscopic irregular firings, due to balance, trigger sustained oscillations by exciting the relaxation dynamics towards the macroscopic focus. The same mechanism induces in balanced excitatory-inhibitory networks quasiperiodic collective oscillations.

Structure Learning for Deep Neural Networks Based on Multiobjective Optimization

This paper focuses on the connecting structure of deep neural networks and proposes a layerwise structure learning method based on multiobjective optimization. A model with better generalization can be obtained by reducing the connecting parameters in deep networks. The aim is to find the optimal structure with high representation ability and better generalization for each layer. Then, the visible data are modeled with respect to structure based on the products of experts. In order to mitigate the difficulty of estimating the denominator in PoE, the denominator is simplified and taken as another objective, i.e., the connecting sparsity. Moreover, for the consideration of the contradictory nature between the representation ability and the network connecting sparsity, the multiobjective model is established. An improved multiobjective evolutionary algorithm is used to solve this model. Two tricks are designed to decrease the computational cost according to the properties of input data. The experiments on single-layer level, hierarchical level, and application level demonstrate the effectiveness of the proposed algorithm, and the learned structures can improve the performance of deep neural networks.

Phase model-based neuron stabilization into arbitrary clusters

Deep brain stimulation (DBS) is a common method of combating pathological conditions associated with Parkinson's disease, Tourette syndrome, essential tremor, and other disorders, but whose mechanisms are not fully understood. One hypothesis, supported experimentally, is that some symptoms of these disorders are associated with pathological synchronization of neurons in the basal ganglia and thalamus. For this reason, there has been interest in recent years in finding efficient ways to desynchronize neurons that are both fast-acting and low-power. Recent results on coordinated reset and periodically forced oscillators suggest that forming distinct clusters of neurons may prove to be more effective than achieving complete desynchronization, in particular by promoting plasticity effects that might persist after stimulation is turned off. Current proposed methods for achieving clustering frequently require either multiple input sources or precomputing the control signal. We propose here a control strategy for clustering, based on an analysis of the reduced phase model for a set of identical neurons, that allows for real-time, single-input control of a population of neurons with low-amplitude, low total energy signals. After demonstrating its effectiveness on phase models, we apply it to full state models to demonstrate its validity. We also discuss the effects of coupling on the efficacy of the strategy proposed and demonstrate that the clustering can still be accomplished in the presence of weak to moderate electrotonic coupling.

Does layer 4 in the barrel cortex function as a balanced circuit when responding to whisker movements?

Neurons in one barrel in layer 4 (L4) in the mouse vibrissa somatosensory cortex are innervated mostly by neurons from the VPM nucleus and by other neurons within the same barrel. During quiet wakefulness or whisking in air, thalamic inputs vary slowly in time, and excitatory neurons rarely fire. A barrel in L4 contains a modest amount of neurons; the synaptic conductances are not very strong and connections are not sparse. Are the dynamical properties of the L4 circuit similar to those expected from fluctuation-dominated, balanced networks observed for large, strongly coupled and sparse cortical circuits? To resolve this question, we analyze a network of 150 inhibitory parvalbumin-expressing fast-spiking inhibitory interneurons innervated by the VPM thalamus with random connectivity, without or with 1600 low-firing excitatory neurons. Above threshold, the population-average firing rate of inhibitory cortical neurons increases linearly with the thalamic firing rate. The coefficient of variation CV is somewhat less than 1. Moderate levels of synchrony are induced by converging VPM inputs and by inhibitory interaction among neurons. The strengths of excitatory and inhibitory currents during whisking are about three times larger than threshold. We identify values of numbers of presynaptic neurons, synaptic delays between inhibitory neurons, and electrical coupling within the experimentally plausible ranges for which spike synchrony levels are low. Heterogeneity in in-degrees increases the width of the firing rate distribution to the experimentally observed value. We conclude that an L4 circuit in the low-synchrony regime exhibits qualitative dynamical properties similar to those of balanced networks.

Mechanisms underlying a thalamocortical transformation during active tactile sensation

During active somatosensation, neural signals expected from movement of the sensors are suppressed in the cortex, whereas information related to touch is enhanced. This tactile suppression underlies low-noise encoding of relevant tactile features and the brain’s ability to make fine tactile discriminations. Layer (L) 4 excitatory neurons in the barrel cortex, the major target of the somatosensory thalamus (VPM), respond to touch, but have low spike rates and low sensitivity to the movement of whiskers. Most neurons in VPM respond to touch and also show an increase in spike rate with whisker movement. Therefore, signals related to self-movement are suppressed in L4. Fast-spiking (FS) interneurons in L4 show similar dynamics to VPM neurons. Stimulation of halorhodopsin in FS interneurons causes a reduction in FS neuron activity and an increase in L4 excitatory neuron activity. This decrease of activity of L4 FS neurons contradicts the "paradoxical effect" predicted in networks stabilized by inhibition and in strongly-coupled networks. To explain these observations, we constructed a model of the L4 circuit, with connectivity constrained by in vitro measurements. The model explores the various synaptic conductance strengths for which L4 FS neurons actively suppress baseline and movement-related activity in layer 4 excitatory neurons. Feedforward inhibition, in concert with recurrent intracortical circuitry, produces tactile suppression. Synaptic delays in feedforward inhibition allow transmission of temporally brief volleys of activity associated with touch. Our model provides a mechanistic explanation of a behavior-related computation implemented by the thalamocortical circuit.

We study how information is transformed between connected brain areas: the thalamus, the gateway to the cortex, and layer 4 (L4) in cortex, which is the first station to process sensory input from the thalamus. When mice perform an active object localization task with their whiskers, thalamic neurons and inhibitory fast-spiking (FS) interneurons in L4 encode whisker movement and touch, whereas L4 excitatory neurons respond almost exclusively to touch. To explain these observations, we constructed a computational model based on measured circuit parameters. The model reveals that without touch, when thalamic activity varies slowly, strong inhibition from FS neurons prevents activity in L4 excitatory neurons. Brief and strong touch-induced thalamic activity excites both excitatory and FS neurons in L4. FS neurons inhibit excitatory neurons with a delay of approximately 1 ms relative to ascending excitation, allowing L4 excitatory neurons to spike. Our results demonstrate that cortical circuits exploit synaptic delays for fast computations. Similar mechanisms likely also operate for rapid stimuli in the visual and auditory systems.

Flexible information routing by transient synchrony

Perception, cognition and behavior rely on flexible communication between microcircuits in distinct cortical regions. The mechanisms underlying rapid information rerouting between such microcircuits are still unknown. It has been proposed that changing patterns of coherence between local gamma rhythms support flexible information rerouting. The stochastic and transient nature of gamma oscillations in vivo, however, is hard to reconcile with such a function. Here we show that models of cortical circuits near the onset of oscillatory synchrony selectively route input signals despite the short duration of gamma bursts and the irregularity of neuronal firing. In canonical multiarea circuits, we find that gamma bursts spontaneously arise with matched timing and frequency and that they organize information flow by large-scale routing states. Specific self-organized routing states can be induced by minor modulations of background activity.

Traveling waves and breathers in an excitatory-inhibitory neural field

We study existence and stability of traveling activity bump solutions in an excitatory-inhibitory (E-I) neural field with Heaviside firing rate functions by deriving existence conditions for traveling bumps and an Evans function to analyze their spectral stability. Subsequently, we show that these existence and stability results reduce, in the limit of wave speed c→0, to the equivalent conditions developed for the stationary bump case. Using the results for the stationary bump case, we show that drift bifurcations of stationary bumps serve as a mechanism for generating traveling bump solutions in the E-I neural field as parameters are varied. Furthermore, we explore the interrelations between stationary and traveling types of bumps and breathers (time-periodic oscillatory bumps) by bridging together analytical and simulation results for stationary and traveling bumps and their bifurcations in a region of parameter space. Interestingly, we find evidence for a codimension-2 drift-Hopf bifurcation occurring as two parameters, inhibitory time constant τ and I-to-I synaptic connection strength w[over ¯]_{ii}, are varied and show that the codimension-2 point serves as an organizing center for the dynamics of these four types of spatially localized solutions. Additionally, we describe a case involving subcritical bifurcations that lead to traveling waves and breathers as τ is varied.

Effective Suppression of Pathological Synchronization in Cortical Networks by Highly Heterogeneous Distribution of Inhibitory Connections

Even without external random input, cortical networks in vivo sustain asynchronous irregular firing with low firing rate. In addition to detailed balance between excitatory and inhibitory activities, recent theoretical studies have revealed that another feature commonly observed in cortical networks, i.e., long-tailed distribution of excitatory synapses implying coexistence of many weak and a few extremely strong excitatory synapses, plays an essential role in realizing the self-sustained activity in recurrent networks of biologically plausible spiking neurons. The previous studies, however, have not considered highly non-random features of the synaptic connectivity, namely, bidirectional connections between cortical neurons are more common than expected by chance and strengths of synapses are positively correlated between pre- and postsynaptic neurons. The positive correlation of synaptic connections may destabilize asynchronous activity of networks with the long-tailed synaptic distribution and induce pathological synchronized firing among neurons. It remains unclear how the cortical network avoids such pathological synchronization. Here, we demonstrate that introduction of the correlated connections indeed gives rise to synchronized firings in a cortical network model with the long-tailed distribution. By using a simplified feed-forward network model of spiking neurons, we clarify the underlying mechanism of the synchronization. We then show that the synchronization can be efficiently suppressed by highly heterogeneous distribution, typically a lognormal distribution, of inhibitory-to-excitatory connection strengths in a recurrent network model of cortical neurons.

Cooperation and competition of gamma oscillation mechanisms

Oscillations of neuronal activity in different frequency ranges are thought to reflect important aspects of cortical network dynamics. Here we investigate how various mechanisms that contribute to oscillations in neuronal networks may interact. We focus on networks with inhibitory, excitatory, and electrical synapses, where the subnetwork of inhibitory interneurons alone can generate interneuron gamma (ING) oscillations and the interactions between interneurons and pyramidal cells allow for pyramidal-interneuron gamma (PING) oscillations. What type of oscillation will such a network generate? We find that ING and PING oscillations compete: The mechanism generating the higher oscillation frequency "wins"; it determines the frequency of the network oscillation and suppresses the other mechanism. For type I interneurons, the network oscillation frequency is equal to or slightly above the higher of the ING and PING frequencies in corresponding reduced networks that can generate only either of them; if the interneurons belong to the type II class, it is in between. In contrast to ING and PING, oscillations mediated by gap junctions and oscillations mediated by inhibitory synapses may cooperate or compete, depending on the type (I or II) of interneurons and the strengths of the electrical and chemical synapses. We support our computer simulations by a theoretical model that allows a full theoretical analysis of the main results. Our study suggests experimental approaches to deciding to what extent oscillatory activity in networks of interacting excitatory and inhibitory neurons is dominated by ING or PING oscillations and of which class the participating interneurons are.

Dynamics of multistable states during ongoing and evoked cortical activity

Single-trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory, and decision-making. Yet, very little is known about the network mechanisms responsible for its genesis. It is often assumed that the onset of state sequences is triggered by an external stimulus. Here we show that state sequences can be observed also in the absence of overt sensory stimulation. Analysis of multielectrode recordings from the gustatory cortex of alert rats revealed ongoing sequences of states, where single neurons spontaneously attain several firing rates across different states. This single-neuron multistability represents a challenge to existing spiking network models, where typically each neuron is at most bistable. We present a recurrent spiking network model that accounts for both the spontaneous generation of state sequences and the multistability in single-neuron firing rates. Each state results from the activation of neural clusters with potentiated intracluster connections, with the firing rate in each cluster depending on the number of active clusters. Simulations show that the model's ensemble activity hops among the different states, reproducing the ongoing dynamics observed in the data. When probed with external stimuli, the model predicts the quenching of single-neuron multistability into bistability and the reduction of trial-by-trial variability. Both predictions were confirmed in the data. Together, these results provide a theoretical framework that captures both ongoing and evoked network dynamics in a single mechanistic model.

Mechanism and function of mixed-mode oscillations in vibrissa motoneurons

Vibrissa motoneurons in the facial nucleus innervate the intrinsic and extrinsic muscles that move the whiskers. Their intrinsic properties affect the way they process fast synaptic input from the vIRT and Bötzinger nuclei together with serotonergic neuromodulation. In response to constant current (I_app) injection, vibrissa motoneurons may respond with mixed mode oscillations (MMOs), in which sub-threshold oscillations (STOs) are intermittently mixed with spikes. This study investigates the mechanisms involved in generating MMOs in vibrissa motoneurons and their function in motor control. It presents a conductance-based model that includes the M-type K⁺ conductance, g_M, the persistent Na⁺ conductance, g_NaP, and the cationic h conductance, g_h. For g_h = 0 and moderate values of g_M and g_NaP, the model neuron generates STOs, but not MMOs, in response to I_app injection. STOs transform abruptly to tonic spiking as the current increases. In addition to STOs, MMOs are generated for g_h>0 for larger values of I_app; the I_app range in which MMOs appear increases linearly with g_h. In the MMOs regime, the firing rate increases with I_app like a Devil's staircase. Stochastic noise disrupts the temporal structure of the MMOs, but for a moderate noise level, the coefficient of variation (CV) is much less than one and varies non-monotonically with I_app. Furthermore, the estimated time period between voltage peaks, based on Bernoulli process statistics, is much higher in the MMOs regime than in the tonic regime. These two phenomena do not appear when moderate noise generates MMOs without an intrinsic MMO mechanism. Therefore, and since STOs do not appear in spinal motoneurons, the analysis can be used to differentiate different MMOs mechanisms. MMO firing activity in vibrissa motoneurons suggests a scenario in which moderate periodic inputs from the vIRT and Bötzinger nuclei control whisking frequency, whereas serotonergic neuromodulation controls whisking amplitude.

Microscopic mechanism for self-organized quasiperiodicity in random networks of nonlinear oscillators

Self-organized quasiperiodicity is one of the most puzzling dynamical phases observed in systems of nonlinear coupled oscillators. The single dynamical units are not locked to the periodic mean field they produce, but they still feature a coherent behavior, through an unexplained complex form of correlation. We consider a class of leaky integrate-and-fire oscillators on random sparse and massive networks with dynamical synapses, featuring self-organized quasiperiodicity, and we show how complex collective oscillations arise from constructive interference of microscopic dynamics. In particular, we find a simple quantitative relationship between two relevant microscopic dynamical time scales and the macroscopic time scale of the global signal. We show that the proposed relation is a general property of collective oscillations, common to all the partially synchronous dynamical phases analyzed. We argue that an analogous mechanism could be at the origin of similar network dynamics.

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.

Sparse short-distance connections enhance calcium wave propagation in a 3D model of astrocyte networks

Traditionally, astrocytes have been considered to couple via gap-junctions into a syncytium with only rudimentary spatial organization. However, this view is challenged by growing experimental evidence that astrocytes organize as a proper gap-junction mediated network with more complex region-dependent properties. On the other hand, the propagation range of intercellular calcium waves (ICW) within astrocyte populations is as well highly variable, depending on the brain region considered. This suggests that the variability of the topology of gap-junction couplings could play a role in the variability of the ICW propagation range. Since this hypothesis is very difficult to investigate with current experimental approaches, we explore it here using a biophysically realistic model of three-dimensional astrocyte networks in which we varied the topology of the astrocyte network, while keeping intracellular properties and spatial cell distribution and density constant. Computer simulations of the model suggest that changing the topology of the network is indeed sufficient to reproduce the distinct ranges of ICW propagation reported experimentally. Unexpectedly, our simulations also predict that sparse connectivity and restriction of gap-junction couplings to short distances should favor propagation while long–distance or dense connectivity should impair it. Altogether, our results provide support to recent experimental findings that point toward a significant functional role of the organization of gap-junction couplings into proper astroglial networks. Dynamic control of this topology by neurons and signaling molecules could thus constitute a new type of regulation of neuron-glia and glia-glia interactions.

Reliable neuronal systems: the importance of heterogeneity

For every engineer it goes without saying: in order to build a reliable system we need components that consistently behave precisely as they should. It is also well known that neurons, the building blocks of brains, do not satisfy this constraint. Even neurons of the same type come with huge variances in their properties and these properties also vary over time. Synapses, the connections between neurons, are highly unreliable in forwarding signals. In this paper we argue that both these fact add variance to neuronal processes, and that this variance is not a handicap of neural systems, but that instead predictable and reliable functional behavior of neural systems depends crucially on this variability. In particular, we show that higher variance allows a recurrently connected neural population to react more sensitively to incoming signals, and processes them faster and more energy efficient. This, for example, challenges the general assumption that the intrinsic variability of neurons in the brain is a defect that has to be overcome by synaptic plasticity in the process of learning.

Generalized activity equations for spiking neural network dynamics

Much progress has been made in uncovering the computational capabilities of spiking neural networks. However, spiking neurons will always be more expensive to simulate compared to rate neurons because of the inherent disparity in time scales-the spike duration time is much shorter than the inter-spike time, which is much shorter than any learning time scale. In numerical analysis, this is a classic stiff problem. Spiking neurons are also much more difficult to study analytically. One possible approach to making spiking networks more tractable is to augment mean field activity models with some information about spiking correlations. For example, such a generalized activity model could carry information about spiking rates and correlations between spikes self-consistently. Here, we will show how this can be accomplished by constructing a complete formal probabilistic description of the network and then expanding around a small parameter such as the inverse of the number of neurons in the network. The mean field theory of the system gives a rate-like description. The first order terms in the perturbation expansion keep track of covariances.

Hierarchical excitatory synaptic connectivity in mouse olfactory cortex

Topological motifs in synaptic connectivity-such as the cortical column-are fundamental to processing of information in cortical structures. However, the mesoscale topology of cortical networks beyond columns remains largely unknown. In the olfactory cortex, which lacks an obvious columnar structure, sensory-evoked patterns of activity have failed to reveal organizational principles of the network and its structure has been considered to be random. We probed the excitatory network in the mouse olfactory cortex using variance analysis of paired whole-cell recording in olfactory cortex slices. On a given trial, triggered network-wide bursts in disinhibited slices had remarkably similar time courses in widely separated and randomly selected cell pairs of pyramidal neurons despite significant trial-to-trial variability within each neuron. Simulated excitatory network models with random topologies only partially reproduced the experimental burst-variance patterns. Network models with local (columnar) or distributed subnetworks, which have been predicted as the basis of encoding odor objects, were also inconsistent with the experimental data, showing greater variability between cells than across trials. Rather, network models with power-law and especially hierarchical connectivity showed the best fit. Our results suggest that distributed subnetworks are weak or absent in the olfactory cortex, whereas a hierarchical excitatory topology may predominate. A hierarchical excitatory network organization likely underlies burst generation in this epileptogenic region, and may also shape processing of sensory information in the olfactory cortex.

Structure-dynamics relationships in bursting neuronal networks revealed using a prediction framework

The question of how the structure of a neuronal network affects its functionality has gained a lot of attention in neuroscience. However, the vast majority of the studies on structure-dynamics relationships consider few types of network structures and assess limited numbers of structural measures. In this in silico study, we employ a wide diversity of network topologies and search among many possibilities the aspects of structure that have the greatest effect on the network excitability. The network activity is simulated using two point-neuron models, where the neurons are activated by noisy fluctuation of the membrane potential and their connections are described by chemical synapse models, and statistics on the number and quality of the emergent network bursts are collected for each network type. We apply a prediction framework to the obtained data in order to find out the most relevant aspects of network structure. In this framework, predictors that use different sets of graph-theoretic measures are trained to estimate the activity properties, such as burst count or burst length, of the networks. The performances of these predictors are compared with each other. We show that the best performance in prediction of activity properties for networks with sharp in-degree distribution is obtained when the prediction is based on clustering coefficient. By contrast, for networks with broad in-degree distribution, the maximum eigenvalue of the connectivity graph gives the most accurate prediction. The results shown for small () networks hold with few exceptions when different neuron models, different choices of neuron population and different average degrees are applied. We confirm our conclusions using larger () networks as well. Our findings reveal the relevance of different aspects of network structure from the viewpoint of network excitability, and our integrative method could serve as a general framework for structure-dynamics studies in biosciences.

Controlling the oscillation phase through precisely timed closed-loop optogenetic stimulation: a computational study

Dynamic oscillatory coherence is believed to play a central role in flexible communication between brain circuits. To test this communication-through-coherence hypothesis, experimental protocols that allow a reliable control of phase-relations between neuronal populations are needed. In this modeling study, we explore the potential of closed-loop optogenetic stimulation for the control of functional interactions mediated by oscillatory coherence. The theory of non-linear oscillators predicts that the efficacy of local stimulation will depend not only on the stimulation intensity but also on its timing relative to the ongoing oscillation in the target area. Induced phase-shifts are expected to be stronger when the stimulation is applied within specific narrow phase intervals. Conversely, stimulations with the same or even stronger intensity are less effective when timed randomly. Stimulation should thus be properly phased with respect to ongoing oscillations (in order to optimally perturb them) and the timing of the stimulation onset must be determined by a real-time phase analysis of simultaneously recorded local field potentials (LFPs). Here, we introduce an electrophysiologically calibrated model of Channelrhodopsin 2 (ChR2)-induced photocurrents, based on fits holding over two decades of light intensity. Through simulations of a neural population which undergoes coherent gamma oscillations—either spontaneously or as an effect of continuous optogenetic driving—we show that precisely-timed photostimulation pulses can be used to shift the phase of oscillation, even at transduction rates smaller than 25%. We consider then a canonic circuit with two inter-connected neural populations oscillating with gamma frequency in a phase-locked manner. We demonstrate that photostimulation pulses applied locally to a single population can induce, if precisely phased, a lasting reorganization of the phase-locking pattern and hence modify functional interactions between the two populations.

Beyond mean field theory: statistical field theory for neural networks

Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi-Peliti-Janssen formalism, are particularly useful in this regard.

Dynamic finite size effects in spiking neural networks

We investigate the dynamics of a deterministic finite-sized network of synaptically coupled spiking neurons and present a formalism for computing the network statistics in a perturbative expansion. The small parameter for the expansion is the inverse number of neurons in the network. The network dynamics are fully characterized by a neuron population density that obeys a conservation law analogous to the Klimontovich equation in the kinetic theory of plasmas. The Klimontovich equation does not possess well-behaved solutions but can be recast in terms of a coupled system of well-behaved moment equations, known as a moment hierarchy. The moment hierarchy is impossible to solve but in the mean field limit of an infinite number of neurons, it reduces to a single well-behaved conservation law for the mean neuron density. For a large but finite system, the moment hierarchy can be truncated perturbatively with the inverse system size as a small parameter but the resulting set of reduced moment equations that are still very difficult to solve. However, the entire moment hierarchy can also be re-expressed in terms of a functional probability distribution of the neuron density. The moments can then be computed perturbatively using methods from statistical field theory. Here we derive the complete mean field theory and the lowest order second moment corrections for physiologically relevant quantities. Although we focus on finite-size corrections, our method can be used to compute perturbative expansions in any parameter.

One avenue towards understanding how the brain functions is to create computational and mathematical models. However, a human brain has on the order of a hundred billion neurons with a quadrillion synaptic connections. Each neuron is a complex cell comprised of multiple compartments hosting a myriad of ions, proteins and other molecules. Even if computing power continues to increase exponentially, directly simulating all the processes in the brain on a computer is not feasible in the foreseeable future and even if this could be achieved, the resulting simulation may be no simpler to understand than the brain itself. Hence, the need for more tractable models. Historically, systems with many interacting bodies are easier to understand in the two opposite limits of a small number or an infinite number of elements and most of the theoretical efforts in understanding neural networks have been devoted to these two limits. There has been relatively little effort directed to the very relevant but difficult regime of large but finite networks. In this paper, we introduce a new formalism that borrows from the methods of many-body statistical physics to analyze finite size effects in spiking neural networks.

Collective dynamics in sparse networks

The microscopic and macroscopic dynamics of random networks is investigated in the strong-dilution limit (i.e., for sparse networks). By simulating chaotic maps, Stuart-Landau oscillators, and leaky integrate-and-fire neurons, we show that a finite connectivity (of the order of a few tens) is able to sustain a nontrivial collective dynamics even in the thermodynamic limit. Although the network structure implies a nonadditive dynamics, the microscopic evolution is extensive (i.e., the number of active degrees of freedom is proportional to the number of network elements).

Population spikes in cortical networks during different functional states

Brain computational challenges vary between behavioral states. Engaged animals react according to incoming sensory information, while in relaxed and sleeping states consolidation of the learned information is believed to take place. Different states are characterized by different forms of cortical activity. We study a possible neuronal mechanism for generating these diverse dynamics and suggest their possible functional significance. Previous studies demonstrated that brief synchronized increase in a neural firing [Population Spikes (PS)] can be generated in homogenous recurrent neural networks with short-term synaptic depression (STD). Here we consider more realistic networks with clustered architecture. We show that the level of synchronization in neural activity can be controlled smoothly by network parameters. The network shifts from asynchronous activity to a regime in which clusters synchronized separately, then, the synchronization between the clusters increases gradually to fully synchronized state. We examine the effects of different synchrony levels on the transmission of information by the network. We find that the regime of intermediate synchronization is preferential for the flow of information between sparsely connected areas. Based on these results, we suggest that the regime of intermediate synchronization corresponds to engaged behavioral state of the animal, while global synchronization is exhibited during relaxed and sleeping states.

Homeostatic scaling of excitability in recurrent neural networks

Neurons adjust their intrinsic excitability when experiencing a persistent change in synaptic drive. This process can prevent neural activity from moving into either a quiescent state or a saturated state in the face of ongoing plasticity, and is thought to promote stability of the network in which neurons reside. However, most neurons are embedded in recurrent networks, which require a delicate balance between excitation and inhibition to maintain network stability. This balance could be disrupted when neurons independently adjust their intrinsic excitability. Here, we study the functioning of activity-dependent homeostatic scaling of intrinsic excitability (HSE) in a recurrent neural network. Using both simulations of a recurrent network consisting of excitatory and inhibitory neurons that implement HSE, and a mean-field description of adapting excitatory and inhibitory populations, we show that the stability of such adapting networks critically depends on the relationship between the adaptation time scales of both neuron populations. In a stable adapting network, HSE can keep all neurons functioning within their dynamic range, while the network is undergoing several (patho)physiologically relevant types of plasticity, such as persistent changes in external drive, changes in connection strengths, or the loss of inhibitory cells from the network. However, HSE cannot prevent the unstable network dynamics that result when, due to such plasticity, recurrent excitation in the network becomes too strong compared to feedback inhibition. This suggests that keeping a neural network in a stable and functional state requires the coordination of distinct homeostatic mechanisms that operate not only by adjusting neural excitability, but also by controlling network connectivity.

The central nervous system is continuously adapting to a wide variety of input signals. Single neurons receive from one to thousands of input signals and need mechanisms to prevent their output activity from locking up in quiescence or saturation. One experimentally observed mechanism is homeostatic scaling of neuronal excitability (HSE), which adapts neuronal responsiveness at the time scale of minutes. Most neurons function in networks of excitatory and inhibitory cells. Maintaining stability of activity in such networks is highly relevant, because deviations can result in pathologies like epilepsy. Can HSE control output activity of single neurons without interfering with network stability? To address this question we implement HSE in a neuronal network model. We show that stable functioning of HSE requires that the adaptation rate of the inhibitory cells is slower than that of the excitatory cells. We subsequently investigate various changes in network organization that demand adaptation by HSE, showing that HSE can successfully control activity levels as long as feedback excitation is not stronger than feedback inhibition. This suggests that maintaining stable, functional networks requires the coordination of distinct homeostatic mechanisms, acting not only through adjustments of single cell responsiveness, but also by controlling network connectivity.

Rewiring-induced chaos in pulse-coupled neural networks

The dependence of the dynamics of pulse-coupled neural networks on random rewiring of excitatory and inhibitory connections is examined. When both excitatory and inhibitory connections are rewired, periodic synchronization emerges with a Hopf-like bifurcation and a subsequent period-doubling bifurcation; chaotic synchronization is also observed. When only excitatory connections are rewired, periodic synchronization emerges with a saddle node-like bifurcation, and chaotic synchronization is also observed. This result suggests that randomness in the system does not necessarily contaminate the system, and sometimes it even introduces rich dynamics to the system such as chaos.

Synchronous chaos and broad band gamma rhythm in a minimal multi-layer model of primary visual cortex

Visually induced neuronal activity in V1 displays a marked gamma-band component which is modulated by stimulus properties. It has been argued that synchronized oscillations contribute to these gamma-band activity. However, analysis of Local Field Potentials (LFPs) across different experiments reveals considerable diversity in the degree of oscillatory behavior of this induced activity. Contrast-dependent power enhancements can indeed occur over a broad band in the gamma frequency range and spectral peaks may not arise at all. Furthermore, even when oscillations are observed, they undergo temporal decorrelation over very few cycles. This is not easily accounted for in previous network modeling of gamma oscillations. We argue here that interactions between cortical layers can be responsible for this fast decorrelation. We study a model of a V1 hypercolumn, embedding a simplified description of the multi-layered structure of the cortex. When the stimulus contrast is low, the induced activity is only weakly synchronous and the network resonates transiently without developing collective oscillations. When the contrast is high, on the other hand, the induced activity undergoes synchronous oscillations with an irregular spatiotemporal structure expressing a synchronous chaotic state. As a consequence the population activity undergoes fast temporal decorrelation, with concomitant rapid damping of the oscillations in LFPs autocorrelograms and peak broadening in LFPs power spectra. We show that the strength of the inter-layer coupling crucially affects this spatiotemporal structure. We predict that layer VI inactivation should induce global changes in the spectral properties of induced LFPs, reflecting their slower temporal decorrelation in the absence of inter-layer feedback. Finally, we argue that the mechanism underlying the emergence of synchronous chaos in our model is in fact very general. It stems from the fact that gamma oscillations induced by local delayed inhibition tend to develop chaos when coupled by sufficiently strong excitation.

Visual stimulation elicits neuronal responses in visual cortex. When the contrast of the used stimuli increases, the power of this induced activity is boosted over a broad frequency range (30–100 Hz), called the “gamma band.” It would be tempting to hypothesize that this phenomenon is due to the emergence of oscillations in which many neurons fire collectively in a rhythmic way. However, previous models trying to explain contrast-related power enhancements using synchronous oscillations failed to reproduce the observed spectra because they originated unrealistically sharp spectral peaks. The aim of our study is to reconcile synchronous oscillations with broad-band power spectra. We argue here that, thanks to the interaction between neuronal populations at different depths in the cortical tissue, the induced oscillatory responses are synchronous, but, at the same time, chaotic. The chaotic nature of the dynamics makes it possible to have broad-band power spectra together with synchrony. Our modeling study allows us formulating qualitative experimental predictions that provide a potential test for our theory. We predict that if the interactions between cortical layers are suppressed, for instance by inactivating neurons in deep layers, the induced responses might become more regular and narrow isolated peaks might develop in their power spectra.

Neurophysiological and computational principles of cortical rhythms in cognition

Synchronous rhythms represent a core mechanism for sculpting temporal coordination of neural activity in the brain-wide network. This review focuses on oscillations in the cerebral cortex that occur during cognition, in alert behaving conditions. Over the last two decades, experimental and modeling work has made great strides in elucidating the detailed cellular and circuit basis of these rhythms, particularly gamma and theta rhythms. The underlying physiological mechanisms are diverse (ranging from resonance and pacemaker properties of single cells to multiple scenarios for population synchronization and wave propagation), but also exhibit unifying principles. A major conceptual advance was the realization that synaptic inhibition plays a fundamental role in rhythmogenesis, either in an interneuronal network or in a reciprocal excitatory-inhibitory loop. Computational functions of synchronous oscillations in cognition are still a matter of debate among systems neuroscientists, in part because the notion of regular oscillation seems to contradict the common observation that spiking discharges of individual neurons in the cortex are highly stochastic and far from being clocklike. However, recent findings have led to a framework that goes beyond the conventional theory of coupled oscillators and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations. From this perspective, a plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention. Finally, implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.