Self-sustained asynchronous irregular states and Up-Down states in thalamic, cortical and thalamocortical networks of nonlinear integrate-and-fire neurons

Temporal-specific complexity of spiking patterns in spontaneous activity induced by a dual complex network structure

Temporal fluctuation of neural activity in the brain has an important function in optimal information processing. Spontaneous activity is a source of such fluctuation. The distribution of excitatory postsynaptic potentials (EPSPs) between cortical pyramidal neurons can follow a log-normal distribution. Recent studies have shown that networks connected by weak synapses exhibit characteristics of a random network, whereas networks connected by strong synapses have small-world characteristics of small path lengths and large cluster coefficients. To investigate the relationship between temporal complexity spontaneous activity and structural network duality in synaptic connections, we executed a simulation study using the leaky integrate-and-fire spiking neural network with log-normal synaptic weight distribution for the EPSPs and duality of synaptic connectivity, depending on synaptic weight. We conducted multiscale entropy analysis of the temporal spiking activity. Our simulation demonstrated that, when strong synaptic connections approach a small-world network, specific spiking patterns arise during irregular spatio-temporal spiking activity, and the complexity at the large temporal scale (i.e., slow frequency) is enhanced. Moreover, we confirmed through a surrogate data analysis that slow temporal dynamics reflect a deterministic process in the spiking neural networks. This modelling approach may improve the understanding of the spatio-temporal complex neural activity in the brain.

Sleep-like slow oscillations improve visual classification through synaptic homeostasis and memory association in a thalamo-cortical model

The occurrence of sleep passed through the evolutionary sieve and is widespread in animal species. Sleep is known to be beneficial to cognitive and mnemonic tasks, while chronic sleep deprivation is detrimental. Despite the importance of the phenomenon, a complete understanding of its functions and underlying mechanisms is still lacking. In this paper, we show interesting effects of deep-sleep-like slow oscillation activity on a simplified thalamo-cortical model which is trained to encode, retrieve and classify images of handwritten digits. During slow oscillations, spike-timing-dependent-plasticity (STDP) produces a differential homeostatic process. It is characterized by both a specific unsupervised enhancement of connections among groups of neurons associated to instances of the same class (digit) and a simultaneous down-regulation of stronger synapses created by the training. This hierarchical organization of post-sleep internal representations favours higher performances in retrieval and classification tasks. The mechanism is based on the interaction between top-down cortico-thalamic predictions and bottom-up thalamo-cortical projections during deep-sleep-like slow oscillations. Indeed, when learned patterns are replayed during sleep, cortico-thalamo-cortical connections favour the activation of other neurons coding for similar thalamic inputs, promoting their association. Such mechanism hints at possible applications to artificial learning systems.

NREM sleep in the rodent neocortex and hippocampus reflects excitable dynamics

During non-rapid eye movement (NREM) sleep, neuronal populations in the mammalian forebrain alternate between periods of spiking and inactivity. Termed the slow oscillation in the neocortex and sharp wave-ripples in the hippocampus, these alternations are often considered separately but are both crucial for NREM functions. By directly comparing experimental observations of naturally-sleeping rats with a mean field model of an adapting, recurrent neuronal population, we find that the neocortical alternations reflect a dynamical regime in which a stable active state is interrupted by transient inactive states (slow waves) while the hippocampal alternations reflect a stable inactive state interrupted by transient active states (sharp waves). We propose that during NREM sleep in the rodent, hippocampal and neocortical populations are excitable: each in a stable state from which internal fluctuations or external perturbation can evoke the stereotyped population events that mediate NREM functions.

Integrate-and-fire network model of activity propagation from thalamus to cortex

The thalamus plays a crucial role in modulating the cortical activity underlying sensory and cognitive processes. In particular, recent experimental findings highlighted that the thalamus does not merely act as a binary gate for sensory stimuli, but rather participates to the processing of sensory information. Clarifying such thalamic influence on cortical dynamics is also important as the thalamus is the target of therapies such as DBS for Tourette patients. In this perspective, various computational models have been proposed in the last decades. However, a detailed description of the propagation of thalamic activity to the cortex is missing. Here we present a simple computational model of thalamocortical connectivity accounting for the propagation of activity from the thalamus to the cortex. The model includes both the single-neuron scale and the mesoscopic level of Local Field Potential (LFP) signals. Numerical simulations at both levels reproduce typical thalamocortical dynamics which are consistent with experimental measurements and robust to parameters changes. In particular, our model correctly reproduces locally generated rhythms as spindle oscillations in the thalamus and gamma oscillations in the cortex. Our model paves the way to deeper investigations of the thalamic influence on cortical dynamics, with and without sensory inputs or therapeutic electrical stimulation.

Biologically Realistic Mean-Field Models of Conductance-Based Networks of Spiking Neurons with Adaptation

Accurate population models are needed to build very large-scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved, such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of adaptive exponential integrate-and-fire excitatory and inhibitory neurons. Using a master equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable of correctly predicting the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high- and low-activity states alternate (up-down state dynamics), leading to slow oscillations. We conclude that such mean-field models are biologically realistic in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large-scale models involving multiple brain areas.

An Efficient Population Density Method for Modeling Neural Networks with Synaptic Dynamics Manifesting Finite Relaxation Time and Short-Term Plasticity

When incorporating more realistic synaptic dynamics, the computational efficiency of population density methods (PDMs) declines sharply due to the increase in the dimension of master equations. To avoid such a decline, we develop an efficient PDM, termed colored-synapse PDM (csPDM), in which the dimension of the master equations does not depend on the number of synapse-associated state variables in the underlying network model. Our goal is to allow the PDM to incorporate realistic synaptic dynamics that possesses not only finite relaxation time but also short-term plasticity (STP). The model equations of csPDM are derived based on the diffusion approximation on synaptic dynamics and probability density function methods for Langevin equations with colored noise. Numerical examples, given by simulations of the population dynamics of uncoupled exponential integrate-and-fire (EIF) neurons, show good agreement between the results of csPDM and Monte Carlo simulations (MCSs). Compared to the original full-dimensional PDM (fdPDM), the csPDM reveals more excellent computational efficiency because of the lower dimension of the master equations. In addition, it permits network dynamics to possess the short-term plastic characteristics inherited from plastic synapses. The novel csPDM has potential applicability to any spiking neuron models because of no assumptions on neuronal dynamics, and, more importantly, this is the first report of PDM to successfully encompass short-term facilitation/depression properties.

Dendritic sodium spikes endow neurons with inverse firing rate response to correlated synaptic activity

Many neurons possess dendrites enriched with sodium channels and are capable of generating action potentials. However, the role of dendritic sodium spikes remain unclear. Here, we study computational models of neurons to investigate the functional effects of dendritic spikes. In agreement with previous studies, we found that point neurons or neurons with passive dendrites increase their somatic firing rate in response to the correlation of synaptic bombardment for a wide range of input conditions, i.e. input firing rates, synaptic conductances, or refractory periods. However, neurons with active dendrites show the opposite behavior: for a wide range of conditions the firing rate decreases as a function of correlation. We found this property in three types of models of dendritic excitability: a Hodgkin-Huxley model of dendritic spikes, a model with integrate and fire dendrites, and a discrete-state dendritic model. We conclude that fast dendritic spikes confer much broader computational properties to neurons, sometimes opposite to that of point neurons.

Dynamics of spontaneous activity in random networks with multiple neuron subtypes and synaptic noise : Spontaneous activity in networks with synaptic noise

Spontaneous cortical population activity exhibits a multitude of oscillatory patterns, which often display synchrony during slow-wave sleep or under certain anesthetics and stay asynchronous during quiet wakefulness. The mechanisms behind these cortical states and transitions among them are not completely understood. Here we study spontaneous population activity patterns in random networks of spiking neurons of mixed types modeled by Izhikevich equations. Neurons are coupled by conductance-based synapses subject to synaptic noise. We localize the population activity patterns on the parameter diagram spanned by the relative inhibitory synaptic strength and the magnitude of synaptic noise. In absence of noise, networks display transient activity patterns, either oscillatory or at constant level. The effect of noise is to turn transient patterns into persistent ones: for weak noise, all activity patterns are asynchronous non-oscillatory independently of synaptic strengths; for stronger noise, patterns have oscillatory and synchrony characteristics that depend on the relative inhibitory synaptic strength. In the region of parameter space where inhibitory synaptic strength exceeds the excitatory synaptic strength and for moderate noise magnitudes networks feature intermittent switches between oscillatory and quiescent states with characteristics similar to those of synchronous and asynchronous cortical states, respectively. We explain these oscillatory and quiescent patterns by combining a phenomenological global description of the network state with local descriptions of individual neurons in their partial phase spaces. Our results point to a bridge from events at the molecular scale of synapses to the cellular scale of individual neurons to the collective scale of neuronal populations.

Transient and Persistent UP States during Slow-wave Oscillation and their Implications for Cell-Assembly Dynamics

The membrane potentials of cortical neurons in vivo exhibit spontaneous fluctuations between a depolarized UP state and a resting DOWN state during the slow-wave sleeps or in the resting states. This oscillatory activity is believed to engage in memory consolidation although the underlying mechanisms remain unknown. Recently, it has been shown that UP-DOWN state transitions exhibit significantly different temporal profiles in different cortical regions, presumably reflecting differences in the underlying network structure. Here, we studied in computational models whether and how the connection configurations of cortical circuits determine the macroscopic network behavior during the slow-wave oscillation. Inspired by cortical neurobiology, we modeled three types of synaptic weight distributions, namely, log-normal, sparse log-normal and sparse Gaussian. Both analytic and numerical results suggest that a larger variance of weight distribution results in a larger chance of having significantly prolonged UP states. However, the different weight distributions only produce similar macroscopic behavior. We further confirmed that prolonged UP states enrich the variety of cell assemblies activated during these states. Our results suggest the role of persistent UP states for the prolonged repetition of a selected set of cell assemblies during memory consolidation.

Landau-Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization

Understanding the origin, nature, and functional significance of complex patterns of neural activity, as recorded by diverse electrophysiological and neuroimaging techniques, is a central challenge in neuroscience. Such patterns include collective oscillations emerging out of neural synchronization as well as highly heterogeneous outbursts of activity interspersed by periods of quiescence, called "neuronal avalanches." Much debate has been generated about the possible scale invariance or criticality of such avalanches and its relevance for brain function. Aimed at shedding light onto this, here we analyze the large-scale collective properties of the cortex by using a mesoscopic approach following the principle of parsimony of Landau-Ginzburg. Our model is similar to that of Wilson-Cowan for neural dynamics but crucially, includes stochasticity and space; synaptic plasticity and inhibition are considered as possible regulatory mechanisms. Detailed analyses uncover a phase diagram including down-state, synchronous, asynchronous, and up-state phases and reveal that empirical findings for neuronal avalanches are consistently reproduced by tuning our model to the edge of synchronization. This reveals that the putative criticality of cortical dynamics does not correspond to a quiescent-to-active phase transition as usually assumed in theoretical approaches but to a synchronization phase transition, at which incipient oscillations and scale-free avalanches coexist. Furthermore, our model also accounts for up and down states as they occur (e.g., during deep sleep). This approach constitutes a framework to rationalize the possible collective phases and phase transitions of cortical networks in simple terms, thus helping to shed light on basic aspects of brain functioning from a very broad perspective.

Up-Down-Like Background Spiking Can Enhance Neural Information Transmission

How neurons transmit information about sensory or internal signals is strongly influenced by ongoing internal activity. Depending on brain state, this background spiking can occur asynchronously or clustered in up states, periods of collective firing that are interspersed by silent down states. Here, we study which effect such up-down (UD) transitions have on signal transmission. In a simple model, we obtain numerical and analytical results for information theoretic measures. We find that, surprisingly, an UD background can benefit information transmission: when background activity is sparse, it is advantageous to distribute spikes into up states rather than uniformly in time. We reproduce the same effect in a more realistic recurrent network and show that signal transmission is further improved by incorporating that up states propagate across cortex as traveling waves. We propose that traveling UD activity might represent a compromise between reducing metabolic strain and maintaining information transmission capabilities.

New class of reduced computationally efficient neuronal models for large-scale simulations of brain dynamics

During slow-wave sleep, brain electrical activity is dominated by the slow (< 1 Hz) electroencephalogram (EEG) oscillations characterized by the periodic transitions between active (or Up) and silent (or Down) states in the membrane voltage of the cortical and thalamic neurons. Sleep slow oscillation is believed to play critical role in consolidation of recent memories. Past computational studies, based on the Hodgkin-Huxley type neuronal models, revealed possible intracellular and network mechanisms of the neuronal activity during sleep, however, they failed to explore the large-scale cortical network dynamics depending on collective behavior in the large populations of neurons. In this new study, we developed a novel class of reduced discrete time spiking neuron models for large-scale network simulations of wake and sleep dynamics. In addition to the spiking mechanism, the new model implemented nonlinearities capturing effects of the leak current, the Ca²⁺ dependent K⁺ current and the persistent Na⁺ current that were found to be critical for transitions between Up and Down states of the slow oscillation. We applied the new model to study large-scale two-dimensional cortical network activity during slow-wave sleep. Our study explained traveling wave dynamics and characteristic synchronization properties of transitions between Up and Down states of the slow oscillation as observed in vivo in recordings from cats. We further predict a critical role of synaptic noise and slow adaptive currents for spike sequence replay as found during sleep related memory consolidation.

Bistability and up/down state alternations in inhibition-dominated randomly connected networks of LIF neurons

Electrophysiological recordings in cortex in vivo have revealed a rich variety of dynamical regimes ranging from irregular asynchronous states to a diversity of synchronized states, depending on species, anesthesia, and external stimulation. The average population firing rate in these states is typically low. We study analytically and numerically a network of sparsely connected excitatory and inhibitory integrate-and-fire neurons in the inhibition-dominated, low firing rate regime. For sufficiently high values of the external input, the network exhibits an asynchronous low firing frequency state (L). Depending on synaptic time constants, we show that two scenarios may occur when external inputs are decreased: (1) the L state can destabilize through a Hopf bifucation as the external input is decreased, leading to synchronized oscillations spanning d δ to β frequencies; (2) the network can reach a bistable region, between the low firing frequency network state (L) and a quiescent one (Q). Adding an adaptation current to excitatory neurons leads to spontaneous alternations between L and Q states, similar to experimental observations on UP and DOWN states alternations.

Information processing in the vertebrate habenula

The habenula is a brain region that has gained increasing popularity over the recent years due to its role in processing value-related and experience-dependent information with a strong link to depression, addiction, sleep and social interactions. This small diencephalic nucleus is proposed to act as a multimodal hub or a switchboard, where inputs from different brain regions converge. These diverse inputs to the habenula carry information about the sensory world and the animal's internal state, such as reward expectation or mood. However, it is not clear how these diverse habenular inputs interact with each other and how such interactions contribute to the function of habenular circuits in regulating behavioral responses in various tasks and contexts. In this review, we aim to discuss how information processing in habenular circuits, can contribute to specific behavioral programs that are attributed to the habenula.

UP-DOWN cortical dynamics reflect state transitions in a bistable network

In the idling brain, neuronal circuits transition between periods of sustained firing (UP state) and quiescence (DOWN state), a pattern the mechanisms of which remain unclear. Here we analyzed spontaneous cortical population activity from anesthetized rats and found that UP and DOWN durations were highly variable and that population rates showed no significant decay during UP periods. We built a network rate model with excitatory (E) and inhibitory (I) populations exhibiting a novel bistable regime between a quiescent and an inhibition-stabilized state of arbitrarily low rate. Fluctuations triggered state transitions, while adaptation in E cells paradoxically caused a marginal decay of E-rate but a marked decay of I-rate in UP periods, a prediction that we validated experimentally. A spiking network implementation further predicted that DOWN-to-UP transitions must be caused by synchronous high-amplitude events. Our findings provide evidence of bistable cortical networks that exhibit non-rhythmic state transitions when the brain rests.

Shaping the Default Activity Pattern of the Cortical Network

Slow oscillations have been suggested as the default emergent activity of the cortical network. This is a low complexity state that integrates neuronal, synaptic, and connectivity properties of the cortex. Shaped by variations of physiological parameters, slow oscillations provide information about the underlying healthy or pathological network. We review how this default activity is shaped, how it acts as a powerful attractor, and how getting out of it is necessary for the brain to recover the levels of complexity associated with conscious states. We propose that slow oscillations provide a robust unifying paradigm for the study of cortical function.

Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated. We evaluate the reduced models for a wide range of biologically plausible input statistics and find that both approximation approaches lead to spike rate models that accurately reproduce the spiking behavior of the underlying adaptive integrate-and-fire population. Particularly the cascade-based models are overall most accurate and robust, especially in the sensitive region of rapidly changing input. For the mean-driven regime, when input fluctuations are not too strong and fast, however, the best performing model is based on the spectral decomposition. The low-dimensional models also well reproduce stable oscillatory spike rate dynamics that are generated either by recurrent synaptic excitation and neuronal adaptation or through delayed inhibitory synaptic feedback. The computational demands of the reduced models are very low but the implementation complexity differs between the different model variants. Therefore we have made available implementations that allow to numerically integrate the low-dimensional spike rate models as well as the Fokker-Planck partial differential equation in efficient ways for arbitrary model parametrizations as open source software. The derived spike rate descriptions retain a direct link to the properties of single neurons, allow for convenient mathematical analyses of network states, and are well suited for application in neural mass/mean-field based brain network models.

Characterizing the dynamics of biophysically modeled, large neuronal networks usually involves extensive numerical simulations. As an alternative to this expensive procedure we propose efficient models that describe the network activity in terms of a few ordinary differential equations. These systems are simple to solve and allow for convenient investigations of asynchronous, oscillatory or chaotic network states because linear stability analyses and powerful related methods are readily applicable. We build upon two research lines on which substantial efforts have been exerted in the last two decades: (i) the development of single neuron models of reduced complexity that can accurately reproduce a large repertoire of observed neuronal behavior, and (ii) different approaches to approximate the Fokker-Planck equation that represents the collective dynamics of large neuronal networks. We combine these advances and extend recent approximation methods of the latter kind to obtain spike rate models that surprisingly well reproduce the macroscopic dynamics of the underlying neuronal network. At the same time the microscopic properties are retained through the single neuron model parameters. To enable a fast adoption we have released an efficient Python implementation as open source software under a free license.

Photosensitivity in generalized epilepsies

Photosensitivity, which is the hallmark of photosensitive epilepsy (PSE), is described as an abnormal EEG response to visual stimuli known as a photoparoxysmal response (PPR). The PPR is a well-recognized phenomenon, occurring in 2-14% of patients with epilepsy but its pathophysiology is not clearly understood. PPR is electrographically described as 2-5Hz spike, spike-wave, or slow wave complexes with frontal and paracentral prevalence. Diagnosis of PPR is confirmed using intermittent photic stimulation (IPS) as well as video monitoring. The PPR can be elicited by certain types of visual stimuli including flicker, high contrast gratings, moving patterns, and rapidly modulating luminance patterns which may be encountered during e.g., watching television, playing video games, or attending discotheques. Photosensitivity may present in different idiopathic (genetic) epilepsy syndromes e.g. juvenile myoclonic epilepsy (JME) as well as non-IGE syndromes e.g. severe myoclonic epilepsy of infancy. Consequently, PPR is present in patients with diverse seizure types including absence, myoclonic, and generalized tonic-clonic (GTC) seizures. Across syndromes, abnormalities in structural connectivity, functional connectivity, cortical excitability, cortical morphology, and behavioral and neuropsychological function have been reported. Treatment of photosensitivity includes antiepileptic drug administration, and the use of non-pharmacological agents, e.g. tinted or polarizing glasses, as well as occupational measures, e.g. avoidance of certain stimuli.

Computational Account of Spontaneous Activity as a Signature of Predictive Coding

Spontaneous activity is commonly observed in a variety of cortical states. Experimental evidence suggested that neural assemblies undergo slow oscillations with Up ad Down states even when the network is isolated from the rest of the brain. Here we show that these spontaneous events can be generated by the recurrent connections within the network and understood as signatures of neural circuits that are correcting their internal representation. A noiseless spiking neural network can represent its input signals most accurately when excitatory and inhibitory currents are as strong and as tightly balanced as possible. However, in the presence of realistic neural noise and synaptic delays, this may result in prohibitively large spike counts. An optimal working regime can be found by considering terms that control firing rates in the objective function from which the network is derived and then minimizing simultaneously the coding error and the cost of neural activity. In biological terms, this is equivalent to tuning neural thresholds and after-spike hyperpolarization. In suboptimal working regimes, we observe spontaneous activity even in the absence of feed-forward inputs. In an all-to-all randomly connected network, the entire population is involved in Up states. In spatially organized networks with local connectivity, Up states spread through local connections between neurons of similar selectivity and take the form of a traveling wave. Up states are observed for a wide range of parameters and have similar statistical properties in both active and quiescent state. In the optimal working regime, Up states are vanishing, leaving place to asynchronous activity, suggesting that this working regime is a signature of maximally efficient coding. Although they result in a massive increase in the firing activity, the read-out of spontaneous Up states is in fact orthogonal to the stimulus representation, therefore interfering minimally with the network function.

Spontaneous bursts of activity, commonly observed in the brain, can be understood in terms of error-correcting computation within a neural network. Bursts arise automatically in a network that is inefficiently correcting its internal representation.

Effects of Small-World Rewiring Probability and Noisy Synaptic Conductivity on Slow Waves: Cortical Network

Physiological rhythms play a critical role in the functional development of living beings. Many biological functions are executed with an interaction of rhythms produced by internal characteristics of scores of cells. While synchronized oscillations may be associated with normal brain functions, anomalies in these oscillations may cause or relate the emergence of some neurological or neuropsychological pathologies. This study was designed to investigate the effects of topological structure and synaptic conductivity noise on the spatial synchronization and temporal rhythmicity of the waves generated by cells in the network. Because of holding the ability of clustering and randomizing with change of parameters, small-world (SW) network topology was chosen. The oscillatory activity of network was tried out by manipulating an insulated SW, cortical network model whose morphology is very close to real world. According to the obtained results, it was observed that at the optimal probabilistic rates of conductivity noise and rewiring of SW, powerful synchronized oscillatory small waves are generated in relation to the internal dynamics of cells, which are in line with the network's input. These two parameters were observed to be quite effective on the excitation-inhibition balance of the network. Accordingly, it may be suggested that the topological dynamics of SW and noisy synaptic conductivity may be associated with the normal and abnormal development of neurobiological structure.

Propagation of Collective Temporal Regularity in Noisy Hierarchical Networks

Neuronal communication between different brain areas is achieved in terms of spikes. Consequently, spike-time regularity is closely related to many cognitive tasks and timing precision of neural information processing. A recent experiment on primate parietal cortex reports that spike-time regularity increases consistently from primary sensory to higher cortical regions. This observation conflicts with the influential view that spikes in the neocortex are fundamentally irregular. To uncover the underlying network mechanism, we construct a multilayered feedforward neural information transmission pathway and investigate how spike-time regularity evolves across subsequent layers. Numerical results reveal that despite the obviously irregular spiking patterns in previous several layers, neurons in downstream layers can generate rather regular spikes, which depends on the network topology. In particular, we find that collective temporal regularity in deeper layers exhibits resonance-like behavior with respect to both synaptic connection probability and synaptic weight, i.e., the optimal topology parameter maximizes the spike-timing regularity. Furthermore, it is demonstrated that synaptic properties, including inhibition, synaptic transient dynamics, and plasticity, have significant impacts on spike-timing regularity propagation. The emergence of the increasingly regular spiking (RS) patterns in higher parietal regions can, thus, be viewed as a natural consequence of spiking activity propagation between different brain areas. Finally, we validate an important function served by increased RS: promoting reliable propagation of spike-rate signals across downstream layers.

Inhibitory control of correlated intrinsic variability in cortical networks

Cortical networks exhibit intrinsic dynamics that drive coordinated, large-scale fluctuations across neuronal populations and create noise correlations that impact sensory coding. To investigate the network-level mechanisms that underlie these dynamics, we developed novel computational techniques to fit a deterministic spiking network model directly to multi-neuron recordings from different rodent species, sensory modalities, and behavioral states. The model generated correlated variability without external noise and accurately reproduced the diverse activity patterns in our recordings. Analysis of the model parameters suggested that differences in noise correlations across recordings were due primarily to differences in the strength of feedback inhibition. Further analysis of our recordings confirmed that putative inhibitory neurons were indeed more active during desynchronized cortical states with weak noise correlations. Our results demonstrate that network models with intrinsically-generated variability can accurately reproduce the activity patterns observed in multi-neuron recordings and suggest that inhibition modulates the interactions between intrinsic dynamics and sensory inputs to control the strength of noise correlations.

DOI:http://dx.doi.org/10.7554/eLife.19695.001

Our brains contain billions of neurons, which are continually producing electrical signals to relay information around the brain. Yet most of our knowledge of how the brain works comes from studying the activity of one neuron at a time. Recently, studies of multiple neurons have shown that they tend to be active together in short bursts called “up” states, which are followed by periods in which they are less active called “down” states. When we are sleeping or under a general anesthetic, the neurons may be completely silent during down states, but when we are awake the difference in activity between the two states is usually less extreme. However, it is still not clear how the neurons generate these patterns of activity.

To address this question, Stringer et al. studied the activity of neurons in the brains of awake and anesthetized rats, mice and gerbils. The experiments recorded electrical activity from many neurons at the same time and found a wide range of different activity patterns. A computational model based on these data suggests that differences in the degree to which some neurons suppress the activity of other neurons may account for this variety. Increasing the strength of these inhibitory signals in the model decreased the fluctuations in electrical activity across entire areas of the brain. Further analysis of the experimental data supported the model’s predictions by showing that inhibitory neurons – which act to reduce electrical activity in other neurons – were more active when there were fewer fluctuations in activity across the brain.

The next step following on from this work would be to develop ways to build computer models that can mimic the activity of many more neurons at the same time. The models could then be used to interpret the electrical activity produced by many different kinds of neuron. This will enable researchers to test more sophisticated hypotheses about how the brain works.

DOI:http://dx.doi.org/10.7554/eLife.19695.002

Stochastic inference with spiking neurons in the high-conductance state

The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro. Based on a propagation of the membrane autocorrelation across spike bursts, we provide an analytical derivation of the neural activation function that holds for a large parameter space, including the high-conductance state. On this basis, we show how an ensemble of leaky integrate-and-fire neurons with conductance-based synapses embedded in a spiking environment can attain the correct firing statistics for sampling from a well-defined target distribution. For recurrent networks, we examine convergence toward stationarity in computer simulations and demonstrate sample-based Bayesian inference in a mixed graphical model. This points to a new computational role of high-conductance states and establishes a rigorous link between deterministic neuron models and functional stochastic dynamics on the network level.

Transition between Functional Regimes in an Integrate-And-Fire Network Model of the Thalamus

The thalamus is a key brain element in the processing of sensory information. During the sleep and awake states, this brain area is characterized by the presence of two distinct dynamical regimes: in the sleep state activity is dominated by spindle oscillations (7 − 15 Hz) weakly affected by external stimuli, while in the awake state the activity is primarily driven by external stimuli. Here we develop a simple and computationally efficient model of the thalamus that exhibits two dynamical regimes with different information-processing capabilities, and study the transition between them. The network model includes glutamatergic thalamocortical (TC) relay neurons and GABAergic reticular (RE) neurons described by adaptive integrate-and-fire models in which spikes are induced by either depolarization or hyperpolarization rebound. We found a range of connectivity conditions under which the thalamic network composed by these neurons displays the two aforementioned dynamical regimes. Our results show that TC-RE loops generate spindle-like oscillations and that a minimum level of clustering (i.e. local connectivity density) in the RE-RE connections is necessary for the coexistence of the two regimes. We also observe that the transition between the two regimes occurs when the external excitatory input on TC neurons (mimicking sensory stimulation) is large enough to cause a significant fraction of them to switch from hyperpolarization-rebound-driven firing to depolarization-driven firing. Overall, our model gives a novel and clear description of the role that the two types of neurons and their connectivity play in the dynamical regimes observed in the thalamus, and in the transition between them. These results pave the way for the development of efficient models of the transmission of sensory information from periphery to cortex.

Discrepancies between Multi-Electrode LFP and CSD Phase-Patterns: A Forward Modeling Study

Multi-electrode recordings of local field potentials (LFPs) provide the opportunity to investigate the spatiotemporal organization of neural activity on the scale of several millimeters. In particular, the phases of oscillatory LFPs allow studying the coordination of neural oscillations in time and space and to tie it to cognitive processing. Given the computational roles of LFP phases, it is important to know how they relate to the phases of the underlying current source densities (CSDs) that generate them. Although CSDs and LFPs are distinct physical quantities, they are often (implicitly) identified when interpreting experimental observations. That this identification is problematic is clear from the fact that LFP phases change when switching to different electrode montages, while the underlying CSD phases remain unchanged. In this study we use a volume-conductor model to characterize discrepancies between LFP and CSD phase-patterns, to identify the contributing factors, and to assess the effect of different electrode montages. Although we focus on cortical LFPs recorded with two-dimensional (Utah) arrays, our findings are also relevant for other electrode configurations. We found that the main factors that determine the discrepancy between CSD and LFP phase-patterns are the frequency of the neural oscillations and the extent to which the laminar CSD profile is balanced. Furthermore, the presence of laminar phase-differences in cortical oscillations, as commonly observed in experiments, precludes identifying LFP phases with those of the CSD oscillations at a given cortical depth. This observation potentially complicates the interpretation of spike-LFP coherence and spike-triggered LFP averages. With respect to reference strategies, we found that the average-reference montage leads to larger discrepancies between LFP and CSD phases as compared with the referential montage, while the Laplacian montage reduces these discrepancies. We therefore advice to conduct analysis of two-dimensional LFP recordings using the Laplacian montage.

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.

Computational simulation: astrocyte-induced depolarization of neighboring neurons mediates synchronous UP states in a neural network

Although recent reports have suggested that synchronous neuronal UP states are mediated by astrocytic activity, the mechanism responsible for this remains unknown. Astrocytic glutamate release synchronously depolarizes adjacent neurons, while synaptic transmissions are blocked. The purpose of this study was to confirm that astrocytic depolarization, propagated through synaptic connections, can lead to synchronous neuronal UP states. We applied astrocytic currents to local neurons in a neural network consisting of model cortical neurons. Our results show that astrocytic depolarization may generate synchronous UP states for hundreds of milliseconds in neurons even if they do not directly receive glutamate release from the activated astrocyte.

Gain modulation of synaptic inputs by network state in auditory cortex in vivo

The cortical network recurrent circuitry generates spontaneous activity organized into Up (active) and Down (quiescent) states during slow-wave sleep or anesthesia. These different states of cortical activation gain modulate synaptic transmission. However, the reported modulation that Up states impose on synaptic inputs is disparate in the literature, including both increases and decreases of responsiveness. Here, we tested the hypothesis that such disparate observations may depend on the intensity of the stimulation. By means of intracellular recordings, we studied synaptic transmission during Up and Down states in rat auditory cortex in vivo. Synaptic potentials were evoked either by auditory or electrical (thalamocortical, intracortical) stimulation while randomly varying the intensity of the stimulus. Synaptic potentials evoked by the same stimulus intensity were compared in Up/Down states. Up states had a scaling effect on the stimulus-evoked synaptic responses: the amplitude of weaker responses was potentiated whereas that of larger responses was maintained or decreased with respect to the amplitude during Down states. We used a computational model to explore the potential mechanisms explaining this nontrivial stimulus-response relationship. During Up/Down states, there is different excitability in the network and the neuronal conductance varies. We demonstrate that the competition between presynaptic recruitment and the changing conductance might be the central mechanism explaining the experimentally observed stimulus-response relationships. We conclude that the effect that cortical network activation has on synaptic transmission is not constant but contingent on the strength of the stimulation, with a larger modulation for stimuli involving both thalamic and cortical networks.

Stochastic transitions into silence cause noise correlations in cortical circuits

The spiking activity of cortical neurons is highly variable. This variability is generally correlated among nearby neurons, an effect commonly interpreted to reflect the coactivation of neurons due to anatomically shared inputs. Recent findings, however, indicate that correlations can be dynamically modulated, suggesting that the underlying mechanisms are not well understood. Here, we investigate the hypothesis that correlations are dominated by neuronal coinactivation: the occurrence of brief silent periods during which all neurons in the local network stop firing. We recorded spiking activity from large populations of neurons in the auditory cortex of anesthetized rats across different brain states. During spontaneous activity, the reduction of correlation accompanying brain state desynchronization was largely explained by a decrease in the density of the silent periods. The presentation of a stimulus caused an initial drop of correlations followed by a rebound, a time course that was mimicked by the instantaneous silence density. We built a rate network model with fluctuation-driven transitions between a silent and an active attractor and assumed that neurons fired Poisson spike trains with a rate following the model dynamics. Variations of the network external input altered the transition rate into the silent attractor and reproduced the relation between correlation and silence density found in the data, both in spontaneous and evoked conditions. This suggests that the observed changes in correlation, occurring gradually with brain state variations or abruptly with sensory stimulation, are due to changes in the likeliness of the microcircuit to transiently cease firing.

Dynamics of self-sustained asynchronous-irregular activity in random networks of spiking neurons with strong synapses

Random networks of integrate-and-fire neurons with strong current-based synapses can, unlike previously believed, assume stable states of sustained asynchronous and irregular firing, even without external random background or pacemaker neurons. We analyze the mechanisms underlying the emergence, lifetime and irregularity of such self-sustained activity states. We first demonstrate how the competition between the mean and the variance of the synaptic input leads to a non-monotonic firing-rate transfer in the network. Thus, by increasing the synaptic coupling strength, the system can become bistable: In addition to the quiescent state, a second stable fixed-point at moderate firing rates can emerge by a saddle-node bifurcation. Inherently generated fluctuations of the population firing rate around this non-trivial fixed-point can trigger transitions into the quiescent state. Hence, the trade-off between the magnitude of the population-rate fluctuations and the size of the basin of attraction of the non-trivial rate fixed-point determines the onset and the lifetime of self-sustained activity states. During self-sustained activity, individual neuronal activity is moreover highly irregular, switching between long periods of low firing rate to short burst-like states. We show that this is an effect of the strong synaptic weights and the finite time constant of synaptic and neuronal integration, and can actually serve to stabilize the self-sustained state.

Dynamic stability of sequential stimulus representations in adapting neuronal networks

The ability to acquire and maintain appropriate representations of time-varying, sequential stimulus events is a fundamental feature of neocortical circuits and a necessary first step toward more specialized information processing. The dynamical properties of such representations depend on the current state of the circuit, which is determined primarily by the ongoing, internally generated activity, setting the ground state from which input-specific transformations emerge. Here, we begin by demonstrating that timing-dependent synaptic plasticity mechanisms have an important role to play in the active maintenance of an ongoing dynamics characterized by asynchronous and irregular firing, closely resembling cortical activity in vivo. Incoming stimuli, acting as perturbations of the local balance of excitation and inhibition, require fast adaptive responses to prevent the development of unstable activity regimes, such as those characterized by a high degree of population-wide synchrony. We establish a link between such pathological network activity, which is circumvented by the action of plasticity, and a reduced computational capacity. Additionally, we demonstrate that the action of plasticity shapes and stabilizes the transient network states exhibited in the presence of sequentially presented stimulus events, allowing the development of adequate and discernible stimulus representations. The main feature responsible for the increased discriminability of stimulus-driven population responses in plastic networks is shown to be the decorrelating action of inhibitory plasticity and the consequent maintenance of the asynchronous irregular dynamic regime both for ongoing activity and stimulus-driven responses, whereas excitatory plasticity is shown to play only a marginal role.

Characterization and compensation of network-level anomalies in mixed-signal neuromorphic modeling platforms

Advancing the size and complexity of neural network models leads to an ever increasing demand for computational resources for their simulation. Neuromorphic devices offer a number of advantages over conventional computing architectures, such as high emulation speed or low power consumption, but this usually comes at the price of reduced configurability and precision. In this article, we investigate the consequences of several such factors that are common to neuromorphic devices, more specifically limited hardware resources, limited parameter configurability and parameter variations due to fixed-pattern noise and trial-to-trial variability. Our final aim is to provide an array of methods for coping with such inevitable distortion mechanisms. As a platform for testing our proposed strategies, we use an executable system specification (ESS) of the BrainScaleS neuromorphic system, which has been designed as a universal emulation back-end for neuroscientific modeling. We address the most essential limitations of this device in detail and study their effects on three prototypical benchmark network models within a well-defined, systematic workflow. For each network model, we start by defining quantifiable functionality measures by which we then assess the effects of typical hardware-specific distortion mechanisms, both in idealized software simulations and on the ESS. For those effects that cause unacceptable deviations from the original network dynamics, we suggest generic compensation mechanisms and demonstrate their effectiveness. Both the suggested workflow and the investigated compensation mechanisms are largely back-end independent and do not require additional hardware configurability beyond the one required to emulate the benchmark networks in the first place. We hereby provide a generic methodological environment for configurable neuromorphic devices that are targeted at emulating large-scale, functional neural networks.

Sustained oscillations, irregular firing, and chaotic dynamics in hierarchical modular networks with mixtures of electrophysiological cell types

The cerebral cortex exhibits neural activity even in the absence of external stimuli. This self-sustained activity is characterized by irregular firing of individual neurons and population oscillations with a broad frequency range. Questions that arise in this context, are: What are the mechanisms responsible for the existence of neuronal spiking activity in the cortex without external input? Do these mechanisms depend on the structural organization of the cortical connections? Do they depend on intrinsic characteristics of the cortical neurons? To approach the answers to these questions, we have used computer simulations of cortical network models. Our networks have hierarchical modular architecture and are composed of combinations of neuron models that reproduce the firing behavior of the five main cortical electrophysiological cell classes: regular spiking (RS), chattering (CH), intrinsically bursting (IB), low threshold spiking (LTS), and fast spiking (FS). The population of excitatory neurons is built of RS cells (always present) and either CH or IB cells. Inhibitory neurons belong to the same class, either LTS or FS. Long-lived self-sustained activity states in our network simulations display irregular single neuron firing and oscillatory activity similar to experimentally measured ones. The duration of self-sustained activity strongly depends on the initial conditions, suggesting a transient chaotic regime. Extensive analysis of the self-sustained activity states showed that their lifetime expectancy increases with the number of network modules and is favored when the network is composed of excitatory neurons of the RS and CH classes combined with inhibitory neurons of the LTS class. These results indicate that the existence and properties of the self-sustained cortical activity states depend on both the topology of the network and the neuronal mixture that comprises the network.

The influence of ion concentrations on the dynamic behavior of the Hodgkin-Huxley model-based cortical network

Action potentials (APs) in the form of very short pulses arise when the cell is excited by any internal or external stimulus exceeding the critical threshold of the membrane. During AP generation, the membrane potential completes its natural cycle through typical phases that can be formatted by ion channels, gates and ion concentrations, as well as the synaptic excitation rate. On the basis of the Hodgkin-Huxley cell model, a cortical network consistent with the real anatomic structure is realized with randomly interrelated small population of neurons to simulate a cerebral cortex segment. Using this model, we investigated the effects of Na(+) and K(+) ion concentrations on the outcome of this network in terms of regularity, phase locking, and synchronization. The results suggested that Na(+) concentration does slightly affect the amplitude but not considerably affects the other parameters specified by depolarization and repolarization. K(+) concentration significantly influences the form, regularity, and synchrony of the network-generated APs. No previous study dealing directly with the effects of both Na(+) and K(+) ion concentrations on regularity and synchronization of the simulated cortical network-generated APs, allowing for the comparison of results obtained using our methods, was encountered in the literature. The results, however, were consistent with those obtained through studies concerning resonance and synchronization from another perspective and with the information revealed through physiological and pharmacological experiments concerning changing ion concentrations or blocking ion channels. Our results demonstrated that the regularity and reliability of brain functions have a strong relationship with cellular ion concentrations, and suggested the management of the dynamic behavior of the cellular network with ion concentrations.

Graded defragmentation of cortical neuronal firing during recovery of consciousness in rats

State-dependent neuronal firing patterns reflect changes in ongoing information processing and cortical function. A disruption of neuronal coordination has been suggested as the neural correlate of anesthesia. Here, we studied the temporal correlation patterns of ongoing spike activity, during a stepwise reduction of the volatile anesthetic desflurane, in the cerebral cortex of freely moving rats. We hypothesized that the recovery of consciousness from general anesthesia is accompanied by specific changes in the spatiotemporal pattern and correlation of neuronal activity. Sixty-four contact microelectrode arrays were chronically implanted in the primary visual cortex (contacts spanning 1.4-mm depth and 1.4-mm width) for recording of extracellular unit activity at four steady-state levels of anesthesia (8-2% desflurane) and wakefulness. Recovery of consciousness was defined as the regaining of the righting reflex (near 4%). High-intensity firing (HI) periods were segmented using a threshold (200-ms) representing the minimum in the neurons' bimodal interspike interval histogram under anesthesia. We found that the HI periods were highly fragmented in deep anesthesia and gradually transformed to a near-continuous firing pattern at wakefulness. As the anesthetic was withdrawn, HI periods became longer and increasingly correlated among the units both locally and across remote recording sites. Paradoxically, in 4 of 8 animals, HI correlation was also high at the deepest level of anesthesia (8%) when local field potentials (LFP) were burst-suppressed. We conclude that recovery from desflurane anesthesia is accompanied by a graded defragmentation of neuronal activity in the cerebral cortex. Hypersynchrony during deep anesthesia is an exception that occurs only with LFP burst suppression.

The impact of cortical deafferentation on the neocortical slow oscillation

Slow oscillation is the main brain rhythm observed during deep sleep in mammals. Although several studies have demonstrated its neocortical origin, the extent of the thalamic contribution is still a matter of discussion. Using electrophysiological recordings in vivo on cats and computational modeling, we found that the local thalamic inactivation or the complete isolation of the neocortical slabs maintained within the brain dramatically reduced the expression of slow and fast oscillations in affected cortical areas. The slow oscillation began to recover 12 h after thalamic inactivation. The slow oscillation, but not faster activities, nearly recovered after 30 h and persisted for weeks in the isolated slabs. We also observed an increase of the membrane potential fluctuations recorded in vivo several hours after thalamic inactivation. Mimicking this enhancement in a network computational model with an increased postsynaptic activity of long-range intracortical afferents or scaling K(+) leak current, but not several other Na(+) and K(+) intrinsic currents was sufficient for recovering the slow oscillation. We conclude that, in the intact brain, the thalamus contributes to the generation of cortical active states of the slow oscillation and mediates its large-scale synchronization. Our study also suggests that the deafferentation-induced alterations of the sleep slow oscillation can be counteracted by compensatory intracortical mechanisms and that the sleep slow oscillation is a fundamental and intrinsic state of the neocortex.

Effects of asymmetric coupling and self-coupling on metastable dynamical transient rotating waves in a ring of sigmoidal neurons

Transient rotating waves in a ring of sigmoidal neurons with asymmetric bidirectional coupling and self-coupling were studied. When a pair of stable steady states and an unstable traveling wave coexisted, rotating waves propagating in a ring were generated in transients. The pinning (propagation failure) of the traveling wave occurred in the presence of asymmetric coupling and self-coupling, and its conditions were obtained. A kinematical equation for the propagation of wave fronts of the traveling and rotating waves was then derived for a large output gain of neurons. The kinematical equation showed that the duration of transient rotating waves increases exponentially with the number of neurons as that in a ring of unidirectionally coupled neurons (metastable dynamical transients). However, the exponential growth rate depended on the asymmetry of bidirectional coupling and the strength of self-coupling. The rate was equal to the propagation time of the traveling wave (a reciprocal of the propagation speed), and it increased near pinned regions. Then transient rotating waves could show metastable dynamics (extremely long duration) even in a ring of a small number of neurons.

A thalamo-cortical neural mass model for the simulation of brain rhythms during sleep

Cortico-thalamic interactions are known to play a pivotal role in many brain phenomena, including sleep, attention, memory consolidation and rhythm generation. Hence, simple mathematical models that can simulate the dialogue between the cortex and the thalamus, at a mesoscopic level, have a great cognitive value. In the present work we describe a neural mass model of a cortico-thalamic module, based on neurophysiological mechanisms. The model includes two thalamic populations (a thalamo-cortical relay cell population, TCR, and its related thalamic reticular nucleus, TRN), and a cortical column consisting of four connected populations (pyramidal neurons, excitatory interneurons, inhibitory interneurons with slow and fast kinetics). Moreover, thalamic neurons exhibit two firing modes: bursting and tonic. Finally, cortical synapses among pyramidal neurons incorporate a disfacilitation mechanism following prolonged activity. Simulations show that the model is able to mimic the different patterns of rhythmic activity in cortical and thalamic neurons (beta and alpha waves, spindles, delta waves, K-complexes, slow sleep waves) and their progressive changes from wakefulness to deep sleep, by just acting on modulatory inputs. Moreover, simulations performed by providing short sensory inputs to the TCR show that brain rhythms during sleep preserve the cortex from external perturbations, still allowing a high cortical activity necessary to drive synaptic plasticity and memory consolidation. In perspective, the present model may be used within larger cortico-thalamic networks, to gain a deeper understanding of mechanisms beneath synaptic changes during sleep, to investigate the specific role of brain rhythms, and to explore cortical synchronization achieved via thalamic influences.

Metastable dynamical patterns and their stabilization in arrays of bidirectionally coupled sigmoidal neurons

Transient patterns in a bistable ring of bidirectionally coupled sigmoidal neurons were studied. When the system had a pair of spatially uniform steady solutions, the instability of unstable spatially nonuniform steady solutions decreased exponentially with the number of neurons because of the symmetry of the system. As a result, transient spatially nonuniform patterns showed dynamical metastability: Their duration increased exponentially with the number of neurons and the duration of randomly generated patterns obeyed a power-law distribution. However, these metastable dynamical patterns were easily stabilized in the presence of small variations in coupling strength. Metastable rotating waves and their pinning in the presence of asymmetry in the direction of coupling and the disappearance of metastable dynamical patterns due to asymmetry in the output function of a neuron were also examined. Further, in a two-dimensional array of neurons with nearest-neighbor coupling, intrinsically one-dimensional patterns were dominant in transients, and self-excitation in these neurons affected the metastable dynamical patterns.

How adaptation currents change threshold, gain, and variability of neuronal spiking

Many types of neurons exhibit spike rate adaptation, mediated by intrinsic slow K(+) currents, which effectively inhibit neuronal responses. How these adaptation currents change the relationship between in vivo like fluctuating synaptic input, spike rate output, and the spike train statistics, however, is not well understood. In this computational study we show that an adaptation current that primarily depends on the subthreshold membrane voltage changes the neuronal input-output relationship (I-O curve) subtractively, thereby increasing the response threshold, and decreases its slope (response gain) for low spike rates. A spike-dependent adaptation current alters the I-O curve divisively, thus reducing the response gain. Both types of an adaptation current naturally increase the mean interspike interval (ISI), but they can affect ISI variability in opposite ways. A subthreshold current always causes an increase of variability while a spike-triggered current decreases high variability caused by fluctuation-dominated inputs and increases low variability when the average input is large. The effects on I-O curves match those caused by synaptic inhibition in networks with asynchronous irregular activity, for which we find subtractive and divisive changes caused by external and recurrent inhibition, respectively. Synaptic inhibition, however, always increases the ISI variability. We analytically derive expressions for the I-O curve and ISI variability, which demonstrate the robustness of our results. Furthermore, we show how the biophysical parameters of slow K(+) conductances contribute to the two different types of an adaptation current and find that Ca(2+)-activated K(+) currents are effectively captured by a simple spike-dependent description, while muscarine-sensitive or Na(+)-activated K(+) currents show a dominant subthreshold component.

Neural Schematics as a unified formal graphical representation of large-scale Neural Network Structures

One of the major outcomes of neuroscientific research are models of Neural Network Structures (NNSs). Descriptions of these models usually consist of a non-standardized mixture of text, figures, and other means of visual information communication in print media. However, as neuroscience is an interdisciplinary domain by nature, a standardized way of consistently representing models of NNSs is required. While generic descriptions of such models in textual form have recently been developed, a formalized way of schematically expressing them does not exist to date. Hence, in this paper we present Neural Schematics as a concept inspired by similar approaches from other disciplines for a generic two dimensional representation of said structures. After introducing NNSs in general, a set of current visualizations of models of NNSs is reviewed and analyzed for what information they convey and how their elements are rendered. This analysis then allows for the definition of general items and symbols to consistently represent these models as Neural Schematics on a two dimensional plane. We will illustrate the possibilities an agreed upon standard can yield on sampled diagrams transformed into Neural Schematics and an example application for the design and modeling of large-scale NNSs.

Adaptation controls synchrony and cluster states of coupled threshold-model neurons

We analyze zero-lag and cluster synchrony of delay-coupled nonsmooth dynamical systems by extending the master stability approach, and apply this to networks of adaptive threshold-model neurons. For a homogeneous population of excitatory and inhibitory neurons we find (i) that subthreshold adaptation stabilizes or destabilizes synchrony depending on whether the recurrent synaptic excitatory or inhibitory couplings dominate, and (ii) that synchrony is always unstable for networks with balanced recurrent synaptic inputs. If couplings are not too strong, synchronization properties are similar for very different coupling topologies, i.e., random connections or spatial networks with localized connectivity. We generalize our approach for two subpopulations of neurons with nonidentical local dynamics, including bursting, for which activity-based adaptation controls the stability of cluster states, independent of a specific coupling topology.

Spontaneous slow oscillations and sequential patterns due to short-term plasticity in a model of the cortex

We study a realistic model of a cortical column taking into account short-term plasticity between pyramidal cells and interneurons. The simulation of leaky integrate-and-fire neurons shows that low-frequency oscillations emerge spontaneously as a result of intrinsic network properties. These oscillations are composed of prolonged phases of high and low activity reminiscent of cortical up and down states, respectively. We simplify the description of the network activity by using a mean field approximation and reduce the system to two slow variables exhibiting some relaxation oscillations. We identify two types of slow oscillations. When the combination of dynamic synapses between pyramidal cells and those between interneurons accounts for the generation of these slow oscillations, the end of the up phase is characterized by asynchronous fluctuations of the membrane potentials. When the slow oscillations are mainly driven by the dynamic synapses between interneurons, the network exhibits fluctuations of membrane potentials, which are more synchronous at the end than at the beginning of the up phase. Additionally, finite size effect and slow synaptic currents can modify the irregularity and frequency, respectively, of these oscillations. Finally, we consider possible roles of a slow oscillatory input modeling long-range interactions in the brain. Spontaneous slow oscillations of local networks are modulated by the oscillatory input, which induces, notably, synchronization, subharmonic synchronization, and chaotic relaxation oscillations in the mean field approximation. In the case of forced oscillations, the slow population-averaged activity of leaky integrate-and-fire neurons can have both deterministic and stochastic temporal features. We discuss the possibility that long-range connectivity controls the emergence of slow sequential patterns in local populations due to the tendency of a cortical column to oscillate at low frequency.

Mechanisms of seizure propagation in 2-dimensional centre-surround recurrent networks

Understanding how seizures spread throughout the brain is an important problem in the treatment of epilepsy, especially for implantable devices that aim to avert focal seizures before they spread to, and overwhelm, the rest of the brain. This paper presents an analysis of the speed of propagation in a computational model of seizure-like activity in a 2-dimensional recurrent network of integrate-and-fire neurons containing both excitatory and inhibitory populations and having a difference of Gaussians connectivity structure, an approximation to that observed in cerebral cortex. In the same computational model network, alternative mechanisms are explored in order to simulate the range of seizure-like activity propagation speeds (0.1-100 mm/s) observed in two animal-slice-based models of epilepsy: (1) low extracellular [Formula: see text], which creates excess excitation and (2) introduction of gamma-aminobutyric acid (GABA) antagonists, which reduce inhibition. Moreover, two alternative connection topologies are considered: excitation broader than inhibition, and inhibition broader than excitation. It was found that the empirically observed range of propagation velocities can be obtained for both connection topologies. For the case of the GABA antagonist model simulation, consistent with other studies, it was found that there is an effective threshold in the degree of inhibition below which waves begin to propagate. For the case of the low extracellular [Formula: see text] model simulation, it was found that activity-dependent reductions in inhibition provide a potential explanation for the emergence of slowly propagating waves. This was simulated as a depression of inhibitory synapses, but it may also be achieved by other mechanisms. This work provides a localised network understanding of the propagation of seizures in 2-dimensional centre-surround networks that can be tested empirically.

Abnormal effective connectivity in the psychosis high-risk state

In a recently published fMRI study (Dauvermann et al., 2013), nonlinear dynamic causal modeling (DCM) was used to examine condition-specific effective connectivity in subjects at high genetic risk of schizophrenia. The authors concluded that nonlinear DCM could lead to new insights in the development of psychotic symptoms and functional and effective dysconnection at the network level in subjects at high familial risk. In this paper, we place these interesting findings in the context of recent evidence from bilinear DCM studies in subjects at high clinical risk with an at-risk mental state (ARMS) for psychosis by considering their consistency and potential differences with implications for future research in the field of emerging psychosis.

How adaptation shapes spike rate oscillations in recurrent neuronal networks

Neural mass signals from in-vivo recordings often show oscillations with frequencies ranging from <1 to 100 Hz. Fast rhythmic activity in the beta and gamma range can be generated by network-based mechanisms such as recurrent synaptic excitation-inhibition loops. Slower oscillations might instead depend on neuronal adaptation currents whose timescales range from tens of milliseconds to seconds. Here we investigate how the dynamics of such adaptation currents contribute to spike rate oscillations and resonance properties in recurrent networks of excitatory and inhibitory neurons. Based on a network of sparsely coupled spiking model neurons with two types of adaptation current and conductance-based synapses with heterogeneous strengths and delays we use a mean-field approach to analyze oscillatory network activity. For constant external input, we find that spike-triggered adaptation currents provide a mechanism to generate slow oscillations over a wide range of adaptation timescales as long as recurrent synaptic excitation is sufficiently strong. Faster rhythms occur when recurrent inhibition is slower than excitation and oscillation frequency increases with the strength of inhibition. Adaptation facilitates such network-based oscillations for fast synaptic inhibition and leads to decreased frequencies. For oscillatory external input, adaptation currents amplify a narrow band of frequencies and cause phase advances for low frequencies in addition to phase delays at higher frequencies. Our results therefore identify the different key roles of neuronal adaptation dynamics for rhythmogenesis and selective signal propagation in recurrent networks.

Population rate dynamics and multineuron firing patterns in sensory cortex

Cortical circuits encode sensory stimuli through the firing of neuronal ensembles, and also produce spontaneous population patterns in the absence of sensory drive. This population activity is often characterized experimentally by the distribution of multineuron "words" (binary firing vectors), and a match between spontaneous and evoked word distributions has been suggested to reflect learning of a probabilistic model of the sensory world. We analyzed multineuron word distributions in sensory cortex of anesthetized rats and cats, and found that they are dominated by fluctuations in population firing rate rather than precise interactions between individual units. Furthermore, cortical word distributions change when brain state shifts, and similar behavior is seen in simulated networks with fixed, random connectivity. Our results suggest that similarity or dissimilarity in multineuron word distributions could primarily reflect similarity or dissimilarity in population firing rate dynamics, and not necessarily the precise interactions between neurons that would indicate learning of sensory features.