The emergence of Up and Down states in cortical networks

The cerebral cortex is continuously active in the absence of external stimuli. An example of this spontaneous activity is the voltage transition between an Up and a Down state, observed simultaneously at individual neurons. Since this phenomenon could be of critical importance for working memory and attention, its explanation could reveal some fundamental properties of cortical organization. To identify a possible scenario for the dynamics of Up–Down states, we analyze a reduced stochastic dynamical system that models an interconnected network of excitatory neurons with activity-dependent synaptic depression. The model reveals that when the total synaptic connection strength exceeds a certain threshold, the phase space of the dynamical system contains two attractors, interpreted as Up and Down states. In that case, synaptic noise causes transitions between the states. Moreover, an external stimulation producing a depolarization increases the time spent in the Up state, as observed experimentally. We therefore propose that the existence of Up–Down states is a fundamental and inherent property of a noisy neural ensemble with sufficiently strong synaptic connections.     

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

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.     

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

Randomly-connected networks of integrate-and-fire (IF) neurons are known to display asynchronous irregular (AI) activity states, which resemble the discharge activity recorded in the cerebral cortex of awake animals. However, it is not clear whether such activity states are specific to simple IF models, or if they also exist in networks where neurons are endowed with complex intrinsic properties similar to electrophysiological measurements. Here, we investigate the occurrence of AI states in networks of nonlinear IF neurons, such as the adaptive exponential IF (Brette-Gerstner-Izhikevich) model. This model can display intrinsic properties such as low-threshold spike (LTS), regular spiking (RS) or fast-spiking (FS). We successively investigate the oscillatory and AI dynamics of thalamic, cortical and thalamocortical networks using such models. AI states can be found in each case, sometimes with surprisingly small network size of the order of a few tens of neurons. We show that the presence of LTS neurons in cortex or in thalamus, explains the robust emergence of AI states for relatively small network sizes. Finally, we investigate the role of spike-frequency adaptation (SFA). In cortical networks with strong SFA in RS cells, the AI state is transient, but when SFA is reduced, AI states can be self-sustained for long times. In thalamocortical networks, AI states are found when the cortex is itself in an AI state, but with strong SFA, the thalamocortical network displays Up and Down state transitions, similar to intracellular recordings during slow-wave sleep or anesthesia. Self-sustained Up and Down states could also be generated by two-layer cortical networks with LTS cells. These models suggest that intrinsic properties such as adaptation and low-threshold bursting activity are crucial for the genesis and control of AI states in thalamocortical networks.     

Emergence and fragmentation of the alpha-band driven by neuronal network dynamics

Rhythmic neuronal network activity underlies brain oscillations. To investigate how connected neuronal networks contribute to the emergence of the α-band and to the regulation of Up and Down states, we study a model based on synaptic short-term depression-facilitation with afterhyperpolarization (AHP). We found that the α-band is generated by the network behavior near the attractor of the Up-state. Coupling inhibitory and excitatory networks by reciprocal connections leads to the emergence of a stable α-band during the Up states, as reflected in the spectrogram. To better characterize the emergence and stability of thalamocortical oscillations containing α and δ rhythms during anesthesia, we model the interaction of two excitatory networks with one inhibitory network, showing that this minimal topology underlies the generation of a persistent α-band in the neuronal voltage characterized by dominant Up over Down states. Finally, we show that the emergence of the α-band appears when external inputs are suppressed, while fragmentation occurs at small synaptic noise or with increasing inhibitory inputs. To conclude, α-oscillations could result from the synaptic dynamics of interacting excitatory neuronal networks with and without AHP, a principle that could apply to other rhythms.     

Sex differences in endogenous cortical network activity: spontaneously recurring Up/Down states

Background

Several molecular and cellular processes in the vertebrate brain exhibit differences between males and females, leading to sexual dimorphism in the formation of neural circuits and brain organization. While studies on large-scale brain networks provide ample evidence for both structural and functional sex differences, smaller-scale local networks have remained largely unexplored. In the current study, we investigate sexual dimorphism in cortical dynamics by means of spontaneous Up/Down states, a type of network activity that is exhibited during slow-wave sleep, quiet wakefulness, and anesthesia and is thought to represent the default activity of the cortex.

Methods

Up state activity was monitored by local field potential recordings in coronal brain slices of male and female mice across three ages with distinct secretion profiles of sex hormones: (i) pre-puberty (17–21 days old), (ii) 3–9 adult (months old), and (iii) old (19–24 months old).

Results

Female mice of all ages exhibited longer and more frequent Up states compared to aged-matched male mice. Power spectrum analysis revealed sex differences in the relative power of Up state events, with female mice showing reduced power in the delta range (1–4 Hz) and increased power in the theta range (4–8 Hz) compared to male mice. No sex differences were found in the characteristics of Up state peak voltage and latency.

Conclusions

The present study revealed for the first time sex differences in intracortical network activity, using an ex vivo paradigm of spontaneously occurring Up/Down states. We report significant sex differences in Up state properties that are already present in pre-puberty animals and are maintained through adulthood and old age.

     

A network model for activity-dependent sleep regulation

We develop and characterize a dynamical network model for activity-dependent sleep regulation. Specifically, in accordance with the activity-dependent theory for sleep, we view organism sleep as emerging from the local sleep states of functional units known as cortical columns; these local sleep states evolve through integration of local activity inputs, loose couplings with neighboring cortical columns, and global regulation (e.g. by the circadian clock). We model these cortical columns as coupled or networked activity-integrators that transition between sleep and waking states based on thresholds on the total activity. The model dynamics for three canonical experiments (which we have studied both through simulation and system-theoretic analysis) match with experimentally observed characteristics of the cortical-column network. Most notably, assuming connectedness of the network graph, our model predicts the recovery of the columns to a synchronized state upon temporary overstimulation of a single column and/or randomization of the initial sleep and activity-integration states. In analogy with other models for networked oscillators, our model also predicts the possibility for such phenomena as mode-locking.     

Stochastic amplification of fluctuations in cortical up-States

Cortical neurons are bistable; as a consequence their local field potentials can fluctuate between quiescent and active states, generating slow [Formula: see text] Hz oscillations which are widely known as transitions between Up and Down States. Despite a large number of studies on Up-Down transitions, deciphering its nature, mechanisms and function are still today challenging tasks. In this paper we focus on recent experimental evidence, showing that a class of spontaneous oscillations can emerge within the Up states. In particular, a non-trivial peak around [Formula: see text] Hz appears in their associated power-spectra, what produces an enhancement of the activity power for higher frequencies (in the [Formula: see text] Hz band). Moreover, this rhythm within Ups seems to be an emergent or collective phenomenon given that individual neurons do not lock to it as they remain mostly unsynchronized. Remarkably, similar oscillations (and the concomitant peak in the spectrum) do not appear in the Down states. Here we shed light on these findings by using different computational models for the dynamics of cortical networks in presence of different levels of physiological complexity. Our conclusion, supported by both theory and simulations, is that the collective phenomenon of "stochastic amplification of fluctuations" - previously described in other contexts such as Ecology and Epidemiology - explains in an elegant and parsimonious manner, beyond model-dependent details, this extra-rhythm emerging only in the Up states but not in the Downs.     

Fluctuation-driven rhythmogenesis in an excitatory neuronal network with slow adaptation

We study an excitatory all-to-all coupled network of N spiking neurons with synaptically filtered background noise and slow activity-dependent hyperpolarization currents. Such a system exhibits noise-induced burst oscillations over a range of values of the noise strength (variance) and level of cell excitability. Since both of these quantities depend on the rate of background synaptic inputs, we show how noise can provide a mechanism for increasing the robustness of rhythmic bursting and the range of burst frequencies. By exploiting a separation of time scales we also show how the system dynamics can be reduced to low-dimensional mean field equations in the limit N → ∞. Analysis of the bifurcation structure of the mean field equations provides insights into the dynamical mechanisms for initiating and terminating the bursts.     

UP States Protect Ongoing Cortical Activity from Thalamic Inputs

Cortical neurons in vitro and in vivo fluctuate spontaneously between two stable membrane potentials: a depolarized UP state and a hyperpolarized DOWN state. UP states temporally correspond with multineuronal firing sequences which may be important for information processing. To examine how thalamic inputs interact with ongoing cortical UP state activity, we used calcium imaging and targeted whole-cell recordings of activated neurons in thalamocortical slices of mouse somatosensory cortex. Whereas thalamic stimulation during DOWN states generated multineuronal, synchronized UP states, identical stimulation during UP states had no effect on the subthreshold membrane dynamics of the vast majority of cells or on ongoing multineuronal temporal patterns. Both thalamocortical and corticocortical PSPs were significantly reduced and neuronal input resistance was significantly decreased during cortical UP states – mechanistically consistent with UP state insensitivity. Our results demonstrate that cortical dynamics during UP states are insensitive to thalamic inputs.     

Maximizing Sensory Dynamic Range by Tuning the Cortical State to Criticality

Modulation of interactions among neurons can manifest as dramatic changes in the state of population dynamics in cerebral cortex. How such transitions in cortical state impact the information processing performed by cortical circuits is not clear. Here we performed experiments and computational modeling to determine how somatosensory dynamic range depends on cortical state. We used microelectrode arrays to record ongoing and whisker stimulus-evoked population spiking activity in somatosensory cortex of urethane anesthetized rats. We observed a continuum of different cortical states; at one extreme population activity exhibited small scale variability and was weakly correlated, the other extreme had large scale fluctuations and strong correlations. In experiments, shifts along the continuum often occurred naturally, without direct manipulation. In addition, in both the experiment and the model we directly tuned the cortical state by manipulating inhibitory synaptic interactions. Our principal finding was that somatosensory dynamic range was maximized in a specific cortical state, called criticality, near the tipping point midway between the ends of the continuum. The optimal cortical state was uniquely characterized by scale-free ongoing population dynamics and moderate correlations, in line with theoretical predictions about criticality. However, to reproduce our experimental findings, we found that existing theory required modifications which account for activity-dependent depression. In conclusion, our experiments indicate that in vivo sensory dynamic range is maximized near criticality and our model revealed an unanticipated role for activity-dependent depression in this basic principle of cortical function.     

Selective detection of abrupt input changes by integration of spike-frequency adaptation and synaptic depression in a computational network model.

Short-term synaptic depression (STD) and spike-frequency adaptation (SFA) are two basic physiological cortical mechanisms for reducing the system's excitability under repetitive stimulation. The computational implications of each one of these mechanisms on information processing have been studied in detail, but not so the dynamics arising from their combination in a realistic biological scenario. We show here, both experimentally with intracellular recordings from cortical slices of the ferret and computationally using a biologically realistic model of a feedforward cortical network, that STD combined with presynaptic SFA results in the resensitization of cortical synaptic efficacies in the course of sustained stimulation. This fundamental effect is then shown in the computational model to have important implications for the network response to time-varying inputs. The main findings are: (1) the addition of SFA to the model endowed with STD improves the network sensitivity to the degree of synchrony in the incoming inputs; (2) presynaptic SFA, whether slow or fast, combined with STD results in postsynaptic neurons responding briskly to abrupt changes in the presynaptic input current and ignoring sustained stimulation, much more effectively than either SFA or STD alone; (3) for slow presynaptic SFA postsynaptic responses to strong inputs decrease inversely to the input, whereas for weak input current to presynaptic neurons transient postsynaptic responses are strongly facilitated, thus enhancing the system's sensitivity for subtle changes in weak presynaptic inputs. Taken together, these results suggest that in systems designed to respond to temporal aspects of the input, SFA and STD might constitute two necessary, linked elements whose simultaneous interplay is important for the performance of the system.     

Chaos and synchrony in a model of a hypercolumn in visual cortex

Neurons in cortical slices emit spikes or bursts of spikes regularly in response to a suprathreshold current injection. This behavior is in marked contrast to the behavior of cortical neurons in vivo, whose response to electrical or sensory input displays a strong degree of irregularity. Correlation measurements show a significant degree of synchrony in the temporal fluctuations of neuronal activities in cortex. We explore the hypothesis that these phenomena are the result of the synchronized chaos generated by the deterministic dynamics of local cortical networks. A model of a hypercolumn in the visual cortex is studied. It consists of two populations of neurons, one inhibitory and one excitatory. The dynamics of the neurons is based on a Hodgkin-Huxley type model of excitable voltage-clamped cells with several cellular and synaptic conductances. A slow potassium current is included in the dynamics of the excitatory population to reproduce the observed adaptation of the spike trains emitted by these neurons. The pattern of connectivity has a spatial structure which is correlated with the internal organization of hypercolumns in orientation columns. Numerical simulations of the model show that in an appropriate parameter range, the network settles in a synchronous chaotic state, characterized by a strong temporal variability of the neural activity which is correlated across the hypercolumn. Strong inhibitory feedback is essential for the stabilization of this state. These results show that the cooperative dynamics of large neuronal networks are capable of generating variability and synchrony similar to those observed in cortex. Auto-correlation and cross-correlation functions of neuronal spike trains are computed, and their temporal and spatial features are analyzed. In other parameter regimes, the network exhibits two additional states: synchronized oscillations and an asynchronous state. We use our model to study cortical mechanisms for orientation selectivity. It is shown that in a suitable parameter regime, when the input is not oriented, the network has a continuum of states, each representing an inhomogeneous population activity which is peaked at one of the orientation columns. As a result, when a weakly oriented input stimulates the network, it yields a sharp orientation tuning. The properties of the network in this regime, including the appearance of virtual rotations and broad stimulus-dependent cross-correlations, are investigated. The results agree with the predictions of the mean field theory which was previously derived for a simplified model of stochastic, two-state neurons. The relation between the results of the model and experiments in visual cortex are discussed.     

A Generalized Framework for Quantifying the Dynamics of EEG Event-Related Desynchronization

Brains were built by evolution to react swiftly to environmental challenges. Thus, sensory stimuli must be processed ad hoc, i.e., independent—to a large extent—from the momentary brain state incidentally prevailing during stimulus occurrence. Accordingly, computational neuroscience strives to model the robust processing of stimuli in the presence of dynamical cortical states. A pivotal feature of ongoing brain activity is the regional predominance of EEG eigenrhythms, such as the occipital alpha or the pericentral mu rhythm, both peaking spectrally at 10 Hz. Here, we establish a novel generalized concept to measure event-related desynchronization (ERD), which allows one to model neural oscillatory dynamics also in the presence of dynamical cortical states. Specifically, we demonstrate that a somatosensory stimulus causes a stereotypic sequence of first an ERD and then an ensuing amplitude overshoot (event-related synchronization), which at a dynamical cortical state becomes evident only if the natural relaxation dynamics of unperturbed EEG rhythms is utilized as reference dynamics. Moreover, this computational approach also encompasses the more general notion of a “conditional ERD,” through which candidate explanatory variables can be scrutinized with regard to their possible impact on a particular oscillatory dynamics under study. Thus, the generalized ERD represents a powerful novel analysis tool for extending our understanding of inter-trial variability of evoked responses and therefore the robust processing of environmental stimuli.     

Neuronal Avalanches Differ from Wakefulness to Deep Sleep – Evidence from Intracranial Depth Recordings in Humans

Neuronal activity differs between wakefulness and sleep states. In contrast, an attractor state, called self-organized critical (SOC), was proposed to govern brain dynamics because it allows for optimal information coding. But is the human brain SOC for each vigilance state despite the variations in neuronal dynamics? We characterized neuronal avalanches – spatiotemporal waves of enhanced activity - from dense intracranial depth recordings in humans. We showed that avalanche distributions closely follow a power law – the hallmark feature of SOC - for each vigilance state. However, avalanches clearly differ with vigilance states: slow wave sleep (SWS) shows large avalanches, wakefulness intermediate, and rapid eye movement (REM) sleep small ones. Our SOC model, together with the data, suggested first that the differences are mediated by global but tiny changes in synaptic strength, and second, that the changes with vigilance states reflect small deviations from criticality to the subcritical regime, implying that the human brain does not operate at criticality proper but close to SOC. Independent of criticality, the analysis confirms that SWS shows increased correlations between cortical areas, and reveals that REM sleep shows more fragmented cortical dynamics.     

Acetylcholine and associative memory in the piriform cortex

The significance of cholinergic modulation for associative memory performance in the piriform cortex was examined in a study combining cellular neurophysiology in brain slices with realistic biophysical network simulations. Three different physiological effects of acetylcholine were identified at the single-cell level: suppression of neuronal adaptation, suppression of synaptic transmission in the intrinsic fibers layer, and activity-dependent increase in synaptic strength. Biophysical simulations show how these three effects are joined together to enhance learning and recall performance of the cortical network. Furthermore, our data suggest that activity-dependent synaptic decay during learning is a crucial factor in determining learning capability of the cortical network. Accordingly, it is predicted that acetylcholine should also enhance long-term depression in the piriform cortex.     

Emergence of symmetric, modular, and reciprocal connections in recurrent networks with Hebbian learning

While learning and development are well characterized in feedforward networks, these features are more difficult to analyze in recurrent networks due to the increased complexity of dual dynamics – the rapid dynamics arising from activation states and the slow dynamics arising from learning or developmental plasticity. We present analytical and numerical results that consider dual dynamics in a recurrent network undergoing Hebbian learning with either constant weight decay or weight normalization. Starting from initially random connections, the recurrent network develops symmetric or near-symmetric connections through Hebbian learning. Reciprocity and modularity arise naturally through correlations in the activation states. Additionally, weight normalization may be better than constant weight decay for the development of multiple attractor states that allow a diverse representation of the inputs. These results suggest a natural mechanism by which synaptic plasticity in recurrent networks such as cortical and brainstem premotor circuits could enhance neural computation and the generation of motor programs. Received: 27 April 1998 / Accepted in revised form: 16 March 1999     

A Markov model for interspike interval distributions of auditory cortical neurons that do not show periodic firings

Spontaneous firing properties of individual auditory cortical neurons are interpreted in terms of local and global order present in functioning brain networks, such as alternating “up” and “down” states. A four-state modulated Markov process is used to model neuronal firings. The system alternates between a bound and an unbound state, both with Poisson-distributed lifetimes. During the unbound state, active and closed states alternate with Poisson-distributed lifetimes. Inside the active state, spikes are generated as a realization of a Poisson process. This combination of processes constitutes a four-state modulated Markov process, determined by five independent parameters. Analytical expressions for the probability density functions (pdfs) that describe the interspike interval (ISI) distribution and autocorrelation function are derived. The pdf for the ISI distribution is shown to be a linear combination of three exponential functions and is expressed through the five system parameters. Through fitting experimental ISI histograms by the theoretical ones, numerical values of the system parameters are obtained for the individual neurons. Both Monte Carlo simulations and goodness-of-fit tests are used to validate the fitting procedure. The values of the estimated system parameters related to the active-closed and bound–unbound processes and their independence on the neurons’ mean firing rate suggest that the underlying quasi-periodic processes reflect properties of the network in which the neurons are embedded. The characteristic times of autocorrelations, determined by the bound–unbound and active-closed processes, are also independent of the neuron’s firing rate. The agreement between experimental and theoretical ISI histograms and autocorrelation functions allows interpretation of the system parameters of the individual neurons in terms of slow and delta waves, and high-frequency oscillations observed in cortical networks. This procedure can identify and track the influence of changing brain states on the single-unit firing patterns in experimental animals.     

Methods for predicting cortical UP and DOWN states from the phase of deep layer local field potentials

During anesthesia, slow-wave sleep and quiet wakefulness, neuronal membrane potentials collectively switch between de- and hyperpolarized levels, the cortical UP and DOWN states. Previous studies have shown that these cortical UP/DOWN states affect the excitability of individual neurons in response to sensory stimuli, indicating that a significant amount of the trial-to-trial variability in neuronal responses can be attributed to ongoing fluctuations in network activity. However, as intracellular recordings are frequently not available, it is important to be able to estimate their occurrence purely from extracellular data. Here, we combine in vivo whole cell recordings from single neurons with multi-site extracellular microelectrode recordings, to quantify the performance of various approaches to predicting UP/DOWN states from the deep-layer local field potential (LFP). We find that UP/DOWN states in deep cortical layers of rat primary auditory cortex (A1) are predictable from the phase of LFP at low frequencies (< 4 Hz), and that the likelihood of a given state varies sinusoidally with the phase of LFP at these frequencies. We introduce a novel method of detecting cortical state by combining information concerning the phase of the LFP and ongoing multi-unit activity.     

Patterns of ongoing activity and the functional architecture of the primary visual cortex

Ongoing spontaneous activity in the cerebral cortex exhibits complex spatiotemporal patterns in the absence of sensory stimuli. To elucidate the nature of this ongoing activity, we present a theoretical treatment of two contrasting scenarios of cortical dynamics: (1) fluctuations about a single background state and (2) wandering among multiple "attractor" states, which encode a single or several stimulus features. Studying simplified network rate models of the primary visual cortex (V1), we show that the single state scenario is characterized by fast and high-dimensional Gaussian-like fluctuations, whereas in the multiple state scenario the fluctuations are slow, low dimensional, and highly non-Gaussian. Studying a more realistic model that incorporates correlations in the feed-forward input, spatially restricted cortical interactions, and an experimentally derived layout of pinwheels, we show that recent optical-imaging data of ongoing activity in V1 are consistent with the presence of either a single background state or multiple attractor states encoding many features.