Exploring the spectrum of dynamical regimes and timescales in spontaneous cortical activity

Rhythms at slow (<1 Hz) frequency of alternating Up and Down states occur during slow-wave sleep states, under deep anaesthesia and in cortical slices of mammals maintained in vitro. Such spontaneous oscillations result from the interplay between network reverberations nonlinearly sustained by a strong synaptic coupling and a fatigue mechanism inhibiting the neurons firing in an activity-dependent manner. Varying pharmacologically the excitability level of brain slices we exploit the network dynamics underlying slow rhythms, uncovering an intrinsic anticorrelation between Up and Down state durations. Besides, a non-monotonic change of Down state duration is also observed, which shrinks the distribution of the accessible frequencies of the slow rhythms. Attractor dynamics with activity-dependent self-inhibition predicts a similar trend even when the system excitability is reduced, because of a stability loss of Up and Down states. Hence, such cortical rhythms tend to display a maximal size of the distribution of Up/Down frequencies, envisaging the location of the system dynamics on a critical boundary of the parameter space. This would be an optimal solution for the system in order to display a wide spectrum of dynamical regimes and timescales.     

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.     

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.     

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.

     

Transcranial electrical currents to probe EEG brain rhythms and memory consolidation during sleep in humans

Previously the application of a weak electric anodal current oscillating with a frequency of the sleep slow oscillation (～0.75 Hz) during non-rapid eye movement sleep (NonREM) sleep boosted endogenous slow oscillation activity and enhanced sleep-associated memory consolidation. The slow oscillations occurring during NonREM sleep and theta oscillations present during REM sleep have been considered of critical relevance for memory formation. Here transcranial direct current stimulation (tDCS) oscillating at 5 Hz, i.e., within the theta frequency range (theta-tDCS) is applied during NonREM and REM sleep. Theta-tDCS during NonREM sleep produced a global decrease in slow oscillatory activity conjoint with a local reduction of frontal slow EEG spindle power (8-12 Hz) and a decrement in consolidation of declarative memory, underlining the relevance of these cortical oscillations for sleep-dependent memory consolidation. In contrast, during REM sleep theta-tDCS appears to increase global gamma (25-45 Hz) activity, indicating a clear brain state-dependency of theta-tDCS. More generally, results demonstrate the suitability of oscillating-tDCS as a tool to analyze functions of endogenous EEG rhythms and underlying endogenous electric fields as well as the interactions between EEG rhythms of different frequencies.     

Gap junctions modulate seizures in a mean-field model of general anesthesia for the cortex

During slow-wave sleep, general anesthesia, and generalized seizures, there is an absence of consciousness. These states are characterized by low-frequency large-amplitude traveling waves in scalp electroencephalogram. Therefore the oscillatory state might be an indication of failure to form coherent neuronal assemblies necessary for consciousness. A generalized seizure event is a pathological brain state that is the clearest manifestation of waves of synchronized neuronal activity. Since gap junctions provide a direct electrical connection between adjoining neurons, thus enhancing synchronous behavior, reducing gap-junction conductance should suppress seizures; however there is no clear experimental evidence for this. Here we report theoretical predictions for a physiologically-based cortical model that describes the general anesthetic phase transition from consciousness to coma, and includes both chemical synaptic and direct electrotonic synapses. The model dynamics exhibits both Hopf (temporal) and Turing (spatial) instabilities; the Hopf instability corresponds to the slow (≲8 Hz) oscillatory states similar to those seen in slow-wave sleep, general anesthesia, and seizures. We argue that a delicately balanced interplay between Hopf and Turing modes provides a canonical mechanism for the default non-cognitive rest state of the brain. We show that the Turing mode, set by gap-junction diffusion, is generally protective against entering oscillatory modes; and that weakening the Turing mode by reducing gap conduction can release an uncontrolled Hopf oscillation and hence an increased propensity for seizure and simultaneously an increased sensitivity to GABAergic anesthesia.     

Oscillations in the oxidation-reduction potential of the brain tissue in rats developing during wakefulness and slow-wave sleep

Variations of the brain cortex redox state potential (E) were recorded in freely moving white rats (mass of 300-350 g) with implanted platinum electrodes (with the platinum reference electrode in the nasal bone) during sleep-wake cycles. It was found that transitions from the slow-wave sleep to wakefulness were accompanied in the number of cortical areas (metabolic-active sites) by the E rise, while the transitions from the wakefulness to slow-ware sleep were associated with a drop of E. However, the episodes of the short-term arousals during the slow-wave sleep were accompanied by the respective decreases in E thus forming the irregular E variations (1.5-3 min in duration). It was also found that the oscillations of a typical pattern (quasisinusoidal with the frequency of 10-20 osc/min and the amplitudes up to several mV) could take place in the metabolic-active cortical sites. These oscillations were defined as fast E oscillations. During the slow-wave sleep, the less regular oscillations with the lower frequency (1.2-10 osc/min) and higher amplitude were recorded in the same cortical sites. These oscillations were defined as slow. It is suggested that the fast metabolic oscillations of wakefulness are mainly controlled by the mitochondria of neuronal populations, whereas the slow metabolic oscillations which occur in the slow-wave sleep are related with glycolysis in populations of glial cells.     

Coupling of Thalamocortical Sleep Oscillations Are Important for Memory Consolidation in Humans

Sleep, specifically non-rapid eye movement (NREM) sleep, is thought to play a critical role in the consolidation of recent memories. Two main oscillatory activities observed during NREM, cortical slow oscillations (SO, 0.5–1.0Hz) and thalamic spindles (12–15Hz), have been shown to independently correlate with memory improvement. Yet, it is not known how these thalamocortical events interact, or the significance of this interaction, during the consolidation process. Here, we found that systemic administration of the GABAergic drug (zolpidem) increased both the phase-amplitude coupling between SO and spindles, and verbal memory improvement in humans. These results suggest that thalamic spindles that occur during transitions to the cortical SO Up state are optimal for memory consolidation. Our study predicts that the timely interactions between cortical and thalamic events during consolidation, contribute to memory improvement and is mediated by the level of inhibitory neurotransmission.     

Slow Oscillation Amplitudes and Up-State Lengths Relate to Memory Improvement

There is growing evidence of the active involvement of sleep in memory consolidation. Besides hippocampal sharp wave-ripple complexes and sleep spindles, slow oscillations appear to play a key role in the process of sleep-associated memory consolidation. Furthermore, slow oscillation amplitude and spectral power increase during the night after learning declarative and procedural memory tasks. However, it is unresolved whether learning-induced changes specifically alter characteristics of individual slow oscillations, such as the slow oscillation up-state length and amplitude, which are believed to be important for neuronal replay. 24 subjects (12 men) aged between 20 and 30 years participated in a randomized, within-subject, multicenter study. Subjects slept on three occasions for a whole night in the sleep laboratory with full polysomnography. Whereas the first night only served for adaptation purposes, the two remaining nights were preceded by a declarative word-pair task or by a non-learning control task. Slow oscillations were detected in non-rapid eye movement sleep over electrode Fz. Results indicate positive correlations between the length of the up-state as well as the amplitude of both slow oscillation phases and changes in memory performance from pre to post sleep. We speculate that the prolonged slow oscillation up-state length might extend the timeframe for the transfer of initial hippocampal to long-term cortical memory representations, whereas the increase in slow oscillation amplitudes possibly reflects changes in the net synaptic strength of cortical networks.     

Synaptic Homeostasis and Restructuring across the Sleep-Wake Cycle

Sleep is critical for hippocampus-dependent memory consolidation. However, the underlying mechanisms of synaptic plasticity are poorly understood. The central controversy is on whether long-term potentiation (LTP) takes a role during sleep and which would be its specific effect on memory. To address this question, we used immunohistochemistry to measure phosphorylation of Ca²⁺/calmodulin-dependent protein kinase II (pCaMKIIα) in the rat hippocampus immediately after specific sleep-wake states were interrupted. Control animals not exposed to novel objects during waking (WK) showed stable pCaMKIIα levels across the sleep-wake cycle, but animals exposed to novel objects showed a decrease during subsequent slow-wave sleep (SWS) followed by a rebound during rapid-eye-movement sleep (REM). The levels of pCaMKIIα during REM were proportional to cortical spindles near SWS/REM transitions. Based on these results, we modeled sleep-dependent LTP on a network of fully connected excitatory neurons fed with spikes recorded from the rat hippocampus across WK, SWS and REM. Sleep without LTP orderly rescaled synaptic weights to a narrow range of intermediate values. In contrast, LTP triggered near the SWS/REM transition led to marked swaps in synaptic weight ranking. To better understand the interaction between rescaling and restructuring during sleep, we implemented synaptic homeostasis and embossing in a detailed hippocampal-cortical model with both excitatory and inhibitory neurons. Synaptic homeostasis was implemented by weakening potentiation and strengthening depression, while synaptic embossing was simulated by evoking LTP on selected synapses. We observed that synaptic homeostasis facilitates controlled synaptic restructuring. The results imply a mechanism for a cognitive synergy between SWS and REM, and suggest that LTP at the SWS/REM transition critically influences the effect of sleep: Its lack determines synaptic homeostasis, its presence causes synaptic restructuring.     

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.     

Beta-amyloid induced changes in A-type K<Superscript>+</Superscript> current can alter hippocampo-septal network dynamics

Alzheimer’s disease (AD) progression is usually associated with memory deficits and cognitive decline. A hallmark of AD is the accumulation of beta-amyloid (Aβ) peptide, which is known to affect the hippocampal pyramidal neurons in the early stage of AD. Previous studies have shown that Aβ can block A-type K⁺ currents in the hippocampal pyramidal neurons and enhance the neuronal excitability. However, the mechanisms underlying such changes and the effects of the hyper-excited pyramidal neurons on the hippocampo-septal network dynamics are still to be investigated. In this paper, Aβ-blocked A-type current is simulated, and the resulting neuronal and network dynamical changes are evaluated in terms of the theta band power. The simulation results demonstrate an initial slight but significant theta band power increase as the A-type current starts to decrease. However, the theta band power eventually decreases as the A-type current is further decreased. Our analysis demonstrates that Aβ blocked A-type currents can increase the pyramidal neuronal excitability by preventing the emergence of a steady state. The increased theta band power is due to more pyramidal neurons recruited into spiking mode during the peak of pyramidal theta oscillations. However, the decreased theta band power is caused by the spiking phase relationship between different neuronal populations, which is critical for theta oscillation, is violated by the hyper-excited pyramidal neurons. Our findings could provide potential implications on some AD symptoms, such as memory deficits and AD caused epilepsy.     

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.     

Stimulus-induced transitions between spike-wave discharges and spindles with the modulation of thalamic reticular nucleus

It is believed that thalamic reticular nucleus (TRN) controls spindles and spike-wave discharges (SWD) in seizure or sleeping processes. The dynamical mechanisms of spatiotemporal evolutions between these two types of activity, however, are not well understood. In light of this, we first use a single-compartment thalamocortical neural field model to investigate the effects of TRN on occurrence of SWD and its transition. Results show that the increasing inhibition from TRN to specific relay nuclei (SRN) can lead to the transition of system from SWD to slow-wave oscillation. Specially, it is shown that stimulations applied in the cortical neuronal populations can also initiate the SWD and slow-wave oscillation from the resting states under the typical inhibitory intensity from TRN to SRN. Then, we expand into a 3-compartment coupled thalamocortical model network in linear and circular structures, respectively, to explore the spatiotemporal evolutions of wave states in different compartments. The main results are: (i) for the open-ended model network, SWD induced by stimulus in the first compartment can be transformed into sleep-like slow UP-DOWN and spindle states as it propagates into the downstream compartments; (ii) for the close-ended model network, weak stimulations performed in the first compartment can result in the consistent experimentally observed spindle oscillations in all three compartments; in contrast, stronger periodic single-pulse stimulations applied in the first compartment can induce periodic transitions between SWD and spindle oscillations. Detailed investigations reveal that multi-attractor coexistence mechanism composed of SWD, spindles and background state underlies these state evolutions. What’s more, in order to demonstrate the state evolution stability with respect to the topological structures of neural network, we further expand the 3-compartment coupled network into 10-compartment coupled one, with linear and circular structures, and nearest-neighbor (NN) coupled network as well as its realization of small-world (SW) topology via random rewiring, respectively. Interestingly, for the cases of linear and circular connetivities, qualitatively similar results were obtained in addition to the more irregularity of firings. However, SWD can be eventually transformed into the consistent low-amplitude oscillations for both NN and SW networks. In particular, SWD evolves into the slow spindling oscillations and background tonic oscillations within the NN and SW network, respectively. Our modeling and simulation studies highlight the effect of network topology in the evolutions of SWD and spindling oscillations, which provides new insights into the mechanisms of cortical seizures development.     

Active neocortical processes during quiescent sleep

The neocortex and the thalamus constitute a unified oscillatory machine during different states of vigilance. The cortically generated slow sleep oscillation has the virtue of grouping other sleep rhythms, including those arising in the thalamus, within complex wave-sequences. Despite the coherent oscillatory activity in corticothalamic circuits, on the functional side there is dissociation between thalamus and neocortex during sleep. While dorsal thalamic neurons undergo inhibitory processes induced by prolonged spikebursts of GABAergic thalamic reticular neurons, the cortex displays, periodically, a rich spontaneous activity and preserves the capacity to process internally generated signals. Simultaneous intracellular recordings from thalamic and cortical neurons show that short-term plasticity processes occur after prolonged and rhythmic spike-bursts fired by thalamic and cortical neurons during slow-wave sleep oscillations. This may serve to support resonant phenomena and reorganize corticothalamic circuitry.     

In vivo electrophysiological evidences for cortical neuron-glia interactions during slow (<1 Hz) and paroxysmal sleep oscillations.

The cortical activity results from complex interactions within networks of neurons and glial cells. The dialogue signals consist of neurotransmitters and various ions, which cross through the extracellular space. Slow (<1 Hz) sleep oscillations were first disclosed and investigated at the neuronal level where they consist of an alternation of the membrane potential between a depolarized and a hyperpolarized state. However, neuronal properties alone could not account for the mechanisms underlying the oscillatory nature of the sleeping cortex. Here I will show the behavior of glial cells during the slow sleep oscillation and its relationship with the variation of the neuronal membrane potential (pairs of neurons and glia recorded simultaneously and intracellularly) suggesting that, in contrast with previous assumptions, glial cells are not idle followers of neuronal activity. I will equally present measurements of the extracellular concentration of K(+) and Ca(2+), ions known to modulate the neuronal excitability. They are also part of the ionic flux that is spatially buffered by glial cells. The timing of the spatial buffering during the slow oscillation suggests that, during normal oscillatory activity, K(+) ions are cleared from active spots and released in the near vicinity, where they modulate the excitability of the neuronal membrane and contribute to maintain the depolarizing phase of the oscillation. Ca(2+) ions undergo a periodic variation of their extracellular concentration, which modulates the synaptic efficacy. The depolarizing phase of the slow oscillation is associated with a gradual depletion of the extracellular Ca(2+) promoting a progressive disfacilitation in the network. This functional synaptic neuronal disconnection is responsible for the ending of the depolarizing phase of the slow oscillation and the onset of a phasic hyperpolarization during which the neuronal network is silent and the intra- and extracellular ionic concentrations return to normal values. Spike-wave seizures often develop during sleep from the slow oscillation. Here I will show how the increased gap junction communication substantiates the facility of the glial syncytium to spatially buffer K(+) ions that were uptaken during the spike-wave seizures, and therefore contributing to the long-range recruitment of cortical territories. Similar mechanisms as those described during the slow oscillation promote the periodic (2-3 Hz) recurrence of spike-wave complexes.     

Integration and segregation of activity in entorhinal-hippocampal subregions by neocortical slow oscillations

Brain systems communicate by means of neuronal oscillations at multiple temporal and spatial scales. In anesthetized rats, we find that neocortical "slow" oscillation engages neurons in prefrontal, somatosensory, entorhinal, and subicular cortices into synchronous transitions between UP and DOWN states, with a corresponding bimodal distribution of their membrane potential. The membrane potential of hippocampal granule cells and CA3 and CA1 pyramidal cells lacked bimodality, yet it was influenced by the slow oscillation in a region-specific manner. Furthermore, in both anesthetized and naturally sleeping rats, the cortical UP states resulted in increased activity of dentate and most CA1 neurons, as well as the highest probability of ripple events. Yet, the CA3-CA1 network could self-organize into gamma bursts and occasional ripples during the DOWN state. Thus, neo/paleocortical and hippocampal networks periodically reset, self-organize, and temporally coordinate their cell assemblies via the slow oscillation.     

Spontaneous hemodynamic oscillations during human sleep and sleep stage transitions characterized with near-infrared spectroscopy

Understanding the interaction between the nervous system and cerebral vasculature is fundamental to forming a complete picture of the neurophysiology of sleep and its role in maintaining physiological homeostasis. However, the intrinsic hemodynamics of slow-wave sleep (SWS) are still poorly known. We carried out 30 all-night sleep measurements with combined near-infrared spectroscopy (NIRS) and polysomnography to investigate spontaneous hemodynamic behavior in SWS compared to light (LS) and rapid-eye-movement sleep (REM). In particular, we concentrated on slow oscillations (3-150 mHz) in oxy- and deoxyhemoglobin concentrations, heart rate, arterial oxygen saturation, and the pulsation amplitude of the photoplethysmographic signal. We also analyzed the behavior of these variables during sleep stage transitions. The results indicate that slow spontaneous cortical and systemic hemodynamic activity is reduced in SWS compared to LS, REM, and wakefulness. This behavior may be explained by neuronal synchronization observed in electrophysiological studies of SWS and a reduction in autonomic nervous system activity. Also, sleep stage transitions are asymmetric, so that the SWS-to-LS and LS-to-REM transitions, which are associated with an increase in the complexity of cortical electrophysiological activity, are characterized by more dramatic hemodynamic changes than the opposite transitions. Thus, it appears that while the onset of SWS and termination of REM occur only as gradual processes over time, the termination of SWS and onset of REM may be triggered more abruptly by a particular physiological event or condition. The results suggest that scalp hemodynamic changes should be considered alongside cortical hemodynamic changes in NIRS sleep studies to assess the interaction between the autonomic and central nervous systems.     

Output-mode transitions are controlled by prolonged inactivation of sodium channels in pyramidal neurons of subiculum

Transitions between different behavioral states, such as sleep or wakefulness, quiescence or attentiveness, occur in part through transitions from action potential bursting to single spiking. Cortical activity, for example, is determined in large part by the spike output mode from the thalamus, which is controlled by the gating of low-voltage–activated calcium channels. In the subiculum—the major output of the hippocampus—transitions occur from bursting in the delta-frequency band to single spiking in the theta-frequency band. We show here that these transitions are influenced strongly by the inactivation kinetics of voltage-gated sodium channels. Prolonged inactivation of sodium channels is responsible for an activity-dependent switch from bursting to single spiking, constituting a novel mechanism through which network dynamics are controlled by ion channel gating.