Neuronal assembly dynamics in the beta1 frequency range permits short-term memory.

Cell assemblies have long been thought to be associated with brain rhythms, notably the gamma rhythm. Here, we use a computational model to show that the beta1 frequency band, as found in rat association cortex, has properties complementary to the gamma band for the creation and manipulation of cell assemblies. We focus on the ability of the beta1 rhythm to respond differently to familiar and novel stimuli, and to provide a framework for combining the two. Simulations predict that assemblies of superficial layer pyramidal cells can be maintained in the absence of continuing input or synaptic plasticity. Instead, the formation of these assemblies relies on the nesting of activity within a beta1 rhythm. In addition, cells receiving further input after assembly formation produce coexistent spiking activity, unlike the competitive spiking activity characteristic of assembly formation with gamma rhythms.

Striatal origin of the pathologic beta oscillations in Parkinson's disease.

Enhanced oscillations at beta frequencies (8-30 Hz) are a signature neural dynamic pathology in the basal ganglia and cortex of Parkinson's disease patients. The mechanisms underlying these pathological beta oscillations remain elusive. Here, using mathematical models, we find that robust beta oscillations can emerge from inhibitory interactions between striatal medium spiny neurons. The interaction of the synaptic GABAa currents and the intrinsic membrane M-current promotes population oscillations in the beta frequency range. Increased levels of cholinergic drive, a condition relevant to the parkinsonian striatum, lead to enhanced beta oscillations in the striatal model. We show experimentally that direct infusion of the cholinergic agonist carbachol into the striatum, but not into the neighboring cortex, of the awake, normal rodent induces prominent beta frequency oscillations in the local field potential. These results provide evidence for amplification of normal striatal network dynamics as a mechanism responsible for the enhanced beta frequency oscillations in Parkinson's disease.

Mapping brain networks in awake mice using combined optical neural control and fMRI.

Behaviors and brain disorders involve neural circuits that are widely distributed in the brain. The ability to map the functional connectivity of distributed circuits, and to assess how this connectivity evolves over time, will be facilitated by methods for characterizing the network impact of activating a specific subcircuit, cell type, or projection pathway. We describe here an approach using high-resolution blood oxygenation level-dependent (BOLD) functional MRI (fMRI) of the awake mouse brain-to measure the distributed BOLD response evoked by optical activation of a local, defined cell class expressing the light-gated ion channel channelrhodopsin-2 (ChR2). The utility of this opto-fMRI approach was explored by identifying known cortical and subcortical targets of pyramidal cells of the primary somatosensory cortex (SI) and by analyzing how the set of regions recruited by optogenetically driven SI activity differs between the awake and anesthetized states. Results showed positive BOLD responses in a distributed network that included secondary somatosensory cortex (SII), primary motor cortex (MI), caudoputamen (CP), and contralateral SI (c-SI). Measures in awake compared with anesthetized mice (0.7% isoflurane) showed significantly increased BOLD response in the local region (SI) and indirectly stimulated regions (SII, MI, CP, and c-SI), as well as increased BOLD signal temporal correlations between pairs of regions. These collective results suggest opto-fMRI can provide a controlled means for characterizing the distributed network downstream of a defined cell class in the awake brain. Opto-fMRI may find use in examining causal links between defined circuit elements in diverse behaviors and pathologies.

Horizontal bands in the belousov reaction.

The formation and propagation of spatial patterns in the presence of an initial gradient in temperature or the concentration of one or more of the reactants is explained kinematically. Experimental verification of this mechanism is given, showing that diffusion plays a very minor role in the formation of the bands.

Modelling of intersegmental coordination in the lamprey central pattern generator for locomotion.

Rhythmic motor activity requires coordination of different muscles or muscle groups so that they are all active with the same cycle duration and appropriate phase relationships. The neural mechanisms for such phase coupling in vertebrate locomotion are not known. Swimming in the lamprey is accomplished by the generation of a travelling wave of body curvature in which the phase coupling between segments is so controlled as to give approximately one full wavelength on the body at any swimming speed. This article reviews work that has combined mathematical analysis, biological experimentation and computer simulation to provide a conceptual framework within which intersegmental coordination can be investigated. Evidence is provided to suggest that in the lamprey, ascending coupling is dominant over descending coupling and controls the intersegmental phase lag during locomotion. The significance of long-range intersegmental coupling is also discussed.

Gap junctions between interneuron dendrites can enhance synchrony of gamma oscillations in distributed networks.

Gamma-frequency (30-70 Hz) oscillations in populations of interneurons may be of functional relevance in the brain by virtue of their ability to induce synchronous firing in principal neurons. Such a role would require that neurons, 1 mm or more apart, be able to synchronize their activity, despite the presence of axonal conduction delays and of the limited axonal spread of many interneurons. We showed previously that interneuron doublet firing can help to synchronize gamma oscillations, provided that sufficiently many pyramidal neurons are active; we also suggested that gap junctions, between the axons of principal neurons, could contribute to the long-range synchrony of gamma oscillations induced in the hippocampus by carbachol in vitro. Here we consider interneuron network gamma: that is, gamma oscillations in pharmacologically isolated networks of tonically excited interneurons, with frequency gated by mutual GABA(A) receptor-mediated IPSPs. We provide simulation and electrophysiological evidence that interneuronal gap junctions (presumably dendritic) can enhance the synchrony of such gamma oscillations, in spatially extended interneuron networks. There appears to be a sharp threshold conductance, below which the interneuron dendritic gap junctions do not exert a synchronizing role.

Inhibition-based rhythms: experimental and mathematical observations on network dynamics.

An increasingly large body of data exists which demonstrates that oscillations of frequency 12-80 Hz are a consequence of, or are inextricably linked to, the behaviour of inhibitory interneurons in the central nervous system. This frequency range covers the EEG bands beta 1 (12-20 Hz), beta 2 (20-30 Hz) and gamma (30-80 Hz). The pharmacological profile of both spontaneous and sensory-evoked EEG potentials reveals a very strong influence on these rhythms by drugs which have direct effects on GABA(A) receptor-mediated synaptic transmission (general anaesthetics, sedative/hypnotics) or indirect effects on inhibitory neuronal function (opiates, ketamine). In addition, a number of experimental models of, in particular, gamma-frequency oscillations, have revealed both common denominators for oscillation generation and function, and subtle differences in network dynamics between the different frequency ranges. Powerful computer and mathematical modelling techniques based around both clinical and experimental observations have recently provided invaluable insight into the behaviour of large networks of interconnected neurons. In particular, the mechanistic profile of oscillations generated as an emergent property of such networks, and the mathematical derivation of this complex phenomenon have much to contribute to our understanding of how and why neurons oscillate. This review will provide the reader with a brief outline of the basic properties of inhibition-based oscillations in the CNS by combining research from laboratory models, large-scale neuronal network simulations, and mathematical analysis.

Delayed orexin signaling consolidates wakefulness and sleep: physiology and modeling.

Orexin-producing neurons are clearly essential for the regulation of wakefulness and sleep because loss of these cells produces narcolepsy. However, little is understood about how these neurons dynamically interact with other wake- and sleep-regulatory nuclei to control behavioral states. Using survival analysis of wake bouts in wild-type and orexin knockout mice, we found that orexins are necessary for the maintenance of long bouts of wakefulness, but orexin deficiency has little impact on wake bouts <1 min. Since orexin neurons often begin firing several seconds before the onset of waking, this suggests a surprisingly delayed onset (>1 min) of functional effects. This delay has important implications for understanding the control of wakefulness and sleep because increasing evidence suggests that different mechanisms are involved in the production of brief and sustained wake bouts. We incorporated these findings into a mathematical model of the mouse sleep/wake network. Orexins excite monoaminergic neurons and we hypothesize that orexins increase the monoaminergic inhibition of sleep-promoting neurons in the ventrolateral preoptic nucleus. We modeled orexin effects as a time-dependent increase in the strength of inhibition from wake- to sleep-promoting populations and the resulting simulated behavior accurately reflects the fragmented sleep/wake behavior of narcolepsy and leads to several predictions. By integrating neurophysiology of the sleep/wake network with emergent properties of behavioral data, this model provides a novel framework for investigating network dynamics and mechanisms associated with normal and pathologic sleep/wake behavior.

Local network parameters can affect inter-network phase lags in central pattern generators.

Weakly coupled phase oscillators and strongly coupled relaxation oscillators have different mechanisms for creating stable phase lags. Many oscillations in central pattern generators combine features of each type of coupling: local networks composed of strongly coupled relaxation oscillators are weakly coupled to similar local networks. This paper analyzes the phase lags produced by this combination of mechanisms and shows how the parameters of a local network, such as the decay time of inhibition, can affect the phase lags between the local networks. The analysis is motivated by the crayfish central pattern generator used for swimming, and uses techniques from geometrical singular perturbation theory.

Neuronal metabolism governs cortical network response state.

The level of arousal in mammals is correlated with metabolic state and specific patterns of cortical neuronal responsivity. In particular, rhythmic transitions between periods of high activity (up phases) and low activity (down phases) vary between wakefulness and deep sleep/anesthesia. Current opinion about changes in cortical response state between sleep and wakefulness is split between neuronal network-mediated mechanisms and neuronal metabolism-related mechanisms. Here, we demonstrate that slow oscillations in network state are a consequence of interactions between both mechanisms. Specifically, recurrent networks of excitatory neurons, whose membrane potential is partly governed by ATP-modulated potassium (K(ATP)) channels, mediate response-state oscillations via the interaction between excitatory network activity involving slow, kainate receptor-mediated events and the resulting activation of ATP-dependent homeostatic mechanisms. These findings suggest that K(ATP) channels function as an interface between neuronal metabolic state and network responsivity in mammalian cortex.

On the human sensorimotor-cortex beta rhythm: sources and modeling.

Cortical oscillations in the beta band (13-35 Hz) are known to be modulated by the GABAergic agonist benzodiazepine. To investigate the mechanisms generating the approximately 20-Hz oscillations in the human cortex, we administered benzodiazepines to healthy adults and monitored cortical oscillatory activity by means of magnetoencephalography. Benzodiazepine increased the power and decreased the frequency of beta oscillations over rolandic areas. Minimum current estimates indicated the effect to take place around the hand area of the primary sensorimotor cortex. Given that previous research has identified sources of the beta rhythm in the motor cortex, our results suggest that these same motor-cortex beta sources are modulated by benzodiazepine. To explore the mechanisms underlying the increase in beta power with GABAergic inhibition, we simulated a conductance-based neuronal network comprising excitatory and inhibitory neurons. The model accounts for the increase in the beta power, the widening of the spectral peak, and the slowing down of the rhythms with benzodiazepines, implemented as an increase in GABAergic conductance. We found that an increase in IPSCs onto inhibitory neurons was more important for generating neuronal synchronization in the beta band than an increase in IPSCs onto excitatory pyramidal cells.

Rhythmogenesis, amplitude modulation, and multiplexing in a cortical architecture.

In a network of excitatory and inhibitory neurons, hyperpolarization-activated inward currents can help to produce population rhythms in which individual cells participate sparsely and randomly. A shift in the activation curve of such a current changes the fraction of the cells participating in any given cycle of the population rhythm, thus changing the amplitude of the field potential. Furthermore, the frequency of the population rhythm remains relatively fixed over a substantial range of amplitudes, allowing the population rhythm to play a separate processing role from that of the individual components.

Timing regulation in a network reduced from voltage-gated equations to a one-dimensional map.

We discuss a method by which the dynamics of a network of neurons, coupled by mutual inhibition, can be reduced to a one-dimensional map. This network consists of a pair of neurons, one of which is an endogenous burster, and the other excitable but not bursting in the absence of phasic input. The latter cell has more than one slow process. The reduction uses the standard separation of slow/fast processes; it also uses information about how the dynamics on the slow manifold evolve after a finite amount of slow time. From this reduction we obtain a one-dimensional map dependent on the parameters of the original biophysical equations. In some parameter regimes, one can deduce that the original equations have solutions in which the active phase of the originally excitable cell is constant from burst to burst, while in other parameter regimes it is not. The existence or absence of this kind of regulation corresponds to qualitatively different dynamics in the one-dimensional map. The computations associated with the reduction and the analysis of the dynamics includes the use of coordinates that parameterize by time along trajectories, and "singular Poincaré maps" that combine information about flows along a slow manifold with information about jumps between branches of the slow manifold.

Multispikes and synchronization in a large neural network with temporal delays.

Coherent rhythms in the gamma frequency range are ubiquitous in the nervous system and thought to be important in a variety of cognitive activities. Such rhythms are known to be able to synchronize with millisecond precision across distances with significant conduction delay; it is mysterious how this can operate in a setting in which cells receive many inputs over a range of time. Here we analyze a version of mechanism, previously proposed, that the synchronization in the CA1 region of the hippocampus depends on the firing of "doublets" by the interneurons. Using a network of local circuits that are arranged in a possibly disordered lattice, we determine the conditions on parameters for existence and stability of synchronous solutions in which the inhibitory interneurons fire single spikes, doublets, or triplets per cycle. We show that the synchronous solution is only marginally stable if the interneurons fire singlets. If they fire doublets, the synchronous state is asymptotically stable in a larger subset of parameter space than if they fire triplets. An unexpected finding is that a small amount of disorder in the lattice structure enlarges the parameter regime in which the doublet solution is stable. Synaptic noise reduces the regime in which the doublet configuration is stable, but only weakly.

Anti-phase solutions in relaxation oscillators coupled through excitatory interactions.

Relaxation oscillators interacting via models of excitatory chemical synapses with sharp thresholds can have stable anti-phase as well as in-phase solutions. The mechanism for anti-phase demonstrated in this paper relies on the fact that, in a large class of neural models, excitatory input slows down the receiving oscillator over a portion of its trajectory. We analyze the effect of this "virtual delay" in an abstract model, and then show that the hypotheses of that model hold for widely used descriptions of bursting neurons.

Rapid synchronization through fast threshold modulation.

Synchronization properties of locally coupled neural oscillators were investigated analytically and by computer simulation. When coupled in a manner that mimics excitatory chemical synapses, oscillators having more than one time scale (relaxation oscillators) are shown to approach synchrony using mechanisms very different from that of oscillators with a more sinusoidal waveform. The relaxation oscillators make critical use of fast modulations of their thresholds, leading to a rate of synchronization relatively independent of coupling strength within some basin of attraction; this rate is faster for oscillators that have conductance-based features than for neural caricatures such as the FitzHugh-Nagumo equations that lack such features. Computer simulations of one-dimensional arrays show that oscillators in the relaxation regime synchronize much more rapidly than oscillators with the same equations whose parameters have been modulated to yield a more sinusoidal waveform. We present a heuristic explanation of this effect based on properties of the coupling mechanisms that can affect the way the synchronization scales with array length. These results suggest that the emergent synchronization behavior of oscillating neural networks can be dramatically influenced by the intrinsic properties of the network components. Possible implications for perceptual feature binding and attention are discussed.

Functional reorganization in thalamocortical networks: transition between spindling and delta sleep rhythms.

Thalamic reticularis, thalamocortical, and cortical cells participate in the 7-14-hz spindling rhythm of early sleep and the slower delta rhythms of deeper sleep, with different firing patterns. In this case study, showing the interactions of intrinsic and synaptic properties, a change in the conductance of one kind of cell effectively rewires the thalamocortical circuit, leading to the transition from the spindling to the delta rhythm. The two rhythms make different uses of the fast (GABAA) and slow (GABAB) inhibition generated by the thalamic reticularis cells.

Dynamics of spiking neurons with electrical coupling.

We analyze the existence and stability of phase-locked states of neurons coupled electrically with gap junctions. We show that spike shape and size, along with driving current (which affects network frequency), play a large role in which phase-locked modes exist and are stable. Our theory makes predictions about biophysical models using spikes of different shapes, and we present simulations to confirm the predictions. We also analyze a large system of all-to-all coupled neurons and show that the splay-phase state can exist only for a certain range of frequencies.

Fine structure of neural spiking and synchronization in the presence of conduction delays.

Hippocampal networks of excitatory and inhibitory neurons that produce gamma-frequency rhythms display behavior in which the inhibitory cells produce spike doublets when there is strong stimulation at separated sites. It has been suggested that the doublets play a key role in the ability to synchronize over a distance. Here we analyze the mechanisms by which timing in the spike doublet can affect the synchronization process. The analysis describes two independent effects: one comes from the timing of excitation from separated local circuits to an inhibitory cell, and the other comes from the timing of inhibition from separated local circuits to an excitatory cell. We show that a network with both of these effects has different synchronization properties than a network with either excitatory or inhibitory type of coupling alone, and we give a rationale for the shorter space scales associated with inhibitory interactions.