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.

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.

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.

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.

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.

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.

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.

Dendritic synchrony and transient dynamics in a coupled oscillator model of the dopaminergic neuron.

Transient increases in spontaneous firing rate of mesencephalic dopaminergic neurons have been suggested to act as a reward prediction error signal. A mechanism previously proposed involves subthreshold calcium-dependent oscillations in all parts of the neuron. In that mechanism, the natural frequency of oscillation varies with diameter of cell processes, so there is a wide variation of natural frequencies on the cell, but strong voltage coupling enforces a single frequency of oscillation under resting conditions. In previous work, mathematical analysis of a simpler system of oscillators showed that the chain of oscillators could produce transient dynamics in which the frequency of the coupled system increased temporarily, as seen in a biophysical model of the dopaminergic neuron. The transient dynamics was shown to be consequence of a slow drift along an invariant subset of phase space, with rate of drift given by a Lyapunov function. In this paper, we show that the same mathematical structure exists for the full biophysical model, giving physiological meaning to the slow drift and the Lyapunov function, which is shown to describe differences in intracellular calcium concentration in different parts of the cell. The duration of transients was long, being comparable to the time constant of calcium disposition. These results indicate that brief changes in input to the dopaminergic neuron can produce long lasting firing rate transients whose form is determined by intrinsic cell properties.

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.

Genetically altered AMPA-type glutamate receptor kinetics in interneurons disrupt long-range synchrony of gamma oscillation.

Gamma oscillations synchronized between distant neuronal populations may be critical for binding together brain regions devoted to common processing tasks. Network modeling predicts that such synchrony depends in part on the fast time course of excitatory postsynaptic potentials (EPSPs) in interneurons, and that even moderate slowing of this time course will disrupt synchrony. We generated mice with slowed interneuron EPSPs by gene targeting, in which the gene encoding the 67-kDa form of glutamic acid decarboxylase (GAD67) was altered to drive expression of the alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) glutamate receptor subunit GluR-B. GluR-B is a determinant of the relatively slow EPSPs in excitatory neurons and is normally expressed at low levels in gamma-aminobutyric acid (GABA)ergic interneurons, but at high levels in the GAD-GluR-B mice. In both wild-type and GAD-GluR-B mice, tetanic stimuli evoked gamma oscillations that were indistinguishable in local field potential recordings. Remarkably, however, oscillation synchrony between spatially separated sites was severely disrupted in the mutant, in association with changes in interneuron firing patterns. The congruence between mouse and model suggests that the rapid time course of AMPA receptor-mediated EPSPs in interneurons might serve to allow gamma oscillations to synchronize over distance.

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.

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.

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.

Networks of interneurons with fast and slow gamma-aminobutyric acid type A (GABAA) kinetics provide substrate for mixed gamma-theta rhythm.

During active exploration, hippocampal neurons exhibit nested rhythmic activity at theta ( approximately 8 Hz) and gamma ( approximately 40 Hz) frequencies. Gamma rhythms may be generated locally by interactions within a class of interneurons mediating fast GABA(A) (GABA(A,fast)) inhibitory postsynaptic currents (IPSCs), whereas theta rhythms traditionally are thought to be imposed extrinsically. However, the hippocampus contains slow biophysical mechanisms that may contribute to the theta rhythm, either as a resonance activated by extrinsic input or as a purely local phenomenon. For example, region CA1 of the hippocampus contains a slower class of GABA(A) (GABA(A,slow)) synapses, believed to be generated by a distinct group of interneurons. Recent evidence indicates that these GABA(A,slow) interneurons project to the GABA(A, fast) interneurons that contribute to hippocampal gamma rhythms. Here, we use biophysically based simulations to explore the possible ramifications of interneuronal circuits containing separate classes of GABA(A,fast) and GABA(A,slow) interneurons. Simulated interneuronal networks with fast and slow synaptic kinetics can generate mixed theta-gamma rhythmicity under restricted conditions, including strong connections among each population, weaker connections between the two populations, and homogeneity of cellular properties and drive. Under a broader range of conditions, including heterogeneity, the networks can amplify and resynchronize phasic responses to weak phase-dispersed external drive at theta frequencies to either GABA(A,slow) or GABA(A,fast) cells. GABA(A, slow) synapses are necessary for this process of amplification and resynchronization.

Gamma rhythms and beta rhythms have different synchronization properties.

Experimental and modeling efforts suggest that rhythms in the CA1 region of the hippocampus that are in the beta range (12-29 Hz) have a different dynamical structure than that of gamma (30-70 Hz). We use a simplified model to show that the different rhythms employ different dynamical mechanisms to synchronize, based on different ionic currents. The beta frequency is able to synchronize over long conduction delays (corresponding to signals traveling a significant distance in the brain) that apparently cannot be tolerated by gamma rhythms. The synchronization properties are consistent with data suggesting that gamma rhythms are used for relatively local computations whereas beta rhythms are used for higher level interactions involving more distant structures.

Alpha-frequency rhythms desynchronize over long cortical distances: a modeling study.

Neocortical networks of excitatory and inhibitory neurons can display alpha(a)-frequency rhythms when an animal is in a resting or unfocused state. Unlike some gamma- and beta-frequency rhythms, experimental observations in cats have shown that these alpha-frequency rhythms need not synchronize over long cortical distances. Here, we develop a network model of synaptically coupled excitatory and inhibitory cells to study this asynchrony. The cells of the local circuit are modeled on the neurons found in layer V of the neocortex where alpha-frequency rhythms are thought to originate. Cortical distance is represented by a pair of local circuits coupled with a delay in synaptic propagation. Mathematical analysis of this model reveals that the h and T currents present in layer V pyramidal (excitatory) cells not only produce and regulate the alpha-frequency rhythm but also lead to the occurrence of spatial asynchrony. In particular, these inward currents cause excitation and inhibition to have nonintuitive effects in the network, with excitation delaying and inhibition advancing the firing time of cells; these reversed effects create the asynchrony. Moreover, increased excitatory to excitatory connections can lead to further desynchronization. However, the local rhythms have the property that, in the absence of excitatory to excitatory connections, if the participating cells are brought close to synchrony (for example, by common input), they will remain close to synchrony for a substantial time.

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.

Synaptic depression creates a switch that controls the frequency of an oscillatory circuit.

Synaptic depression is a form of short-term plasticity exhibited by many synapses. Nonetheless, the functional significance of synaptic depression in oscillatory networks is not well understood. We show that, in a recurrent inhibitory network that includes an intrinsic oscillator, synaptic depression can give rise to two distinct modes of network operation. When the maximal conductance of the depressing synapse is small, the oscillation period is determined by the oscillator component. Increasing the maximal conductance beyond a threshold value activates a positive-feedback mechanism that greatly enhances the synaptic strength. In this mode, the oscillation period is determined by the strength and dynamics of the depressing synapse. Because of the regenerative nature of the feedback mechanism, the circuit can be switched from one mode of operation to another by a very small change in the maximal conductance of the depressing synapse. Our model was inspired by experimental work on the pyloric network of the lobster. The pyloric network produces a simple motor rhythm generated by a pacemaker neuron that receives feedback inhibition from a depressing synapse. In some preparations, elimination of the synapse had no effect on the period of the rhythm, whereas in other preparations, there was a significant decrease in the period. We propose that the pyloric network can operate in either of the two modes suggested by the model, depending on the maximal conductance of the depressing synapse.

Network oscillations generated by balancing graded asymmetric reciprocal inhibition in passive neurons.

We describe a novel mechanism by which network oscillations can arise from reciprocal inhibitory connections between two entirely passive neurons. The model was inspired by the activation of the gastric mill rhythm in the crab stomatogastric ganglion by the modulatory commissural ganglion neuron 1 (MCN1), but it is studied here in general terms. One model neuron has a linear current-voltage (I-V) curve with a low (L) resting potential, and the second model neuron has a linear current-voltage curve with a high (H) resting potential. The inhibitory connections between them are graded. There is an extrinsic modulatory excitatory input to the L neuron, and the L neuron presynaptically inhibits the modulatory neuron. Activation of the extrinsic modulatory neuron elicits stable network oscillations in which the L and H neurons are active in alternation. The oscillations arise because the graded reciprocal synapses create the equivalent of a negative-slope conductance region in the I-V curves for the cells. Geometrical methods are used to analyze the properties of and the mechanism underlying these network oscillations.

Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons.

We study some mechanisms responsible for synchronous oscillations and loss of synchrony at physiologically relevant frequencies (10-200 Hz) in a network of heterogeneous inhibitory neurons. We focus on the factors that determine the level of synchrony and frequency of the network response, as well as the effects of mild heterogeneity on network dynamics. With mild heterogeneity, synchrony is never perfect and is relatively fragile. In addition, the effects of inhibition are more complex in mildly heterogeneous networks than in homogeneous ones. In the former, synchrony is broken in two distinct ways, depending on the ratio of the synaptic decay time to the period of repetitive action potentials (tau s/T), where T can be determined either from the network or from a single, self-inhibiting neuron. With tau s/T > 2, corresponding to large applied current, small synaptic strength or large synaptic decay time, the effects of inhibition are largely tonic and heterogeneous neurons spike relatively independently. With tau s/T < 1, synchrony breaks when faster cells begin to suppress their less excitable neighbors; cells that fire remain nearly synchronous. We show numerically that the behavior of mildly heterogeneous networks can be related to the behavior of single, self-inhibiting cells, which can be studied analytically.