Biomedical subjects

N Kopell

Publications and source records attributed to N Kopell.

At least 19 recordsLinked to original sources

PubMed2001

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.

Animals↗

PubMed2001

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.

Animals↗

PubMed2000

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.

Electroencephalography↗

PubMed2000

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.

Animals↗

PubMed2000

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.

Action Potentials↗

PubMed2000

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.

Action Potentials↗

PubMed1999

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.

Action Potentials↗

PubMed1999

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.

Animals↗

PubMed1999

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.

Animals↗

PubMed1998

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.

Brain Mapping↗

PubMed1998

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.

Computer Simulation↗

PubMed1998

Frequency control in synchronized networks of inhibitory neurons.

We analyze the control of frequency for a synchronized inhibitory neuronal network. The analysis is done for a reduced membrane model with a biophysically based synaptic influence. We argue that such a reduced model can quantitatively capture the frequency behavior of a larger class of neuronal models. We show that in different parameter regimes, the network frequency depends in different ways on the intrinsic and synaptic time constants. Only in one portion of the parameter space, called phasic, is the network period proportional to the synaptic decay time. These results are discussed in connection with previous work of the authors, which showed that for mildly heterogeneous networks, the synchrony breaks down, but coherence is preserved much more for systems in the phasic regime than in the other regimes. These results imply that for mildly heterogeneous networks, the existence of a coherent rhythm implies a linear dependence of the network period on synaptic decay time and a much weaker dependence on the drive to the cells. We give experimental evidence for this conclusion.

Action Potentials↗

PubMed1997

Modulation of oscillator interactions in the crab stomatogastric ganglion by crustacean cardioactive peptide.

The modulation of the pyloric rhythm of the stomatogastric ganglion of the crab, Cancer borealis, by crustacean cardioactive peptide (CCAP) is described. CCAP activated pyloric rhythms in most silent preparations, and altered the phase relationships of pyloric motor neuron firing in all preparations. In CCAP, the pyloric rhythms were characterized by long lateral pyloric (LP) neuron bursts of action potentials. The threshold for CCAP action was approximately 10(-10) M, with increasing effects at higher CCAP concentrations. The changes in motor pattern evoked by CCAP produced significant changes in LP-innervated muscle movement. These movements were additionally potentiated by CCAP applications to isolated nerve-muscle preparations. Thus, enhanced motor neuron firing and increase of the gain of the neuromuscular junctions are likely to operate coordinately in response to hormonally released CCAP. High CCAP concentrations sometimes resulted in modification of the normal 1:1 alternation between the pyloric dilator (PD) and LP neurons to patterns of 2:1, 3:1, or 4:1 alternation. CCAP seems to activate slow intrinsic oscillations in the LP neuron, as well as enhance faster oscillations in the pacemaker group of PD/anterior burster (AB) neurons. Simulations of fast and slow oscillators with reciprocal inhibitory coupling suggest mechanisms that could account for the mode switch from 1:1 alternation to multiple PD bursts alternating with one LP neuron burst.

Action Potentials↗

PubMed1997

How does the crayfish swimmeret system work? Insights from nearest-neighbor coupled oscillator models.

Rhythmic movements of crayfish swimmerets are coordinated by a neural circuit that links their four abdominal ganglia. Each swimmeret is driven by its own small local circuit, or pattern-generating module. We modeled this network as a chain of four oscillators, bidirectionally coupled to their nearest neighbors, and tested the model's ability to reproduce experimentally observed changes in intersegmental phases and in period caused by differential excitation of selected abdominal ganglia. The choices needed to match the experimental data lead to the following predictions: coupling between ganglia is asymmetric; the ascending and descending coupling have approximately equal strengths; intersegmental coupling does not significantly affect the frequency of the system; and excitation affects the intrinsic frequencies of the oscillators and might also change properties of intersegmental coupling.

Animals↗

PubMed1996

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.

Cerebral Cortex↗

PubMed1996

Parabolic bursting revisited.

Many excitable membrane systems display bursting oscillations, in which the membrane potential switches periodically between an active phase of rapid spiking and a silent phase of slow, quasi steady-state behavior. A burster is called parabolic when the spike frequency is lower both at the beginning and end of the active phase. We show that classes of voltage-gated conductance equations can be reduced to the mathematical mechanism previously analyzed by Ermentrout and Kopell in [7]. The reduction uses a series of coordinate changes and shows that the mechanism in [7] applies more generally than previously believed. The key hypothesis for the more general theory is that a certain slow periodic orbit must stay close to a curve of degenerate homoclinic points for the fast system, at least during the active phase. We do not require that the slow system have a periodic orbit when the voltage is held constant.

Animals↗

PubMed1995

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.

Animals↗

PubMed1994

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.

Animals↗