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N Kopell

Publications and source records attributed to N Kopell.

27 records · Page 2Linked to original sources
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↗
PubMed1994

Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks.

We describe four different mechanisms that lead to oscillations in a network of two reciprocally inhibitory cells. In two cases (intrinsic release and intrinsic escape) the frequency of the network oscillation is insensitive to the threshold voltage of the synaptic potentials. In the other two cases (synaptic release and synaptic escape) the network frequency is strongly determined by the threshold voltage of the synaptic connections. The distinction between the different mechanisms blurs as the function describing synaptic activation becomes less steep and as the model neurons are removed from the relaxation regime. These mechanisms provide insight into the parameters that control network frequency in motor systems that depend on reciprocal inhibition.

Animals↗
PubMed1993

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.

Computer Simulation↗
PubMed1992

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.

Animals↗
PubMed1990

Forcing of coupled nonlinear oscillators: studies of intersegmental coordination in the lamprey locomotor central pattern generator.

1. This paper reports the results of an investigation of the basic mechanisms underlying intersegmental coordination in lamprey locomotion, by the use of a combined mathematical and biological approach. 2. Mathematically, the lamprey central pattern generator (CPG) is described as a chain of coupled nonlinear oscillators; experimentally, entrainment of fictive locomotion by imposed movement has been investigated. Interpretation of the results in the context of the theory has allowed conclusions to be drawn about the nature of ascending and descending coupling in the lamprey spinal CPG. 3. Theory predicts and data show that 1) the greater the number of oscillators in the chain, the smaller is the entrainment frequency range and 2) it is possible to entrain both above and below the rest frequency at one end but only above or below at the other end. 4. In the context of the experimental results, the theory indicates the following: 1) ascending coupling sets the intersegmental phase lags, whereas descending coupling changes the frequency of the coupled oscillators; 2) there are differences in the ascending and descending coupling other than strength; and it also suggests that 3) coupling slows down the oscillators.

Afferent Pathways↗
PubMedDate not supplied

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.

Animals↗
PubMedDate not supplied

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.

Action Potentials↗