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Biomedical subjects

N Kopell

Publications and source records attributed to N Kopell.

10 recordsLinked to original sources
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↗
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↗
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↗