Biomedical subjects

Bard Ermentrout

Publications and source records attributed to Bard Ermentrout.

7 recordsLinked to original sources

PubMed2006

Gap junctions destroy persistent states in excitatory networks.

Gap junctions between excitatory neurons are shown to disrupt the persistent state. The asynchronous state of the network loses stability via a Hopf bifurcation and then the active state is destroyed via a homoclinic bifurcation with a stationary state. A partial differential equation (PDE) is developed to analyze the Hopf and the homoclinic bifurcations. The simplified dynamics are compared to a biophysical model where similar behavior is observed. In the low noise case, the dynamics of the PDE is shown to be very complicated and includes possible chaotic behavior. The onset of synchrony is studied by the application of averaging to obtain a simple criterion for destabilization of the asynchronous persistent state.

Excitatory Postsynaptic Potentials↗

PubMed2006

Phase resetting and coupling of noisy neural oscillators.

A number of experimental groups have recently computed Phase Response Curves (PRCs) for neurons. There is a great deal of noise in the data. We apply methods from stochastic nonlinear dynamics to coupled noisy phase-resetting maps and obtain the invariant density of phase distributions. By exploiting the special structure of PRCs, we obtain some approximations for the invariant distributions. Comparisons to Monte-Carlo simulations are made. We show how phase-dependence of the noise can move the peak of the invariant density away from the peak expected from the analysis of the deterministic system and thus lead to noise-induced bifurcations.

Action Potentials↗

PubMed2004

Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks.

Electrical and chemical synapses exist within the same networks of inhibitory cells, and each kind of synapse is known to be able to foster synchrony among oscillating neurons. Using numerical and analytical techniques, we show here that the electrical and inhibitory coupling play different roles in the synchronization of rhythms in inhibitory networks. The parameter range chosen is motivated by gamma rhythms, in which the gamma-aminobutyric acid type A (GABAA)-mediated inhibition is relatively strong. Under this condition, addition of a small electrical conductance can increase the degree of synchronization far more than a much larger increase in inhibitory conductance. The inhibitory synapses act to eliminate the effects of different initial conditions, whereas the electrical synapses mitigate suppression of firing due to heterogeneity in the network. Analytical techniques include tracking trajectories of coupled cells between spikes; the analysis shows that, in networks in which the degree of excitability is heterogeneous, inhibition can increase the dispersion of the voltages between spikes, whereas electrical coupling reduces such dispersion.

Action Potentials↗

PubMed2003

Multiple-spike waves in a one-dimensional integrate-and-fire neural network.

This paper builds on the past study of single-spike waves in one-dimensional integrate-and-fire networks to provide a framework for the study of waves with arbitrary (finite or countably infinite) collections of spike times. Based on this framework, we prove an existence theorem for single-spike traveling waves, and we combine analysis and numerics to study two-spike traveling waves, periodic traveling waves, and general infinite spike trains. For a fixed wave speed, finite-spike waves, periodic waves, and other infinite-spike waves may all occur, and we discuss the relationships among them. We also relate the waves considered analytically to waves generated in numerical simulations by the transient application of localized excitation.

Action Potentials↗

PubMed2003

Dynamical consequences of fast-rising, slow-decaying synapses in neuronal networks.

Synapses that rise quickly but have long persistence are shown to have certain computational advantages. They have some unique mathematical properties as well and in some instances can make neurons behave as if they are weakly coupled oscillators. This property allows us to determine their synchronization properties. Furthermore, slowly decaying synapses allow recurrent networks to maintain excitation in the absence of inputs, whereas faster decaying synapses do not. There is an interaction between the synaptic strength and the persistence that allows recurrent networks to fire at low rates if the synapses are sufficiently slow. Waves and localized structures are constructed in spatially extended networks with slowly decaying synapses.

Neural Networks, Computer↗

PubMedDate not supplied

Mathematical neuroscience: from neurons to circuits to systems.

Applications of mathematics and computational techniques to our understanding of neuronal systems are provided. Reduction of membrane models to simplified canonical models demonstrates how neuronal spike-time statistics follow from simple properties of neurons. Averaging over space allows one to derive a simple model for the whisker barrel circuit and use this to explain and suggest several experiments. Spatio-temporal pattern formation methods are applied to explain the patterns seen in the early stages of drug-induced visual hallucinations.

Action Potentials↗

PubMedDate not supplied

Model for transition from waves to synchrony in the olfactory lobe of Limax.

A biophysical model for the interactions between bursting (B) cells and nonbursting (NB) cells in the procerebral lobe of Limax is developed and tested. Phase-sensitivity of the NB cells is exhibited due to the strong inhibition from the rhythmically bursting B cells. Electrical and chemical junctions coupled with a parameter gradient lead to sustained periodic waves in the lobe. Excitatory interactions between the NB cells, which rarely fire, lead to stimulus evoked synchrony in the lobe oscillations. A novel calcium current is suggested to explain the effects of nitric oxide (NO) on the lobe. Gap junctions are shown both experimentally and through simulations to be required for the oscillating field potentials.

Action Potentials↗