G. Bard Ermentrout

When inhibition not excitation synchronizes neural firing

Excitatory and inhibitory synaptic coupling can have counter-intuitive effects on the synchronization of neuronal firing. While it might appear that excitatory coupling would lead to synchronization, we show that frequently inhibition rather than excitation synchronizes firing. We study two identical neurons described by integrate-and-fire models, general phase-coupled models or the Hodgkin-Huxley model with mutual, non-instantaneous excitatory or inhibitory synapses between them. We find that if the rise time of the synapse is longer than the duration of an action potential, inhibition not excitation leads to synchronized firing.

Traveling electrical waves in cortex: insights from phase dynamics and speculation on a computational role.

The theory of coupled phase oscillators provides a framework to understand the emergent properties of networks of neuronal oscillators. When the architecture of the network is dominated by short-range connections, the pattern of electrical output is predicted to correspond to traveling plane and rotating waves, in addition to synchronized output. We argue that this theory provides the foundation for understanding the traveling electrical waves that are observed across olfactory, visual, and visuomotor areas of cortex in a variety of species. The waves are typically present during periods outside of stimulation, while synchronous activity typically dominates in the presence of a strong stimulus. We suggest that the continuum of phase shifts during epochs with traveling waves provides a means to scan the incoming sensory stream for novel features. Experiments to test our theoretical approach are presented.

Spatially Structured Activity in Synaptically Coupled Neuronal Networks: I. Traveling Fronts and Pulses

We consider traveling front and pulse solutions to a system of integro-differential equations used to describe the activity of synaptically coupled neuronal networks in a single spatial dimension. Our first goal is to establish a series of direct links between the abstract nature of the equations and their interpretation in terms of experimental findings in the cortex and other brain regions. This is accomplished first by presenting a biophysically motivated derivation of the system and then by establishing a framework for comparison between numerical and experimental measures of activity propagation speed. Our second goal is to establish the existence of traveling pulse solutions using more rigorous methods. Two techniques are presented. The first, a shooting argument, reduces the problem from finding a specific solution to an integro-differential equation system to finding any solution to an ODE system. The second, a singular perturbation argument, provides a construction of traveling pulse solutions un...

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.

Existence and uniqueness of travelling waves for a neural network

A one-dimensional scalar neural network with two stable steady states is analysed. It is shown that there exists a unique monotone travelling wave front which joins the two stable states. Some additional properties of the wave such as the direction of its velocity are discussed.

Dynamics of membrane excitability determine interspike interval variability: a link between spike generation mechanisms and cortical spike train statistics

We propose a biophysical mechanism for the high interspike interval variability observed in cortical spike trains. The key lies in the nonlinear dynamics of cortical spike generation, which are consistent with type I membranes where saddle-node dynamics underlie excitability (Rinzel & Ermentrout, 1989). We present a canonical model for type I membranes, the -neuron. The -neuron is a phase model whose dynamics reflect salient features of type I membranes. This model generates spike trains with coefficient of variation (CV) above 0.6 when brought to firing by noisy inputs. This happens because the timing of spikes for a type I excitable cell is exquisitely sensitive to the amplitude of the suprathreshold stimulus pulses. A noisy input current, giving random amplitude kicks to the cell, evokes highly irregular firing across a wide range of firing rates; an intrinsically oscillating cell gives regular spike trains. We corroborate the results with simulations of the Morris-Lecar (M-L) neural model with random synaptic inputs: type I M-L yields high CVs. When this model is modified to have type II dynamics (periodicity arises via a Hopf bifurcation), however, it gives regular spike trains (CV below 0.3). Our results suggest that the high CV values such as those observed in cortical spike trains are an intrinsic characteristic of type I membranes driven to firing by random inputs. In contrast, neural oscillators or neurons exhibiting type II excitability should produce regular spike trains.

Reliability, synchrony and noise

The brain is noisy. Neurons receive tens of thousands of highly fluctuating inputs and generate spike trains that appear highly irregular. Much of this activity is spontaneous - uncoupled to overt stimuli or motor outputs - leading to questions about the functional impact of this noise. Although noise is most often thought of as disrupting patterned activity and interfering with the encoding of stimuli, recent theoretical and experimental work has shown that noise can play a constructive role - leading to increased reliability or regularity of neuronal firing in single neurons and across populations. These results raise fundamental questions about how noise can influence neural function and computation.

Turning On and Off with Excitation: The Role of Spike-Timing Asynchrony and Synchrony in Sustained Neural Activity

Delay-related sustained activity in the prefrontal cortex of primates, a neurological analogue of working memory, has been proposed to arise from synaptic interactions in local cortical circuits. The implication is that memories are coded by spatially localized foci of sustained activity. We investigate the mechanisms by which sustained foci are initiated, maintained, and extinguished by excitation in networks of Hodgkin-Huxley neurons coupled with biophysical spatially structured synaptic connections. For networks with a balance between excitation and inhibition, a localized transient stimulus robustly initiates a localized focus of activity. The activity is then maintained by recurrent excitatory AMPA-like synapses. We find that to maintain the focus, the firing must be asynchronous. Consequently, inducing transient synchrony through an excitatory stimulus extinguishes the sustained activity. Such a monosynaptic excitatory turn-off mechanism is compatible with the working memory being wiped clean by an efferent copy of the motor command. The activity that codes working memories may be structured so that the motor command is both the read-out and a direct clearing signal. We show examples of data that is compatible with our theory.

Correlation-induced synchronization of oscillations in olfactory bulb neurons.

Oscillations are a common feature of odor-evoked and spontaneous activity in the olfactory system in vivo and in vitro and are thought to play an important role in information processing and memory in a variety of brain areas. Theoretical and experimental studies have described several mechanisms by which oscillations can be generated and synchronized. Here, we investigate the hypothesis that correlated noisy inputs are able to generate synchronous oscillations in olfactory bulb mitral cells in vitro. We consider several alternative mechanisms and conclude that olfactory bulb synchronous oscillations are likely to arise because of the response of uncoupled oscillating neurons to aperiodic but correlated inputs. This mechanism has been described theoretically, but we provide the first experimental evidence that such a mechanism may underlie synchronization in real neurons. In physiological experiments, we show that this mechanism can generate gamma-band oscillations in populations of olfactory bulb mitral cells. This mechanism synchronizes oscillatory firing by using shared fast fluctuations in stochastic inputs across neurons, without requiring any synaptic or electrical coupling. We discuss the properties and limitations of synchronization by this mechanism and suggest that it may underlie fast oscillations in many brain areas.

A quantitative population model of whisker barrels: Re-examining the Wilson-Cowan equations

Beginning from a biologically based integrate and fire model of a rat whisker barrel, we employ semirigorous techniques to reduce the system to a simple set of equations, similar to the Wilson-Cowan equations, while retaining the ability for both qualitative and quantitative comparisons with the biological system. This is made possible through the clarification of three distinct measures of population activity: voltage, firing rate, and a new term called synaptic drive. The model is activated by prerecorded neural activity obtained from thalamic “barreloid” neurons in response to whisker stimuli. Output is produced in the form of population PSTHs, one each corresponding to activity of spiny (excitatory) and smooth (inhibitory) barrel neurons, which is quantitatively comparable to PSTHs from electrophysiologically studied regular-spike and fast-spike neurons. Through further analysis, the model yields novel physiological predictions not readily apparent from the full model or from experimental studies.