310 research outputs found
Gap junctions and emergent rhythms
Gap junction coupling is ubiquitous in the brain, particularly between the dendritic trees of inhibitory interneurons. Such direct non-synaptic interaction allows for direct electrical communication between cells. Unlike spike-time driven synaptic neural network models, which are event based, any model with gap junctions must necessarily involve a single neuron model that can represent the shape of an action potential. Indeed, not only do neurons communicating via gaps feel super-threshold spikes, but they also experience, and respond to, sub-threshold voltage signals. In this chapter we show that the so-called absolute integrate-and-fire model is ideally suited to such studies. At the single neuron level voltage traces for the model may be obtained in closed form, and are shown to mimic those of fast-spiking inhibitory neurons. Interestingly in the presence of a slow spike adaptation current the model is shown to support periodic bursting oscillations. For both tonic and bursting modes the phase response curve can be calculated in closed form. At the network level we focus on global gap junction coupling and show how to analyze the asynchronous firing state in large networks. Importantly, we are able to determine the emergence of non-trivial network rhythms due to strong coupling instabilities. To illustrate the use of our theoretical techniques (particularly the phase-density formalism used to determine stability) we focus on a spike adaptation induced transition from asynchronous tonic activity to synchronous bursting in a gap-junction coupled network
Introducing numerical bounds to improve event-based neural network simulation
Although the spike-trains in neural networks are mainly constrained by the
neural dynamics itself, global temporal constraints (refractoriness, time
precision, propagation delays, ..) are also to be taken into account. These
constraints are revisited in this paper in order to use them in event-based
simulation paradigms.
We first review these constraints, and discuss their consequences at the
simulation level, showing how event-based simulation of time-constrained
networks can be simplified in this context: the underlying data-structures are
strongly simplified, while event-based and clock-based mechanisms can be easily
mixed. These ideas are applied to punctual conductance-based generalized
integrate-and-fire neural networks simulation, while spike-response model
simulations are also revisited within this framework.
As an outcome, a fast minimal complementary alternative with respect to
existing simulation event-based methods, with the possibility to simulate
interesting neuron models is implemented and experimented.Comment: submitte
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.Comment: 18 pages, 3 figures, Kluwer.sty. J. Comp. Neurosci. (in press).
Originally submitted to the neuro-sys archive which was never publicly
announced (was 9803001
Gap junctions and emergent rhythms
Gap junction coupling is ubiquitous in the brain, particularly between the dendritic trees of inhibitory interneurons. Such direct non-synaptic interaction allows for direct electrical communication between cells. Unlike spike-time driven synaptic neural network models, which are event based, any model with gap junctions must necessarily involve a single neuron model that can represent the shape of an action potential. Indeed, not only do neurons communicating via gaps feel super-threshold spikes, but they also experience, and respond to, sub-threshold voltage signals. In this chapter we show that the so-called absolute integrate-and-fire model is ideally suited to such studies. At the single neuron level voltage traces for the model may be obtained in closed form, and are shown to mimic those of fast-spiking inhibitory neurons. Interestingly in the presence of a slow spike adaptation current the model is shown to support periodic bursting oscillations. For both tonic and bursting modes the phase response curve can be calculated in closed form. At the network level we focus on global gap junction coupling and show how to analyze the asynchronous firing state in large networks. Importantly, we are able to determine the emergence of non-trivial network rhythms due to strong coupling instabilities. To illustrate the use of our theoretical techniques (particularly the phase-density formalism used to determine stability) we focus on a spike adaptation induced transition from asynchronous tonic activity to synchronous bursting in a gap-junction coupled network
How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A model-based argumentation
This paper addresses two questions in the context of neuronal networks
dynamics, using methods from dynamical systems theory and statistical physics:
(i) How to characterize the statistical properties of sequences of action
potentials ("spike trains") produced by neuronal networks ? and; (ii) what are
the effects of synaptic plasticity on these statistics ? We introduce a
framework in which spike trains are associated to a coding of membrane
potential trajectories, and actually, constitute a symbolic coding in important
explicit examples (the so-called gIF models). On this basis, we use the
thermodynamic formalism from ergodic theory to show how Gibbs distributions are
natural probability measures to describe the statistics of spike trains, given
the empirical averages of prescribed quantities. As a second result, we show
that Gibbs distributions naturally arise when considering "slow" synaptic
plasticity rules where the characteristic time for synapse adaptation is quite
longer than the characteristic time for neurons dynamics.Comment: 39 pages, 3 figure
Membrane resonance enables stable and robust gamma oscillations
Neuronal mechanisms underlying beta/gamma oscillations (20-80 Hz) are not completely understood. Here, we show that in vivo beta/gamma oscillations in the cat visual cortex sometimes exhibit remarkably stable frequency even when inputs fluctuate dramatically. Enhanced frequency stability is associated with stronger oscillations measured in individual units and larger power in the local field potential. Simulations of neuronal circuitry demonstrate that membrane properties of inhibitory interneurons strongly determine the characteristics of emergent oscillations. Exploration of networks containing either integrator or resonator inhibitory interneurons revealed that: (i) Resonance, as opposed to integration, promotes robust oscillations with large power and stable frequency via a mechanism called RING (Resonance INduced Gamma); resonance favors synchronization by reducing phase delays between interneurons and imposes bounds on oscillation cycle duration; (ii) Stability of frequency and robustness of the oscillation also depend on the relative timing of excitatory and inhibitory volleys within the oscillation cycle; (iii) RING can reproduce characteristics of both Pyramidal INterneuron Gamma (PING) and INterneuron Gamma (ING), transcending such classifications; (iv) In RING, robust gamma oscillations are promoted by slow but are impaired by fast inputs. Results suggest that interneuronal membrane resonance can be an important ingredient for generation of robust gamma oscillations having stable frequency
Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models
The presence of gap junction coupling among neurons of the central nervous systems has been appreciated for some time now. In recent years there has been an upsurge of interest from the mathematical community in understanding the contribution of these direct electrical connections between cells to large-scale brain rhythms. Here we analyze a class of exactly soluble single neuron models, capable of producing realistic action potential shapes, that can be used as the basis for understanding dynamics at the network level. This work focuses on planar piece-wise linear models that can mimic the firing response of several different cell types. Under constant current injection the periodic response and phase response curve (PRC) is calculated in closed form. A simple formula for the stability of a periodic orbit is found using Floquet theory. From the calculated PRC and the periodic orbit a phase interaction function is constructed that allows the investigation of phase-locked network states using the theory of weakly coupled oscillators. For large networks with global gap junction connectivity we develop a theory of strong coupling instabilities of the homogeneous, synchronous and splay state. For a piece-wise linear caricature of the Morris-Lecar model, with oscillations arising from a homoclinic bifurcation, we show that large amplitude oscillations in the mean membrane potential are organized around such unstable orbits
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Multi-electrode array recording and data analysis methods for molluscan central nervous systems
In this work the use of the central nervous system (CNS) of the aquatic
snail Lymnaea stagnalis on planar multi-electrode arrays (MEAs) was
developed and analysis methods for the data generated were created.
A variety of different combinations of configurations of tissue from the
Lymnaea CNS were explored to determine the signal characteristics
that could be recorded by sixty channel MEAs. In particular, the
suitability of the semi-intact system consisting of the lips, oesophagus,
CNS, and associated nerve connectives was developed for use on
the planar MEA. The recording target area of the dorsal surface of
the buccal ganglia was selected as being the most promising for study
and recordings of its component cells during fictive feeding behaviour
stimulated by sucrose were made. The data produced by this type of
experimentation is very high volume and so its analysis required the
development of a custom set of software tools. The goal of this tool
set is to find the signal from individual neurons in the data streams of
the electrodes of a planar MEA, to estimate their position, and then
to predict their causal connectivity. To produce such an analysis techniques
for noise filtration, neural spike detection, and group detection
of bursts of spikes were created to pre-process electrode data streams.
The Kohonen self-organising map (SOM) algorithm was adapted for
the purpose of separating detected spikes into data streams representing
the spike output of individual cells found in the target system. A
significant addition to SOM algorithm was developed by the concurrent
use of triangulation methods based on current source density
analysis to predict the position of individual cells based on their spike
output on more than one electrode. The likely functional connectivity
of individual neurons identified by the SOM technique were analysed
through the use of a statistical causality method known as Granger
causality/causal connectivity. This technique was used to produce a
map of the likely connectivity between neural sources
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