1,882 research outputs found
Model of the early development of thalamo-cortical connections and area patterning via signaling molecules
The mammalian cortex is divided into architectonic and functionally distinct
areas. There is growing experimental evidence that their emergence and
development is controlled by both epigenetic and genetic factors. The latter
were recently implicated as dominating the early cortical area specification.
In this paper, we present a theoretical model that explicitly considers the
genetic factors and that is able to explain several sets of experiments on
cortical area regulation involving transcription factors Emx2 and Pax6, and
fibroblast growth factor FGF8. The model consists of the dynamics of thalamo-
cortical connections modulated by signaling molecules that are regulated
genetically, and by axonal competition for neocortical space. The model can
make predictions and provides a basic mathematical framework for the early
development of the thalamo-cortical connections and area patterning that can be
further refined as more experimental facts become known.Comment: brain, model, neural development, cortical area patterning, signaling
molecule
The Utility of Phase Models in Studying Neural Synchronization
Synchronized neural spiking is associated with many cognitive functions and
thus, merits study for its own sake. The analysis of neural synchronization
naturally leads to the study of repetitive spiking and consequently to the
analysis of coupled neural oscillators. Coupled oscillator theory thus informs
the synchronization of spiking neuronal networks. A crucial aspect of coupled
oscillator theory is the phase response curve (PRC), which describes the impact
of a perturbation to the phase of an oscillator. In neural terms, the
perturbation represents an incoming synaptic potential which may either advance
or retard the timing of the next spike. The phase response curves and the form
of coupling between reciprocally coupled oscillators defines the phase
interaction function, which in turn predicts the synchronization outcome
(in-phase versus anti-phase) and the rate of convergence. We review the two
classes of PRC and demonstrate the utility of the phase model in predicting
synchronization in reciprocally coupled neural models. In addition, we compare
the rate of convergence for all combinations of reciprocally coupled Class I
and Class II oscillators. These findings predict the general synchronization
outcomes of broad classes of neurons under both inhibitory and excitatory
reciprocal coupling.Comment: 18 pages, 5 figure
Formation of antiwaves in gap-junction-coupled chains of neurons
Using network models consisting of gap junction coupled Wang-Buszaki neurons,
we demonstrate that it is possible to obtain not only synchronous activity
between neurons but also a variety of constant phase shifts between 0 and \pi.
We call these phase shifts intermediate stable phaselocked states. These phase
shifts can produce a large variety of wave-like activity patterns in
one-dimensional chains and two-dimensional arrays of neurons, which can be
studied by reducing the system of equations to a phase model. The 2\pi periodic
coupling functions of these models are characterized by prominent higher order
terms in their Fourier expansion, which can be varied by changing model
parameters. We study how the relative contribution of the odd and even terms
affect what solutions are possible, the basin of attraction of those solutions
and their stability. These models may be applicable to the spinal central
pattern generators of the dogfish and also to the developing neocortex of the
neonatal rat
Stochastic firing rate models
We review a recent approach to the mean-field limits in neural networks that
takes into account the stochastic nature of input current and the uncertainty
in synaptic coupling. This approach was proved to be a rigorous limit of the
network equations in a general setting, and we express here the results in a
more customary and simpler framework. We propose a heuristic argument to derive
these equations providing a more intuitive understanding of their origin. These
equations are characterized by a strong coupling between the different moments
of the solutions. We analyse the equations, present an algorithm to simulate
the solutions of these mean-field equations, and investigate numerically the
equations. In particular, we build a bridge between these equations and
Sompolinsky and collaborators approach (1988, 1990), and show how the coupling
between the mean and the covariance function deviates from customary
approaches
Renewal theory of coupled neuronal pools
A theory is provided to analyze the dynamics of delay-coupled pools of spiking neurons based on stability
analysis of stationary firing. Transitions between stable and unstable regimes can be predicted by bifurcation analysis of the underlying integral dynamics. Close to the bifurcation point the network exhibits slowly changingactivities and allows for slow collective phenomena like continuous attractors
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