2,574 research outputs found
Synchronization and oscillatory dynamics in heterogeneous mutually inhibited neurons
We study some mechanisms responsible for synchronous oscillations and loss of
synchrony at physiologically relevant frequencies (10-200 Hz) in a network of
heterogeneous inhibitory neurons. We focus on the factors that determine the
level of synchrony and frequency of the network response, as well as the
effects of mild heterogeneity on network dynamics. With mild heterogeneity,
synchrony is never perfect and is relatively fragile. In addition, the effects
of inhibition are more complex in mildly heterogeneous networks than in
homogeneous ones. In the former, synchrony is broken in two distinct ways,
depending on the ratio of the synaptic decay time to the period of repetitive
action potentials (), where can be determined either from the
network or from a single, self-inhibiting neuron. With ,
corresponding to large applied current, small synaptic strength or large
synaptic decay time, the effects of inhibition are largely tonic and
heterogeneous neurons spike relatively independently. With ,
synchrony breaks when faster cells begin to suppress their less excitable
neighbors; cells that fire remain nearly synchronous. We show numerically that
the behavior of mildly heterogeneous networks can be related to the behavior of
single, self-inhibiting cells, which can be studied analytically.Comment: 17 pages, 6 figures, Kluwer.sty. Journal of Compuational Neuroscience
(in press). Originally submitted to the neuro-sys archive which was never
publicly announced (was 9802001
Asynchronous response of coupled pacemaker neurons
We study a network model of two conductance-based pacemaker neurons of
differing natural frequency, coupled with either mutual excitation or
inhibition, and receiving shared random inhibitory synaptic input. The networks
may phase-lock spike-to-spike for strong mutual coupling. But the shared input
can desynchronize the locked spike-pairs by selectively eliminating the lagging
spike or modulating its timing with respect to the leading spike depending on
their separation time window. Such loss of synchrony is also found in a large
network of sparsely coupled heterogeneous spiking neurons receiving shared
input.Comment: 11 pages, 4 figures. To appear in Phys. Rev. Let
Synchronization of coupled neural oscillators with heterogeneous delays
We investigate the effects of heterogeneous delays in the coupling of two
excitable neural systems. Depending upon the coupling strengths and the time
delays in the mutual and self-coupling, the compound system exhibits different
types of synchronized oscillations of variable period. We analyze this
synchronization based on the interplay of the different time delays and support
the numerical results by analytical findings. In addition, we elaborate on
bursting-like dynamics with two competing timescales on the basis of the
autocorrelation function.Comment: 18 pages, 14 figure
Attentional modulation of firing rate and synchrony in a model cortical network
When attention is directed into the receptive field of a V4 neuron, its
contrast response curve is shifted to lower contrast values (Reynolds et al,
2000, Neuron 26:703). Attention also increases the coherence between neurons
responding to the same stimulus (Fries et al, 2001, Science 291:1560). We
studied how the firing rate and synchrony of a densely interconnected cortical
network varied with contrast and how they were modulated by attention. We found
that an increased driving current to the excitatory neurons increased the
overall firing rate of the network, whereas variation of the driving current to
inhibitory neurons modulated the synchrony of the network. We explain the
synchrony modulation in terms of a locking phenomenon during which the ratio of
excitatory to inhibitory firing rates is approximately constant for a range of
driving current values. We explored the hypothesis that contrast is represented
primarily as a drive to the excitatory neurons, whereas attention corresponds
to a reduction in driving current to the inhibitory neurons. Using this
hypothesis, the model reproduces the following experimental observations: (1)
the firing rate of the excitatory neurons increases with contrast; (2) for high
contrast stimuli, the firing rate saturates and the network synchronizes; (3)
attention shifts the contrast response curve to lower contrast values; (4)
attention leads to stronger synchronization that starts at a lower value of the
contrast compared with the attend-away condition. In addition, it predicts that
attention increases the delay between the inhibitory and excitatory synchronous
volleys produced by the network, allowing the stimulus to recruit more
downstream neurons.Comment: 36 pages, submitted to Journal of Computational Neuroscienc
Rhythms of the nervous system: mathematical themes and variations
The nervous system displays a variety of rhythms in both waking and sleep. These rhythms have been closely associated with different behavioral and cognitive states, but it is still unknown how the nervous system makes use of these rhythms to perform functionally important tasks. To address those questions, it is first useful to understood in a mechanistic way the origin of the rhythms, their interactions, the signals which create the transitions among rhythms, and the ways in which rhythms filter the signals to a network of neurons. This talk discusses how dynamical systems have been used to investigate the origin, properties and interactions of rhythms in the nervous system. It focuses on how the underlying physiology of the cells and synapses of the networks shape the dynamics of the network in different contexts, allowing the variety of dynamical behaviors to be displayed by the same network. The work is presented using a series of related case studies on different rhythms. These case studies are chosen to highlight mathematical issues, and suggest further mathematical work to be done. The topics include: different roles of excitation and inhibition in creating synchronous assemblies of cells, different kinds of building blocks for neural oscillations, and transitions among rhythms. The mathematical issues include reduction of large networks to low dimensional maps, role of noise, global bifurcations, use of probabilistic formulations.Published versio
Neural synchrony in cortical networks : history, concept and current status
Following the discovery of context-dependent synchronization of oscillatory neuronal responses in the visual system, the role of neural synchrony in cortical networks has been expanded to provide a general mechanism for the coordination of distributed neural activity patterns. In the current paper, we present an update of the status of this hypothesis through summarizing recent results from our laboratory that suggest important new insights regarding the mechanisms, function and relevance of this phenomenon. In the first part, we present recent results derived from animal experiments and mathematical simulations that provide novel explanations and mechanisms for zero and nero-zero phase lag synchronization. In the second part, we shall discuss the role of neural synchrony for expectancy during perceptual organization and its role in conscious experience. This will be followed by evidence that indicates that in addition to supporting conscious cognition, neural synchrony is abnormal in major brain disorders, such as schizophrenia and autism spectrum disorders. We conclude this paper with suggestions for further research as well as with critical issues that need to be addressed in future studies
Neural synchrony in cortical networks : history, concept and current status
Following the discovery of context-dependent synchronization of oscillatory neuronal responses in the visual system, the role of neural synchrony in cortical networks has been expanded to provide a general mechanism for the coordination of distributed neural activity patterns. In the current paper, we present an update of the status of this hypothesis through summarizing recent results from our laboratory that suggest important new insights regarding the mechanisms, function and relevance of this phenomenon. In the first part, we present recent results derived from animal experiments and mathematical simulations that provide novel explanations and mechanisms for zero and nero-zero phase lag synchronization. In the second part, we shall discuss the role of neural synchrony for expectancy during perceptual organization and its role in conscious experience. This will be followed by evidence that indicates that in addition to supporting conscious cognition, neural synchrony is abnormal in major brain disorders, such as schizophrenia and autism spectrum disorders. We conclude this paper with suggestions for further research as well as with critical issues that need to be addressed in future studies
Synchronization of electrically coupled resonate-and-fire neurons
Electrical coupling between neurons is broadly present across brain areas and
is typically assumed to synchronize network activity. However, intrinsic
properties of the coupled cells can complicate this simple picture. Many cell
types with strong electrical coupling have been shown to exhibit resonant
properties, and the subthreshold fluctuations arising from resonance are
transmitted through electrical synapses in addition to action potentials. Using
the theory of weakly coupled oscillators, we explore the effect of both
subthreshold and spike-mediated coupling on synchrony in small networks of
electrically coupled resonate-and-fire neurons, a hybrid neuron model with
linear subthreshold dynamics and discrete post-spike reset. We calculate the
phase response curve using an extension of the adjoint method that accounts for
the discontinuity in the dynamics. We find that both spikes and resonant
subthreshold fluctuations can jointly promote synchronization. The subthreshold
contribution is strongest when the voltage exhibits a significant post-spike
elevation in voltage, or plateau. Additionally, we show that the geometry of
trajectories approaching the spiking threshold causes a "reset-induced shear"
effect that can oppose synchrony in the presence of network asymmetry, despite
having no effect on the phase-locking of symmetrically coupled pairs
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
One-Dimensional Population Density Approaches to Recurrently Coupled Networks of Neurons with Noise
Mean-field systems have been previously derived for networks of coupled,
two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting
exponential (AdEx) and quartic integrate and fire (QIF), among others.
Unfortunately, the mean-field systems have a degree of frequency error and the
networks analyzed often do not include noise when there is adaptation. Here, we
derive a one-dimensional partial differential equation (PDE) approximation for
the marginal voltage density under a first order moment closure for coupled
networks of integrate-and-fire neurons with white noise inputs. The PDE has
substantially less frequency error than the mean-field system, and provides a
great deal more information, at the cost of analytical tractability. The
convergence properties of the mean-field system in the low noise limit are
elucidated. A novel method for the analysis of the stability of the
asynchronous tonic firing solution is also presented and implemented. Unlike
previous attempts at stability analysis with these network types, information
about the marginal densities of the adaptation variables is used. This method
can in principle be applied to other systems with nonlinear partial
differential equations.Comment: 26 Pages, 6 Figure
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