922 research outputs found
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
Phase-locking in weakly heterogeneous neuronal networks
We examine analytically the existence and stability of phase-locked states in
a weakly heterogeneous neuronal network. We consider a model of N neurons with
all-to-all synaptic coupling where the heterogeneity is in the firing frequency
or intrinsic drive of the neurons. We consider both inhibitory and excitatory
coupling. We derive the conditions under which stable phase-locking is
possible. In homogeneous networks, many different periodic phase-locked states
are possible. Their stability depends on the dynamics of the neuron and the
coupling. For weak heterogeneity, the phase-locked states are perturbed from
the homogeneous states and can remain stable if their homogeneous conterparts
are stable. For enough heterogeneity, phase-locked solutions either lose
stability or are destroyed completely. We analyze the possible states the
network can take when phase-locking is broken.Comment: RevTex, 27 pages, 3 figure
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
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
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
Loss of synchrony in an inhibitory network of type-I oscillators
Synchronization of excitable cells coupled by reciprocal inhibition is a topic of significant interest due to the important role that inhibitory synaptic interaction plays in the generation and regulation of coherent rhythmic activity in a variety of neural systems. While recent work revealed the synchronizing influence of inhibitory coupling on the dynamics of many networks, it is known that strong coupling can destabilize phase-locked firing. Here we examine the loss of synchrony caused by an increase in inhibitory coupling in networks of type-I Morris-Lecar model oscillators, which is characterized by a period-doubling cascade and leads to mode-locked states with alternation in the firing order of the two cells, as reported recently by Maran and Canavier (2007) for a network of Wang-Buzsáki model neurons. Although alternating- order firing has been previously reported as a near-synchronous state, we show that the stable phase difference between the spikes of the two Morris-Lecar cells can constitute as much as 70% of the unperturbed oscillation period. Further, we examine the generality of this phenomenon for a class of type-I oscillators that are close to their excitation thresholds, and provide an intuitive geometric description of such leap-frog dynamics. In the Morris-Lecar model network, the alternation in the firing order arises under the condition of fast closing of K+ channels at hyperpolarized potentials, which leads to slow dynamics of membrane potential upon synaptic inhibition, allowing the presynaptic cell to advance past the postsynaptic cell in each cycle of the oscillation. Further, we show that non-zero synaptic decay time is crucial for the existence of leap-frog firing in networks of phase oscillators. However, we demonstrate that leap-frog spiking can also be obtained in pulse-coupled inhibitory networks of one-dimensional oscillators with a multi-branched phase domain, for instance in a network of quadratic integrate-and-fire model cells. Also, we show that the entire bifurcation structure of the network can be explained by a simple scaling of the STRC (spike- time response curve) amplitude, using a simplified quadratic STRC as an example, and derive the general conditions on the shape of the STRC function that leads to leap-frog firing. Further, for the case of a homogeneous network, we establish quantitative conditions on the phase resetting properties of each cell necessary for stable alternating-order spiking, complementing the analysis of Goel and Ermentrout (2002) of the order-preserving phase transition map. We show that the extension of STRC to negative values of phase is necessary to predict the response of a model cell to several close non-weak perturbations. This allows us for instance to accurately describe the dynamics of non-weakly coupled network of three model cells. Finally, the phase return map is also extended to the heterogenous network, and is used to analyze both the order-alternating firing and the order-preserving non-zero phase locked state in this case
Stability Analysis of Phase-Locked Bursting in Inhibitory Neuron Networks
Networks of neurons, which form central pattern generators (CPGs), are important for controlling animal behaviors. Of special interest are configurations or CPG motifs composed of reciprocally inhibited neurons, such as half-center oscillators (HCOs). Bursting rhythms of HCOs are shown to include stable synchrony or in-phase bursting. This in-phase bursting can co-exist with anti-phase bursting, commonly expected as the single stable state in HCOs that are connected with fast non-delayed synapses. The finding contrasts with the classical view that reciprocal inhibition has to be slow or time-delayed to synchronize such bursting neurons. Phase-locked rhythms are analyzed via Lyapunov exponents estimated with variational equations, and through the convergence rates estimated with Poincar\\u27e return maps. A new mechanism underlying multistability is proposed that is based on the spike interactions, which confer a dual property on the fast non-delayed reciprocal inhibition; this reveals the role of spikes in generating multiple co-existing phase-locked rhythms. In particular, it demonstrates that the number and temporal characteristics of spikes determine the number and stability of the multiple phase-locked states in weakly coupled HCOs. The generality of the multistability phenomenon is demonstrated by analyzing diverse models of bursting networks with various inhibitory synapses; the individual cell models include the reduced leech heart interneuron, the Sherman model for pancreatic beta cells, the Purkinje neuron model and Fitzhugh-Rinzel phenomenological model. Finally, hypothetical and experiment-based CPGs composed of HCOs are investigated. This study is relevant for various applications that use CPGs such as robotics, prosthetics, and artificial intelligence
Mathematical frameworks for oscillatory network dynamics in neuroscience
The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear—for example, heteroclinic network attractors. In this review we present a set of mathemat- ical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical frame- work for further successful applications of mathematics to understanding network dynamics in neuroscience
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