169 research outputs found
Resonant spike propagation in coupled neurons with subthreshold activity
Màster en Biofísica, curs 2006-2007Chemical coupling between neurons is only active when the presynaptic neuron is firing, and thus it does not allow for the propagation of subthreshold activity. Electrical coupling via gap junctions, on the other hand, is also ubiquitous and, due to its diffusive nature, transmits both subthreshold and suprathreshold activity between neurons. We study theoretically the propagation of spikes between two neurons that exhibit subthreshold oscillations, and which are coupled via both chemical synapses and gap junctions. Due to the electrical coupling, the periodic subthreshold activity is synchronized in the two neurons, and affects propagation of spikes in such a way that for certain values of the delay in the synaptic coupling, propagation is not possible. This effect could provide a mechanism for the modulation of information transmission in neuronal networks
Noise-induced synchronization and anti-resonance in excitable systems; Implications for information processing in Parkinson's Disease and Deep Brain Stimulation
We study the statistical physics of a surprising phenomenon arising in large
networks of excitable elements in response to noise: while at low noise,
solutions remain in the vicinity of the resting state and large-noise solutions
show asynchronous activity, the network displays orderly, perfectly
synchronized periodic responses at intermediate level of noise. We show that
this phenomenon is fundamentally stochastic and collective in nature. Indeed,
for noise and coupling within specific ranges, an asymmetry in the transition
rates between a resting and an excited regime progressively builds up, leading
to an increase in the fraction of excited neurons eventually triggering a chain
reaction associated with a macroscopic synchronized excursion and a collective
return to rest where this process starts afresh, thus yielding the observed
periodic synchronized oscillations. We further uncover a novel anti-resonance
phenomenon: noise-induced synchronized oscillations disappear when the system
is driven by periodic stimulation with frequency within a specific range. In
that anti-resonance regime, the system is optimal for measures of information
capacity. This observation provides a new hypothesis accounting for the
efficiency of Deep Brain Stimulation therapies in Parkinson's disease, a
neurodegenerative disease characterized by an increased synchronization of
brain motor circuits. We further discuss the universality of these phenomena in
the class of stochastic networks of excitable elements with confining coupling,
and illustrate this universality by analyzing various classical models of
neuronal networks. Altogether, these results uncover some universal mechanisms
supporting a regularizing impact of noise in excitable systems, reveal a novel
anti-resonance phenomenon in these systems, and propose a new hypothesis for
the efficiency of high-frequency stimulation in Parkinson's disease
Spectra and waiting-time densities in firing resonant and nonresonant neurons
The response of a neural cell to an external stimulus can follow one of the
two patterns: Nonresonant neurons monotonously relax to the resting state after
excitation while resonant ones show subthreshold oscillations. We investigate
how do these subthreshold properties of neurons affect their suprathreshold
response. Vice versa we ask: Can we distinguish between both types of neuronal
dynamics using suprathreshold spike trains? The dynamics of neurons is given by
stochastic FitzHugh-Nagumo and Morris-Lecar models with either having a focus
or a node as the stable fixpoint. We determine numerically the spectral power
density as well as the interspike interval density in response to a random
(noise-like) signals. We show that the information about the type of dynamics
obtained from power spectra is of limited validity. In contrast, the interspike
interval density gives a very sensitive instrument for the diagnostics of
whether the dynamics has resonant or nonresonant properties. For the latter
value we formulate a fit formula and use it to reconstruct theoretically the
spectral power density, which coincides with the numerically obtained spectra.
We underline that the renewal theory is applicable to analysis of
suprathreshold responses even of resonant neurons.Comment: 7 pages, 8 figure
Associative memory storing an extensive number of patterns based on a network of oscillators with distributed natural frequencies in the presence of external white noise
We study associative memory based on temporal coding in which successful
retrieval is realized as an entrainment in a network of simple phase
oscillators with distributed natural frequencies under the influence of white
noise. The memory patterns are assumed to be given by uniformly distributed
random numbers on so that the patterns encode the phase differences
of the oscillators. To derive the macroscopic order parameter equations for the
network with an extensive number of stored patterns, we introduce the effective
transfer function by assuming the fixed-point equation of the form of the TAP
equation, which describes the time-averaged output as a function of the
effective time-averaged local field. Properties of the networks associated with
synchronization phenomena for a discrete symmetric natural frequency
distribution with three frequency components are studied based on the order
parameter equations, and are shown to be in good agreement with the results of
numerical simulations. Two types of retrieval states are found to occur with
respect to the degree of synchronization, when the size of the width of the
natural frequency distribution is changed.Comment: published in Phys. Rev.
Coherence resonance in neuronal populations: mean-field versus network model
The counter-intuitive phenomenon of coherence resonance describes a
non-monotonic behavior of the regularity of noise-induced oscillations in the
excitable regime, leading to an optimal response in terms of regularity of the
excited oscillations for an intermediate noise intensity. We study this
phenomenon in populations of FitzHugh-Nagumo (FHN) neurons with different
coupling architectures. For networks of FHN systems in excitable regime,
coherence resonance has been previously analyzed numerically. Here we focus on
an analytical approach studying the mean-field limits of the locally and
globally coupled populations. The mean-field limit refers to the averaged
behavior of a complex network as the number of elements goes to infinity. We
derive a mean-field limit approximating the locally coupled FHN network with
low noise intensities. Further, we apply mean-field approach to the globally
coupled FHN network. We compare the results of the mean-field and network
frameworks for coherence resonance and find a good agreement in the globally
coupled case, where the correspondence between the two approaches is
sufficiently good to capture the emergence of anticoherence resonance. Finally,
we study the effects of the coupling strength and noise intensity on coherence
resonance for both the network and the mean-field model.Comment: 31 pages, 11 figure
High-Frequency Stimulation of Excitable Cells and Networks
High-frequency (HF) stimulation has been shown to block conduction in excitable cells including neurons and cardiac myocytes. However, the precise mechanisms underlying conduction block are unclear. Using a multi-scale method, the influence of HF stimulation is investigated in the simplified FitzhHugh-Nagumo and biophysically-detailed Hodgkin-Huxley models. In both models, HF stimulation alters the amplitude and frequency of repetitive firing in response to a constant applied current and increases the threshold to evoke a single action potential in response to a brief applied current pulse. Further, the excitable cells cannot evoke a single action potential or fire repetitively above critical values for the HF stimulation amplitude. Analytical expressions for the critical values and thresholds are determined in the FitzHugh-Nagumo model. In the Hodgkin-Huxley model, it is shown that HF stimulation alters the dynamics of ionic current gating, shifting the steady-state activation, inactivation, and time constant curves, suggesting several possible mechanisms for conduction block. Finally, we demonstrate that HF stimulation of a network of neurons reduces the electrical activity firing rate, increases network synchronization, and for a sufficiently large HF stimulation, leads to complete electrical quiescence. In this study, we demonstrate a novel approach to investigate HF stimulation in biophysically-detailed ionic models of excitable cells, demonstrate possible mechanisms for HF stimulation conduction block in neurons, and provide insight into the influence of HF stimulation on neural networks
Synchronization Analysis of Winner-Take-All Neuronal Networks
With the physical limitations of current CMOS technology, it becomes necessary to design and develop new methods to perform simple and complex computations. Nature is efficient, so many in the scientific community attempt to mimic it when optimizing or creating new systems and devices. The human brain is looked to as an efficient computing device, inspiring strong interest in developing powerful computer systems that resemble its architecture and behavior such as neural networks. There is much research focusing on both circuit designs that behave like neurons and arrangement of these electromechanical neurons to compute complex operations.
It has been shown previously that the synchronization characteristics of neural oscillators can be used not only for primitive computation functions such as convolution but for complex non-Boolean computations. With strong interest in the research community to develop biologically representative neural networks, this dissertation analyzes and simulates biologically plausible networks, the four-dimensional Hodgkin-Huxley and the simpler two-dimensional Fitzhugh-Nagumo neural models, fashioned in winner-take-all neuronal networks. The synchronization behavior of these neurons coupled together is studied in detail. Different neural network topologies are considered including lateral inhibition and inhibition via a global interneuron. Then, this dissertation analyzes the winner-take-all behaviors, in terms of both firing rates and phases, of neuronal networks with different topologies. A technique based on phase response curve is suggested for the analysis of synchronization phase characteristics of winner-take-all networks. Simulations are performed to validate the analytical results. This study promotes the understanding of winner-take-all operations in biological neuronal networks and provides a fundamental basis for applications of winner-take-all networks in modern computing systems
Border collision bifurcations of stroboscopic maps in periodically driven spiking models
In this work we consider a general non-autonomous hybrid system based on the
integrate-and-fire model, widely used as simplified version of neuronal models
and other types of excitable systems. Our unique assumption is that the system
is monotonic, possesses an attracting subthreshold equilibrium point and is
forced by means of periodic pulsatile (square wave) function.\\ In contrast to
classical methods, in our approach we use the stroboscopic map (time- return
map) instead of the so-called firing-map. It becomes a discontinuous map
potentially defined in an infinite number of partitions. By applying theory for
piecewise-smooth systems, we avoid relying on particular computations and we
develop a novel approach that can be easily extended to systems with other
topologies (expansive dynamics) and higher dimensions.\\ More precisely, we
rigorously study the bifurcation structure in the two-dimensional parameter
space formed by the amplitude and the duty cycle of the pulse. We show that it
is covered by regions of existence of periodic orbits given by period adding
structures. They do not only completely describe all the possible spiking
asymptotic dynamics but also the behavior of the firing rate, which is a
devil's staircase as a function of the parameters
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