321 research outputs found
A biophysical model explains the spontaneous bursting behavior in the developing retina
During early development, waves of activity propagate across the retina and
play a key role in the proper wiring of the early visual system. During the
stage II these waves are triggered by a transient network of neurons, called
Starburst Amacrine Cells (SACs), showing a bursting activity which disappears
upon further maturation. While several models have attempted to reproduce
retinal waves, none of them is able to mimic the rhythmic autonomous bursting
of individual SACs and reveal how these cells change their intrinsic properties
during development. Here, we introduce a mathematical model, grounded on
biophysics, which enables us to reproduce the bursting activity of SACs and to
propose a plausible, generic and robust, mechanism that generates it. The core
parameters controlling repetitive firing are fast depolarizing -gated
calcium channels and hyperpolarizing -gated potassium channels. The
quiescent phase of bursting is controlled by a slow after hyperpolarization
(sAHP), mediated by calcium-dependent potassium channels. Based on a
bifurcation analysis we show how biophysical parameters, regulating calcium and
potassium activity, control the spontaneously occurring fast oscillatory
activity followed by long refractory periods in individual SACs. We make a
testable experimental prediction on the role of voltage-dependent potassium
channels on the excitability properties of SACs and on the evolution of this
excitability along development. We also propose an explanation on how SACs can
exhibit a large variability in their bursting periods, as observed
experimentally within a SACs network as well as across different species, yet
based on a simple, unique, mechanism. As we discuss, these observations at the
cellular level have a deep impact on the retinal waves description.Comment: 25 pages, 13 figures, submitte
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
Temporal dissipative solitons in the Morris-Lecar model with time-delayed feedback
We study the dynamics and bifurcations of temporal dissipative solitons in an excitable system under time-delayed feedback. As a prototypical model displaying different types of excitability, we use the Morris-Lecar model. In the limit of large delay, soliton like solutions of delay-differential equations can be treated as homoclinic solutions of an equation with an advanced argument. Based on this, we use concepts of classical homoclinic bifurcation theory to study different types of pulse solutions and to explain their dependence on the system parameters. In particular, we show how a homoclinic orbit flip of a single-pulse soliton leads to the destabilization of equidistant multi-pulse solutions and to the emergence of stable pulse packages. It turns out that this transition is induced by a heteroclinic orbit flip in the system without feedback, which is related to the excitability properties of the Morris-Lecar model
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
Phase models and clustering in networks of oscillators with delayed coupling
We consider a general model for a network of oscillators with time delayed,
circulant coupling. We use the theory of weakly coupled oscillators to reduce
the system of delay differential equations to a phase model where the time
delay enters as a phase shift. We use the phase model to study the existence
and stability of cluster solutions. Cluster solutions are phase locked
solutions where the oscillators separate into groups. Oscillators within a
group are synchronized while those in different groups are phase-locked. We
give model independent existence and stability results for symmetric cluster
solutions. We show that the presence of the time delay can lead to the
coexistence of multiple stable clustering solutions. We apply our analytical
results to a network of Morris Lecar neurons and compare these results with
numerical continuation and simulation studies
Influence of Sodium Inward Current on Dynamical Behaviour of Modified Morris-Lecar Model
This paper presents a modified Morris-Lecar model by incorporating the sodium
inward current. The dynamical behaviour of the model in response to key
parameters is investigated. The model exhibits various excitability properties
as the values of parameters are varied. We have examined the effects of changes
in maximum ion conductances and external current on the dynamics of the
membrane potential. A detailed numerical bifurcation analysis is conducted. The
bifurcation structures obtained in this study are not present in existing
bifurcation studies of original Morris-Lecar model. The results in this study
provides the interpretation of electrical activity in excitable cells and a
platform for further study
Scaling law for the transient behavior of type-II neuron models
We study the transient regime of type-II biophysical neuron models and
determine the scaling behavior of relaxation times near but below the
repetitive firing critical current, . For both
the Hodgkin-Huxley and Morris-Lecar models we find that the critical exponent
is independent of the numerical integration time step and that both systems
belong to the same universality class, with . For appropriately
chosen parameters, the FitzHugh-Nagumo model presents the same generic
transient behavior, but the critical region is significantly smaller. We
propose an experiment that may reveal nontrivial critical exponents in the
squid axon.Comment: 6 pages, 9 figures, accepted for publication in Phys. Rev.
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