736 research outputs found
Bistable dynamics underlying excitability of ion homeostasis in neuron models
When neurons fire action potentials, dissipation of free energy is usually
not directly considered, because the change in free energy is often negligible
compared to the immense reservoir stored in neural transmembrane ion gradients
and the long-term energy requirements are met through chemical energy, i.e.,
metabolism. However, these gradients can temporarily nearly vanish in
neurological diseases, such as migraine and stroke, and in traumatic brain
injury from concussions to severe injuries. We study biophysical neuron models
based on the Hodgkin-Huxley (HH) formalism extended to include time-dependent
ion concentrations inside and outside the cell and metabolic energy-driven
pumps. We reveal the basic mechanism of a state of free energy-starvation (FES)
with bifurcation analyses showing that ion dynamics is for a large range of
pump rates bistable without contact to an ion bath. This is interpreted as a
threshold reduction of a new fundamental mechanism of 'ionic excitability' that
causes a long-lasting but transient FES as observed in pathological states. We
can in particular conclude that a coupling of extracellular ion concentrations
to a large glial-vascular bath can take a role as an inhibitory mechanism
crucial in ion homeostasis, while the Na/K pumps alone are insufficient
to recover from FES. Our results provide the missing link between the HH
formalism and activator-inhibitor models that have been successfully used for
modeling migraine phenotypes, and therefore will allow us to validate the
hypothesis that migraine symptoms are explained by disturbed function in ion
channel subunits, Na/K pumps, and other proteins that regulate ion
homeostasis.Comment: 14 pages, 8 figures, 4 table
Macroscopic equations governing noisy spiking neuronal populations
At functional scales, cortical behavior results from the complex interplay of
a large number of excitable cells operating in noisy environments. Such systems
resist to mathematical analysis, and computational neurosciences have largely
relied on heuristic partial (and partially justified) macroscopic models, which
successfully reproduced a number of relevant phenomena. The relationship
between these macroscopic models and the spiking noisy dynamics of the
underlying cells has since then been a great endeavor. Based on recent
mean-field reductions for such spiking neurons, we present here {a principled
reduction of large biologically plausible neuronal networks to firing-rate
models, providing a rigorous} relationship between the macroscopic activity of
populations of spiking neurons and popular macroscopic models, under a few
assumptions (mainly linearity of the synapses). {The reduced model we derive
consists of simple, low-dimensional ordinary differential equations with}
parameters and {nonlinearities derived from} the underlying properties of the
cells, and in particular the noise level. {These simple reduced models are
shown to reproduce accurately the dynamics of large networks in numerical
simulations}. Appropriate parameters and functions are made available {online}
for different models of neurons: McKean, Fitzhugh-Nagumo and Hodgkin-Huxley
models
Multimodal transition and stochastic antiresonance in squid giant axons
The experimental data of N. Takahashi, Y. Hanyu, T. Musha, R. Kubo, and G.
Matsumoto, Physica D \textbf{43}, 318 (1990), on the response of squid giant
axons stimulated by periodic sequence of short current pulses is interpreted
within the Hodgkin-Huxley model. The minimum of the firing rate as a function
of the stimulus amplitude in the high-frequency regime is due to the
multimodal transition. Below this singular point only odd multiples of the
driving period remain and the system is highly sensitive to noise. The
coefficient of variation has a maximum and the firing rate has a minimum as a
function of the noise intensity which is an indication of the stochastic
coherence antiresonance. The model calculations reproduce the frequency of
occurrence of the most common modes in the vicinity of the transition. A linear
relation of output frequency vs. for above the transition is also
confirmed.Comment: 5 pages, 9 figure
Effect of channel block on the spiking activity of excitable membranes in a stochastic Hodgkin-Huxley model
The influence of intrinsic channel noise on the spontaneous spiking activity
of poisoned excitable membrane patches is studied by use of a stochastic
generalization of the Hodgkin-Huxley model. Internal noise stemming from the
stochastic dynamics of individual ion channels is known to affect the
collective properties of the whole ion channel cluster. For example, there
exists an optimal size of the membrane patch for which the internal noise alone
causes a regular spontaneous generation of action potentials. In addition to
varying the size of ion channel clusters, living organisms may adapt the
densities of ion channels in order to optimally regulate the spontaneous
spiking activity. The influence of channel block on the excitability of a
membrane patch of certain size is twofold: First, a variation of ion channel
densities primarily yields a change of the conductance level. Second, a
down-regulation of working ion channels always increases the channel noise.
While the former effect dominates in the case of sodium channel block resulting
in a reduced spiking activity, the latter enhances the generation of
spontaneous action potentials in the case of a tailored potassium channel
blocking. Moreover, by blocking some portion of either potassium or sodium ion
channels, it is possible to either increase or to decrease the regularity of
the spike train.Comment: 10 pages, 3 figures, published 200
Channel noise effects on neural synchronization
Synchronization in neural networks is strongly tied to the implementation of
cognitive processes, but abnormal neuronal synchronization has been linked to a
number of brain disorders such as epilepsy and schizophrenia. Here we examine
the effects of channel noise on the synchronization of small Hodgkin-Huxley
neuronal networks. The principal feature of a Hodgkin-Huxley neuron is the
existence of protein channels that transition between open and closed states
with voltage dependent rate constants. The Hodgkin-Huxley model assumes
infinitely many channels, so fluctuations in the number of open channels do not
affect the voltage. However, real neurons have finitely many channels which
lead to fluctuations in the membrane voltage and modify the timing of the
spikes, which may in turn lead to large changes in the degree of
synchronization. We demonstrate that under mild conditions, neurons in the
network reach a steady state synchronization level that depends only on the
number of neurons in the network. The channel noise only affects the time it
takes to reach the steady state synchronization level.Comment: 7 Figure
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Nonlinear resonance and excitability in interconnected systems
Engineering design amounts to develop components and interconnect them to obtain a desired behaviour. While in the context of equilibrium dynamics there is a well-developed theory that can account for robustness and optimality in this process, we still lack a corresponding methodology for nonequilibrium dynamics and in particular oscillatory behaviours. With the aim of fostering such a theory, this thesis studies two basic interconnections in the contexts of nonlinear resonance and excitability, two phenomena with the potential of encompassing a large number of applications.
The first interconnection is considered in the context of vibration absorption. It corresponds to coupling two Duffing oscillators, the prototypical example of nonlinear resonator. Of primary interest is the frequency response of the system, which quantifies the behaviour in presence of harmonic forces. The analysis focuses on how isolated families of solutions appear and merge with a main one. Using singularity theory it is possible to organise these solutions in the space of parameters and delimit their presence through numerical methods.
The second interconnection studied in this dissertation appears in the context of excitable circuits. Combining a fast excitable system and a slower oscillatory system that share a similar structure naturally leads to bursting. The resulting system has a slow-fast structure that can be leveraged in the analysis. The first step of this analysis is a novel slow-fast model of bistability between a rest state and a spiking attractor. Following this, the analysis moves to the complete interconnection, and in particular on how it can generate different patterns of bursting activity
An organizing center in a planar model of neuronal excitability
The paper studies the excitability properties of a generalized
FitzHugh-Nagumo model. The model differs from the purely competitive
FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating
variables such as activation of calcium currents. Excitability is explored by
unfolding a pitchfork bifurcation that is shown to organize five different
types of excitability. In addition to the three classical types of neuronal
excitability, two novel types are described and distinctly associated to the
presence of cooperative variables
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