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1.
We studied the combined influence of noise and constant current stimulations on the Hodgkin–Huxley neuron model through time
and frequency analysis of the membrane-potential dynamics. We observed that, in agreement with experimental data (Guttman
et al. 1974), at low noise and low constant current stimulation the behavior of the model is well approximated by that of
the linearized Hodgkin–Huxley system. Conversely, nonlinearities due to firing dominate at large noise or current stimulations.
The transition between the two regimes is abrupt, and takes place in the same range of noise and current intensities as the
noise-induced transition characterized by the qualitative change in the stationary distribution of the membrane potential
(Tanabe and Pakdaman 2001a). The implications of these results are discussed.
Received: 27 July 2001 / Accepted in revised form: 18 December 2001 相似文献
2.
Patrick J. Bradley Kurt Wiesenfeld Robert J. Butera 《Journal of computational neuroscience》2011,30(2):455-469
A significant degree of heterogeneity in synaptic conductance is present in neuron to neuron connections. We study the dynamics
of weakly coupled pairs of neurons with heterogeneities in synaptic conductance using Wang–Buzsaki and Hodgkin–Huxley model
neurons which have Types I and II excitability, respectively. This type of heterogeneity breaks a symmetry in the bifurcation
diagrams of equilibrium phase difference versus the synaptic rate constant when compared to the identical case. For weakly
coupled neurons coupled with identical values of synaptic conductance a phase locked solution exists for all values of the
synaptic rate constant, α. In particular, in-phase and anti-phase solutions are guaranteed to exist for all α. Heterogeneity in synaptic conductance results in regions where no phase locked solution exists and the general loss of the
ubiquitous in-phase and anti-phase solutions of the identically coupled case. We explain these results through examination
of interaction functions using the weak coupling approximation and an in-depth analysis of the underlying multiple cusp bifurcation
structure of the systems of coupled neurons. 相似文献
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5.
Christoph Börgers Martin Krupa Stan Gielen 《Journal of computational neuroscience》2010,28(3):509-526
A population of uncoupled neurons can often be brought close to synchrony by a single strong inhibitory input pulse affecting
all neurons equally. This mechanism is thought to underlie some brain rhythms, in particular gamma frequency (30–80 Hz) oscillations
in the hippocampus and neocortex. Here we show that synchronization by an inhibitory input pulse often fails for populations
of classical Hodgkin–Huxley neurons. Our reasoning suggests that in general, synchronization by inhibitory input pulses can
fail when the transition of the target neurons from rest to spiking involves a Hopf bifurcation, especially when inhibition
is shunting, not hyperpolarizing. Surprisingly, synchronization is more likely to fail when the inhibitory pulse is stronger
or longer-lasting. These findings have potential implications for the question which neurons participate in brain rhythms,
in particular in gamma oscillations. 相似文献
6.
Modelled temperature-dependent excitability behaviour of a single ranvier node for a human peripheral sensory nerve fibre 总被引:1,自引:1,他引:0
The objective of this study was to determine whether the Hodgkin–Huxley model for unmyelinated nerve fibres could be modified
to predict excitability behaviour at Ranvier nodes. Only the model parameters were modified to those of human, with the equations
left unaltered. A model of a single Ranvier node has been developed as part of a larger model to describe excitation behaviour
in a generalised human peripheral sensory nerve fibre. Parameter values describing the ionic and leakage conductances, corresponding
equilibrium potentials, resting membrane potential and membrane capacitance of the original Hodgkin–Huxley model were modified
to reflect the corresponding parameter values for human. Parameter temperature dependence was included. The fast activating
potassium current kinetics were slowed down to represent those of a slow activating and deactivating potassium current, which
do not inactivate. All calculations were performed in MATLABTM. Action potential shape and amplitude were satisfactorily predicted at 20, 25 and 37°C, and were not influenced by activation
or deactivation of the slow potassium current. The calculated chronaxie time constant was 65.5 μs at 37°C. However, chronaxie
times were overestimated at temperatures lower than body temperature. 相似文献
7.
Chains of coupled oscillators of simple “rotator” type have been used to model the central pattern generator (CPG) for locomotion
in lamprey, among numerous applications in biology and elsewhere. In this paper, motivated by experiments on lamprey CPG with
brainstem attached, we investigate a simple oscillator model with internal structure which captures both excitable and bursting
dynamics. This model, and that for the coupling functions, is inspired by the Hodgkin–Huxley equations and two-variable simplifications
thereof. We analyse pairs of coupled oscillators with both excitatory and inhibitory coupling. We also study traveling wave
patterns arising from chains of oscillators, including simulations of “body shapes” generated by a double chain of oscillators
providing input to a kinematic musculature model of lamprey..
Received: 25 November 1996 / Revised version: 9 December 1997 相似文献
8.
Keener JP 《Journal of mathematical biology》2009,58(3):447-457
We show that many Markov models of ion channel kinetics have globally attracting stable invariant manifolds, even when the
Markov process is time dependent. The primary implication of this is that, since the dimension of the invariant manifold is
often substantially smaller than the full master equation system, simulations of ion channel kinetics can be substantially
simplified, with no approximation. We show that this applies to certain models of potassium channels, sodium channels, ryanodine
receptors and IP3 receptors. We also use this to show that the original Hodgkin–Huxley formulations of potassium channel conductance and sodium
channel conductance are the exact solutions of full Markov models for these channels.
相似文献
9.
Brette R Rudolph M Carnevale T Hines M Beeman D Bower JM Diesmann M Morrison A Goodman PH Harris FC Zirpe M Natschläger T Pecevski D Ermentrout B Djurfeldt M Lansner A Rochel O Vieville T Muller E Davison AP El Boustani S Destexhe A 《Journal of computational neuroscience》2007,23(3):349-398
We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation
strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in
particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation
environments presently available (restricted to those freely available, open source and documented). For each simulation tool,
its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a
given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including
Hodgkin–Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven
or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes
are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration
strategy and simulation tool to use for a given modeling problem related to spiking neural networks.
Action Editor: Barry J. Richmond 相似文献
10.
In this paper, a dynamic model is proposed to quantify the relationship between fluid flow and Cl−-selective membrane current in vascular endothelial cells (VECs). It is assumed that the external shear stress would first
induce channel deformation in VECs. This deformation could activate the Cl− channels on the membrane, thus allowing Cl− transport across the membrane. A modified Hodgkin–Huxley model is embedded into our dynamic system to describe the electrophysiological
properties of the membrane, such as the Cl−-selective membrane current (I), voltage (V) and conductance. Three flow patterns, i. e., steady flow, oscillatory flow, and pulsatile flow, are applied in our simulation
studies. When the extracellular Cl− concentration is constant, the I-V characteristics predicted by our dynamic model shows strong consistency with the experimental observations. It is also interesting
to note that the Cl− currents under different flow patterns show some differences, indicating that VECs distinguish among and respond differently
to different types of flows. When the extracellular Cl− concentration keeps constant or varies slowly with time (i.e. oscillates at 0.02 Hz), the convection and diffusion of Cl− in extracellular space can be ignored and the Cl− current is well captured by the modified Hodgkin–Huxley model alone. However, when the extracellular Cl− varies fast (i.e., oscillates at 0.2 Hz), the convection and diffusion effect should be considered because the Cl− current dynamics is different from the case where the convection-diffusion effect is simply ignored. The proposed dynamic
model along with the simulation results could not only provide more insights into the flow-regulated electrophysiological
behavior of the cell membrane but also help to reveal new findings in the electrophysiological experimental investigations
of VECs in response to dynamic flow and biochemical stimuli. 相似文献
11.
Hodgkin–Huxley (HH) models of neuronal membrane dynamics consist of a set of nonlinear differential equations that describe
the time-varying conductance of various ion channels. Using observations of voltage alone we show how to estimate the unknown
parameters and unobserved state variables of an HH model in the expected circumstance that the measurements are noisy, the
model has errors, and the state of the neuron is not known when observations commence. The joint probability distribution
of the observed membrane voltage and the unobserved state variables and parameters of these models is a path integral through
the model state space. The solution to this integral allows estimation of the parameters and thus a characterization of many
biological properties of interest, including channel complement and density, that give rise to a neuron’s electrophysiological
behavior. This paper describes a method for directly evaluating the path integral using a Monte Carlo numerical approach.
This provides estimates not only of the expected values of model parameters but also of their posterior uncertainty. Using
test data simulated from neuronal models comprising several common channels, we show that short (<50 ms) intracellular recordings
from neurons stimulated with a complex time-varying current yield accurate and precise estimates of the model parameters as
well as accurate predictions of the future behavior of the neuron. We also show that this method is robust to errors in model
specification, supporting model development for biological preparations in which the channel expression and other biophysical
properties of the neurons are not fully known. 相似文献
12.
Complex nonlinear dynamics of the Hodgkin-Huxley equations induced by time scale changes 总被引:3,自引:0,他引:3
The Hodgkin–Huxley equations with a slight modification are investigated, in which the inactivation process (h) of sodium channels or the activation process of potassium channels (n) is slowed down. We show that the equations produce a variety of action potential waveforms ranging from a plateau potential,
such as in heart muscle cells, to chaotic bursting firings. When h is slowed down – differently from the case of n variable being slow – chaotic bursting oscillations are observed for a wide range of parameter values although both variables
cause a decrease in the membrane potential. The underlying nonlinear dynamics of various action potentials are analyzed using
bifurcation theory and a so-called slow–fast decomposition analysis. It is shown that a simple topological property of the
equilibrium curves of slow and fast subsystems is essential to the production of chaotic oscillations, and this is the cause
of the large difference in global firing characteristics between the h-slow and n-slow cases.
Received: 9 August 2000 / Accepted in revised form: 10 January 2001 相似文献
13.
In the past decades, many studies have focussed on the relation between the input and output of neurons with the aim to understand
information processing by neurons. A particular aspect of neuronal information, which has not received much attention so far,
concerns the problem of information transfer when a neuron or a population of neurons receives input from two or more (populations
of) neurons, in particular when these (populations of) neurons carry different types of information. The aim of the present
study is to investigate the responses of neurons to multiple inputs modulated in the gamma frequency range. By a combination
of theoretical approaches and computer simulations, we test the hypothesis that enhanced modulation of synchronized excitatory
neuronal activity in the gamma frequency range provides an advantage over a less synchronized input for various types of neurons.
The results of this study show that the spike output of various types of neurons [i.e. the leaky integrate and fire neuron,
the quadratic integrate and fire neuron and the Hodgkin–Huxley (HH) neuron] and that of excitatory–inhibitory coupled pairs
of neurons, like the Pyramidal Interneuronal Network Gamma (PING) model, is highly phase-locked to the larger of two gamma-modulated
input signals. This implies that the neuron selectively responds to the input with the larger gamma modulation if the amplitude
of the gamma modulation exceeds that of the other signals by a certain amount. In that case, the output of the neuron is entrained
by one of multiple inputs and that other inputs are not represented in the output. This mechanism for selective information
transmission is enhanced for short membrane time constants of the neuron. 相似文献
14.
In retinal synapses between cones and luminosity type horizontal cells (LHC), it was previously found in this laboratory that
repetitive red flashes progressively strengthened the LHC’s response to red flash, whereas weakened the LHC’s response to
green flash; repetitive green flash remarkably depressed the LHC’s red response, but caused little changes in the cell’s green
response. However, the detailed mechanisms underlying these phenomena are not entirely clear. In the present study, based
on an ion-channel model described mainly in the form of Hodgkin–Huxley equations, possible mechanisms of the short-term synaptic
modification are investigated. The simulation results suggest that: (1) the auto-enhancement effect might be induced by the
Ca2+-dependent process on the post-synaptic AMPA receptors, which could lead to changes of the ionic channel’s properties; (2)
the asymmetric response to red- and green-flashes and the mutual-chromatic suppression effects might be attributed to the
regulatory effects on the presynaptic glutamate release. 相似文献
15.
We examine the effects of stochastic input currents on the firing behaviour of two coupled Type 1 or Type 2 neurons. In Hodgkin–Huxley
model neurons with standard parameters, which are Type 2, in the bistable regime, synaptic transmission can initiate oscillatory
joint spiking, but white noise can terminate it. In Type 1 cells (models), typified by a quadratic integrate and fire model,
synaptic coupling can cause oscillatory behaviour in excitatory cells, but Gaussian white noise can again terminate it. We
locally determine an approximate basin of attraction, of the periodic orbit and explain the firing behaviour in terms of the effects of noise on the probability of escape of trajectories
from 相似文献
16.
The objective of this study was to determine if a recently developed human Ranvier node model, which is based on a modified
version of the Hodgkin–Huxley model, could predict the excitability behaviour in human peripheral sensory nerve fibres with
diameters ranging from 5.0 to 15.0 μm. The Ranvier node model was extended to include a persistent sodium current and was
incorporated into a generalised single cable nerve fibre model. Parameter temperature dependence was included. All calculations
were performed in Matlab. Sensory nerve fibre excitability behaviour characteristics predicted by the new nerve fibre model
at different temperatures and fibre diameters compared well with measured data. Absolute refractory periods deviated from
measured data, while relative refractory periods were similar to measured data. Conduction velocities showed both fibre diameter
and temperature dependence and were underestimated in fibres thinner than 12.5 μm. Calculated strength–duration time constants
ranged from 128.5 to 183.0 μs at 37°C over the studied nerve fibre diameter range, with chronaxie times about 30% shorter
than strength–duration time constants. Chronaxie times exhibited temperature dependence, with values overestimated by a factor
5 at temperatures lower than body temperature. Possible explanations include the deviated absolute refractory period trend
and inclusion of a nodal strangulation relationship.
At the time of this research J. E. Smit was with the University of Pretoria. 相似文献
17.
A wide diversity of models have been proposed to account for the spiking response of central neurons, from the integrate-and-fire
(IF) model and its quadratic and exponential variants, to multiple-variable models such as the Izhikevich (IZ) model and the
well-known Hodgkin–Huxley (HH) type models. Such models can capture different aspects of the spiking response of neurons,
but there is few objective comparison of their performance. In this article, we provide such a comparison in the context of
well-defined stimulation protocols, including, for each cell, DC stimulation, and a series of excitatory conductance injections,
arising in the presence of synaptic background activity. We use the dynamic-clamp technique to characterize the response of
regular-spiking neurons from guinea-pig visual cortex by computing families of post-stimulus time histograms (PSTH), for different
stimulus intensities, and for two different background activities (low- and high-conductance states). The data obtained are
then used to fit different classes of models such as the IF, IZ, or HH types, which are constrained by the whole data set.
This analysis shows that HH models are generally more accurate to fit the series of experimental PSTH, but their performance
is almost equaled by much simpler models, such as the exponential or pulse-based IF models. Similar conclusions were also
reached by performing partial fitting of the data, and examining the ability of different models to predict responses that
were not used for the fitting. Although such results must be qualified by using more sophisticated stimulation protocols,
they suggest that nonlinear IF models can capture surprisingly well the response of cortical regular-spiking neurons and appear
as useful candidates for network simulations with conductance-based synaptic interactions. 相似文献
18.
19.
We develop and study two neural network models of perceptual alternations. Both models have a star-like architecture of connections
with a central element connected to a set of peripheral elements. A particular perception is simulated in terms of partial
synchronization between the central element and some sub-group of peripheral elements. The first model is constructed from
phase oscillators and the mechanism of perceptual alternations is based on chaotic intermittency under fixed parameter values.
Similar to experimental evidence, the distribution of times between perceptual alternations is represented by the gamma distribution.
The second model is built of spiking neurons of the Hodgkin–Huxley type. The mechanism of perceptual alternations is based
on plasticity of inhibitory synapses which increases the inhibition from the central unit to the neural assembly representing
the current percept. As a result another perception is formed. Simulations show that the second model is in good agreement
with behavioural data on switching times between percepts of ambiguous figures and with experimental results on binocular
rivalry of two and four percepts.
This article is part of a special issue on Neuronal Dynamics of Sensory Coding.
This special issue is in honour of Professor Pepe Segundo who is one of the pioneers in the study of neural coding. Pepe has
been an active participant in many Neural Coding Workshops sharing his great knowledge and experience of research in this
field. I (R. Borisyuk) was very happy to meet Pepe for the first time in Prague when attending the first Neural Coding Workshop
in 1995. From that time we regularly met at Neural Coding Workshops and these meetings have always been very stimulating and
fruitful for my research. Remarkably, the first paper I studied at the beginning of my scientific career was a seminal paper
by Moore et al. (1970). For me, this paper provided a great opportunity to learn the basic statistical techniques for the
analysis of multiple spike trains and neural coding. According to the Institute of Scientific Information, this paper has
been cited 380 times! This exciting paper has inspired my research into the synaptic and functional connectivity of neural
circuits derived from spike-train recordings (Borisyuk et al. 1985; Stuart et al. 2005) and guided my search for new ideas
on neural coding. 相似文献
20.
The dynamics of two interacting theoretical populations inhabiting a heterogeneous environment are modelled by a system of
two weakly coupled reaction–diffusion equations having spatially dependent reaction terms. Longterm persistence of both populations
is guaranteed by an invasibility condition, which is itself expressed via the signs of certain eigenvalues of related linear
elliptic operators with spatially dependent lowest order coefficients. The effects of change in these coefficients upon the
eigenvalues are here exploited to study the effects of spatial heterogeneity on the persistence of interacting species through
two particular ecological topics of interest. The first concerns when the location of favorable hunting grounds within the
overall environment does or does not affect the success of a predator in predator–prey models, while the second concerns cases
of competition models in which the outcome of competition in a spatially varying environment differs from that which would
be expected in a spatially homogeneous environment.
Received: 9 June 1997 相似文献