1,738 research outputs found
Accurate and Fast Simulation of Channel Noise in Conductance-Based Model Neurons by Diffusion Approximation
Stochastic channel gating is the major source of intrinsic neuronal noise whose functional consequences at the microcircuit- and network-levels have been only partly explored. A systematic study of this channel noise in large ensembles of biophysically detailed model neurons calls for the availability of fast numerical methods. In fact, exact techniques employ the microscopic simulation of the random opening and closing of individual ion channels, usually based on Markov models, whose computational loads are prohibitive for next generation massive computer models of the brain. In this work, we operatively define a procedure for translating any Markov model describing voltage- or ligand-gated membrane ion-conductances into an effective stochastic version, whose computer simulation is efficient, without compromising accuracy. Our approximation is based on an improved Langevin-like approach, which employs stochastic differential equations and no Montecarlo methods. As opposed to an earlier proposal recently debated in the literature, our approximation reproduces accurately the statistical properties of the exact microscopic simulations, under a variety of conditions, from spontaneous to evoked response features. In addition, our method is not restricted to the Hodgkin-Huxley sodium and potassium currents and is general for a variety of voltage- and ligand-gated ion currents. As a by-product, the analysis of the properties emerging in exact Markov schemes by standard probability calculus enables us for the first time to analytically identify the sources of inaccuracy of the previous proposal, while providing solid ground for its modification and improvement we present here
Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States
The phenomena that emerge from the interaction of the stochastic opening and
closing of ion channels (channel noise) with the non-linear neural dynamics are
essential to our understanding of the operation of the nervous system. The
effects that channel noise can have on neural dynamics are generally studied
using numerical simulations of stochastic models. Algorithms based on discrete
Markov Chains (MC) seem to be the most reliable and trustworthy, but even
optimized algorithms come with a non-negligible computational cost. Diffusion
Approximation (DA) methods use Stochastic Differential Equations (SDE) to
approximate the behavior of a number of MCs, considerably speeding up
simulation times. However, model comparisons have suggested that DA methods did
not lead to the same results as in MC modeling in terms of channel noise
statistics and effects on excitability. Recently, it was shown that the
difference arose because MCs were modeled with coupled activation subunits,
while the DA was modeled using uncoupled activation subunits. Implementations
of DA with coupled subunits, in the context of a specific kinetic scheme,
yielded similar results to MC. However, it remained unclear how to generalize
these implementations to different kinetic schemes, or whether they were faster
than MC algorithms. Additionally, a steady state approximation was used for the
stochastic terms, which, as we show here, can introduce significant
inaccuracies. We derived the SDE explicitly for any given ion channel kinetic
scheme. The resulting generic equations were surprisingly simple and
interpretable - allowing an easy and efficient DA implementation. The algorithm
was tested in a voltage clamp simulation and in two different current clamp
simulations, yielding the same results as MC modeling. Also, the simulation
efficiency of this DA method demonstrated considerable superiority over MC
methods.Comment: 32 text pages, 10 figures, 1 supplementary text + figur
The what and where of adding channel noise to the Hodgkin-Huxley equations
One of the most celebrated successes in computational biology is the
Hodgkin-Huxley framework for modeling electrically active cells. This
framework, expressed through a set of differential equations, synthesizes the
impact of ionic currents on a cell's voltage -- and the highly nonlinear impact
of that voltage back on the currents themselves -- into the rapid push and pull
of the action potential. Latter studies confirmed that these cellular dynamics
are orchestrated by individual ion channels, whose conformational changes
regulate the conductance of each ionic current. Thus, kinetic equations
familiar from physical chemistry are the natural setting for describing
conductances; for small-to-moderate numbers of channels, these will predict
fluctuations in conductances and stochasticity in the resulting action
potentials. At first glance, the kinetic equations provide a far more complex
(and higher-dimensional) description than the original Hodgkin-Huxley
equations. This has prompted more than a decade of efforts to capture channel
fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of
these approaches, while intuitively appealing, produce quantitative errors when
compared to kinetic equations; others, as only very recently demonstrated, are
both accurate and relatively simple. We review what works, what doesn't, and
why, seeking to build a bridge to well-established results for the
deterministic Hodgkin-Huxley equations. As such, we hope that this review will
speed emerging studies of how channel noise modulates electrophysiological
dynamics and function. We supply user-friendly Matlab simulation code of these
stochastic versions of the Hodgkin-Huxley equations on the ModelDB website
(accession number 138950) and
http://www.amath.washington.edu/~etsb/tutorials.html.Comment: 14 pages, 3 figures, review articl
Channel noise induced stochastic facilitation in an auditory brainstem neuron model
Neuronal membrane potentials fluctuate stochastically due to conductance
changes caused by random transitions between the open and close states of ion
channels. Although it has previously been shown that channel noise can
nontrivially affect neuronal dynamics, it is unknown whether ion-channel noise
is strong enough to act as a noise source for hypothesised noise-enhanced
information processing in real neuronal systems, i.e. 'stochastic
facilitation.' Here, we demonstrate that biophysical models of channel noise
can give rise to two kinds of recently discovered stochastic facilitation
effects in a Hodgkin-Huxley-like model of auditory brainstem neurons. The
first, known as slope-based stochastic resonance (SBSR), enables phasic neurons
to emit action potentials that can encode the slope of inputs that vary slowly
relative to key time-constants in the model. The second, known as inverse
stochastic resonance (ISR), occurs in tonically firing neurons when small
levels of noise inhibit tonic firing and replace it with burst-like dynamics.
Consistent with previous work, we conclude that channel noise can provide
significant variability in firing dynamics, even for large numbers of channels.
Moreover, our results show that possible associated computational benefits may
occur due to channel noise in neurons of the auditory brainstem. This holds
whether the firing dynamics in the model are phasic (SBSR can occur due to
channel noise) or tonic (ISR can occur due to channel noise).Comment: Published by Physical Review E, November 2013 (this version 17 pages
total - 10 text, 1 refs, 6 figures/tables); Associated matlab code is
available online in the ModelDB repository at
http://senselab.med.yale.edu/ModelDB/ShowModel.asp?model=15148
A perturbation analysis of spontaneous action potential initiation by stochastic ion channels
A stochastic interpretation of spontaneous action potential initiation is developed for the Morris- Lecar equations. Initiation of a spontaneous action potential can be interpreted as the escape from one of the wells of a double well potential, and we develop an asymptotic approximation of the mean exit time using a recently-developed quasi-stationary perturbation method. Using the fact that the activating ionic channel’s random openings and closings are fast relative to other processes, we derive an accurate estimate for the mean time to fire an action potential (MFT), which is valid for a below-threshold applied current. Previous studies have found that for above-threshold applied current, where there is only a single stable fixed point, a diffusion approximation can be used. We also explore why different diffusion approximation techniques fail to estimate the MFT
Metastability in a stochastic neural network modeled as a velocity jump Markov process
One of the major challenges in neuroscience is to determine how noise that is
present at the molecular and cellular levels affects dynamics and information
processing at the macroscopic level of synaptically coupled neuronal
populations. Often noise is incorprated into deterministic network models using
extrinsic noise sources. An alternative approach is to assume that noise arises
intrinsically as a collective population effect, which has led to a master
equation formulation of stochastic neural networks. In this paper we extend the
master equation formulation by introducing a stochastic model of neural
population dynamics in the form of a velocity jump Markov process. The latter
has the advantage of keeping track of synaptic processing as well as spiking
activity, and reduces to the neural master equation in a particular limit. The
population synaptic variables evolve according to piecewise deterministic
dynamics, which depends on population spiking activity. The latter is
characterised by a set of discrete stochastic variables evolving according to a
jump Markov process, with transition rates that depend on the synaptic
variables. We consider the particular problem of rare transitions between
metastable states of a network operating in a bistable regime in the
deterministic limit. Assuming that the synaptic dynamics is much slower than
the transitions between discrete spiking states, we use a WKB approximation and
singular perturbation theory to determine the mean first passage time to cross
the separatrix between the two metastable states. Such an analysis can also be
applied to other velocity jump Markov processes, including stochastic
voltage-gated ion channels and stochastic gene networks
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