2,172 research outputs found
Entrainment and chaos in a pulse-driven Hodgkin-Huxley oscillator
The Hodgkin-Huxley model describes action potential generation in certain
types of neurons and is a standard model for conductance-based, excitable
cells. Following the early work of Winfree and Best, this paper explores the
response of a spontaneously spiking Hodgkin-Huxley neuron model to a periodic
pulsatile drive. The response as a function of drive period and amplitude is
systematically characterized. A wide range of qualitatively distinct responses
are found, including entrainment to the input pulse train and persistent chaos.
These observations are consistent with a theory of kicked oscillators developed
by Qiudong Wang and Lai-Sang Young. In addition to general features predicted
by Wang-Young theory, it is found that most combinations of drive period and
amplitude lead to entrainment instead of chaos. This preference for entrainment
over chaos is explained by the structure of the Hodgkin-Huxley phase resetting
curve.Comment: Minor revisions; modified Fig. 3; added reference
Mechanisms of Zero-Lag Synchronization in Cortical Motifs
Zero-lag synchronization between distant cortical areas has been observed in
a diversity of experimental data sets and between many different regions of the
brain. Several computational mechanisms have been proposed to account for such
isochronous synchronization in the presence of long conduction delays: Of
these, the phenomenon of "dynamical relaying" - a mechanism that relies on a
specific network motif - has proven to be the most robust with respect to
parameter mismatch and system noise. Surprisingly, despite a contrary belief in
the community, the common driving motif is an unreliable means of establishing
zero-lag synchrony. Although dynamical relaying has been validated in empirical
and computational studies, the deeper dynamical mechanisms and comparison to
dynamics on other motifs is lacking. By systematically comparing
synchronization on a variety of small motifs, we establish that the presence of
a single reciprocally connected pair - a "resonance pair" - plays a crucial
role in disambiguating those motifs that foster zero-lag synchrony in the
presence of conduction delays (such as dynamical relaying) from those that do
not (such as the common driving triad). Remarkably, minor structural changes to
the common driving motif that incorporate a reciprocal pair recover robust
zero-lag synchrony. The findings are observed in computational models of
spiking neurons, populations of spiking neurons and neural mass models, and
arise whether the oscillatory systems are periodic, chaotic, noise-free or
driven by stochastic inputs. The influence of the resonance pair is also robust
to parameter mismatch and asymmetrical time delays amongst the elements of the
motif. We call this manner of facilitating zero-lag synchrony resonance-induced
synchronization, outline the conditions for its occurrence, and propose that it
may be a general mechanism to promote zero-lag synchrony in the brain.Comment: 41 pages, 12 figures, and 11 supplementary figure
Chaos at the border of criticality
The present paper points out to a novel scenario for formation of chaotic
attractors in a class of models of excitable cell membranes near an
Andronov-Hopf bifurcation (AHB). The mechanism underlying chaotic dynamics
admits a simple and visual description in terms of the families of
one-dimensional first-return maps, which are constructed using the combination
of asymptotic and numerical techniques. The bifurcation structure of the
continuous system (specifically, the proximity to a degenerate AHB) endows the
Poincare map with distinct qualitative features such as unimodality and the
presence of the boundary layer, where the map is strongly expanding. This
structure of the map in turn explains the bifurcation scenarios in the
continuous system including chaotic mixed-mode oscillations near the border
between the regions of sub- and supercritical AHB. The proposed mechanism
yields the statistical properties of the mixed-mode oscillations in this
regime. The statistics predicted by the analysis of the Poincare map and those
observed in the numerical experiments of the continuous system show a very good
agreement.Comment: Chaos: An Interdisciplinary Journal of Nonlinear Science
(tentatively, Sept 2008
Biophysical modelling of a drosophila photoreceptor
It remains unclear how visual information is co-processed
by different layers of neurons in the retina. In particular, relatively little is known how retina translates vast environmental light changes into
neural responses of limited range. We began examining this question in a bottom-up way in a relatively simple °y eye. To gain understanding of how complex bio-molecular interactions govern the conversion of light input into voltage output (phototransduction), we are building a
biophysical model of the Drosophila R1-R6 photoreceptor. Our model, which relates molecular dynamics of the underlying biochemical reactions to external light input, attempts to capture the molecular dynamics of
phototransduction gain control in a quantitative way
Automatic Construction of Predictive Neuron Models through Large Scale Assimilation of Electrophysiological Data.
We report on the construction of neuron models by assimilating electrophysiological data with large-scale constrained nonlinear optimization. The method implements interior point line parameter search to determine parameters from the responses to intracellular current injections of zebra finch HVC neurons. We incorporated these parameters into a nine ionic channel conductance model to obtain completed models which we then use to predict the state of the neuron under arbitrary current stimulation. Each model was validated by successfully predicting the dynamics of the membrane potential induced by 20-50 different current protocols. The dispersion of parameters extracted from different assimilation windows was studied. Differences in constraints from current protocols, stochastic variability in neuron output, and noise behave as a residual temperature which broadens the global minimum of the objective function to an ellipsoid domain whose principal axes follow an exponentially decaying distribution. The maximum likelihood expectation of extracted parameters was found to provide an excellent approximation of the global minimum and yields highly consistent kinetics for both neurons studied. Large scale assimilation absorbs the intrinsic variability of electrophysiological data over wide assimilation windows. It builds models in an automatic manner treating all data as equal quantities and requiring minimal additional insight
Dynamics of Current, Charge and Mass
Electricity plays a special role in our lives and life. Equations of electron
dynamics are nearly exact and apply from nuclear particles to stars. These
Maxwell equations include a special term the displacement current (of vacuum).
Displacement current allows electrical signals to propagate through space.
Displacement current guarantees that current is exactly conserved from inside
atoms to between stars, as long as current is defined as Maxwell did, as the
entire source of the curl of the magnetic field. We show how the Bohm
formulation of quantum mechanics allows easy definition of current. We show how
conservation of current can be derived without mention of the polarization or
dielectric properties of matter. Matter does not behave the way physicists of
the 1800's thought it does with a single dielectric constant, a real positive
number independent of everything. Charge moves in enormously complicated ways
that cannot be described in that way, when studied on time scales important
today for electronic technology and molecular biology. Life occurs in ionic
solutions in which charge moves in response to forces not mentioned or
described in the Maxwell equations, like convection and diffusion. Classical
derivations of conservation of current involve classical treatments of
dielectrics and polarization in nearly every textbook. Because real dielectrics
do not behave in a classical way, classical derivations of conservation of
current are often distrusted or even ignored. We show that current is conserved
exactly in any material no matter how complex the dielectric, polarization or
conduction currents are. We believe models, simulations, and computations
should conserve current on all scales, as accurately as possible, because
physics conserves current that way. We believe models will be much more
successful if they conserve current at every level of resolution, the way
physics does.Comment: Version 4 slight reformattin
Observability and Synchronization of Neuron Models
Observability is the property that enables to distinguish two different
locations in -dimensional state space from a reduced number of measured
variables, usually just one. In high-dimensional systems it is therefore
important to make sure that the variable recorded to perform the analysis
conveys good observability of the system dynamics. In the case of networks
composed of neuron models, the observability of the network depends
nontrivially on the observability of the node dynamics and on the topology of
the network. The aim of this paper is twofold. First, a study of observability
is conducted using four well-known neuron models by computing three different
observability coefficients. This not only clarifies observability properties of
the models but also shows the limitations of applicability of each type of
coefficients in the context of such models. Second, a multivariate singular
spectrum analysis (M-SSA) is performed to detect phase synchronization in
networks composed by neuron models. This tool, to the best of the authors'
knowledge has not been used in the context of networks of neuron models. It is
shown that it is possible to detect phase synchronization i)~without having to
measure all the state variables, but only one from each node, and ii)~without
having to estimate the phase
Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems
Voltage-dependent ion channels determine the electric properties of axonal
cell membranes. They not only allow the passage of ions through the cell
membrane but also contribute to an additional charging of the cell membrane
resulting in the so-called capacitance loading. The switching of the channel
gates between an open and a closed configuration is intrinsically related to
the movement of gating charge within the cell membrane. At the beginning of an
action potential the transient gating current is opposite to the direction of
the current of sodium ions through the membrane. Therefore, the excitability is
expected to become reduced due to the influence of a gating current. Our
stochastic Hodgkin-Huxley like modeling takes into account both the channel
noise -- i.e. the fluctuations of the number of open ion channels -- and the
capacitance fluctuations that result from the dynamics of the gating charge. We
investigate the spiking dynamics of membrane patches of variable size and
analyze the statistics of the spontaneous spiking. As a main result, we find
that the gating currents yield a drastic reduction of the spontaneous spiking
rate for sufficiently large ion channel clusters. Consequently, this
demonstrates a prominent mechanism for channel noise reduction.Comment: 18 page
Mean Field description of and propagation of chaos in recurrent multipopulation networks of Hodgkin-Huxley and Fitzhugh-Nagumo neurons
We derive the mean-field equations arising as the limit of a network of
interacting spiking neurons, as the number of neurons goes to infinity. The
neurons belong to a fixed number of populations and are represented either by
the Hodgkin-Huxley model or by one of its simplified version, the
Fitzhugh-Nagumo model. The synapses between neurons are either electrical or
chemical. The network is assumed to be fully connected. The maximum
conductances vary randomly. Under the condition that all neurons initial
conditions are drawn independently from the same law that depends only on the
population they belong to, we prove that a propagation of chaos phenomenon
takes places, namely that in the mean-field limit, any finite number of neurons
become independent and, within each population, have the same probability
distribution. This probability distribution is solution of a set of implicit
equations, either nonlinear stochastic differential equations resembling the
McKean-Vlasov equations, or non-local partial differential equations resembling
the McKean-Vlasov-Fokker- Planck equations. We prove the well-posedness of
these equations, i.e. the existence and uniqueness of a solution. We also show
the results of some preliminary numerical experiments that indicate that the
mean-field equations are a good representation of the mean activity of a finite
size network, even for modest sizes. These experiment also indicate that the
McKean-Vlasov-Fokker- Planck equations may be a good way to understand the
mean-field dynamics through, e.g., a bifurcation analysis.Comment: 55 pages, 9 figure
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