272 research outputs found
Quantifying the relative contributions of divisive and subtractive feedback to rhythm generation.
PublishedResearch Support, N.I.H., ExtramuralBiological systems are characterized by a high number of interacting components. Determining the role of each component is difficult, addressed here in the context of biological oscillations. Rhythmic behavior can result from the interplay of positive feedback that promotes bistability between high and low activity, and slow negative feedback that switches the system between the high and low activity states. Many biological oscillators include two types of negative feedback processes: divisive (decreases the gain of the positive feedback loop) and subtractive (increases the input threshold) that both contribute to slowly move the system between the high- and low-activity states. Can we determine the relative contribution of each type of negative feedback process to the rhythmic activity? Does one dominate? Do they control the active and silent phase equally? To answer these questions we use a neural network model with excitatory coupling, regulated by synaptic depression (divisive) and cellular adaptation (subtractive feedback). We first attempt to apply standard experimental methodologies: either passive observation to correlate the variations of a variable of interest to system behavior, or deletion of a component to establish whether a component is critical for the system. We find that these two strategies can lead to contradictory conclusions, and at best their interpretive power is limited. We instead develop a computational measure of the contribution of a process, by evaluating the sensitivity of the active (high activity) and silent (low activity) phase durations to the time constant of the process. The measure shows that both processes control the active phase, in proportion to their speed and relative weight. However, only the subtractive process plays a major role in setting the duration of the silent phase. This computational method can be used to analyze the role of negative feedback processes in a wide range of biological rhythms.This work is supported by National Institutes of Health (NIH) grant DK043200 (JT, RB). JR values the hospitality and resources provided by the
Laboratory of Biological Modeling, NIDDK-IR, on the NIH campus. The funders had no role in study design, data collection and analysis, decision to publish, or
preparation of the manuscript
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.
Dynamics of lattice spins as a model of arrhythmia
We consider evolution of initial disturbances in spatially extended systems
with autonomous rhythmic activity, such as the heart. We consider the case when
the activity is stable with respect to very smooth (changing little across the
medium) disturbances and construct lattice models for description of
not-so-smooth disturbances, in particular, topological defects; these models
are modifications of the diffusive XY model. We find that when the activity on
each lattice site is very rigid in maintaining its form, the topological
defects - vortices or spirals - nucleate a transition to a disordered,
turbulent state.Comment: 17 pages, revtex, 3 figure
New dynamics in cerebellar Purkinje cells: torus canards
We describe a transition from bursting to rapid spiking in a reduced
mathematical model of a cerebellar Purkinje cell. We perform a slow-fast
analysis of the system and find that -- after a saddle node bifurcation of
limit cycles -- the full model dynamics follow temporarily a repelling branch
of limit cycles. We propose that the system exhibits a dynamical phenomenon new
to realistic, biophysical applications: torus canards.Comment: 4 pages; 4 figures (low resolution); updated following peer-review:
language and definitions updated, Figures 1 and 4 updated, typos corrected,
references added and remove
On the noise-induced passage through an unstable periodic orbit II: General case
Consider a dynamical system given by a planar differential equation, which
exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is
known that under random perturbations, the distribution of locations where the
system's first exit from the interior of the unstable orbit occurs, typically
displays the phenomenon of cycling: The distribution of first-exit locations is
translated along the unstable periodic orbit proportionally to the logarithm of
the noise intensity as the noise intensity goes to zero. We show that for a
large class of such systems, the cycling profile is given, up to a
model-dependent change of coordinates, by a universal function given by a
periodicised Gumbel distribution. Our techniques combine action-functional or
large-deviation results with properties of random Poincar\'e maps described by
continuous-space discrete-time Markov chains.Comment: 44 pages, 4 figure
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
Excitability in ramped systems: the compost-bomb instability
Copyright © 2010 The Royal SocietyOpen Access articleThe paper studies a novel excitability type where a large excitable response appears when a system’s parameter is varied gradually, or ramped, above some critical rate. This occurs even though there is a (unique) stable quiescent state for any fixed setting of the ramped parameter. We give a necessary and a sufficient condition for the existence of a critical ramping rate in a general class of slow–fast systems with folded slow (critical) manifold. Additionally, we derive an analytical condition for the critical rate by relating the excitability threshold to a canard trajectory through a folded saddle singularity. The general framework is used to explain a potential climate tipping point termed the ‘compost-bomb instability’—an explosive release of soil carbon from peatlands into the atmosphere occurs above some critical rate of global warming even though there is a unique asymptotically stable soil carbon equilibrium for any fixed atmospheric temperature
Traveling wave solutions in the Burridge-Knopoff model
The slider-block Burridge-Knopoff model with the Coulomb friction law is
studied as an excitable medium. It is shown that in the continuum limit the
system admits solutions in the form of the self-sustained shock waves traveling
with constant speed which depends only on the amount of the accumulated stress
in front of the wave. For a wide class of initial conditions the behavior of
the system is determined by these shock waves and the dynamics of the system
can be expressed in terms of their motion. The solutions in the form of the
periodic wave trains and sources of counter-propagating waves are analyzed. It
is argued that depending on the initial conditions the system will either tend
to synchronize or exhibit chaotic spatiotemporal behavior.Comment: 12 pages (ReVTeX), 7 figures (Postscript) to be published in Phys.
Rev.
A comparative study of different integrate-and-fire neurons: spontaneous activity, dynamical response, and stimulus-induced correlation
Stochastic integrate-and-fire (IF) neuron models have found widespread
applications in computational neuroscience. Here we present results on the
white-noise-driven perfect, leaky, and quadratic IF models, focusing on the
spectral statistics (power spectra, cross spectra, and coherence functions) in
different dynamical regimes (noise-induced and tonic firing regimes with low or
moderate noise). We make the models comparable by tuning parameters such that
the mean value and the coefficient of variation of the interspike interval
match for all of them. We find that, under these conditions, the power spectrum
under white-noise stimulation is often very similar while the response
characteristics, described by the cross spectrum between a fraction of the
input noise and the output spike train, can differ drastically. We also
investigate how the spike trains of two neurons of the same kind (e.g. two
leaky IF neurons) correlate if they share a common noise input. We show that,
depending on the dynamical regime, either two quadratic IF models or two leaky
IFs are more strongly correlated. Our results suggest that, when choosing among
simple IF models for network simulations, the details of the model have a
strong effect on correlation and regularity of the output.Comment: 12 page
Bistability and resonance in the periodically stimulated Hodgkin-Huxley model with noise
We describe general characteristics of the Hodgkin-Huxley neuron's response
to a periodic train of short current pulses with Gaussian noise. The
deterministic neuron is bistable for antiresonant frequencies. When the stimuli
arrive at the resonant frequency the firing rate is a continuous function of
the current amplitude and scales as , where
is an approximate threshold. Intervals of continuous irregular response
alternate with integer mode-locked regions with bistable excitation edge. There
is an even-all multimodal transition between the 2:1 and 3:1 states in the
vicinity of the main resonance, which is analogous to the odd-all transition
discovered earlier in the high-frequency regime. For and small
noise the firing rate has a maximum at the resonant frequency. For larger noise
and subthreshold stimulation the maximum firing rate initially shifts towards
lower frequencies, then returns to higher frequencies in the limit of large
noise. The stochastic coherence antiresonance, defined as the maximum of the
coefficient of variation as a function of noise intensity, occurs over a wide
range of parameter values, including monostable regions.Comment: The size of the figures in this version is larger than in the
published articl
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