626 research outputs found
Stationary states in Langevin dynamics under asymmetric L\'evy noises
Properties of systems driven by white non-Gaussian noises can be very
different from these systems driven by the white Gaussian noise. We investigate
stationary probability densities for systems driven by -stable L\'evy
type noises, which provide natural extension to the Gaussian noise having
however a new property mainly a possibility of being asymmetric. Stationary
probability densities are examined for a particle moving in parabolic, quartic
and in generic double well potential models subjected to the action of
-stable noises. Relevant solutions are constructed by methods of
stochastic dynamics. In situations where analytical results are known they are
compared with numerical results. Furthermore, the problem of estimation of the
parameters of stationary densities is investigated.Comment: 9 pages, 9 figures, 3 table
Ultrasensitivity and Fluctuations in the Barkai-Leibler Model of Chemotaxis Receptors in {\it Escherichia coli}
A stochastic version of the Barkai-Leibler model of chemotaxis receptors in
{\it E. coli} is studied here to elucidate the effects of intrinsic network
noise in their conformational dynamics. It was originally proposed to explain
the robust and near-perfect adaptation of {\it E. coli} observed across a wide
range of spatially uniform attractant/repellent (ligand) concentrations. A
receptor is either active or inactive and can stochastically switch between the
two states. Enzyme CheR methylates inactive receptors while CheB demethylates
active ones and the probability for it to be active depends on its level of
methylation and ligandation. A simple version of the model with two methylation
sites per receptor (M=2) shows zero-order ultrasensitivity (ZOU) akin to the
classical 2-state model of covalent modification studied by Goldbeter and
Koshland (GK). For extremely small and large ligand concentrations, the system
reduces to two 2-state GK modules. A quantitative measure of the spontaneous
fluctuations in activity (variance) estimated mathematically under linear noise
approximation (LNA) is found to peak near the ZOU transition. The variance is a
weak, non-monotonic and decreasing functions of ligand and receptor
concentrations. Gillespie simulations for M=2 show excellent agreement with
analytical results obtained under LNA. Numerical results for M=2, 3 and 4 show
ZOU in mean activity; the variance is found to be smaller for larger M. The
magnitude of receptor noise deduced from available experimental data is
consistent with our predictions. A simple analysis of the downstream signaling
pathway shows that this noise is large enough to have a beneficial effect on
the motility of the organism. The response of mean receptor activity to small
time-dependent changes in the external ligand concentration, computed within
linear response theory, is found to have a bilobe form.Comment: Accepted in PLoS On
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