654 research outputs found
Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models
Chemical reactions inside cells occur in compartment volumes in the range of
atto- to femtolitres. Physiological concentrations realized in such small
volumes imply low copy numbers of interacting molecules with the consequence of
considerable fluctuations in the concentrations. In contrast, rate equation
models are based on the implicit assumption of infinitely large numbers of
interacting molecules, or equivalently, that reactions occur in infinite
volumes at constant macroscopic concentrations. In this article we compute the
finite-volume corrections (or equivalently the finite copy number corrections)
to the solutions of the rate equations for chemical reaction networks composed
of arbitrarily large numbers of enzyme-catalyzed reactions which are confined
inside a small sub-cellular compartment. This is achieved by applying a
mesoscopic version of the quasi-steady state assumption to the exact
Fokker-Planck equation associated with the Poisson Representation of the
chemical master equation. The procedure yields impressively simple and compact
expressions for the finite-volume corrections. We prove that the predictions of
the rate equations will always underestimate the actual steady-state substrate
concentrations for an enzyme-reaction network confined in a small volume. In
particular we show that the finite-volume corrections increase with decreasing
sub-cellular volume, decreasing Michaelis-Menten constants and increasing
enzyme saturation. The magnitude of the corrections depends sensitively on the
topology of the network. The predictions of the theory are shown to be in
excellent agreement with stochastic simulations for two types of networks
typically associated with protein methylation and metabolism.Comment: 13 pages, 4 figures; published in The Journal of Chemical Physic
Modifications of the Levi core
We construct a family of subdistributions of the Levi core
called modified Levi cores
indexed over closed
distributions that contain the Levi null distribution
and are contained in the complex tangent bundle
of a smooth bounded pseudoconvex domain . We show that Catlin's
Property () holds on if and only if Property () holds on the
support of one, and hence all, of the modified Levi cores. In ,
all of the modified Levi cores coincide. For a smooth bounded pseudoconvex
complete Hartogs domain in that satisfies Property (), we
show that its modified Levi core is trivial. This contrasts with
, which can be nontrivial for such domains.Comment: 13 page
How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?
The chemical Fokker-Planck equation and the corresponding chemical Langevin
equation are commonly used approximations of the chemical master equation.
These equations are derived from an uncontrolled, second-order truncation of
the Kramers-Moyal expansion of the chemical master equation and hence their
accuracy remains to be clarified. We use the system-size expansion to show that
chemical Fokker-Planck estimates of the mean concentrations and of the variance
of the concentration fluctuations about the mean are accurate to order
for reaction systems which do not obey detailed balance and at
least accurate to order for systems obeying detailed balance,
where is the characteristic size of the system. Hence the chemical
Fokker-Planck equation turns out to be more accurate than the linear-noise
approximation of the chemical master equation (the linear Fokker-Planck
equation) which leads to mean concentration estimates accurate to order
and variance estimates accurate to order . This
higher accuracy is particularly conspicuous for chemical systems realized in
small volumes such as biochemical reactions inside cells. A formula is also
obtained for the approximate size of the relative errors in the concentration
and variance predictions of the chemical Fokker-Planck equation, where the
relative error is defined as the difference between the predictions of the
chemical Fokker-Planck equation and the master equation divided by the
prediction of the master equation. For dimerization and enzyme-catalyzed
reactions, the errors are typically less than few percent even when the
steady-state is characterized by merely few tens of molecules.Comment: 39 pages, 3 figures, accepted for publication in J. Chem. Phy
Strong Stein neighborhood bases
Let D be a smooth bounded pseudoconvex domain in C^n. We give several
characterizations for the closure of D to have a strong Stein neighborhood
basis in the sense that D has a defining function r such that {z\in C^n:r(z)<a}
is pseudoconvex for sufficiently small a>0. We also show that this condition is
invariant under proper holomorphic maps that extend smoothly to the boundary.Comment: 14 pages, fixed same references, to appear in Complex Var. Elliptic
Eq
Rigorous elimination of fast stochastic variables from the linear noise approximation using projection operators
The linear noise approximation (LNA) offers a simple means by which one can
study intrinsic noise in monostable biochemical networks. Using simple physical
arguments, we have recently introduced the slow-scale LNA (ssLNA) which is a
reduced version of the LNA under conditions of timescale separation. In this
paper, we present the first rigorous derivation of the ssLNA using the
projection operator technique and show that the ssLNA follows uniquely from the
standard LNA under the same conditions of timescale separation as those
required for the deterministic quasi-steady state approximation. We also show
that the large molecule number limit of several common stochastic model
reduction techniques under timescale separation conditions constitutes a
special case of the ssLNA.Comment: 10 pages, 1 figure, submitted to Physical Review E; see also BMC
Systems Biology 6, 39 (2012
High diagnostic stability of confirmed migraine and confirmed tension-type headache according to the ICHD-3 beta in adolescents
Background: Stable headache diagnosis classification is a prerequisite for identification of headache type specific risk factors. Does the stability of a headache diagnosis over time vary between migraine and tension-type headache (TTH)? Are there differences in diagnosis stability between a probable and a definite headache diagnosis? Findings: In a sample of 783 students (ages 12 to 18 years) participating in a headache intervention study in greater Munich, the stability of headache classification according to the International Classification of Headache Disorder - third edition (beta version) (ICHD-3 beta) after a follow-up of 7 months was examined. Differences in stability of probable or definite migraine and probable or definite TTH were assessed. The stability of the headache diagnosis was assessed as predictive value of headache diagnosis with regard to confirmation of the headache type using the same diagnostic instrument 7 months later. Predictive values with 95% confidence intervals (CI) are reported. Of students with initial migraine, a diagnosis of migraine was confirmed in 65.71% of students after 7 months (95%-CI {[}59.40-71.64]). A clear distinction between probable (44.71%, 95%-CI {[}33.91-53.89]) and confirmed diagnosis (76.88% 95%-CI {[}69.56-83.17]) of migraine was observed. For TTH the predictive value was 62.66% (95%-CI {[}57.07-68.01]) overall with a lower stability for probable (46.10%, 95%-CI {[}37.68-54.69]) compared to the confirmed diagnosis (69.71%, 95%-CI {[}23.58-37.67]). Conclusion: While confirmed migraine and confirmed TTH diagnoses seem stable over time, stability of a probable diagnosis for either headache type was lower
Self-reported neck and shoulder pain in adolescents is associated with episodic and chronic migraine
Aim: The aim of this study was to verify the association between self-reported neck/shoulder pain and migraine and to compare findings of chronic and episodic migraine in adolescents. Methods In this cross-sectional study, 601 secondary-school students filled in questionnaires about headache appearance, type and frequency, neck and shoulder pain and lifestyle factors. Results: The adjusted strength of the association between reported neck and shoulder pain and migraine (assessed in multinomial regression models) increased with the frequency of migraine: less than once a week (OR=1.40;95% CI=(0.85-2.30)), weekly (OR=2.14;95% CI=(1.42-3.24)), and at least 15 days/month (OR=7.27;95% CI=(3.42-15.44)). Conclusion: In adolescents the association between self-reported neck and shoulder pain and migraine is most pronounced in migraine with a high attack frequency
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