873 research outputs found
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
Numerical Comparison of Experimentally Measured Ultrasound through a Multilayered Specimen
The integrity of bonded structures is of paramount importance in the safe and reliable operation of aircraft equipment. Fuselages, helicopter rotor blades and nose cones are multilayered composite structures bonded together. The operational readiness and security of these units depend to a large extent on the integrity of the interfacial bonds. Adhesive and cohesive strength studies do not appear promising because failure is really dominated by defects and not by some average physical properties of the adhesive and the interface [1].</p
Passive Scalar: Scaling Exponents and Realizability
An isotropic passive scalar field advected by a rapidly-varying velocity
field is studied. The tail of the probability distribution for
the difference in across an inertial-range distance is found
to be Gaussian. Scaling exponents of moments of increase as
or faster at large order , if a mean dissipation conditioned on is
a nondecreasing function of . The computed numerically
under the so-called linear ansatz is found to be realizable. Some classes of
gentle modifications of the linear ansatz are not realizable.Comment: Substantially revised to conform with published version. Revtex (4
pages) with 2 postscript figures. Send email to [email protected]
Recommended from our members
Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations
We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated
The Astrophysical Reaction Rate for the 18F(p,α) 15O Reaction
Proton and alpha widths for a 3/2+ ( l p = 0) state in 19Ne at Ex-7.1 MeV have been extracted using the results of recent measurements of the 18F(p,α)15O reaction. This l p = 0 resonance dominates the astrophysical reaction rates at temperatures T9\u3e0.5
Preparations for Recoil Detection System at the Cooler T-Site
This research was sponsored by the National Science Foundation Grant NSF PHY-931478
Unstable decay and state selection II
The decay of unstable states when several metastable states are available for
occupation is investigated using path-integral techniques. Specifically, a
method is described which allows the probabilities with which the metastable
states are occupied to be calculated by finding optimal paths, and fluctuations
about them, in the weak noise limit. The method is illustrated on a system
described by two coupled Langevin equations, which are found in the study of
instabilities in fluid dynamics and superconductivity. The problem involves a
subtle interplay between non-linearities and noise, and a naive approximation
scheme which does not take this into account is shown to be unsatisfactory. The
use of optimal paths is briefly reviewed and then applied to finding the
conditional probability of ending up in one of the metastable states, having
begun in the unstable state. There are several aspects of the calculation which
distinguish it from most others involving optimal paths: (i) the paths do not
begin and end on an attractor, and moreover, the final point is to a large
extent arbitrary, (ii) the interplay between the fluctuations and the leading
order contribution are at the heart of the method, and (iii) the final result
involves quantities which are not exponentially small in the noise strength.
This final result, which gives the probability of a particular state being
selected in terms of the parameters of the dynamics, is remarkably simple and
agrees well with the results of numerical simulations. The method should be
applicable to similar problems in a number of other areas such as state
selection in lasers, activationless chemical reactions and population dynamics
in fluctuating environments.Comment: 28 pages, 6 figures. Accepted for publication in Phys. Rev.
Resonant alpha capture by 7Be and 7Li
Resonances at Eα=401,814, and 953 keV were observed in the 7Li(α,γ) reaction. From the thick target yields the corresponding states in 11B at 8920, 9185, and 9274 keV were found to have center-of-mass resonance strengths of 0.0088±0.0014, 0.317±0.047, and 1.72±0.17 eV, respectively. The radiative widths deduced for the latter two states are 0.17-0.03+0.06 and 1.15±0.16 eV, respectively. Using a 40 mCi 7Be target, α-capture resonances were observed at Eα=884 (11C* = 8105 keV) and 1376 (11C* = 8421 keV) keV with center-of-mass resonance strengths of 0.331±0.041 and 3.80±0.57 eV, respectively. The radiative widths deduced for these states are 0.350±0.056 and 3.1±1.3 eV, respectively. The observed decay rates are compared with theoretical calculations
Evaluation of rate law approximations in bottom-up kinetic models of metabolism.
BackgroundThe mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question.ResultsIn this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction mass action rate law that removes the role of the enzyme from the reaction kinetics. We utilized in vivo data for the human red blood cell to compare the effect of rate law choices against the backdrop of physiological flux and concentration differences. We found that the Michaelis-Menten rate law with measured enzyme parameters yields an excellent approximation of the full system dynamics, while other assumptions cause greater discrepancies in system dynamic behavior. However, iteratively replacing mechanistic rate laws with approximations resulted in a model that retains a high correlation with the true model behavior. Investigating this consistency, we determined that the order of magnitude differences among fluxes and concentrations in the network were greatly influential on the network dynamics. We further identified reaction features such as thermodynamic reversibility, high substrate concentration, and lack of allosteric regulation, which make certain reactions more suitable for rate law approximations.ConclusionsOverall, our work generally supports the use of approximate rate laws when building large scale kinetic models, due to the key role that physiologically meaningful flux and concentration ranges play in determining network dynamics. However, we also showed that detailed mechanistic models show a clear benefit in prediction accuracy when data is available. The work here should help to provide guidance to future kinetic modeling efforts on the choice of rate law and parameterization approaches
- …