720 research outputs found
Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions
A stochastic model of autocatalytic chemical reactions is studied both
numerically and analytically. The van Kampen perturbative scheme is
implemented, beyond the second order approximation, so to capture the non
Gaussianity traits as displayed by the simulations. The method is targeted to
the characterization of the third moments of the distribution of fluctuations,
originating from a system of four populations in mutual interaction. The theory
predictions agree well with the simulations, pointing to the validity of the
van Kampen expansion beyond the conventional Gaussian solution.Comment: 15 pages, 8 figures, submitted to Phys. Rev.
Steady-state fluctuations of a genetic feedback loop:an exact solution
Genetic feedback loops in cells break detailed balance and involve
bimolecular reactions; hence exact solutions revealing the nature of the
stochastic fluctuations in these loops are lacking. We here consider the master
equation for a gene regulatory feedback loop: a gene produces protein which
then binds to the promoter of the same gene and regulates its expression. The
protein degrades in its free and bound forms. This network breaks detailed
balance and involves a single bimolecular reaction step. We provide an exact
solution of the steady-state master equation for arbitrary values of the
parameters, and present simplified solutions for a number of special cases. The
full parametric dependence of the analytical non-equilibrium steady-state
probability distribution is verified by direct numerical solution of the master
equations. For the case where the degradation rate of bound and free protein is
the same, our solution is at variance with a previous claim of an exact
solution (Hornos et al, Phys. Rev. E {\bf 72}, 051907 (2005) and subsequent
studies). We show explicitly that this is due to an unphysical formulation of
the underlying master equation in those studies.Comment: 31 pages, 3 figures. Accepted for publication in the Journal of
Chemical Physics (2012
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
Mathematical Model of the Impact of a Nonantibiotic Treatment for Clostridium difficile on the Endemic Prevalence of Vancomycin-Resistant Enterococci in a Hospital Setting
Introduction. Clostridium difficile-associated disease (CDAD) is treated using antibiotics, which often leads to the emergence of antibiotic-resistant bacteria such as vancomycin-resistant enterococci (VRE). This study estimated the impact of a non antibiotic treatment for CDAD on VRE prevalence. Methods. A previously published model describing the impact of in-hospital antibiotic use on VRE prevalence was adapted to include CDAD treatment. Simulations compared the prevalence of VRE when nonantibiotic versus antibiotic therapy was used. Results. Nonantibiotic treatment in 50% of CDAD patients resulted in an 18% relative reduction in the prevalence of VRE colonization compared with antibiotic use only. Sensitivity analysis found the model to be most sensitive to rates of antibiotic initiation and discontinuation, prevalence of VRE in admitted patients, length of stay of colonized patients, probability of CDAD acquisition, and hand-washing compliance. Conclusion. Nonantibiotic treatment of patients hospitalized with CDAD may significantly reduce the incidence of VRE colonization
Accurate discretization of advection-diffusion equations
We present an exact mathematical transformation which converts a wide class
of advection-diffusion equations into a form allowing simple and direct spatial
discretization in all dimensions, and thus the construction of accurate and
more efficient numerical algorithms. These discretized forms can also be viewed
as master equations which provides an alternative mesoscopic interpretation of
advection-diffusion processes in terms of diffusion with spatially varying
hopping rates
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
The use of computer simulation modeling to estimate complications in patients with type 2 diabetes mellitus : comparative validation of the cornerstone diabetes simulation model
Objective The objective of this study was to assess the validity of the Cornerstone Diabetes Simulation (CDS), a Microsoft Excel(R)-based patient-level simulation for type 2 diabetes mellitus based on risk equations from the revised United Kingdom Prospective Diabetes Study Outcomes Model (UKPDS-OM2, also known as UKPDS 82). Methods Three levels of validation were conducted. Internal validation was assessed through independent review and model stress-testing. External validation was addressed by populating the CDS with baseline characteristics and treatment effects from three major diabetes clinical trials used in the Fifth Mount Hood Diabetes Challenge (MH5) for computer simulation models. Cross-validation of predicted outcomes was tested versus eight models that participated in the MH5. Simulated results were compared with observed clinical outcomes via the coefficient of determination (R-2) for both the absolute risk of each clinical outcome and the difference in absolute risk between control and intervention arm in each trial. We ensured transparency of all model inputs and assumptions in reporting. Results The CDS could be used to predict 18 of 39 single and composite endpoints across the three trials. The model obtained an R-2 of 0.637 for predicted versus observed absolute risks, and an R-2 of 0.442 for predicted versus observed risk differences between control and intervention. Among the other eight models, only one obtained a higher R-2 value under both definitions, albeit based on only four predicted endpoints. Conclusions The CDS provides good predictions of diabetes-related complications when compared to observed trial outcomes and previously validated models. The model has value as a validated tool in cost-effectiveness evaluations
Directed cell migration in the presence of obstacles
BACKGROUND: Chemotactic movement is a common feature of many cells and microscopic organisms. In vivo, chemotactic cells have to follow a chemotactic gradient and simultaneously avoid the numerous obstacles present in their migratory path towards the chemotactic source. It is not clear how cells detect and avoid obstacles, in particular whether they need a specialized biological mechanism to do so. RESULTS: We propose that cells can sense the presence of obstacles and avoid them because obstacles interfere with the chemical field. We build a model to test this hypothesis and find that this naturally enables efficient at-a-distance sensing to be achieved with no need for a specific and active obstacle-sensing mechanism. We find that (i) the efficiency of obstacle avoidance depends strongly on whether the chemotactic chemical reacts or remains unabsorbed at the obstacle surface. In particular, it is found that chemotactic cells generally avoid absorbing barriers much more easily than non-absorbing ones. (ii) The typically low noise in a cell's motion hinders the ability to avoid obstacles. We also derive an expression estimating the typical distance traveled by chemotactic cells in a 3D random distribution of obstacles before capture; this is a measure of the distance over which chemotaxis is viable as a means of directing cells from one point to another in vivo. CONCLUSION: Chemotactic cells, in many cases, can avoid obstacles by simply following the spatially perturbed chemical gradients around obstacles. It is thus unlikely that they have developed specialized mechanisms to cope with environments having low to moderate concentrations of obstacles
Effects of bursty protein production on the noisy oscillatory properties of downstream pathways
Experiments show that proteins are translated in sharp bursts; similar bursty phenomena have been observed for protein import into compartments. Here we investigate the effect of burstiness in protein expression and import on the stochastic properties of downstream pathways. We consider two identical pathways with equal mean input rates, except in one pathway proteins are input one at a time and in the other proteins are input in bursts. Deterministically the dynamics of these two pathways are indistinguishable. However the stochastic behavior falls in three categories: (i) both pathways display or do not display noise-induced oscillations; (ii) the non-bursty input pathway displays noise-induced oscillations whereas the bursty one does not; (iii) the reverse of (ii). We derive necessary conditions for these three cases to classify systems involving autocatalysis, trimerization and genetic feedback loops. Our results suggest that single cell rhythms can be controlled by regulation of burstiness in protein production
Three Styles in the Study of Violence
This is a postprint (accepted manuscript) version of the article published in Reviews in Anthropology 37:1-19. The final version of the article can be found at http://dx.doi.org/10.1080/00938150701829525 (login required to access content). The version made available in Digital Common was supplied by the author.Accepted Manuscripttru
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