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

On Radiation Pressure in Static, Dusty HII Regions

Radiation pressure acting on gas and dust causes HII regions to have central densities that are lower than the density near the ionized boundary. HII regions in static equilibrium comprise a family of similarity solutions, parametrized by 3 parameters: beta, gamma, and the product (Q_0 n_rms); beta characterizes the stellar spectrum, gamma characterizes the dust/gas ratio, Q_0 is the ionizing output from the star (photons/s), and n_rms is the rms density within the ionized region. Adopting standard values for beta and gamma, varying (Q_0 n_rms) generates a one-parameter family of density profiles, ranging from nearly uniform density (small Q_0 n_rms), to hollow-sphere HII regions (large Q_0 n_rms). When (Q_0 n_rms) exceeds 10^{52} cm^{-3} s^{-1}, dusty HII regions have conspicuous central cavities, even if no stellar wind is present. For given beta, gamma and (Q_0 n_rms), a fourth quantity, which can be Q_0, determines the overall size and density of the HII region. Examples of density and emissivity profiles are given. We show how quantities of interest -- such as the peak-to-center emissivity ratio, the rms-to-mean density ratio, the edge-to-rms density ratio, and the fraction of the ionizing photons absorbed by the gas -- depend on the 3 parameters beta, gamma, and (Q_0 n_rms). For dusty HII regions, compression of the gas and dust into an ionized shell results in a substantial increase in the fraction of the >13.6 eV photons that actually ionize H (relative to a uniform density HII region with the same dust/gas ratio and density n=n_rms). We discuss the extent to which radial drift of dust grains in HII regions can alter the dust-to-gas ratio. The applicability of these solutions to real HII regions is discussed.Comment: New material and figures that were not in version 1. To appear in Ap

A thermal model for adaptive competition in a market

New continuous and stochastic extensions of the minority game, devised as a fundamental model for a market of competitive agents, are introduced and studied in the context of statistical physics. The new formulation reproduces the key features of the original model, without the need for some of its special assumptions and, most importantly, it demonstrates the crucial role of stochastic decision-making. Furthermore, this formulation provides the exact but novel non-linear equations for the dynamics of the system.Comment: 4 RevTeX pages, 3 EPS figures. Revised versio

Reinforced communication and social navigation generate groups in model networks

To investigate the role of information flow in group formation, we introduce a model of communication and social navigation. We let agents gather information in an idealized network society, and demonstrate that heterogeneous groups can evolve without presuming that individuals have different interests. In our scenario, individuals' access to global information is constrained by local communication with the nearest neighbors on a dynamic network. The result is reinforced interests among like-minded agents in modular networks; the flow of information works as a glue that keeps individuals together. The model explains group formation in terms of limited information access and highlights global broadcasting of information as a way to counterbalance this fragmentation. To illustrate how the information constraints imposed by the communication structure affects future development of real-world systems, we extrapolate dynamics from the topology of four social networks.Comment: 7 pages, 3 figure

The Deuterium Abundance at z=0.701 towards QSO 1718+4807

We present constraints on the deuterium to hydrogen ratio (D/H) in the metal-poor gas cloud at redshift $z=0.701$ towards QSO 1718+4807. We use new Keck spectra in addition to Hubble Space Telescope (HST) and International Ultraviolet Explorer (IUE) spectra. We use an improved redshift and a lower \HI column density to model the absorption. The HST spectrum shows an asymmetric Lyman-$\alpha$ (\lya) feature which is produced by either \HI at a second velocity, or a high abundance of D. Three models with a single simple H+D component give $8 \times 10^{-5} < D/H < 57 \times 10^{-5}$ (95%), a much larger range than reported by Webb et al (1997a,b). A more sophisticated velocity distribution, or a second component is necessary for lower D/H. With two components, which could be a part of one absorbing structure, or separate clouds in a galaxy halo, we find $D/H < 50 \times 10^{-5}$. We do not know if this second component is present, but it is reasonable because 40 -- 100% of absorption systems with similar redshifts and \HI column densities have more than one component.Comment: 13 pages, 4 figures, to appear in the Astronomical Journal (Jan 1999

Church and the End Times

The Rapture, by Charles Feinberg; The Resurrections and Judgments, by Arthur B. Whiting; The Tribulation, by Gerald B. Stanton; The Millennium, by Louis T. Talbot. As heard over The Bible Institute Hour

Church and the End Times

As heard over the Bible Institute Hour; four important Bible themes.https://digitalcommons.biola.edu/biola-radio-pubs/1000/thumbnail.jp

Effect of Formaldehyde Treatment on Bacteria-Infected Hatching Eggs of Gallus gallus domesticus Linnaeus, 1758

The effectiveness of formaldehyde egg disinfection is well documented in literature despite its reported toxicity. This study focused on the need for an optimum formaldehyde concentration (FC) that significantly reduces microbial load with minimal damaging effect on egg viability and hatchability. Using a true experimental design, bacterial load on formaldehyde-treated (FT) and control groups of eggs and hatchability were compared. Gram-staining and biochemical tests identified five bacterial species: Escherichia coli, Enterobacter sp., Bacillus cereus, Staphylococcus aureus and Micrococcus sp. with the two coliform bacteria, E. coli and Enterobacter sp., dominating. Comparison of median differences of bacterial load on eggs before and after formaldehyde treatment by Wilcoxon Signed-Rank Test showed marginal significance in bacterial load reduction (Z = -2.016, P = 0.044). This difference was observed for bacterial load between the control group (CG) and the FT group with FC 30/20 ml/g (U = 3.0, P = 0.047). The hatchability of the CG differed significantly from four FT groups of eggs with FC 30/20 ml/g showing the highest level of significance [χ² (1) = 14.71; P = 0.0001]. A FC of 30/20 ml/g produced the best domestic fowl egg disinfection compared to other FCs and hatchability decreased with increasing formalin volume