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

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 $\Omega^{-3/2}$ for reaction systems which do not obey detailed balance and at least accurate to order $\Omega^{-2}$ for systems obeying detailed balance, where $\Omega$ 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 $\Omega^{-1/2}$ and variance estimates accurate to order $\Omega^{-3/2}$. 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 potential for linking cohort participants to official criminal records:a pilot study using the Avon Longitudinal Study of Parents and Children (ALSPAC)

Introduction: Linking longitudinal cohort resources with police-recorded records of criminal activity has the potential to inform public health style approaches to policing, and may reduce potential sources of bias from self-reported criminal data collected by cohort studies. A pilot linkage of police records to the Avon Longitudinal Study of Parents and Children (ALSPAC) allows us to consider the acceptability of this linkage, its utility as a data resource, differences in self-reported crime according to consent status for data linkage, and the appropriate governance mechanism to support such a linkage. Methods: We carried out a pilot study linking data from the ALSPAC birth cohort to Ministry of Justice (MoJ) records on criminal cautions and convictions. This pilot was conducted on a fully anonymous basis, meaning we cannot link the identified records to any participant or the wider information within the dataset. Using ALSPAC data, we used summary statistics to investigate differences in socio-economic background and self-reported criminal activity by consent status for crime linkage. We used MoJ records to identify the geographic and temporal concentration of criminality in the ALSPAC cohort. Results: We found that the linkage appears acceptable to participants (4% of the sample opted out), levels of criminal caution and conviction are high enough to support research, and that the majority of crimes occurred in Avon & Somerset (the policing area local to ALSPAC). Those who did not respond to consent requests had higher levels of self-reported criminal behaviour compared to participants who provided explicit consent. Conclusions: These findings suggest that data linkage in ALSPAC provides opportunities to study criminal behaviour and that linked individual-level records could provide robust research in the area. Our findings also suggest the potential for bias when only including participants who have explicitly consented to data linkage, highlighting the limitations of opt-in consent strategies

TeV Particle Astrophysics II: Summary comments

A unifying theme of this conference was the use of different approaches to understand astrophysical sources of energetic particles in the TeV range and above. In this summary I review how gamma-ray astronomy, neutrino astronomy and (to some extent) gravitational wave astronomy provide complementary avenues to understanding the origin and role of high-energy particles in energetic astrophysical sources.Comment: 6 pages, 4 figures; Conference summary talk for "TeV Particle Astrophysics II" at University of Wisconsin, Madison, 28-31 August 200

A stochastic automaton shows how enzyme assemblies may contribute to metabolic efficiency

<p>Abstract</p> <p>Background</p> <p>The advantages of grouping enzymes into metabolons and into higher order structures have long been debated. To quantify these advantages, we have developed a stochastic automaton that allows experiments to be performed in a virtual bacterium with both a membrane and a cytoplasm. We have investigated the general case of transport and metabolism as inspired by the phosphoenolpyruvate:sugar phosphotransferase system (PTS) for glucose importation and by glycolysis.</p> <p>Results</p> <p>We show that PTS and glycolytic metabolons can increase production of pyruvate eightfold at low concentrations of phosphoenolpyruvate. A fourfold increase in the numbers of enzyme EI led to a 40% increase in pyruvate production, similar to that observed <it>in vivo </it>in the presence of glucose. Although little improvement resulted from the assembly of metabolons into a hyperstructure, such assembly can generate gradients of metabolites and signaling molecules.</p> <p>Conclusion</p> <p><it>in silico </it>experiments may be performed successfully using stochastic automata such as HSIM (Hyperstructure Simulator) to help answer fundamental questions in metabolism about the properties of molecular assemblies and to devise strategies to modify such assemblies for biotechnological ends.</p

1968

Maintenance of Golf Carts by Thomas Pepe (page 1) Why a Golf Course Superintendent Should Play Golf by Stephen Skowronski (2) Tree Pruning by Martin Walsh (3) Golf Course Labor: A Dilemma by Robert Barber (5) Turf Problems by Alexander M. Radko (A-1) 1967 Turfgrass Problems by Lee Record (A-3) Southern Turfgrass Production and Problems by Ralph W. White Jr. (A-5) Canadian Turf Grass Production and Problems by David Moote (A-8) Turf Research Abroad by C.R. Skogley (A-13) Turf Research at Home by Victor B. Younger (A-14) Turfgrass Research - An Industrial Approach by J. A. Simmons (A-16) Cutting Labor Costs in Turfgrass Managemnt by Tom Mascaro (A-24) The Reluctant human by John W. Denison (A-28) The Problem Drinker - Management Responsibility by G.E. Osburn (A-31) Contemporary Design Standards by Geoffrey S. Cornish (A-34) Construction - Superintendents\u27 Viewpoint by Robert E. Grant (A-36) Construction b Contract and the Role of the Superintendent by David Canavan (A-39) Seed Production by Robert J. Peterson (A-41) Cemetery Turf Maintenance on a High and Low Budget by Stanley Sosenski (A-45) Ten Steps to a Good Lawn by John Zak (A-49) Review of Herbicides for Turf Weed Control by Alvin A. Baber (A-53

1973

Skunks Shoot Back by William Stewart (page 1) The Daily Plan: A Management Factor by Rob McIntyre (2) Teed Off by Samuel Pavadore (3) A Responsible Neighbor by Gerald Moscato (4) Drainage by David Clement (A-1) Fairway Renovation at Baltusrol Golf Club by Joseph R. Flaherty (A-4) Converting to Kentucky Bluegrass Fairways by Thomas Rewinski (A-10) Grooming the Golf Course by Melvin B. Lucas, Jr. (A-12) Turf Diseases of 1972, Controls and Prevention for 1973 by Stanley J. Zontek (A-13) Noncropland Weed Control by John E. Gallagher (A-16) Soil Factors Affecting Arsenic Toxicity by Robert N. Carrow (A-24) The Necessity of Cart Paths and Traffic Regulations by William G. Buchanan (A-27) Herbicides for Turfgrass Areas by John A. Jagschitz (A-29) Perspectives on Lawn Making and Keeping by Robert Schery (A-33) Stadium Turf Maintenance by George P. Toma (A-39) Highway Turfgrass by Robert W. Duell (A-44) Cemetery Maintenance by Martin Stolpe (A-50) Keeping Records by Al Barauskas (A-54) Planning Capital Expenditures by Sherwood A. Moore (A-59) British Golf Course Architecture -Historical Influences- Current Trends by F.W. Hawtree (A-64) Golf Course Architecture in North America By Geoffrey S. Cornish (A-70

Viability Conditions for a Compartmentalized Protometabolic System: A Semi-Empirical Approach

In this work we attempt to find out the extent to which realistic prebiotic compartments, such as fatty acid vesicles, would constrain the chemical network dynamics that could have sustained a minimal form of metabolism. We combine experimental and simulation results to establish the conditions under which a reaction network with a catalytically closed organization (more specifically, an ()-system) would overcome the potential problem of self-suffocation that arises from the limited accessibility of nutrients to its internal reaction domain. The relationship between the permeability of the membrane, the lifetime of the key catalysts and their efficiency (reaction rate enhancement) turns out to be critical. In particular, we show how permeability values constrain the characteristic time scale of the bounded protometabolic processes. From this concrete and illustrative example we finally extend the discussion to a wider evolutionary context