Linear noise approximation is valid over limited times for any chemical system that is sufficiently large.

The linear noise approximation (LNA) is a way of approximating the stochastic time evolution of a well-stirred chemically reacting system. It can be obtained either as the lowest order correction to the deterministic chemical reaction rate equation (RRE) in van Kampen's system-size expansion of the chemical master equation (CME), or by linearising the two-term-truncated chemical Kramers-Moyal equation. However, neither of those derivations sheds much light on the validity of the LNA. The problematic character of the system-size expansion of the CME for some chemical systems, the arbitrariness of truncating the chemical Kramers-Moyal equation at two terms, and the sometimes poor agreement of the LNA with the solution of the CME, have all raised concerns about the validity and usefulness of the LNA. Here, the authors argue that these concerns can be resolved by viewing the LNA as an approximation of the chemical Langevin equation (CLE). This view is already implicit in Gardiner's derivation of the LNA from the truncated Kramers-Moyal equation, as that equation is mathematically equivalent to the CLE. However, the CLE can be more convincingly derived in a way that does not involve either the truncated Kramers-Moyal equation or the system-size expansion. This derivation shows that the CLE will be valid, at least for a limited span of time, for any system that is sufficiently close to the thermodynamic (large-system) limit. The relatively easy derivation of the LNA from the CLE shows that the LNA shares the CLE's conditions of validity, and it also suggests that what the LNA really gives us is a description of the initial departure of the CLE from the RRE as we back away from the thermodynamic limit to a large but finite system. The authors show that this approach to the LNA simplifies its derivation, clarifies its limitations, and affords an easier path to its solution.

Legitimacy of the stochastic Michaelis-Menten approximation.

Michaelis-Menten kinetics are commonly used to represent enzyme-catalysed reactions in biochemical models. The Michaelis-Menten approximation has been thoroughly studied in the context of traditional differential equation models. The presence of small concentrations in biochemical systems, however, encourages the conversion to a discrete stochastic representation. It is shown that the Michaelis-Menten approximation is applicable in discrete stochastic models and that the validity conditions are the same as in the deterministic regime. The authors then compare the Michaelis-Menten approximation to a procedure called the slow-scale stochastic simulation algorithm (ssSSA). The theory underlying the ssSSA implies a formula that seems in some cases to be different from the well-known Michaelis-Menten formula. Here those differences are examined, and some special cases of the stochastic formulas are confirmed using a first-passage time analysis. This exercise serves to place the conventional Michaelis-Menten formula in a broader rigorous theoretical framework.

Education and occupations preceding Parkinson disease: a population-based case-control study.

OBJECTIVE: To investigate the association of Parkinson disease (PD) with education and occupations using a case-control study design. METHODS: The authors used the medical records-linkage system of the Rochester Epidemiology Project to identify all subjects who developed PD in Olmsted County, MN, from 1976 through 1995. Each incident case was matched by age (+/-1 year) and sex to a general population control. The authors collected information about education and occupations using two independent sources of data: a review of the complete medical records in the system and a telephone interview. Occupations were coded using the 1980 Standard Occupational Classification. RESULTS: Subjects with 9 or more years of education were at increased risk of PD (OR = 2.0; 95% CI = 1.1 to 3.6; p = 0.02), and there was a trend of increasing risk with increasing education (test for linear trend, p = 0.02; medical records data). Physicians were at significantly increased risk of PD using both sources of occupational data. By contrast, four occupational groups showed a significantly decreased risk of PD using one source of data: construction and extractive workers (e.g., miners, oil well drillers), production workers (e.g., machine operators, fabricators), metal workers, and engineers. These associations with increased or decreased risk did not change noticeably after adjustment for education. CONCLUSION: Subjects with higher education and physicians have an increased risk of Parkinson disease (PD), while subjects with some occupations presumed to involve high physical activity have a decreased risk of PD.