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.

Characterization of high molecular weight polyethylenes using high temperature asymmetrical flow field-flow fractionation with on-line infrared, light scattering, and viscometry detection.

High temperature asymmetrical flow field-flow fractionation (HTAF4) coupled to infrared (IR), multi-angle light scattering (MALS), and viscometry (Visc) detection is introduced as a tool for the characterization of high molecular weight polyethylenes. The high molecular weight fraction strongly affects the rheological behaviour and processability of polyethylene materials and can often not be accurately resolved by current technology such as high temperature size-exclusion chromatography (HTSEC). Molecular weight (M), radius of gyration (Rg), and intrinsic viscosity [eta] of linear high density polyethylene (HDPE) and branched low density polyethylene (LDPE) samples are studied in detail by HTAF4 and are compared to HTSEC. HTAF4 showed a better separation and mass recovery than HTSEC for very high molecular weight fractions in HDPE and LDPE samples. As no stationary phase is present in an HTAF4 channel, the technique does not show the typical drawbacks associated with HTSEC analysis of high molecular weight polyethylenes, such as, exclusion effects, shear degradation, and anomalous late elution of highly branched material. HTAF4 is applied to study the relation between the molecular weight and the zero shear viscosity eta0 for high molecular weight HDPE. It was found that the zero shear viscosity values predicted from HTAF4 results are in good qualitative agreement with measured values obtained from dynamic mechanical spectroscopy (DMS) experiments, whereas eta0 values predicted from HTSEC do not show a strong correlation. The low molecular weight cutoff of HTAF4 is approximately 5x10(4) as a result of relatively large pores in the HTAF4 channel membrane. HTAF4 is, therefore, currently not suited to analyze low molecular weight materials.

Pectin microgels and their subunit structure.

High-performance size exclusion chromatography revealed that alkaline-extracted peach fruit pectin dissolved in 0.05 M NaNO3 comprised a hierarchy of at least four aggregated, macromolecular-sized species. Each of the three largest species was found to be comparable in length to the three smallest subunits of an interconnecting gel network visualized by transmission electron microscopy of pectin, rapidly dried from solution. The interconnecting subunits of the gel network were rods or segmented rods and the integrated network formed a circular gel about 1 micron in diameter. Shadowed samples prepared from 5 and 50 mM NaCl or aqueous glycerol solutions produced images of partially dissociated subunits.

Macromolecular components of tomato fruit pectin.

Chelate and alkaline-soluble pectin extracted from cell walls of pericarp tissue from mature green, turning, and red ripe (Lycopersicon esculentum Mill.) fruit (cv. Rutgers), were studied by high-performance size-exclusion chromatography. Computer-aided curve fitting of the chromatograms to a series of Gaussian-shaped components revealed that pectin from all fractions was composed of a linear combination of five macromolecular-sized species. The relative sizes of these macromolecules as obtained from their radii of gyration were 1:2:4:8:16. Dialysis against 0.05 M NaCl induced partial dissociation of the biopolymers. Apparently, the weight fraction of smaller sized species increased at the expense of larger ones. Also, the dissociation produced low-molecular-weight fragments. Behavior in the presence of 0.05 M NaCl led to the conclusion that cell wall pectin acted as if it were an aggregated mosaic, held together at least partially through noncovalent interactions.