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The incongruous "unexpected inapplicability of the Crook's fluctuation theorem" is due to an inexplicable, inappropriate use of inconsistent expressions. The girding is secure.

Most natural processes occur far from equilibrium and cannot be treated within the framework of classical thermodynamics. In 1998, Oono and Paniconi [Oono, Y. & Paniconi, M. (1998) Prog. Theor. Phys. Suppl. 130, 29-44] proposed a general phenomenological framework, steady-state thermodynamics, encompassing nonequilibrium steady states and transitions between such states. In 2001, Hatano and Sasa [Hatano, T. & Sasa, S. (2001) Phys. Rev. Lett. 86, 3463-3466] derived a testable prediction of this theory. Specifically, they were able to show that the exponential average of Y, a quantity similar to a dissipated work, should be equal to zero for arbitrary transitions between nonequilibrium steady states, -ln = 0. We have tested this strong prediction by measuring the dissipation and fluctuations of microspheres optically driven through water. We have found that -ln approximately 0 for three different nonequilibrium systems, supporting Hatano and Sasa's proposed extension of thermodynamics to arbitrary steady states and irreversible transitions.

The transition path sampling methodology is adapted to the efficient sampling of large fluctuations in nonequilibrium systems evolving according to Langevin's equations of motion. This technique is used to simulate the behavior of the bistable Maier-Stein system at noise intensities much lower than those previously possible.

We investigate the internal structure of a polymer during collapse from an expanded coil to a compact globule. Collapse is more probable in local regions of high curvature, so a smoothing of the fractal polymer structure occurs that proceeds systematically from the shortest to the longest length scales. A proposed universal scaling relationship is tested by comparison with Monte Carlo simulations. We speculate that the universal form applies to various fractal systems with local processes that promote smoothness over time. The results complement earlier work showing that on the macroscale polymer collapse proceeds by driven diffusion of the polymer ends.

There are only a very few known relations in statistical dynamics that are valid for systems driven arbitrarily far-from-equilibrium. One of these is the fluctuation theorem, which places conditions on the entropy production probability distribution of nonequilibrium systems. Another recently discovered far from equilibrium expression relates nonequilibrium measurements of the work done on a system to equilibrium free energy differences. In this paper, we derive a generalized version of the fluctuation theorem for stochastic, microscopically reversible dynamics. Invoking this generalized theorem provides a succinct proof of the nonequilibrium work relation.

Humicola lanuginosa lipase (HIL) and Rhizomucor miehei lipase (RrnL), isolated from commercial preparations of Lipolase and Lipozyme, respectively, were solubilized in AOT-stabilized water-in-oil (w/o) microemulsions in n-heptane and aspects of their hydrolysis and condensation activity examined. The temperature dependence of HIL hydrolysis activity in unbuffered R = 10 microemulsions matched very closely that for tributyrin hydrolysis by Lipolase in an aqueous emulsion assay. Apparent activation energies were measured as 13 +/- 2 and 15 +/- 2 kJ mol / respectively. Condensation activity, however, was essentially independent of temperature over the range 5 degrees to 37 degrees C. The stability of HIL over a 30-day period was very good at all pH levels (6.1, 7.2, 9.3) and R values studied (5, 7.5, 10, 20), except when high pHs and low R values were combined. The excellent stability was reflected by the linearity of the productivity profiles which facilitate system optimization. The temperature dependence of RmL hydrolysis activity toward pNPC(4) showed a maximum at 40 degrees C and an apparent E(act) = 20 +/- 2 kJ mol(-1) was calculated based on the linear region of the profile (5 degrees to 40 degrees C). RmL esterification activity showed only a slight dependence on temperature over the studied range (0 degrees to 40 degrees C) and an apparent E(act) = 5 +/- 1 kJ mol(-1) was measured for octyl decanoate synthesis. Both RmL and HIL, therefore, have potential for application in low temperature biotransformations in microemulsion-based media. The stability of RmL over a 30-day period was good in R = 7.5 and R = 10 microemulsions containing pH 6.1 buffer, and this was reflected in the linearity of their respective productivity profiles. RmL stability was markedly poorer at more alkaline pH, however, and proved to be sensitive to relatively small changes in the R value.

Lipolase and Lipozyme are produced in large quantities (as a result of genetic engineering and overexpression) for the detergents market and provide a cheap source of highly active biocatalysts. Humicola lanuginosa lipase (HIL) and Rhizomucor miehei lipase (RmL) have been isolated in partially purified form from commercial preparations of Lipolase and Lipozyme, respectively. These lipases were solubilized in Aerosol-OT (AOT)-stabilized water-in-oil (w/o) microemulsions in n-heptane. HIL and RmL activity in these microemulsions was assayed by spectrophotometric measurement of the initial rate of p-nitophenyl butyrate hydrolysis, and by chromatographic determination of the initial rate of octyl decanoate synthesis from 1-octanol and decanoic acid. The hydrolytic activity of HIL in microemulsions measured as a function of buffer pH prior to dispersal, followed a sigmoidal profile with the highest activities observed at alkaline pHs. This broadly matches the pH-activity profile for tributyrin hydrolysis by Lipolase in an aqueous emulsion assay. The hydrolytic activity of RmL in the same microemulsions, measured as a function of pH, gave a bell-shaped profile with a maximum activity at pH 7.5. Again, the observed pH-activity profile was similar to that reported for a purified RmL in a tributyrin-based aqueous emulsion assay. In contrast, the esterification activity exhibited by both HIL and RmL in AOT microemulsions over the available range pH 6.1 to 10.4, decreases as the pH increases, most likely reflecting the effect of substrate ionization. The dependence of the hydrolytic and condensation activity of HIL on R, the mole ratio of water to surfactant, were similar with both profiles exhibiting a maximum at R = 5. The hydrolytic and esterification activities of RmL followed similar R-dependent profiles, but the profiles in this case exhibited a maximum at R = 10. The water activities at these R values were directly measured as 0.78 and 0.9, respectively. Measured water activities were unperturbed by the presence of lipase at the concentrations used in these studies.