Transparent boundary conditions for wave propagation on unbounded domains

The numerical solution of the time dependent wave equation in an unbounded domain generally leads to a truncation of this domain, which requires the introduction of an artificial boundary with associated boundary conditions. Such nonreflecting conditions ensure the equivalence between the solution of the original problem in the unbounded region and the solution inside the artificial boundary. We consider the acoustic wave equation and derive exact transparent boundary conditions that are local in time and can be directly used in explicit methods. These conditions annihilate wave harmonics up to a given order on a spherical artificial boundary, and we show how to combine the derived boundary condition with a finite difference method. The analysis is complemented by a numerical example in two spatial dimensions that illustrates the usefulness and accuracy of transparent boundary conditions.

Controlled oxidative protein refolding using an ion-exchange column

Column-based refolding of complex and highly disulfide-bonded proteins simplifies protein renaturation at both preparative and process scale by integrating and automating a number of operations commonly used in dilution refolding. Bovine serum albumin (BSA) was used as a model protein for refolding and oxido-shuffling on an ion-exchange column to give a refolding yield of 55 % after 40 Ih incubation. Successful on-column refolding was conducted at protein concentrations of up to 10 mg/ml and refolded protein, purified from misfolded forms, was eluted directly from the column at a concentration of 3 mg/ml. This technique integrates the dithiothreitol removal, refolding, concentration and purification steps, achieving a high level of process simplification and automation, and a significant saving in reagent costs when scaled. Importantly, the current result suggests that it is possible to controllably refold disulfide-bonded proteins using common and inexpensive matrices, and that it is not always necessary to control protein-surface interactions using affinity tags and expensive chromatographic matrices. Moreover, it is possible to strictly control the oxidative refolding environment once denatured protein is bound to the ion-exchange column, thus allowing precisely controlled oxido-shuffling. (c) 2005 Elsevier B.V. All rights reserved.

C-terminal charged cluster of MscL, RKKEE, functions as a pH sensor

The RKKEE cluster of charged residues located within the cytoplasmic helix of the bacterial mechanosensitive channel, MscL, is essential for the channel function. The structure of MscL determined by x-ray crystallography and electron paramagnetic resonance spectroscopy has revealed discrepancies toward the C-terminus suggesting that the structure of the C-terminal helical bundle differs depending on the pH of the cytoplasm. In this study we examined the effect of pH as well as charge reversal and residue substitution within the RKKEE cluster on the mechanosensitivity of Escherichia coli MscL reconstituted into liposomes using the patch-clamp technique. Protonation of either positively or negatively charged residues within the cluster, achieved by changing the experimental pH or residue substitution within the RKKEE cluster, significantly increased the free energy of activation for the MscL channel due to an increase in activation pressure. Our data suggest that the orientation of the C-terminal helices relative to the aqueous medium is pH dependent, indicating that the RKKEE cluster functions as a proton sensor by adjusting the channel sensitivity to membrane tension in a pH-dependent fashion. A possible implication of our results for the physiology of bacterial cells is briefly discussed.