When all solutions of x′ = −∑ qi(t) x(t − Ti(t)) oscillate

In this paper the long-term behavior of solutions to the equation in the title are examined, where q_i(t) and T_i(t) are positive. In particular, it is shown that if lim inf_{t → ∝} ∑_{i = 1}ⁿT_i(t) q_i(t) > 1/e, all solutions oscillate about 0 infinitely often.     

Cranberry changes the physicochemical surface properties of E. coli and adhesion with uroepithelial cells

Cranberries have been suggested to decrease the attachment of bacteria to uroepithelial cells (UC), thus preventing urinary tract infections, although the mechanisms are not well understood. A thermodynamic approach was used to calculate the Gibbs free energy of adhesion changes (DeltaG(adh)) for bacteria-UC interactions, based on measuring contact angles with three probe liquids. Interfacial tensions and DeltaG(adh) values were calculated for Escherichia coli HB101pDC1 (P-fimbriated) and HB101 (non-fimbriated) exposed to cranberry juice (0-27 wt.%). HB101pDC1 can form strong bonds with the Gal-Gal disaccharide receptor on uroepithelial cells, while HB101-UC interactions are only non-specific. For HB101 interacting with UC, DeltaG(adh) was always negative, suggesting favorable adhesion, and the values were insensitive to cranberry juice concentration. For the HB101pDC1-UC system, DeltaG(adh) became positive at 27wt.% cranberry juice, suggesting that adhesion was unfavorable. Acid-base (AB) interactions dominated the interfacial tensions, compared to Lifshitz-van der Waals (LW) interactions. Exposure to cranberry juice increased the AB component of the interfacial tension of HB101pDC1. LW interactions were small and insensitive to cranberry juice concentration. The number of bacteria attached to UC was quantified in batch adhesion assays and quantitatively correlated with DeltaG(adh). Since the thermodynamic approach should not agree with the experimental results when specific interactions are present, such as HB101pDC-UC ligand-receptor bonds, our results may suggest that cranberry juice disrupts bacterial ligand-UC receptor binding. These results help form the mechanistic explanation of how cranberry products can be used to prevent bacterial attachment to host tissue, and may lead to the development of better therapies based on natural products.     

Structure, electronic properties and catalytic behaviour of an activity-enhancing CYP102A1 (P450(BM3)) variant

The substrate-free crystal structure of a five-mutation directed evolution variant of CYP102A1 (P450(BM3)) with generic activity-enhancing properties ("KT2") has been determined to 1.9-? resolution. There is a close resemblance to substrate-bound structures of the wild-type enzyme (WT). The disruption of two salt bridges that link the G- and I-helices in WT causes conformational changes that break several hydrogen bonds and reduce the angle of the kink in the I-helix where dioxygen activation is thought to take place. The side-chain of a key active site residue, Phe87, is rotated in one molecule of the asymmetric unit, and the side-chains of Phe158 and Phe261 cascade into the orientations found in fatty-acid-bound forms of the enzyme. The iron is out of the porphyrin plane, towards the proximal cysteine. Unusually, the axial water ligand to the haem iron is not hydrogen-bonded to Ala264. The first electron transfer from the reductase domain to the haem domain of substrate-free KT2 is almost as fast as in palmitate-bound WT even though the reduction potential of the haem domain is only slightly more oxidising than that of substrate-free WT. However, NADPH is turned over slowly in the absence of substrate, so the catalytic cycle is gated by a step subsequent to the first electron transfer-a contrast to WT. Propylbenzene binding slightly raises the first electron transfer rate in WT but not in KT2. It is proposed that the generic rate accelerating properties of KT2 arise from the substrate-free form being in a catalytically ready conformation, such that substrate-induced changes to the structure play a less significant role in promoting the first electron transfer than in WT.     

A general synthesis of the acarnidines

A general synthetic route to the biologically active marine natural products, the acarnidines (10a–c),¹ and bolecules of the acarnidine type, is presented. The substituted homospermidine skeleton of the acarnidines was synthesised via an aldimine intermediate prepared from mono-BOC protected 1,5-diaminopentane (5) and the aldehyde (4).     

Synchrotron X‐ray CT characterization of titanium parts fabricated by additive manufacturing. Part II. Defects

Synchrotron X‐ray tomography (SXRT) has been applied to the study of defects within three‐dimensional printed titanium parts. These parts were made using the Arcam EBM^® (electron beam melting) process which uses powdered titanium alloy, Ti64 (Ti alloy with approximately 6%Al and 4%V) as the feed and an electron beam for the sintering/welding. The experiment was conducted on the Imaging and Medical Beamline of the Australian Synchrotron. The samples represent a selection of complex shapes with a variety of internal morphologies. Inspection via SXRT has revealed a number of defects which may not otherwise have been seen. The location and nature of such defects combined with detailed knowledge of the process conditions can contribute to understanding the interplay between design and manufacturing strategy. This fundamental understanding may subsequently be incorporated into process modelling, prediction of properties and the development of robust methodologies for the production of defect‐free parts.