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Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry.  相似文献   
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Polymers conjugated to the exterior of a protein mediate its interactions with surroundings, enhance its processability and can be used to direct its macroscopic assemblies. Most studies to date have focused on peptide–polymer conjugates based on hydrophilic polymers. Engineering amphiphilicity into protein motifs by covalently linking hydrophobic polymers has the potential to interface peptides and proteins with synthetic polymers, organic solvents, and lipids to fabricate functional hybrid materials. Here, we synthesized amphiphilic peptide–polymer conjugates in which a hydrophobic polymer is conjugated to the exterior of a heme‐binding four‐helix bundle and systematically investigated the effects of the hydrophobicity of the conjugated polymer on the peptide structure and the integrity of the heme‐binding pocket. In aqueous solution with surfactants present, the side‐conjugated hydrophobic polymers unfold peptides and may induce an α‐helix to β‐sheet conformational transition. These effects decrease as the polymer becomes less hydrophobic and directly correlate with the polymer hydrophobicity. Upon adding organic solvent to solubilize the hydrophobic polymers, however, the deleterious effects of hydrophobic polymers on the peptide structures can be eliminated. Present studies demonstrate that protein structure is sensitive to the local environment. It is feasible to dissolve amphiphilic peptide–polymer conjugates in organic solvents to enhance their solution processability while maintaining the protein structures.

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FUB-AMB, an indazole carboxamide synthetic cannabinoid recreational drug, was one of the compounds most frequently reported to governmental agencies worldwide between 2016 and 2019. It has been implicated in intoxications and fatalities, posing a risk to public health. In the current study, FUB-AMB was incubated with human liver microsomes (HLM) to assess its metabolic fate and stability and to determine if its major ester hydrolysis metabolite (M1) was present in 12 authentic forensic human blood samples from driving under the influence of drug cases and postmortem investigations using UHPLC–MS/MS. FUB-AMB was rapidly metabolized in HLM, generating M1 that was stable through a 120-min incubation period, a finding that indicates a potential long detection window in human biological samples. M1 was identified in all blood samples, and no parent drug was detected. The authors propose that M1 is a reliable marker for inclusion in laboratory blood screens for FUB-AMB; this metabolite may be pharmacologically active like its precursor FUB-AMB. M1 frequently appears in samples in which the parent drug is undetectable and can point to the causative agent. The results suggest that it is imperative that synthetic cannabinoid laboratory assay panels include metabolites, especially known or potential pharmacologically active metabolites, particularly for compounds with short half-lives.  相似文献   
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