A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

Ca(2+)-mediated thiolysis of peptide-resin linkage as an option for preparing protected peptide thioesters

A mild new procedure for preparing protected peptide thioesters, based oil Ca(2+)-assisted thiolysis of peptide-Kaiser oxime resin (KOR) linkage, is described. Ac-Ile-Ser(Bzl)-Asp(OcHx)-SR (Ac: acetyl; Bzl: benzyl; cHx: cyclohexyl), model peptide, was readily released from the resin by incubating the peptide-KOR at 60 degrees C in mixtures of DMF with n-butanethiol [R = (CH(2))(3)CH(3)] or ethyl 3-mercaptopropionate [R = (CH(2))(2)COOCHCH(3)] containing Ca(CH(3)COO)(2). After serine and aspartic acid side-chain deprotection under acid conditions, Ac-Ile-Ser-Asp-S(CH(2))(2)COOCH(2)CH(3) was successfully obtained with good quality and high yield. This type of C-terminal modified peptide may act as an excellent acyl donor in peptide segment condensation by the thioester method, native chemical ligation and enzymatic methods. (c) 2008 Elsevier Ltd. All rights reserved.