The Gauss-Kronecker curvature of minimal hypersurfaces in four-dimensional space forms

LetQ(4)( c) be a four-dimensional space form of constant curvature c. In this paper we show that the infimum of the absolute value of the Gauss-Kronecker curvature of a complete minimal hypersurface in Q(4)(c), c <= 0, whose Ricci curvature is bounded from below, is equal to zero. Further, we study the connected minimal hypersurfaces M(3) of a space form Q(4)( c) with constant Gauss-Kronecker curvature K. For the case c <= 0, we prove, by a local argument, that if K is constant, then K must be equal to zero. We also present a classification of complete minimal hypersurfaces of Q(4)( c) with K constant.

Effect of cholesterol on the interaction of the amphibian antimicrobial peptide DD K with liposomes

DD K is an antimicrobial peptide previously isolated from the skin of the amphibian Phyllomedusa distincta. The effect of cholesterol on synthetic DD K binding to egg lecithin liposomes was investigated by intrinsic fluorescence of tryptophan residue, measurements of kinetics of 5(6)-carboxyfluorescein (CF) leakage, dynamic light scattering and isothermal titration microcalorimetry. An 8 nm blue shift of tryptophan maximum emission fluorescence was observed when DD K was in the presence of lecithin liposomes compared to the value observed for liposomes containing 43 mol% cholesterol. The rate and the extent of CF release were also significantly reduced by the presence of cholesterol. Dynamic light scattering showed that lecithin liposome size increase from 115 to 140 nm when titrated with DD K but addition of cholesterol reduces the liposome size increments. Isothermal titration microcalorimetry studies showed that DD K binding both to liposomes containing cholesterol as to liposomes devoid of it is more entropically than enthalpically favored. Nevertheless, the peptide concentration necessary to furnish an adjustable titration curve is much higher for liposomes containing cholesterol at 43 mol% (2 mmol L-1) than in its absence (93 mu mol L-1). Apparent binding constant values were 2160 and 10,000 L mol(-1), respectively. The whole data indicate that DD K binding to phosphatidylcholine liposomes is significantly affected by cholesterol, which contributes to explain the low hemolytic activity of the peptide. (C) 2007 Elsevier Inc. All rights reserved.