Brief note on the variation of constants formula for fuzzy differential equations

This note gives a theory of state transition matrices for linear systems of fuzzy differential equations. This is used to give a fuzzy version of the classical variation of constants formula. A simple example of a time-independent control system is used to illustrate the methods. While similar problems to the crisp case arise for time-dependent systems, in time-independent cases the calculations are elementary solutions of eigenvalue-eigenvector problems. In particular, for nonnegative or nonpositive matrices, the problems at each level set, can easily be solved in MATLAB to give the level sets of the fuzzy solution. (C) 2002 Elsevier Science B.V. All rights reserved.

Conformationally constrained macrocycles that mimic tripeptide beta-strands in water and aprotic solvents

The beta-strand conformation is unknown for short peptides in aqueous solution, yet it is a fundamental building block in proteins and the crucial recognition motif for proteolytic enzymes that enable formation and turnover of all proteins. To create a generalized scaffold as a peptidomimetic that is preorganized in a beta-strand, we individually synthesized a series of 15-22-membered macrocyclic analogues of tripeptides and analyzed their structures. Each cycle is highly constrained by two trans amide bonds and a planar aromatic ring with a short nonpeptidic linker between them. A measure of this ring strain is the restricted rotation of the component tyrosinyl aromatic ring (DeltaG(rot) 76.7 kJ mol(-1) (16-membered ring), 46.1 kJ mol(-1) (17-membered ring)) evidenced by variable temperature proton NMR spectra (DMF-d(7), 200-400 K). Unusually large amide coupling constants ((3)J(NH-CHalpha) 9-10 Hz) corresponding to large dihedral angles were detected in both protic and aprotic solvents for these macrocycles, consistent with a high degree of structure in solution. The temperature dependence of all amide NH chemical shifts (Deltadelta/T7-12 ppb/deg) precluded the presence of transannular hydrogen bonds that define alternative turn structures. Whereas similar sized conventional cyclic peptides usually exist in solution as an equilibrium mixture of multiple conformers, these macrocycles adopt a well-defined beta-strand structure even in water as revealed by 2-D NMR spectral data and by a structure calculation for the smallest (15-membered) and most constrained macrocycle. Macrocycles that are sufficiently constrained to exclusively adopt a beta-strand-mimicking structure in water may be useful pre-organized and generic templates for the design of compounds that interfere with beta-strand recognition in biology.

Responsiveness, affinity constants and beta-adrenoceptor reserves for isoprenaline on aortae from normo-, pre and hypertensive rats

The objective of this study was to determine the responsiveness, affinity constants and beta-adrenoceptor reserves for isoprenaline on the isolated aorta in the maturation of normotensive and hypertensive rats. The effects of a very slowly reversible antagonist, bromoacetylalprenololmenthane (BAAM), on the relaxant responses of the aortae of 5- and 14-week-old Wistar Kyoto normotensive rats (WKY) and spontaneously hypertensive rats (SHRs) to isoprenaline were determined. Five-week-old SHRs are pre-hypertensive and the aortic rings are less responsive to isoprenaline than age-matched WKY (pD(2) values: WKY, 8.40; SHRs, 8.03). Similar relaxant responses to forskolin were obtained on the aortae of 5- and 14-week-old WKY and SHRs. The K-A value for isoprenaline at the aortic beta(2)-adrenoceptors of the 5-week-old WKY was 2.1 x 10(-7) M, and similar values were obtained on the aortae of 5-week-old SHR and 14-week-old WKY and SHRs. In the maturation of the WKY aortae from 5 to 14 weeks, there was a reduction in the maximum response, a major loss of sensitivity and a loss of 2-adrenoceptor reserve for isoprenaline. On 5-week-old SHR aorta, the sensitivity to isoprenaline was 2.5-fold lower, and the beta(2)-adrenoceptor reserve was less than on age-matched WKY. In the development of hypertension on the SHR aorta from 5 to 14 weeks, there was a reduction in the maximum response to isoprenaline. At 14 weeks, the sensitivity and the 2-adrenoceptor reserve to isoprenaline were similar, but the maximum responses were lower on the SHR than WKY. As there are differences in pre-hypertensive SHR and age-matched WKY aortic responses to isoprenaline, it is no longer valid to consider that the loss of responsiveness to isoprenaline in hypertension is solely owing to the hypertension. There are no changes in affinity, but major changes in the sensitivity, maximum responses and aortic beta(2)-adrenoceptor reserves to isoprenaline in the maturation of normotensive and pre-hypertensive aortae.

Structural variations and formation constants of first-row transition metal complexes of biologically active aroylhydrazones

Iron chelators of the 2-pyridinecarbaldehyde isonicotinoylhydrazone (HPCIH) class show high potential for the treatment of iron overload diseases. In the present study, selected first-row transition metal (from Mn to Zn) complexes with HPCIH and 2-pyridinecarbaldehyde (4'-aminobenzoyl)hydrazone (HPCAH) were synthesised and characterised. Crystallography reveals that HPCAH exclusively forms bis complexes with divalent transition metals, with each ligand coordinating meridionally through its pyridine-N, imine-N and carbonyl-O atoms, forming distorted octahedral cis-MN4O2 complexes. Complexes of HPCIH were more varied and unpredictable, with metal/ligand ratios of 1:1, 1:2, 2:2 and 3:2 obtained with different metal ions. The isonicotinoyl ring N-atom in HPCIH was found to be an effective ligand, and this resulted in the varied metal/ligand ratios observed. The formation constants of divalent metal complexes with HPCIH were determined by potentiometric titrations and the values obtained were consistent with similar tridentate ligands and with the Irving-Williams order. ((C) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2003).