Computing Zeros of Analytic Functions in the Complex Plane without using Derivatives

A new approach to evaluating all multiple complex roots of analytical function f(z) confined to the specified rectangular domain of complex plane has been developed and implemented in Fortran code. Generally f (z), despite being holomorphic function, does not have a closed analytical form thereby inhibiting explicit evaluation of its derivatives. The latter constraint poses a major challenge to implementation of the robust numerical algorithm. This work is at the instrumental level and provides an enabling tool for solving a broad class of eigenvalue problems and polynomial approximations.

Role of conformational constraints of position 7 of the disulphide bridge of h-alpha-CGRP derivatives in their agonist versus antagonist properties

Previous structure-activity studies have shown that the disulphide bridge of calcitonin gene-related peptide (CGRP) is important for the highly potent, CGRP receptor-mediated effects of this peptide. In this study penicillamine (Pen) was substituted for one or both of the cysteinyl residues to determine conformational and topographical properties of the disulphide bridge favourable for binding to CGRP receptors and/or receptor activation. Pen constrains the conformational flexibility of disulphide bridges in other peptides. Binding affinities were measured using a radioligand binding assay with membranes prepared from pig coronary arteries and I-125-h-alpha-CGRP. Functional effects were characterized using a previously reported pig coronary artery relaxation bioassay. The binding affinity of [Pen(2)]h-alpha-CGRP was not significantly different from that of h-alpha-CGRP. All other analogues showed reduced affinity for CGRP receptors. [Pen(2)]h-alpha-CGRP also caused relaxation of coronary arteries. The remaining analogues either caused relaxation with significantly reduced potency or failed to relax the arteries at concentrations up to 1 x 10(-5) M. All analogues that did not relax coronary arteries contained a D-Pen in position 7 and inhibited CGRP-induced relaxation. [D-Pen(2,7)]h-alpha- CGRP was the most potent antagonist with a K-B value of 630 nM. This affinity is similar to that of the classical CGRP receptor antagonist, h-alpha-CGRP(8-37), on these arteries (K-B, 212 nM). These studies show that modifying the topography of the disulphide bridge can cause large and variable effects on ligand binding and activation of CGRP receptors. The contribution of position 7 to the conformation and topography of the disulphide bridge of h-alpha-CGRP is crucial to the future design of agonists of CGRP receptors. Furthermore, position 7 is important for the development of new CGRP receptor antagonists with structures based on the whole sequence of h-alpha-CGRP.

Chemoenzymatic synthesis of trans-dihydrodiol derivatives of monosubstituted benzenes from the corresponding cis-dihydrodiol isomers

Enantiopure trans-dihydrodiols have been obtained by a chemoenzymatic synthesis from the corresponding cis-dihydrodiol metabolites, obtained by dioxygenase-catalysed arene cis-dihydroxylation at the 2,3-bond of monosubstituted benzene substrates. This generally applicable, seven-step synthetic route to trans-dihydrodiols involves a regioselective hydrogenation and a Mitsunobu inversion of configuration at C-2, followed by benzylic bromination and dehydrobromination steps. The method has also been extended to the synthesis of both enantiomers of the trans-dihydrodiol derivatives of toluene, through substitution of a vinyl bromine atom of the corresponding trans-dihydrodiol enantiomers derived from bromobenzene. Through incorporation of hydrogenolysis and diMTPA ester diastereoisomer resolution steps into the synthetic route, both trans-dihydrodiol enantiomers of monohalobenzenes were obtained from the cis-dihydrodiols of 4-haloiodobenzenes.

syn-Benzene dioxides: chemoenzymatic synthesis from 2,3-cis-dihydrodiol derivatives of monosubstituted benzenes and their application in the synthesis of regioisomeric 1,2- and 3,4-cis-dihydrodiols and 1,4-dioxocins

cis-2,3-Dihydrodiol metabolites of monosubstituted halobenzenes and toluene have been used as synthetic precursors of the corresponding 3,4-cis-dihydrodiols. Enantiopure syn-benzene dioxide intermediates were reduced to the 3,4-cis-dihydrodiols and thermally racemised via the corresponding 1,4-dioxocins. The syn-benzene dioxide-1,4-dioxocin valence tautomeric equilibrium ratio was found to be dependent on the substituent position. The methodology has also been applied to the synthesis of both enantiomers of the 1,2-(ipso)- and 3,4-cis-dihydrodiols of toluene. This chemoenzymatic approach thus makes available, for the first time, all three possible cis-dihydrodiol regioisomers of a monosubstituted benzene.

Enzyme-catalysed synthesis and reactions of benzene oxide/oxepine derivatives of methyl benzoates

A series of twelve benzoate esters was metabolised, by species of the Phellinus genus of wood-rotting fungi, to yield the corresponding benzyl alcohol derivatives and eight salicylates. The isolation of a stable oxepine metabolite, from methyl benzoate, allied to evidence of the migration and retention of a carbomethoxy group ( the NIH Shift), during enzyme-catalysed ortho-hydroxylation of alkyl benzoates to form salicylates, is consistent with a mechanism involving an initial arene epoxidation step. This mechanism was confirmed by the isolation of a remarkably stable, optically active, substituted benzene oxide metabolite of methyl 2-( trifluoromethyl) benzoate, which slowly converted into the racemic form. The arene oxide was found to undergo a cycloaddition reaction with 4-phenyl-1,2,4-triazoline-3,5-dione to yield a crystalline cycloadduct whose structure and racemic nature was established by X-ray crystallography. The metabolite was also found to undergo some novel benzene oxide reactions, including epoxidation to give an anti-diepoxide, base-catalysed hydrolysis to form a trans-dihydrodiol and acid-catalysed aromatisation to yield a salicylate derivative via the NIH Shift of a carbomethoxy group.

'Foreign' Terror? London Bombings, Resistance and the Failing State

The British government's response to the London bombings sought to make the terror of that day foreign, even though it appeared largely domestic. This helped construct it as unusual, contingent, part of the uncontrollable ‘otherness’ of the ‘foreign’. However, it also drew the response into the arena of British foreign policy, where the ‘failing state’ has been the dominant conceptualisation of insecurity and terrorism, especially since September 11th. When the bombings are examined through the ‘failing state’ disturbing and important problems are uncovered. Primarily, the ‘failing state’ discourse deconstructs under the influence of the terrorism in London, revealing that Britain itself is a ‘failing state’ by its own description and producing a generalisation of state ‘failure’. It thereby reveals several possible sites for responding to and resisting the government's representation.