Hyper-Kähler manifolds and multiply intersecting branes

Generalized membrane solutions of D = 11 supergravity, for which the transverse space is a toric hyper-Kahler manifold, are shown to have IIB duals representing the intersection of parallel 3-branes with 5-branes whose orientations are determined by their charge vectors. These IIB solutions, which generically preserve 3/16 of the supersymmetry, can be further mapped to solutions of D = 11 supergravity representing the intersection of parallel membranes with any number of fivebranes at arbitrary angles. Alternatively, a subclass (corresponding to non-singular D = 11 solutions) can be mapped to solutions representing the intersection on a string of any number of D-5-branes at arbitrary angles, again preserving 3/16 supersymmetry, as we verify in a special case by a quaternionic extension of the analysis of Berkooz, Douglas and Leigh. We also use similar methods to find new 1/8 supersymmetric solutions of orthogonally intersecting branes.     

Existence of best N-convex approximants in L1

We consider here best approximation by n-convex functions. We first show that if f∈L₁[0,1], then there is, a best L₁-approximant to f by functions which are n-convex on (0,1). We then show that if f∈L_∞[0,1], then any best L_p-approximant, f_p, to f by n-convex, functions is bounded and hence, f has the Pólya-one property, i.e., f_p converges a.e. as p decreases to one.     

Structural insight into the inactivation of <Emphasis Type="Italic">Mycobacterium tuberculosis</Emphasis> non-classical transpeptidase Ldt<Subscript>Mt2</Subscript> by biapenem and tebipenem

Background

The carbapenem subclass of β-lactams is among the most potent antibiotics available today. Emerging evidence shows that, unlike other subclasses of β-lactams, carbapenems bind to and inhibit non-classical transpeptidases (L,D-transpeptidases) that generate 3 → 3 linkages in bacterial peptidoglycan. The carbapenems biapenem and tebipenem exhibit therapeutically valuable potencies against Mycobacterium tuberculosis (Mtb).

Results

Here, we report the X-ray crystal structures of Mtb L,D-transpeptidase-2 (Ldt_Mt2) complexed with biapenem or tebipenem. Despite significant variations in carbapenem sulfur side chains, biapenem and tebipenem ultimately form an identical adduct that docks to the outer cavity of Ldt_Mt2. We propose that this common adduct is an enzyme catalyzed decomposition of the carbapenem adduct by a mechanism similar to S-conjugate elimination by β-lyases.

Conclusion

The results presented here demonstrate biapenem and tebipenem bind to the outer cavity of Ldt_Mt2, covalently inactivate the enzyme, and subsequently degrade via an S-conjugate elimination mechanism. We discuss structure based drug design based on the findings and propose that the S-conjugate elimination can be leveraged to design novel agents to deliver and locally release antimicrobial factors to act synergistically with the carbapenem carrier.

     

A Stark future for quantum control

We present an overview of developments using the nonresonant dynamic Stark effect within the fields of time-resolved molecular dynamics and quantum control, drawing on examples from our own recent work. Particular emphasis is placed on the notion that "dynamics" and "control" are not distinct disciplines and that a clear synergy exits between these areas which has, up to now, been somewhat underexploited. The dynamic Stark effect is a universal interaction which we expect to have broad applicability.     

The synthesis and properties of certain N-methylated 5-diazouracils

The reduction of 1-methyl-, 3-methyl- and 1,3-dimethyl-5-nitrouracil (Ia-c) to the corresponding 5-aminouracils (IIa-c) is described. Diazotization of 5-amino-1-methyluracil (IIa) and 5-amino-1,3-dimethyluracil (IIc) gave 5-diazouracils which were characterized as thermally stable C6 covalent hydrates (III and XIII). Diazotization of 5-amino-3-methyluracil (IIb) gave anhydro 5-diazo-3-methyluracil (X) which underwent covalent methanolation and thermally reversible covalent hydration. Treatment of III and XIII with hot methanol resulted in solvent exchange of the C6 hydroxyl groups by a mechanism which may involve initial formation of diazoethers. Treatment of the methanolates (IV, XI and XIV) with dimethylamine resulted in coupling at the diazo group with a concomitant expulsion of the C6 methoxyl groups to give 5-(3,3-dimethyl-1-triazeno)uracils (XVa-c).     

Stability at a local maximum in higher dimensional anti-deSitter space and applications to supergravity

The stability of anti-deSitter background solutions of gravity/scalar systems with respect to small fluetuations of the scalar fields is analyzed. As in the four dimensional case, one finds stability even about a local maximum provided that the effective scalar field masses are not “too tachyonic,” and for sufficiently low mass there are two possible boundary conditions that allow a well-defined and conserved energy. Unlike the d = 4 case only one boundary condition is applicable to the known gauged supergravity theories in d = 5 and d = 7. For d = 7 the stability criterion is satisfied while for d = 5 stability is marginal.     

The vanishing volume of N = 1 superspace

We show that the supergeometry of the new minimal formulation of N = 1 supergravity is a limiting case of the non-minimal supergeometry for which the volume of superspace vanishes. The action for supergravity in this case is then no longer the superdeterminant of the vielbein but is analogous to a special form of the Fayet-Iliopoulos term allowed only for the new minimal supergeometry. We discuss the restrictions on matter couplings imposed by the new and non-minimal supergeometries.