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We provide a rigorous canonical quantization for the following toral automorphisms: cat maps, generalized kicked maps, and generalized Harper maps. For each of these systems we construct a unitary propagator and prove the existence of a well-defined classical limit. We also provide an alternative derivation of Hannay and Berry results for the cat map propagator on the plane.

The design of potent and selective non-peptide antagonists of endothelin-1 (ET-1) and its related isopeptides are important tools defining the role of ET in human diseases. In this report we will describe the detailed structure-activity relationship (SAR) studies that led to the discovery of a potent series of butenolide ETA selective antagonists. Starting from a micromolar screening hit, PD012527, use of Topliss decision tree analysis led to the discovery of the nanomolar ET(A) selective antagonist PD155080. Further structural modifications around the butenolide ring led directly to the subnanomolar ETA selective antagonist PD156707, IC50's = 0.3 (ET(A)) and 780 nM (ET(B)). This series of compounds exhibited functional activity exemplified by PD156707. This derivative inhibited the ETA receptor mediated release of arachidonic acid from rabbit renal artery vascular smooth muscle cells with an IC50 = 1.1 nM and also inhibited the ET-1 induced contraction of rabbit femoral artery rings (ETA mediated) with a pA2 = 7.6. PD156707 also displayed in vivo functional activity inhibiting the hemodynamic responses due to exogenous administration of ET-1 in rats in a dose dependent fashion. Evidence for the pH dependence of the open and closed tautomerization forms of PD156707 was demonstrated by an NMR study. X-ray crystallographic analysis of the closed butenolide form of PD156707 shows the benzylic group located on the same side of the butenolide ring as the gamma-hydroxyl and the remaining two phenyl groups on the butenolide ring essentially orthogonal to the butenolide ring. Pharmacokinetic parameters for PD156707 in dogs are also presented.

Gelatinase A is a key enzyme in the family of matrix metalloproteinases (matrixins) that are involved in the degradation of the extracellular matrix. As this process is an integral part of tumour cell metastasis and angiogenesis, gelatinase is an important target for therapeutic intervention. The X-ray crystal structure of the gelatinase A catalytic domain (GaCD) complexed with batimastat (BB94), a hydroxamate inhibitor, shows an active site with a large S1' specificity pocket. The structure is similar to previously solved structures of stromelysin catalytic domain (SCD) but with differences in VR1 and VR2, two surface-exposed loops on either side of the entrance to the active site. Comparison of GaCD with other members of the matrix metalloproteinase (MMP) family highlights the conservation of key secondary structural elements and the significant differences in the specificity pockets, knowledge of which should enhance our ability to design specific inhibitors for this important anticancer target.

We present here a canonical quantization for the baker's map. The method we use is quite different from that used in Balazs and Voros (ref. \QCITE{cite}{}{BV}) and Saraceno (ref. \QCITE{cite}{}{S}). We first construct a natural ``baker covering map'' on the plane $\QTO{mathbb}{\mathbb{R}}^{2}$. We then use as the quantum algebra of observables the subalgebra of operators on $L^{2}(\QTO{mathbb}{\mathbb{R}}) $ generated by $\left\{\exp (2\pi i\hat{x}) ,\exp (2\pi i\hat{p}) \right\} $ . We construct a unitary propagator such that as $\hbar \to 0$ the classical dynamics is returned. For Planck's constant $h=1/N$, we show that the dynamics can be reduced to the dynamics on an $N$-dimensional Hilbert space, and the unitary $N\times N$ matrix propagator is the same as given in ref. \QCITE{cite}{}{BV} except for a small correction of order $h$. This correction is shown to preserve the classical symmetry $x\to 1-x$ and $p\to 1-p$ in the quantum dynamics for periodic boundary conditions., Comment: 27 pages, 3 figures. Annals of Physics, to appear

We study the ergodic properties for a class of quantized toral automorphisms, namely the cat and Kronecker maps. The present work uses and extends the results of [KL]. We show that quantized cat maps are strongly mixing, while Kronecker maps are ergodic and non-mixing. We also study the structure of these quantum maps and show that they are effected by unitary endomorphisms of a suitable vector bundle over a torus. The fiberwise parts of these endomorphisms form a family of finite dimensional quantizations, parametrized by the points of a torus, which includes the quantization proposed in [HB]., 21 pages, plain Tex