Mirror-image oligonucleotide ligands (Spiegelmers) that bind to the pharmacologically relevant target gonadotropin-releasing hormone I (GnRH) with high affinity and high specificity have been identified using the Spiegelmer technology. GnRH is a decapeptide that plays an important role in mammalian reproduction and sexual maturation and is associated with several benign and malignant diseases. First, aptamers that bind to D-GnRH with dissociation constants of 50-100 nM were isolated out of RNA and DNA libraries. The respective enantiomers of the DNA and RNA aptamers were synthesized, and their binding to L-GnRH was shown. These Spiegelmers bind to L-GnRH with similar affinity to that of the corresponding aptamers that bind to D-GnRH. We further demonstrated dose-dependent inhibition of GnRH-induced Ca(2+) release in Chinese hamster ovary cells that were stably transfected with the human GnRH receptor.
Abstract. A rigorous formulation of Vessiot's vector field approach to the analysis of general systems of partial differential equations is provided. It is shown that this approach is equivalent to the formal theory of differential equations and that it can be carried through if, and only if, the given system is involutive. As a by-product, we provide a novel characterisation of transversal integral elements via the contact map.
We present an intrinsic definition of a (possibly time-dependent) Hamiltonian differential equation as a submanifold of the first-order jet bundle over a fibred cosymplectic manifold. The equivalence of the standard constraint algorithm in mechanics to the completion procedure in differential equations theory is explicitly demonstrated. As an application, we study covariant classical mechanics. Finally, some problems with constraint algorithms in field theories are indicated.
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