Solutions of a Lagrangian system on

A Lagrangian system on

Isotropic isotopy and symplectic null sets

Capacity is an important numerical invariant of symplectic manifolds. This paper studies when a subset of a symplectic manifold is null, i.e., can be removed without affecting the ambient capacity. After examples of open null sets and codimension-2 non-null sets, geometric techniques are developed to perturb any isotopy of a loop to a hamiltonian flow; it follows that sets of dimension 0 and 1 are null. For isotropic sets of higher dimensions, obstructions to the perturbation are found in homotopy groups of the orthogonal groups.

Crystal structure of a DNA decamer showing a novel pseudo four-way helix-helix junction.

The crystal structure of the decanucleotide d(CGCAATTGCG)2 has been solved by a combination of molecular replacement and heavy-atom procedures and has been refined to an R factor of 20.2% at 2.7 A. It is not a fully base-paired duplex but has a central core of eight Watson-Crick base pairs flanked by unpaired terminal guanosines and cytosines. These participate in hydrogen-bonding arrangements with adjacent decamer duplexes in the crystal lattice. The unpaired guanosines are bound in the G+C regions of duplex minor grooves. The cytosines have relatively high mobility, even though they are constrained to be in one region where they are involved in base-paired triplets with G.C base pairs. The 5'-AATT sequence in the duplex region has a narrow minor groove, providing further confirmation of the sequence-dependent nature of groove width.