Protein prosthesis: a nonnatural residue accelerates folding and increases stability

Nonnatural residues can endow proteins with desirable properties. Here, replacing a proline residue that has a cis peptide bond in native ribonuclease A with 5,5-dimethyl-l-proline is shown to accelerate protein folding by 6-fold and enhance conformational stability by DeltaTm = 2.8 +/- 0.3 degrees C while having no effect on enzymatic activity. The rational use of this and other prosthetic segments could enable chemotherapeutic proteins to survive longer in vivo or retain activity after oral administration.     

Asymptotic behavior of positive solution branches of elliptic problems with linear part at resonance

We consider Dirichlet problems for semilinear elliptic equations whose linear part is at resonance. For various types of nonlinearities we provide sufficient conditions for the solvability of these problems for certain types of forcing terms. Depending upon the dimension of the independent variable and the shape of the domain, we obtain multiple existence results and show that in some cases infinitely many solutions may exist.Dedicated to Klaus Kirchgässner on the occasion of his 60th birthdayThe authors' work on this project has been supported by several institutions and thanks are due to the University of Utah for granting Schaaf a one year's visiting professorship during 1989–1990, to the DFG and the University of Stuttgart for providing Schmitt with the opportunity to visit that institution during the summer semester 1989. Final preparation was supported by a grant from NSF.     

Improved linear multi-step methods for stochastic ordinary differential equations

We consider linear multi-step methods for stochastic ordinary differential equations and study their convergence properties for problems with small noise or additive noise. We present schemes where the drift part is approximated by well-known methods for deterministic ordinary differential equations. In previous work, we considered Maruyama-type schemes, where only the increments of the driving Wiener process are used to discretize the diffusion part. Here, we suggest the improvement of the discretization of the diffusion part by also taking into account mixed classical-stochastic integrals. We show that the relation of the applied step sizes to the smallness of the noise is essential in deciding whether the new methods are worthwhile. Simulation results illustrate the theoretical findings.     

On the Description of the Content-Equality by a Relation

In the geometry of polyhedra we understand by an elementary content-functional a real valued, non-negative, finite additive measure on the set of polyhedra which is invariant under isometries. There are close relations between the content-measurement and the relation of equidecomposability. Two polyhedra are called equidecomposable if they are decomposed into pairwise congruent pieces. For an example we consider the set of all polygons in the euclidean plane. It is well known that planar polygons have the same area if and only if they are equidecomposable. In the three-dimensional euclidean space one also can describe the content-equality of polyhedra by a relation. Two polyhedra have the same volume if they are equidecomposable with respect to equiaffine mappings (see [3]). In [4] the concept of an invariant content of polyhedra in a topological Klein space is introduced. Each regular closed quasicompact set ot the space is called polyhedron. Under this supposition two polyhedra have equal contents if they are equivalent by decomposition. The relation “equivalent by decomposition” is closely related to the relation “equidecomposable”.     

Synthesis of fully substituted polyhydroxylated pyrrolizidines via Cope-House cyclization

Total synthesis of the proposed structure of (-)-hyacinthacine C(5) and its epimers at C6 and C7 is described. A key step of the synthesis was the construction of the bicyclic pyrrolizidine system by means of a nucleophilic addition of a dithiane to a cyclic nitrone followed by a Cope-House cyclization.