Andreas W. M. Dress

DIALIGN: finding local similarities by multiple sequence alignment.

MOTIVATION DIALIGN is a new method for pairwise as well as multiple alignment of nucleic acid and protein sequences. While standard alignment programs rely on comparing single residues and imposing gap penalties, DIALIGN constructs alignments by comparing whole segments of the sequences. No gap penalty is employed. This point of view is especially adequate if sequences are not globally related, but share only local similarities, as is the case in genomic DNA sequences and in many protein families. RESULTS Using four different data sets, we show that DIALIGN is able correctly to align conserved motifs in protein sequences. Alignments produced by DIALIGN are compared systematically to the results of five other alignment programs. AVAILABILITY DIALIGN is available to the scientific community free of charge for non-commercial use. Executables for various UNIX platforms including LINUX can be downloaded at http://www.gsf.de/biodv/dialign.html CONTACT werner, morgenstern@gsf.de

A canonical decomposition theory for metrics on a finite set

Abstract We consider specific additive decompositions d = d 1 + … + d n of metrics, defined on a finite set X (where a metric may give distance zero to pairs of distinct points). The simplest building stones are the slit metrics , associated to splits (i.e., bipartitions) of the given set X . While an additive decomposition of a Hamming metric into split metrics is in no way unique, we achieve uniqueness by restricting ourselves to coherent decompositions, that is, decompositions d = d 1 + … + d n such that for every map f : X → R with f ( x ) + f ( y ) ⩾ d ( x , y ) for all x , y ϵ X there exist maps f 1 , …, f n : X → R with f = f 1 + … + f n and f i ( x ) + f i ( y ) ⩾ d i ( x , y ) for all i = 1,…, n and all x , y ϵ X . These coherent decompositions are closely related to a geometric decomposition of the injective hull of the given metric. A metric with a coherent decomposition into a (weighted) sum of split metrics will be called totally split-decomposable . Tree metrics (and more generally, the sum of two tree metrics) are particular instances of totally split-decomposable metrics. Our main result confirms that every metric admits a coherent decomposition into a totally split-decomposable metric and a split-prime residue, where all the split summands and hence the decomposition can be determined in polynomial time, and that a family of splits can occur this way if and only if it does not induce on any four-point subset all three splits with block size two.

Giant metal-oxide-based spheres and their topology: from pentagonal building blocks to keplerates and unusual spin systems

Novel synthesis strategies based on the geometrical and topological principles outlined here open up pathways to a new class of spherical clusters with icosahedral symmetry of the type (pentagon)(12)(linker)(30)- also called keplerates -where the centers of the 12 pentagons span an icosahedron and the centers of the 30 linkers an icosidodecahedron. Remarkably, sizing of a spherical molecule is possible for the first time. In addition to their large size of several nanometers, these molecules show unusually high symmetries. When large numbers of paramagnetic metal centers like 30 Fe-III or 20 VO2+ are integrated within their structure, extraordinary spin topologies can be realized on a discrete molecular level. Further functionalization of these systems allows, e.g. to link them forming chains or layers in solid state reactions at room temperature

Analyzing proteome topology and function by automated multidimensional fluorescence microscopy

Temporal and spatial regulation of proteins contributes to function. We describe a multidimensional microscopic robot technology for high-throughput protein colocalization studies that runs cycles of fluorescence tagging, imaging and bleaching in situ. This technology combines three advances: a fluorescence technique capable of mapping hundreds of different proteins in one tissue section or cell sample; a method selecting the most prominent combinatorial molecular patterns by representing the data as binary vectors; and a system for imaging the distribution of these protein clusters in a so-called toponome map. By analyzing many cell and tissue types, we show that this approach reveals rules of hierarchical protein network organization, in which the frequency distribution of different protein clusters obeys Zipfs law, and state-specific lead proteins appear to control protein network topology and function. The technology may facilitate the development of diagnostics and targeted therapies.

Reconstructing the shape of a tree from observed dissimilarity data

Branching structures, alias topological tree structures are fundamental to any hierarchical classification that aims to relate objects according to their similarities or dissimilarities. This paper provides a rigorous treatment of these structures, and continues previous work of Colonius and Schulze on H-structures. Thus extensive use is made of the so-called neighbors relation associated with a dissimilarity index. Arbitrary dissimilarity data are then analyzed by comparing their neighbors relations with ideal, that is, tree-like relations: if it matches an ideal relation, then one can readily construct a tree representing the data that is optimal in a certain sense. Finally, some algorithms are proposed for fitting observed data to tree-like data.

Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: A note on combinatorial properties of metric spaces

Abstract The concept of tight extensions of a metric space is introduced, the existence of an essentially unique maximal tight extension T x —the “tight span,” being an abstract analogon of the convex hull—is established for any given metric space X and its properties are studied. Applications with respect to (1) the existence of embeddings of a metric space into trees, (2) optimal graphs realizing a metric space, and (3) the cohomological dimension of groups with specific length functions are discussed.

Systematic enumeration of crystalline networks

The systematic enumeration of all possible networks of atoms ininorganic structures is of considerable interest. Of particular importance are the 4-connected networks (those in which each atom is connected to exactly four neighbours), which are relevant to a wide range of systems — crystalline elements, hydrates, covalently bonded crystals, silicates and many synthetic compounds. Systematic enumeration is especially desirable in the study of zeolites and related materials, of which there are now 121 recognized structural types, with several new types being identified every year. But as the number of possible 4-connected three-dimensional networks is infinite, and as there exists no systematic procedure for their derivation, the prediction of new structural types has hitherto relied on empirical methods (see, for example, refs 2–4). Here we report a partial solution to this problem, basedon recent advances in mathematical tiling theory. We establish that there are exactly 9, 117 and 926 topological types of, respectively, 4-connected uninodal, binodal and trinodal networks, derived from simple tilings based on tetrahedra. (Here nodality refers to the number of topologically distinct vertices from which the network is composed.) We also show that there are at least 145 more distinct uninodal networks based on a more complex tiling unit. Of the total number of networks that we have derived, only two contain neither three- nor four-membered rings, and most of the binodal and trinodal networks are new.

T -theory: an overview

Abstract T-theory is the name that we adopt for the theory of trees, injective envelopes of metric spaces, and all of the areas that are connected with these topics, which has been developed over the past 10–15 years in Bielefeld. Its motivation was originally—and still is to a large extent—the development of mathematical tools for reconstructing phylogenetic trees.T-theory expanded considerably when its relationships with the theory of affine buildings, valuated matroids, and decompositions of metrics were discovered. In this paper, we give a brief introduction to this theory, which we hope will serve as a useful reference to some of the main results, and also as a guide for further investigations into whatT-theory has to offer.

A Constructive Enumeration of Fullerenes

In this paper, a fast and complete method to enumerate fullerene structures is given. It is based on a top-down approach, and it is fast enough to generate, for example, all 1812 isomers ofC60in less than 20 s on an SGI-workstation. The method described can easily be generalized for 3-regular spherical maps with no face having more than 6 edges in its boundary.

Gated sets in metric spaces

The concept of a gated subset in a metric space is studied, and it is shown that properties of disjoint pairs of gated subsets can be used to investigate projections in Tits buildings.