Asymmetry in the Multiprotein Systems of Molecular Biology

Signaling in living systems needs to achieve high specificity, to be reversible, and to achieve high signal to noise. Signaling mediated by multiprotein systems has evolved that avoids the requirement for high-affinity binary complexes that would be difficult to reverse and which, in the overcrowded cell, would lead to excessive noise in the system. Symmetrical structures are only occasionally formed. When they are, it is principally to colocate components, for example, the tyrosyl kinases of growth factors, where dimers form. Symmetry is, however, often broken, presumably to create more sensitivity and specificity in the signaling system by assembling other components, into higher-order multiprotein systems. The binding of a single heparin to two 1:1 FGF:FGFR complexes is an example, as is the binding of a single ligase to the Xrcc4 dimer, perhaps so creating a further DNA-binding site.     

Palladium-catalyzed α-arylation of ketones on solid support: scope and limitations

The palladium-catalyzed α-arylation of ketones on solid support is described. Using modified Buchwald-Hartwig reaction conditions, the coupling of immobilized 4-bromobenzamide with various aromatic, heteroaromatic, and aliphatic ketones was investigated. Subsequent cleavage from the resin provided the desired α-aryl ketones almost in moderate to high yields and good to excellent purities. The scope and limitations of this protocol will be discussed.     

New Combinatorial Descriptions of the Triangulations of Cyclic Polytopes and the Second Higher Stasheff–Tamari Posets

This paper is concerned with the d-dimensional cyclic polytope with n vertices, C(n,d), and the set of its triangulations, S(n,d). We show that there is a bijection between S(n,d) and certain partitions of the set of increasing d-tuples on the integers 1 to n–1. We give a combinatorial characterization of the second higher Stasheff–Tamari poset, which is a partial ordering of S(n,d), and we determine its 2-dimension. There is a well-known representation of triangulations of an n-gon by right bracket vectors. We generalize this to cyclic polytopes of higher dimensions.     

A note on canonical functions

We construct a generic extension in which the ℵ₂nd canonical function on ℵ₁ exists. Supported by NSF and by a Fulbright grant. Publ. 378. Partially supported by the B.S.F.     

Cayley graphs of finitely generated groups

There does not exist a Borel choice of generators for each finitely generated group which has the property that isomorphic groups are assigned isomorphic Cayley graphs.

     

Buchbesprechungen

Ohne Zusammenfassung     

Bayesian Probabilities and the Histories Algebra

We attempt a justification of a generalisation of the consistent histories programme using a notion of probability that is valid for all complete sets of history propositions. This consists of introducing Cox's axioms of probability theory and showing that our candidate notion of probability obeys them. We also give a generalisation of Bayes' theorem and comment upon how Bayesianism should be useful for the quantum gravity/cosmology programmes. PACS: 02.50.Cw;03.65.Ta;04.60.-m.     

On disjoint configurations in infinite graphs

For a graph A and a positive integer n, let nA denote the union of n disjoint copies of A; similarly, the union of ?₀ disjoint copies of A is referred to as ?₀A. It is shown that there exist (connected) graphs A and G such that nA is a minor of G for all n??, but ?₀A is not a minor of G. This supplements previous examples showing that analogous statements are true if, instead of minors, isomorphic embeddings or topological minors are considered. The construction of A and G is based on the fact that there exist (infinite) graphs G₁, G₂,… such that G_i is not a minor of G_j for all i ≠ j. In contrast to previous examples concerning isomorphic embeddings and topological minors, the graphs A and G presented here are not locally finite. The following conjecture is suggested: for each locally finite connected graph A and each graph G, if nA is a minor of G for all n ? ?, then ?₀A is a minor of G, too. If true, this would be a far‐reaching generalization of a classical result of R. Halin on families of disjoint one‐way infinite paths in graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 222–229, 2002; DOI 10.1002/jgt.10016     

Dynamic NMR study of the flexibility of 2-amino-3-aroyl-4,6-diaryl-pyrylium salts

Dynamic NMR investigations of a number of 2-amino-3-aroyl-4,6-diaryl-pyrylium salts were carried out. The barrier to rotation of the partial C, N double bond was determined and proved to be in the range of 62 to 63 kJ/mol. Quantum chemical calculations of bond orders and electron densities of the different atoms in the molecules show the distinct double bond character of the exocyclic C, N bond. This is in agreement with the relatively high barrier to rotation. By quantum chemical ab initio 3-21G calculations, the dynamic behaviour of this kind of compounds was simulated; two pairs (image and mirror image) of ground state conformations, in coincidence with the experiment, were obtained. Received: 10 May 1996 / Revised: 1 July 1996 / Accepted: 4 July 1996