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.     

Fluorinations with complex metal fluorides. Part 6 [1] fluorination of yridine and related compounds with caesium tetrafluorocobaltate(III) [2]

Pyridine has been fluorinated over caesium tetrafluorocobaltate(III) (CsCo^IIIF₄) at 300–400°C to give a mixture of undecafluoro-N-methylpyrrolidine, bis(trifluoromethyl)amine, pentafluoropyridine and several polyfluoropyridines; the product composition depended to some extent on the geometry of the reactor. The fluorinations of pentafluoropyridine, piperidine and undecafluoropiperidine were also investigated.     

On the evolution of islands

Letn cells be arranged in a ring, or alternatively, in a row. Initially, all cells are unmarked. Sequentially, one of the unmarked cells is chosen at random and marked until, aftern steps, each cell is marked. After thekth cell has been marked the configuration of marked cells defines some number of islands: maximal sets of adjacent marked cells. Let ξ _k denote the random number of islands afterk cells have been marked. We give explicit expressions for moments of products of ξ _k ’s and for moments of products of 1/ξ _k ’s. These are used in a companion paper to prove that if a random graph on the natural number is made by drawing an edge betweeni≧1 andj>i with probabilityλ/j, then the graph is almost surely connected ifλ>1/4 and almost surely disconnected ifλ≦1/4.     

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.

     

Concentration for self‐bounding functions and an inequality of Talagrand

We see that the entropy method yields strong concentration results for general self‐bounding functions of independent random variables. These give an improvement of a concentration result of Talagrand much used in discrete mathematics. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

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