The mu-way intersection problem for m-cycle systems

An m-cycle system of order upsilon is a partition of the edge-set of a complete graph of order upsilon into m-cycles. The mu -way intersection problem for m-cycle systems involves taking mu systems, based on the same vertex set, and determining the possible number of cycles which can be common to all mu systems. General results for arbitrary m are obtained, and detailed intersection values for (mu, m) = (3, 4), (4, 5),(4, 6), (4, 7), (8, 8), (8, 9). (For the case (mu, m)= (2, m), see Billington (J. Combin. Des. 1 (1993) 435); for the case (Cc,m)=(3,3), see Milici and Quattrochi (Ars Combin. A 24 (1987) 175. (C) 2001 Elsevier Science B.V. All rights reserved.

Star decompositions of cubes

Let Sk denote the complete bipartite graph K-1k and let e,, denote the ii-cube. We prove that the obvious necessary conditions for the existence of an S-k-decomposition of Q(n) are sufficient.

On the intersection problem for 1-factorizations and near 1-factorizations of K-v

The number of 1-factors (near 1-factors) that mu 1-factorizations (near 1-factorizations) of the complete graph K-v, v even (v odd), can have in common, is studied. The problem is completely settled for mu = 2 and mu = 3.

Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

On the Oberwolfach problem with two similar length cycles

For all in greater than or equal to 3, the Oberwolfach problem is solved for the case where the 2-factors consist of two cycles of lengths in and m + 1, and for the case where the 2-factors consist of two cycles of lengths m and m + 2.

Syntaxin 7 complexes with mouse Vps10p tail interactor 1b, Syntaxin 6, vesicle-associated membrane protein (VAMP)8, and VAMP7 in B16 melanoma cells

Syntaxin 7 is a mammalian target soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) involved in membrane transport between late endosomes and lysosomes. The aim of the present study was to use immunoaffinity techniques to identify proteins that interact with Syntaxin 7. We reasoned that this would be facilitated by the use of cells producing high levels of Syntaxin 7, Screening of a large number of tissues and cell lines revealed that Syntaxin 7 is expressed at very high levels in B16 melanoma cells. Moreover, the expression of Syntaxin 7 increased in these cells as they underwent melanogenesis. From a large scale Syntaxin 7 immunoprecipitation, we have identified six polypeptides using a combination of electrospray mass spectrometry and immunoblotting. These polypeptides corresponded to Syntaxin 7, Syntaxin 6, mouse Vps10p tail interactor 1b (mVti1b), alpha -synaptosome-associated protein (SNAP), vesicle-associated membrane protein (VAMP)8, VAMP7, and the protein phosphatase 1M regulatory subunit. We also observed partial colocalization between Syntaxin 6 and Syntaxin 7, between Syntaxin 6 and mVti1b, but not between Syntaxin 6 and the early endosomal t-SNARE Syntaxin 13. Based on these and data reported previously, we propose that Syntaxin 7/mVti1b/Syntaxin 6 may form discrete SNARE complexes with either VAMP7 or VAMPS to regulate fusion events within the late endosomal pathway and that these events may play a critical role in melanogenesis.

Vps45p stabilizes the syntaxin homologue Tlg2p and positively regulates SNARE complex formation

Sec1p-like/Munc-18 (SM) proteins bind to t-SNAREs and inhibit ternary complex formation. Paradoxically, the absence of SM proteins does not result in constitutive membrane fusion, Here, we show that in yeast cells lacking the SM protein Vps45p, the t-SNARE Tlg2p is down-regulated, to undetectable levels, by rapid proteasomal degradation. In the absence of Vps45p, Tlg2p can be stabilized through abolition of proteasome activity. Surprisingly, the stabilized Tlg2p was targeted to the correct intracellular location. However, the stabilized Tlg2p is non-functional and unable to bind its cognate SNARE binding partners, Tlg1p and Vti1p, in the absence of Vps45p, A truncation mutant lacking the first 230 residues of Tlg2p no longer bound Vps45p but was able to form complexes with Tlg1p and Vti1p in the absence of the SM protein. These data provide us with two valuable insights into the function of SM proteins. First, SM proteins act as chaperone-like molecules for their cognate t-SNAREs, Secondly, SM proteins play an essential role in the activation process allowing their cognate t-SNARE to participate in ternary complex formation.

A simulated annealing algorithm for finding consensus sequences

Motivation: A consensus sequence for a family of related sequences is, as the name suggests, a sequence that captures the features common to most members of the family. Consensus sequences are important in various DNA sequencing applications and are a convenient way to characterize a family of molecules. Results: This paper describes a new algorithm for finding a consensus sequence, using the popular optimization method known as simulated annealing. Unlike the conventional approach of finding a consensus sequence by first forming a multiple sequence alignment, this algorithm searches for a sequence that minimises the sum of pairwise distances to each of the input sequences. The resulting consensus sequence can then be used to induce a multiple sequence alignment. The time required by the algorithm scales linearly with the number of input sequences and quadratically with the length of the consensus sequence. We present results demonstrating the high quality of the consensus sequences and alignments produced by the new algorithm. For comparison, we also present similar results obtained using ClustalW. The new algorithm outperforms ClustalW in many cases.