Common multiples of complete graphs and a 4-cycle

A graph G is a common multiple of two graphs H-1 and H-2 if there exists a decomposition of G into edge-disjoint copies of H-1 and also a decomposition of G into edge-disjoint copies of H-2. In this paper, we consider the case where H-1 is the 4-cycle C-4 and H-2 is the complete graph with n vertices K-n. We determine, for all positive integers n, the set of integers q for which there exists a common multiple of C-4 and K-n having precisely q edges. (C) 2003 Elsevier B.V. All rights reserved.

The common tetratricopeptide repeat acceptor site for steroid receptor-associated immunophilins and Hop is located in the dimerization domain of hsp90

Structurally related tetratricopeptide repeat motifs in steroid receptor-associated immunophilins and the STI1 homolog, Hop, mediate the interaction with a common cellular target, hsp90, We have identified the binding domain in hsp90 for cyclophilin 40 (CyP40) using a two-hybrid system screen of a mouse cDNA library. All isolated clones encoded the intact carboxyl terminus of hsp90 and overlapped with a common region corresponding to amino acids 558-724 of murine hsp84, The interaction was confirmed in vitro with bacterially expressed CyP40 and deletion mutants of hsp90 beta and was delineated further to a 124-residue COOH-terminal segment of hsp90, Deletion of the conserved MEEVD sequence at the extreme carboxyl terminus of hsp90 precludes interaction with CyP40, signifying an important role for this motif in hsp90 function. We show that CyP40 and Hop display similar interaction profiles with hsp90 truncation mutants and present evidence for the direct competition of Hop and FK506-binding protein 52 with CyP40 for binding to the hsp90 COOH-terminal region. Our results are consistent with a common tetratricopeptide repeat interaction site for Hop and steroid receptor associated immunophilins within a discrete COOH-terminal domain of hsp90. This region of hsp90 mediates ATP-independent chaperone activity, overlaps the hsp90 dimerization domain, and includes structural elements important for steroid receptor interaction.

The origin of the metazoan biphasic life cycle: New insights from an ancient phylum

The biphasic life cycle, characterised by metamorphosis from a pelagic larva to a benthic adult, is found throughout the Metazoa. So is sexual reproduction via eggs and sperm. Amidst a tangled web of hypotheses on the origin of metazoan biphasy, current weight of opinion lies with a simple, larva-like holopelagic ancestor that independently settled multiple times to incorporate a benthic phase into the life cycle. This school of thought derives from Haeckel's interpretation of the gastrula as the recapitulation of a gastrean ancestor that evolved via selection on a simple, planktonic hollow ball-of-cells to develop the capacity to feed. We suggest that a paradigm shift is required to accomodate accumulating evidence of the genomic and developmental complexity of the metazoan last common ancestor, which was likely to have already possessed a biphasic lifecycle. Here we incorporate recent evidence from basal metazoans, in particular poriferans, to argue that a more parsimonious theory of the origin of biphasy is as a direct consequence of sexual reproduction in an ancestral benthic adult form. The metazoan embryo can itself be considered the precursor to a biphasic life cycle, wherein the embryo represents one phase and the adult another. Embryos in the water column are subject to natural selection for longeveity and dispersal, which sets them on the evolutionary trajectory towards the crown metazoan planktonic larvae. This alternate view considers the conserved use of regulatory genes in disparate metazoans as a reflection of both the complexity of the LCA and the antiquity of the biphasic life cycle. It does not require that extant embryogenesis, including gastrulation, recapitulates evolution.

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.

G2 phase cell cycle arrest in human skin following UV irradiation

The contribution of the short wavelength ultraviolet (UV) component of sunlight to the aetiology of skin cancer has been widely acknowledged, although its direct contribution to tumour initiation or progression is still poorly understood. The loss of normal cell cycle controls, particularly checkpoint controls, are a common feature of cancer. UV radiation causes both GI and G2 phase checkpoint arrest in vitro cultured cells. In this study we have investigated the cell cycle responses to suberythemal doses of UV on skin. We have utilized short-term whole organ skin cultures, and multi parameter immunohistochemical and biochemical analysis to demonstrate that basal and suprabasal layer melanocytes and keratinocytes undergo a G2 phase cell cycle arrest for up to 48 h following irradiation. The arrest is associated with increased p16 expression but no apparent p53 involvement. This type of organ culture provides a very useful model system, combining the ease of in vitro manipulation with the ability to perform detailed molecular analysis in a normal tissue environment.

Atm knock-in mice harboring an in-frame deletion corresponding to the human ATM 7636del9 common mutation exhibit a variant phenotype

ATM, the gene mutated in the human immunodeficiency disorder ataxia-telangiectasia (A-T), plays a central role in recognizing ionizing radiation damage in DNA and in controlling several cell cycle checkpoints. We describe here a murine model in which a nine-nucleotide in-frame deletion has been introduced into the Atm gene by homologous recombination followed by removal of the selectable marker cassette by Cre-loxP site-specific, recombination-mediated excision. This mouse, Abm-Delta SRI, was designed as a model of one of the most common deletion mutations (7636de19) found in A-T patients. The murine Atm deletion results in the loss of three amino acid residues (SRI; 2556-2558) but produces near full-length detectable Atm protein that lacks protein kinase activity. Radiosensitivity was observed in Atm-Delta SRI mice, whereas the immunological profile of these mice showed greater heterogeneity of T-cell subsets than observed in Atm(-/-) mice. The life span of Atm-Delta SRI mice was significantly longer than that of Atm(-/-) mice when maintained under nonspecific pathogen-free conditions. This can be accounted for by a lower incidence of thymic lymphomas in Atm-Delta SRI mice up to 40 weeks, after which time the animals died of other causes. The thymic lymphomas in Atm-Delta SRI mice were characterized by extensive apoptosis, which appears to be attributable to an increased number of cells expressing Fas ligand. A variety of other tumors including B-cell lymphomas, sarcomas, and carcinomas not seen in Atm(-/-) mice were observed in older Atm-Delta SRI animals. Thus, expression of mutant protein in Atm-Delta SRI knock-in mice gives rise to a discernibly different phenotype to Atm(-/-) mice, which may account for the heterogeneity seen in A-T patients with different mutations.

On the volume of 4-cycle trades

A 4-cycle trade of volume t corresponds to a simple graph G without isolated vertices, where the edge set can be partitioned into t 4-cycles in at least two different ways such that the two collections of 4-cycles have no 4-cycles in common. The foundation of the trade is v = \V(G)\. This paper determines for which values oft and a there exists a 4-cycle trade of volume t and foundation v.

Configurations in 4-cycle systems

A 4-cycle system of order n, denoted by 4CS(n), exists if and only if nequivalent to1 (mod 8). There are four configurations which can be formed by two 4-cycles in a 4CS(n). Formulas connecting the number of occurrences of each such configuration in a 4CS(n) are given. The number of occurrences of each configuration is determined completely by the number d of occurrences of the configuration D consisting of two 4-cycles sharing a common diagonal. It is shown that for every nequivalent to1 (mod 8) there exists a 4CS(n) which avoids the configuration D, i.e. for which d=0. The exact upper bound for d in a 4CS(n) is also determined.

Brca1 inactivation induces p27Kip1-dependent cell cycle arrest and delayed development in the mouse mammary gland

One common characteristic of breast cancers arising in carriers of the predisposition gene BRCA1 is a loss of expression of the CDK inhibitor p27(Kip1) (p27), suggesting that p27 interacts epistatically with BRCA1. To investigate this relationship, we examined expression of p27 in mice expressing a dominant negative allele of Brca1 (MMTV-trBr) in the mammary gland. While these mice rarely develop tumors, they showed a 50% increase in p27 protein and a delay in mammary gland development associated with reduced proliferation. In contrast, on a p27 heterozygote background, MMTV-trBrca1 mice showed an increase in S phase cells, and normal mammary development. p27 was the only protein in the cyclin cyclin-dependent kinase network to show altered expression, suggesting that it may be a central mediator of cell cycle arrest in response to loss of function of BRCA1. Furthermore, in human mammary epithelial MCF7 cells expressing BRCA1-specific RNAi and in the BRCA1-deficient human tumor cell line HCC1937, p27 is elevated at the mRNA level compared to cells expressing wild-type BRCA1. We hypothesize that disruption of BRCA1 induces an increase in p27 that inhibits proliferation. Accordingly, reduction in p27 expression leads to enhancement of cellular proliferation in the absence of BRCA1.

Phylogenetic position and ultrastructure of two Dermocystidium species (Ichthyosporea) from the common perch (Perca fluviatilis)

Sequences of small-subunit rRNA genes were determined for Dermocystidium percae and a new Dermocystidium species established as D. fennicum sp. n. from perch in Finland. On the basis of alignment and phylogenetic analysis both species were placed in the Dermocystidium-Rhinosporidium clade within Ichthyosporea, D. fennicum as a specific sister taxon to D. salmonis, and D. percae in a clade different from D. fennicum. The ultrastructures of both species well agree with the characteristics approved within Ichthyosporea: walled spores produce uniflagellate zoospores lacking a collar or cortical alveoli. The two Dermocystidium species resemble Rhinosporidium seeberi (as described by light microscope), a member of the nearest relative genus, but differ in that in R. seeberi plasmodia have thousands of nuclei discernible, endospores are discharged through a pore in the wall of the sporangium, and zoospores have not been revealed. The plasmodial stages of both Dermocystidium species have a most unusual behaviour of nuclei, although we do not actually know how the nuclei transform during the development. Early stages have an ordinary nucleus with double, fenestrated envelope. In middle-aged plasmodia ordinary nuclei seem to be totally absent or are only seldom discernible until prior to sporogony, when rather numerous nuclei again reappear. Meanwhile single-membrane vacuoles with coarsely granular content, or complicated membranous systems were discernible. Ordinary nuclei may be re-formed within these vacuoles or systems. In D. percae small canaliculi and in D. fennicum minute vesicles may aid the nucleus-cytoplasm interchange of matter before formation of double-membrane-enveloped nuclei. Dermocystidium represents a unique case when a stage of the life cycle of an eukaryote lacks a typical nucleus.

The origin of the pelagobenthic metazoan life cycle: what's sex got to do with it?

The biphasic (pelagobenthic) life cycle is found throughout the animal kingdom, and includes gametogenesis, embryogenesis, and metamorphosis. From a tangled web of hypotheses on the origin and evolution of the metazoan pelagobenthic life cycle, current opinion appears to favor a simple, larval-like holopelagic ancestor that independently settled multiple times to incorporate a benthic phase into the life cycle. This hypothesis derives originally from Haeckel's (1874) Gastraea theory of ontogeny recapitulating phylogeny, in which the gastrula is viewed as the recapitulation of a gastracan ancestor that evolved via selection on a simple, planktonic hollow ball of cells to develop the capacity to feed. Here, we propose an equally plausible hypothesis that the origin of the metazoan pelagobenthic life cycle was a direct consequence of sexual reproduction in a likely holobenthic ancestor. In doing so, we take into account new insights from poriferan development and from molecular phylogenies. In this scenario, the gastrula does not represent a recapitulation, but simply an embryological stage that is an outcome of sexual reproduction. The embryo can itself be considered as the precursor to a biphasic lifestyle, with the embryo representing one phase and the adult another phase. This hypothesis is more parsimonious because it precludes the need for multiple, independent origins of the benthic form. It is then reasonable to consider that multilayered, ciliated embryos ultimately released into the water column are subject to natural selection for dispersal/longevity/feeding that sets them on the evolutionary trajectory towards the crown metazoan planktonic larvae. These new insights from poriferan development thus clearly support the intercalation hypothesis of bilaterian larval evolution, which we now believe should be extended to discussions of the origin of biphasy in the metazoan last common ancestor.

Short-term effects of cycle and treadmill training on exercise tolerance in peripheral arterial disease

Background. To explore the efficacy of cycle training in the treatment of intermittent claudication, the present study compared performance and physiologic effects of cycle training with more conventional treadmill walking training in a group of patients with claudication. Method: Forty-two individuals with peripheral arterial disease and intermittent claudication (24 men, 18 women) were stratified by gender and the presence or absence of type 2 diabetes mellitus and then randomized to a treadmill (n = 13), cycle (n = 15), or control group (n = 14). Treadmill and cycle groups trained three times a week for 6 weeks, whereas the control group did not train during this period. Maximal and pain-free exercise times were measured on graded treadmill and cycle tests before and after training. Results. Treadmill training significantly improved maximal and pain-free treadmill walking times but did not improve cycle performance. Cycle training significantly improved maximal cycle time but did not improve treadmill performance. However, there was evidence of a stronger cross-transfer effect between the training modes for patients who reported a common limiting symptom during cycling and walking at baseline. There was also considerable variation in the training response to cycling, and a subgroup of responsive patients in the cycle group improved their walking performance by more than the average response observed in the treadmill group. Conclusion: These findings suggest that cycle exercise is not effective in improving walking performance in all claudication patients but might be an effective alternative to walking in those who exhibit similar limiting symptoms during both types of exercise.

Common multiples of complete graphs

A graph H is said to divide a graph G if there exists a set S of subgraphs of G, all isomorphic to H, such that the edge set of G is partitioned by the edge sets of the subgraphs in S. Thus, a graph G is a common multiple of two graphs if each of the two graphs divides G.