On the Spectrum of Wenger Graphs

Let $q=p^e$, where $p$ is a prime and $e\geq 1$ is an integer. For $m\geq 1$, let $P$ and $L$ be two copies of the $(m+1)$-dimensional vector spaces over the finite field $\mathbb{F}_q$. Consider the bipartite graph $W_m(q)$ with partite sets $P$ and $L$ defined as follows: a point $(p)=(p_1,p_2,\ldots,p_{m+1})\in P$ is adjacent to a line $[l]=[l_1,l_2,\ldots,l_{m+1}]\in L$ if and only if the following $m$ equalities hold: $l_{i+1} + p_{i+1}=l_{i}p_1$ for $i=1,\ldots, m$. We call the graphs $W_m(q)$ Wenger graphs. In this paper, we determine all distinct eigenvalues of the adjacency matrix of $W_m(q)$ and their multiplicities. We also survey results on Wenger graphs.Comment: 9 pages; accepted for publication to J. Combin. Theory, Series

A primate virus generates transformed human cells by fusion

A model that explains both the origin and sporadic nature of cancer argues that cancer cells are a chance result of events that cause genomic and epigenetic variability. The prevailing view is that these events are mutations that affect chromosome segregation or stability. However, genomic and epigenetic variability is also triggered by cell fusion, which is often caused by viruses. Yet, cells fused by viruses are considered harmless because they die. We provide evidence that a primate virus uses both viral and exosomal proteins involved in cell fusion to produce transformed proliferating human cells. Although normal cells indeed fail to proliferate after fusion, expression of an oncogene or a mutated tumor suppressor p53 in just one of the fusion partners is sufficient to produce heterogeneous progeny. We also show that this virus can produce viable oncogenically transformed cells by fusing cells that are otherwise destined to die. Therefore, we argue that viruses can contribute to carcinogenesis by fusing cells

Recycling of epidermal growth factor-receptor complexes in A431 cells: identification of dual pathways

The intracellular sorting of EGF-receptor complexes (EGF-RC) has been studied in human epidermoid carcinoma A431 cells. Recycling of EGF was found to occur rapidly after internalization at 37 degrees C. The initial rate of EGF recycling was reduced at 18 degrees C. A significant pool of internalized EGF was incapable of recycling at 18 degrees C but began to recycle when cells were warmed to 37 degrees C. The relative rate of EGF outflow at 37 degrees C from cells exposed to an 18 degrees C temperature block was slower (t1/2 approximately 20 min) than the rate from cells not exposed to a temperature block (t1/2 approximately 5-7 min). These data suggest that there might be both short- and long-time cycles of EGF recycling in A431 cells. Examination of the intracellular EGF-RC dissociation and dynamics of short- and long-time recycling indicated that EGF recycled as EGF-RC. Moreover, EGF receptors that were covalently labeled with a photoactivatable derivative of 125I-EGF recycled via the long-time pathway at a rate similar to that of 125I-EGF. Since EGF-RC degradation was also blocked at 18 degrees C, we propose that sorting to the lysosomal and long-time recycling pathway may occur after a highly temperature-sensitive step, presumably in the late endosomes

Antiapoptotic herpesvirus Bcl-2 homologs escape caspase-mediated conversion to proapoptotic proteins

The antiapoptotic Bcl-2 and Bcl-x(L) proteins of mammals are converted into potent proapoptotic factors when they are cleaved by caspases, a family of apoptosis-inducing proteases (E. H.-Y. Cheng, D. G. Kirsch, R. J. Clem, R. Ravi, M. B. Kastan, A. Bedi, K. Ueno, and J. M. Hardwick, Science 278:1966-1968, 1997; R. J. Clem, E. H.-Y. Cheng, C. L. Karp, D. G. Kirsch, K. Ueno, A. Takahashi, M. B. Kastan, D. E. Griffin, W. C. Earnshaw, M. A. Veliuona, and J. M. Hardwick, Proc. Natl. Acad. Sci. USA 95:554-559, 1998). Gamma herpesviruses also encode homologs of the Bcl-2 family. All tested herpesvirus Bcl-2 homologs possess antiapoptotic activity, including the more distantly related homologs encoded by murine gammaherpesvirus 68 (gammaHV68) and bovine herpesvirus 4 (BHV4), as described here. To determine if viral Bcl-2 proteins can be converted into death factors, similar to their cellular counterparts, five herpesvirus Bcl-2 homologs from five different viruses were tested for their susceptibility to caspases. Only the viral Bcl-2 protein encoded by gammaHV68 was susceptible to caspase digestion. However, unlike the caspase cleavage products of cellular Bcl-2, Bcl-x(L), and Bid, which are potent inducers of apoptosis, the cleavage product of gammaHV68 Bcl-2 lacked proapoptotic activity. KSBcl-2, encoded by the Kaposi's sarcoma-associated herpesvirus, was the only viral Bcl-2 homolog that was capable of killing cells when expressed as an N-terminal truncation. However, because KSBcl-2 was not cleavable by caspases, the latent proapoptotic activity of KSBcl-2 apparently cannot be released. The Bcl-2 homologs encoded by herpesvirus saimiri, Epstein-Barr virus, and BHV4 were not cleaved by apoptotic cell extracts and did not possess latent proapoptotic activities. Thus, herpesvirus Bcl-2 homologs escape negative regulation by retaining their antiapoptotic activities and/or failing to be converted into proapoptotic proteins by caspases during programmed cell death

Oncogene-dependent apoptosis in extracts from drug-resistant cells

Many genotoxic agents kill tumor cells by inducing apoptosis; hence, mutations that suppress apoptosis produce resistance to chemotherapy. Although directly activating the apoptotic machinery may bypass these mutations, how to achieve this activation in cancer cells selectively is not clear. In this study, we show that the drug-resistant 293 cell line is unable to activate components of the apoptotic machinery-the ICE-like proteases (caspases)-following treatment with an anticancer drug. Remarkably, extracts from untreated cells spontaneously activate caspases and induce apoptosis in a cell-free system, indicating that drug-resistant cells have not only the apoptotic machinery but also its activator. Comparing extracts from cells with defined genetic differences, we show that this activator is generated by the adenovirus E1A oncogene and is absent from normal cells. We provide preliminary characterization of this oncogene generated activity (OGA) and show that partially purified OGA activates caspases when added to extracts from untransformed cells. We suggest that agents that link OGA to caspases in cells would kill tumor cells otherwise resistant to conventional cancer therapy. As this killing relies on an activity generated by an oncogene, the effect of these agents should be selective for transformed cells

Tight local approximation results for max-min linear programs

In a bipartite max-min LP, we are given a bipartite graph \myG = (V \cup I \cup K, E), where each agent $v \in V$ is adjacent to exactly one constraint $i \in I$ and exactly one objective $k \in K$. Each agent $v$ controls a variable $x_v$. For each $i \in I$ we have a nonnegative linear constraint on the variables of adjacent agents. For each $k \in K$ we have a nonnegative linear objective function of the variables of adjacent agents. The task is to maximise the minimum of the objective functions. We study local algorithms where each agent $v$ must choose $x_v$ based on input within its constant-radius neighbourhood in \myG. We show that for every $\epsilon>0$ there exists a local algorithm achieving the approximation ratio ${\Delta_I (1 - 1/\Delta_K)} + \epsilon$. We also show that this result is the best possible -- no local algorithm can achieve the approximation ratio ${\Delta_I (1 - 1/\Delta_K)}$. Here $\Delta_I$ is the maximum degree of a vertex $i \in I$, and $\Delta_K$ is the maximum degree of a vertex $k \in K$. As a methodological contribution, we introduce the technique of graph unfolding for the design of local approximation algorithms.Comment: 16 page