Characterizations of k-copwin graphs

AbstractWe give two characterizations of the graphs on which k cops have a winning strategy in the game of Cops and Robber. One of these is in terms of an order relation, and one is in terms of a vertex ordering. Both generalize characterizations known for the case k=1

A note on the Cops & Robber game on graphs embedded in non-orientable surfaces

The Cops and Robber game is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if they can catch the robber. The minimum number of cops needed to win on a graph is called its cop number. It is known that the cop number of a graph embedded on a surface $X$ of genus $g$ is at most $3g/2 + 3$, if $X$ is orientable (Schroeder 2004), and at most $2g+1$, otherwise (Nowakowski & Schroeder 1997). We improve the bounds for non-orientable surfaces by reduction to the orientable case using covering spaces. As corollaries, using Schroeder's results, we obtain the following: the maximum cop number of graphs embeddable in the projective plane is 3; the cop number of graphs embeddable in the Klein Bottle is at most 4, and an upper bound is $3g/2 + 3/2$ for all other $g$.Comment: 5 pages, 1 figur

The development and preliminary validation of a Preference-Based Stroke Index (PBSI)

BACKGROUND: Health-related quality of life (HRQL) is a key issue in disabling conditions like stroke. Unfortunately, HRQL is often difficult to quantify in a comprehensive measure that can be used in cost analyses. Preference-based HRQL measures meet this challenge. To date, there are no existing preference-based HRQL measure for stroke that could be used as an outcome in clinical and economic studies of stroke. The aim of this study was to develop the first stroke-specific health index, the Preference-based Stroke Index (PBSI). METHODS: The PBSI includes 10 items; walking, climbing stairs, physical activities/sports, recreational activities, work, driving, speech, memory, coping and self-esteem. Each item has a 3-point response scale. Items known to be impacted by a stroke were selected. Scaling properties and preference-weights obtained from individuals with stroke and their caregivers were used to develop a cumulative score. RESULTS: Compared to the EQ-5D, the PBSI showed no ceiling effect in a high-functioning stroke population. Moderately high correlations were found between the physical function (r = 0.78), vitality (r = 0.67), social functioning (r = 0.64) scales of the SF-36 and the PBSI. The lowest correlation was with the role emotional scale of the SF-36 (r = 0.32). Our results indicated that the PBSI can differentiate patients by severity of stroke (p < 0.05) and level of functional independence (p < 0.0001). CONCLUSIONS: Content validity and preliminary evidence of construct validity has been demonstrated. Further work is needed to develop a multiattribute utility function to gather information on psychometric properties of the PBSI

Ablation of β1 integrin in mammary epithelium reveals a key role for integrin in glandular morphogenesis and differentiation

Integrin-mediated adhesion regulates the development and function of a range of tissues; however, little is known about its role in glandular epithelium. To assess the contribution of β1 integrin, we conditionally deleted its gene in luminal epithelia during different stages of mouse mammary gland development and in cultured primary mammary epithelia. Loss of β1 integrin in vivo resulted in impaired alveologenesis and lactation. Cultured β1 integrin–null cells displayed abnormal focal adhesion function and signal transduction and could not form or maintain polarized acini. In vivo, epithelial cells became detached from the extracellular matrix but remained associated with each other and did not undergo overt apoptosis. β1 integrin–null mammary epithelial cells did not differentiate in response to prolactin stimulation because of defective Stat5 activation. In mice where β1 integrin was deleted after the initiation of differentiation, fewer defects in alveolar morphology occurred, yet major deficiencies were also observed in milk protein and milk fat production and Stat5 activation, indicating a permissive role for β1 integrins in prolactin signaling. This study demonstrates that β1 integrin is critical for the alveolar morphogenesis of a glandular epithelium and for maintenance of its differentiated function. Moreover, it provides genetic evidence for the cooperation between integrin and cytokine signaling pathways

Adjuvant endocrine therapy for premenopausal women with early breast cancer

Adjuvant endocrine therapy is a pivotal component of treatment for premenopausal women with early-stage hormone receptor-positive breast cancer. Currently, the standard endocrine therapy for premenopausal women is tamoxifen; a role for ovarian suppression or ablation has also been identified. Uncertainty remains about the optimal use of endocrine therapy in this setting. The role of ovarian suppression with tamoxifen or aromatase inhibitor, the optimal duration of adjuvant endocrine therapy and the utility of biomarkers and pharmacogenetic studies to select therapy are questions worthy of further investigation

Substrates of the \u3cem\u3eArabidopsis thaliana\u3c/em\u3e Protein Isoaspartyl Methyltransferase 1 Identified Using Phage Display and Biopanning

The role of protein isoaspartyl methyltransferase (PIMT) in repairing a wide assortment of damaged proteins in a host of organisms has been inferred from the affinity of the enzyme for isoaspartyl residues in a plethora of amino acid contexts. The identification of PIMT target proteins in plant seeds, where the enzyme is highly active and proteome long-lived, has been hindered by large amounts of isoaspartate-containing storage proteins. Mature seed phage display libraries circumvented this problem. Inclusion of the PIMT co-substrate, S-adenosylmethionine (AdoMet), during panning permitted PIMT to retain aged phage in greater numbers than controls lacking co-substrate or when PIMT protein binding was poisoned with S-adenosyl homocysteine. After four rounds, phage titer plateaued in AdoMet-containing pans, whereas titer declined in both controls. This strategy identified 17 in-frame PIMT target proteins, including a cupin-family protein similar to those identified previously using on-blot methylation. All recovered phage had at least one susceptible Asp or Asn residue. Five targets were recovered independently. Two in-frame targets were produced in Escherichia coli as recombinant proteins and shown by on-blot methylation to acquire isoAsp, becoming a PIMT target. Both gained isoAsp rapidly in solution upon thermal insult. Mutant analysis of plants deficient in any of three in-frame PIMT targets resulted in demonstrable phenotypes. An over-representation of clones encoding proteins involved in protein production suggests that the translational apparatus comprises a subgroup for which PIMT-mediated repair is vital for orthodox seed longevity. Impaired PIMT activity would hinder protein function in these targets, possibly resulting in poor seed performance

Covalent targeting of remote cysteine residues to develop CDK12 and CDK13 inhibitors

Cyclin-dependent kinases 12 and 13 (CDK12 and CDK13) play critical roles in the regulation of gene transcription. However, the absence of CDK12 and CDK13 inhibitors has hindered the ability to investigate the consequences of their inhibition in healthy cells and cancer cells. Here we describe the rational design of a first-in-class CDK12 and CDK13 covalent inhibitor, THZ531. Co-crystallization of THZ531 with CDK12–cyclin K indicates that THZ531 irreversibly targets a cysteine located outside the kinase domain. THZ531 causes a loss of gene expression with concurrent loss of elongating and hyperphosphorylated RNA polymerase II. In particular, THZ531 substantially decreases the expression of DNA damage response genes and key super-enhancer-associated transcription factor genes. Coincident with transcriptional perturbation, THZ531 dramatically induced apoptotic cell death. Small molecules capable of specifically targeting CDK12 and CDK13 may thus help identify cancer subtypes that are particularly dependent on their kinase activities.United States. National Institutes of Health (HG002668)United States. National Institutes of Health (CA109901

Covalent targeting of remote cysteine residues to develop CDK12 and CDK13 inhibitors

Cyclin-dependent kinases 12 and 13 (CDK12 and CDK13) play critical roles in the regulation of gene transcription. However, the absence of CDK12 and CDK13 inhibitors has hindered the ability to investigate the consequences of their inhibition in healthy cells and cancer cells. Here we describe the rational design of a first-in-class CDK12 and CDK13 covalent inhibitor, THZ531. Co-crystallization of THZ531 with CDK12–cyclin K indicates that THZ531 irreversibly targets a cysteine located outside the kinase domain. THZ531 causes a loss of gene expression with concurrent loss of elongating and hyperphosphorylated RNA polymerase II. In particular, THZ531 substantially decreases the expression of DNA damage response genes and key super-enhancer-associated transcription factor genes. Coincident with transcriptional perturbation, THZ531 dramatically induced apoptotic cell death. Small molecules capable of specifically targeting CDK12 and CDK13 may thus help identify cancer subtypes that are particularly dependent on their kinase activities.United States. National Institutes of Health (HG002668)United States. National Institutes of Health (CA109901