An average case analysis of a greedy algorithm for the on-line Steiner tree problem

AbstractThis paper gives the average distance analysis for the Euclidean tree constructed by a simple greedy but efficient algorithm of the on-line Steiner tree problem. The algorithm accepts the data one by one following the order of input sequence. When a point arrives, the algorithm adds the shortest edge, between the new point and the points arriving already, to the previously constructed tree to form a new tree. We first show that, given n points uniformly on a unit disk in the plane, the expected Euclidean distance between a point and its jth (1 ≤ j ≤ n − 1) nearest neighbor is less than or equal to (53)√jn when n is large. Based upon this result, we show that the expected length of the tree constructed by the on-line algorithm is not greater than 4.34 times the expected length of the minimum Steiner tree when the number of input points is large

Manipulation of magnetic nanoparticle retention and hemodynamic consequences in microcirculation: assessment by laser speckle imaging

Magnetic nanoparticles (MNPs) have been proposed for targeted or embolization therapeutics. How MNP retention occurs in circulation may critically determine local hemodynamics, tissue distribution of MNPs, and the therapeutic effects. We attempted to establish a microcirculation model to study the magnetic capture of MNPs in small vessels and to determine the factors affecting MNP retention. Two-dimensional hemodynamic changes in response to magnet-induced MNP retention in the microvessels of the cremaster muscle in vivo were observed in a real-time manner using a laser speckle imaging technique. Changes in tissue perfusion of the cremaster muscle appeared to be closely correlated with the location of the magnet placement underneath the muscle in response to intra-arterial administration of dextran-coated MNPs. Magnet-related retention was observed along the edge of the magnet, as corroborated by the results of histology analysis and microcomputed tomography. In these preparations, tissue iron content almost doubled, as revealed by inductively coupled plasma optical emission spectroscopy. In addition, MNP retention was associated with reduced downstream flow in a dose-dependent manner. Dissipation of MNPs (5 mg/kg) occurred shortly after removal of the magnet, which was associated with significant recovery of tissue flow. However, MNP dissipation did not easily occur after administration of a higher MNP dose (10 mg/kg) or prolonged exposure to the magnetic field. An ultrasound after removal of the magnet may induce the partial dispersion of MNPs and thus partially improve hemodynamics. In conclusion, our results revealed the important correlation of local MNP retention and hemodynamic changes in microcirculation, which can be crucial in the application of MNPs for effective targeted therapeutics

Genomic profiling of malignant peritoneal mesothelioma reveals recurrent alterations in epigenetic regulatory genes BAP1, SETD2, and DDX3X.

Malignant mesothelioma is a rare cancer that arises from the mesothelial cells that line the pleural cavity and less commonly from the peritoneal lining of the abdomen and pelvis. Most pleural mesotheliomas arise in patients with a history of asbestos exposure, whereas the association of peritoneal mesotheliomas with exposure to asbestos and other potential carcinogens is less clear, suggesting that the genetic alterations that drive malignant peritoneal mesothelioma may be unique from those in pleural mesothelioma. Treatment options for all malignant mesotheliomas are currently limited, with no known targeted therapies available. To better understand the molecular pathogenesis of malignant peritoneal mesothelioma, we sequenced 510 cancer-related genes in 13 patients with malignant mesothelioma arising in the peritoneal cavity. The most frequent genetic alteration was biallelic inactivation of the BAP1 gene, which occurred in 9/13 cases, with an additional two cases demonstrating monoallelic loss of BAP1. All 11 of these cases demonstrated loss of BAP1 nuclear staining by immunohistochemistry, whereas two tumors without BAP1 alteration and all 42 cases of histologic mimics in peritoneum (8 multilocular peritoneal inclusion cyst, 6 well-differentiated papillary mesothelioma of the peritoneum, 16 adenomatoid tumor, and 12 low-grade serous carcinoma of the ovary) demonstrated intact BAP1 nuclear staining. Additional recurrently mutated genes in this cohort of malignant peritoneal mesotheliomas included NF2 (3/13), SETD2 (2/13), and DDX3X (2/13). While these genes are known to be recurrently mutated in pleural mesotheliomas, the frequencies are distinct in peritoneal mesotheliomas, with nearly 85% of peritoneal tumors harboring BAP1 alterations versus only 20-30% of pleural tumors. Together, these findings demonstrate the importance of epigenetic modifiers including BAP1, SETD2, and DDX3X in mesothelial tumorigenesis and suggest opportunities for targeted therapies

Abrogated Response to Cellular Stress Identifies DCIS Associated with Subsequent Tumor Events and Defines Basal-like Breast Tumors

SummaryApproximately 15%–30% of women diagnosed with ductal carcinoma in situ (DCIS) develop a subsequent tumor event within 10 years after surgical lumpectomy. To date, little is known about the molecular pathways that confer this differential risk for developing subsequent disease. In this study, we demonstrate that expression of biomarkers indicative of an abrogated response to cellular stress predicts DCIS with worse outcome and is a defining characteristic of basal-like invasive tumors. Mechanistic studies identify the Rb pathway as a key regulator of this response. Conversely, biomarkers indicative of an intact response to cellular stress are strongly associated with a disease-free prognosis. Assessment of these biomarkers in DCIS begins to allow prediction of tumor formation years before it actually occurs

Multiple Cancer/Testis Antigens Are Preferentially Expressed in Hormone-Receptor Negative and High-Grade Breast Cancers

BACKGROUND: Cancer/testis (CT) antigens are protein antigens normally expressed only in germ cells of testis, and yet are expressed in a proportion of a wide variety of human cancers. CT antigens can elicit spontaneous immune responses in cancer patients with CT-positive cancers, and CT antigen-based therapeutic cancer vaccine trials are ongoing for "CT-rich" tumors. Although some previous studies found breast cancer to be "CT-poor", our recent analysis identified increased CT mRNA transcripts in the ER-negative subset of breast cancer. METHODOLOGY/PRINCIPAL FINDINGS: In this study, we performed a comprehensive immunohistochemical study to investigate the protein expression of eight CT genes in 454 invasive ductal carcinomas, including 225 ER/PR/HER2-negative (triple-negative) carcinomas. We found significantly more frequent expression of all eight CT antigens in ER-negative cancers, and five of them--MAGEA, CT7, NY-ESO-1, CT10 and CT45, were expressed in 12-24% of ER-negative cancers, versus 2-6% of ER-positive cancers (p<0.001 to 0.003). In comparison, GAGE, SAGE1 and NXF2 were only expressed in 3-5% of ER-negative and 0-2% of ER-positive cancers. ER-negative cancers were also more likely to simultaneously co-express multiple CT antigens, with 27% (34/125) of ER-negative, CT-positive tumors expressing three or more CT antigens. HER2 status had no consistent effect on CT expression, and triple-negative carcinomas showed similar frequencies of MAGEA and NY-ESO-1 expression as ER-negative/HER2-positive carcinomas. More frequent CT expression was also found in tumors with higher nuclear grade (p<0.001 to p = 0.01) and larger in size (>2 cm). CONCLUSIONS/SIGNIFICANCE: CT antigens are preferentially expressed in hormone receptor-negative and high-grade breast cancer. Considering the limited treatment options for ER/PR/HER2 triple-negative breast cancer, the potential of CT-based immunotherapy should be explored

Intratumor Heterogeneity of the Estrogen Receptor and the Long-term Risk of Fatal Breast Cancer.

Background:Breast cancer patients with estrogen receptor (ER)-positive disease have a continuous long-term risk for fatal breast cancer, but the biological factors influencing this risk are unknown. We aimed to determine whether high intratumor heterogeneity of ER predicts an increased long-term risk (25 years) of fatal breast cancer. Methods:The STO-3 trial enrolled 1780 postmenopausal lymph node-negative breast cancer patients randomly assigned to receive adjuvant tamoxifen vs not. The fraction of cancer cells for each ER intensity level was scored by breast cancer pathologists, and intratumor heterogeneity of ER was calculated using Rao's quadratic entropy and categorized into high and low heterogeneity using a predefined cutoff at the second tertile (67%). Long-term breast cancer-specific survival analyses by intra-tumor heterogeneity of ER were performed using Kaplan-Meier and multivariable Cox proportional hazard modeling adjusting for patient and tumor characteristics. Results:A statistically significant difference in long-term survival by high vs low intratumor heterogeneity of ER was seen for all ER-positive patients (P &lt; .001) and for patients with luminal A subtype tumors (P = .01). In multivariable analyses, patients with high intratumor heterogeneity of ER had a twofold increased long-term risk as compared with patients with low intratumor heterogeneity (ER-positive: hazard ratio [HR] = 1.98, 95% confidence interval [CI] = 1.31 to 3.00; luminal A subtype tumors: HR = 2.43, 95% CI = 1.18 to 4.99). Conclusions:Patients with high intratumor heterogeneity of ER had an increased long-term risk of fatal breast cancer. Interestingly, a similar long-term risk increase was seen in patients with luminal A subtype tumors. Our findings suggest that intratumor heterogeneity of ER is an independent long-term prognosticator with potential to change clinical management, especially for patients with luminal A tumors

The molecular basis of breast cancer pathological phenotypes

The histopathological evaluation of morphological features in breast tumours provides prognostic information to guide therapy. Adjunct molecular analyses provide further diagnostic, prognostic and predictive information. However, there is limited knowledge of the molecular basis of morphological phenotypes in invasive breast cancer. This study integrated genomic, transcriptomic and protein data to provide a comprehensive molecular profiling of morphological features in breast cancer. Fifteen pathologists assessed 850 invasive breast cancer cases from The Cancer Genome Atlas (TCGA). Morphological features were significantly associated with genomic alteration, DNA methylation subtype, PAM50 and microRNA subtypes, proliferation scores, gene expression and/or RPPA subtype. Marked nuclear pleomorphism, necrosis, inflammation and high mitotic count were associated with Basal-like subtype and have similar molecular basis. Omics-based signatures were constructed to predict morphological features. The association of morphology transcriptome signatures with overall survival in oestrogen receptor (ER)-positive and ER-negative breast cancer was first assessed using the METABRIC dataset; signatures that remained prognostic in the METABRIC multivariate analysis were further evaluated in five additional datasets. The transcriptomic signature of epithelial tubule formation was prognostic in ER-positive breast cancer. No signature was prognostic in ER-negative. This study provided new insights into the molecular basis of breast cancer morphological phenotypes. The integration of morphological with molecular data has potential to refine breast cancer classification, predict response to therapy, enhance our understanding of breast cancer biology and improve clinical management. This work is publicly accessible at www.dx.ai/tcga_breast

Identification of a robust gene signature that predicts breast cancer outcome in independent data sets

BACKGROUND: Breast cancer is a heterogeneous disease, presenting with a wide range of histologic, clinical, and genetic features. Microarray technology has shown promise in predicting outcome in these patients. METHODS: We profiled 162 breast tumors using expression microarrays to stratify tumors based on gene expression. A subset of 55 tumors with extensive follow-up was used to identify gene sets that predicted outcome. The predictive gene set was further tested in previously published data sets. RESULTS: We used different statistical methods to identify three gene sets associated with disease free survival. A fourth gene set, consisting of 21 genes in common to all three sets, also had the ability to predict patient outcome. To validate the predictive utility of this derived gene set, it was tested in two published data sets from other groups. This gene set resulted in significant separation of patients on the basis of survival in these data sets, correctly predicting outcome in 62–65% of patients. By comparing outcome prediction within subgroups based on ER status, grade, and nodal status, we found that our gene set was most effective in predicting outcome in ER positive and node negative tumors. CONCLUSION: This robust gene selection with extensive validation has identified a predictive gene set that may have clinical utility for outcome prediction in breast cancer patients

Pathologic and biologic response to preoperative endocrine therapy in patients with ER-positive ductal carcinoma in situ

Abstract Background Endocrine therapy is commonly recommended in the adjuvant setting for patients as treatment for ductal carcinoma in situ (DCIS). However, it is unknown whether a neoadjuvant (preoperative) anti-estrogen approach to DCIS results in any biological change. This study was undertaken to investigate the pathologic and biomarker changes in DCIS following neoadjuvant endocrine therapy compared to a group of patients who did not undergo preoperative anti-estrogenic treatment to determine whether such treatment results in detectable histologic alterations. Methods Patients (n = 23) diagnosed with ER-positive pure DCIS by stereotactic core biopsy were enrolled in a trial of neoadjuvant anti-estrogen therapy followed by definitive excision. Patients on hormone replacement therapy, with palpable masses, or with histologic or clinical suspicion of invasion were excluded. Premenopausal women were treated with tamoxifen and postmenopausal women were treated with letrozole. Pathologic markers of proliferation, inflammation, and apoptosis were evaluated at baseline and at three months. Biomarker changes were compared to a cohort of patients who had not received preoperative treatment. Results Median age of the cohort was 53 years (range 38–78); 14 were premenopausal. Following treatment, predominant morphologic changes included increased multinucleated histiocytes and degenerated cells, decreased duct extension, and prominent periductal fibrosis. Two postmenopausal patients had ADH only with no residual DCIS at excision. Postmenopausal women on letrozole had significant reduction of PR, and Ki67 as well as increase in CD68-positive cells. For premenopausal women on tamoxifen treatment, the only significant change was increase in CD68. No change in cleaved caspase 3 was found. Two patients had invasive cancer at surgery. Conclusion Preoperative therapy for DCIS is associated with significant pathologic alterations. These changes may be clinically significant. Further work is needed to identify which women may be the best candidates for such treatment for DCIS, and whether best responders may safely avoid surgical intervention. Trial Registration ClinicalTrials.gov NCT0029074