Wnt5a is involved in activating several non-canonical WNT signaling pathways, through binding to different members of the Frizzled- and Ror-family receptors. Wnt5a signaling is critical for regulating normal developmental processes, including proliferation, differentiation, migration, adhesion and polarity. However, the aberrant activation or inhibition of Wnt5a signaling is emerging as an important event in cancer progression, exerting both oncogenic and tumor suppressive effects. Recent studies show the involvement of Wnt5a in regulating cancer cell invasion, metastasis, metabolism and inflammation. In this article, we review findings regarding the molecular mechanisms and roles of Wnt5a signaling in various cancer types, and highlight Wnt5a in ovarian cancer.

This paper attempts to give a self-contained development of dividing theory (also called forking theory) in a strongly homogeneous structure. Dividing is a combinatorial property of the invariant relations on a structure that have yielded deep results for the models of so-called "simple" first-order theories. Below we describe for the nonspecialist how this paper fits in the broader context of geometrical stability theory. Naturally, some background in first-order model theory helps to understand these motivating results; however virtually no knowledge of logic is assumed in this paper. Readers desiring a more thorough description of geometrical stability theory are referred to the surveys [Hru97] and [Hru98].Traditionally, geometrical stability theory is a collection of results that apply to definable relations on arbitrary models of a complete first-order theory. It is equivalent and convenient to restrict our attention to the definable relations on a fixed representative model of the theory, called a universal domain. Using the terminology of the abstract, a universal domain is an uncountable model M equipped with the first-order definable relations R which is strongly |M |-homogeneous and compact ; i.e., if { X i : i ∈ I }, where |I| < |M |, is a family of definable relations on M so that i∈F X i = ∅ for any finite F ⊂ I, then i∈I X i = ∅. For our purposes the reader can assume there is a one-to-one correspondence between (complete first-order) theories and universal domains.A massive amount of abstract model theory was developed en route to Shelah's proof of Morley's Conjecture about the number of models, ranging over uncountable cardinals, of a fixed first-order theory [She90]. Most of the work concerned the case of a stable theory, which will not be defined here for the sake of brevity. What is relevant is that most theorems describing the models of a stable theory rely on the forking independence relation. The forking independence relation, F , is a ternary relation on the subsets of the universal domain of a theory, where F (A, B; C) is read "A is forking independent from B over C" (see Remark 2.2). In a stable theory forking independence is symmetric (over C), has finite character (in A and B), bounded dividing, the free extension property and is transitive. (See Definition 2.5, Theorem 2.14 and Corollary 2.15 for precise statements of these properties.) These properties facilitate the introduction of several notions of dimension that lead to procedures for determining when two models are isomorphic. The combinatorial-geometric properties of the definable relations reflected in these dimensions profoundly impact the structure of the models beyond the question of fixing an isomorphism type. The results connected to algebra, known as geometrical

There is growing evidence that cancer of the ascending (right-side) colon is different from cancer of the descending (left-side) colon at the molecular level. Using microarray data from 102 right-side colon carcinomas and 95 left-side colon carcinomas we show that different pathways dominate progression to relapse in right-side and left-side colon cancer. Right-side tumors at a high risk for relapse exhibit elevated expression of cell cycle control genes and elevated Wnt signaling. On the other hand, relapse-prone left-side tumors show elevated expression of genes that promote stromal expansion and reduced expression of tumor suppressor genes that initiate Wnt signaling. Single gene prognostic biomarkers are found separately for right-side and left-side disease. In left-side tumors with low expression levels of NADPH oxidase 4 (NOX4) the 5-year relapse-free survival probability is 0.89 95%CI(0.80 – 0.99), and in tumors with elevated NOX4 expression the probability is 0.51 95%CI(0.37 – 0.70). Right-side tumors with elevated expression levels of caudal type homeobox 2 (CDX2) have a 5-year relapse-free survival probability of 0.88 95%CI(0.80 – 0.96), and those with low CDX2 expression have a corresponding probability of 0.39 95%CI(0.15 – 0.78). Both NOX4 and CDX2 are much less prognostic on the opposite sides. This newly identified role of NOX4 in colon cancer is further investigated using the SW620 lymph-node metastasis colon adenocarcinoma cell line and RNA interference. We show that NOX4 is expressed in the SW620 cell line and that application of NOX4 siRNA causes a significant reduction in reactive oxidative species production.

In this paper a class of simple theories, called the low theories is developed, and the following is proved.Theorem. Let T be a low theory, A a set and a, b elements realizing the same strong type over A. Then, a and b realize the same Lasear strong type over A.

BackgroundMany breast cancer patients remain free of distant metastasis even without adjuvant chemotherapy. While standard histopathological tests fail to identify these good prognosis patients with adequate precision, analyses of gene expression patterns in primary tumors have resulted in more successful diagnostic tests. These tests use continuous measurements of the mRNA concentrations of numerous genes to determine a risk of metastasis in lymph node negative breast cancer patients with other clinical traits.MethodsA survival model is constructed from genes that are both connected with relapse and have expression patterns that define distinct subtypes, suggestive of different cellular states. This in silico study uses publicly available microarray databases generated with Affymetrix GeneChip technology. The genes in our model, as represented by array probes, have distinctive distributions in a patient cohort, consisting of a large normal component of low expression values; and a long right tail of high expression values. The cutoff between low and high expression of a probe is determined from the distribution using the theory of mixture models. The good prognosis group in our model consists of the samples in the low expression component of multiple genes.ResultsHere, we define a novel test for risk of metastasis in estrogen receptor positive (ER+) breast cancer patients, using four probes that determine distinct subtypes. The good prognosis group in this test, denoted AP4-, consists of the samples with low expression of each of the four probes. Two probes target MKI67, antigen identified by monoclonal antibody Ki-67, one targets CDC6, cell division cycle 6 homolog (S. cerevisiae), and a fourth targets SPAG5, sperm associated antigen 5. The long-term metastasis-free survival probability for samples in AP4- is sufficiently high to render chemotherapy of questionable benefit.ConclusionA breast cancer subtype defined by low expression of a few genes, using a minimum of statistical modeling, has significant prognostic power. This test is of potential clinical benefit in deciding a course of treatment for early stage breast cancer patients.