The cadherin-catenin proteins have in common with heat shock proteins (HSP) the capacity to bind/interact proteins of other classes. Moreover, there are common molecular pathways that connect the HSP response and the cadherin-catenin protein system. In the present study, we have explored whether in breast cancer the HSP might interact functionally with the cadherin-catenin cell adhesion system. Beta-catenin was immunoprecipitated from breast cancer biopsy samples, and the protein complexes isolated in this way were probed with antibodies against HSP family members. We are thus the first to demonstrate a specific interaction between beta-catenin and Hsp27. However, beta-catenin did not bind Hsp60, Hsp70, Hsp90, gp96, or the endoplasmic reticulum stress response protein CHOP. To confirm the finding of Hsp27-beta-catenin interaction, the 27-kDa immunoprecipitated band was excised from one-dimensional polyacrylamide gel electrophoresis gels and submitted to liquid chromatography-tandem mass spectrometry with electrospray ionization, confirming a role for Hsp27. In addition, beta-catenin interacted with other proteins including heat shock transcription factor 1, P-cadherin, and caveolin-1. In human breast cancer biopsy samples, beta-catenin was coexpressed in the same tumor areas and in the same tumor cells that expressed Hsp27. However, this coexpression was strong when beta-catenin was present in the cytoplasm of the tumor cells and not when beta-catenin was expressed at the cell surface only. Furthermore, murine breast cancer cells transfected with hsp25 showed a redistribution of beta-catenin from the cell membrane to the cytoplasm. When the prognostic significance of cadherin-catenin expression was examined by immunohistochemistry in breast cancer patients (n = 215, follow-up = >10 years), we found that the disease-free survival and overall survival were significantly shorter for patients expressing P-cadherin and for patients showing expression of beta-catenin in the cytoplasm only (not at the cell surface). The interactions of beta-catenin with Hsp27 and with HSF1 may explain some of the molecular pathways that influence tumor cell survival and the clinical significance in the prognosis of the breast cancer patients.

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The variogram is a standard tool in the analysis of spatial data, and its shape provides useful information on the form of spatial correlation that may be present. However, it is also useful to be able to assess the evidence for the presence of any spatial correlation. A method of doing this, based on an assessment of whether the true function underlying the variogram is constant, is proposed. Nonparametric smoothing of the squared differences of the observed variables, on a suitably transformed scale, is used to estimate variogram shape. A statistic based on a ratio of quadratic forms is proposed and the test is constructed by investigating the distributional properties of this statistic under the assumption of an independent Gaussian process. The power of the test is investigated. Reference bands are proposed as a graphical follow-up. An example is discussed.

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The variogram is one of the most important tools in the assessment of spatial variability and a crucial parameter for kriging. It is widely known that an estimator for the variogram cannot be used as its representator in some contexts because of its lack of conditional semi negative definiteness. Consequently, once the variogram is estimated, a valid family must be chosen to fit an appropriate model. Under isotropy, this selection is carried out ''by eye'' from the observation of the variogram estimated curve. In this paper, a statistical methodology is proposed to explore a valid model for the variogram. The statistic for this approach is based on quadratic forms depending on smoothed random variables which gather the underlying spatial variation. The distribution of the test statistic is approximated by a shifted chi-square distribution. A simulation study is also carried out to check the power and size of the test. Reference bands, as a complementary graphical tool, are calculated. An example from the literature is used to illustrate the methodologies presented.

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