Summary Progesterone receptor (PR) expression is employed as a biomarker of estrogen receptor-α (ERα) function and breast cancer prognosis. We now show that PR is not merely an ERα-induced gene target, but is also an ERα-associated protein that modulates its behaviour. In the presence of agonist ligands, PR associates with ERα to direct ERα chromatin binding events within breast cancer cells, resulting in a unique gene expression programme that is associated with good clinical outcome. Progesterone inhibited estrogen-mediated growth of ERα+ cell line xenografts and primary ERα+ breast tumour explants and had increased anti-proliferative effects when coupled with an ERα antagonist. Copy number loss of PgR is a common feature in ERα+ breast cancers, explaining lower PR levels in a subset of cases. Our findings indicate that PR functions as a molecular rheostat to control ERα chromatin binding and transcriptional activity, which has important implications for prognosis and therapeutic interventions.

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Estrogen receptor-α (ER) is the driving transcription factor in most breast cancers, and its associated proteins can influence drug response, but direct methods for identifying interacting proteins have been limited. We purified endogenous ER using an approach termed RIME (rapid immunoprecipitation mass spectrometry of endogenous proteins) and discovered the interactome under agonist- and antagonist-liganded conditions in breast cancer cells, revealing transcriptional networks in breast cancer. The most estrogen-enriched ER interactor is GREB1, a potential clinical biomarker with no known function. GREB1 is shown to be a chromatin-bound ER coactivator and is essential for ER-mediated transcription, because it stabilizes interactions between ER and additional cofactors. We show a GREB1-ER interaction in three xenograft tumors, and using a directed protein-protein approach, we find GREB1-ER interactions in half of ER(+) primary breast cancers. This finding is supported by histological expression of GREB1, which shows that GREB1 is expressed in half of ER(+) cancers, and predicts good clinical outcome. These findings reveal an unexpected role for GREB1 as an estrogen-specific ER cofactor that is expressed in drug-sensitive contexts.

A lthough research evaluating the impact of supply chain integration on performance has advanced substantially in the last decade, inconsistency and considerable variability of empirical findings leave unanswered questions for both research and practice. Using a meta-analysis, we examine empirical studies to clarify the actual relationship, suggest new directions, and ultimately contribute toward the development of supply chain management theory. We focus on "strategic" supply chain integration rather than on functional or operational/tactical studies, which would weaken the practical value of the analysis and findings. To ascertain focus and homogeneity of the sample, we adopt a rigorous search protocol and sample construction. We find that integration-performance relationships are complex and nuanced such that integration should not be universally viewed as improving performance. We identify relationships that are more generalizable and also those that need additional scrutiny. Finally, we discuss the implications of our findings and provide directions for future research.

Breast cancer is a heterogeneous disease and several distinct subtypes exist based on differential gene expression patterns. Molecular apocrine tumours were recently identified as an additional subgroup, characterised as oestrogen receptor negative and androgen receptor positive (ER- AR+), but with an expression profile resembling ER+ luminal breast cancer. One possible explanation for the apparent incongruity is that ER gene expression programmes could be recapitulated by AR. Using a cell line model of ER- AR+ molecular apocrine tumours (termed MDA-MB-453 cells), we map global AR binding events and find a binding profile that is similar to ER binding in breast cancer cells. We find that AR binding is a near-perfect subset of FoxA1 binding regions, a level of concordance never previously seen with a nuclear receptor. AR functionality is dependent on FoxA1, since silencing of FoxA1 inhibits AR binding, expression of the majority of the molecular apocrine gene signature and growth cell growth. These findings show that AR binds and regulates ER cis-regulatory elements in molecular apocrine tumours, resulting in a transcriptional programme reminiscent of ER-mediated transcription in luminal breast cancers.

Androgen receptor (AR) signaling exerts an antiestrogenic, growth-inhibitory influence in normal breast tissue, and this role may be sustained in estrogen receptor α (ERα)-positive luminal breast cancers. Conversely, AR signaling may promote growth of a subset of ERα-negative, AR-positive breast cancers with a molecular apocrine phenotype. Understanding the molecular mechanisms whereby androgens can elicit distinct gene expression programs and opposing proliferative responses in these two breast cancer phenotypes is critical to the development of new therapeutic strategies to target the AR in breast cancer.

In this paper we establish a mathematical framework for a range of inverse problems for functions, given a finite set of noisy observations. The problems are hence underdetermined and are often ill-posed. We study these problems from the viewpoint of Bayesian statistics, with the resulting posterior probability measure being defined on a space of functions. We develop an abstract framework for such problems which facilitates application of an infinite-dimensional version of Bayes theorem, leads to a well-posedness result for the posterior measure (continuity in a suitable probability metric with respect to changes in data), and also leads to a theory for the existence of maximizing the posterior probability (MAP) estimators for such Bayesian inverse problems on function space. A central idea underlying these results is that continuity properties and bounds on the forward model guide the choice of the prior measure for the inverse problem, leading to the desired results on well-posedness and MAP estimators; the PDE analysis and probability theory required are thus clearly dileneated, allowing a straightforward derivation of results. We show that the abstract theory applies to some concrete applications of interest by studying problems arising from data assimilation in fluid mechanics. The objective is to make inference about the underlying velocity field, on the basis of either Eulerian or Lagrangian observations. We study problems without model error, in which case the inference is on the initial condition, and problems with model error in which case the inference is on the initial condition and on the driving noise process or, equivalently, on the entire time-dependent velocity field. In order to undertake a relatively uncluttered mathematical analysis we consider the two-dimensional Navier-Stokes equation on a torus. The case of Eulerian observationsdirect observations of the velocity field itself-is then a model for weather forecasting. The case of Lagrangian observations-observations of passive tracers advected by the flow-is then a model for data arising in oceanography. The methodology which we describe herein may be applied to many other inverse problems in which it is of interest to find, given observations, an infinitedimensional object, such as the initial condition for a PDE. A similar approach might be adopted, for example, to determine an appropriate mathematical

This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into finite-dimensional Euclidean spaces. The first part brings together a number of abstract embedding results, and provides a unified treatment of four definitions of dimension that arise in disparate fields: Lebesgue covering dimension (from classical 'dimension theory'), Hausdorff dimension (from geometric measure theory), upper box-counting dimension (from dynamical systems), and Assouad dimension (from the theory of metric spaces). These abstract embedding results are applied in the second part of the book to the finite-dimensional global attractors that arise in certain infinite-dimensional dynamical systems, deducing practical consequences from the existence of such attractors: a version of the Takens time-delay embedding theorem valid in spatially extended systems, and a result on parametrisation by point values. This book will appeal to all researchers with an interest in dimension theory, particularly those working in dynamical systems.