Some flows in shape optimization

Geometric flows related to shape optimization problems of Bernoulli type are investigated. The evolution law is the sum of a curvature term and a nonlocal term of Hele-Shaw type. We introduce generalized set solutions, the definition of which is widely inspired by viscosity solutions. The main result is an inclusion preservation principle for generalized solutions. As a consequence, we obtain existence, uniqueness and stability of solutions. Asymptotic behavior for the flow is discussed: we prove that the solutions converge to a generalized Bernoulli exterior free boundary problem

A novel androgen receptor splice variant is up-regulated during prostate cancer progression and promotes androgen depletion-resistant growth

The androgen receptor (AR) plays a key role in progression to incurable androgen ablation–resistant prostate cancer (PCA). We have identified three novel AR splice variants lacking the ligand-binding domain (designated as AR3, AR4, and AR5) in hormone-insensitive PCA cells. AR3, one of the major splice variants expressed in human prostate tissues, is constitutively active, and its transcriptional activity is not regulated by androgens or antiandrogens. Immunohistochemistry analysis on tissue microarrays containing 429 human prostate tissue samples shows that AR3 is significantly up-regulated during PCA progression and AR3 expression level is correlated with the risk of tumor recurrence after radical prostatectomy. Overexpression of AR3 confers ablation-independent growth of PCA cells, whereas specific knockdown of AR3 expression (without altering AR level) in hormone-resistant PCA cells attenuates their growth under androgen-depleted conditions in both cell culture and xenograft models, suggesting an indispensable role of AR3 in ablation-independent growth of PCA cells. Furthermore, AR3 may play a distinct, yet essential, role in ablation-independent growth through the regulation of a unique set of genes, including AKT1, which are not regulated by the prototype AR. Our data suggest that aberrant expression of AR splice variants may be a novel mechanism underlying ablation independence during PCA progression, and AR3 may serve as a prognostic marker to predict patient outcome in response to hormonal therapy. Given that these novel AR splice variants are not inhibited by currently available antiandrogen drugs, development of new drugs targeting these AR isoforms may potentially be effective for treatment of ablation-resistant PCA