Inhibition of the ATPase activity of the chaperone protein HSP90 is a potential strategy for treatment of cancers. We have determined structures of the HSP90alpha N-terminal domain complexed with the purine-based inhibitor, PU3, and analogs with enhanced potency both in enzyme and cell-based assays. The compounds induce upregulation of HSP70 and downregulation of the known HSP90 client proteins Raf-1, CDK4, and ErbB2, confirming that the molecules inhibit cell growth by a mechanism dependent on HSP90 inhibition. We have also determined the first structure of the N-terminal domain of HSP90beta, complexed with PU3. The structures allow a detailed rationale to be developed for the observed affinity of the PU3 class of compounds for HSP90 and also provide a structural framework for design of compounds with improved binding affinity and drug-like properties.

Dedicated to the memory of Andrei ZelevinskyKeywords: Tropical linear spaces Tropical hyperplane arrangements Matchings Matroid polytope subdivisions Transversal matroids Mixed subdivisions Stiefel mapThe tropical Stiefel map associates to a tropical matrix A its tropical Plücker vector of maximal minors, and thus a tropical linear space L(A). We call the L(A)s obtained in this way Stiefel tropical linear spaces. We prove that they are dual to certain matroid subdivisions of polytopes of transversal matroids, and we relate their combinatorics to a canonically associated tropical hyperplane arrangement. We also explore a broad connection with the secondary fan of the Newton polytope of the product of all maximal minors of a matrix. In addition, we investigate the natural parametrization of L(A) arising from the tropical linear map defined by A.

Many important invariants for matroids and polymatroids, such as the Tutte polynomial, the Billera-Jia-Reiner quasi-symmetric function, and the invariant $\mathcal G$ introduced by the first author, are valuative. In this paper we construct the $\Z$-modules of all $\Z$-valued valuative functions for labeled matroids and polymatroids on a fixed ground set, and their unlabeled counterparts, the $\Z$-modules of valuative invariants. We give explicit bases for these modules and for their dual modules generated by indicator functions of polytopes, and explicit formulas for their ranks. Our results confirm a conjecture of the first author that $\mathcal G$ is universal for valuative invariants.Comment: 54 pp, 9 figs. Mostly minor changes; Cor 10.5 and formula for products of $u$s corrected; Prop 7.2 is new. To appear in Advances in Mathematic

Progressive meningiomas that have failed surgery and radiation have a poor prognosis and no standard therapy. While meningiomas are more common in females overall, progressive meningiomas are enriched in males. We performed a comprehensive molecular characterization of 169 meningiomas from 53 patients with progressive/high-grade tumors, including matched primary and recurrent samples. Exome sequencing in an initial cohort (n = 24) detected frequent alterations in genes residing on the X chromosome, with somatic intragenic deletions of the dystrophin-encoding and muscular dystrophy-associated DMD gene as the most common alteration (n = 5, 20.8%), along with alterations of other known X-linked cancer-related genes KDM6A (n =2, 8.3%), DDX3X, RBM10 and STAG2 (n = 1, 4.1% each). DMD inactivation (by genomic deletion or loss of protein expression) was ultimately detected in 17/53 progressive meningioma patients (32%). Importantly, patients with tumors harboring DMD inactivation had a shorter overall survival (OS) than their wild-type counterparts [5.1 years (95% CI 1.3-9.0) vs. median not reached (95% CI 2.9-not reached, p = 0.006)]. Given the known poor prognostic association of TERT alterations in these tumors, we also assessed for these events, and found seven patients with TERT promoter mutations and three with TERT rearrangements in this cohort (n = 10, 18.8%), including a recurrent novel RETREG1-TERT rearrangement that was present in two patients. In a multivariate model, DMD inactivation (p = 0.033, HR = 2.6, 95% CI 1.0-6.6) and TERT alterations (p = 0.005, HR = 3.8, 95% CI 1.5-9.9) were mutually independent in predicting unfavorable outcomes. Thus, DMD alterations identify a subset of progressive/high-grade meningiomas with worse outcomes.