Constructing free actions of p-groups on products of spheres

We prove that, for p an odd prime, every finite p-group of rank 3 acts freely on a finite complex X homotopy equivalent to a product of three spheres

Mechanisms and therapeutic targeting of NT5C2 mutations in relapsed acute lymphoblastic leukemia

Acute lymphoblastic leukemia (ALL) is an aggressive hematologic malignancy that results from the unregulated growth of B-cell and T-cell lymphoid progenitors. Despite the implementation of risk-stratification and improved multi-agent therapeutic regimens, 20% of pediatric and 50% of adult patients fail to achieve remission and end up relapsing. NT5C2 (5’ cytosolic nucleotidase II) is the most frequently mutated gene specifically found in relapsed ALL. NT5C2 mutations are present in 20% of relapsed T-ALLs and 3-10% of relapsed B-ALLs and present as heterozygous gain of function alleles exhibiting increased nucleotidase activity. As NT5C2 can dephosphorylate and inactivate the cytotoxic metabolites generated by 6-mercaptopurine, a chemotherapy used in the treatment of ALL, these NT5C2 activating mutations can contribute to thiopurine chemotherapy resistance (Tzoneva, Perez-Garcia et al. 2013). Here we perform an extensive structure-function study to understand how relapse-associated NT5C2 mutations result in increased nucleotidase activity and contribute to chemotherapy resistance in ALL. Crystallization of 15 NT5C2 WT and mutant structures as well as enzymatic, structural modeling, and genetic screens identified three regulatory mechanisms of NT5C2, which are disrupted by these gain of function alleles. Class I NT5C2 mutations lock the protein in an active configuration through stabilization of the helixA region, which allows for substrate processing and catalysis. Class II NT5C2 mutations disrupt an intramolecular switch off domain involving the arm region and the intermonomeric positively charged pocket. And a single C-terminus truncating mutant creates a third class of mutations, which show increased nucleotidase activity due to the loss of the C-terminus blockade against allosteric activation. These studies provide new insight into the regulatory controls that mediate NT5C2 activity providing a framework for the development of targeted inhibitors for the treatment of relapsed ALL. In addition to looking at relapse associated NT5C2 mutations on a structural level, we also explored how NT5C2 mutations shape the clonal architecture and evolutionary dynamics during tumor initiation and disease progression in ALL. To formally address these questions, we developed a murine NOTCH1-driven T-ALL with conditional knock-in of the Nt5c2R367Q mutation, the most recurrent mutation found in relapsed ALL, from the endogenous locus. Using this model, we confirmed that Nt5c2+/R367Q lymphoblasts show increased resistance to 6-MP in vitro and in vivo. We also found that Nt5c2+/R367Q mutant lymphoblasts exhibit impaired cell fitness and decreased leukemia initiating cell capacity. Metabolomic profiling and guanosine rescue experiments show that this decrease in cell fitness is due to excess clearance of purine metabolites out of the cell as a result of deregulated Nt5c2 nucleotidase activity. However, in the context of 6-MP therapy, Nt5c2+/R367Q mutant cells are positively selected for in mixed population studies in vitro and in vivo. These results identify a clear selective advantage for NT5C2 mutant cells in the context of 6-MP chemotherapy. In addition, NT5C2 mutant chemoresistant cells show collateral sensitivity to inhibition of inosine monophosphate dehydrogenase (IMPDH) with mizoribine, which further disrupts guanosine production pointing to a potentially selective therapy against NT5C2 mutant cells. We also show here the initial development of a small molecule NT5C2 inhibitor for the treatment of relapsed ALL. Using a malachite green based NT5C2 nucleotidase assay, we performed a small molecule high throughput assay and identified HTP_2 as a lead compound with low micromolar inhibitory activity against NT5C2 R367Q mutant recombinant protein. HTP_2 can reverse 6-MP resistance in Nt5c2+/R367Q mouse lymphoblasts and NT5C2 R29Q mutant expressing human cell lines. Interestingly, HTP_2 treatment also results in increased sensitivity to 6-MP therapy in NT5C2 wild-type cells, suggesting a role for wild-type NT5C2 activity in the clearance of 6-MP and supporting a potential therapeutic use for NT5C2 inhibitors in potentiating the effects of 6-MP based chemotherapy in NT5C2 wild-type cells as well. NT5C2 knockdown cells and Nt5c2 knockout mice show no apparent toxicities suggesting that systemic inhibition of NT5C2 could be fairly well tolerated. In all, this work presents a framework for the development of a high affinity NT5C2 inhibitor for the reversal of 6-MP resistance in relapsed ALL patients. These studies presented here address the role of NT5C2 mutant proteins as drivers of resistance and as therapeutic targets in relapsed ALL. Improved understanding of the molecular mechanisms responsible for increased NT5C2 nucleotidase activity and on the process of clonal evolution during disease progression provide important insight into the mechanism driving ALL resistance and relapse. The identification of IMPDH inhibition as a collateral vulnerability in NT5C2 mutant ALL cells and the development of a first-in-class NT5C2 inhibitor serve as framework for the development of new combination therapies aimed at curtailing the emergence of these thiopurine-resistant relapse driving clones in ALL

Bridges with pillars: a graphical calculus of knot algebra

AbstractThe paper comprises a graphical calculus which is designed to deal with the Coxeter-Dynkin series of type E and some generalizations. Temperley-Lieb algebras of type E are defined as quotients of Hecke algebras and the module structure of the algebra associated to E6 is determined. The graphical calculus is a refinement of the calculus for the ordinary Temperley-Lieb algebra: a planar strip is decomposed by the arcs of a diagram into domains and the domains are used to incorporate additional information into the figure

A detailed description of the uncertainty analysis for High Area Ratio Rocket Nozzle tests at the NASA Lewis Research Center

A preliminary uncertainty analysis has been performed for the High Area Ratio Rocket Nozzle test program which took place at the altitude test capsule of the Rocket Engine Test Facility at the NASA Lewis Research Center. Results from the study establish the uncertainty of measured and calculated parameters required for the calculation of rocket engine specific impulse. A generalized description of the uncertainty methodology used is provided. Specific equations and a detailed description of the analysis are presented. Verification of the uncertainty analysis model was performed by comparison with results from the experimental program's data reduction code. Final results include an uncertainty for specific impulse of 1.30 percent. The largest contributors to this uncertainty were calibration errors from the test capsule pressure and thrust measurement devices

K- and L-theory of the semi-direct product of the discrete 3-dimensional Heisenberg group by Z/4

We compute the group homology, the topological K-theory of the reduced C^*-algebra, the algebraic K-theory and the algebraic L-theory of the group ring of the semi-direct product of the three-dimensional discrete Heisenberg group by Z/4. These computations will follow from the more general treatment of a certain class of groups G which occur as extensions 1-->K-->G-->Q-->1 of a torsionfree group K by a group Q which satisfies certain assumptions. The key ingredients are the Baum-Connes and Farrell-Jones Conjectures and methods from equivariant algebraic topology.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper37.abs.htm

Smith Theory for algebraic varieties

We show how an approach to Smith Theory about group actions on CW-complexes using Bredon cohomology can be adapted to work for algebraic varieties.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-8.abs.htm

Homotopy Theory of Strong and Weak Topological Insulators

We use homotopy theory to extend the notion of strong and weak topological insulators to the non-stable regime (low numbers of occupied/empty energy bands). We show that for strong topological insulators in d spatial dimensions to be "truly d-dimensional", i.e. not realizable by stacking lower-dimensional insulators, a more restrictive definition of "strong" is required. However, this does not exclude weak topological insulators from being "truly d-dimensional", which we demonstrate by an example. Additionally, we prove some useful technical results, including the homotopy theoretic derivation of the factorization of invariants over the torus into invariants over spheres in the stable regime, as well as the rigorous justification of replacing $T^d$ by $S^d$ and $T^{d_k}\times S^{d_x}$ by $S^{d_k+d_x}$ as is common in the current literature.Comment: 11 pages, 3 figure

Reevaluating the Forum Non Conveniens Doctrine in Multiterritorial Copyright Infringement Cases

The tension between the internationalization of copyright and the territorial remedies national laws provide is illustrated when the same infringer infringes a copyright in multiple countries. The copyright owner can bring suit in each country separately or attempt to consolidate all claims into one forum. Commentators have identified that in consolidated suits, even if jurisdiction over the foreign claims is proper, the discretionary forum non conveniens doctrine rmains a wild card. This Comment explores in greater depth why the doctrine is unpredictable and argues that it is being abused by U.S. federal courts in multiterritorial copyright suits, exacerbating the problem the Internet has caused copyright enforcement The courts\u27 liberal use of dismissals has forced copyright owners to bring separate claims in multiple fora, effectively terminating the claims due to the enormous costs of litigating in multiple countries. Foreign claim consolidation mitigates the problem of expensive, piecemeal remedies from individual national courts and allows copyright owners a more realistic method of enforcement

The essential ideal in group cohomology does not square to zero

Let G be the Sylow 2-subgroup of the unitary group $SU_3(4)$. We find two essential classes in the mod-2 cohomology ring of G whose product is nonzero. In fact, the product is the ``last survivor'' of Benson-Carlson duality. Recent work of Pakianathan and Yalcin then implies a result about connected graphs with an action of G. Also, there exist essential classes which cannot be written as sums of transfers from proper subgroups. This phenomenon was first observed on the computer. The argument given here uses the elegant calculation by J. Clark, with minor corrections.Comment: 9 pages; three typos corrected, one was particularly confusin