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The main purpose of this paper is to introduce a method to “stabilise” certain spaces of homomorphisms from finitely generated free abelian groups to a Lie group G, namely Hom(ℤn, G). We show that this stabilised space of homomorphisms decomposes after suspending once with “summands” which can be reassembled, in a sense to be made precise below, into the individual spaces Hom(ℤn, G) after suspending once. To prove this decomposition, a stable decomposition of an equivariant function space is also developed. One main result is that the topological space of all commuting elements in a compact Lie group is homotopy equivalent to an equivariant function space after inverting the order of the Weyl group. In addition, the homology of the stabilised space admits a very simple description in terms of the tensor algebra generated by the reduced homology of a maximal torus in favorable cases. The stabilised space also allows the description of the additive reduced homology of the individual spaces Hom(ℤn, G), with the order of the Weyl group inverted. [ABSTRACT FROM PUBLISHER]

A continuous map Cd⟶CN is a complex k-regular embedding if any kk pairwise distinct points in Cd are mapped by f into k complex linearly independent vectors in CN. The existence of such maps is closely connected with classical problems of algebraic/differential topology, such as embedding/immersion problems. Our central result on complex k-regular embeddings extends results of Cohen & Handel (1978), Chisholm (1979) and Blagojević, Lück & Ziegler (2013) on real kk-regular embeddings. We give the following lower bounds for the existence of complex k-regular embeddings. Let pp be an odd prime, k≥1 and d=pt for t≥1. If there exists a complex k-regular embedding Cd⟶CN, then d(k−αp(k))+αp(k)≤N. Here αp(k) denotes the sum of coefficients in the p-adic expansion of k. These lower bounds are obtained by modifying the framework of Cohen & Handel (1978) and a study of Chern classes of complex regular representations. As a main technical result we establish for this an extended Vassiliev conjecture, the following upper bound for the height of the cohomology of an unordered configuration space: If d≥2 and k≥2 are integers, and pp is an odd prime. Then h(H∗(F(Rd,k)/Sk;Fp))≤min{pt:2pt≥d}. Furthermore, we give similar lower bounds for the existence of complex ℓ-Skew embeddings Cd⟶CN, for which we require that the images of the tangent spaces at any ℓ distinct points are Skew complex affine subspaces of CN. In addition we give improved lower bounds for the Lusternik–Schnirelmann category of F(Cd,k)/Sk as well as for the sectional category of the covering F(Cd,k)⟶F(Cd,k)/Sk. [ABSTRACT FROM AUTHOR]

The complexity of a module is an important homological invariant that measures the polynomial rate of growth of its minimal projective resolution. For the symmetric group Σn, the Lie module Lie(n) has attracted a great deal of interest in recent years. We prove here that the complexity of Lie(n) in characteristic p is t, where pt is the largest power of p dividing n, thus proving a conjecture of Erdmann, Lim and Tan. The proof uses work of Arone and Kankaanrinta which describes the homology H•(Σn, Lie(n)) and earlier work of Hemmer and Nakano on complexity for modules over Σn that involves restriction to Young subgroups. [ABSTRACT FROM AUTHOR]

Dual leucine zipper kinase (DLK,MAP3K12) was recently identifiedas an essential regulator of neuronal degeneration in multiple contexts.Here we describe the generation of potent and selective DLK inhibitorsstarting from a high-throughput screening hit. Using proposed hinge-bindinginteractions to infer a binding mode and specific design parametersto optimize for CNS druglike molecules, we came to focus on the di(pyridin-2-yl)aminesbecause of their combination of desirable potency and good brain penetrationfollowing oral dosing. Our lead inhibitor GNE-3511 (26) displayed concentration-dependent protection of neurons from degenerationin vitro and demonstrated dose-dependent activity in two differentanimal models of disease. These results suggest that specific pharmacologicalinhibition of DLK may have therapeutic potential in multiple indications. [ABSTRACT FROM AUTHOR]

Let G denote a topological group. In this paper the descending central series of free groups are used to construct simplicial spaces of homomorphisms with geometric realizations B(q, G) that provide a filtration of the classifying space BG. In particular this setting gives rise to a single space constructed out of all the spaces of ordered commuting n–tuples of elements in G. Basic properties of these constructions are discussed, including the homotopy type and cohomology when the group G is either a finite group or a compact connected Lie group. For a finite group the construction gives rise to a covering space with monodromy related to a delicate result in group theory equivalent to the odd-order theorem of Feit–Thompson. The techniques here also yield a counting formula for the cardinality of Hom(π, G) where π is any descending central series quotient of a finitely generated free group. Another application is the determination of the structure of the spaces B(2, G) obtained from commuting n-tuples in G for finite groups such that the centralizer of every non–central element is abelian (known as transitively commutative groups), which played a key role in work by Suzuki on the structure of finite simple groups. [ABSTRACT FROM PUBLISHER]

A series of inhibitors of mTOR kinase based on a quaternary-substituted dihydrofuropyrimidine was designed and synthesized. The most potent compounds in this series inhibited mTOR kinase with Ki < 1.0 nM and were highly (>100×) selective for mTOR over the closely related PI3 kinases. Compounds in this series showed inhibition of the pathway and antiproliferative activity in cell-based assays. Furthermore, these compounds had excellent mouse PK, and showed a robust PK−PD relationship in a mouse model of cancer. [ABSTRACT FROM AUTHOR]

Abstract: The main result of this paper is an application of the topology of the space to obtain results for the cohomology of the symmetric group on d letters, , with ‘twisted’ coefficients in various choices of Young modules and to show that these computations reduce to certain natural questions in representation theory. The authors extend classical methods for analyzing the homology of certain spaces with mod-p coefficients to describe the homology as a module for the general linear group over an algebraically closed field k of characteristic p. As a direct application, these results provide a method of reducing the computation of (where , are Young modules) to a representation theoretic problem involving the determination of tensor products and decomposition numbers. In particular, in characteristic two, for many d, a complete determination of can be found. This is the first nontrivial class of symmetric group modules where a complete description of the cohomology in all degrees can be given. For arbitrary d the authors determine for . An interesting phenomenon is uncovered-namely a stability result reminiscent of generic cohomology for algebraic groups. For each i the cohomology stabilizes as a increases. The methods in this paper are also powerful enough to determine, for any p and λ, precisely when . Such modules with vanishing cohomology are of great interest in representation theory because their support varieties constitute the representation theoretic nucleus. [Copyright &y& Elsevier]

Abstract: A series of IAP antagonists based on thiazole or benzothiazole amide isosteres was designed and synthesized. These compounds were tested for binding to the XIAP-BIR3 and ML-IAP BIR using a fluorescence polarization assay. The most potent of these compounds, 19a and 33b, were found to have K i’s of 20–30nM against ML-IAP and 50–60nM against XIAP-BIR3. [Copyright &y& Elsevier]

Given a pair of a partial abelian monoid M and a pointed space X, let C M(ℝ∞, X) denote the configuration space of finite distinct points in ℝ∞ parametrized by the partial monoid X ∧ M. In this note we will show that if M is embedded in a topological abelian group and if we put ± M = { a − b | a, b ∈ M} then the natural map C M(ℝ∞, X) → C± M(ℝ∞, X) induced by the inclusion M ⊂ ± M is a group completion. This result can be applied to show that for any finite set M such that {0} ⊊ M ⊂ ℤ, C M(ℝ∞, X) is weakly equivalent to the infinite loop space ࡎ∞Σ∞ X if X is connected. [ABSTRACT FROM AUTHOR]

Batzelladine F (1) was synthesized in enantioselective and stereoselective fashion in 15 steps (longest linear sequence) and 1.7% overall yield from two readily available enantioenriched β-hydroxy esters, methyl (R)-3-hydroxydecanoate and methyl (R)-3-hydroxybutyrate. Tethered Biginelli condensations are used to assemble both tricyclic guanidine fragments, with the second tethered Biginelli condensation (14 + 16 ↵ 17) also being employed to join the guanidine fragments. Three diastereomers of batzelladine F, 2–4, were prepared also. A combination of HPLC, optical rotation and CD spectroscopy was employed to distinguish stereoisomers 1–4, proving that 1 is the correct structure of the hexacyclic marine alkaloid batzelladine F. [ABSTRACT FROM AUTHOR]

Stereoselective synthesis of octahydro-5,6,6a-triazaacenaphthalenes 29 and 34 having the anti-relationship of the angular hydrogens flanking the pyrrolidine nitrogen confirmed suspicions that the relative configuration of the left-hand tricyclic guanidine fragment of batzelladine F should be revised to have the syn relationship of these hydrogens. Several strategies were examined for coupling tricyclic guanidine fragments to prepare potential structures for batzelladine F. Eventually, a convergent synthesis strategy was devised, whose central step was a fragment-coupling tethered-Biginelli reaction (Scheme 17). Using this approach we synthesized four potential structures of batzelladine F, 35–38. None of these compounds, nor their enantiomers, were identical to natural batzelladine F. Reinvestigation of mass spectra of natural batzelladine F, and fragments 88 and 89 obtained upon saponification of batzelladine F, demonstrated that the originally proposed connectivity of this alkaloid was also incorrect. The revised connectivity, 90, of natural batzelladine F depicted in Scheme 21 is proposed. [ABSTRACT FROM AUTHOR]

Given a hyperplane arrangement in a complex vector space of dimension ℓ, there is a natural associated “redundant” arrangement of codimension k subspaces in a complex vector space of dimension kℓ. Topological invariants of the complement of this subspace arrangement are related to those of the complement of the original hyperplane arrangement. In particular, if the hyperplane arrangement is fiber-type, then, apart from grading, the Lie algebra obtained from the descending central series for the fundamental group of the complement of the hyperplane arrangement is isomorphic to the Lie algebra of primitive elements in the homology of the loop space for the complement of the associated subspace arrangement. Furthermore, this last Lie algebra is given by the homotopy groups modulo torsion of the loop space of the complement of the subspace arrangement. Looping further yields an associated Poisson algebra which satisfies generalizations of the “universal infinitesimal Poisson braid relations.” [ABSTRACT FROM AUTHOR]

Developing and sustaining a "zero-trust architecture" is essentially impossible today. The concept is currently a moving target, and its meaning is in the eye of the beholder. One thing we know for certain is that it's a misnomer. [ABSTRACT FROM AUTHOR]

This article reflects on the implications of the passage of the Budget Reconciliation Act by the Congress for the Medicaid program. The passage of the act could signal the start of a restructuring and retrenchment of the Medicaid program. Under the act, individual states will have the choice of reducing benefits and imposing significant costs on Medicaid recipients, including copayments. Illinois has enacted the All Kids program, which is a major expansion of the publicly supported health coverage programs in Illinois, at the same time that Congress is allowing or requiring states to make these changes that may result in drastic reductions in their Medicaid programs.

In this article we study extensions of ℤ2-graded L∞ algebras on a vector space of two even and one odd dimension. In particular, we determine all extensions of a super Lie algebra as an L∞ algebra. Our convention on the parities is the opposite of the usual one, because we define our structures on the symmetric coalgebra of the parity reversion of a space. 2000 Mathematics Subject Classification: 14D15, 13D10, 14B12, 16S80, 16E40, 17B55, 17B70. [ABSTRACT FROM AUTHOR]

USP7 is a deubiquitinase implicated in destabilizing the tumor suppressor p53, and for this reason it has gained increasing attention as a potential oncology target for small molecule inhibitors. Herein we describe the biophysical, biochemical, and computational approaches that led to the identification of 4-(2-aminopyridin-3-yl)phenol compounds described by Kategaya (Nature 2017, 550, 534-538) as specific inhibitors of USP7. Fragment based lead discovery (FBLD) by NMR combined with virtual screening and re-mining of biochemical high-throughput screening (HTS) hits led to the discovery of a series of ligands that bind in the "palm" region of the catalytic domain of USP7 and inhibit its catalytic activity. These ligands were then optimized by structure-based design to yield cell-active molecules with reasonable physical properties. This discovery process not only involved multiple techniques working in concert but also illustrated a unique way in which hits from orthogonal screening approaches complemented each other for lead identification. [ABSTRACT FROM AUTHOR]

In Gram-negative bacteria, the first step of lipid A biosynthesis is catalyzed by UDP-N-acetylglucosamine acyltransferase (LpxA) through the transfer of a R-3-hydroxyacyl chain from the acyl carrier protein (ACP) to the 3-hydroxyl group of UDP-GlcNAc. Previous studies suggest that LpxA is a critical determinant of the acyl chain length found in lipid A, which varies among species of bacteria. In Escherichia coli and Leptospira interrogans, LpxA prefers to incorporate longer R-3-hydroxyacyl chains (C14 and C12, respectively), whereas in Pseudomonas aeruginosa, the enzyme is selective for R-3-hydroxydecanoyl, a 10-hydrocarbon long acyl chain. We now report three P. aeruginosa LpxA crystal structures: apo protein, substrate complex with UDP-GlcNAc, and product complex with UDP-3-O-(R-3-hydroxydecanoyl)-GlcNAc. A comparison between the apo form and complexes identifies key residues that position UDP-GlcNAc appropriately for catalysis and supports the role of catalytic His121 in activating the UDP-GlcNAc 3-hydroxyl group for nucleophilic attack during the reaction. The product-complex structure, for the first time, offers structural insights into how Met169 serves to constrain the length of the acyl chain and thus functions as the so-called hydrocarbon ruler. Furthermore, compared with ortholog LpxA structures, the purported oxyanion hole, formed by the backbone amide group of Gly139, displays a different conformation in P. aeruginosa LpxA, which suggests flexibility of this structural feature important for catalysis and the potential need for substrate-induced conformational change in catalysis. Taken together, the three structures provide valuable insights into P. aeruginosa LpxA catalysis and substrate specificity as well as templates for future inhibitor discovery. [ABSTRACT FROM AUTHOR]

Inhibition of caspase-6 is a potential therapeutic strategy for some neurodegenerative diseases, but it has been difficult to develop selective inhibitors against caspases. We report the discovery and characterization of a potent inhibitor of caspase- 6 that acts by an uncompetitive binding mode that is an unprecedented mechanism of inhibition against this target class. Biochemical assays demonstrate that, while exquisitely selective for caspase-6 over caspase-3 and -7, the compound's inhibitory activity is also dependent on the amino acid sequence and P1' character of the peptide substrate. The crystal structure of the ternary complex of caspase-6, substrate-mimetic and an 11 nM inhibitor reveals the molecular basis of inhibition. The general strategy to develop uncompetitive inhibitors together with the unique mechanism described herein provides a rationale for engineering caspase selectivity. [ABSTRACT FROM AUTHOR]

A series of compounds were designed and synthesized asantagonists of cIAP1/2, ML-IAP, and XIAP based on the N-terminus,AVPI, of mature Smac. Compound 1(GDC-0152) has the bestprofile of these compounds; it binds to the XIAP BIR3 domain, theBIR domain of ML-IAP, and the BIR3 domains of cIAP1 and cIAP2 with Kivalues of 28, 14, 17, and43 nM, respectively. These compounds promote degradation of cIAP1,induce activation of caspase-3/7, and lead to decreased viabilityof breast cancer cells without affecting normal mammary epithelialcells. Compound 1inhibits tumor growth when dosed orallyin the MDA-MB-231 breast cancer xenograft model. Compound 1was advanced to human clinical trials, and it exhibited linear pharmacokineticsover the dose range (0.049 to 1.48 mg/kg) tested. Mean plasma clearancein humans was 9 ± 3 mL/min/kg, and the volume of distributionwas 0.6 ± 0.2 L/kg. [ABSTRACT FROM AUTHOR]

Caspase-6 is a cysteinyl protease implicated in neurodegenerative conditions including Alzheimer's and Huntington's disease making it an attractive target for therapeutic intervention. A greater understanding of the role of caspase-6 in disease has been hampered by a lack of suitable cellular assays capable of specifically detecting caspase-6 activity in an intact cell environment. This is mainly due to the use of commercially available peptide substrates and inhibitors which lack the required specificity to facilitate development of this type of assay. We report here a 384-well whole-cell chemiluminescent ELISA assay that monitors the proteolytic degradation of endogenously expressed lamin A/C during the early stages of caspase-dependent apoptosis. The specificity of lamin A/C proteolysis by caspase-6 was demonstrated against recombinant caspase family members and further confirmed in genetic deletion studies. In the assay, plasma membrane integrity remained intact as assessed by release of lactate dehydrogenase from the intracellular environment and the exclusion of cell impermeable peptide inhibitors, despite the induction of an apoptotic state. The method described here is a robust tool to support drug discovery efforts targeting caspase-6 and is the first reported to specifically monitor endogenous caspase-6 activity in a cellular context. [ABSTRACT FROM AUTHOR]

In order to study functorial changes caused by homotopy localizations on the fundamental group of unbased simplicial sets, it is convenient to use groupoids instead of groups, and therefore localizations of groupoids become useful. In this article we develop homotopy localization techniques in the model category of groupoids, with emphasis on the relationship with homotopy localizations of simplicial sets and also with discrete localizations of groups. [ABSTRACT FROM AUTHOR]

With current anti-HIV treatments targeting only 4 of the 15 HIV proteins, many potential viral vulnerabilities remain unexploited. We report small-molecule inhibitors of the HIV-1 protein Nef. In addition to expanding the anti-HIV arsenal, small-molecule inhibitors against untargeted HIV proteins could be used to dissect key events in the HIV lifecycle. Numerous incompletely characterized interactions between Nef and cellular ligands, for example, present a challenge to understanding molecular events during HIV progression to AIDS. Assays with phage-displayed Nef from HIVNL4-3 were used to identify a series of guanidine alkaloid-based inhibitors of Nef interactions with p53, actin, and p56lck. The guanidines, synthetic analogs of batzellidine and crambescidin natural products, inhibit the Nef-ligand interactions with IC50 values in the low micromolar range. In addition, sensitive in vivo assays for Nef inhibition are reported. Although compounds that are effective in vitro proved to be too cytotoxic for cellular assays, the reported Nef inhibitors provide proof-of-concept for disrupting a new HIV target and offer useful leads for drug development. [ABSTRACT FROM AUTHOR]

The lipid A biosynthesis pathway is essential in Pseudomonas aeruginosa. LpxA and LpxD are the first and third enzymes in this pathway respectively, and are regarded as promising antibiotic targets. The unique structural similarities between these two enzymes make them suitable targets for dual-binding inhibitors, a characteristic that would decrease the likelihood of mutational resistance and increase cell-based activity. We report the discovery of multiple small molecule ligands that bind to P. aeruginosa LpxA and LpxD, including dual-binding ligands. Binding poses were determined for select compounds by X-ray crystallography. The new structures reveal a previously uncharacterized magnesium ion residing at the core of the LpxD trimer. In addition, ligand binding in the LpxD active site resulted in conformational changes in the distal C-terminal helix-bundle, which forms extensive contacts with acyl carrier protein (ACP) during catalysis. These ligand-dependent conformational changes suggest a potential allosteric influence of reaction intermediates on ACP binding, and vice versa. Taken together, the novel small molecule ligands and their crystal structures provide new chemical scaffolds for ligand discovery targeting lipid A biosynthesis, while revealing structural features of interest for future investigation of LpxD function. [ABSTRACT FROM AUTHOR]