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The first author with B. Sturmfels studied the variety of matrices with eigenvectors in a given linear subspace, called Kalman variety. We extend that study from matrices to symmetric tensors, proving in the tensor setting the irreducibility of the Kalman variety and computing its codimension and degree. Furthermore we consider the Kalman variety of tensors having singular t-ples with the first component in a given linear subspace and we prove analogous results, which are new even in the case of matrices. Main techniques come from Algebraic Geometry, using Chern classes for enumerative computations., Comment: 11 pages and one table

In this paper, we study the Hessian map $h_{d,r}$, which associates to any hypersurface of degree $d$ in ${{\mathbb{P}}}^r$ its Hessian hypersurface, and the general properties of this map and prove that $h_{d,1}$ is birational onto its image if $d\geqslant 5.$ We also study in detail the maps $h_{3,1}$, $h_{4,1}$, and $h_{3,2}$ and the restriction of the Hessian map to the locus of hypersurfaces of degree $d$ with Waring rank $r+2$ in ${{\mathbb{P}}}^r$, proving that this restriction is injective as soon as $r\geqslant 2$ and $d\geqslant 3$, which implies that $h_{3,3}$ is birational onto its image. We also prove that the differential of the Hessian map is of maximal rank on the generic hypersurfaces of degree $d$ with Waring rank $r+2$ in ${{\mathbb{P}}}^r$, as soon as $r\geqslant 2$ and $d\geqslant 3$.

Let $q$ be a nondegenerate quadratic form on $V$. Let $X\subset V$ be invariant for the action of a Lie group $G$ contained in $SO(V,q)$. For any $f\in V$ consider the function $d_f$ from $X$ to $C$ defined by $d_f(x)=q(f-x)$. We show that the critical points of $d_f$ lie in the subspace orthogonal to ${\mathfrak g}\cdot f$, that we call critical space. In particular any closest point to $f$ in $X$ lie in the critical space. This construction applies to singular t-ples for tensors and to flag varieties and generalizes a previous result of Draisma, Tocino and the author. As an application, we compute the Euclidean Distance degree of a complete flag variety., 9 pages

Myc transcription factors are well-established drivers of human cancers. However, despite being amongst the most frequently mutated, translocated and overexpressed oncogenes, no therapy targeting the Myc family members directly has been developed to date. To sustain uncontrolled cell proliferation and tumor growth, Myc-driven cancers are known to be addicted to protein translation. This addiction creates a dependency on critical components of the translational machinery providing in turn a unique opportunity for therapeutic intervention. We hypothesized that targeting the translational termination factor GSPT1, a key regulator of protein synthesis, would constitute a vulnerability for Myc-driven tumors. GSPT1 contains a well-defined degron allowing for the recruitment of the E3 ligase cereblon (CRBN) and subsequent proteasomal degradation in the presence of molecular glue degraders. Herein we describe a novel orally bioavailable GSPT1-directed small molecule degrader MRT-2359, which has been rationally designed and optimized to selectively induce apoptosis in translationally addicted cells. MRT-2359 promotes complex formation between CRBN and GSPT1 and potently induces GSPT1 degradation in a CRBN- and degron-dependent manner. The high selectivity of MRT-2359 was subsequently demonstrated by the lack of activity in cells expressing a non-degradable GSPT1 mutant. Although MRT-2359 degrades GSPT1 in all the cell lines tested, profiling in a large panel of cancer lines revealed profound and preferential antiproliferative activity in Myc-driven cell lines, such as high N-Myc expressing non-small cell lung cancer (NSCLC) lines and high L-Myc expressing small cell lung cancer (SCLC) lines. In the Myc-driven cells, degradation of GSPT1 led to translational repression as manifested by a global shift from polysomes to monosomes resulting in the reduction of a subset of proteins as assessed by quantitative proteomics. In particular, N- or L-Myc protein levels decreased and as a consequence the known Myc target genes were downregulated at the mRNA level. Despite the robust degradation of GSPT1, no marked effect was observed in low N-Myc lines, confirming the selective activity of our GSPT1 degrader in Myc-driven lung cancers. Finally, oral administration of MRT-2359 in high N-Myc NSCLC xenografts and PDXs led to complete intratumoral GSPT1 degradation and concomitant decrease in N-Myc protein levels, resulting in tumor regression. In contrast, MRT-2359 had limited or no activity in low N-Myc NSCLC models, further corroborating the selective vulnerability of Myc-driven tumors to GSPT1 degradation. Together these data support the therapeutic potential of GSPT1-directed MGDs in Myc-driven solid tumors addicted to the protein translation machinery and warrant rapid evaluation towards the clinic. Citation Format: Gerald Gavory, Mahmoud Ghandi, Anne-Cecile d’Alessandro, Debora Bonenfant, Agustin Chicas, Frederic Delobel, Brad Demarco, Alexander Flohr, Christopher King, Anne-Laure Laine, Vittoria Massafra, Rajiv Narayan, Arnaud Osmont, Giorgio Ottaviani, Dave Peck, Sarah Pessa, Nooreen Rubin, Thomas Ryckmans, Martin Schillo, Ambika Singh, Simone Tortoioli, Dominico Vigil, Vladislav Zarayskiy, John Castle, Filip Janku, Owen Wallace, Silvia Buonamici, Bernhard Fasching. Identification of MRT-2359 a potent, selective and orally bioavailable GSPT1-directed molecular glue degrader (MGD) for the treatment of cancers with Myc-induced translational addiction [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 3929.

Aldosterone synthase (CYP11B2) inhibitors have been explored in recent years as an alternative therapeutic option to mineralocorticoid receptor (MR) antagonists to reduce elevated aldosterone levels, which are associated with deleterious effects on various organ systems including the heart, vasculature, kidney, and central nervous system (CNS). A benzamide pyridine hit derived from a focused screen was successfully developed into a series of potent and selective 3-pyridyl isoindolin-1-ones CYP11B2 inhibitors. Our systematic structure-activity relationship study enabled us to identify unique structural features that result in high selectivity against the closely homologous cortisol synthase (CYP11B1). We evaluated advanced lead molecules, exemplified by compound 52, in an in vivo cynomolgus monkey acute adrenocorticotropic hormone (ACTH) challenge model and demonstrated a superior 100-fold in vivo selectivity against CYP11B1.

We present a fine-structure entanglement classification under stochastic local operation and classical communication (SLOCC) for multiqubit pure states. To this end, we employ specific algebraic-geometry tools that are SLOCC invariants, secant varieties, to show that for $n$-qubit systems there are $\lceil\frac{2^{n}}{n+1}\rceil$ entanglement families. By using another invariant, $\ell$-multilinear ranks, each family can be further split into a finite number of subfamilies. Not only does this method facilitate the classification of multipartite entanglement, but it also turns out to be operationally meaningful as it quantifies entanglement as a resource., Comment: 11 pages, 2 figures, Minor changes, Published version

Two fundamental invariants attached to a projective variety are its classical algebraic degree and its Euclidean Distance degree (ED degree). In this paper, we study the asymptotic behavior of these two degrees of some Segre products and their dual varieties. We analyze the asymptotics of degrees of (hypercubical) hyperdeterminants, the dual hypersurfaces to Segre varieties. We offer an alternative viewpoint on the stabilization of the ED degree of some Segre varieties. Although this phenomenon was incidentally known from Friedland-Ottaviani's formula expressing the number of singular vector tuples of a general tensor, our approach provides a geometric explanation. Finally, we establish the stabilization of the degree of the dual variety of a Segre product $X\times Q_{n}$, where $X$ is a projective variety and $Q_n\subset \mathbb{P}^{n+1}$ is a smooth quadric hypersurface., Comment: 24 pages

This paper describes the characterization of male- and female-mediated effects in a standard ICH rat fertility and early embryonic development study with a discontinued clinical small molecule. In the standard study, the test item had no effect on the number of treated females becoming pregnant, but litter sizes were reduced at the high dose level. In the treated male rats, increased incidences of abnormal sperm, decreases in average sperm path and straight line velocities, and minimal retention of mature sperm in the seminiferous tubules were observed at all dose-levels tested. These findings were unexpected in view of a lack of histopathological changes in the reproductive organs of either gender in 4-week repeat dose studies in rats and monkeys. A follow-up fertility study was conducted using an innovative flexible study design and a single high-dose level. In the first instance, treated male rats were mated with untreated females, followed by necropsy of a subset of males. The intention was then to re-mate the males after an 8-week wash-out period with either treated or untreated females depending on the outcome of the first mating. On this occasion, litter sizes were not affected, but the testicular effects were reproduced. A second mating with treated females reproduced the reduced litter sizes due to increased pre- and post-implantation loss, demonstrating that the effect on fecundity was female-mediated. The testicular changes in males were shown to be reversible after a 12-week recovery period.

We define tensors, corresponding to cubic polynomials, which have the same exponent $\omega$ as the matrix multiplication tensor. In particular, we study the symmetrized matrix multiplication tensor $sM_n$ defined on an $n\times n$ matrix $A$ by $sM_n(A)=trace(A^3)$. The use of polynomials enables the introduction of additional techniques from algebraic geometry in the study of the matrix multiplication exponent $\omega$., Comment: 14 pages + appendix of 3 pages with numerical decompositions

Background & Aims The hallmarks of chronic HBV infection are a high viral load (HBV DNA) and even higher levels (>100-fold in excess of virions) of non-infectious membranous particles containing the tolerogenic viral S antigen (HBsAg). Currently, standard treatment effectively reduces viremia but only rarely results in a functional cure (defined as sustained HBsAg loss). There is an urgent need to identify novel therapies that reduce HBsAg levels and restore virus-specific immune responsiveness in patients. We report the discovery of a novel, potent and orally bioavailable small molecule inhibitor of HBV gene expression (RG7834). Methods RG7834 antiviral characteristics and selectivity against HBV were evaluated in HBV natural infection assays and in a urokinase-type plasminogen activator/severe combined immunodeficiency humanized mouse model of HBV infection, either alone or in combination with entecavir. Results Unlike nucleos(t)ide therapies, which reduce viremia but do not lead to an effective reduction in HBV antigen expression, RG7834 significantly reduced the levels of viral proteins (including HBsAg), as well as lowering viremia. Consistent with its proposed mechanism of action, time course RNA-seq analysis revealed a fast and selective reduction in HBV mRNAs in response to RG7834 treatment. Furthermore, oral treatment of HBV-infected humanized mice with RG7834 led to a mean HBsAg reduction of 1.09 log 10 compared to entecavir, which had no significant effect on HBsAg levels. Combination of RG7834, entecavir and pegylated interferon α-2a led to significant reductions of both HBV DNA and HBsAg levels in humanized mice. Conclusion We have identified a novel oral HBV viral gene expression inhibitor that blocks viral antigen and virion production, that is highly selective for HBV, and has a unique antiviral profile that is clearly differentiated from nucleos(t)ide analogues. Lay summary We discovered a novel small molecule viral expression inhibitor that is highly selective for HBV and unlike current therapy inhibits the expression of viral proteins by specifically reducing HBV mRNAs. RG7834 can therefore potentially provide anti-HBV benefits and increase HBV cure rates, by direct reduction of viral agents needed to complete the viral life cycle, as well as a reduction of viral agents involved in evasion of the host immune responses.

Long-term in vitro liver models are now widely explored for human hepatic metabolic clearance prediction, enzyme phenotyping, cross-species metabolism, comparison of low clearance drugs, and induction studies. Here, we present studies using a long-term liver model, which show how metabolism and active transport, drug-drug interactions, and enzyme induction in healthy and diseased states, such as hepatitis B virus (HBV) infection, may be assessed in a single test system to enable effective data integration for physiologically based pharmacokinetic (PBPK) modeling. The approach is exemplified in the case of (3S)-4-[[(4R)-4-(2-Chloro-4-fluorophenyl)-5-methoxycarbonyl-2-thiazol-2-yl-1,4-dihydropyrimidin-6-yl]methyl]morpholine-3-carboxylic acid RO6889678, a novel inhibitor of HBV with a complex absorption, distribution, metabolism, and excretion (ADME) profile. RO6889678 showed an intracellular enrichment of 78-fold in hepatocytes, with an apparent intrinsic clearance of 5.2 µl/min per mg protein and uptake and biliary clearances of 2.6 and 1.6 µl/min per mg protein, respectively. When apparent intrinsic clearance was incorporated into a PBPK model, the simulated oral human profiles were in good agreement with observed data at low doses but were underestimated at high doses due to unexpected overproportional increases in exposure with dose. In addition, the induction potential of RO6889678 on cytochrome P450 (P450) enzymes and transporters at steady state was assessed and cotreatment with ritonavir revealed a complex drug-drug interaction with concurrent P450 inhibition and moderate UDP-glucuronosyltransferase induction. Furthermore, we report on the first evaluation of in vitro pharmacokinetics studies using HBV-infected HepatoPac cocultures. Thus, long-term liver models have great potential as translational research tools exploring pharmacokinetics of novel drugs in vitro in health and disease.

The Myc family of transcription factors is a well-established driver of human cancers. However, despite being amongst the most frequently mutated, translocated and overexpressed oncogenes, no therapy directly targeting the Myc family members has been developed to date. Abnormal activation of Myc results in uncontrolled cell growth that is associated with high translational output and ramp up of the protein translational machinery. This creates a dependency to protein translation and in turn represents a potential therapeutic vulnerability for Myc-driven tumors. Based on these considerations, we hypothesized that targeting the translational termination factor GSPT1, a key player of protein synthesis, may constitute a vulnerability for Myc-driven tumors. Using our proprietary Quantitative and Engineered Elimination of Neosubstrates (QuEENTM) platform we characterized and explored the known G-loop degron in GSPT1 that renders it amenable to cereblon-induced degradation by molecular glue degraders (MGDs). We rationally designed and subsequently screened a proprietary library of cereblon-binding small molecules, including GSPT1-directed MGDs, in human mammary epithelial cells (HMECs) expressing doxycycline-inducible c-Myc. Doxycycline treatment led to sustained c-Myc expression and as a consequence to the induction of key biomarkers of enhanced protein translation, such as phospho 4EBP1 (p4EBP1). We identified MRT-048 as a potent and highly selective GSPT1 degrader and demonstrated its ability to induce cell death in Myc-driven HMEC cells whilst sparing control cells (EC50 0.64 μM vs 30 μM respectively). This confirmed the selective vulnerability of Myc-driven cell growth to GSPT1 degradation. In follow-up studies, we confirmed the correlation between p4EBP1 as biomarker of Myc-activation and sensitivity to MRT-048 in a large panel of breast cancer cell lines. Moreover, MRT-048 treatment of animals xenografted with breast cancer cells induced tumor regression and was associated with complete GSPT1 degradation. Mechanistically, we observed that GSPT1 degradation induced by MRT-048 led to inhibition of genes regulated by Myc and ribosomal stalling at stop codons of several mRNAs. Additionally, polysome profiling of cancer cells treated with MRT-048 was associated with a global reduction of the intensities of the polysome peaks and concomitant increase in the monosome peaks as previously observed in GSPT1 knockdown experiments, suggesting that GSPT1 degradation by our MGD molecules affects both the termination and initiation stages of protein translation. We believe these data support the therapeutic potential of GSPT1-directed MGDs in Myc-driven tumors dependent on protein translation machinery. Citation Format: Gerald Gavory, Bernhard Fasching, Debora Bonenfant, Amine Sadok, Ambika Singh, Martin Schillo, Vittoria Massafra, Anne-Cecile d’Alessandro, John Castle, Mahmoud Ghandi, Agustin Chicas, Frederic Delobel, Alexander Flohr, Giorgio Ottaviani, Thomas Ryckmans, Anne-Laure Laine, Oliv Eidam, Hannah Wang, Ilona Bernett, Laura Chan, Chiara Gorrini, Theo Roumiliotis, Jyoti Choudhary, Yann-Vai LeBihan, Marc Cabry, Mark Stubbs, Rosemary Burke, Rob Van Montfort, John Caldwell, Rajesh Chopra, Ian Collins, Silvia Buonamici. Identification of GSPT1-directed molecular glue degrader (MGD) for the treatment of Myc-driven breast cancer [abstract]. In: Proceedings of the AACR-NCI-EORTC Virtual International Conference on Molecular Targets and Cancer Therapeutics; 2021 Oct 7-10. Philadelphia (PA): AACR; Mol Cancer Ther 2021;20(12 Suppl):Abstract nr LBA004.

Oncogenic EGFR mutations occur in approximately 50% of glioblastomas (GBM) and largely reside in the extracellular domain. Prior attempts to reposition current generation EGFR inhibitors to treat GBM likely failed due to poor brain penetration and an inability to potently target the full spectrum of oncogenic mutations. As EGFR oncogenic mutations are found to be co-expressed in many GBMs, it is important that an inhibitor be broadly active against the entire family of relevant EGFR mutants. Additionally, a successful inhibitor would require a pharmacokinetic (PK) profile that allows for sufficient penetration of the blood brain barrier to elicit robust target engagement of the brain tumor. Using these design principles, we designed a series of highly potent molecules exemplified by BDTX-507. This molecule is an irreversible inhibitor of EGFR with antiproliferative IC50's less than 10 nM against the spectrum of GBM-relevant EGFR mutations. PK/PD studies demonstrated sustained pERK suppression exceeding 24 hours following a single QD dose. Furthermore, when dosed in GBM xenografts, including an intracranial Viii PDX (GBM6), robust tumor regressions and improved survival were observed. Emerging from this series were two advanced compounds, BDTX-700 and BDTX-1535, which also demonstrated potent inhibition of the GBM EGFR spectrum, selectivity v. wild-type EGFR, and an excellent CNS PK profile. BDTX-1535 is currently being evaluated in IND-enabling studies for future clinical evaluation in GBM patients. Citation Format: Matthew O'Connor, Matt Lucas, Darlene Romashko, Sara Rasmussen, Tai-An Lin, Nigel Waters, Raffaele Fiorenza, Iwona Wrona, Deborah Chen, Theodore Nicolaides, David R. Raleigh, Tomoko Ozawa, George Trainor, Luca Arista, Alexander Flohr, Giorgio Ottaviani, Chris Roberts, Elizabeth Buck. CNS penetrant, irreversible inhibitors potently inhibit the family of allosteric oncogenic EGFR mutants expressed in GBM and demonstrate efficacy in patient-derived xenograft models [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2021; 2021 Apr 10-15 and May 17-21. Philadelphia (PA): AACR; Cancer Res 2021;81(13_Suppl):Abstract nr LB140.

Allosteric oncogenic mutations occur outside the canonical ATP-binding site of EGFR and HER2, for which there are no approved single agent therapies that target this family. BDTX-189 is a potent, selective, irreversible inhibitor of the family of nearly 50 allosteric EGFR and HER2 mutant variants. The goal of this translational analysis was to predict the clinical pharmacokinetic (PK) profile of BDTX-189 utilizing in vitro data on the absorption, distribution and metabolism of BDTX-189 as well as in vivo PK data in preclinical species. The prospective PK modeling was conducted prior to initiation of a Phase 1/2 study, to provide predictions of clinical exposures and active dose range. A challenge in the design of irreversible inhibitors with optimal PK properties is the lack of reliable methods to predict their disposition and elimination in human. The PK of covalent drugs is often driven by extrahepatic elimination pathways, and therefore conventional approaches to predict human clearance using human hepatocytes or allometric scaling can lead to poor predictive accuracy. We employed a novel physiologically-based PK (PBPK) modeling strategy that accounted for compound-specific determinants of BDTX-189 metabolism and disposition. PK studies following intravenous (IV) and oral (PO) administration were conducted in preclinical species as well as in vitro studies to understand the ADME properties of BDTX-189. These preclinical data formed the basis of a PBPK modeling approach to predict the likely PK profile of BDTX-189 in human. The mechanistic assumptions used in the final models were able to recapitulate the observed animal PK after both IV and PO administration and thus predictions utilizing similar assumptions for human were considered plausible. Taken together with BDTX-189 exposure-response data in mouse models of anti-tumor efficacy, this enabled the prediction of potentially active dose levels in patients. Preclinical PBPK modeling indicated that BDTX-189 would be readily orally absorbed with a short elimination half-life (approximately 2 hours) while maintaining suppression of ErbB pathway biomarkers over the dosing interval, consistent with the irreversible mechanism of action and the desired ‘hit-and-run' PK/pharmacodynamic (PD) profile. Active dose levels in human were projected to be in the 400 - 800 mg QD range, based on the exposure - tumor growth inhibition relationship in multiple mouse PDX models harboring ErbB allosteric mutations. This study demonstrates that a PBPK modeling approach and an understanding of the determinants of clearance can provide an effective framework for preclinical-to-clinical translation. BDTX-189 is currently under clinical evaluation in the ongoing MasterKey-01 trial (NCT04209465), and clinical PK will be reported in due course. Citation Format: Giorgio Ottaviani, Matthew O'Connor, Alexander Flohr, Darlene Romashko, Alexander Mayweg, Elizabeth Buck, Nigel Waters. Prospective preclinical modeling to estimate clinical pharmacokinetics and doses of BDTX-189, an inhibitor of allosteric ErbB mutations in advanced solid malignancies [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2021; 2021 Apr 10-15 and May 17-21. Philadelphia (PA): AACR; Cancer Res 2021;81(13_Suppl):Abstract nr LB127.

Aim: Midazolam is a commonly used marker substrate for the in vivo assessment of CYP3A activity. Reliable pharmacokinetic assessment at sub-pharmacological doses of midazolam requires an ultra-sensitive analytical method. Methods: A new, ultra-sensitive LC–MS/MS method for the determination of midazolam in human plasma using SPE was developed and fully validated. The lowest limit of quantitation is 0.1 pg/ml with a sample volume of 500 μl. Results/conclusion: The following parameters were validated: sensitivity, assay accuracy and precision, linearity, selectivity, and stability of midazolam at pertinent analytical and storage conditions. The validated method was utilized successfully for the sample assay during a midazolam microdosing study for the evaluation of CYP3A4 activity of a clinical candidate.

Si puo comprendere la matematica con forbici, colla, spago e mattoncini da costruzione? This volume, which features almost every work from the 2014 and 2016 editions of the Riccardo Ricci Mathematical Laboratory Award, explains how it is possible to understand Mathematics, even using the most advanced technologies such as lasers. The featured works were performed by groups of high school students, under the supervision of the teachers who have personally wrote the drafting. Those are creative and imaginative works, whose reading is recommended to teachers interested in a laboratory approach to Mathematics, as well as to all enthusiasts of the subject. The Award recalls Riccardo Ricci (1953-2013)’s didactic spirit: he was professor of Dynamic Systems at the University of Florence and a point of reference in the city’s mathematical community, also thanks to his roles as referent of the Scientific Degree Project and teacher in the courses of teacher training.Si puo comprendere la matematica con forbici, colla, spago e mattoncini da costruzione? Questo volume, che presenta quasi tutte le opere in concorso nelle edizioni 2014 e 2016 del Premio Laboratorio Matematico Riccardo Ricci, racconta come cio sia possibile, anche attraverso le tecnologie piu avanzate come il laser. I lavori presentati sono prodotti da gruppi di studenti della scuola superiore di secondo grado, con la supervisione dei docenti che ne hanno curato personalmente la stesura. Sono opere ricche di creativita e fantasia, la cui lettura e consigliata ai docenti interessati all’approccio laboratoriale alla matematica e a tutti gli appassionati e cultori della materia. Il Premio ricorda lo spirito didattico di Riccardo Ricci (1953-2013), docente di Sistemi dinamici presso l’Universita di Firenze e punto di riferimento nella comunita matematica fiorentina, grazie anche al suo ruolo di referente del Progetto Lauree Scientifiche e di docente nei corsi di formazione per gli insegnanti.

Dual inhibition of fatty acid binding proteins 4 and 5 (FABP4 and FABP5) is expected to provide beneficial effects on a number of metabolic parameters such as insulin sensitivity and blood glucose levels and should protect against atherosclerosis. Starting from a FABP4 selective focused screening hit, biostructure information was used to modulate the selectivity profile in the desired way and to design potent dual FABP4/5 inhibitors with good selectivity against FABP3. With very good pharmacokinetic properties and no major safety alerts, compound 12 was identified as a suitable tool compound for further in vivo investigations.

EGFR mutations identified in glioblastomas (GBM) occur nearly exclusively at the allosteric extracellular domain (ECD) and constitutively activate oncogenic signaling. Despite wide success in treating tumors expressing EGFR catalytic site mutants, no drug has demonstrated clinical utility against tumors expressing the extracellular domain EGFR mutants. We demonstrate that the family of ECD mutations are not only co-expressed in GBM, but that they all activate the oncogene through a similar disulfide bond-mediated receptor dimerization mechanism. This dimerization occurs independent of ligands and renders the Locked-dimer (LoDi)-EGFR insensitive to agents that target the EGFR kinase domain mutants in NSCLC. The kinase conformation induced by these ECD mutations seen in glioblastomas is both oncogenic and altered from kinase domain mutations, thus necessitating a new approach to targeting. By screening against cells expressing LoDi-EGFR mutants, we have identified the first inhibitors that potently and selectively target LoDi-EGFR mutants versus both canonical active site oncogenic mutants and wild type EGFR. Through an optimization effort, we have identified a novel family of potent and selective LoDi-EGFR mutant inhibitors that effectively penetrate the blood brain barrier (BBB) following oral dosing in preclinical studies. A leading exemplar, BDTX-GBM-001, inhibits the 5 major LoDi-EGFR mutants expressed in GBM with antiproliferative potency of ~10 nM while showing favorable selectivity versus the human kinome. When dosed orally in the intracranial GBM6 patient derived xenograft model at 50, 30, and 15 mg/kg, a dose responsive decrease in tumor growth, as well as a statistically significant increase in survival, were observed. These data support the continued evaluation of rationally designed BBB penetrant inhibitors selectively targeting the common LoDi-EGFR mutants and enable the first chance to fully test the clinical hypothesis of EGFR driver mutants in GBM.

Astrocytes are involved in non-cell-autonomous pathogenic cascades in amyotrophic lateral sclerosis (ALS); however, their role is still debated. We show that astrocytic NF-κB activation drives microglial proliferation and leukocyte infiltration in the SOD1 (G93A) ALS model. This response prolongs the presymptomatic phase, delaying muscle denervation and decreasing disease burden, but turns detrimental in the symptomatic phase, accelerating disease progression. The transition corresponds to a shift in the microglial phenotype showing two effects that can be dissociated by temporally controlling NF-κB activation. While NF-κB activation in astrocytes induced a Wnt-dependent microglial proliferation in the presymptomatic phase with neuroprotective effects on motoneurons, in later stage, astrocyte NF-κB-dependent microglial activation caused an accelerated disease progression. Notably, suppression of the early microglial response by CB ₂ R agonists had acute detrimental effects. These data identify astrocytes as important regulators of microglia expansion and immune response. Therefore, stage-dependent microglia modulation may be an effective therapeutic strategy in ALS.

This volume collects the papers presented in the occasion of the MEGA (Effective Methods in Algebraic Geometry) conference held in Nice (France) from June 12th to 16th, 2017. The volume was open to original research contributions presented in the Conference and also to further contributions. According to the MEGA tradition, Algebraic Geometry is interpreted broadly, including, among other topics, symbolic computations, commutative algebra, polynomial optimization, combinatorial techniques, tropical geometry and applications. The papers in this volume can be divided along the following themes Effective methods in commutative algebra, Hilbert functions, monomial ideals: papers 1-3; Projective Geometry and Singularities, Vector bundles on Projective Spaces: papers 4-6; Tropical Geometry, Combinatorics of Polyhedra and its use in Optimization problems: papers 7-10; Real solutions to polynomial equations: papers 11-12. We conclude this foreword with a very brief discussion of each of the papers.

Inappropriately high levels of aldosterone are associated with many serious medical conditions, including renal and cardiac failure. A focused screen hit has been optimized into a potent and selective aldosterone synthase (CYP11B2) inhibitor with in vitro activity against rat, mouse, human, and cynomolgus monkey enzymes, showing a selectivity factor of 160 against cytochrome CYP11B1 in the last species. The novel tetrahydroisoquinoline compound (+)-(R)-6 selectively reduced aldosterone plasma levels in vivo in a dose-dependent manner in db/db mice and cynomolgus monkeys. The selectivity against CYP11B1 as predicted by cellular inhibition data and free plasma fraction translated well to Synacthen challenged cynomolgus monkeys up to a dose of 0.1 mg kg(-1). This compound, displaying good in vivo potency and selectivity in mice and monkeys, is ideally suited to perform mechanistic studies in relevant rodent models and to provide the information necessary for translation to non-human primates and ultimately to man.

The cannabinoid receptor 2 (CB2) system is described to modulate various pathological conditions, including inflammation and fibrosis. A series of new heterocyclic small-molecule CB2 receptor agonists were identified from a high-throughput screen. Lead optimization gave access to novel, highly potent, and selective (over CB1) triazolopyrimidine derivatives. A preliminary structure-activity relationship was established, and physicochemical properties in this compound class were significantly improved toward better solubility, lipophilicity, and microsomal stability. An optimized triazolopyrimidine derivative, (3S)-1-[5-tert-butyl-3-[(1-cyclopropyltetrazol-5-yl)methyl]triazolo[4,5-d]pyrimidin-7-yl]pyrrolidin-3-ol (39), was tested in a kidney ischemia-reperfusion model, in which it showed efficacy at a dose of 10 mg kg(-1) (p.o.). A significant depletion of the three measured kidney markers indicated a protective role of CB2 receptor activation toward inflammatory kidney damage. Compound 39 was also protective in a model of renal fibrosis. Oral treatment with 39 at 3 mg kg(-1) per day significantly decreased the amount of fibrosis by ∼ 40% which was induced by unilateral ureter obstruction.

In the tensor space $\mathrm{Sym}^d {\mathbb R}^2$ of binary forms we study the best rank $k$ approximation problem. The critical points of the best rank $1$ approximation problem are the eigenvectors and it is known that they span a hyperplane. We prove that the critical points of the best rank $k$ approximation problem lie in the same hyperplane., 9 pages