Equilibrium hydrostatic equation and Newtonian limit of the singular f(R) gravity

We derive the equilibrium hydrostatic equation of a spherical star for any gravitational Lagrangian density of the form $L=\sqrt{-g}f(R)$. The Palatini variational principle for the Helmholtz Lagrangian in the Einstein gauge is used to obtain the field equations in this gauge. The equilibrium hydrostatic equation is obtained and is used to study the Newtonian limit for $f(R)=R-\frac{a^{2}}{3R}$. The same procedure is carried out for the more generally case $f(R)=R-\frac{1}{n+2}\frac{a^{n+1}}{R^{n}}$ giving a good Newtonian limit.Comment: Revised version, to appear in Classical and Quantum Gravity

Compactifying the state space for alternative theories of gravity

In this paper we address important issues surrounding the choice of variables when performing a dynamical systems analysis of alternative theories of gravity. We discuss the advantages and disadvantages of compactifying the state space, and illustrate this using two examples. We first show how to define a compact state space for the class of LRS Bianchi type I models in $R^n$-gravity and compare to a non--compact expansion--normalised approach. In the second example we consider the flat Friedmann matter subspace of the previous example, and compare the compact analysis to studies where non-compact non--expansion--normalised variables were used. In both examples we comment on the existence of bouncing or recollapsing orbits as well as the existence of static models.Comment: 18 pages, revised to match published versio

Vav3 Is Involved in GABAergic Axon Guidance Events Important for the Proper Function of Brainstem Neurons Controlling Cardiovascular, Respiratory, and Renal Parameters

Vav3 is a phosphorylation GDP/GTP exchange factor for Rho/Rac GTPases. Recently, it has been described that Vav3 knockout mice develop hypertension and sympathoexcitation. In this work, we report the neurological cause of this phenotype

Dynamics of f(R)-cosmologies containing Einstein static models

We study the dynamics of homogeneous isotropic FRW cosmologies with positive spatial curvature in $f(R)$-gravity, paying special attention to the existence of Einstein static models and only study forms of $f(R)=R^n$ for which these static models have been shown to exist. We construct a compact state space and identify past and future attractors of the system and recover a previously discovered future attractor corresponding to an expanding accelerating model. We also discuss the existence of universes which have both a past and future bounce, a phenomenon which is absent in General Relativity.Comment: 14 pages, 6 figure

Nuclear Vav3 is required for polycomb repression complex-1 activity in B-cell lymphoblastic leukemogenesis

Acute B-cell lymphoblastic leukemia (B-ALL) results from oligo-clonal evolution of B-cell progenitors endowed with initiating and propagating leukemia properties. The activation of both the Rac guanine nucleotide exchange factor (Rac GEF) Vav3 and Rac GTPases is required for leukemogenesis mediated by the oncogenic fusion protein BCR-ABL. Vav3 expression becomes predominantly nuclear upon expression of BCR-ABL signature. In the nucleus, Vav3 interacts with BCR-ABL, Rac, and the polycomb repression complex (PRC) proteins Bmi1, Ring1b and Ezh2. The GEF activity of Vav3 is required for the proliferation, Bmi1-dependent B-cell progenitor self-renewal, nuclear Rac activation, protein interaction with Bmi1, mono-ubiquitination of H2A(K119) (H2AK119Ub) and repression of PRC-1 (PRC1) downstream target loci, of leukemic B-cell progenitors. Vav3 deficiency results in de-repression of negative regulators of cell proliferation and repression of oncogenic transcriptional factors. Mechanistically, we show that Vav3 prevents the Phlpp2-sensitive and Akt (S473)-dependent phosphorylation of Bmi1 on the regulatory residue S314 that, in turn, promotes the transcriptional factor reprogramming of leukemic B-cell progenitors. These results highlight the importance of non-canonical nuclear Rho GTPase signaling in leukemogenesis.This project was funded by the National Institutes of Health Grants R01-CA273016 (N.N.N. and J.A.C.) and U54-DK126108 (J.A.C.), the Leukemia & Lymphoma Society of North America (J.A.C and N.N.N.; and N.N.N. and J.A.C.), and William Lawrence & Blanche Hughes Foundation (J.A.C. and N.N.)

Spherical symmetry in f(R)f(R)-gravity

Spherical symmetry in $f(R)$ gravity is discussed in details considering also the relations with the weak field limit. Exact solutions are obtained for constant Ricci curvature scalar and for Ricci scalar depending on the radial coordinate. In particular, we discuss how to obtain results which can be consistently compared with General Relativity giving the well known post-Newtonian and post-Minkowskian limits. Furthermore, we implement a perturbation approach to obtain solutions up to the first order starting from spherically symmetric backgrounds. Exact solutions are given for several classes of $f(R)$ theories in both $R =$ constant and $R = R(r)$.Comment: 13 page

Counteranion-Dependent Reaction Pathways in the Protonation of Cationic Ruthenium−Vinylidene Complexes

The tetraphenylborate salts of the cationic vinylidene complexes [Cp*Ru=C=CHR(iPr2PNHPy)]+ (R = p-C6H4CF3 (1a-BPh4), Ph (1b-BPh4), p-C6H4CH3 (1c- BPh4), p-C6H4Br (1d-BPh4), tBu (1e-BPh4), H (1f-BPh4)) have been protonated using an excess of HBF4·OEt2 in CD2Cl2, furnishing the dicationic carbyne complexes [Cp*Ru≡CCH2R(iPr2PNHPy)]2+ (R = p-C6H4CF3 (2a), Ph (2b), p-C6H4CH3 (2c), p-C6H4Br (2d), tBu (2e), H (2f)), which were characterized in solution at low temperature by NMR spectroscopy. The corresponding reaction of the chloride salts 1a-Cl, 1b-Cl, 1c-Cl, and 1d-Cl followed a different pathway, instead affording the novel alkene complexes [Cp*RuCl(κ1(N),η2(C,C)-C5H4N-NHPiPr2CH=CHR)][BF4] (3a−d). In these species, the entering proton is located at the α- carbon atom of the former vinylidene ligand, which also forms a P−C bond with the phosphorus atom of the iPr2PNHPy ligand. To shed light on the reaction mechanism, DFT calculations have been performed by considering several protonation sites. The computational results suggest metal protonation followed by insertion. The coordination of chloride to ruthenium leads to alkenyl species which can undergo a P−C coupling to yield the corresponding alkene complexes. The noncoordinating nature of [BPh4]− does not allow the stabilization of the unsaturated species coming from the insertion step, thus preventing this alternative pathway

Human Vav1 Expression in Hematopoietic and Cancer Cell Lines Is Regulated by c-Myb and by CpG Methylation

Vav1 is a signal transducer protein that functions as a guanine nucleotide exchange factor for the Rho/Rac GTPases in the hematopoietic system where it is exclusively expressed. Recently, Vav1 was shown to be involved in several human malignancies including neuroblastoma, lung cancer, and pancreatic ductal adenocarcinoma (PDA). Although some factors that affect vav1 expression are known, neither the physiological nor pathological regulation of vav1 expression is completely understood. We demonstrate herein that mutations in putative transcription factor binding sites at the vav1 promoter affect its transcription in cells of different histological origin. Among these sites is a consensus site for c-Myb, a hematopoietic-specific transcription factor that is also found in Vav1-expressing lung cancer cell lines. Depletion of c-Myb using siRNA led to a dramatic reduction in vav1 expression in these cells. Consistent with this, co-transfection of c-Myb activated transcription of a vav1 promoter-luciferase reporter gene construct in lung cancer cells devoid of Vav1 expression. Together, these results indicate that c-Myb is involved in vav1 expression in lung cancer cells. We also explored the methylation status of the vav1 promoter. Bisulfite sequencing revealed that the vav1 promoter was completely unmethylated in human lymphocytes, but methylated to various degrees in tissues that do not normally express vav1. The vav1 promoter does not contain CpG islands in proximity to the transcription start site; however, we demonstrated that methylation of a CpG dinucleotide at a consensus Sp1 binding site in the vav1 promoter interferes with protein binding in vitro. Our data identify two regulatory mechanisms for vav1 expression: binding of c-Myb and CpG methylation of 5′ regulatory sequences. Mutation of other putative transcription factor binding sites suggests that additional factors regulate vav1 expression as well

Vav proteins are key regulators of Card9 signaling for innate antifungal immunity

Fungal infections are major causes of morbidity and mortality, especially in immunocompromised individuals. The innate immune system senses fungal pathogens through Syk-coupled C-type lectin receptors (CLRs), which signal through the conserved immune adaptor Card9. Although Card9 is essential for antifungal defense, the mechanisms that couple CLR-proximal events to Card9 control are not well defined. Here, we identify Vav proteins as key activators of the Card9 pathway. Vav1, Vav2, and Vav3 cooperate downstream of Dectin-1, Dectin-2, and Mincle to engage Card9 for NF-κB control and proinflammatory gene transcription. Although Vav family members show functional redundancy, Vav1/2/3(-/-) mice phenocopy Card9(-/-) animals with extreme susceptibility to fungi. In this context, Vav3 is the single most important Vav in mice, and a polymorphism in human VAV3 is associated with susceptibility to candidemia in patients. Our results reveal a molecular mechanism for CLR-mediated Card9 regulation that controls innate immunity to fungal infections