Spherically Symmetric Solutions in Macroscopic Gravity

Schwarzschild's solution to the Einstein Field Equations was one of the first and most important solutions that lead to the understanding and important experimental tests of Einstein's theory of General Relativity. However, Schwarzschild's solution is essentially based on an ideal theory of gravitation, where all inhomogeneities are ignored. Therefore, any generalization of the Schwarzschild solution should take into account the effects of small perturbations that may be present in the gravitational field. The theory of Macroscopic Gravity characterizes the effects of the inhomogeneities through a non-perturbative and covariant averaging procedure. With similar assumptions on the geometry and matter content, a solution to the averaged field equations as dictated by Macroscopic Gravity are derived. The resulting solution provides a possible explanation for the flattening of galactic rotation curves, illustrating that Dark Matter is not real but may only be the result of averaging inhomogeneities in a spherically symmetric background.Comment: 14 pages, added and updated references, some paragraphs rewritten for clarity, typographical errors fixed, results have not change

Isotropic singularity in inhomogeneous brane cosmological models

We discuss the asymptotic dynamical evolution of spatially inhomogeneous brane-world cosmological models close to the initial singularity. By introducing suitable scale-invariant dependent variables and a suitable gauge, we write the evolution equations of the spatially inhomogeneous $G_{2}$ brane cosmological models with one spatial degree of freedom as a system of autonomous first-order partial differential equations. We study the system numerically, and we find that there always exists an initial singularity, which is characterized by the fact that spatial derivatives are dynamically negligible. More importantly, from the numerical analysis we conclude that there is an initial isotropic singularity in all of these spatially inhomogeneous brane cosmologies for a range of parameter values which include the physically important cases of radiation and a scalar field source. The numerical results are supported by a qualitative dynamical analysis and a calculation of the past asymptotic decay rates. Although the analysis is local in nature, the numerics indicates that the singularity is isotropic for all relevant initial conditions. Therefore this analysis, and a preliminary investigation of general inhomogeneous ($G_0$) models, indicates that it is plausible that the initial singularity is isotropic in spatially inhomogeneous brane-world cosmological models and consequently that brane cosmology naturally gives rise to a set of initial data that provide the conditions for inflation to subsequently take place.Comment: 32 pages with 8 pictures. submitted to Class. Quant. Gra

Galiellalactone Inhibits Stem Cell-Like ALDH-Positive Prostate Cancer Cells

Galiellalactone is a potent and specific inhibitor of STAT3 signaling which has been shown to possess growth inhibitory effects on prostate cancer cells expressing active STAT3. In this study we aimed to investigate the effect of galiellalactone on prostate cancer stem cell-like cells. We explored the expression of aldehyde dehydrogenase (ALDH) as a marker for cancer stem cell-like cells in different human prostate cancer cell lines and the effects of galiellalactone on ALDH expressing (ALDH+) prostate cancer cells. ALDH+ subpopulations were detected and isolated from the human prostate cancer cell lines DU145 and long-term IL-6 stimulated LNCaP cells using ALDEFLUOR® assay and flow cytometry. In contrast to ALDH− cells, ALDH+ prostate cancer cells showed cancer stem cell-like characteristics such as increased self-renewing and colony forming capacity and tumorigenicity. In addition, ALDH+ cells showed an increased expression of putative prostate cancer stem cell markers (CD44 and integrin α2β1). Furthermore, ALDH+ cells expressed phosphorylated STAT3. Galiellalactone treatment decreased the proportion of ALDH+ prostate cancer cells and induced apoptosis of ALDH+ cells. The gene expression of ALDH1A1 was downregulated in vivo in galiellalactone treated DU145 xenografts. These findings emphasize that targeting the STAT3 pathway in prostate cancer cells, including prostate cancer stem cell-like cells, is a promising therapeutic approach and that galiellalactone is an interesting compound for the development of future prostate cancer drugs

The aldehyde dehydrogenase enzyme 7A1 is functionally involved in prostate cancer bone metastasis

High aldehyde dehydrogenase (ALDH) activity can be used to identify tumor-initiating and metastasis-initiating cells in various human carcinomas, including prostate cancer. To date, the functional importance of ALDH enzymes in prostate carcinogenesis, progression and metastasis has remained elusive. Previously we identified strong expression of ALDH7A1 in human prostate cancer cell lines, primary tumors and matched bone metastases. In this study, we evaluated whether ALDH7A1 is required for the acquisition of a metastatic stem/progenitor cell phenotype in human prostate cancer. Knockdown of ALDH7A1 expression resulted in a decrease of the α2hi/αvhi/CD44+ stem/progenitor cell subpopulation in the human prostate cancer cell line PC-3M-Pro4. In addition, ALDH7A1 knockdown significantly inhibited the clonogenic and migratory ability of human prostate cancer cells in vitro. Furthermore, a number of genes/factors involved in migration, invasion and metastasis were affected including transcription factors (snail, snail2, and twist) and osteopontin, an ECM molecule involved in metastasis. Knockdown of ALDH7A1 resulted in decreased intra-bone growth and inhibited experimentally induced (bone) metastasis, while intra-prostatic growth was not affected. In line with these observations, evidence is presented that TGF-β, a key player in cancer invasiveness and bone metastasis, strongly induced ALDH activity while BMP7 (an antagonist of TGF-β signaling) down-regulated ALDH activity. Our findings show, for the first time, that the ALDH7A1 enzyme is functionally involved in the formation of bone metastases and that the effect appeared dependent on the microenvironment, i.e., bone versus prostate

On the Asymptotic Behaviour of Cosmological Models in Scalar-Tensor Theories of Gravity

We study the qualitative properties of cosmological models in scalar-tensor theories of gravity by exploiting the formal equivalence of these theories with general relativity minimally coupled to a scalar field under a conformal transformation and field redefinition. In particular, we investigate the asymptotic behaviour of spatially homogeneous cosmological models in a class of scalar-tensor theories which are conformally equivalent to general relativistic Bianchi cosmologies with a scalar field and an exponential potential whose qualitative features have been studied previously. Particular attention is focussed on those scalar-tensor theory cosmological models, which are shown to be self-similar, that correspond to general relativistic models that play an important r\^{o}le in describing the asymptotic behaviour of more general models (e.g., those cosmological models that act as early-time and late-time attractors).Comment: 22 pages, submitted to Phys Rev

The Dynamics of Brane-World Cosmological Models

Brane-world cosmology is motivated by recent developments in string/M-theory and offers a new perspective on the hierarchy problem. In the brane-world scenario, our Universe is a four-dimensional subspace or {\em brane} embedded in a higher-dimensional {\em bulk} spacetime. Ordinary matter fields are confined to the brane while the gravitational field can also propagate in the bulk, leading to modifications of Einstein's theory of general relativity at high energies. In particular, the Randall-Sundrum-type models are self-consistent and simple and allow for an investigation of the essential non-linear gravitational dynamics. The governing field equations induced on the brane differ from the general relativistic equations in that there are nonlocal effects from the free gravitational field in the bulk, transmitted via the projection of the bulk Weyl tensor, and the local quadratic energy-momentum corrections, which are significant in the high-energy regime close to the initial singularity. In this review we discuss the asymptotic dynamical evolution of spatially homogeneous brane-world cosmological models containing both a perfect fluid and a scalar field close to the initial singularity. Using dynamical systems techniques it is found that, for models with a physically relevant equation of state, an isotropic singularity is a past-attractor in all orthogonal spatially homogeneous models (including Bianchi type IX models). In addition, we describe the dynamics in a class of inhomogeneous brane-world models, and show that these models also have an isotropic initial singularity. These results provide support for the conjecture that typically the initial cosmological singularity is isotropic in brane-world cosmology.Comment: Einstein Centennial Review Article: to appear in CJ

CRIPTO and its signaling partner GRP78 drive the metastatic phenotype in human osteotropic prostate cancer

CRIPTO (CR-1, TDGF1) is a cell surface/secreted oncoprotein actively involved in development and cancer. Here, we report that high expression of CRIPTO correlates with poor survival in stratified risk groups of prostate cancer (PCa) patients. CRIPTO and its signaling partner glucose-regulated protein 78 (GRP78) are highly expressed in PCa metastases and display higher levels in the metastatic ALDHhigh sub-population of PC-3M-Pro4Luc2 PCa cells compared with non-metastatic ALDHlow. Coculture of the osteotropic PC-3M-Pro4Luc2 PCa cells with differentiated primary human osteoblasts induced CRIPTO and GRP78 expression in cancer cells and increases the size of the ALDHhigh sub-population. Additionally, CRIPTO or GRP78 knockdown decreases proliferation, migration, clonogenicity and the size of the metastasis-initiating ALDHhigh sub-population. CRIPTO knockdown reduces the invasion of PC-3M-Pro4Luc2 cells in zebrafish and inhibits bone metastasis in a preclinical mouse model. These results highlight a functional role for CRIPTO and GRP78 in PCa metastasis and suggest that targeting CRIPTO/GRP78 signaling may have significant therapeutic potential.Oncogene advance online publication, 10 April 2017; doi:10.1038/onc.2017.87

Equation of state for Universe from similarity symmetries

In this paper we proposed to use the group of analysis of symmetries of the dynamical system to describe the evolution of the Universe. This methods is used in searching for the unknown equation of state. It is shown that group of symmetries enforce the form of the equation of state for noninteracting scaling multifluids. We showed that symmetries give rise the equation of state in the form $p=-\Lambda+w_{1}\rho(a)+w_{2}a^{\beta}+0$ and energy density $\rho=\Lambda+\rho_{01}a^{-3(1+w)}+\rho_{02}a^{\beta}+\rho_{03}a^{-3}$, which is commonly used in cosmology. The FRW model filled with scaling fluid (called homological) is confronted with the observations of distant type Ia supernovae. We found the class of model parameters admissible by the statistical analysis of SNIa data. We showed that the model with scaling fluid fits well to supernovae data. We found that $\Omega_{\text{m},0} \simeq 0.4$ and $n \simeq -1$ ($\beta = -3n$), which can correspond to (hyper) phantom fluid, and to a high density universe. However if we assume prior that $\Omega_{\text{m},0}=0.3$ then the favoured model is close to concordance $\Lambda$CDM model. Our results predict that in the considered model with scaling fluids distant type Ia supernovae should be brighter than in $\Lambda$CDM model, while intermediate distant SNIa should be fainter than in $\Lambda$CDM model. We also investigate whether the model with scaling fluid is actually preferred by data over $\Lambda$CDM model. As a result we find from the Akaike model selection criterion prefers the model with noninteracting scaling fluid.Comment: accepted for publication versio