An action principle for the Einstein-Weyl equations

A longstanding open problem in mathematical physics has been that of finding an action principle for the Einstein–Weyl (EW) equations. In this paper, we present for the first time such an action principle in three dimensions in which the Weyl vector is not exact. More precisely, our model contains, in addition to the Weyl nonmetricity, a traceless part. If the latter is (consistently) set to zero, the equations of motion boil down to the EW equations. In particular, we consider a metric affine f(R) gravity action plus additional terms involving Lagrange multipliers and gravitational Chern–Simons contributions. In our framework, the metric and the connection are considered as independent objects, and no a priori assumptions on the nonmetricity and the torsion of the connection are made. The dynamics of the Weyl vector turns out to be governed by a special case of the generalized monopole equation, which represents a conformal self-duality condition in three dimensions

Einstein manifolds with torsion and nonmetricity

Manifolds endowed with torsion and nonmetricity are interesting both from the physical and the mathematical points of view. In this paper, we generalize some results presented in the literature. We study Einstein manifolds (i.e., manifolds whose symmetrized Ricci tensor is proportional to the metric) in d dimensions with nonvanishing torsion that has both a trace and a traceless part, and analyze invariance under extended conformal transformations of the corresponding field equations. Then, we compare our results to the case of Einstein manifolds with zero torsion and nonvanishing nonmetricity, where the latter is given in terms of the Weyl vector (Einstein-Weyl spaces). We find that the trace part of the torsion can alternatively be interpreted as the trace part of the nonmetricity. The analysis is subsequently extended to Einstein spaces with both torsion and nonmetricity, where we also discuss the general setting in which the nonmetricity tensor has both a trace and a traceless part. Moreover, we consider and investigate actions involving scalar curvatures obtained from torsionful or nonmetric connections, analyzing their relations with other gravitational theories that appeared previously in the literature. In particular, we show that the Einstein-Cartan action and the scale invariant gravity (also known as conformal gravity) action describe the same dynamics. Then, we consider the Einstein-Hilbert action coupled to a three-form field strength and show that its equations of motion imply that the manifold is Einstein with totally antisymmetric torsion

An update of the chemiosmotic theory as suggested by possible proton currents inside the coupling membrane

Understanding how biological systems convert and store energy is a primary purpose of basic research. However, despite Mitchell's chemiosmotic theory, we are far from the complete description of basic processes such as oxidative phosphorylation (OXPHOS) and photosynthesis. After more than half a century, the chemiosmotic theory may need updating, thanks to the latest structural data on respiratory chain complexes. In particular, up-to date technologies, such as those using fluorescence indicators following proton displacements, have shown that proton translocation is lateral rather than transversal with respect to the coupling membrane. Furthermore, the definition of the physical species involved in the transfer (proton, hydroxonium ion or proton currents) is still an unresolved issue, even though the latest acquisitions support the idea that protonic currents, difficult to measure, are involved. Moreover, F o F 1 -ATP synthase ubiquitous motor enzyme has the peculiarity (unlike most enzymes) of affecting the thermodynamic equilibrium of ATP synthesis. It seems that the concept of diffusion of the proton charge expressed more than two centuries ago by Theodor von Grotthuss is to be taken into consideration to resolve these issues. All these uncertainties remind us that also in biology it is necessary to consider the Heisenberg indeterminacy principle, which sets limits to analytical questions

High Glucose Impairs Expression and Activation of MerTK in ARPE-19 Cells

MerTK (Mer Tyrosine Kinase) is a cell surface receptor that regulates phagocytosis of pho-toreceptor outer segments (POS) in retinal pigment epithelial (RPE) cells. POS phagocytosis is im-paired in several pathologies, including diabetes. In this study, we investigate whether hyperglyce-mic conditions may affect MerTK expression and activation in ARPE-19 cells, a retinal pigment epithelial cellular model. ARPE-19 cells were cultured in standard (CTR) or high-glucose (HG) me-dium for 24 h. Then, we analyzed: mRNA levels and protein expression of MerTK and ADAM9, a protease that cleaves the extracellular region of MerTK; the amount of cleaved Mer (sMer); and the ability of GAS6, a MerTK ligand, to induce MerTK phosphorylation. Since HG reduces miR-126 levels, and ADAM9 is a target of miR-126, ARPE-19 cells were transfected with miR-126 inhibitor or mimic; then, we evaluated ADAM9 expression, sMer, and POS phagocytosis. We found that HG reduced expression and activation of MerTK. Contextually, HG increased expression of ADAM9 and the amount of sMer. Overexpression of miR-126 reduced levels of sMer and improved phago-cytosis in ARPE-19 cells cultured with HG. In this study, we demonstrate that HG compromises MerTK expression and activation in ARPE-19 cells. Our results suggest that HG up-regulates ADAM9 expression, leading to increased shedding of MerTK. The consequent rise in sMer coupled to reduced expression of MerTK impairs binding and internalization of POS in ARPE-19 cells

A multidrug approach to modulate the mitochondrial metabolism impairment and relative oxidative stress in fanconi anemia complementation group a

Fanconi Anemia (FA) is a rare recessive genetic disorder characterized by aplastic anemia due to a defective DNA repair system. In addition, dysfunctional energy metabolism, lipid droplets accumulation, and unbalanced oxidative stress are involved in FA pathogenesis. Thus, to modulate the altered metabolism, Fanc-A lymphoblast cell lines were treated with quercetin, a flavonoid compound, C75 (4-Methylene-2-octyl-5-oxotetrahydrofuran-3-carboxylic acid), a fatty acid synthesis inhibitor, and rapamycin, an mTOR inhibitor, alone or in combination. As a control, isogenic FA cell lines corrected with the functional Fanc-A gene were used. Results showed that: (i) quercetin recovered the energy metabolism efficiency, reducing oxidative stress; (ii) C75 caused the lipid accumulation decrement and a slight oxidative stress reduction, without improving the energy metabolism; (iii) rapamycin reduced the aerobic metabolism and the oxidative stress, without increasing the energy status. In addition, all molecules reduce the accumulation of DNA double-strand breaks. Two-by-two combinations of the three drugs showed an additive effect compared with the action of the single molecule. Specifically, the quercetin/C75 combination appeared the most efficient in the mitochondrial and lipid metabolism improvement and in oxidative stress production reduction, while the quercetin/rapamycin combination seemed the most efficient in the DNA breaks decrement. Thus, data reported herein suggest that FA is a complex and multifactorial disease, and a multidrug strategy is necessary to correct the metabolic alterations

A multistationary loop model of ALS unveils critical molecular interactions involving mitochondria and glucose metabolism

Amyotrophic lateral sclerosis (ALS) is a poor-prognosis disease with puzzling pathogenesis and inconclusive treatments. We develop a mathematical model of ALS based on a system of interactive feedback loops, focusing on the mutant SOD1G93A mouse. Misfolded mutant SOD1 aggregates in motor neuron (MN) mitochondria and triggers a first loop characterized by oxidative phosphorylation impairment, AMP kinase over-activation, 6-phosphofructo-2-kinase (PFK3) rise, glucose metabolism shift from pentose phosphate pathway (PPP) to glycolysis, cell redox unbalance, and further worsening of mitochondrial dysfunction. Oxidative stress then triggers a second loop, involving the excitotoxic glutamatergic cascade, with cytosolic Ca2+ overload, increase of PFK3 expression, and further metabolic shift from PPP to glycolysis. Finally, cytosolic Ca2+ rise is also detrimental to mitochondria and oxidative phosphorylation, thus closing a third loop. These three loops are overlapped and positive (including an even number of inhibitory steps), hence they form a candidate multistationary (bistable) system. To describe the system dynamics, we model the interactions among the functional agents with differential equations. The system turns out to admit two stable equilibria: the healthy state, with high oxidative phosphorylation and preferential PPP, and the pathological state, with AMP kinase activation, PFK3 over expression, oxidative stress, excitotoxicity and MN degeneration. We demonstrate that the loop system is monotone: all functional agents consistently act toward the healthy or pathological condition, depending on low or high mutant SOD1 input. We also highlight that molecular interactions involving PFK3 are crucial, as their deletion disrupts the system\u2019s bistability leading to a single healthy equilibrium point. Hence, our mathematical model unveils that promising ALS management strategies should be targeted to mechanisms that keep low PFK3 expression and activity within MNs