Quasibounded plurisubharmonic functions

We extend the notion of quasibounded harmonic functions to the plurisubharmonic setting. As an application, using the theory of Jensen measures, we show that certain generalized Dirichlet problems with unbounded boundary data admit unique solutions, and that these solutions are continuous outside a pluripolar set

Dark matter and dark energy denote the gravitation of the expanding universe

We reason that it is the gravitation of all ordinary matter, extending from the dense distant past to the sparse present, rather than dark matter, that shows up in galaxy rotation and velocity dispersion. Likewise, we argue that it is this gradient in the gravitational energy due to the expansion, rather than dark energy, that explains Type 1a supernovae brightness vs. redshift data. Our conclusions follow from statistical mechanics, the thermodynamic theory based on the atomistic axiom that everything comprises quanta. In line with the Einstein field equations, the vacuum quanta embodying gravitation, geometrized as spacetime, equate in dynamic balance to the quanta embodying the substance of the stress-energy tensor. In accordance with quantum field theory, the proposed ground-state field of paired light quanta complies with Bose-Einstein statistics and assumes an excited state around a particle.Peer reviewe

Variations on a theorem by Edwards

We discuss two variations of Edwards' duality theorem. More precisely, we prove one version of the theorem for cones not necessarily containing all constant functions. In particular, we allow the functions in the cone to have a non-empty common zero set. In the second variation, we replace suprema of point evaluations and infima over Jensen measures by suprema of other continuous functionals and infima over a set measures defined through a natural order relation induced by the cone. As applications, we give some results on propagation of discontinuities for Perron--Bremermann envelopes in hyperconvex domains as well as a characterization of minimal elements in the order relation mentioned above

Proton pumping by cytochrome c oxidase : A 40 year anniversary

Abstract Cytochrome c oxidase is a remarkable energy transducer that seems to work almost purely by Coulombic principles without the need for significant protein conformational changes. In recent years it has become possible to follow key partial reactions of the catalytic cycle in real time, both with respect to electron and proton movements. These experiments have largely set the stage for the proton pump mechanism. The structures of the catalytic binuclear heme‑copper site that is common to the huge family of heme‑copper oxidases, are today well understood throughout the catalytic cycle of oxygen reduction to water based on both spectroscopic studies and quantum chemical calculations. Here, we briefly review this progress, and add some recent details into how the proton pump mechanism is protected from failure by leakage.Peer reviewe

Cytochrome c Oxidase : Remaining Questions About the Catalytic Mechanism

Non peer reviewe

On the role of ubiquinone in the proton translocation mechanism of respiratory complex I

Complex I converts oxidoreduction energy into a proton electrochemical gradient across the inner mitochondrial or bacterial cell membrane. This gradient is the primary source of energy for aerobic synthesis of ATP. Oxidation of reduced nicotinamide adenine dinucleotide (NADH) by ubiquinone (Q) yields NAD(+) and ubiquinol (QH(2)), which is tightly coupled to translocation of four protons from the negatively to the positively charged side of the membrane. Electrons from NADH oxidation reach the iron-sulfur centre N2 positioned near the bottom of a tunnel that extends circa 30 angstrom from the membrane domain into the hydrophilic domain of the complex. The tunnel is occupied by ubiquinone, which can take a distal position near the N2 centre or proximal positions closer to the membrane. Here, we review important structural, kinetic and thermodynamic properties of ubiquinone that define its role in complex I function. We suggest that this function exceeds that of a mere substrate or electron acceptor and propose that ubiquinone may be the redox element of complex I coupling electron transfer to proton translocation.Peer reviewe

Structures of the intermediates in the catalytic cycle of mitochondrial cytochrome c oxidase

Cytochrome c oxidase is the terminal complex of the respiratory chains in the mitochondria of nearly all eu-karyotes. It catalyzes the reduction of molecular O-2 to water using electrons from the respiratory chain, delivered via cytochrome c on the external surface of the inner mitochondrial membrane. The protons required for water formation are taken from the matrix side of the membrane, making catalysis vectorial. This vectorial feature is further enhanced by the fact that the redox catalysis is coupled to the translocation of protons from the inside to the outside of the inner mitochondrial membrane. We are dealing with a molecular machine that converts redox free energy into a protonmotive force (pmf). Here, we review the current extensive knowledge of the structural changes in the active heme-copper site that accompany catalysis, based on a large variety of time-resolved spectroscopic experiments, X-ray and cryoEM structures, and advanced computational chemistry.Peer reviewe

Change in electron and spin density upon electron transfer to haem

AbstractHaems are the cofactors of cytochromes and important catalysts of biological electron transfer. They are composed of a planar porphyrin structure with iron coordinated at the centre. It is known from spectroscopy that ferric low-spin haem has one unpaired electron at the iron, and that this spin is paired as the haem receives an electron upon reduction (I. Bertini, C. Luchinat, NMR of Paramagnetic Molecules in Biological Systems, Benjamin/Cummins Publ. Co., Menlo Park, CA, 1986, pp. 165–170; H.M. Goff, in: A.B.P. Lever, H.B. Gray (Eds.), Iron Porphyrins, Part I, Addison-Wesley Publ. Co., Reading, MA, 1983, pp. 237–281; G. Palmer, in: A.B.P. Lever, H.B. Gray (Eds.), Iron Porphyrins, Part II, Addison-Wesley Publ. Co., Reading, MA, 1983, pp. 43–88). Here we show by quantum chemical calculations on a haem a model that upon reduction the spin pairing at the iron is accompanied by effective delocalisation of electrons from the iron towards the periphery of the porphyrin ring, including its substituents. The change of charge of the iron atom is only approx. 0.1 electrons, despite the unit difference in formal oxidation state. Extensive charge delocalisation on reduction is important in order for the haem to be accommodated in the low dielectric of a protein, and may have impact on the distance dependence of the rates of electron transfer. The lost individuality of the electron added to the haem on reduction is another example of the importance of quantum mechanical effects in biological systems