Mitochondrial Na+ controls oxidative phosphorylation and hypoxic redox signalling

All metazoans depend on O2 delivery and consumption by the mitochondrial oxidative phosphorylation (OXPHOS) system to produce energy. A decrease in O2 availability (hypoxia) leads to profound metabolic rewiring. In addition, OXPHOS uses O2 to produce reactive oxygen species (ROS) that can drive cell adaptations through redox signalling, but also trigger cell damage1–4, and both phenomena occur in hypoxia4–8. However, the precise mechanism by which acute hypoxia triggers mitochondrial ROS production is still unknown. Ca2+ is one of the best known examples of an ion acting as a second messenger9, yet the role ascribed to Na+ is to serve as a mere mediator of membrane potential and collaborating in ion transport10. Here we show that Na+ acts as a second messenger regulating OXPHOS function and ROS production by modulating fluidity of the inner mitochondrial membrane (IMM). We found that a conformational shift in mitochondrial complex I during acute hypoxia11 drives the acidification of the matrix and solubilization of calcium phosphate precipitates. The concomitant increase in matrix free-Ca2+ activates the mitochondrial Na+/Ca2+ exchanger (NCLX), which imports Na+ into the matrix. Na+ interacts with phospholipids reducing IMM fluidity and mobility of free ubiquinone between complex II and complex III, but not inside supercomplexes. As a consequence, superoxide is produced at complex III, generating a redox signal. Inhibition of mitochondrial Na+ import through NCLX is sufficient to block this pathway, preventing adaptation to hypoxia. These results reveal that Na+ import into the mitochondrial matrix controls OXPHOS function and redox signalling through an unexpected interaction with phospholipids, with profound consequences in cellular metabolism

Ideals in Triangulated Categories: Phantoms, Ghosts and Skeleta

AbstractWe begin by showing that in a triangulated category, specifying a projective class is equivalent to specifying an ideal I of morphisms with certain properties and that if I has these properties, then so does each of its powers. We show how a projective class leads to an Adams spectral sequence and give some results on the convergence and collapsing of this spectral sequence. We use this to study various ideals. In the stable homotopy category we examine phantom maps, skeletal phantom maps, superphantom maps, and ghosts. (A ghost is a map which induces the zero map of homotopy groups.) We show that ghosts lead to a stable analogue of the Lusternik–Schnirelmann category of a space, and we calculate this stable analogue for low-dimensional real projective spaces. We also give a relation between ghosts and the Hopf and Kervaire invariant problems. In the case ofA∞modules over anA∞ring spectrum, the ghost spectral sequence is a universal coefficient spectral sequence. From the phantom projective class we derive a generalized Milnor sequence for filtered diagrams of finite spectra, and from this it follows that the group of phantom maps fromXtoYcan always be described as alim←1group. The last two sections focus on algebraic examples. In the derived category of an abelian category we study the ideal of maps inducing the zero map of homology groups and find a natural setting for a result of Kelly on the vanishing of composites of such maps. We also explain how pure exact sequences relate to phantom maps in the derived category of a ring and give an example showing that phantoms can compose non-trivially

Topological aspects of controllability and observability on the manifold of singular and regular systems

AbstractIn a previous article (J. D. Cobb, J. Math. Anal Appl., Nov. 1986) we considered the class of all singular and regular linear time-invariant systems and proved some basic topological properties of that set. In this paper we examine specific implications of those results to control theory and demonstrate, among other things, that controllability and observability are generic properties even when singular systems are included in the construction. We also derive related results for other important subclasses of systems, proving that only some of the remaining fundamental system properties are generic. Finally, we extend existing results on connectedness and show that the number of connected components of the controllable and observable sets is diminished whenever singular systems are brought into the picture

Fundamental properties of the manifold of singular and regular linear systems

AbstractWe construct a real analytic manifold L of systems of the form Eẋ = Ax + Bu, y = Cx and show that L is the “completion,” with respect to solutions, of the set of regular (state-space) systems, i.e., those systems with nonsingular E. Other geometric and analytic properties of L are established, including genericity of the regular Systems