In agreement with the data, the quantum correlation between spins violates Bell’s inequality by following a cosine curve when one analyzer is rotated relative to the other. In contrast, the linear correlation attributed to hidden variables has never been observed. Besides these well-established facts, we show here that classical covariance, Pearson correlation, between spins projected as up or down on the analyzer axes also follows the cosine form hitherto uniquely ascribed to the quantum mechanical expectation value. The common cause for the classical correlation is the conservation of intrinsic angular momentum that aligns the two spins antiparallel at the breakup. Thus, as long as the spins retain their orientations relative to each other, the measurement of one spin in a chosen frame of reference also discloses the opposite orientation of the other in that frame. Realizing that classical correlation has the same functional form as quantum entanglement sheds light on the foundations of modern physics and quantum computing.

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 (QH2), 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 Å 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.

We present a brief review of the mitochondrial respiratory chain with emphasis on complexes I, III and IV, which contribute to the generation of protonmotive force across the inner mitochondrial membrane, and drive the synthesis of ATP by the process called oxidative phosphorylation. The basic structural and functional details of these complexes are discussed. In addition, we briefly review the information on the so-called supercomplexes, aggregates of complexes I-IV, and summarize basic physiological aspects of cell respiration.

The signaling molecule nitric oxide (NO) is synthesized in animals by structurally related NO synthases (NOSs), which contain NADPH/FAD- and FMN-binding domains. During catalysis, NADPH-derived electrons transfer into FAD and then distribute into the FMN domain for further transfer to internal or external heme groups. Conformational freedom of the FMN domain is thought to be essential for the electron transfer (ET) reactions in NOSs. To directly examine this concept, we utilized a "Cys-lite" neuronal NOS flavoprotein domain and substituted Cys for two residues (Glu-816 and Arg-1229) forming a salt bridge between the NADPH/FAD and FMN domains in the conformationally closed structure to allow cross-domain disulfide bond formation or cross-linking by bismaleimides of various lengths. The disulfide bond cross-link caused a ≥95% loss of cytochrome c reductase activity that was reversible with DTT treatment, whereas graded cross-link lengthening gradually increased activity, thus defining the conformational constraints in the catalytic process. We used spectroscopic and stopped-flow techniques to further investigate how the changes in FMN domain conformational freedom impact the following: (i) the NADPH interaction; (ii) kinetics of electron loading (flavin reduction); (iii) stabilization of open versus closed conformational forms in two different flavin redox states; (iv) reactivity of the reduced FMN domain toward cytochrome c; (v) response to calmodulin binding; and (vi) the rates of interflavin ET and the FMN domain conformational dynamics. Together, our findings help explain how the spatial and temporal behaviors of the FMN domain impact catalysis by the NOS flavoprotein domain and how these behaviors are governed to enable electron flow through the enzyme.

Cell death is a fundamental process for organogenesis, immunity and cell renewal. During the last decades a broad range of molecular tools were identified as important players for several different cell death pathways (apoptosis, pyroptosis, necrosis, autosis…). Aside from these direct regulators of cell death programs, several lines of evidence proposed connexins and pannexins as potent effectors of cell death. In the present review we discussed the potential roles played by connexins, pannexins and innexins in the different cell death programs at different scales from gap junction intercellular communication to protein–protein interactions. This article is part of a Special Issue entitled: Gap Junction Proteins edited by Jean Claude Herve.

Cytochrome c oxidase is the terminal complex of the respiratory chains in the mitochondria of nearly all eukaryotes. It catalyzes the reduction of molecular O2 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.

Aerobic life is powered by membrane-bound enzymes that catalyze the transfer of electrons to oxygen and protons across a biological membrane. Cytochrome c oxidase (CcO) functions as a terminal electron acceptor in mitochondrial and bacterial respiratory chains, driving cellular respiration and transducing the free energy from O2 reduction into proton pumping. Here we show that CcO creates orientated electric fields around a nonpolar cavity next to the active site, establishing a molecular switch that directs the protons along distinct pathways. By combining large-scale quantum chemical density functional theory (DFT) calculations with hybrid quantum mechanics/molecular mechanics (QM/MM) simulations and atomistic molecular dynamics (MD) explorations, we find that reduction of the electron donor, heme a, leads to dissociation of an arginine (Arg438)-heme a3 D-propionate ion-pair. This ion-pair dissociation creates a strong electric field of up to 1 V Å-1 along a water-mediated proton array leading to a transient proton loading site (PLS) near the active site. Protonation of the PLS triggers the reduction of the active site, which in turn aligns the electric field vectors along a second, "chemical," proton pathway. We find a linear energy relationship of the proton transfer barrier with the electric field strength that explains the effectivity of the gating process. Our mechanism shows distinct similarities to principles also found in other energy-converting enzymes, suggesting that orientated electric fields generally control enzyme catalysis.

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.

Cytochrome ba3 from Thermus thermophilus belongs to the B family of heme-copper oxidases and pumps protons across the membrane with an as yet unknown mechanism. The K channel of the A family heme-copper oxidases provides delivery of a substrate proton from the internal water phase to the binuclear heme-copper center (BNC) during the reductive phase of the catalytic cycle, while the D channel is responsible for transferring both substrate and pumped protons. By contrast, in the B family oxidases there is no D-channel and the structural equivalent of the K channel seems to be responsible for the transfer of both categories of protons. Here we have studied the effect of the T315V substitution in the K channel on the kinetics of membrane potential generation coupled to the oxidative half-reaction of the catalytic cycle of cytochrome ba3. The results suggest that the mutated enzyme does not pump protons during the reaction of the fully reduced form with molecular oxygen in a single turnover. Specific inhibition of proton pumping in the T315V mutant appears to be a consequence of inability to provide rapid (τ ~ 100 μs) reprotonation of the internal transient proton donor(s) of the K channel. In contrast to the A family, the K channel of the B-type oxidases is necessary for the electrogenic transfer of both pumped and substrate protons during the oxidative half-reaction of the catalytic cycle.

Bacteria power their energy metabolism using membrane-bound respiratory enzymes that capture chemical energy and transduce it by pumping protons or Na+ ions across their cell membranes. Recent breakthroughs in molecular bioenergetics have elucidated the architecture and function of many bacterial respiratory enzymes, although key mechanistic principles remain debated. In this Review, we present an overview of the structure, function and bioenergetic principles of modular bacterial respiratory chains and discuss their differences from the eukaryotic counterparts. We also discuss bacterial supercomplexes, which provide central energy transduction systems in several bacteria, including important pathogens, and which could open up possible avenues for treatment of disease.

The protonmotive mitochondrial respiratory chain, comprising complexes I, III and IV, transduces free energy of the electron transfer reactions to an electrochemical proton gradient across the inner mitochondrial membrane. This gradient is used to drive synthesis of ATP and ion and metabolite transport. The efficiency of energy conversion is of interest from a physiological point of view, since the energy transduction mechanisms differ fundamentally between the three complexes. Here, we have chosen actively phosphorylating mitochondria as the focus of analysis. For all three complexes we find that the thermodynamic efficiency is about 80-90% and that the degree of coupling between the redox and proton translocation reactions is very high during active ATP synthesis. However, when net ATP synthesis stops at a high ATP/ADP.Pi ratio, and mitochondria reach "State 4" with an elevated proton gradient, the degree of coupling drops substantially. The mechanistic cause and the physiological implications of this effect are discussed.

We previously observed an unexpected fivefold (35 vs. 200 days) difference in the survival of respiratory chain complex III (CIII) deficient Bcs1l p.S78G mice between two congenic backgrounds. Here, we identify a spontaneous homoplasmic mtDNA variant ( m.G14904A , mt-Cyb p.D254N ), affecting the CIII subunit cytochrome b (MT-CYB), in the background with short survival. We utilize maternal inheritance of mtDNA to confirm this as the causative variant and show that it further decreases the low CIII activity in Bcs1l p.S78G tissues to below survival threshold by 35 days of age. Molecular dynamics simulations predict D254N to restrict the flexibility of MT-CYB ef loop, potentially affecting RISP dynamics. In Rhodobacter cytochrome bc 1 complex the equivalent substitution causes a kinetics defect with longer occupancy of RISP head domain towards the quinol oxidation site. These findings represent a unique case of spontaneous mitonuclear epistasis and highlight the role of mtDNA variation as modifier of mitochondrial disease phenotypes.

Cell respiration is mainly catalysed by the so-called heme–copper oxygen reductases, which are characterised by a binuclear active site containing an oxygen-binding heme group and a nearby copper ion. The copper ion is ligated by three histidine residues, one of which is covalently bonded to a tyrosine residue and takes active part in the reduction of O2 to water. In addition, a low-spin heme is located adjacent to the oxygen-binding heme serving as the immediate electron donor to the binuclear site. Binding of O2 is followed by a “concerted” four-electron reduction confined within the binuclear site, leaving the site in a highly oxidised configuration, akin to the classical Compound I of the peroxidases and catalase. The catalytic cycle is then completed by sequential additions of four electrons to the binuclear centre, one at a time, to end up in the initial reduced state that binds the next O2. These four electron transfers are intimately coupled to proton translocation across the mitochondrial (or bacterial) membrane, which gives the function of the heme–copper oxygen reductases an additional intriguing dimension.

Complex I couples the free energy released from quinone (Q) reduction to pump protons across the biological membrane in the respiratory chains of mitochondria and many bacteria. The Q reduction site is separated by a large distance from the proton-pumping membrane domain. To address the molecular mechanism of this long-range proton-electron coupling, we perform here full atomistic molecular dynamics simulations, free energy calculations, and continuum electrostatics calculations on complex I from Thermus thermophilus We show that the dynamics of Q is redox-state-dependent, and that quinol, QH2, moves out of its reduction site and into a site in the Q tunnel that is occupied by a Q analog in a crystal structure of Yarrowia lipolytica We also identify a second Q-binding site near the opening of the Q tunnel in the membrane domain, where the Q headgroup forms strong interactions with a cluster of aromatic and charged residues, while the Q tail resides in the lipid membrane. We estimate the effective diffusion coefficient of Q in the tunnel, and in turn the characteristic time for Q to reach the active site and for QH2 to escape to the membrane. Our simulations show that Q moves along the Q tunnel in a redox-state-dependent manner, with distinct binding sites formed by conserved residue clusters. The motion of Q to these binding sites is proposed to be coupled to the proton-pumping machinery in complex I.

This review focuses on the type A cytochrome c oxidases (CcO), which are found in all mitochondria and also in several aerobic bacteria. CcO catalyzes the respiratory reduction of dioxygen (O2) to water by an intriguing mechanism, the details of which are fairly well understood today as a result of research for over four decades. Perhaps even more intriguingly, the membrane-bound CcO couples the O2 reduction chemistry to translocation of protons across the membrane, thus contributing to generation of the electrochemical proton gradient that is used to drive the synthesis of ATP as catalyzed by the rotary ATP synthase in the same membrane. After reviewing the structure of the core subunits of CcO, the active site, and the transfer paths of electrons, protons, oxygen, and water, we describe the states of the catalytic cycle and point out the few remaining uncertainties. Finally, we discuss the mechanism of proton translocation and the controversies in that area that still prevail.

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.