Beyond the chemiosmotic theory: analysis of key fundamental aspects of energy coupling in oxidative phosphorylation in the light of a torsional mechanism of energy transduction and ATP synthesis--invited review part 2

A protet-based model that can account for energy coupling in oxidative and photosynthetic phosphorylation

Two-stage (e.g. light-dark) phosphorylation experiments showed that there is a stored 'high-energy' intermediate linking electron transport and phosphorylation. Large, artificial electrochemical proton gradients (protonmotive forces or pmfs) can also drive phosphorylation, a fact seen as strongly supportive of the chemiosmotic coupling hypothesis that a pmf is the 'high-energy' intermediate. However, in such experiments there is an experimental threshold (pmf >170 mV, equivalent to ΔpH ∼2.8) below which no phosphorylation is in fact observed, and 220 mV are required to recreate in vivo rates. This leads to the correct question, which is then whether those values of the pmf generated by electron transport are large enough. Even the lower ones as required for any phosphorylation (leave alone those required to explain in vivo rates) are below the threshold [1, 2], whether measured directly with microelectrodes or via the use of membrane-permeant ions and/or acids/bases (which are always transporter substrates [3], so all such measurements are in fact artefactual). The single case that seemed large enough (220 mV) is now admitted to be a diffusion potential artefact [4]. Many other observables (inadequate bulk H+ in 'O2-pulse'-type experiments, alkaliphilic bacteria, dual-inhibitor titrations, uncoupler-binding proteins, etc.) are consistent with the view that values of the pmf, and especially of Δψ, are actually very low. A protet-based charge separation model [2], a protonic version analogous to how energy may be stored in devices called electrets, provides a high-energy intermediate that can explain the entire literature, including the very striking demonstration [5] that close proximity is required between electron transport and ATP synthase complexes for energy coupling between them to allow phosphorylation to occur. A chief purpose of this article is thus to summarise the extensive and self-consistent literature, much of which is of some antiquity and rarely considered by modern researchers, despite its clear message of the inadequacy of chemiosmotic coupling to explain these phenomena.

Size matters in metabolic scaling: Critical role of the thermodynamic efficiency of ATP synthesis and its dependence on mitochondrial H+ leak across mammalian species

In this last article of the trilogy, the unified biothermokinetic theory of ATP synthesis developed in the previous two papers is applied to a major problem in comparative physiology, biochemistry, and ecology-that of metabolic scaling as a function of body mass across species. A clear distinction is made between intraspecific and interspecific relationships in energy metabolism, clearing up confusion that had existed from the very beginning since Kleiber first proposed his mouse-to-elephant rule almost a century ago. It is shown that the overall mass exponent of basal/standard metabolic rate in the allometric relationship [Formula: see text] is composed of two parts, one emerging from the relative intraspecific constancy of the slope (b), and the other (b') arising from the interspecific variation of the mass coefficient, a(M) with body size. Quantitative analysis is shown to reveal the hidden underlying relationship followed by the interspecific mass coefficient, a(M)=P0M0.10, and a universal value of P0=3.23 watts, W is derived from empirical data on mammals from mouse to cattle. The above relationship is shown to be understood only within an evolutionary biological context, and provides a physiological explanation for Cope's rule. The analysis also helps in fundamentally understanding how variability and a diversity of scaling exponents arises in allometric relations in biology and ecology. Next, a molecular-level understanding of the scaling of metabolism across mammalian species is shown to be obtained by consideration of the thermodynamic efficiency of ATP synthesis η, taking mitochondrial proton leak as a major determinant of basal metabolic rate in biosystems. An iterative solution is obtained by solving the mathematical equations of the biothermokinetic ATP theory, and the key thermodynamic parameters, e.g. the degree of coupling q, the operative P/O ratio, and the metabolic efficiency of ATP synthesis η are quantitatively evaluated for mammals from rat to cattle. Increases in η (by ∼15%) over a 2000-fold body size range from rat to cattle, primarily arising from an ∼3-fold decrease in the mitochondrial H+ leak rate are quantified by the unified ATP theory. Biochemical and mechanistic consequences for the interpretation of basal metabolism, and the various molecular implications arising are discussed in detail. The results are extended to maximum metabolic rate, and interpreted mathematically as a limiting case of the general ATP theory. The limitations of the analysis are pointed out. In sum, a comprehensive quantitative analysis based on the unified biothermokinetic theory of ATP synthesis is shown to solve a central problem in biology, physiology, and ecology on the scaling of energy metabolism with body size.

The Warburg Effect Reinterpreted 100 yr on: A First-Principles Stoichiometric Analysis and Interpretation from the Perspective of ATP Metabolism in Cancer Cells

The Warburg Effect is a longstanding enigma in cancer biology. Despite the passage of 100 yr since its discovery, and the accumulation of a vast body of research on the subject, no convincing biochemical explanation has been given for the original observations of aerobic glycolysis in cancer cell metabolism. Here, we have worked out a first-principles quantitative analysis of the problem from the principles of stoichiometry and available electron balance. The results have been interpreted using Nath's unified theory of energy coupling and adenosine triphosphate (ATP) synthesis, and the original data of Warburg and colleagues have been analyzed from this new perspective. Use of the biomass yield based on ATP per unit substrate consumed, [Formula: see text], or the Nath-Warburg number, NaWa has been shown to excellently model the original data on the Warburg Effect with very small standard deviation values, and without employing additional fitted or adjustable parameters. Based on the results of the quantitative analysis, a novel conservative mechanism of synthesis, utilization, and recycling of ATP and other key metabolites (eg, lactate) is proposed. The mechanism offers fresh insights into metabolic symbiosis and coupling within and/or among proliferating cells. The fundamental understanding gained using our approach should help in catalyzing the development of more efficient metabolism-targeting anticancer drugs.

Phosphorus Chemistry at the Roots of Bioenergetics: Ligand Permutation as the Molecular Basis of the Mechanism of ATP Synthesis/Hydrolysis by FOF1-ATP Synthase

The integration of phosphorus chemistry with the mechanism of ATP synthesis/hydrolysis requires dynamical information during ATP turnover and catalysis. Oxygen exchange reactions occurring at β-catalytic sites of the FOF1-ATP synthase/F1-ATPase imprint a unique record of molecular events during the catalytic cycle of ATP synthesis/hydrolysis. They have been shown to provide valuable time-resolved information on enzyme catalysis during ATP synthesis and ATP hydrolysis. The present work conducts new experiments on oxygen exchange catalyzed by submitochondrial particles designed to (i) measure the relative rates of Pi-ATP, Pi-HOH, and ATP-HOH isotope exchanges; (ii) probe the effect of ADP removal on the extent of inhibition of the exchanges, and (iii) test their uncoupler sensitivity/resistance. The objectives have been realized based on new experiments on submitochondrial particles, which show that both the Pi-HOH and ATP-HOH exchanges occur at a considerably higher rate relative to the Pi-ATP exchange, an observation that cannot be explained by previous mechanisms. A unifying explanation of the kinetic data that rationalizes these observations is given. The experimental results in (ii) show that ADP removal does not inhibit the intermediate Pi-HOH exchange when ATP and submitochondrial particles are incubated, and that the nucleotide requirement of the intermediate Pi-HOH exchange is adequately met by ATP, but not by ADP. These results contradicts the central postulate in Boyer's binding change mechanism of reversible catalysis at a F1 catalytic site with Keq~1 that predicts an absolute requirement of ADP for the occurrence of the Pi-HOH exchange. The prominent intermediate Pi-HOH exchange occurring under hydrolytic conditions is shown to be best explained by Nath's torsional mechanism of energy transduction and ATP synthesis/hydrolysis, which postulates an essentially irreversible cleavage of ATP by mitochondria/particles, independent from a reversible formation of ATP from ADP and Pi. The explanation within the torsional mechanism is also shown to rationalize the relative insensitivity of the intermediate Pi-HOH exchange to uncouplers observed in the experiments in (iii) compared to the Pi-ATP and ATP-HOH exchanges. This is shown to lead to new concepts and perspectives based on ligand displacement/substitution and ligand permutation for the elucidation of the oxygen exchange reactions within the framework of fundamental phosphorus chemistry. Fast mechanisms that realize the rotation/twist, tilt, permutation and switch of ligands, as well as inversion at the γ-phosphorus synchronously and simultaneously and in a concerted manner, have been proposed, and their stereochemical consequences have been analyzed. These considerations take us beyond the binding change mechanism of ATP synthesis/hydrolysis in bioenergetics.

Elucidating Events within the Black Box of Enzyme Catalysis in Energy Metabolism: Insights into the Molecular Mechanism of ATP Hydrolysis by F1-ATPase

Oxygen exchange reactions occurring at β-catalytic sites of the FOF1-ATP synthase/F1-ATPase imprint a unique record of molecular events during the catalytic cycle of ATP synthesis/hydrolysis. This work presents a new theory of oxygen exchange and tests it on oxygen exchange data recorded on ATP hydrolysis by mitochondrial F1-ATPase (MF1). The apparent rate constant of oxygen exchange governing the intermediate Pi-HOH exchange accompanying ATP hydrolysis is determined by kinetic analysis over a ~50,000-fold range of substrate ATP concentration (0.1-5000 μM) and a corresponding ~200-fold range of reaction velocity (3.5-650 [moles of Pi/{moles of F1-ATPase}-1 s-1]). Isotopomer distributions of [18O]Pi species containing 0, 1, 2, and 3 labeled oxygen atoms predicted by the theory have been quantified and shown to be in perfect agreement with the experimental distributions over the entire range of medium ATP concentrations without employing adjustable parameters. A novel molecular mechanism of steady-state multisite ATP hydrolysis by the F1-ATPase has been proposed. Our results show that steady-state ATP hydrolysis by F1-ATPase occurs with all three sites occupied by Mg-nucleotide. The various implications arising from models of energy coupling in ATP synthesis/hydrolysis by the ATP synthase/F1-ATPase have been discussed. Current models of ATP hydrolysis by F1-ATPase, including those postulated from single-molecule data, are shown to be effectively bisite models that contradict the data. The trisite catalysis formulated by Nath's torsional mechanism of energy transduction and ATP synthesis/hydrolysis since its first appearance 25 years ago is shown to be in better accord with the experimental record. The total biochemical information on ATP hydrolysis is integrated into a consistent model by the torsional mechanism of ATP synthesis/hydrolysis and shown to elucidate the elementary chemical and mechanical events within the black box of enzyme catalysis in energy metabolism by F1-ATPase.

Beyond binding change: the molecular mechanism of ATP hydrolysis by F1-ATPase and its biochemical consequences

F1-ATPase is a universal multisubunit enzyme and the smallest-known motor that, fueled by the process of ATP hydrolysis, rotates in 120o steps. A central question is how the elementary chemical steps occurring in the three catalytic sites are coupled to the mechanical rotation. Here, we performed cold chase promotion experiments and measured the rates and extents of hydrolysis of preloaded bound ATP and promoter ATP bound in the catalytic sites. We found that rotation was caused by the electrostatic free energy change associated with the ATP cleavage reaction followed by Pi release. The combination of these two processes occurs sequentially in two different catalytic sites on the enzyme, thereby driving the two rotational sub-steps of the 120o rotation. The mechanistic implications of this finding are discussed based on the overall energy balance of the system. General principles of free energy transduction are formulated, and their important physical and biochemical consequences are analyzed. In particular, how exactly ATP performs useful external work in biomolecular systems is discussed. A molecular mechanism of steady-state, trisite ATP hydrolysis by F1-ATPase, consistent with physical laws and principles and the consolidated body of available biochemical information, is developed. Taken together with previous results, this mechanism essentially completes the coupling scheme. Discrete snapshots seen in high-resolution X-ray structures are assigned to specific intermediate stages in the 120o hydrolysis cycle, and reasons for the necessity of these conformations are readily understood. The major roles played by the "minor" subunits of ATP synthase in enabling physiological energy coupling and catalysis, first predicted by Nath's torsional mechanism of energy transduction and ATP synthesis 25 years ago, are now revealed with great clarity. The working of nine-stepped (bMF1, hMF1), six-stepped (TF1, EF1), and three-stepped (PdF1) F1 motors and of the α3β3γ subcomplex of F1 is explained by the same unified mechanism without invoking additional assumptions or postulating different mechanochemical coupling schemes. Some novel predictions of the unified theory on the mode of action of F1 inhibitors, such as sodium azide, of great pharmaceutical importance, and on more exotic artificial or hybrid/chimera F1 motors have been made and analyzed mathematically. The detailed ATP hydrolysis cycle for the enzyme as a whole is shown to provide a biochemical basis for a theory of "unisite" and steady-state multisite catalysis by F1-ATPase that had remained elusive for a very long time. The theory is supported by a probability-based calculation of enzyme species distributions and analysis of catalytic site occupancies by Mg-nucleotides and the activity of F1-ATPase. A new concept of energy coupling in ATP synthesis/hydrolysis based on fundamental ligand substitution chemistry has been advanced, which offers a deeper understanding, elucidates enzyme activation and catalysis in a better way, and provides a unified molecular explanation of elementary chemical events occurring at enzyme catalytic sites. As such, these developments take us beyond binding change mechanisms of ATP synthesis/hydrolysis proposed for oxidative phosphorylation and photophosphorylation in bioenergetics.

The Need for Consistency with Physical Laws and Logic in Choosing Between Competing Molecular Mechanisms in Biological Processes: A Case Study in Modeling ATP Synthesis

Traditionally, proposed molecular mechanisms of fundamental biological processes have been tested against experiment. However, owing to a plethora of reasons-difficulty in designing, carrying out, and interpreting key experiments, use of different experimental models and systems, conduct of studies under widely varying experimental conditions, fineness in distinctions between competing mechanisms, complexity of the scientific issues, and the resistance of some scientists to discoveries that are contrary to popularly held beliefs-this has not solved the problem despite decades of work in the field/s. The author would like to prescribe an alternative way: that of testing competing models/mechanisms for their adherence to scientific laws and principles, and checking for errors in logic. Such tests are fairly commonly carried out in the mathematics, physics, and engineering literature. Further, reported experimental measurements should not be smaller than minimum detectable values for the measurement technique employed and should truly reflect function of the actual system without inapplicable extrapolation. Progress in the biological fields would be greatly accelerated, and considerable scientific acrimony avoided by adopting this approach. Some examples from the fundamental field of ATP synthesis in oxidative phosphorylation (OXPHOS) have been reviewed that also serve to illustrate the approach. The approach has never let the author down in his 35-yr-long experience on biological mechanisms. This change in thinking should lead to a considerable saving of both time and resources, help channel research efforts toward solution of the right problems, and hopefully provide new vistas to a younger generation of open-minded biological scientists.

Supercomplex supercomplexes: Raison d’etre and functional significance of supramolecular organization in oxidative phosphorylation

Following structural determination by recent advances in electron cryomicroscopy, it is now well established that the respiratory Complexes I–IV in oxidative phosphorylation (OXPHOS) are organized into supercomplexes in the respirasome. Nonetheless, the reason for the existence of the OXPHOS supercomplexes and their functional role remains an enigma. Several hypotheses have been proposed for the existence of these supercomplex supercomplexes. A commonly-held view asserts that they enhance catalysis by substrate channeling. However, this – and other views – has been challenged based on structural and biophysical information. Hence, new ideas, concepts, and frameworks are needed. Here, a new model of energy transfer in OXPHOS is developed on the basis of biochemical data on the pure competitive inhibition of anionic substrates like succinate by the classical anionic uncouplers of OXPHOS (2,4-dinitrophenol, carbonyl cyanide 4-(trifluoromethoxy)phenylhydrazone, and dicoumarol), and pharmacological data on the unique site-selective, energy-linked inhibition of energy conservation pathways in mitochondria induced by the guanidine derivatives. It is further found that uncouplers themselves are site-specific and exhibit differential selectivity and efficacy in reversing the inhibition caused by the Site 1/Complex I or Site 2/Complexes II–III-selective guanidine derivatives. These results lead to new vistas and sufficient complexity in the network of energy conservation pathways in the mitochondrial respiratory chain that necessitate discrete points of interaction with two classes of guanidine derivatives and uncoupling agents and thereby separate and distinct energy transfer pathways between Site 1 and Site 2 and the intermediate that energizes adenosine triphosphate (ATP) synthesis by Complex V. Interpretation based on Mitchell’s single-ion chemiosmotic theory that postulates only a single energy pool is inadequate to rationalize the data and account for the required complexity. The above results and available information are shown to be explained by Nath’s two-ion theory of energy coupling and ATP synthesis, involving coupled movement of succinate anions and protons, along with the requirement postulated by the theory for maintenance of homeostasis and ion translocation across the energy-transducing membrane of both succinate monoanions and succinate dianions by Complexes I–V in the OXPHOS supercomplexes. The new model of energy transfer in mitochondria is mapped onto the solved structures of the supercomplexes and integrated into a consistent model with the three-dimensional electron microscope computer tomography visualization of the internal structure of the cristae membranes in mammalian mitochondria. The model also offers valuable insights into diseased states induced in type 2 diabetes and especially in Alzheimer’s and other neurodegenerative diseases that involve mitochondrial dysfunction.

Energy landscapes and dynamics of ion translocation through membrane transporters: a meeting ground for physics, chemistry, and biology

The dynamics of ion translocation through membrane transporters is visualized from a comprehensive point of view by a Gibbs energy landscape approach. The ΔG calculations have been performed with the Kirkwood-Tanford-Warshel (KTW) electrostatic theory that properly takes into account the self-energies of the ions. The Gibbs energy landscapes for translocation of a single charge and an ion pair are calculated, compared, and contrasted as a function of the order parameter, and the characteristics of the frustrated system with bistability for the ion pair are described and quantified in considerable detail. These calculations have been compared with experimental data on the ΔG of ion pairs in proteins. It is shown that, under suitable conditions, the adverse Gibbs energy barrier can be almost completely compensated by the sum of the electrostatic energy of the charge-charge interactions and the solvation energy of the ion pair. The maxima in ΔG_KTW with interionic distance in the bound H⁺ - A^- charge pair on the enzyme is interpreted in thermodynamic and molecular mechanistic terms, and biological implications for molecular mechanisms of ATP synthesis are discussed. The timescale at which the order parameter moves between two stable states has been estimated by solving the dynamical equations of motion, and a wealth of novel insights into energy transduction during ATP synthesis by the membrane-bound F_OF₁-ATP synthase transporter is offered. In summary, a unifying analytical framework that integrates physics, chemistry, and biology has been developed for ion translocation by membrane transporters for the first time by means of a Gibbs energy landscape approach.

Charge transfer across biomembranes: A solution to the conundrum of high desolvation free energy penalty in ion transport

Charge transfer across membranes is an important problem in a wide variety of fundamental physicochemical and biological processes. Since Mitchell's concept of the ion well advanced in 1968, several models of ion translocation across biomembranes, for instance through the membrane-bound FO portion of ATP synthase have been proposed. None of these models has considered the large desolvation free energy penalty of ~500 meV incurred in transferring a protonic charge from the aqueous phase into the membrane that hinders such charge transfer processes. The difficulty has been pointed out repeatedly. However, the problem of how the adverse ∆Gdesolvation barrier is overcome in order to enable rapid ion translocation in biomembranes has not been satisfactorily resolved. Hence the fact that the self-energy of the charges has been overlooked can be regarded as a main source of confusion in the field of bioenergetics. Further, in order to consider charges of a finite size (and not just point charges), the free energy of transferring the ions from water into a membrane phase of lower dielectric εm needs to be evaluated. Here a solution to the longstanding conundrum has been proposed by including the bound anion - the second ion in Nath's two-ion theory of energy coupling and ATP synthesis - in the free energy calculations. The mechanistic importance of the H+ - A- charge pair in causing rotation and ATP synthesis by ion-protein interactions is highlighted. The ∆G calculations have been performed by using the Kirkwood-Tanford-Warshel (KTW) theory that takes into account the self-energies of the ions. The results show that the adverse ∆Gdesolvation can be almost exactly compensated by the sum of the electrostatic free energy of the charge-charge interactions and the dipole solvation energy for long-range ion pairs. Results of free energy compensation using the KTW theory have been compared with experimental data on the ∆G of ion pairs and shown to be in reasonable agreement. A general thermodynamic cycle for coupled ion transfer has been constructed to further elucidate facilitated ion permeation between water and membrane phases. Molecular interpretations of the results and their implications for various mechanisms of energy transduction have been discussed. We firmly believe that use of electrostatic theories such as the KTW theory that properly include the desolvation free energy penalty arising from the self-energy of the relevant ions are crucial for quantifying charge transfer processes in bioenergetics. Finally, the clear-cut implication is that proton-only and single-ion theories of ATP synthesis, such as the chemiosmotic theory, are grossly inadequate to comprehend energy storage and transduction in biological processes.

Mitochondrial energetics with transmembrane electrostatically localized protons: do we have a thermotrophic feature?

Transmembrane electrostatically localized protons (TELP) theory has been recently recognized as an important addition over the classic Mitchell's chemiosmosis; thus, the proton motive force (pmf) is largely contributed from TELP near the membrane. As an extension to this theory, a novel phenomenon of mitochondrial thermotrophic function is now characterized by biophysical analyses of pmf in relation to the TELP concentrations at the liquid-membrane interface. This leads to the conclusion that the oxidative phosphorylation also utilizes environmental heat energy associated with the thermal kinetic energy (kBT) of TELP in mitochondria. The local pmf is now calculated to be in a range from 300 to 340 mV while the classic pmf (which underestimates the total pmf) is in a range from 60 to 210 mV in relation to a range of membrane potentials from 50 to 200 mV. Depending on TELP concentrations in mitochondria, this thermotrophic function raises pmf significantly by a factor of 2.6 to sixfold over the classic pmf. Therefore, mitochondria are capable of effectively utilizing the environmental heat energy with TELP for the synthesis of ATP, i.e., it can lock heat energy into the chemical form of energy for cellular functions.

Coupling mechanisms in ATP synthesis: Rejoinder to "Response to molecular-level understanding of biological energy coupling and transduction"

Recently, an exchange of views on key fundamental aspects of biological energy coupling and ATP synthesis in the vital process of oxidative phosphorylation appeared in the pages of this journal. The very difficult scientific problems are analyzed and clarified. Errors in the mathematical/thermodynamic equations of a previous analysis have been identified that invalidate previous assertions, and the correct equations are derived. The major differences between the two competing models - localized versus delocalized - for biological energy coupling and transduction are discussed from physical, chemical, and mathematical perspectives. The opposing views are summarized, so that the reader can assess for himself or herself the merits of the two coupling mechanisms. A fresh attempt has been made to go to the root of bioenergetics by calculating the desolvation free energy barrier, ∆G_desolvation for ion transport across biomembranes. Several constructive suggestions are made that have the power to resolve the basic contradictions and the areas of fundamental conflict, and reach a consensus by catalyzing the progress of future research in this interdisciplinary field.

Molecular-level understanding of biological energy coupling and transduction: Response to "Chemiosmotic misunderstandings"

In a recent paper entitled "Chemiosmotic misunderstandings", it is claimed that "enough shortcomings in Mitchell's chemiosmotic theory have not been found and that a novel paradigm that offers at least as much explanatory power as chemiosmosis is not ready." This view is refuted by a wealth of molecular-level experimental data and strong new theoretical and computational evidence. It is shown that the chemiosmotic theory was beset with a large number of major shortcomings ever since the time when it was first proposed in the 1960s. These multiple shortcomings and flaws of chemiosmosis were repeatedly pointed out in incisive critiques by biochemical authorities of the late 20th century. All the shortcomings and flaws have been shown to be rectified by a quantitative, unified molecular-level theory that leads to a deeper and far more accurate understanding of biological energy coupling and ATP synthesis. The new theory is shown to be consistent with pioneering X-ray and cryo-EM structures and validated by state-of-the-art single-molecule techniques. Several new biochemical experimental tests are proposed and constructive ways for providing a revitalizing conceptual background and theory for integration of the available experimental information are suggested.

A Novel Conceptual Model for the Dual Role of FOF1-ATP Synthase in Cell Life and Cell Death

The mitochondrial permeability transition (MPT) has been one of the longstanding enigmas in biology. Its cause is currently at the center of an extensive scientific debate, and several hypotheses on its molecular nature have been put forward. The present view holds that the transition arises from the opening of a high-conductance channel in the energy-transducing membrane, the permeability transition pore (PTP), also called the mitochondrial megachannel or the multiconductance channel (MMC). Here, the novel hypothesis is proposed that the aqueous access channels at the interface of the c-ring and the a-subunit of FO in the FOF1-ATP synthase are repurposed during induction of apoptosis and constitute the elusive PTP/ MMC. A unifying principle based on regulation by local potentials is advanced to rationalize the action of the myriad structurally and chemically diverse inducers and inhibitors of PTP/MMC. Experimental evidence in favor of the hypothesis and its differences from current models of PTP/MMC are summarized. The hypothesis explains in considerable detail how the binding of Ca2+ to a β-catalytic site (site 3) in the F1 portion of ATP synthase triggers the opening of the PTP/MMC. It is also shown to connect to longstanding proposals within Nath's torsional mechanism of energy transduction and ATP synthesis as to how the binding of MgADP to site 3 does not induce PTP/MMC, but instead catalyzes physiological ATP synthesis in cell life. In the author's knowledge, this is the first model that explains how Ca2+ transforms the FOF1-ATP synthase from an exquisite energy-conserving enzyme in cell life into an energy-dissipating structure that promotes cell death. This has major implications for basic as well as for clinical research, such as for the development of drugs that target the MPT, given the established role of PTP/MMC dysregulation in cancer, ischemia, cardiac hypertrophy, and various neurodegenerative diseases.

Consolidation of Nath's torsional mechanism of ATP synthesis and two-ion theory of energy coupling in oxidative phosphorylation and photophosphorylation

In a recent publication, Manoj raises criticisms against consensus views on the ATP synthase. The radical statements and assertions are shown to contradict a vast body of available knowledge that includes i) pioneering single-molecule biochemical and biophysical studies from the respected experimental groups of Kinosita, Yoshida, Noji, Börsch, Dunn, Gräber, Frasch, and Dimroth etc., ii) state-of-the-art X-ray and EM/cryo-EM structural information garnered over the decades by the expert groups of Leslie-Walker, Kühlbrandt, Mueller, Meier, Rubinstein, Sazanov, Duncan, and Pedersen on ATP synthase, iii) the pioneering energy-based computer simulations of Warshel, and iv) the novel theoretical and experimental works of Nath. Valid objections against Mitchell's chemiosmotic theory and Boyer's binding change mechanism put forth by Manoj have been addressed satisfactorily by Nath's torsional mechanism of ATP synthesis and two-ion theory of energy coupling and published 10 to 20 years ago, but these papers are not cited by him. This communication shows conclusively and in great detail that none of his objections apply to Nath's mechanism/theory. Nath's theory is further consolidated based on its previous predictive record, its consistency with biochemical evidence, its unified nature, its application to other related energy transductions and to disease, and finally its ability to guide the design of new experiments. Some constructive suggestions for high-resolution structural experiments that have the power to delve into the heart of the matter and throw unprecedented light on the nature of coupled ion translocation in the membrane-bound F_O portion of F₁F_O-ATP synthase are made.

Entropy Production and Its Application to the Coupled Nonequilibrium Processes of ATP Synthesis

Starting from the universal concept of entropy production, a large number of new results are obtained and a wealth of novel thermodynamic, kinetic, and molecular mechanistic insights are provided into the coupling of oxidation and ATP synthesis in the vital process of oxidative phosphorylation (OX PHOS). The total dissipation, Φ, in OX PHOS with succinate as respiratory substrate is quantified from measurements, and the partitioning of Φ into the elementary components of ATP synthesis, leak, slip, and other losses is evaluated for the first time. The thermodynamic efficiency, η, of the coupled process is calculated from the data on Φ and shown to agree well with linear nonequilibrium thermodynamic calculations. Equations for the P/O ratio based on total oxygen consumed and extra oxygen consumed are derived from first principles and the source of basal (state 4) mitochondrial respiration is postulated from molecular mechanistic considerations based on Nath’s two-ion theory of energy coupling within the torsional mechanism of energy transduction and ATP synthesis. The degree of coupling, q, between oxidation and ATP synthesis is determined from the experimental data and the irreversible thermodynamics analysis. The optimality of biological free energy converters is explored in considerable detail based on (i) the standard biothermodynamic approach, and (ii) a new biothermokinetic approach developed in this work, and an effective solution that is shown to arise from consideration of the molecular aspects in Nath’s theory is formulated. New experimental data in state 4 with uncouplers and redox inhibitors of OX PHOS and on respiratory control in the physiological state 3 with ADP and uncouplers are presented. These experimental observations are shown to be incompatible with Mitchell’s chemiosmotic theory. A novel scheme of coupling based on Nath’s two-ion theory of energy coupling within the torsional mechanism is proposed and shown to explain the data and also pass the test of consistency with the thermodynamics, taking us beyond the chemiosmotic theory. It is concluded that, twenty years since its first proposal, Nath’s torsional mechanism of energy transduction and ATP synthesis is now well poised to catalyze the progress of experimental and theoretical research in this interdisciplinary field.

Integration of demand and supply sides in the ATP energy economics of cells

The central aspects of the energy economics of living cells revolve around the synthesis and utilization of molecules of adenosine triphosphate (ATP). Current descriptions of cell metabolism and its regulation in most textbooks of biochemistry assume that enzymes and transporters behave in the same way in isolation and in a cell. Calculations of the mechanistic or maximal P/O ratios in oxidative phosphorylation by mammalian cells generally consider only the supply side of the problem without linking to ATP-demand processes. The purpose of this article is to calculate the mechanistic P/O ratio by integration of the supply and demand sides of ATP reactions. The mechanistic stoichiometry calculated from an integrated approach is compared with that obtained from the standard model that considers only ATP supply. After accounting for leaks, slips, and other losses, the actual or operative P/O calculated by the integrated method is found to be in good agreement with the experimental values of the P/O ratio determined in mitochondria for both succinate and NADH-linked respiratory substrates. The thermodynamic consequences of these results and the biological implications are discussed. An integrated model of oxidative phosphorylation that goes beyond the chemiosmotic theory is presented, and a solution to the longstanding fundamental problem of respiratory control is found.

Interpretation of the mechanism of action of antituberculosis drug bedaquiline based on a novel two-ion theory of energy coupling in ATP synthesis

Tuberculosis (TB) claims the lives of 1.3 million people each year, more than any other bacterial infection. Hence great interest was generated in health communities upon the recent introduction of the new diarylquinoline anti-TB drug, bedaquiline. Bedaquiline acts by binding to the c-subunit in the membrane-bound FO portion of the F1FO-adenosine triphosphate (ATP) synthase, the universal enzyme that produces the ATP needed by cells. However, the mechanism of killing by bedaquiline is not fully understood. Recent observations related to the bactericidal effects of bedaquiline, which show that it is a potent uncoupler of respiration-driven ATP synthesis in Mycobacterium smegmatis are summarized. These observations are then interpreted from the standpoint of Nath's two-ion theory of energy coupling in ATP synthesis (Nath, Biophys. Chem. 2017; 230:45-52). Especial importance is given to the interpretation of biochemical fluorescence quenching data, and the differences between the uncoupling induced by bedaquiline from that by the classical anionic uncouplers of oxidative phosphorylation are highlighted. Suggestions for new experiments that could lead to a better understanding of the uncoupling mechanism are made. A model of uncoupling action by the drug is presented, and the biochemical basis underlying uncoupling of ATP synthesis and lethality in mycobacteria is elucidated. The major biological implications arising from these novel insights are discussed. It is hoped that the analysis will lead to a more fundamental understanding of biological energy coupling, uncoupling and transduction, and to an integrated view for the design of novel antimicrobials by future research in the field.

Aerobic Respiration: Criticism of the Proton-centric Explanation Involving Rotary Adenosine Triphosphate Synthesis, Chemiosmosis Principle, Proton Pumps and Electron Transport Chain

The acclaimed explanation for mitochondrial oxidative phosphorylation (mOxPhos, or cellular respiration) is a deterministic proton-centric scheme involving four components: Rotary adenosine triphosphate (ATP)-synthesis, Chemiosmosis principle, Proton pumps, and Electron transport chain (abbreviated as RCPE hypothesis). Within this write-up, the RCPE scheme is critically analyzed with respect to mitochondrial architecture, proteins’ distribution, structure-function correlations and their interactive dynamics, overall reaction chemistry, kinetics, thermodynamics, evolutionary logic, and so on. It is found that the RCPE proposal fails to explain key physiological aspects of mOxPhos in several specific issues and also in holistic perspectives. Therefore, it is imperative to look for new explanations for mOxPhos.

Molecular mechanistic insights into uncoupling of ion transport from ATP synthesis

A procedure is evolved to assess the maximum uncoupling activity of the classical unsubstituted phenolic uncouplers of mitochondrial oxidative phosphorylation (OX PHOS) 2,4-dinitrophenol and 2,6-dinitrophenol. The uncoupler concentrations, C, required for maximum uncoupling efficacy are found to be a strong function of the pH, and a linear relationship of pC with pH is obtained between pH 5 to pH 9. The slopes of the uncoupler concentrations in the aqueous and lipid phases as a function of pH have been estimated. It is shown that the experimental results can be derived from first principles by an enzyme kinetic model for uncoupling that is based on the same equations as formulated for the coupling of ion transport to ATP synthesis in a companion paper after imposition of the special conditions arising from the uncoupling process. The results reveal the catalysis of a reaction that involves both the anionic and protonated forms of the phenolic uncouplers in the vicinity of their binding sites in a non-aqueous region of the cristae membranes of mitochondria. The rate-limiting step in the overall process of uncoupling has been identified based on the uncoupling data. The data cannot be explained by a simple conduction of protons by uncouplers from one bulk aqueous phase to another as postulated by Mitchell's chemiosmotic theory. It is shown that Nath's two-ion theory of energy coupling/uncoupling in ATP synthase is consistent with the results. A molecular mechanism for uncoupling of ATP synthesis by the dinitrophenols is presented and the chief differences between coupling and uncoupling in ATP catalysis are summarized. The pharmacological consequences of our analysis of uncoupling are discussed, with particular reference to the mode of action of the anti-tuberculosis drug bedaquiline that specifically targets the c-subunit of the F₁F_O-ATP synthase and uncouples respiration from ATP synthesis in Mycobacterium tuberculosis. Hence the work is shown to be important both from the point of view of fundamental biology and is also pregnant with possibilities for practical pharmaceutical applications.

Molecular mechanistic insights into coupling of ion transport to ATP synthesis

A wealth of molecular mechanistic insights has been provided into the coupling of ion transport to ATP synthesis based on a two-ion theory of biological energy coupling. A kinetic scheme that considers the mode of functioning of a single F₁F_O-ATP synthase molecule with H⁺-A^- cotransport and unidirectional rotation of the c-rotor in the membrane-bound F_O-portion of the enzyme has been developed. Mathematical analysis leads to a detailed enzyme kinetic model applicable to a population of molecules which is compared with experimental data on the pH dependence of ATP synthesis. The model agrees well with the experimental data, and a single equation with a single set of standard enzymological kinetic parameters has been shown to explain the experimental data over the entire range of conditions for the chloroplast ATP synthase. The analysis gives novel insights into kinetic and mechanistic characteristics of ATP synthesis in F_O. These include an order imposed on ion binding and unbinding events in F_O, the essential role of the anion in direct activation of the ATP synthase (in addition to its role as a permeant ion), and the integration in a novel way of the functions of cooperativity and cotransport of dicarboxylic acid anions and protons during physiological ATP synthesis. Further, Wyman's pioneering classical work on the thermodynamics of linked functions has been shown to offer a new approach to distinguish between various models of energy coupling in ATP synthesis. All these results have been found to be inconsistent with Mitchell's chemiosmotic theory and are shown to be in agreement with Nath's torsional mechanism of energy transduction and ATP synthesis.

Two-ion theory of energy coupling in ATP synthesis rectifies a fundamental flaw in the governing equations of the chemiosmotic theory

The vital coupled processes of oxidative phosphorylation and photosynthetic phosphorylation synthesize molecules of adenosine-5'-triphosphate (ATP), the universal biological energy currency, and sustain all life on our planet. The chemiosmotic theory of energy coupling in oxidative and photophosphorylation was proposed by Mitchell >50years ago. It has had a contentious history, with part of the accumulated body of experimental evidence supporting it, and part of it in conflict with the theory. Although the theory was strongly criticized by many prominent scientists, the controversy has never been resolved. Here, the mathematical steps of Mitchell's original derivation leading to the principal equation of the chemiosmotic theory are scrutinized, and a fundamental flaw in them has been identified. Surprisingly, this flaw had not been detected earlier. Discovery of such a defect negates, or at least considerably weakens, the theoretical foundations on which the chemiosmotic theory is based. Ad hoc or simplistic ways to remedy this defect are shown to be scientifically unproductive and sterile. A novel two-ion theory of biological energy coupling salvages the situation by rectifying the fundamental flaw in the chemiosmotic theory, and the governing equations of the new theory have been shown to accurately quantify and predict extensive recent experimental data on ATP synthesis by F₁F_O-ATP synthase without using adjustable parameters. Some major biological implications arising from the new thinking are discussed. The principles of energy transduction and coupling proposed in the new paradigm are shown to be of a very general and universal nature. It is concluded that the timely availability after a 25-year research struggle of Nath's torsional mechanism of energy transduction and ATP synthesis is a rational alternative that has the power to solve the problems arising from the past, and also meet present and future challenges in this important interdisciplinary field of research.

Analysis of molecular mechanisms of ATP synthesis from the standpoint of the principle of electrical neutrality

Theories of biological energy coupling in oxidative phosphorylation (OX PHOS) and photophosphorylation (PHOTO PHOS) are reviewed and applied to ATP synthesis by an experimental system containing purified ATP synthase reconstituted into liposomes. The theories are critically evaluated from the standpoint of the principle of electrical neutrality. It is shown that the obligatory requirement to maintain overall electroneutrality of bulk aqueous phases imposes strong constraints on possible theories of energy coupling and molecular mechanisms of ATP synthesis. Mitchell's chemiosmotic theory is found to violate the electroneutrality of bulk aqueous phases and is shown to be untenable on these grounds. Purely electroneutral mechanisms or mechanisms where the anion/countercation gradient is dissipated or simply flows through the lipid bilayer are also shown to be inadequate. A dynamically electrogenic but overall electroneutral mode of ion transport postulated by Nath's torsional mechanism of energy transduction and ATP synthesis is shown to be consistent both with the experimental findings and the principle of electrical neutrality. It is concluded that the ATP synthase functions as a proton-dicarboxylic acid anion cotransporter in OX PHOS or PHOTO PHOS. A logical chemical explanation for the selection of dicarboxylic acids as intermediates in OX PHOS and PHOTO PHOS is suggested based on the pioneering classical thermodynamic work of Christensen, Izatt, and Hansen. The nonequilibrium thermodynamic consequences for theories in which the protons originate from water vis-a-vis weak organic acids are compared and contrasted, and several new mechanistic and thermodynamic insights into biological energy transduction by ATP synthase are offered. These considerations make the new theory of energy coupling more complete, and lead to a deeper understanding of the molecular mechanism of ATP synthesis.

The thermodynamic efficiency of ATP synthesis in oxidative phosphorylation

As the chief energy source of eukaryotic cells, it is important to determine the thermodynamic efficiency of ATP synthesis in oxidative phosphorylation (OX PHOS). Previous estimates of the thermodynamic efficiency of this vital process have ranged from Lehninger's original back-of-the-envelope calculation of 38% to the often quoted value of 55-60% in current textbooks of biochemistry, to high values of 90% from recent information theoretic considerations, and reports of realizations of close to ideal 100% efficiencies by single molecule experiments. Hence this problem has been reinvestigated from first principles. The overall thermodynamic efficiency of ATP synthesis in the mitochondrial energy transduction OX PHOS process has been found to lie between 40 and 41% from four different approaches based on a) estimation using structural and biochemical data, b) fundamental nonequilibrium thermodynamic analysis, c) novel insights arising from Nath's torsional mechanism of energy transduction and ATP synthesis, and d) the overall balance of cellular energetics. The torsional mechanism also offers an explanation for the observation of a thermodynamic efficiency approaching 100% in some experiments. Applications of the unique, molecular machine mode of functioning of F₁F_O-ATP synthase involving direct inter-conversion of chemical and mechanical energies in the design and fabrication of novel, man-made mechanochemical devices have been envisaged, and some new ways to exorcise Maxwell's demon have been proposed. It is hoped that analysis of the fundamental problem of energy transduction in OX PHOS from a fresh perspective will catalyze new avenues of research in this interdisciplinary field.

Oxidative phosphorylation revisited

The fundamentals of oxidative phosphorylation and photophosphorylation are revisited. New experimental data on the involvement of succinate and malate anions respectively in oxidative phosphorylation and photophosphorylation are presented. These new data offer a novel molecular mechanistic explanation for the energy coupling and ATP synthesis carried out in mitochondria and chloroplast thylakoids. The mechanism does not suffer from the flaws in Mitchell's chemiosmotic theory that have been pointed out in many studies since its first appearance 50 years ago, when it was hailed as a ground-breaking mechanistic explanation of what is perhaps the most important process in cellular energetics. The new findings fit very well with the predictions of Nath's torsional mechanism of energy transduction and ATP synthesis. It is argued that this mechanism, based on at least 15 years of experimental and theoretical work by Sunil Nath, constitutes a fundamentally different theory of the energy conversion process that eliminates all the inconsistencies in Mitchell's chemiosmotic theory pointed out by other authors. It is concluded that the energy-transducing complexes in oxidative phosphorylation and photosynthesis are proton-dicarboxylic acid anion cotransporters and not simply electrogenic proton translocators. These results necessitate revision of previous theories of biological energy transduction, coupling, and ATP synthesis. The novel molecular mechanism is extended to cover ATP synthesis in prokaryotes, in particular to alkaliphilic and haloalkaliphilic bacteria, essentially making it a complete theory addressing mechanistic, kinetic, and thermodynamic details. Finally, based on the new interpretation of oxidative phosphorylation, quantitative values for the P/O ratio, the amount of ATP generated per redox package of the reduced substrates, are calculated and compared with experimental values for fermentation on different substrates. It is our hope that the presentation of oxidative phosphorylation and photophosphorylation from a wholly new perspective will rekindle scientific discussion of a key process in bioenergetics and catalyze new avenues of research in a truly interdisciplinary field.

Molecular recognition of nucleotides in water by scorpiand-type receptors based on nucleobase discrimination

The detection of nucleotides is of crucial importance because they are the basic building blocks of nucleic acids. Scorpiand-based polyamine receptors functionalized with pyridine or anthracene units are able to form stable complexes with nucleotides in water, based on coulombic, π-π stacking, and hydrogen-bonding interactions. This behavior has been rationalized by means of an exploration with NMR spectroscopy and DFT calculations. Binding constants were determined by potentiometry. Fluorescence spectroscopy studies have revealed the potential of these receptors as sensors to effectively and selectively distinguish guanosine-5'-triphosphate (GTP) from adenosine-5'-triphosphate (ATP).

Human F1F0 ATP synthase, mitochondrial ultrastructure and OXPHOS impairment: a (super-)complex matter?

Mitochondrial morphogenesis is a key process of cell physiology. It is essential for the proper function of this double membrane-delimited organelle, as it ensures the packing of the inner membrane in a very ordered pattern called cristae. In yeast, the mitochondrial ATP synthase is able to form dimers that can assemble into oligomers. Two subunits (e and g) are involved in this supramolecular organization. Deletion of the genes encoding these subunits has no effect on the ATP synthase monomer assembly or activity and only affects its dimerization and oligomerization. Concomitantly, the absence of subunits e and g and thus, of ATP synthase supercomplexes, promotes the modification of mitochondrial ultrastructure suggesting that ATP synthase oligomerization is involved in cristae morphogenesis. We report here that in mammalian cells in culture, the shRNA-mediated down-regulation of subunits e and g affects the stability of ATP synthase and results in a 50% decrease of the available functional enzyme. Comparable to what was shown in yeast, when subunits e and g expression are repressed, ATP synthase dimers and oligomers are less abundant when assayed by native electrophoresis. Unexpectedly, mammalian ATP synthase dimerization/oligomerization impairment has functional consequences on the respiratory chain leading to a decrease in OXPHOS activity. Finally these structural and functional alterations of the ATP synthase have a strong impact on the organelle itself leading to the fission of the mitochondrial network and the disorganization of mitochondrial ultrastructure. Unlike what was shown in yeast, the impairment of the ATP synthase oligomerization process drastically affects mitochondrial ATP production. Thus we propose that mutations or deletions of genes encoding subunits e and g may have physiopathological implications.

Combined mathematical methods in the description of the F(o)F(1)-ATP synthase catalytic cycle

The FoF1-ATP synthase is one of the key enzymes in supplying energy production in almost all living systems. In this paper, we provide a theoretical description of its catalytic cycle using combined mathematical methods. These methods include Langevin dynamics for the rotation of the central protein core and the Monte-Carlo method to model nucleotide and proton binding. This model is the first in which ATP synthesis and hydrolysis can occur depending on the nucleotide concentration and system conditions. The main advantage of the presented model is the possibility of obtaining results for both single-molecular protein-machines and large ensembles of proteins. The calculated rates are close to the experimentally measured rates for a single enzyme. The model has been formalised as a computer simulation that allows researchers to evaluate ATP production in different types of living cells.

New perspectives on photosynthetic phosphorylation in the light of a torsional mechanism of energy transduction and ATP synthesis

New perspectives on photophosphorylation have been offered from the standpoint of the torsional mechanism of energy transduction and ATP synthesis. New experimental data on the involvement of malate anions in ATP synthesis in an acid-base malate bath procedure has been reported on spinach chloroplast thylakoids as the model system. The data cannot be reconciled with the chemiosmotic theory but has been shown to be naturally explained by the torsional mechanism. The path of malic acid in the acid and base stages of the experiment has been traced, offering further strong support to the new paradigm. Classical observations in the field have been re-interpreted in the light of these findings. A new concept of ion translocation, energy transduction and coupling at the overall physiological level in photophosphorylation has been presented and a large number of novel experimentally testable predictions have been made and shown to arise as logical consequences of the new perspectives.

A role for anions in ATP synthesis and its molecular mechanistic interpretation

ATP, the 'universal biological energy currency', is synthesized by utilizing energy either from oxidation of fuels or from light, via the process of oxidative and photo-phosphorylation respectively. The process is mediated by the enzyme F(1)F(0)-ATP synthase, using the free energy of ion gradients in the final energy catalyzing step, i.e., the synthesis of ATP from ADP and inorganic phosphate (P(i)). The details of the molecular mechanism of ATP synthesis are among the most important fundamental issues in biology and hence need to be properly understood. In this work, a role for anions in making ATP has been found. New experimental data has been reported on the inhibition of ATP synthesis at nanomolar concentrations by the potent, specific anion channel blockers 4,4'-diisothiocyanostilbene-2, 2'-disulphonic acid (DIDS) and tributyltin chloride (TBTCl). Based on these inhibition studies, attention has been drawn to anion translocation (in addition to proton translocation) as a requirement for ATP synthesis. The type of inhibition has been quantified and an overall kinetic scheme for mixed inhibition that explains the data has been evolved. The experimental data and the type of inhibition found have been interpreted in the light of the torsional mechanism of energy transduction and ATP synthesis (Nath J Bioenerg Biomembr 42:293-300, 2010a; J Bioenerg Biomembr 42:301-309, 2010b). This detailed and unified mechanism resolves long-standing problems and inconsistencies in the first theories (Slater Nature 172:975-978, 1953; Williams J Theor Biol 1:1-17, 1961; Mitchell Nature 191:144-148, 1961; Mitchell Biol Rev 41:445-502, 1966), makes several novel predictions that are experimentally verifiable (Nath Biophys J 90:8-21, 2006a; Process Biochem 41:2218-2235, 2006b), and provides us with a new and fruitful paradigm in bioenergetics. The interpretation presented here provides intelligent answers to the unexplained existing results in the literature. It is shown that mechanistic interpretation of the experimental data requires substantial addition to available conceptual foundations such that present concepts, theories, and mechanisms must be revised.