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 ß-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.

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 ΔGKTW 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 FOF1-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.

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.

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.

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.

2-Site versus 3-site models of ATP hydrolysis by F1-ATPase: definitive mathematical proof using combinatorics and conservation equations.

The F1-ATPase enzyme is the smallest-known molecular motor that rotates in 120° steps, driven by the hydrolysis of ATP. It is a multi-subunit enzyme that contains three catalytic sites. A central question is how the elementary chemical reactions that occur in the three sites are coupled to mechanical rotation. Various models and coupling schemes have been formulated in an attempt to answer this question. They can be classified as 2-site (bi-site) models, exemplified by Boyer's binding change mechanism first proposed 50 years ago, and 3-site (tri-site) models such as Nath's torsional mechanism, first postulated 25 years ago and embellished 1 year back. Experimental data collated using diverse approaches have conclusively shown that steady-state ATP hydrolysis by F1-ATPase occurs in tri-site mode. Hence older models have been continually modified to make them conform to the new facts. Here, we have developed a pure mathematical approach based on combinatorics and conservation laws to test if proposed models are 2-site or 3-site. Based on this novel combinatorial approach, we have proved that older and modified models are effectively bi‒site models in that catalysis and rotation in F1-ATPase occurs in these models with only two catalytic sites occupied by bound nucleotide. Hence these models contradict consensus experimental data. The recent 2023 model of ATP hydrolysis by F1-ATPase has been proved to be a true tri-site model based on our novel mathematical approach. Such pure mathematical proofs constitute an important step forward for ATP mechanism. However, in what must be considered an aspect with great scientific potential, the power of such mathematical proofs has not been fully exploited to solve molecular biological problems, in our opinion. We believe that the creative application of pure mathematical proofs (for another example see Nath in Theory Biosci 141:249-260, 2022) can help resolve with finality various longstanding molecular-level issues that arise as a matter of course in the analysis of fundamental biological problems. Such issues have proved extraordinarily difficult to resolve by standard experimental, theoretical, or computational approaches.

Thermodynamic analysis of energy coupling by determination of the Onsager phenomenological coefficients for a 3×3 system of coupled chemical reactions and transport in ATP synthesis and its mechanistic implications.

The nonequilibrium coupled processes of oxidation and ATP synthesis in the fundamental process of oxidative phosphorylation (OXPHOS) are of vital importance in biosystems. These coupled chemical reaction and transport bioenergetic processes using the OXPHOS pathway meet >90% of the ATP demand in aerobic systems. On the basis of experimentally determined thermodynamic OXPHOS flux-force relationships and biochemical data for the ternary system of oxidation, ion transport, and ATP synthesis, the Onsager phenomenological coefficients have been computed, including an estimate of error. A new biothermokinetic theory of energy coupling has been formulated and on its basis the thermodynamic parameters, such as the overall degree of coupling, q and the phenomenological stoichiometry, Z of the coupled system have been evaluated. The amount of ATP produced per oxygen consumed, i.e. the actual, operating P/O ratio in the biosystem, the thermodynamic efficiency of the coupled reactions, η, and the Gibbs free energy dissipation, Φ have been calculated and shown to be in agreement with experimental data. At the concentration gradients of ADP and ATP prevailing under state 3 physiological conditions of OXPHOS that yield Vmax rates of ATP synthesis, a maximum in Φ of ∼0.5J(hmgprotein)-1, corresponding to a thermodynamic efficiency of ∼60% for oxidation on succinate, has been obtained. Novel mechanistic insights arising from the above have been discussed. This is the first report of a 3 × 3 system of coupled chemical reactions with transport in a biological context in which the phenomenological coefficients have been evaluated from experimental data.

Coupling and biological free-energy transduction processes as a bridge between physics and life: Molecular-level instantiation of Ervin Bauer's pioneering concepts in biological thermodynamics.

The nonequilibrium coupled processes of oxidation and ATP synthesis in the biological process of oxidative phosphorylation (OXPHOS) are fundamental to all life on our planet. These steady-state energy transduction processes ‒ coupled by proton and anion/counter-cation concentration gradients in the OXPHOS pathway ‒ generate ∼95 % of the ATP requirement of aerobic systems for cellular function. The rapid energy cycling and homeostasis of metabolites involved in this coupling are shown to be responsible for maintenance and regulation of stable nonequilibrium states, the latter first postulated in pioneering biothermodynamics work by Ervin Bauer between 1920 and 1935. How exactly does this occur? This is shown to be answered by molecular considerations arising from Nath's torsional mechanism of ATP synthesis and two-ion theory of energy coupling developed in 25 years of research work on the subject. A fresh analysis of the biological thermodynamics of coupling that goes beyond the previous work of Stucki and others and shows how the system functions at the molecular level has been carried out. Thermodynamic parameters, such as the overall degree of coupling, q of the coupled system are evaluated for the state 4 to state 3 transition in animal mitochondria with succinate as substrate. The actual or operative P to O ratio, the efficiency of the coupled reactions, η, and the Gibbs energy dissipation, Φ have been calculated and shown to be in good agreement with experimental data. Novel mechanistic insights arising from the above have been discussed. A fourth law/principle of thermodynamics is formulated for a sub-class of physical and biological systems. The critical importance of constraints and time-varying boundary conditions for function and regulation is discussed in detail. Dynamic internal structural changes essential for torsional energy storage within the γ-subunit in a single molecule of the FOF1-ATP synthase and its transduction have been highlighted. These results provide a molecular-level instantiation of Ervin Bauer's pioneering concepts in biological thermodynamics.

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.

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 α3ß3γ 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.

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 ß-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.

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.

Network representation and analysis of energy coupling mechanisms in cellular metabolism by a graph-theoretical approach.

Mechanisms coupling the chemical reactions of oxidation and ATP synthesis in cellular metabolism by the fundamental biological process of oxidative phosphorylation (OX PHOS) in mitochondria provide > 90% of the energy requirements in living organisms. Mathematical graph theory methods have been extensively used to characterize various metabolic, regulatory, and disease networks in biology. However, networks of energy coupling mechanisms in OX PHOS have not been represented and analyzed previously by these approaches. Here, the problem of biological energy coupling is translated into a graph-theoretical framework, and all possible coupling schemes between oxidation and ATP synthesis are represented as graphs connecting these processes by various intermediates or states. The problem is shown to be transformed into the hard problem of finding a Hamiltonian tour in the networks of possible constituent mechanisms, given the constraints of a cyclical nature of operation of enzymes and biological molecular machines. Accessible mathematical proofs of three theorems that guarantee sufficient conditions for the existence of a Hamiltonian cycle in simple graphs are provided. The results of the general theorems are applied to the set of possible coupling mechanisms in OX PHOS and shown to (1) unequivocally differentiate between the major theories and mechanisms of energy coupling, (2) greatly reduce the possibilities for detailed consideration, and (3) deduce the biologically selected mechanism using additional constraints from the cumulative experimental record. Finally, an algorithm is constructed to implement the graph-theoretical procedure. In summary, the enormous power and generality of mathematical theorems and approaches in graph theory are shown to help solve a fundamental problem in biology.

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.

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.

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, ∆Gdesolvation 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.

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 1.

In Part 1 of this invited article, we consider the fundamental aspects of energy coupling in oxidative phosphorylation. The central concepts of the chemiosmotic theory are re-examined and the major problems with its experimental verification are analyzed and reassessed from first principles. Several of its assumptions and interpretations (with regard, for instance, to consideration of the membrane as an inert barrier, the occurrence of energy transduction at thermodynamic equilibrium, the completely delocalized nature of the protonmotive force, and the notion of indirect coupling) are shown to be questionable. Important biological implications of this analysis for molecular mechanisms of biological energy transduction are enumerated. A fresh molecular mechanism of the uncoupling of oxidative phosphorylation by classical weak acid anion uncouplers and an adequate explanation for the existence of uncoupler-resistant mutants (which until now has remained a mystery) has been proposed based on novel insights arising from a new torsional mechanism of energy transduction and ATP synthesis.

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.

The core of this second article shows how logical errors and inconsistencies in previous theories of energy coupling in oxidative phosphorylation are overcome by use of a torsional mechanism and the unified theory of ATP synthesis/hydrolysis. The torsional mechanism is shown to satisfy the pioneering and verified features of previous mechanisms. A considerable amount of data is identified that is incompatible with older theories but is now explained in a logically consistent and unified way. Key deficiencies in older theories are pinpointed and their resolution elucidated. Finally, major differences between old and new approaches are tabulated. The new theory now provides the elusive details of energy coupling and transduction, and allows several novel and experimentally verifiable predictions to be made and a considerable number of applications in nanotechnology, energy conversion, systems biology, and in health and disease are foreseen.