The thermodynamic efficiency of ATP synthesis in oxidative phosphorylation

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.

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.

Maggot Kinase and Natural Thrombolytic Proteins

Thrombolytic enzymes constitute a class of proteases with antithrombotic functions. Derived from natural products and abundant in nature, certain thrombolytic enzymes, such as urokinase, earthworm kinase, and streptokinase, have been widely used in the clinical treatment of vascular embolic diseases. Fly maggots, characterized by their easy growth and low cost, are a traditional Chinese medicine recorded in the Compendium of Materia Medica. These maggots can also be used as raw material for the extraction and preparation of thrombolytic enzymes (maggot kinase). In this review, we assembled global research reports on natural thrombolytic enzymes through a literature search and reviewed the functions and structures of natural thrombolytic enzymes to provide a reference for natural thrombophilic drug screening and development.

Calcium-induced upregulation of energy metabolism heats neurons during neural activity

Cellular temperature affects every biochemical reaction, underscoring its critical role in cellular functions. In neurons, temperature not only modulates neurotransmission but is also a key determinant of neurodegenerative diseases. Considering that the brain consumes a disproportionately high amount of energy relative to its weight, neural circuits likely generate a lot of heat, which can increase cytosolic temperature. However, the changes in temperature within neurons and the mechanisms of heat generation during neural excitation remain unclear. In this study, we achieved simultaneous imaging of Ca2+ and temperature using the genetically encoded indicators, B-GECO and B-gTEMP. We then compared the spatiotemporal distributions of Ca2+ responses and temperature. Following neural excitation induced by veratridine, an activator of the voltage-gated Na+ channel, we observed an approximately 2 °C increase in cytosolic temperature occurring 30 s after the Ca2+ response. The temperature elevation was observed in the non-nuclear region, while Ca2+ increased throughout the cell body. Moreover, this temperature increase was suppressed under Ca2+-free conditions and by inhibitors of ATP synthesis. These results indicate that Ca2+-induced upregulation of energy metabolism serves as the heat source during neural excitation.

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.

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.

Mitochondrial temperature homeostasis resists external metabolic stresses

Based on studies with a fluorescent reporter dye, Mito Thermo Yellow (MTY), and the genetically encoded gTEMP ratiometric fluorescent temperature indicator targeted to mitochondria, the temperature of active mitochondria in four mammalian and one insect cell line was estimated to be up to 15°C above that of the external environment to which the cells were exposed. High mitochondrial temperature was maintained in the face of a variety of metabolic stresses, including substrate starvation or modification, decreased ATP demand due to inhibition of cytosolic protein synthesis, inhibition of the mitochondrial adenine nucleotide transporter and, if an auxiliary pathway for electron transfer was available via the alternative oxidase, even respiratory poisons acting downstream of oxidative phosphorylation (OXPHOS) complex I. We propose that the high temperature of active mitochondria is an inescapable consequence of the biochemistry of OXPHOS and is homeostatically maintained as a primary feature of mitochondrial metabolism.

Warm Cells, Hot Mitochondria: Achievements and Problems of Ultralocal Thermometry

Temperature is a crucial regulator of the rate and direction of biochemical reactions and cell processes. The recent data indicating the presence of local thermal gradients associated with the sites of high-rate thermogenesis, on the one hand, demonstrate the possibility for the existence of "thermal signaling" in a cell and, on the other, are criticized on the basis of thermodynamic calculations and models. Here, we review the main thermometric techniques and sensors developed for the determination of temperature inside living cells and diverse intracellular compartments. A comparative analysis is conducted of the results obtained using these methods for the cytosol, nucleus, endo-/sarcoplasmic reticulum, and mitochondria, as well as their biological consistency. Special attention is given to the limitations, possible sources of errors and ambiguities of the sensor's responses. The issue of biological temperature limits in cells and organelles is considered. It is concluded that the elaboration of experimental protocols for ultralocal temperature measurements that take into account both the characteristics of biological systems, as well as the properties and limitations of each type of sensor is of critical importance for the generation of reliable results and further progress in this field.

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.

Modeling cell populations metabolism and competition under maximum power constraints

Ecological interactions are fundamental at the cellular scale, addressing the possibility of a description of cellular systems that uses language and principles of ecology. In this work, we use a minimal ecological approach that encompasses growth, adaptation and survival of cell populations to model cell metabolisms and competition under energetic constraints. As a proof-of-concept, we apply this general formulation to study the dynamics of the onset of a specific blood cancer-called Multiple Myeloma. We show that a minimal model describing antagonist cell populations competing for limited resources, as regulated by microenvironmental factors and internal cellular structures, reproduces patterns of Multiple Myeloma evolution, due to the uncontrolled proliferation of cancerous plasma cells within the bone marrow. The model is characterized by a class of regime shifts to more dissipative states for selectively advantaged malignant plasma cells, reflecting a breakdown of self-regulation in the bone marrow. The transition times obtained from the simulations range from years to decades consistently with clinical observations of survival times of patients. This irreversible dynamical behavior represents a possible description of the incurable nature of myelomas based on the ecological interactions between plasma cells and the microenvironment, embedded in a larger complex system. The use of ATP equivalent energy units in defining stocks and flows is a key to constructing an ecological model which reproduces the onset of myelomas as transitions between states of a system which reflects the energetics of plasma cells. This work provides a basis to construct more complex models representing myelomas, which can be compared with model ecosystems.

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.

Analysis of differential proteins between non-capacitated and capacitated boar sperm and verification of the effect of phosphofructokinase on capacitation

The objective of this study was to analyze the differences in the proteins in non-capacitated and capacitated boar sperm and to identify the functions of the differential proteins and key capacitation proteins of boar sperm before and after capacitation. Transwell chambers were used to separate capacitated sperm proteins using a unique polycarbonate membrane. Meanwhile, isotopic tags for relative and absolute quantification combined with LC‒MS/MS analysis were used for quantitative determination of differential proteins. Through the comparative analysis of different databases, 475 different proteins were identified in non-capacitated sperm and capacitated sperm, of which 303 were significantly upregulated and 172 were significantly downregulated. These differentially-expressed proteins are mainly involved in redox processes, cell biosynthesis processes and cell aromatic compound metabolism biological processes. They also participate in the signaling pathways of phosphorylation, ketone synthesis and degradation, most of which interact to varying degrees. Among these differentially-expressed proteins, phosphofructokinase attracted our attention as a potential capacitated protein. We further verified that phosphofructokinase can promote boar sperm capacitation by immunoblotting.

How hot can mitochondria be? Incubation at temperatures above 43 °C induces the degradation of respiratory complexes and supercomplexes in intact cells and isolated mitochondria

Mitochondrial function generates an important fraction of the heat that contributes to cellular and organismal temperature maintenance, but the actual values of this parameter reached in the organelles is a matter of debate. The studies addressing this issue have reported divergent results: from detecting in the organelles the same temperature as the cell average or the incubation temperature, to increasing differences of up to 10 degrees above the incubation value. Theoretical calculations based on physical laws exclude the possibility of relevant temperature gradients between mitochondria and their surroundings. These facts have given rise to a conundrum or paradox about hot mitochondria. We have examined by Blue-Native electrophoresis, both in intact cells and in isolated organelles, the stability of respiratory complexes and supercomplexes at different temperatures to obtain information about their tolerance to heat stress. We observe that, upon incubation at values above 43 °C and after relatively short periods, respiratory complexes, and especially complex I and its supercomplexes, are unstable even when the respiratory activity is inhibited. These results support the conclusion that high temperatures (>43 °C) cause damage to mitochondrial structure and function and question the proposal that these organelles can physiologically work at close to 50 °C.

Heat Release by Isolated Mouse Brain Mitochondria Detected with Diamond Thermometer

The production of heat by mitochondria is critical for maintaining body temperature, regulating metabolic rate, and preventing oxidative damage to mitochondria and cells. Until the present, mitochondrial heat production has been characterized only by methods based on fluorescent probes, which are sensitive to environmental variations (viscosity, pH, ionic strength, quenching, etc.). Here, for the first time, the heat release of isolated mitochondria was unambiguously measured by a diamond thermometer (DT), which is absolutely indifferent to external non-thermal parameters. We show that during total uncoupling of transmembrane potential by CCCP application, the temperature near the mitochondria rises by 4-22 °C above the ambient temperature with an absolute maximum of 45 °C. Such a broad variation in the temperature response is associated with the heterogeneity of the mitochondria themselves as well as their aggregations in the isolated suspension. Spontaneous temperature bursts with comparable amplitude were also detected prior to CCCP application, which may reflect involvement of some mitochondria to ATP synthesis or membrane potential leaking to avoid hyperproduction of reactive oxygen species. The results obtained with the diamond temperature sensor shed light on the "hot mitochondria" paradox.

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.

The multiple facets of mitochondrial regulations controlling cellular thermogenesis

Understanding temperature production and regulation in endotherm organisms becomes a crucial challenge facing the increased frequency and intensity of heat strokes related to global warming. Mitochondria, located at the crossroad of metabolism, respiration, Ca²⁺ homeostasis, and apoptosis, were recently proposed to further act as cellular radiators, with an estimated inner temperature reaching 50 °C in common cell lines. This inner thermogenesis might be further exacerbated in organs devoted to produce consistent efforts as muscles, or heat as brown adipose tissue, in response to acute solicitations. Consequently, pathways promoting respiratory chain uncoupling and mitochondrial activity, such as Ca²⁺ fluxes, uncoupling proteins, futile cycling, and substrate supplies, provide the main processes controlling heat production and cell temperature. The mitochondrial thermogenesis might be further amplified by cytoplasmic mechanisms promoting the over-consumption of ATP pools. Considering these new thermic paradigms, we discuss here all conventional wisdoms linking mitochondrial functions to cellular thermogenesis in different physiological conditions.

Cyanide resistant respiration and the alternative oxidase pathway: A journey from plants to mammals

In a large number of organisms covering all phyla, the mitochondrial respiratory chain harbors, in addition to the conventional elements, auxiliary proteins that confer adaptive metabolic plasticity. The alternative oxidase (AOX) represents one of the most studied auxiliary proteins, initially identified in plants. In contrast to the standard respiratory chain, the AOX mediates a thermogenic cyanide-resistant respiration; a phenomenon that has been of great interest for over 2 centuries in that energy is not conserved when electrons flow through it. Here we summarize centuries of studies starting from the early observations of thermogenicity in plants and the identification of cyanide resistant respiration, to the fascinating discovery of the AOX and its current applications in animals under normal and pathological conditions.

What physiological role(s) does the alternative oxidase perform in animals?

Although the alternative oxidase, AOX, was known to be widespread in the animal kingdom by 2004, its exact physiological role in animals remains poorly understood. Here we present what evidence has accumulated thus far, indicating that it may play a role in enabling animals to resist various kinds of stress, including toxins, abnormal oxygen or nutrient levels, protein unfolding, dessication and pathogen attack. Much of our knowledge comes from studies in model organisms, where any benefits from exogenously expressed AOX may be masked by its unregulated expression, which may itself be stressful. The further question arises as to why AOX has been lost from some major crown groups, namely vertebrates, insects and cephalopods, if it plays important roles favouring the survival of other animals. We conclude by presenting some speculative ideas addressing this question, and an outline of how it might be approached experimentally.

Mito-Q promotes porcine oocytes maturation by maintaining mitochondrial thermogenesis via UCP2 downregulation

Mitochondrial thermogenesis is an adaptive response of cells to their surrounding stress. Oxidative stress is one of the common stresses during in vitro maturation (IVM) of oocytes, which leads to mitochondrial dysfunction. This study aimed to probe the effects of the mitochondria-targeted antioxidant Mito-Q on oocyte development and unravel the role of Mito-Q in mitochondrial ATP production and thermogenesis regulation. Our results showed that Mito-Q had a positive effect on porcine oocytes maturation and subsequent embryo development. During oocytes IVM, Mito-Q could reduce ATP levels and ROS, increase lipid droplets accumulation, induce autophagy, and maintain mitochondrial temperature stability. Moreover, in metaphase II (MII) oocytes, Mito-Q would induce mitochondrial uncoupling manifested by decreased ATP, attenuated mitochondrial membrane potential (MMP), and increased mitochondrial thermogenesis. Notably, the expression of mitochondrial uncoupling protein (UCP2) was significantly reduced in oocytes treated with Mito-Q. Further study indicated that specific depletion of UCP2 in oocytes also resulted in increased thermogenesis, decreased ATP and declined MMP, suggesting that UCP2 downregulation may participate in Mito-Q-induced mitochondrial uncoupling. In summary, our data demonstrate that Mito-Q promotes oocyte maturation in vitro and maintains the stability of mitochondrial thermogenesis by inhibiting UCP2 expression.

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.

Growth and Meat Quality of Grass Carp (Ctenopharyngodon idellus) Responded to Dietary Protein (Soybean Meal) Level Through the Muscle Metabolism and Gene Expression of Myosin Heavy Chains

The aim of this study was to investigate the effect of dietary protein level (soybean meal) on growth performance, flesh quality of grass carp, and the related molecular mechanisms. The results showed that appropriate dietary protein levels improved the growth performance, hardness, and pH of muscle while decreasing muscle crude lipid content and cooking loss and altering the antioxidant capacity and metabolic enzymes activities. In addition, appropriate dietary protein promoted the gene expression of myhc-1, myhc-4, myf5, myod, myog, and fgf6a, whereas inhibited that of myhc-7, myhc-2, mrf4, and mstn. Transcriptome profiling of muscle revealed that the flesh quality-specific differences were related to tight junctions and intramuscular fat (IMF) accumulation. GSEA showed that fatty acid metabolism and oxidative phosphorylation were downregulated in SM5 compared with SM1. To conclude, appropriate protein levels improved the growth and flesh quality by regulating muscle antioxidant capacity and gene expression of myhcs and fat metabolism-related signaling molecules.

Mitochondrial respiration in rats during hypothermia resulting from central drug administration

The ability to induce a hypothermia resembling that of natural torpor would be greatly beneficial in medical and non-medical fields. At present, two procedures based on central nervous pharmacological manipulation have been shown to be effective in bringing core body temperature well below 30 °C in the rat, a non-hibernator: the first, based on the inhibition of a key relay in the central thermoregulatory pathway, the other, based on the activation of central adenosine A1 receptors. Although the role of mitochondria in the activation and maintenance of torpor has been extensively studied, no data are available for centrally induced hypothermia in non-hibernators. Thus, in the present work the respiration rate of mitochondria in the liver and in the kidney of rats following the aforementioned hypothermia-inducing treatments was studied. Moreover, to have an internal control, the same parameters were assessed in a well-consolidated model, i.e., mice during fasting-induced torpor. Our results show that state 3 respiration rate, which significantly decreased in the liver of mice, was unchanged in rats. An increase of state 4 respiration rate was observed in both species, although it was not statistically significant in rats under central adenosine stimulation. Also, a significant decrease of the respiratory control ratio was detected in both species. Finally, no effects were detected in kidney mitochondria in both species. Overall, in these hypothermic conditions liver mitochondria of rats remained active and apparently ready to be re-activated to produce energy and warm up the cells. These findings can be interpreted as encouraging in view of the finalization of a translational approach to humans.

In vitro biosynthesis of ATP from adenosine and polyphosphate

Adenosine triphosphate (ATP) acts as a crucial energy currency in vivo, and it is a widely used energy and/or phosphate donor for enzyme-catalyzed reactions in vitro. In this study, we established an in vitro multi-enzyme cascade system for ATP production. Using adenosine and inorganic polyphosphate (polyP) as key substrates, we combined adenosine kinase and two functionally distinct polyphosphate kinases (PPKs) in a one-pot reaction to achieve chain-like ATP regeneration and production. Several sources of PPK were screened and characterized, and two suitable PPKs were selected to achieve high rates of ATP production. Among these, Sulfurovum lithotrophicum PPK (SlPPK) exhibited excellent activity over a wide pH range (pH 4.0-9.0) and synthesized ATP from ADP using short-chain polyP. Furthermore, it had a half-life > 155.6 h at 45 °C. After optimizing the reaction conditions, we finally carried out the coupling-catalyzed reaction with different initial adenosine concentrations of 10, 20, and 30 mM. The highest yields of ATP were 76.0, 70.5, and 61.3%, respectively.

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.

Why exercise builds muscles: titin mechanosensing controls skeletal muscle growth under load

Muscles sense internally generated and externally applied forces, responding to these in a coordinated hierarchical manner at different timescales. The center of the basic unit of the muscle, the sarcomeric M-band, is perfectly placed to sense the different types of load to which the muscle is subjected. In particular, the kinase domain of titin (TK) located at the M-band is a known candidate for mechanical signaling. Here, we develop a quantitative mathematical model that describes the kinetics of TK-based mechanosensitive signaling and predicts trophic changes in response to exercise and rehabilitation regimes. First, we build the kinetic model for TK conformational changes under force: opening, phosphorylation, signaling, and autoinhibition. We find that TK opens as a metastable mechanosensitive switch, which naturally produces a much greater signal after high-load resistance exercise than an equally energetically costly endurance effort. Next, for the model to be stable and give coherent predictions, in particular for the lag after the onset of an exercise regime, we have to account for the associated kinetics of phosphate (carried by ATP) and for the nonlinear dependence of protein synthesis rates on muscle fiber size. We suggest that the latter effect may occur via the steric inhibition of ribosome diffusion through the sieve-like myofilament lattice. The full model yields a steady-state solution (homeostasis) for muscle cross-sectional area and tension and, a quantitatively plausible hypertrophic response to training, as well as atrophy after an extended reduction in tension.

Communication consumes 35 times more energy than computation in the human cortex, but both costs are needed to predict synapse number

Darwinian evolution tends to produce energy-efficient outcomes. On the other hand, energy limits computation, be it neural and probabilistic or digital and logical. Taking a particular energy-efficient viewpoint, we define neural computation and make use of an energy-constrained computational function. This function can be optimized over a variable that is proportional to the number of synapses per neuron. This function also implies a specific distinction between adenosine triphosphate (ATP)-consuming processes, especially computation per se vs. the communication processes of action potentials and transmitter release. Thus, to apply this mathematical function requires an energy audit with a particular partitioning of energy consumption that differs from earlier work. The audit points out that, rather than the oft-quoted 20 W of glucose available to the human brain, the fraction partitioned to cortical computation is only 0.1 W of ATP [L. Sokoloff, Handb. Physiol. Sect. I Neurophysiol. 3, 1843-1864 (1960)] and [J. Sawada, D. S. Modha, "Synapse: Scalable energy-efficient neurosynaptic computing" in Application of Concurrency to System Design (ACSD) (2013), pp. 14-15]. On the other hand, long-distance communication costs are 35-fold greater, 3.5 W. Other findings include 1) a [Formula: see text]-fold discrepancy between biological and lowest possible values of a neuron's computational efficiency and 2) two predictions of N, the number of synaptic transmissions needed to fire a neuron (2,500 vs. 2,000).

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.

The conundrum of hot mitochondria

The mitochondrion is often referred as the cellular powerhouse because the organelle oxidizes organic acids and NADH derived from nutriments, converting around 40% of the Gibbs free energy change of these reactions into ATP, the major energy currency of cell metabolism. Mitochondria are thus microscopic furnaces that inevitably release heat as a by-product of these reactions, and this contributes to body warming, especially in endotherms like birds and mammals. Over the last decade, the idea has emerged that mitochondria could be warmer than the cytosol, because of their intense energy metabolism. It has even been suggested that our own mitochondria could operate under normal conditions at a temperature close to 50 °C, something difficult to reconcile with the laws of thermal physics. Here, using our combined expertise in biology and physics, we exhaustively review the reports that led to the concept of a hot mitochondrion, which is essentially based on the development and use of a variety of molecular thermosensors whose intrinsic fluorescence is modified by temperature. Then, we discuss the physical concepts of heat diffusion, including mechanisms like phonons scattering, which occur in the nanoscale range. Although most of approaches with thermosensors studies present relatively sparse data and lack absolute temperature calibration, overall, they do support the hypothesis of hot mitochondria. However, there is no convincing physical explanation that would allow the organelle to maintain a higher temperature than its surroundings. We nevertheless proposed some research directions, mainly biological, that might help throw light on this intriguing conundrum.

The bioenergetics of COVID-19 immunopathology and the therapeutic potential of biophysical radiances

In developing an effective clinical tool against COVID-19, we need to consider why SARS-CoV-2 infections develop along remarkably different trajectories: from completely asymptomatic to a severe course of disease. In this paper we hypothesize that the progressive exhaustion and loss of lymphocytes associated with severe stages of COVID-19 result from an intracellular energy deficit in an organism which has already been depleted by preexisting chronic diseases, acute psychological stress and the aging process. A bioenergetics view of COVID-19 immunopathology opens a new biophysical opportunity to enhance impaired immune function via proposed pathways of photomagnetic catalysis of ATP synthesis, regenerative photobiomodulation and the ultrasonic acceleration of cell restructuring. Moreover, we suggest that a coherent application of multiple biophysical radiances (coMra) may synergistically enhance energy-matter-information kinetics of basal self-regeneration of cells and thus improve immune function and accelerate recovery.

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Bioenergetics offers a unifying framework of COVID-19 immunopathology.

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Functional reserve of immune cells depends on the kinetics of basal housekeeping.

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Various biophysical stimuli enhance the kinetics of cellular self-regeneration.

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A coherent application of multiple radiances has potential to treat COVID-19.

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.

Microbial synergy and stoichiometry in heap biooxidation of low-grade porphyry arsenic-bearing gold ore

Heap biooxidation method was used to evaluate the availability of Paodaoling gold ore in Anhui province, China. 15,000 tons of gold ores (≤ 10 mm in diameter) were bioxidized under mesophilic conditions. Under the synergistic effect of microbial community, arsenic and sulfur were oxidized by 42% and 38% after 80 days. Relatively, leaching of gold was improved from 36 to 78% after heap biooxidation. The sequencing results showed there were 28 operational taxonomic units identified the microbial community in the heap. The main genera were Acidithiobacillus, Ferroplasma, Acidiferrobacter and Nitrospira. According to stoichiometry, the content of microorganisms with various functions tended to be balanced. The biomass production rate was 10 g/s, the CO₂ fixation rate was 18 g/s, and the oxygen consumption rate was 60 g/s. This study provides a good basis for the further design and application of heap biooxidation technology.

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.

Omnipresent Maxwell's demons orchestrate information management in living cells

The development of synthetic biology calls for accurate understanding of the critical functions that allow construction and operation of a living cell. Besides coding for ubiquitous structures, minimal genomes encode a wealth of functions that dissipate energy in an unanticipated way. Analysis of these functions shows that they are meant to manage information under conditions when discrimination of substrates in a noisy background is preferred over a simple recognition process. We show here that many of these functions, including transporters and the ribosome construction machinery, behave as would behave a material implementation of the information-managing agent theorized by Maxwell almost 150 years ago and commonly known as Maxwell's demon (MxD). A core gene set encoding these functions belongs to the minimal genome required to allow the construction of an autonomous cell. These MxDs allow the cell to perform computations in an energy-efficient way that is vastly better than our contemporary computers.

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.

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.

Bond Graph Modeling of Chemiosmotic Biomolecular Energy Transduction

Engineering systems modeling and analysis based on the bond graph approach has been applied to biomolecular systems. In this context, the notion of a Faraday-equivalent chemical potential is introduced which allows chemical potential to be expressed in an analogous manner to electrical volts thus allowing engineering intuition to be applied to biomolecular systems. Redox reactions, and their representation by half-reactions, are key components of biological systems which involve both electrical and chemical domains. A bond graph interpretation of redox reactions is given which combines bond graphs with the Faraday-equivalent chemical potential. This approach is particularly relevant when the biomolecular system implements chemoelectrical transduction - for example chemiosmosis within the key metabolic pathway of mitochondria: oxidative phosphorylation. An alternative way of implementing computational modularity using bond graphs is introduced and used to give a physically based model of the mitochondrial electron transport chain To illustrate the overall approach, this model is analyzed using the Faraday-equivalent chemical potential approach and engineering intuition is used to guide affinity equalisation: a energy based analysis of the mitochondrial electron transport chain.