An exploration of how the thermodynamic efficiency of bioenergetic membrane systems varies with c-subunit stoichiometry of F₁F₀ ATP synthases

Nuclear Quantum Effects Explain Chemiosmosis: The Power of the Proton

ATP is a universal bio-currency, with chemiosmosis the metabolic mint by which currency is printed. Chemiosmosis leverages a membrane potential and ion gradient, typically a proton gradient, to generate ATP. The current chemiosmotic hypothesis is both cannon and dogma. However, there are obstacles to the unqualified and uncritical acceptance of this model. Intriguingly the proton is sufficiently small to exhibit quantum phenomena of wave-particle duality, often thought the exclusive prerogative of smaller subcellular particles. Evidence shows that chemiosmosis is by necessity critically dependent upon these nuclear quantum effects (NQE) of hydrogen, most notably as a proton. It is well established scientific orthodoxy that protons in water and hydrogen atoms of water molecules exhibit quantum phenomena. The effect is amplified by the hydrogen bonding and juxta-membrane location of protons in mitochondria and chloroplasts. NQE explains the otherwise inexplicable features of chemiosmosis, including the paucity of protons, the rate of the proton movement and ATP genesis in otherwise subliminal proton motive forces and thus functionality of alkaliphiles. It also accounts for the efficiencies of chemiosmosis reported at greater than 100% in certain contexts, which violates the second law of thermodynamics under the paradigm of classical physics. Mitochondria may have evolved to exploit quantum biology with notable features such as dimeric ATP synthases adumbrating the first double-slip experiment with the protons. The dramatic global deceleration of mitochondrial chemiosmosis and all cellular function following proton substitution with is heavier isotopes, deuterium and tritium: "deuteruction", is testimony to the primacy of nuclear quantum effects in this Quantum Chemiosmosis. Indeed the speed of evolution itself and its inexorable route to homeothermy may be due to the power of nuclear quantum effects of the smallest nucleus, the proton. The atom that is almost nothing was selected to bring about the most important processes and complex manifestations of life.

Wiring proton gradients for energy conversion

Light-switchable buffer solutions based on merocyanine photoacids can be used as efficient photoenergy harvesting systems. Varying the solvation environment of merocyanine photoacids in water-methanol mixtures allows one to carefully tune their photoacidity, relaxation kinetics, and solubility, opening up the possibility to install persistent pH gradients of approximately 4 pH units under 500 nm light. When interfaced between two electrodes and exposed to asymmetric light irradiation, these solutions can be photoactivated precisely both in space and time, generating open circuit voltages as high as 240 mV that can last hours under steady-state irradiation - an outcome that is akin the peak performance of biological transmembrane proton pumps.

Oxidative Phosphorylation Does Not Violate the Second Law of Thermodynamics

In a recent series of papers, James W. Lee reported that mitochondrial oxidative phosphorylation violates the second law of thermodynamics and that it is allowed to do so because it is a "Type-B" process that features lateral and longitudinal membrane asymmetry. We show here that these contentions are based on problematic interpretations of the literature. More reliable values of ΔGredox and ΔGATP synthesis show that the second law is not violated. More recent reports on the structures of the redox-driven proton pumps (Complexes I, III, and IV) suggest that longitudinal membrane asymmetry does not exist. Finally, Lee's predictions for the concentration of protons localized at the P-side surface of the bioenergetic membrane are likely to be much too high due to several errors; thus, his predicted high values of ΔpHsurface that violate the second law are likely to be wrong. There is currently no strong experimental or theoretical evidence to support the contention that oxidative phosphorylation violates the second law of thermodynamics.

Electrometric and Electron Paramagnetic Resonance Measurements of a Difference in the Transmembrane Electrochemical Potential: Photosynthetic Subcellular Structures and Isolated Pigment-Protein Complexes

A transmembrane difference in the electrochemical potentials of protons (ΔμH+) serves as a free energy intermediate in energy-transducing organelles of the living cell. The contributions of two components of the ΔμH+ (electrical, Δψ, and concentrational, ΔpH) to the overall ΔμH+ value depend on the nature and lipid composition of the energy-coupling membrane. In this review, we briefly consider several of the most common instrumental (electrometric and EPR) methods for numerical estimations of Δψ and ΔpH. In particular, the kinetics of the flash-induced electrometrical measurements of Δψ in bacterial chromatophores, isolated bacterial reaction centers, and Photosystems I and II of the oxygenic photosynthesis, as well as the use of pH-sensitive molecular indicators and kinetic data regarding pH-dependent electron transport in chloroplasts, have been reviewed. Further perspectives on the application of these methods to solve some fundamental and practical problems of membrane bioenergetics are discussed.

Serpentinization as the source of energy, electrons, organics, catalysts, nutrients and pH gradients for the origin of LUCA and life

Serpentinization in hydrothermal vents is central to some autotrophic theories for the origin of life because it generates compartments, reductants, catalysts and gradients. During the process of serpentinization, water circulates through hydrothermal systems in the crust where it oxidizes Fe (II) in ultramafic minerals to generate Fe (III) minerals and H2. Molecular hydrogen can, in turn, serve as a freely diffusible source of electrons for the reduction of CO2 to organic compounds, provided that suitable catalysts are present. Using catalysts that are naturally synthesized in hydrothermal vents during serpentinization H2 reduces CO2 to formate, acetate, pyruvate, and methane. These compounds represent the backbone of microbial carbon and energy metabolism in acetogens and methanogens, strictly anaerobic chemolithoautotrophs that use the acetyl-CoA pathway of CO2 fixation and that inhabit serpentinizing environments today. Serpentinization generates reduced carbon, nitrogen and - as newer findings suggest - reduced phosphorous compounds that were likely conducive to the origins process. In addition, it gives rise to inorganic microcompartments and proton gradients of the right polarity and of sufficient magnitude to support chemiosmotic ATP synthesis by the rotor-stator ATP synthase. This would help to explain why the principle of chemiosmotic energy harnessing is more conserved (older) than the machinery to generate ion gradients via pumping coupled to exergonic chemical reactions, which in the case of acetogens and methanogens involve H2-dependent CO2 reduction. Serpentinizing systems exist in terrestrial and deep ocean environments. On the early Earth they were probably more abundant than today. There is evidence that serpentinization once occurred on Mars and is likely still occurring on Saturn's icy moon Enceladus, providing a perspective on serpentinization as a source of reductants, catalysts and chemical disequilibrium for life on other worlds.

The real reason why ATP hydrolysis is spontaneous at pH > 7: It's (mostly) the proton concentration!

Common wisdom holds that ATP hydrolysis is spontaneous because of the weakness of its phosphoanhydride bonds, electrostatic repulsion within the polyanionic ATP4- molecule, and resonance stabilization of the inorganic phosphate and ADP products. By examining the pH-dependence of the hydrolysis Gibbs free energy, we show that in fact, above pH 7, ATP hydrolysis is spontaneous due mainly to the low concentration of the H+ that is released as product. Hence, ATP is essentially just an electrophilic target whose attack by H2 O causes the acidity of the water nucleophile to increase dramatically; the spontaneity of the resulting acid ionization supplies much of the released Gibbs free energy. We also find that fermentation lowers pH not due to its organic acid products (e.g., lactic, acetic, formic, or succinic acids), but again, due to the H+ product of ATP hydrolysis.

Modeling control and transduction of electrochemical gradients in acid-stressed bacteria

Transmembrane electrochemical gradients drive solute uptake and constitute a substantial fraction of the cellular energy pool in bacteria. These gradients act not only as "homeostatic contributors," but also play a dynamic and keystone role in several bacterial functions, including sensing, stress response, and metabolism. At the system level, multiple gradients interact with ion transporters and bacterial behavior in a complex, rapid, and emergent manner; consequently, experiments alone cannot untangle their interdependencies. Electrochemical gradient modeling provides a general framework to understand these interactions and their underlying mechanisms. We quantify the generation, maintenance, and interactions of electrical, proton, and potassium potential gradients under lactic acid-stress and lactic acid fermentation. Further, we elucidate a gradient-mediated mechanism for intracellular pH sensing and stress response. We demonstrate that this gradient model can yield insights on the energetic limitations of membrane transport, and can predict bacterial behavior across changing environments.

Inferring Subsystem Efficiencies in Bipartite Molecular Machines

Molecular machines composed of coupled subsystems transduce free energy between different external reservoirs, in the process internally transducing energy and information. While subsystem efficiencies of these molecular machines have been measured in isolation, less is known about how they behave in their natural setting when coupled together and acting in concert. Here, we derive upper and lower bounds on the subsystem efficiencies of a bipartite molecular machine. We demonstrate their utility by estimating the efficiencies of the F_{o} and F_{1} subunits of ATP synthase and that of kinesin pulling a diffusive cargo.

Optimal Control of the F1-ATPase Molecular Motor

F₁-ATPase is a rotary molecular motor that in vivo is subject to strong nonequilibrium driving forces. There is great interest in understanding the operational principles governing its high efficiency of free-energy transduction. Here we use a near-equilibrium framework to design a nontrivial control protocol to minimize dissipation in rotating F₁ to synthesize adenosine triphosphate. We find that the designed protocol requires much less work than a naive (constant-velocity) protocol across a wide range of protocol durations. Our analysis points to a possible mechanism for energetically efficient driving of F₁ in vivo and provides insight into free-energy transduction for a broader class of biomolecular and synthetic machines.

A critique of the capacitor-based "Transmembrane Electrostatically Localized Proton" hypothesis

In his Transmembrane Electrostatically Localized Proton hypothesis (TELP), James W. Lee has modeled the bioenergetic membrane as a simple capacitor. According to this model, the surface concentration of protons is completely independent of proton concentration in the bulk phase, and is linearly proportional to the transmembrane potential. Such a proportionality runs counter to the results of experimental measurements, molecular dynamics simulations, and electrostatics calculations. We show that the TELP model dramatically overestimates the surface concentration of protons, and we discuss the electrostatic reasons why a simple capacitor is not an appropriate model for the bioenergetic membrane.

Internal energy and information flows mediate input and output power in bipartite molecular machines

Microscopic biological systems operate far from equilibrium, are subject to strong fluctuations, and are composed of many coupled components with interactions varying in nature and strength. Researchers are actively investigating the general design principles governing how biomolecular machines achieve effective free-energy transduction in light of these challenges. We use a model of two strongly coupled stochastic rotary motors to explore the effect of coupling strength between components of a molecular machine. We observe prominent thermodynamic characteristics at intermediate coupling strength, near that which maximizes output power: a maximum in power and information transduced from the upstream to the downstream system, and equal subsystem entropy production rates. These observations are unified through a bound on the machine's input and output power, which accounts for both the energy and information transduced between subsystems.

The Proton in Biochemistry: Impacts on Bioenergetics, Biophysical Chemistry, and Bioorganic Chemistry

The proton is the smallest atomic particle, and in aqueous solution it is the smallest hydrated ion, having only two waters in its first hydration shell. In this article we survey key aspects of the proton in chemistry and biochemistry, starting with the definitions of pH and pK _a and their application inside biological cells. This includes an exploration of pH in nanoscale spaces, distinguishing between bulk and interfacial phases. We survey the Eigen and Zundel models of the structure of the hydrated proton, and how these can be used to explain: a) the behavior of protons at the water-hydrophobic interface, and b) the extraordinarily high mobility of protons in bulk water via Grotthuss hopping, and inside proteins via proton wires. Lastly, we survey key aspects of the effect of proton concentration and proton transfer on biochemical reactions including ligand binding and enzyme catalysis, as well as pH effects on biochemical thermodynamics, including the Chemiosmotic Theory. We find, for example, that the spontaneity of ATP hydrolysis at pH ≥ 7 is not due to any inherent property of ATP (or ADP or phosphate), but rather to the low concentration of H⁺. Additionally, we show that acidification due to fermentation does not derive from the organic acid waste products, but rather from the proton produced by ATP hydrolysis.

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

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

Energy Renewal: Isothermal Utilization of Environmental Heat Energy with Asymmetric Structures

Through the research presented herein, it is quite clear that there are two thermodynamically distinct types (A and B) of energetic processes naturally occurring on Earth. Type A, such as glycolysis and the tricarboxylic acid cycle, apparently follows the second law well; Type B, as exemplified by the thermotrophic function with transmembrane electrostatically localized protons presented here, does not necessarily have to be constrained by the second law, owing to its special asymmetric function. This study now, for the first time, numerically shows that transmembrane electrostatic proton localization (Type-B process) represents a negative entropy event with a local protonic entropy change (ΔSL) in a range from -95 to -110 J/K∙mol. This explains the relationship between both the local protonic entropy change (ΔSL) and the mitochondrial environmental temperature (T) and the local protonic Gibbs free energy (ΔGL=TΔSL) in isothermal environmental heat utilization. The energy efficiency for the utilization of total protonic Gibbs free energy (ΔGT including ΔGL=TΔSL) in driving the synthesis of ATP is estimated to be about 60%, indicating that a significant fraction of the environmental heat energy associated with the thermal motion kinetic energy (kBT) of transmembrane electrostatically localized protons is locked into the chemical form of energy in ATP molecules. Fundamentally, it is the combination of water as a protonic conductor, and thus the formation of protonic membrane capacitor, with asymmetric structures of mitochondrial membrane and cristae that makes this amazing thermotrophic feature possible. The discovery of energy Type-B processes has inspired an invention (WO 2019/136037 A1) for energy renewal through isothermal environmental heat energy utilization with an asymmetric electron-gated function to generate electricity, which has the potential to power electronic devices forever, including mobile phones and laptops. This invention, as an innovative Type-B mimic, may have many possible industrial applications and is likely to be transformative in energy science and technologies for sustainability on Earth.

Rotor subunits adaptations in ATP synthases from photosynthetic organisms

Driven by transmembrane electrochemical ion gradients, F-type ATP synthases are the primary source of the universal energy currency, adenosine triphosphate (ATP), throughout all domains of life. The ATP synthase found in the thylakoid membranes of photosynthetic organisms has some unique features not present in other bacterial or mitochondrial systems. Among these is a larger-than-average transmembrane rotor ring and a redox-regulated switch capable of inhibiting ATP hydrolysis activity in the dark by uniquely adapted rotor subunit modifications. Here, we review recent insights into the structure and mechanism of ATP synthases specifically involved in photosynthesis and explore the cellular physiological consequences of these adaptations at short and long time scales.

Graphene Quantum Dots as Intracellular Imaging-Based Temperature Sensors

Non-invasive temperature sensing is necessary to analyze biological processes occurring in the human body, including cellular enzyme activity, protein expression, and ion regulation. To probe temperature-sensitive processes at the nanoscale, novel luminescence nanothermometers are developed based on graphene quantum dots (GQDs) synthesized via top-down (RGQDs) and bottom-up (N-GQDs) approaches from reduced graphene oxide and glucosamine precursors, respectively. Because of their small 3-6 nm size, non-invasive optical sensitivity to temperature change, and high biocompatibility, GQDs enable biologically safe sub-cellular resolution sensing. Both GQD types exhibit temperature-sensitive yet photostable fluorescence in the visible and near-infrared for RGQDs, utilized as a sensing mechanism in this work. Distinctive linear and reversible fluorescence quenching by up to 19.3% is observed for the visible and near-infrared GQD emission in aqueous suspension from 25 °C to 49 °C. A more pronounced trend is observed with GQD nanothermometers internalized into the cytoplasm of HeLa cells as they are tested in vitro from 25 °C to 45 °C with over 40% quenching response. Our findings suggest that the temperature-dependent fluorescence quenching of bottom-up and top-down-synthesized GQDs studied in this work can serve as non-invasive reversible/photostable deterministic mechanisms for temperature sensing in microscopic sub-cellular biological environments.

Nonequilibrium Energy Transduction in Stochastic Strongly Coupled Rotary Motors

Living systems at the molecular scale are composed of many constituents with strong and heterogeneous interactions, operating far from equilibrium, and subject to strong fluctuations. These conditions pose significant challenges to efficient, precise, and rapid free energy transduction, yet nature has evolved numerous molecular machines that do just this. Using a simple model of the ingenious rotary machine F_oF₁-ATP synthase, we investigate the interplay between nonequilibrium driving forces, thermal fluctuations, and interactions between strongly coupled subsystems. This model reveals design principles for effective free energy transduction. Most notably, while tight coupling is intuitively appealing, we find that output power is maximized at intermediate-strength coupling, which permits lubrication by stochastic fluctuations with only minimal slippage.

Engineering transport systems for microbial production

The rapid development in the field of metabolic engineering has enabled complex modifications of metabolic pathways to generate a diverse product portfolio. Manipulating substrate uptake and product export is an important research area in metabolic engineering. Optimization of transport systems has the potential to enhance microbial production of renewable fuels and chemicals. This chapter comprehensively reviews the transport systems critical for microbial production as well as current genetic engineering strategies to improve transport functions and thus production metrics. In addition, this chapter highlights recent advancements in engineering microbial efflux systems to enhance cellular tolerance to industrially relevant chemical stress. Lastly, future directions to address current technological gaps are discussed.

Optimization of ATP Synthase c-Rings for Oxygenic Photosynthesis

The conversion of sunlight into useable cellular energy occurs via the proton-coupled electron transfer reactions of photosynthesis. Light is absorbed by photosynthetic pigments and transferred to photochemical reaction centers to initiate electron and proton transfer reactions to store energy in a redox gradient and an electrochemical proton gradient (proton motive force, pmf), composed of a concentration gradient (ΔpH) and an electric field (Δψ), which drives the synthesis of ATP through the thylakoid FoF1-ATP synthase. Although ATP synthase structure and function are conserved across biological kingdoms, the number of membrane-embedded ion-binding c subunits varies between organisms, ranging from 8 to 17, theoretically altering the H+/ATP ratio for different ATP synthase complexes, with profound implications for the bioenergetic processes of cellular metabolism. Of the known c-ring stoichiometries, photosynthetic c-rings are among the largest identified stoichiometries, and it has been proposed that decreasing the c-stoichiometry could increase the energy conversion efficiency of photosynthesis. Indeed, there is strong evidence that the high H+/ATP of the chloroplast ATP synthase results in a low ATP/nicotinamide adenine dinucleotide phosphate (NADPH) ratio produced by photosynthetic linear electron flow, requiring secondary processes such as cyclic electron flow to support downstream metabolism. We hypothesize that the larger c subunit stoichiometry observed in photosynthetic ATP synthases was selected for because it allows the thylakoid to maintain pmf in a range where ATP synthesis is supported, but avoids excess Δψ and ΔpH, both of which can lead to production of reactive oxygen species and subsequent photodamage. Numerical kinetic simulations of the energetics of chloroplast photosynthetic reactions with altered c-ring size predicts the energy storage of pmf and its effects on the photochemical reaction centers strongly support this hypothesis, suggesting that, despite the low efficiency and suboptimal ATP/NADPH ratio, a high H+/ATP is favored to avoid photodamage. This has important implications for the evolution and regulation of photosynthesis as well as for synthetic biology efforts to alter photosynthetic efficiency by engineering the ATP synthase.

Amino Acid and Sugar Catabolism in the Marine Bacterium Phaeobacter inhibens DSM 17395 from an Energetic Viewpoint

Growth energetics and metabolic efficiency contribute to the lifestyle and habitat imprint of microorganisms. Roseobacters constitute one of the most abundant and successful marine bacterioplankton groups. Here, we reflect on the energetics and metabolic efficiency of Phaeobacter inhibens DSM 17395, a versatile heterotrophic roseobacter. Fourteen different substrates (five sugars and nine amino acids) and their degradation pathways were assessed for energetic efficiencies based on catabolic ATP yields, calculated from net formed ATP and reducing equivalents. The latter were converted into ATP by employing the most divergent coupling ratios (i.e., ions per ATP) currently known for F₁F_o ATP synthases in heterotrophic bacteria. The catabolic ATP yields of the pathways studied in P. inhibens differed ∼3-fold. The actual free energy costs for ATP synthesis were estimated at 81.6 kJ per mol ATP (3.3 ions per ATP) or 104.2 kJ per mol ATP (4.3 ions per ATP), yielding an average thermodynamic efficiency of ∼37.7% or ∼29.5%, respectively. Growth performance (rates, yields) and carbon assimilation efficiency were determined for P. inhibens growing in process-controlled bioreactors with 10 different single substrates (Glc, Man, N-acetylglucosamine [Nag], Phe, Trp, His, Lys, Thr, Val, or Leu) and with 2 defined substrate mixtures. The efficiencies of carbon assimilation into biomass ranged from ∼28% to 61%, with His/Trp and Thr/Leu yielding the lowest and highest levels. These efficiencies correlated with catabolic and ATP yields only to some extent. Substrate-specific metabolic demands and/or functions, as well as the compositions of the substrate mixtures, apparently affected the energetic costs of growth. These include energetic burdens associated with, e.g., slow growth, stress, and/or the production of tropodithietic acid.IMPORTANCE Heterotrophic members of the bacterioplankton serve the marine ecosystem by transforming organic matter, an activity that is governed by the bacterial growth efficiencies (BGEs) obtained under given environmental conditions. In marine ecology, the concept of BGE refers to the carbon assimilation efficiency within natural communities. The marine bacterium studied here, Phaeobacter inhibens DSM 17395, is a copiotrophic representative of the globally abundant Roseobacter group, and the 15 catabolic pathways investigated are widespread among these marine heterotrophs. Combining pathway-specific catabolic ATP yields with in-depth quantitative physiological data could (i) provide a new baseline for the study of growth energetics and efficiency in further Roseobacter group members and other copiotrophic marine bacteria in productive coastal ecosystems and (ii) contribute to a better understanding of the factors controlling BGE (including the additional energetic burden arising from widespread secondary-metabolite formation) based on laboratory studies with pure cultures.

Theory of Nonequilibrium Free Energy Transduction by Molecular Machines

Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared with more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.

Electrostatically localized proton bioenergetics: better understanding membrane potential

In Mitchell's chemiosmotic theory, membrane potential Δ ψ was given as the electric potential difference across the membrane. However, its physical origin for membrane potential Δ ψ was not well explained. Using the Lee proton electrostatic localization model with a newly formulated equation for protonic motive force (pmf) that takes electrostatically localized protons into account, membrane potential has now been better understood as the voltage difference contributed by the localized surface charge density ( [ H L + ] + ∑ i = 1 n [ M L i + ] ) at the liquid-membrane interface as in an electrostatically localized protons/cations-membrane-anions capacitor. That is, the origin of membrane potential Δ ψ is now better understood as the electrostatic formation of the localized surface charge density that is the sum of the electrostatically localized proton concentration [ H L + ] and the localized non-proton cations density ∑ i = 1 n [ M L i + ] at the liquid membrane interface. The total localized surface charge density equals to the ideal localized proton population density [ H L + ] 0 before the cation-proton exchange process; since the cation-proton exchange process does not change the total localized charges density, neither does it change to the membrane potential Δ ψ . The localized proton concentration [ H L + ] represents the dominant component, which accounts about 78% of the total localized surface charge density at the cation-proton exchange equilibrium state in animal mitochondria. Liquid water as a protonic conductor may play a significant role in the biological activities of membrane potential formation and utilization.

Mechanisms for achieving high speed and efficiency in biomolecular machines

How does a biomolecular machine achieve high speed at high efficiency? We explore optimization principles using a simple two-state dynamical model. With this model, we establish physical principles-such as the optimal way to distribute free-energy changes and barriers across the machine cycle-and connect them to biological mechanisms. We find that a machine can achieve high speed without sacrificing efficiency by varying its conformational free energy to directly link the downhill, chemical energy to the uphill, mechanical work and by splitting a large work step into more numerous, smaller substeps. Experimental evidence suggests that these mechanisms are commonly used by biomolecular machines. This model is useful for exploring questions of evolution and optimization in molecular machines.

Biophysical comparison of ATP-driven proton pumping mechanisms suggests a kinetic advantage for the rotary process depending on coupling ratio

ATP-driven proton pumps, which are critical to the operation of a cell, maintain cytosolic and organellar pH levels within a narrow functional range. These pumps employ two very different mechanisms: an elaborate rotary mechanism used by V-ATPase H⁺ pumps, and a simpler alternating access mechanism used by P-ATPase H⁺ pumps. Why are two different mechanisms used to perform the same function? Systematic analysis, without parameter fitting, of kinetic models of the rotary, alternating access and other possible mechanisms suggest that, when the ratio of protons transported per ATP hydrolyzed exceeds one, the one-at-a-time proton transport by the rotary mechanism is faster than other possible mechanisms across a wide range of driving conditions. When the ratio is one, there is no intrinsic difference in the free energy landscape between mechanisms, and therefore all mechanisms can exhibit the same kinetic performance. To our knowledge all known rotary pumps have an H⁺:ATP ratio greater than one, and all known alternating access ATP-driven proton pumps have a ratio of one. Our analysis suggests a possible explanation for this apparent relationship between coupling ratio and mechanism. When the conditions under which the pump must operate permit a coupling ratio greater than one, the rotary mechanism may have been selected for its kinetic advantage. On the other hand, when conditions require a coupling ratio of one or less, the alternating access mechanism may have been selected for other possible advantages resulting from its structural and functional simplicity.

The thermodynamic efficiency of ATP synthesis in oxidative phosphorylation

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

Limitations to photosynthesis by proton motive force-induced photosystem II photodamage

The thylakoid proton motive force (pmf) generated during photosynthesis is the essential driving force for ATP production; it is also a central regulator of light capture and electron transfer. We investigated the effects of elevated pmf on photosynthesis in a library of Arabidopsis thaliana mutants with altered rates of thylakoid lumen proton efflux, leading to a range of steady-state pmf extents. We observed the expected pmf-dependent alterations in photosynthetic regulation, but also strong effects on the rate of photosystem II (PSII) photodamage. Detailed analyses indicate this effect is related to an elevated electric field (Δψ) component of the pmf, rather than lumen acidification, which in vivo increased PSII charge recombination rates, producing singlet oxygen and subsequent photodamage. The effects are seen even in wild type plants, especially under fluctuating illumination, suggesting that Δψ-induced photodamage represents a previously unrecognized limiting factor for plant productivity under dynamic environmental conditions seen in the field.

Limitations to photosynthesis by proton motive force-induced photosystem II photodamage

The thylakoid proton motive force (pmf) generated during photosynthesis is the essential driving force for ATP production; it is also a central regulator of light capture and electron transfer. We investigated the effects of elevated pmf on photosynthesis in a library of Arabidopsis thaliana mutants with altered rates of thylakoid lumen proton efflux, leading to a range of steady-state pmf extents. We observed the expected pmf-dependent alterations in photosynthetic regulation, but also strong effects on the rate of photosystem II (PSII) photodamage. Detailed analyses indicate this effect is related to an elevated electric field (Δψ) component of the pmf, rather than lumen acidification, which in vivo increased PSII charge recombination rates, producing singlet oxygen and subsequent photodamage. The effects are seen even in wild type plants, especially under fluctuating illumination, suggesting that Δψ-induced photodamage represents a previously unrecognized limiting factor for plant productivity under dynamic environmental conditions seen in the field.

DOI:http://dx.doi.org/10.7554/eLife.16921.001

Biophysical comparison of ATP synthesis mechanisms shows a kinetic advantage for the rotary process

The ATP synthase (F-ATPase) is a highly complex rotary machine that synthesizes ATP, powered by a proton electrochemical gradient. Why did evolution select such an elaborate mechanism over arguably simpler alternating-access processes that can be reversed to perform ATP synthesis? We studied a systematic enumeration of alternative mechanisms, using numerical and theoretical means. When the alternative models are optimized subject to fundamental thermodynamic constraints, they fail to match the kinetic ability of the rotary mechanism over a wide range of conditions, particularly under low-energy conditions. We used a physically interpretable, closed-form solution for the steady-state rate for an arbitrary chemical cycle, which clarifies kinetic effects of complex free-energy landscapes. Our analysis also yields insights into the debated "kinetic equivalence" of ATP synthesis driven by transmembrane pH and potential difference. Overall, our study suggests that the complexity of the F-ATPase may have resulted from positive selection for its kinetic advantage.

Phospholipids and glycolipids mediate proton containment and circulation along the surface of energy-transducing membranes

Proton bioenergetics provides the energy for growth and survival of most organisms in the biosphere ranging from unicellular marine phytoplankton to humans. Chloroplasts harvest light and generate a proton electrochemical gradient (proton motive force) that drives the production of ATP needed for carbon dioxide fixation and plant growth. Mitochondria, bacteria and archaea generate proton motive force to energize growth and other physiologies. Energy transducing membranes are at the heart of proton bioenergetics and are responsible for catalyzing the conversion of energy held in high-energy electrons→electron transport chain→proton motive force→ATP. Whereas the electron transport chain is understood in great detail there are major gaps in understanding mechanisms of proton transfer or circulation during proton bioenergetics. This paper is built on the proposition that phospho- and glyco-glycerolipids form proton transport circuitry at the membrane's surface. By this proposition, an emergent membrane property, termed the hyducton, confines active/unbound protons or hydronium ions to a region of low volume close to the membrane surface. In turn, a von Grotthuß mechanism rapidly moves proton substrate in accordance with nano-electrochemical poles on the membrane surface created by powerful proton pumps such as ATP synthase.

Thermodynamics and kinetics of the FoF1-ATPase: application of the probability isotherm

We use the results of recent publications as vehicles with which to discuss the thermodynamics of the proton-driven mitochondrial F o F1-ATP synthase, focusing particularly on the possibility that there may be dissociation between rotatory steps and ATP synthesis/hydrolysis. Such stoichiometric 'slippage' has been invoked in the literature to explain observed non-ideal behaviour. Numerical solution of the Rate Isotherm (the kinetic equivalent of the more fundamental Probability Isotherm) suggests that such 'slippage' is an unlikely explanation; instead, we suggest that the experimental results may be more consistent with damage to the enzyme caused by its isolation from the biomembrane and its experimental fixation, resulting in non-physiological friction within the enzyme's rotary mechanism. We emphasize the unavoidable constraint of the Second Law as instantiated by the obligatory dissipation of Gibbs Free Energy if the synthase is to operate at anything other than thermodynamic equilibrium. We use further numerical solution of the Rate Isotherm to demonstrate that there is no necessary association of low thermodynamic efficiency with high metabolic rates in a bio-world in which the dominating mechanism of metabolic control is multifactorial enzyme activation.

The c-Ring of the F1FO-ATP Synthase: Facts and Perspectives

The F1FO-ATP synthase is the only enzyme in nature endowed with bi-functional catalytic mechanism of synthesis and hydrolysis of ATP. The enzyme functions, not only confined to energy transduction, are tied to three intrinsic features of the annular arrangement of c subunits which constitutes the so-called c-ring, the core of the membrane-embedded FO domain: (i) the c-ring constitution is linked to the number of ions (H(+) or Na(+)) channeled across the membrane during the dissipation of the transmembrane electrochemical gradient, which in turn determines the species-specific bioenergetic cost of ATP, the "molecular currency unit" of energy transfer in all living beings; (ii) the c-ring is increasingly involved in the mitochondrial permeability transition, an event linked to cell death and to most mitochondrial dysfunctions; (iii) the c subunit species-specific amino acid sequence and susceptibility to post-translational modifications can address antibacterial drug design according to the model of enzyme inhibitors which target the c subunits. Therefore, the simple c-ring structure not only allows the F1FO-ATP synthase to perform the two opposite tasks of molecular machine of cell life and death, but it also amplifies the enzyme's potential role as a drug target.

How does transmembrane electrochemical potential drive the rotation of Fo motor in an ATP synthase?

While the field of ATP synthase research has a long history filled with landmark discoveries, recent structural works provide us with important insights into the mechanisms that links the proton movement with the rotation of the Fo motor. Here, we propose a mechanism of unidirectional rotation of the Fo complex, which is in agreement with these new structural insights as well as our more general ΔΨ-driving hypothesis of membrane proteins: A proton path in the rotor-stator interface is formed dynamically in concert with the rotation of the Fo rotor. The trajectory of the proton viewed in the reference system of the rotor (R-path) must lag behind that of the stator (S-path). The proton moves from a higher energy site to a lower site following both trajectories simultaneously. The two trajectories meet each other at the transient proton-binding site, resulting in a relative rotation between the rotor and stator. The kinetic energy of protons gained from ΔΨ is transferred to the c-ring as the protons are captured sequentially by the binding sites along the proton path, thus driving the unidirectional rotation of the c-ring. Our ΔΨ-driving hypothesis on Fo motor is an attempt to unveil the robust mechanism of energy conversion in the highly conserved, ubiquitously expressed rotary ATP synthases.

A low phosphorylation potential in the acetogen Acetobacterium woodii reflects its lifestyle at the thermodynamic edge of life

The anaerobic, acetogenic bacterium Acetobacterium woodii grows on hydrogen and carbon dioxide and uses the Wood-Ljungdahl pathway to fix carbon but also to synthesize ATP. The free energy change of acetogenesis from H2 + CO2 allows for synthesis of only a fraction of an ATP under environmental conditions, and A. woodii is clearly a paradigm for microbial life under extreme energy limitation. However, it was unknown how much energy is required to make ATP under these conditions. In the present study, we determined the phosphorylation potential in cells metabolizing three different acetogenic substrates. It accounts to 37.9 ± 1.3 kJ/mol ATP during acetogenesis from fructose, 32.1 ± 0.3 kJ/mol ATP during acetogenesis from H2 + CO2 and 30.2 ± 0.9 kJ/mol ATP during acetogenesis from CO, the lowest phosphorylation potential ever described. The physiological consequences in terms of energy conservation under extreme energy limitation are discussed.

Opposite rotation directions in the synthesis and hydrolysis of ATP by the ATP synthase: hints from a subunit asymmetry

The ATP synthase can be imagined as a reversible H(+)-translocating channel embedded in the membrane, FO portion, coupled to a protruding catalytic portion, F1. Under physiological conditions the F1FO complex synthesizes ATP by exploiting the transmembrane electrochemical gradient of protons and their downhill movement. Alternatively, under other patho-physiological conditions it exploits ATP hydrolysis to energize the membrane by uphill pumping protons. The reversibility of the mechanism is guaranteed by the structural coupling between the hydrophilic F1 and the hydrophobic FO. Which of the two opposite processes wins in the energy-transducing membrane complex depends on the thermodynamic balance between the protonmotive force (Δp) and the phosphorylation potential of ATP (ΔG P). Accordingly, while Δp prevalence drives ATP synthesis by translocating protons from the membrane P-side to the N-side and generating anticlockwise torque rotation (viewed from the matrix), ΔG P drives ATP hydrolysis by chemomechanical coupling of FO to F1 with clockwise torque. The direction of rotation is the same in all the ATP synthases, due to the conserved steric arrangement of the chiral a subunit of FO. The ability of this coupled bi-functional complex to produce opposite rotations in ATP synthesis and hydrolysis is explained on the basis of the a subunit asymmetry.

The a subunit asymmetry dictates the two opposite rotation directions in the synthesis and hydrolysis of ATP by the mitochondrial ATP synthase

The main and best known role of the mitochondrial ATP synthase is to synthesize ATP by exploiting the transmembrane electrochemical gradient of protons and their downhill movement. However, under different conditions, the same enzyme can also switch to the opposite function of ATP hydrolysis and exploits its energy to pump protons against their gradient and energize the membrane. The change in functionality is linked to the change of direction of rotation of the two matched sectors of this unique complex, namely the hydrophilic F1, which performs the catalysis, and the hydrophobic membrane-embedded FO, which channels protons. Accordingly, viewed from the matrix side, ATP synthesis is driven by counterclockwise rotation and ATP hydrolysis by clockwise rotation of the FO rotor which is transmitted to F1. ATP dissipation through this mechanism features some diseases such as myocardial ischemia. Increasing evidence shoulders the hypothesis that the asymmetry of the a subunit of FO and particularly the steric arrangement of the two inner semi-channels for protons, play a key role in conferring to the coupled bi-functional complex the ability to reverse rotation by switching from ATP synthesis to ATP hydrolysis and vice versa. Accordingly, the conserved steric arrangement of the chiral a subunit of FO yields the same direction of rotation for all the ATP synthases. According to this hypothesis, the a subunit chirality imposes the direction of rotation of the rotor according to the proton gradient across the membrane. It seems likely that the direction of rotation of the membrane-embedded c-ring, which is adjacent to the a-subunit and acts as a rotor, may be under multiple control, being rotation essential to make the whole enzyme machinery work. However, the asymmetric features of the a subunit would make it the master regulator, thus directly determining which of the two functions, ATP production or ATP dissipation, will be performed. The handedness of a subunit should be considered in drug design to counteract tissue damage under all pathological conditions linked to functional impairment of ATP synthase.