Thermodynamics of proton transport coupled ATP synthesis

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.

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.

Modulation of the H+/ATP coupling ratio by ADP and ATP as a possible regulatory feature in the F-type ATP synthases

F-type ATP synthases are transmembrane enzymes, which play a central role in the metabolism of all aerobic and photosynthetic cells and organisms, being the major source of their ATP synthesis. Catalysis occurs via a rotary mechanism, in which the free energy of a transmembrane electrochemical ion gradient is converted into the free energy of ATP phosphorylation from ADP and Pi, and vice versa. An ADP, tightly bound to one of the three catalytic sites on the stator head, is associated with catalysis inhibition, which is relieved by the transmembrane proton gradient and by ATP. By preventing wasteful ATP hydrolysis in times of low osmotic energy and low ATP/ADP ratio, such inhibition constitutes a classical regulatory feedback effect, likely to be an integral component of in vivo regulation. The present miniview focuses on an additional putative regulatory phenomenon, which has drawn so far little attention, consisting in a substrate-induced tuning of the H+/ATP coupling ratio during catalysis, which might represent an additional key to energy homeostasis in the cell. Experimental pieces of evidence in support of such a phenomenon are reviewed.

Disentangling chloroplast ATP synthase regulation by proton motive force and thiol modulation in Arabidopsis leaves

The chloroplast ATP synthase (CF₁F_o) contains a specific feature to the green lineage: a γ-subunit redox domain that contains a cysteine couple which interacts with the torque-transmitting βDELSEED-loop. This thiol modulation equips CF₁F_o with an important environmental fine-tuning mechanism. In vitro, disulfide formation in the γ-redox domain slows down the activity of the CF₁F_o at low transmembrane electrochemical proton gradient ( [Formula: see text] ), which agrees with its proposed role as chock based on recently solved structure. The γ-dithiol formation at the onset of light is crucial to maximize photosynthetic efficiency since it lowers the [Formula: see text] activation level for ATP synthesis in vitro. Here, we validate these findings in vivo by utilizing absorption spectroscopy in Arabidopsis thaliana. To do so, we monitored the [Formula: see text] present in darkness and identified its mitochondrial sources. By following the fate and components of light-induced extra [Formula: see text] , we estimated the ATP lifetime that lasted up to tens of minutes after long illuminations. Based on the relationship between [Formula: see text] and CF₁F_o activity, we conclude that the dithiol configuration in vivo facilitates photosynthesis by driving the same ATP synthesis rate at a significative lower [Formula: see text] than in the γ-disulfide state. The presented in vivo findings are an additional proof of the importance of CF₁F_o thiol modulation, reconciling biochemical in vitro studies and structural insights.

Mechanisms of Energy Transduction by Charge Translocating Membrane Proteins

Life relies on the constant exchange of different forms of energy, i.e., on energy transduction. Therefore, organisms have evolved in a way to be able to harvest the energy made available by external sources (such as light or chemical compounds) and convert these into biological useable energy forms, such as the transmembrane difference of electrochemical potential (Δμ̃). Membrane proteins contribute to the establishment of Δμ̃ by coupling exergonic catalytic reactions to the translocation of charges (electrons/ions) across the membrane. Irrespectively of the energy source and consequent type of reaction, all charge-translocating proteins follow two molecular coupling mechanisms: direct- or indirect-coupling, depending on whether the translocated charge is involved in the driving reaction. In this review, we explore these two coupling mechanisms by thoroughly examining the different types of charge-translocating membrane proteins. For each protein, we analyze the respective reaction thermodynamics, electron transfer/catalytic processes, charge-translocating pathways, and ion/substrate stoichiometries.

Thermodynamic marking of FOF1 ATP synthase

F_OF₁ ATP synthase is a ~100% efficient molecular machine for energy conversion in biology, and holds great lessons for man-made energy technology and nanotechnology. In light of formidable biocomplexity of the F_OF₁ machinery, its modeling from pure physical principles remains difficult and rare. Here we construct a thermodynamic model of F_OF₁ from experimentally accessible quantities plus a single entropy production that generally has vanishingly small values (<1k_B). Based on the physical inputs, this model captures F_OF₁ performance observed over an exhaustively wide range of proton-motive force and nucleotide concentrations. The model predicts a distinct 1/8k_BT slope for ATP synthesis rate versus proton-motive force, which is verified by experimental data and represents a profound thermodynamic marking of this amazingly efficient machine operating near a universal limit of the 2nd law of thermodynamics. The model further predicts two symmetries of heat productions, which are testable by available experimental techniques and offer quantitative constraints on F_OF₁'s possible mechanisms behind its ~100% efficiency.

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

The most recent contribution by Sunil Nath in these pages is, mostly, a repetition of his previous claims regarding failures of the chemiosmotic hypotheses, supplemented with some fresh misunderstandings of the points I had sought to clarify in my previous critique⁠. Considerable portions rehash 50-60 years-old controversies, with no apparent understanding that the current chemiosmotic hypothesis, while birthed by Mitchell, differs from Mitchell's details in many respects. As such, Nath has devoted much time dealing with a few errors (or wrong hypotheses) by Mitchell (in a few places I would almost venture to say "typographical mistakes in typesetting") and presents the ensuing conclusions as "refutations" of the chemiosmotic paradigm, completely neglecting that such details (such as the precise H⁺/ATP or H⁺:O ratios) are completely irrelevant to the reality (or not) of an electron-transport chain that uses the free energy liberated by electron-transfer to remove H⁺ from a compartment, to which it returns through and ATP synthase which uses the energy in that spontaneous return to drive ATP synthesis. The thermodynamical mistakes and misunderstandings of the relevant literature present in Nath's new contribution are so numerous, though, that I feel forced to call the attention of the readers of "Biophysical Chemistry" to them.

Temperature-dependent regulation of electron transport and ATP synthesis in chloroplasts in vitro and in silico

The significance of temperature-dependent regulation of photosynthetic apparatus (PSA) is determined by the fact that plant temperature changes with environmental temperature. In this work, we present a brief overview of temperature-dependent regulation of photosynthetic processes in class B chloroplasts (thylakoids) and analyze these processes using a computer model that takes into account the key stages of electron and proton transport coupled to ATP synthesis. The rate constants of partial reactions were parametrized on the basis of experimental temperature dependences of partial photosynthetic processes: (1) photosystem II (PSII) turnover and plastoquinone (PQ) reduction, (2) the plastoquinol (PQH₂) oxidation by the cytochrome (Cyt) b₆f complex, (3) the ATP synthase activity, and (4) the proton leak from the thylakoid lumen. We consider that PQH₂ oxidation is the rate-limiting step in the intersystem electron transport. The parametrization of the rate constants of these processes is based on earlier experimental data demonstrating strong correlations between the functional and structural properties of thylakoid membranes that were probed with the lipid-soluble spin labels embedded into the membranes. Within the framework of our model, we could adequately describe a number of experimental temperature dependences of photosynthetic reactions in thylakoids. Computer modeling of electron and proton transport coupled to ATP synthesis supports the notion that PQH₂ oxidation by the Cyt b₆f complex and proton pumping into the lumen are the basic temperature-dependent processes that determine the overall electron flux from PSII to molecular oxygen and the net ATP synthesis upon variations of temperature. The model describes two branches of the temperature dependence of the post-illumination reduction of [Formula: see text] characterized by different activation energies (about 60 and ≤ 3.5 kJ mol^-1). The model predicts the bell-like temperature dependence of ATP formation, which arises from the balance of several factors: (1) the thermo-induced acceleration of electron transport through the Cyt b₆f complex, (2) deactivation of PSII photochemistry at sufficiently high temperatures, and (3) acceleration of the passive proton outflow from the thylakoid lumen bypassing the ATP synthase complex. The model describes the temperature dependence of experimentally measured parameter P/2e, determined as the ratio between the rates of ATP synthesis and pseudocyclic electron transport (H₂O → PSII → PSI → O₂).

Protonic conductor: better understanding neural resting and action potential

With the employment of the transmembrane electrostatic proton localization theory with a new membrane potential equation, neural resting and action potential is now much better understood as the voltage contributed by the localized protons/cations at a neural liquid- membrane interface. Accordingly, the neural resting/action potential is essentially a protonic/cationic membrane capacitor behavior. It is now understood with a newly formulated action potential equation: when action potential is <0 (negative number), the localized protons/cations charge density at the liquid-membrane interface along the periplasmic side is >0 (positive number); when the action potential is >0, the concentration of the localized protons and localized nonproton cations is <0, indicating a "depolarization" state. The nonlinear curve of the localized protons/cations charge density in the real-time domain of an action potential spike appears as an inverse mirror image to the action potential. The newly formulated action potential equation provides biophysical insights for neuron electrophysiology, which may represent a complementary development to the classic Goldman-Hodgkin-Katz equation. With the use of the action potential equation, the biological significance of axon myelination is now also elucidated as to provide protonic insulation and prevent any ions both inside and outside of the neuron from interfering with the action potential signal, so that the action potential can quickly propagate along the axon with minimal (e.g., 40 times less) energy requirement.NEW & NOTEWORTHY The newly formulated action potential equation provides biophysical insights for neuron electrophysiology, which may represent a complementary development to the classic Goldman-Hodgkin-Katz equation. The nonlinear curve of the localized protons/cations charge density in the real-time domain of an action potential spike appears as an inverse mirror image to the action potential. The biological significance of axon myelination is now elucidated as to provide protonic insulation and prevent any ions from interfering with action potential signal.

Chemiosmotic misunderstandings

Recent publications have questioned the appropriateness of the chemiosmotic theory, a key tenet of modern bioenergetics originally described by Mitchell and since widely improved upon and applied. In one of them, application of Gauss' law to a model charge distribution in mitochondria was argued to refute the possibility of ATP generation through H⁺ movement in the absence of a counterion, whereas a different author advocated, for other reasons, the impossibility of chemiosmosis and proposed that a novel energy-generation scheme (referred to as "murburn") relying on superoxide-catalyzed (or superoxide-promoted) ADP phosphorylation would operate instead. In this letter, those proposals are critically examined and found to be inconsistent with established experimental data and new theoretical calculations.

Evolution of C4 photosynthesis predicted by constraint-based modelling

Constraint-based modelling (CBM) is a powerful tool for the analysis of evolutionary trajectories. Evolution, especially evolution in the distant past, is not easily accessible to laboratory experimentation. Modelling can provide a window into evolutionary processes by allowing the examination of selective pressures which lead to particular optimal solutions in the model. To study the evolution of C4 photosynthesis from a ground state of C3 photosynthesis, we initially construct a C3 model. After duplication into two cells to reflect typical C4 leaf architecture, we allow the model to predict the optimal metabolic solution under various conditions. The model thus identifies resource limitation in conjunction with high photorespiratory flux as a selective pressure relevant to the evolution of C4. It also predicts that light availability and distribution play a role in guiding the evolutionary choice of possible decarboxylation enzymes. The data shows evolutionary CBM in eukaryotes predicts molecular evolution with precision.

Integrated thermodynamic analysis of electron bifurcating [FeFe]-hydrogenase to inform anaerobic metabolism and H2 production

Electron bifurcating, [FeFe]-hydrogenases are recently described members of the hydrogenase family and catalyze a combination of exergonic and endergonic electron exchanges between three carriers (2 ferredoxin_red^- + NAD(P)H + 3 H⁺ = 2 ferredoxin_ox + NAD(P)⁺ + 2 H₂). A thermodynamic analysis of the bifurcating, [FeFe]-hydrogenase reaction, using electron path-independent variables, quantified potential biological roles of the reaction without requiring enzyme details. The bifurcating [FeFe]-hydrogenase reaction, like all bifurcating reactions, can be written as a sum of two non-bifurcating reactions. Therefore, the thermodynamic properties of the bifurcating reaction can never exceed the properties of the individual, non-bifurcating, reactions. The bifurcating [FeFe]-hydrogenase reaction has three competitive properties: 1) enabling NAD(P)H-driven proton reduction at pH₂ higher than the concurrent operation of the two, non-bifurcating reactions, 2) oxidation of NAD(P)H and ferredoxin simultaneously in a 1:1 ratio, both are produced during typical glucose fermentations, and 3) enhanced energy conservation (~10 kJ mol^-1 H₂) relative to concurrent operation of the two, non-bifurcating reactions. Our analysis demonstrated ferredoxin E°' largely determines the sensitivity of the bifurcating reaction to pH₂, modulation of the reduced/oxidized electron carrier ratios contributed less to equilibria shifts. Hydrogenase thermodynamics data were integrated with typical and non-typical glycolysis pathways to evaluate achieving the 'Thauer limit' (4 H₂ per glucose) as a function of temperature and pH₂. For instance, the bifurcating [FeFe]-hydrogenase reaction permits the Thauer limit at 60 °C if pH ₂ ≤ ~10 mbar. The results also predict Archaea, expressing a non-typical glycolysis pathway, would not benefit from a bifurcating [FeFe]-hydrogenase reaction; interestingly, no Archaea have been observed experimentally with a [FeFe]-hydrogenase enzyme.

Computational modelling predicts substantial carbon assimilation gains for C3 plants with a single-celled C4 biochemical pump

Achieving global food security for the estimated 9 billion people by 2050 is a major scientific challenge. Crop productivity is fundamentally restricted by the rate of fixation of atmospheric carbon. The dedicated enzyme, RubisCO, has a low turnover and poor specificity for CO2. This limitation of C3 photosynthesis (the basic carbon-assimilation pathway present in all plants) is alleviated in some lineages by use of carbon-concentrating-mechanisms, such as the C4 cycle-a biochemical pump that concentrates CO2 near RubisCO increasing assimilation efficacy. Most crops use only C3 photosynthesis, so one promising research strategy to boost their productivity focuses on introducing a C4 cycle. The simplest proposal is to use the cycle to concentrate CO2 inside individual chloroplasts. The photosynthetic efficiency would then depend on the leakage of CO2 out of a chloroplast. We examine this proposal with a 3D spatial model of carbon and oxygen diffusion and C4 photosynthetic biochemistry inside a typical C3-plant mesophyll cell geometry. We find that the cost-efficiency of C4 photosynthesis depends on the gas permeability of the chloroplast envelope, the C4 pathway having higher quantum efficiency than C3 for permeabilities below 300 μm/s. However, at higher permeabilities the C4 pathway still provides a substantial boost to carbon assimilation with only a moderate decrease in efficiency. The gains would be capped by the ability of chloroplasts to harvest light, but even under realistic light regimes a 100% boost to carbon assimilation is possible. This could be achieved in conjunction with lower investment in chloroplasts if their cell surface coverage is also reduced. Incorporation of this C4 cycle into C3 crops could thus promote higher growth rates and better drought resistance in dry, high-sunlight climates.

The Cytochrome b 6 f Complex: Biophysical Aspects of Its Functioning in Chloroplasts

This chapter presents an overview of structural properties of the cytochrome (Cyt) b ₆ f complex and its functioning in chloroplasts. The Cyt b ₆ f complex stands at the crossroad of photosynthetic electron transport pathways, providing connectivity between Photosystem (PSI) and Photosysten II (PSII) and pumping protons across the membrane into the thylakoid lumen. After a brief review of the chloroplast electron transport chain, the consideration is focused on the structural organization of the Cyt b ₆ f complex and its interaction with plastoquinol (PQH₂, reduced form of plastoquinone), a mediator of electron transfer from PSII to the Cyt b ₆ f complex. The processes of PQH₂ oxidation by the Cyt b ₆ f complex have been considered within the framework of the Mitchell's Q-cycle. The overall rate of the intersystem electron transport is determined by PQH₂ turnover at the quinone-binding site Q_o of the Cyt b ₆ f complex. The rate of PQH₂ oxidation is controlled by the intrathylakoid pH_in, which value determines the protonation/deprotonation events in the Q_o-center. Two other regulatory mechanisms associated with the Cyt b ₆ f complex are briefly overviewed: (i) redistribution of electron fluxes between alternative (linear and cyclic) pathways, and (ii) "state transitions" related to redistribution of solar energy between PSI and PSII.

A facilitated diffusion model constrained by the probability isotherm: a pedagogical exercise in intuitive non-equilibrium thermodynamics

This paper seeks to develop a more thermodynamically sound pedagogy for students of biological transport than is currently available from either of the competing schools of linear non-equilibrium thermodynamics (LNET) or Michaelis-Menten kinetics (MMK). To this end, a minimal model of facilitated diffusion was constructed comprising four reversible steps: cis-substrate binding, cis→trans bound enzyme shuttling, trans-substrate dissociation and trans→cis free enzyme shuttling. All model parameters were subject to the second law constraint of the probability isotherm, which determined the unidirectional and net rates for each step and for the overall reaction through the law of mass action. Rapid equilibration scenarios require sensitive 'tuning' of the thermodynamic binding parameters to the equilibrium substrate concentration. All non-equilibrium scenarios show sigmoidal force-flux relations, with only a minority of cases having their quasi-linear portions close to equilibrium. Few cases fulfil the expectations of MMK relating reaction rates to enzyme saturation. This new approach illuminates and extends the concept of rate-limiting steps by focusing on the free energy dissipation associated with each reaction step and thereby deducing its respective relative chemical impedance. The crucial importance of an enzyme's being thermodynamically 'tuned' to its particular task, dependent on the cis- and trans-substrate concentrations with which it deals, is consistent with the occurrence of numerous isoforms for enzymes that transport a given substrate in physiologically different circumstances. This approach to kinetic modelling, being aligned with neither MMK nor LNET, is best described as intuitive non-equilibrium thermodynamics, and is recommended as a useful adjunct to the design and interpretation of experiments in biotransport.

Photosynthetic Electron and Proton Transport in Chloroplasts: EPR Study of ΔpH Generation, an Overview

This is a brief overview focused on the electron paramagnetic resonance applications to the study of the proton transport processes in chloroplasts. After brief description of structural and functional organization of the chloroplast electron transport chain, our attention is focused on the measurements of trans-thylakoid pH difference (ΔpH) with pH-sensitive spin-probes. The use of spin-probes is based either (i) on measuring the ΔpH-partitioning of spin-probes between the thylakoid lumen and external volume, or (ii) on monitoring changes in the electron paramagnetic resonance spectra of pH-sensitive nitroxide radicals located in the lumen. Along with the use of spin-probes, the intra-thylakoid pH (pH_in) can be determined by the "kinetic" method, which relies on the fact that the rate-limiting step in the chain of photosynthetic electron transfer (plastoquinol oxidation by the cytochrome b ₆ f complex) is controlled by pH_in. The results of ΔpH determinations in chloroplasts based on the use of pH-sensitive spin-probes and measurements of post-illumination reduction of photoreaction centers of Photosystem I are discussed in the context of the problem of energy coupling in laterally heterogeneous lamellar system of chloroplasts.

Perfect chemomechanical coupling of FoF1-ATP synthase

F_oF₁-ATP synthase (F_oF₁) couples H⁺ flow in F_o domain and ATP synthesis/hydrolysis in F₁ domain through rotation of the central rotor shaft, and the H⁺/ATP ratio is crucial to understand the coupling mechanism and energy yield in cells. Although H⁺/ATP ratio of the perfectly coupling enzyme can be predicted from the copy number of catalytic β subunits and that of H⁺ binding c subunits as c/β, the actual H⁺/ATP ratio can vary depending on coupling efficiency. Here, we report actual H⁺/ATP ratio of thermophilic Bacillus F_oF₁, whose c/β is 10/3. Proteoliposomes reconstituted with the F_oF₁ were energized with ΔpH and Δψ by the acid-base transition and by valinomycin-mediated diffusion potential of K⁺ under various [ATP]/([ADP]⋅[Pi]) conditions, and the initial rate of ATP synthesis/hydrolysis was measured. Analyses of thermodynamically equilibrated states, where net ATP synthesis/hydrolysis is zero, show linear correlation between the chemical potential of ATP synthesis/hydrolysis and the proton motive force, giving the slope of the linear function, that is, H⁺/ATP ratio, 3.3 ± 0.1. This value agrees well with the c/β ratio. Thus, chemomechanical coupling between F_o and F₁ is perfect.

Catalytic robustness and torque generation of the F1-ATPase

The F₁-ATPase is the catalytic portion of the F_oF₁ ATP synthase and acts as a rotary molecular motor when it hydrolyzes ATP. Two decades have passed since the single-molecule rotation assay of F₁-ATPase was established. Although several fundamental issues remain elusive, basic properties of F-type ATPases as motor proteins have been well characterized, and a large part of the reaction scheme has been revealed by the combination of extensive structural, biochemical, biophysical, and theoretical studies. This review is intended to provide a concise summary of the fundamental features of F₁-ATPases, by use of the well-described model F₁ from the thermophilic Bacillus PS3 (TF₁). In the last part of this review, we focus on the robustness of the rotary catalysis of F₁-ATPase to provide a perspective on the re-designing of novel molecular machines.

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.