Nonequilibrium Dissipation-free Transport in F1-ATPase and the Thermodynamic Role of Asymmetric Allosterism

F₁-ATPase (or F₁), the highly efficient and reversible biochemical engine, has motivated physicists as well as biologists to imagine the design principles governing machines in the fluctuating world. Recent experiments have clarified yet another interesting property of F₁; the dissipative heat inside the motor is very small, irrespective of the velocity of rotation and energy transport. Conceptual interest is devoted to the fact that the amount of internal dissipation is not simply determined by the sequence of equilibrium pictures, but also relies on the rotational-angular dependence of nucleotide affinity, which is a truly nonequilibrium aspect. We propose that the totally asymmetric allosteric model (TASAM), where adenosine triphosphate (ATP) binding to F₁ is assumed to have low dependence on the angle of the rotating shaft, produces results that are most consistent with the experiments. Theoretical analysis proves the crucial role of two time scales in the model, which explains the universal mechanism to produce the internal dissipation-free feature. The model reproduces the characteristic torque dependence of the rotational velocity of F₁ and predicts that the internal dissipation upon the ATP synthesis direction rotation becomes large at the low nucleotide condition.     

The regulatory subunit ε in Escherichia coli FOF1-ATP synthase

F-type ATP synthases are extraordinary multisubunit proteins that operate as nanomotors. The Escherichia coli (E. coli) enzyme uses the proton motive force (pmf) across the bacterial plasma membrane to drive rotation of the central rotor subunits within a stator subunit complex. Through this mechanical rotation, the rotor coordinates three nucleotide binding sites that sequentially catalyze the synthesis of ATP. Moreover, the enzyme can hydrolyze ATP to turn the rotor in the opposite direction and generate pmf. The direction of net catalysis, i.e. synthesis or hydrolysis of ATP, depends on the cell's bioenergetic conditions. Different control mechanisms have been found for ATP synthases in mitochondria, chloroplasts and bacteria. This review discusses the auto-inhibitory behavior of subunit ε found in F_OF₁-ATP synthases of many bacteria. We focus on E. coli F_OF₁-ATP synthase, with insights into the regulatory mechanism of subunit ε arising from structural and biochemical studies complemented by single-molecule microscopy experiments.     

One rotary mechanism for F1-ATPase over ATP concentrations from millimolar down to nanomolar

F₁-ATPase is a rotary molecular motor in which the central γ-subunit rotates inside a cylinder made of α₃β₃-subunits. The rotation is driven by ATP hydrolysis in three catalytic sites on the β-subunits. How many of the three catalytic sites are filled with a nucleotide during the course of rotation is an important yet unsettled question. Here we inquire whether F₁ rotates at extremely low ATP concentrations where the site occupancy is expected to be low. We observed under an optical microscope rotation of individual F₁ molecules that carried a bead duplex on the γ-subunit. Time-averaged rotation rate was proportional to the ATP concentration down to 200 pM, giving an apparent rate constant for ATP binding of 2 × 10⁷ M⁻¹s⁻¹. A similar rate constant characterized bulk ATP hydrolysis in solution, which obeyed a simple Michaelis-Menten scheme between 6 mM and 60 nM ATP. F₁ produced the same torque of ~40 pN·nm at 2 mM, 60 nM, and 2 nM ATP. These results point to one rotary mechanism governing the entire range of nanomolar to millimolar ATP, although a switchover between two mechanisms cannot be dismissed. Below 1 nM ATP, we observed less regular rotations, indicative of the appearance of another reaction scheme.     

The mechanism of rotating proton pumping ATPases

Two proton pumps, the F-ATPase (ATP synthase, F_oF₁) and the V-ATPase (endomembrane proton pump), have different physiological functions, but are similar in subunit structure and mechanism. They are composed of a membrane extrinsic (F₁ or V₁) and a membrane intrinsic (F_o or V_o) sector, and couple catalysis of ATP synthesis or hydrolysis to proton transport by a rotational mechanism. The mechanism of rotation has been extensively studied by kinetic, thermodynamic and physiological approaches. Techniques for observing subunit rotation have been developed. Observations of micron-length actin filaments, or polystyrene or gold beads attached to rotor subunits have been highly informative of the rotational behavior of ATP hydrolysis-driven rotation. Single molecule FRET experiments between fluorescent probes attached to rotor and stator subunits have been used effectively in monitoring proton motive force-driven rotation in the ATP synthesis reaction. By using small gold beads with diameters of 40-60 nm, the E. coli F₁ sector was found to rotate at surprisingly high speeds (> 400 rps). This experimental system was used to assess the kinetics and thermodynamics of mutant enzymes. The results revealed that the enzymatic reaction steps and the timing of the domain interactions among the β subunits, or between the β and γ subunits, are coordinated in a manner that lowers the activation energy for all steps and avoids deep energy wells through the rotationally-coupled steady-state reaction. In this review, we focus on the mechanism of steady-state F₁-ATPase rotation, which maximizes the coupling efficiency between catalysis and rotation.     

Effect of external torque on the ATP-driven rotation of F1-ATPase

F₁-ATPase is a rotary molecular motor powered by the torque generated by another rotary motor F₀ to synthesize ATP in vivo. Therefore elucidation of the behavior of F₁ under external torque is very important. Here, we applied controlled external torque by electrorotation and investigated the ATP-driven rotation for the first time. The rotation was accelerated by assisting torque and decelerated by hindering torque, but F₁ rarely showed rotations in the ATP synthesis direction. This is consistent with the prediction by models based on the assumption that the rotation is tightly coupled to ATP hydrolysis and synthesis. At low ATP concentrations (2 and 5 μM), 120° stepwise rotation was observed. Due to the temperature rise during experiment, quantitative interpretation of the data is difficult, but we found that the apparent rate constant of ATP binding clearly decreased by hindering torque and increased by assisting torque.     

Stiffness of γ subunit of F1-ATPase

F₁-ATPase is a molecular motor in which the γ subunit rotates inside the α₃β₃ ring upon adenosine triphosphate (ATP) hydrolysis. Recent works on single-molecule manipulation of F₁-ATPase have shown that kinetic parameters such as the on-rate of ATP and the off-rate of adenosine diphosphate (ADP) strongly depend on the rotary angle of the γ subunit (Hirono-Hara et al. 2005; Iko et al. 2009). These findings provide important insight into how individual reaction steps release energy to power F₁ and also have implications regarding ATP synthesis and how reaction steps are reversed upon reverse rotation. An important issue regarding the angular dependence of kinetic parameters is that the angular position of a magnetic bead rotation probe could be larger than the actual position of the γ subunit due to the torsional elasticity of the system. In the present study, we assessed the stiffness of two different portions of F₁ from thermophilic Bacillus PS3: the internal part of the γ subunit embedded in the α₃β₃ ring, and the complex of the external part of the γ subunit and the α₃β₃ ring (and streptavidin and magnetic bead), by comparing rotational fluctuations before and after crosslinkage between the rotor and stator. The torsional stiffnesses of the internal and remaining parts were determined to be around 223 and 73 pNnm/radian, respectively. Based on these values, it was estimated that the actual angular position of the internal part of the γ subunit is one-fourth of the magnetic bead position upon stalling using an external magnetic field. The estimated elasticity also partially explains the accommodation of the intrinsic step size mismatch between F_o and F₁-ATPase.     

Single-Molecule Analysis of the Rotation of F1-ATPase under High Hydrostatic Pressure

F₁-ATPase is the water-soluble part of ATP synthase and is an ATP-driven rotary molecular motor that rotates the rotary shaft against the surrounding stator ring, hydrolyzing ATP. Although the mechanochemical coupling mechanism of F₁-ATPase has been well studied, the molecular details of individual reaction steps remain unclear. In this study, we conducted a single-molecule rotation assay of F₁ from thermophilic bacteria under various pressures from 0.1 to 140 MPa. Even at 140 MPa, F₁ actively rotated with regular 120° steps in a counterclockwise direction, showing high conformational stability and retention of native properties. Rotational torque was also not affected. However, high hydrostatic pressure induced a distinct intervening pause at the ATP-binding angles during continuous rotation. The pause was observed under both ATP-limiting and ATP-saturating conditions, suggesting that F₁ has two pressure-sensitive reactions, one of which is evidently ATP binding. The rotation assay using a mutant F₁(βE190D) suggested that the other pressure-sensitive reaction occurs at the same angle at which ATP binding occurs. The activation volumes were determined from the pressure dependence of the rate constants to be +100 Å³ and +88 Å³ for ATP binding and the other pressure-sensitive reaction, respectively. These results are discussed in relation to recent single-molecule studies of F₁ and pressure-induced protein unfolding.     

Theoretical Analysis of the F1-ATPase Experimental Data

F₁-ATPase is a rotatory molecular motor fueled by ATP nucleotides. Different loads can be attached to the motor axis to show that it rotates in main discrete steps of 120° with substeps of ∼80° and 40°. Experimental data show the dependence on the mean rotational velocity ω with respect to the external control parameters: the nucleotide concentration [ATP] and the friction of the load γ_L. In this work we present a theoretical analysis of the experimental data whose main results are: 1), A derivation of a simple analytical formula for ω([ATP], γ_L) that compares favorably with experiments; 2), The introduction of a two-state flashing ratchet model that exhibits experimental phenomenology of a greater specificity than has been, to our knowledge, previously available; 3), The derivation of an argument to obtain the values of the substep sizes; 4), An analysis of the energy constraints of the model; and 5), The theoretical analysis of the coupling ratio between the ATP consumed and the success of a forward step. We also discuss the compatibility of our approach with recent experimental observations.     

Torque Generation Mechanism of F1-ATPase upon NTP Binding

Molecular machines fueled by NTP play pivotal roles in a wide range of cellular activities. One common feature among NTP-driven molecular machines is that NTP binding is a major force-generating step among the elementary reaction steps comprising NTP hydrolysis. To understand the mechanism in detail,in this study, we conducted a single-molecule rotation assay of the ATP-driven rotary motor protein F₁-ATPase using uridine triphosphate (UTP) and a base-free nucleotide (ribose triphosphate) to investigate the impact of a pyrimidine base or base depletion on kinetics and force generation. Although the binding rates of UTP and ribose triphosphate were 10³ and 10⁶ times, respectively, slower than that of ATP, they supported rotation, generating torque comparable to that generated by ATP. Affinity change of F₁ to UTP coupled with rotation was determined, and the results again were comparable to those for ATP, suggesting that F₁ exerts torque upon the affinity change to UTP via rotation similar to ATP-driven rotation. Thus, the adenine-ring significantly enhances the binding rate, although it is not directly involved in force generation. Taking into account the findings from another study on F₁ with mutated phosphate-binding residues, it was proposed that progressive bond formation between the phosphate region and catalytic residues is responsible for the rotation-coupled change in affinity.     

Torque Generation Mechanism of F1-ATPase upon NTP Binding

Molecular machines fueled by NTP play pivotal roles in a wide range of cellular activities. One common feature among NTP-driven molecular machines is that NTP binding is a major force-generating step among the elementary reaction steps comprising NTP hydrolysis. To understand the mechanism in detail,in this study, we conducted a single-molecule rotation assay of the ATP-driven rotary motor protein F₁-ATPase using uridine triphosphate (UTP) and a base-free nucleotide (ribose triphosphate) to investigate the impact of a pyrimidine base or base depletion on kinetics and force generation. Although the binding rates of UTP and ribose triphosphate were 10³ and 10⁶ times, respectively, slower than that of ATP, they supported rotation, generating torque comparable to that generated by ATP. Affinity change of F₁ to UTP coupled with rotation was determined, and the results again were comparable to those for ATP, suggesting that F₁ exerts torque upon the affinity change to UTP via rotation similar to ATP-driven rotation. Thus, the adenine-ring significantly enhances the binding rate, although it is not directly involved in force generation. Taking into account the findings from another study on F₁ with mutated phosphate-binding residues, it was proposed that progressive bond formation between the phosphate region and catalytic residues is responsible for the rotation-coupled change in affinity.     

Irregular activity oscillations of a rotary molecular motor: A simple kinetic model of F<Subscript>1</Subscript>-ATPase

F₁-ATPase is a catalytic part of the F₁F_o-ATP synthase molecular motor. The cooperative hydrolysis of ATP at three catalytic sites of F₁-ATPase is accompanied by the rotation of the central γ-subunit inside a cylinder formed by three α-subunits and three β-subunits. Experimental works of different authors have shown that the γ-subunit rotates with irregular dwells. A simple kinetic model suggested in this article provides an explanation as to why dwells occur during the rotation of F₁-ATPase. According to this model, rotation dwells happen as a result of deterministic chaos, which in turn occurs at rate constants that are close to those demonstrated experimentally. The time duration of dwells in the model is in agreement with that observed experimentally. Our model explains the known irregular occupancy of catalytic sites of F₁-ATPase by nucleotides.     

Single-Molecule Analysis of the Rotation of F1-ATPase under High Hydrostatic Pressure

F₁-ATPase is the water-soluble part of ATP synthase and is an ATP-driven rotary molecular motor that rotates the rotary shaft against the surrounding stator ring, hydrolyzing ATP. Although the mechanochemical coupling mechanism of F₁-ATPase has been well studied, the molecular details of individual reaction steps remain unclear. In this study, we conducted a single-molecule rotation assay of F₁ from thermophilic bacteria under various pressures from 0.1 to 140 MPa. Even at 140 MPa, F₁ actively rotated with regular 120° steps in a counterclockwise direction, showing high conformational stability and retention of native properties. Rotational torque was also not affected. However, high hydrostatic pressure induced a distinct intervening pause at the ATP-binding angles during continuous rotation. The pause was observed under both ATP-limiting and ATP-saturating conditions, suggesting that F₁ has two pressure-sensitive reactions, one of which is evidently ATP binding. The rotation assay using a mutant F₁(βE190D) suggested that the other pressure-sensitive reaction occurs at the same angle at which ATP binding occurs. The activation volumes were determined from the pressure dependence of the rate constants to be +100 Å³ and +88 Å³ for ATP binding and the other pressure-sensitive reaction, respectively. These results are discussed in relation to recent single-molecule studies of F₁ and pressure-induced protein unfolding.     

Regulation of the F1F0-ATP Synthase Rotary Nanomotor in its Monomeric-Bacterial and Dimeric-Mitochondrial Forms

The F₁F₀-adenosine triphosphate (ATP) synthase rotational motor synthesizes most of the ATP required for living from adenosine diphosphate, Pi, and a proton electrochemical gradient across energy-transducing membranes of bacteria, chloroplasts, and mitochondria. However, as a reversible nanomotor, it also hydrolyzes ATP during de-energized conditions in all energy-transducing systems. Thus, different subunits and mechanisms have emerged in nature to control the intrinsic rotation of the enzyme to favor the ATP synthase activity over its opposite and commonly wasteful ATPase turnover. Recent advances in the structural analysis of the bacterial and mitochondrial ATP synthases are summarized to review the distribution and mechanism of the subunits that are part of the central rotor and regulate its gyration. In eubacteria, the ε subunit works as a ratchet to favor the rotation of the central stalk in the ATP synthase direction by extending and contracting two α-helixes of its C-terminal side and also by binding ATP with low affinity in thermophilic bacteria. On the other hand, in bovine heart mitochondria, the so-called inhibitor protein (IF₁) interferes with the intrinsic rotational mechanism of the central γ subunit and with the opening and closing of the catalytic β-subunits to inhibit its ATPase activity. Besides its inhibitory role, the IF₁ protein also promotes the dimerization of the bovine and rat mitochondrial enzymes, albeit it is not essential for dimerization of the yeast F₁F₀ mitochondrial complex. High-resolution electron microscopy of the dimeric enzyme in its bovine and yeast forms shows a conical shape that is compatible with the role of the ATP synthase dimer in the formation of tubular the cristae membrane of mitochondria after further oligomerization. Dimerization of the mitochondrial ATP synthase diminishes the rotational drag of the central rotor that would decrease the coupling efficiency between rotation of the central stalk and ATP synthesis taking place at the F₁ portion. In addition, F₁F₀ dimerization and its further oligomerization also increase the stability of the enzyme to natural or experimentally induced destabilizing conditions.     

Thermodynamic analysis of F1‐ATPase rotary catalysis using high‐speed imaging

F₁-ATPase (F₁) is a rotary motor protein fueled by ATP hydrolysis. Although the mechanism for coupling rotation and catalysis has been well studied, the molecular details of individual reaction steps remain elusive. In this study, we performed high-speed imaging of F₁ rotation at various temperatures using the total internal reflection dark-field (TIRDF) illumination system, which allows resolution of the F₁ catalytic reaction into elementary reaction steps with a high temporal resolution of 72 µs. At a high concentration of ATP, F₁ rotation comprised distinct 80° and 40° substeps. The 80° substep, which exhibited significant temperature dependence, is triggered by the temperature-sensitive reaction, whereas the 40° substep is triggered by ATP hydrolysis and the release of inorganic phosphate (P_i). Then, we conducted Arrhenius analysis of the reaction rates to obtain the thermodynamic parameters for individual reaction steps, that is, ATP binding, ATP hydrolysis, P_i release, and TS reaction. Although all reaction steps exhibited similar activation free energy values, ΔG^‡ = 53–56 kJ mol⁻¹, the contributions of the enthalpy (ΔH^‡), and entropy (ΔS^‡) terms were significantly different; the reaction steps that induce tight subunit packing, for example, ATP binding and TS reaction, showed high positive values of both ΔH^‡ and ΔS^‡. The results may reflect modulation of the excluded volume as a function of subunit packing tightness at individual reaction steps, leading to a gain or loss in water entropy.     

Acceleration of the ATP-binding rate of F1-ATPase by forcible forward rotation

F₁-ATPase (F₁) is a reversible ATP-driven rotary motor protein. When its rotary shaft is reversely rotated, F₁ produces ATP against the chemical potential of ATP hydrolysis, suggesting that F₁ modulates the rate constants and equilibriums of catalytic reaction steps depending on the rotary angle of the shaft. Although the chemomechanical coupling scheme of F₁ has been determined, it is unclear how individual catalytic reaction steps depend on its rotary angle. Here, we report direct evidence that the ATP-binding rate of F₁ increases upon the forward rotation of the rotor, and its binding affinity to ATP is enhanced by rotation.     

The coupled chemomechanics of the F1-ATPase molecular motor

The enzyme F₁-ATPase is a rotary nanomotor in which the central γ subunit rotates inside the cavity made of α₃β₃ subunits. The experiments showed that the rotation proceeds in steps of 120° and each 120° step consists of 80° and 40° substeps. Here the Author proposes a stochastic wave mechanics of the F₁-ATPase motor and combines it with the structure-based kinetics of the F₁-ATPase to form a chemomechanic coupled model. The model can reproduce quantitatively and explain the experimental observations about the F₁ motor. Using the model, several rate-limited situations about γ subunit rotation are proposed, the effects of the friction and the load on the substeps are investigated and the chemomechanic coupled time during ATP hydrolysis cycle is determined.     

Mechanical Modulation of ATP-binding Affinity of V1-ATPase

V₁-ATPase is a rotary motor protein that rotates the central shaft in a counterclockwise direction hydrolyzing ATP. Although the ATP-binding process is suggested to be the most critical reaction step for torque generation in F₁-ATPase (the closest relative of V₁-ATPase evolutionarily), the role of ATP binding for V₁-ATPase in torque generation has remained unclear. In the present study, we performed single-molecule manipulation experiments on V₁-ATPase from Thermus thermophilus to investigate how the ATP-binding process is modulated upon rotation of the rotary shaft. When V₁-ATPase showed an ATP-waiting pause, it was stalled at a target angle and then released. Based on the response of the V₁-ATPase released, the ATP-binding probability was determined at individual stall angles. It was observed that the rate constant of ATP binding (k_on) was exponentially accelerated with forward rotation, whereas the rate constant of ATP release (k_off) was exponentially reduced. The angle dependence of the k_off of V₁-ATPase was significantly smaller than that of F₁-ATPase, suggesting that the ATP-binding process is not the major torque-generating step in V₁-ATPase. When V₁-ATPase was stalled at the mean binding angle to restrict rotary Brownian motion, k_on was evidently slower than that determined from free rotation, showing the reaction rate enhancement by conformational fluctuation. It was also suggested that shaft of V₁-ATPase should be rotated at least 277° in a clockwise direction for efficient release of ATP under ATP-synthesis conditions.     

Fo-driven Rotation in the ATP Synthase Direction against the Force of F1 ATPase in the FoF1 ATP Synthase

Living organisms rely on the F_oF₁ ATP synthase to maintain the non-equilibrium chemical gradient of ATP to ADP and phosphate that provides the primary energy source for cellular processes. How the F_o motor uses a transmembrane electrochemical ion gradient to create clockwise torque that overcomes F₁ ATPase-driven counterclockwise torque at high ATP is a major unresolved question. Using single F_oF₁ molecules embedded in lipid bilayer nanodiscs, we now report the observation of F_o-dependent rotation of the c10 ring in the ATP synthase (clockwise) direction against the counterclockwise force of ATPase-driven rotation that occurs upon formation of a leash with F_o stator subunit a. Mutational studies indicate that the leash is important for ATP synthase activity and support a mechanism in which residues aGlu-196 and cArg-50 participate in the cytoplasmic proton half-channel to promote leash formation.     

Robustness of the Rotary Catalysis Mechanism of F1-ATPase

F₁-ATPase (F₁) is the rotary motor protein fueled by ATP hydrolysis. Previous studies have suggested that three charged residues are indispensable for catalysis of F₁ as follows: the P-loop lysine in the phosphate-binding loop, GXXXXGK(T/S); a glutamic acid that activates water molecules for nucleophilic attack on the γ-phosphate of ATP (general base); and an arginine directly contacting the γ-phosphate (arginine finger). These residues are well conserved among P-loop NTPases. In this study, we investigated the role of these charged residues in catalysis and torque generation by analyzing alanine-substituted mutants in the single-molecule rotation assay. Surprisingly, all mutants continuously drove rotary motion, even though the rotational velocity was at least 100,000 times slower than that of wild type. Thus, although these charged residues contribute to highly efficient catalysis, they are not indispensable to chemo-mechanical energy coupling, and the rotary catalysis mechanism of F₁ is far more robust than previously thought.     

Mitochondria as ATP consumers in cellular pathology

ATP provided by oxidative phosphorylation supports highly complex and energetically expensive cellular processes. Yet, in several pathological settings, mitochondria could revert to ATP consumption, aggravating an existing cellular pathology. Here we review (i) the pathological conditions leading to ATP hydrolysis by the reverse operation of the mitochondrial F_oF₁-ATPase, (ii) molecular and thermodynamic factors influencing the directionality of the F_oF₁-ATPase, (iii) the role of the adenine nucleotide translocase as the intermediary adenine nucleotide flux pathway between the cytosol and the mitochondrial matrix when mitochondria become ATP consumers, (iv) the role of the permeability transition pore in bypassing the ANT, thereby allowing the flux of ATP directly to the hydrolyzing F_oF₁-ATPase, (v) the impact of the permeability transition pore on glycolytic ATP production, and (vi) endogenous and exogenous interventions for limiting ATP hydrolysis by the mitochondrial F_oF₁-ATPase.