Coupling of rotation and catalysis in F(1)-ATPase revealed by single-molecule imaging and manipulation

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

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

H+-slip correlated to rotor free-wheeling as cause of F1FO-ATPase dysfunction in primary mitochondrial disorders

Inborn errors of metabolism are related to mitochondrial disorders caused by dysfunction of the oxidative phosphorylation (OXPHOS) system. Congenital hypermetabolism in the infant is a rare disease belonging to Luft syndrome, nonthyroidal hypermetabolism, arising from a singular example of a defect in OXPHOS. The mitochondria lose coupling of mitochondrial substrates oxidation from the ADP phosphorylation. Since Luft syndrome is due to uncoupled cell respiration responsible for deficient in ATP production that originates in the respiratory complexes, a de novo heterozygous variant in the catalytic subunit of mitochondrial F1FO-ATPase arises as the main cause of an autosomal dominant syndrome of hypermetabolism associated with dysfunction in ATP production, which does not involve the respiratory complexes. The F1FO-ATPase works as an embedded molecular machine with a rotary action using two different motor engines. The FO, which is an integral domain in the membrane, dissipates the chemical potential difference for H+, a proton motive force (Δp), across the inner membrane to generate a torsion. The F1 domain-the hydrophilic portion responsible for ATP turnover-is powered by the molecular rotary action to synthesize ATP. The structural and functional coupling of F1 and FO domains support the energy transduction for ATP synthesis. The dissipation of Δp by means of an H+ slip correlated to rotor free-wheeling of the F1FO-ATPase has been discovered to cause enzyme dysfunction in primary mitochondrial disorders. In this insight, we try to offer commentary and analysis of the molecular mechanism in these impaired mitochondria.

Conformational ensemble of yeast ATP synthase at low pH reveals unique intermediates and plasticity in F1-Fo coupling

Mitochondrial adenosine triphosphate (ATP) synthase uses the proton gradient across the inner mitochondrial membrane to synthesize ATP. Structural and single molecule studies conducted mostly at neutral or basic pH have provided details of the reaction mechanism of ATP synthesis. However, pH of the mitochondrial matrix is slightly acidic during hypoxia and pH-dependent conformational changes in the ATP synthase have been reported. Here we use single-particle cryo-EM to analyze the conformational ensemble of the yeast (Saccharomyces cerevisiae) ATP synthase at pH 6. Of the four conformations resolved in this study, three are reaction intermediates. In addition to canonical catalytic dwell and binding dwell structures, we identify two unique conformations with nearly identical positions of the central rotor but different catalytic site conformations. These structures provide new insights into the catalytic mechanism of the ATP synthase and highlight elastic coupling between the catalytic and proton translocating domains.

Product inhibition slow down the moving velocity of processive chitinase and sliding-intermediate state blocks re-binding of product

Processive movement is the key reaction for crystalline polymer degradation by enzyme. Product release is an important phenomenon in resetting the moving cycle, but how it affects chitinase kinetics was unknown. Therefore, we investigated the effect of diacetyl chitobiose (C2) on the biochemical activity and movement of chitinase A from Serratia marcescens (SmChiA). The apparent inhibition constant of C2 on crystalline chitin degradation of SmChiA was 159 μM. The binding position of C2 obtained by X-ray crystallography was at subsite +1, +2 and Trp275 interact with C2 at subsite +1. This binding state is consistent with the competitive inhibition obtained by biochemical analysis. The apparent inhibition constant of C2 on the moving velocity of high-speed (HS) AFM observations was 330 μM, which is close to the biochemical results, indicating that the main factor in crystalline chitin degradation is also the decrease in degradation activity due to inhibition of processive movement. The Trp275 is a key residue for making a sliding intermediate complex. SmChiA W275A showed weaker activity and affinity than WT against crystalline chitin because it is less processive than WT. In addition, biochemical apparent inhibition constant for C2 of SmChiA W275A was 45.6 μM. W275A mutant showed stronger C2 inhibition than WT even though the C2 binding affinity is weaker than WT. This result indicated that Trp275 is important for the interaction at subsite +1, but also important for making sliding intermediate complex and physically block the rebinding of C2 on the catalytic site for crystalline chitin degradation.

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

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

Technical advances in high-speed atomic force microscopy

It has been 30 years since the outset of developing high-speed atomic force microscopy (HS-AFM), and 15 years have passed since its establishment in 2008. This advanced microscopy is capable of directly visualizing individual biological macromolecules in dynamic action and has been widely used to answer important questions that are inaccessible by other approaches. The number of publications on the bioapplications of HS-AFM has rapidly increased in recent years and has already exceeded 350. Although less visible than these biological studies, efforts have been made for further technical developments aimed at enhancing the fundamental performance of HS-AFM, such as imaging speed, low sample disturbance, and scan size, as well as expanding its functionalities, such as correlative microscopy, temperature control, buffer exchange, and sample manipulations. These techniques can expand the range of HS-AFM applications. After summarizing the key technologies underlying HS-AFM, this article focuses on recent technical advances and discusses next-generation HS-AFM.

Elucidating Events within the Black Box of Enzyme Catalysis in Energy Metabolism: Insights into the Molecular Mechanism of ATP Hydrolysis by F1-ATPase

Oxygen exchange reactions occurring at β-catalytic sites of the FOF1-ATP synthase/F1-ATPase imprint a unique record of molecular events during the catalytic cycle of ATP synthesis/hydrolysis. This work presents a new theory of oxygen exchange and tests it on oxygen exchange data recorded on ATP hydrolysis by mitochondrial F1-ATPase (MF1). The apparent rate constant of oxygen exchange governing the intermediate Pi-HOH exchange accompanying ATP hydrolysis is determined by kinetic analysis over a ~50,000-fold range of substrate ATP concentration (0.1-5000 μM) and a corresponding ~200-fold range of reaction velocity (3.5-650 [moles of Pi/{moles of F1-ATPase}-1 s-1]). Isotopomer distributions of [18O]Pi species containing 0, 1, 2, and 3 labeled oxygen atoms predicted by the theory have been quantified and shown to be in perfect agreement with the experimental distributions over the entire range of medium ATP concentrations without employing adjustable parameters. A novel molecular mechanism of steady-state multisite ATP hydrolysis by the F1-ATPase has been proposed. Our results show that steady-state ATP hydrolysis by F1-ATPase occurs with all three sites occupied by Mg-nucleotide. The various implications arising from models of energy coupling in ATP synthesis/hydrolysis by the ATP synthase/F1-ATPase have been discussed. Current models of ATP hydrolysis by F1-ATPase, including those postulated from single-molecule data, are shown to be effectively bisite models that contradict the data. The trisite catalysis formulated by Nath's torsional mechanism of energy transduction and ATP synthesis/hydrolysis since its first appearance 25 years ago is shown to be in better accord with the experimental record. The total biochemical information on ATP hydrolysis is integrated into a consistent model by the torsional mechanism of ATP synthesis/hydrolysis and shown to elucidate the elementary chemical and mechanical events within the black box of enzyme catalysis in energy metabolism by F1-ATPase.

Digital Cascade Assays for ADP- or ATP-Producing Enzymes Using a Femtoliter Reactor Array Device

Digital enzyme assays are emerging biosensing methods for highly sensitive quantitative analysis of biomolecules with single-molecule detection sensitivity. However, current digital enzyme assays require a fluorogenic substrate for detection, which limits the applicability of this method to certain enzymes. ATPases and kinases are representative enzymes for which fluorogenic substrates are not available; however, these enzymes form large domains and play a central role in biology. In this study, we implemented a fluorogenic cascade reaction in a femtoliter reactor array device to develop a digital bioassay platform for ATPases and kinases. The digital cascade assay enabled quantitative measurement of the single-molecule activity of F1-ATPase, the catalytic portion of ATP synthase. We also demonstrated a digital assay for human choline kinase α. Furthermore, we developed a digital cascade assay for ATP-synthesizing enzymes and demonstrated a digital assay for pyruvate kinase. These results show the high versatility of this assay platform. Thus, the digital cascade assay has great potential for the highly sensitive detection and accurate characterization of various ADP- and ATP-producing enzymes, such as kinases, which may serve as disease biomarkers.

Angle-dependent rotation velocity consistent with ADP release in bacterial F1-ATPase

A model-based method is used to extract a short-lived state in the rotation kinetics of the F1-ATPase of a bacterial species, Paracoccus denitrificans (PdF1). Imaged as a single molecule, PdF1 takes large 120ø steps during it rotation. The apparent lack of further substeps in the trajectories not only renders the rotation of PdF1 unlike that of other F-ATPases, but also hinders the establishment of its mechano-chemical kinetic scheme. We addressed these challenges using the angular velocity extracted from the single-molecule trajectories and compare it with its theoretically calculated counterpart. The theory-experiment comparison indicate the presence of a 20μs lifetime state, 40o after ATP binding. We identify a kinetic cycle in which this state is a three-nucleotide occupancy state prior to ADP release from another site. A similar state was also reported in our earlier study of the Thermophilic bacillus F1-ATPase (lifetime ∼ 10 μ s), suggesting thereby a common mechanism for removing a nucleotide release bottleneck in the rotary mechanism.

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.

Mechanism of ATP hydrolysis dependent rotation of bacterial ATP synthase

F₁ domain of ATP synthase is a rotary ATPase complex in which rotation of central γ-subunit proceeds in 120° steps against a surrounding α₃β₃ fueled by ATP hydrolysis. How the ATP hydrolysis reactions occurring in three catalytic αβ dimers are coupled to mechanical rotation is a key outstanding question. Here we describe catalytic intermediates of the F₁ domain in F_oF₁ synthase from Bacillus PS3 sp. during ATP mediated rotation captured using cryo-EM. The structures reveal that three catalytic events and the first 80° rotation occur simultaneously in F₁ domain when nucleotides are bound at all the three catalytic αβ dimers. The remaining 40° rotation of the complete 120° step is driven by completion of ATP hydrolysis at α_Dβ_D, and proceeds through three sub-steps (83°, 91°, 101°, and 120°) with three associated conformational intermediates. All sub-steps except for one between 91° and 101° associated with phosphate release, occur independently of the chemical cycle, suggesting that the 40° rotation is largely driven by release of intramolecular strain accumulated by the 80° rotation. Together with our previous results, these findings provide the molecular basis of ATP driven rotation of ATP synthases.

Physical pictures of rotation mechanisms of F1- and V1-ATPases: Leading roles of translational, configurational entropy of water

We aim to develop a theory based on a concept other than the chemo-mechanical coupling (transduction of chemical free energy of ATP to mechanical work) for an ATP-driven protein complex. Experimental results conflicting with the chemo-mechanical coupling have recently emerged. We claim that the system comprises not only the protein complex but also the aqueous solution in which the protein complex is immersed and the system performs essentially no mechanical work. We perform statistical-mechanical analyses on V₁-ATPase (the A₃B₃DF complex) for which crystal structures in more different states are experimentally known than for F₁-ATPase (the α₃β₃γ complex). Molecular and atomistic models are employed for water and the structure of V₁-ATPase, respectively. The entropy originating from the translational displacement of water molecules in the system is treated as a pivotal factor. We find that the packing structure of the catalytic dwell state of V₁-ATPase is constructed by the interplay of ATP bindings to two of the A subunits and incorporation of the DF subunit. The packing structure represents the nonuniformity with respect to the closeness of packing of the atoms in constituent proteins and protein interfaces. The physical picture of rotation mechanism of F₁-ATPase recently constructed by Kinoshita is examined, and common points and differences between F₁- and V₁-ATPases are revealed. An ATP hydrolysis cycle comprises binding of ATP to the protein complex, hydrolysis of ATP into ADP and Pi in it, and dissociation of ADP and Pi from it. During each cycle, the chemical compounds bound to the three A or β subunits and the packing structure of the A₃B₃ or α₃β₃ complex are sequentially changed, which induces the unidirectional rotation of the central shaft for retaining the packing structure of the A₃B₃DF or α₃β₃γ complex stabilized for almost maximizing the water entropy. The torque driving the rotation is generated by water with no input of chemical free energy. The presence of ATP is indispensable as a trigger of the torque generation. The ATP hydrolysis or synthesis reaction is tightly coupled to the rotation of the central shaft in the normal or inverse direction through the water-entropy effect.

Beyond binding change: the molecular mechanism of ATP hydrolysis by F1-ATPase and its biochemical consequences

F1-ATPase is a universal multisubunit enzyme and the smallest-known motor that, fueled by the process of ATP hydrolysis, rotates in 120o steps. A central question is how the elementary chemical steps occurring in the three catalytic sites are coupled to the mechanical rotation. Here, we performed cold chase promotion experiments and measured the rates and extents of hydrolysis of preloaded bound ATP and promoter ATP bound in the catalytic sites. We found that rotation was caused by the electrostatic free energy change associated with the ATP cleavage reaction followed by Pi release. The combination of these two processes occurs sequentially in two different catalytic sites on the enzyme, thereby driving the two rotational sub-steps of the 120o rotation. The mechanistic implications of this finding are discussed based on the overall energy balance of the system. General principles of free energy transduction are formulated, and their important physical and biochemical consequences are analyzed. In particular, how exactly ATP performs useful external work in biomolecular systems is discussed. A molecular mechanism of steady-state, trisite ATP hydrolysis by F1-ATPase, consistent with physical laws and principles and the consolidated body of available biochemical information, is developed. Taken together with previous results, this mechanism essentially completes the coupling scheme. Discrete snapshots seen in high-resolution X-ray structures are assigned to specific intermediate stages in the 120o hydrolysis cycle, and reasons for the necessity of these conformations are readily understood. The major roles played by the "minor" subunits of ATP synthase in enabling physiological energy coupling and catalysis, first predicted by Nath's torsional mechanism of energy transduction and ATP synthesis 25 years ago, are now revealed with great clarity. The working of nine-stepped (bMF1, hMF1), six-stepped (TF1, EF1), and three-stepped (PdF1) F1 motors and of the α3β3γ subcomplex of F1 is explained by the same unified mechanism without invoking additional assumptions or postulating different mechanochemical coupling schemes. Some novel predictions of the unified theory on the mode of action of F1 inhibitors, such as sodium azide, of great pharmaceutical importance, and on more exotic artificial or hybrid/chimera F1 motors have been made and analyzed mathematically. The detailed ATP hydrolysis cycle for the enzyme as a whole is shown to provide a biochemical basis for a theory of "unisite" and steady-state multisite catalysis by F1-ATPase that had remained elusive for a very long time. The theory is supported by a probability-based calculation of enzyme species distributions and analysis of catalytic site occupancies by Mg-nucleotides and the activity of F1-ATPase. A new concept of energy coupling in ATP synthesis/hydrolysis based on fundamental ligand substitution chemistry has been advanced, which offers a deeper understanding, elucidates enzyme activation and catalysis in a better way, and provides a unified molecular explanation of elementary chemical events occurring at enzyme catalytic sites. As such, these developments take us beyond binding change mechanisms of ATP synthesis/hydrolysis proposed for oxidative phosphorylation and photophosphorylation in bioenergetics.

Rotary properties of hybrid F1-ATPases consisting of subunits from different species

F₁-ATPase (F₁) is an ATP-driven rotary motor protein ubiquitously found in many species as the catalytic portion of F_oF₁-ATP synthase. Despite the highly conserved amino acid sequence of the catalytic core subunits: α and β, F₁ shows diversity in the maximum catalytic turnover rate V_max and the number of rotary steps per turn. To study the design principle of F₁, we prepared eight hybrid F₁s composed of subunits from two of three genuine F₁s: thermophilic Bacillus PS3 (TF₁), bovine mitochondria (bMF₁), and Paracoccus denitrificans (PdF₁), differing in the V_max and the number of rotary steps. The V_max of the hybrids can be well fitted by a quadratic model highlighting the dominant roles of β and the couplings between α-β. Although there exist no simple rules on which subunit dominantly determines the number of steps, our findings show that the stepping behavior is characterized by the combination of all subunits.

Structure of the human ATP synthase

Biological energy currency ATP is produced by F₁F_o-ATP synthase. However, the molecular mechanism for human ATP synthase action remains unknown. Here, we present snapshot images for three main rotational states and one substate of human ATP synthase using cryoelectron microscopy. These structures reveal that the release of ADP occurs when the β subunit of F₁F_o-ATP synthase is in the open conformation, showing how ADP binding is coordinated during synthesis. The accommodation of the symmetry mismatch between F₁ and F_o motors is resolved by the torsional flexing of the entire complex, especially the γ subunit, and the rotational substep of the c subunit. Water molecules are identified in the inlet and outlet half-channels, suggesting that the proton transfer in these two half-channels proceed via a Grotthus mechanism. Clinically relevant mutations are mapped to the structure, showing that they are mainly located at the subunit-subunit interfaces, thus causing instability of the complex.

Direct identification of the rotary angle of ATP cleavage in F1-ATPase from Bacillus PS3

F1-ATPase is the world's smallest biological rotary motor driven by ATP hydrolysis at three catalytic β subunits. The 120° rotational step of the central shaft γ consists of 80° substep driven by ATP binding and a subsequent 40° substep. In order to correlate timing of ATP cleavage at a specific catalytic site with a rotary angle, we designed a new F1-ATPase (F1) from thermophilic Bacillus PS3 carrying β(E190D/F414E/F420E) mutations, which cause extremely slow rates of both ATP cleavage and ATP binding. We produced an F1 molecule that consists of one mutant β and two wild-type βs (hybrid F1). As a result, the new hybrid F1 showed two pausing angles that are separated by 200°. They are attributable to two slowed reaction steps in the mutated β, thus providing the direct evidence that ATP cleavage occurs at 200° rather than 80° subsequent to ATP binding at 0°. This scenario resolves the long-standing unclarified issue in the chemomechanical coupling scheme and gives insights into the mechanism of driving unidirectional rotation.

Rotary mechanism of V/A-ATPases-how is ATP hydrolysis converted into a mechanical step rotation in rotary ATPases?

V/A-ATPase is a rotary molecular motor protein that produces ATP through the rotation of its central rotor. The soluble part of this protein, the V₁ domain, rotates upon ATP hydrolysis. However, the mechanism by which ATP hydrolysis in the V₁ domain couples with the mechanical rotation of the rotor is still unclear. Cryo-EM snapshot analysis of V/A-ATPase indicated that three independent and simultaneous catalytic events occurred at the three catalytic dimers (AB_open, AB_semi, and AB_closed), leading to a 120° rotation of the central rotor. Besides the closing motion caused by ATP bound to AB_open, the hydrolysis of ATP bound to AB_semi drives the 120° step. Our recent time-resolved cryo-EM snapshot analysis provides further evidence for this model. This review aimed to provide a comprehensive overview of the structure and function of V/A-ATPase from a thermophilic bacterium, one of the most well-studied rotary ATPases to date.

Synchronizing Two Distinct Nano-Circular Sliding Motions in Six-Component Machinery for Double Catalysis

The heteroleptic multi-component double slider-on-deck system DS3 exhibits tight coupling of motional speed of two distinct nano-circular sliders (k₂₉₈ =77 and 41 kHz) despite a 2.2 nm separation. In comparison, the single sliders in DS1 and DS2 move at vastly different speed (k₂₉₈ =1.1 vs. 350 kHz). Synchronization of the motions in DS3 remains even when one slows the movement of the faster slider using small molecular brake pads. In contrast to the individual DS1 and DS2 systems, DS3 is a powerful catalyst for a two-step reaction by using the motion of both sliders to drive two catalytic processes.

Regulation of the mammalian-brain V-ATPase through ultraslow mode-switching

Vacuolar-type adenosine triphosphatases (V-ATPases)1-3 are electrogenic rotary mechanoenzymes structurally related to F-type ATP synthases4,5. They hydrolyse ATP to establish electrochemical proton gradients for a plethora of cellular processes1,3. In neurons, the loading of all neurotransmitters into synaptic vesicles is energized by about one V-ATPase molecule per synaptic vesicle6,7. To shed light on this bona fide single-molecule biological process, we investigated electrogenic proton-pumping by single mammalian-brain V-ATPases in single synaptic vesicles. Here we show that V-ATPases do not pump continuously in time, as suggested by observing the rotation of bacterial homologues8 and assuming strict ATP-proton coupling. Instead, they stochastically switch between three ultralong-lived modes: proton-pumping, inactive and proton-leaky. Notably, direct observation of pumping revealed that physiologically relevant concentrations of ATP do not regulate the intrinsic pumping rate. ATP regulates V-ATPase activity through the switching probability of the proton-pumping mode. By contrast, electrochemical proton gradients regulate the pumping rate and the switching of the pumping and inactive modes. A direct consequence of mode-switching is all-or-none stochastic fluctuations in the electrochemical gradient of synaptic vesicles that would be expected to introduce stochasticity in proton-driven secondary active loading of neurotransmitters and may thus have important implications for neurotransmission. This work reveals and emphasizes the mechanistic and biological importance of ultraslow mode-switching.

F1FO ATP synthase molecular motor mechanisms

The F-ATP synthase, consisting of F1 and FO motors connected by a central rotor and the stators, is the enzyme responsible for synthesizing the majority of ATP in all organisms. The F1 (αβ)3 ring stator contains three catalytic sites. Single-molecule F1 rotation studies revealed that ATP hydrolysis at each catalytic site (0°) precedes a power-stroke that rotates subunit-γ 120° with angular velocities that vary with rotational position. Catalytic site conformations vary relative to subunit-γ position (βE, empty; βD, ADP bound; βT, ATP-bound). During a power stroke, βE binds ATP (0°–60°) and βD releases ADP (60°–120°). Årrhenius analysis of the power stroke revealed that elastic energy powers rotation via unwinding the γ-subunit coiled-coil. Energy from ATP binding at 34° closes βE upon subunit-γ to drive rotation to 120° and forcing the subunit-γ to exchange its tether from βE to βD, which changes catalytic site conformations. In F1FO, the membrane-bound FO complex contains a ring of c-subunits that is attached to subunit-γ. This c-ring rotates relative to the subunit-a stator in response to transmembrane proton flow driven by a pH gradient, which drives subunit-γ rotation in the opposite direction to force ATP synthesis in F1. Single-molecule studies of F1FO embedded in lipid bilayer nanodisks showed that the c-ring transiently stopped F1-ATPase-driven rotation every 36° (at each c-subunit in the c10-ring of E. coli F1FO) and was able to rotate 11° in the direction of ATP synthesis. Protonation and deprotonation of the conserved carboxyl group on each c-subunit is facilitated by separate groups of subunit-a residues, which were determined to have different pKa’s. Mutations of any of any residue from either group changed both pKa values, which changed the occurrence of the 11° rotation proportionately. This supports a Grotthuss mechanism for proton translocation and indicates that proton translocation occurs during the 11° steps. This is consistent with a mechanism in which each 36° of rotation the c-ring during ATP synthesis involves a proton translocation-dependent 11° rotation of the c-ring, followed by a 25° rotation driven by electrostatic interaction of the negatively charged unprotonated carboxyl group to the positively charged essential arginine in subunit-a.

Structural basis of unisite catalysis of bacterial F0F1-ATPase

Adenosine triphosphate (ATP) synthases (F₀F₁-ATPases) are crucial for all aerobic organisms. F₁, a water-soluble domain, can catalyze both the synthesis and hydrolysis of ATP with the rotation of the central γε rotor inside a cylinder made of α ₃ β ₃ in three different conformations (referred to as β _E, β _TP, and β _DP). In this study, we determined multiple cryo-electron microscopy structures of bacterial F₀F₁ exposed to different reaction conditions. The structures of nucleotide-depleted F₀F₁ indicate that the ε subunit directly forces β _TP to adopt a closed form independent of the nucleotide binding to β _TP. The structure of F₀F₁ under conditions that permit only a single catalytic β subunit per enzyme to bind ATP is referred to as unisite catalysis and reveals that ATP hydrolysis unexpectedly occurs on β _TP instead of β _DP, where ATP hydrolysis proceeds in the steady-state catalysis of F₀F₁. This indicates that the unisite catalysis of bacterial F₀F₁ significantly differs from the kinetics of steady-state turnover with continuous rotation of the shaft.

How Does F1-ATPase Generate Torque?: Analysis From Cryo-Electron Microscopy and Rotational Catalysis of Thermophilic F1

The F₁-ATPase is a rotary motor fueled by ATP hydrolysis. Its rotational dynamics have been well characterized using single-molecule rotation assays. While F₁-ATPases from various species have been studied using rotation assays, the standard model for single-molecule studies has been the F₁-ATPase from thermophilic Bacillus sp. PS3, named TF₁. Single-molecule studies of TF₁ have revealed fundamental features of the F₁-ATPase, such as the principal stoichiometry of chemo-mechanical coupling (hydrolysis of 3 ATP per turn), torque (approximately 40 pN·nm), and work per hydrolysis reaction (80 pN·nm = 48 kJ/mol), which is nearly equivalent to the free energy of ATP hydrolysis. Rotation assays have also revealed that TF₁ exhibits two stable conformational states during turn: a binding dwell state and a catalytic dwell state. Although many structures of F₁ have been reported, most of them represent the catalytic dwell state or its related states, and the structure of the binding dwell state remained unknown. A recent cryo-EM study on TF₁ revealed the structure of the binding dwell state, providing insights into how F₁ generates torque coupled to ATP hydrolysis. In this review, we discuss the torque generation mechanism of F₁ based on the structure of the binding dwell state and single-molecule studies.

Structure of ATP synthase under strain during catalysis

ATP synthases are macromolecular machines consisting of an ATP-hydrolysis-driven F₁ motor and a proton-translocation-driven F_O motor. The F₁ and F_O motors oppose each other’s action on a shared rotor subcomplex and are held stationary relative to each other by a peripheral stalk. Structures of resting mitochondrial ATP synthases revealed a left-handed curvature of the peripheral stalk even though rotation of the rotor, driven by either ATP hydrolysis in F₁ or proton translocation through F_O, would apply a right-handed bending force to the stalk. We used cryoEM to image yeast mitochondrial ATP synthase under strain during ATP-hydrolysis-driven rotary catalysis, revealing a large deformation of the peripheral stalk. The structures show how the peripheral stalk opposes the bending force and suggests that during ATP synthesis proton translocation causes accumulation of strain in the stalk, which relaxes by driving the relative rotation of the rotor through six sub-steps within F₁, leading to catalysis.

CryoEM of mitochondrial ATP synthase frozen during rotary catalysis reveals dramatic conformational changes in the peripheral stalk subcomplex, which enable the enzyme’s efficient synthesis of ATP.

F1-ATPase Rotary Mechanism: Interpreting Results of Diverse Experimental Modes With an Elastic Coupling Theory

In this chapter, we review single-molecule observations of rotary motors, focusing on the general theme that their mechanical motion proceeds in substeps with each substep described by an angle-dependent rate constant. In the molecular machine F1-ATPase, the stepping rotation is described for individual steps by forward and back reaction rate constants, some of which depend strongly on the rotation angle. The rotation of a central shaft is typically monitored by an optical probe. We review our recent work on the theory for the angle-dependent rate constants built to treat a variety of single-molecule and ensemble experiments on the F1-ATPase, and relating the free energy of activation of a step to the standard free energy of reaction for that step. This theory, an elastic molecular transfer theory, provides a framework for a multistate model and includes the probe used in single-molecule imaging and magnetic manipulation experiments. Several examples of its application are the following: (a) treatment of the angle-dependent rate constants in stalling experiments, (b) use of the model to enhance the time resolution of the single-molecule imaging apparatus and to detect short-lived states with a microsecond lifetime, states hidden by the fluctuations of the imaging probe, (c) treatment of out-of-equilibrium "controlled rotation" experiments, (d) use of the model to predict, without adjustable parameters, the angle-dependent rate constants of nucleotide binding and release, using data from other experiments, and (e) insights obtained from correlation of kinetic and cryo-EM structural data. It is also noted that in the case where the release of ADP would be a bottleneck process, the binding of ATP to another site acts to accelerate the release by 5-6 orders of magnitude. The relation of the present set of studies to previous and current theoretical work in the field is described. An overall goal is to gain mechanistic insight into the biological function in relation to structure.

Structural snapshots of V/A-ATPase reveal the rotary catalytic mechanism of rotary ATPases

V/A-ATPase is a motor protein that shares a common rotary catalytic mechanism with F_oF₁ ATP synthase. When powered by ATP hydrolysis, the V₁ domain rotates the central rotor against the A₃B₃ hexamer, composed of three catalytic AB dimers adopting different conformations (AB_open, AB_semi, and AB_closed). Here, we report the atomic models of 18 catalytic intermediates of the V₁ domain of V/A-ATPase under different reaction conditions, determined by single particle cryo-EM. The models reveal that the rotor does not rotate immediately after binding of ATP to the V₁. Instead, three events proceed simultaneously with the 120˚ rotation of the shaft: hydrolysis of ATP in AB_semi, zipper movement in AB_open by the binding ATP, and unzipper movement in AB_closed with release of both ADP and Pi. This indicates the unidirectional rotation of V/A-ATPase by a ratchet-like mechanism owing to ATP hydrolysis in AB_semi, rather than the power stroke model proposed previously for F₁-ATPase.

The rotary ATPases use a rotary catalytic mechanism to drive transmembrane proton movement powered by ATP hydrolysis. Here, the authors report a collection of V/A-ATPase V₁ domain structures, providing insights into rotary mechanism of the enzyme and potentially other rotary motor proteins driven by ATP hydrolysis.

Melatonin: Regulation of Biomolecular Condensates in Neurodegenerative Disorders

Biomolecular condensates are membraneless organelles (MLOs) that form dynamic, chemically distinct subcellular compartments organizing macromolecules such as proteins, RNA, and DNA in unicellular prokaryotic bacteria and complex eukaryotic cells. Separated from surrounding environments, MLOs in the nucleoplasm, cytoplasm, and mitochondria assemble by liquid-liquid phase separation (LLPS) into transient, non-static, liquid-like droplets that regulate essential molecular functions. LLPS is primarily controlled by post-translational modifications (PTMs) that fine-tune the balance between attractive and repulsive charge states and/or binding motifs of proteins. Aberrant phase separation due to dysregulated membrane lipid rafts and/or PTMs, as well as the absence of adequate hydrotropic small molecules such as ATP, or the presence of specific RNA proteins can cause pathological protein aggregation in neurodegenerative disorders. Melatonin may exert a dominant influence over phase separation in biomolecular condensates by optimizing membrane and MLO interdependent reactions through stabilizing lipid raft domains, reducing line tension, and maintaining negative membrane curvature and fluidity. As a potent antioxidant, melatonin protects cardiolipin and other membrane lipids from peroxidation cascades, supporting protein trafficking, signaling, ion channel activities, and ATPase functionality during condensate coacervation or dissolution. Melatonin may even control condensate LLPS through PTM and balance mRNA- and RNA-binding protein composition by regulating N6-methyladenosine (m6A) modifications. There is currently a lack of pharmaceuticals targeting neurodegenerative disorders via the regulation of phase separation. The potential of melatonin in the modulation of biomolecular condensate in the attenuation of aberrant condensate aggregation in neurodegenerative disorders is discussed in this review.

The six steps of the complete F1-ATPase rotary catalytic cycle

F₁F_o ATP synthase interchanges phosphate transfer energy and proton motive force via a rotary catalysis mechanism. Isolated F₁-ATPase catalytic cores can hydrolyze ATP, passing through six intermediate conformational states to generate rotation of their central γ-subunit. Although previous structural studies have contributed greatly to understanding rotary catalysis in the F₁-ATPase, the structure of an important conformational state (the binding-dwell) has remained elusive. Here, we exploit temperature and time-resolved cryo-electron microscopy to determine the structure of the binding- and catalytic-dwell states of Bacillus PS3 F₁-ATPase. Each state shows three catalytic β-subunits in different conformations, establishing the complete set of six states taken up during the catalytic cycle and providing molecular details for both the ATP binding and hydrolysis strokes. We also identify a potential phosphate-release tunnel that indicates how ADP and phosphate binding are coordinated during synthesis. Overall these findings provide a structural basis for the entire F₁-ATPase catalytic cycle.

Extreme parsimony in ATP consumption by 20S complexes in the global disassembly of single SNARE complexes

Fueled by ATP hydrolysis in N-ethylmaleimide sensitive factor (NSF), the 20S complex disassembles rigid SNARE (soluble NSF attachment protein receptor) complexes in single unraveling step. This global disassembly distinguishes NSF from other molecular motors that make incremental and processive motions, but the molecular underpinnings of its remarkable energy efficiency remain largely unknown. Using multiple single-molecule methods, we found remarkable cooperativity in mechanical connection between NSF and the SNARE complex, which prevents dysfunctional 20S complexes that consume ATP without productive disassembly. We also constructed ATP hydrolysis cycle of the 20S complex, in which NSF largely shows randomness in ATP binding but switches to perfect ATP hydrolysis synchronization to induce global SNARE disassembly, minimizing ATP hydrolysis by non-20S complex-forming NSF molecules. These two mechanisms work in concert to concentrate ATP consumption into functional 20S complexes, suggesting evolutionary adaptations by the 20S complex to the energetically expensive mechanical task of SNARE complex disassembly.

Fueled by ATP hydrolysis in N-ethylmaleimide sensitive factor (NSF), the 20S complex disassembles SNARE complexes in a single unravelling step. Here authors use single-molecule methods to show cooperativity between the NSF and SNARE complex, which prevents ATP consumption without productive disassembly.

Optimal Rectification without Forward-Current Suppression by Biological Molecular Motor

We experimentally show that biological molecular motor F_{1}-ATPase (F_{1}) implements an optimal rectification mechanism. The rectification mechanism hardly suppresses the synthesis of adenosine triphosphate by F_{1}, which is F_{1}'s physiological role, while inhibiting the unfavorable hydrolysis of adenosine triphosphate. This optimal rectification contrasts highly with that of a simple ratchet model, where the inhibition of the backward current is inevitably accompanied by the suppression of the forward current. Our detailed analysis of single-molecule trajectories demonstrates a novel but simple rectification mechanism of F_{1} with parallel landscapes and asymmetric transition rates.

The nucleotide binding affinities of two critical conformations of Escherichia coli ATP synthase

ATP synthase is essential in aerobic energy metabolism, and the rotary catalytic mechanism is one of the core concepts to understand the energetic functions of ATP synthase. Disulfide bonds formed by oxidizing a pair of cysteine mutations halted the rotation of the γ subunit in two critical conformations, the ATP-waiting dwell (αE284C/γQ274C) and the catalytic dwell (αE284C/γL276C). Tryptophan fluorescence was used to measure the nucleotide binding affinities for MgATP, MgADP and MgADP-AlF₄ (a transition state analog) to wild-type and mutant F₁ under reducing and oxidizing conditions. In the reduced state, αE284C/γL276C F₁ showed a wild-type-like nucleotide binding pattern; after oxidation to lock the enzyme in the catalytic dwell state, the nucleotide binding parameters remained unchanged. In contrast, αE284C/γQ274C F₁ showed significant differences in the affinities of the oxidized versus the reduced state. Locking the enzyme in the ATP-waiting dwell reduced nucleotide binding affinities of all three catalytic sites. Most importantly, the affinity of the low affinity site was reduced to such an extent that it could no longer be detected in the binding assay (K_d > 5 mM). The results of the present study allow to present a model for the catalytic mechanism of ATP synthase under consideration of the nucleotide affinity changes during a 360° cycle of the rotor.

Semi-automated single-molecule microscopy screening of fast-dissociating specific antibodies directly from hybridoma cultures

Fast-dissociating, specific antibodies are single-molecule imaging probes that transiently interact with their targets and are used in biological applications including image reconstruction by integrating exchangeable single-molecule localization (IRIS), a multiplexable super-resolution microscopy technique. Here, we introduce a semi-automated screen based on single-molecule total internal reflection fluorescence (TIRF) microscopy of antibody-antigen binding, which allows for identification of fast-dissociating monoclonal antibodies directly from thousands of hybridoma cultures. We develop monoclonal antibodies against three epitope tags (FLAG-tag, S-tag, and V5-tag) and two F-actin crosslinking proteins (plastin and espin). Specific antibodies show fast dissociation with half-lives ranging from 0.98 to 2.2 s. Unexpectedly, fast-dissociating yet specific antibodies are not so rare. A combination of fluorescently labeled Fab probes synthesized from these antibodies and light-sheet microscopy, such as dual-view inverted selective plane illumination microscopy (diSPIM), reveal rapid turnover of espin within long-lived F-actin cores of inner-ear sensory hair cell stereocilia, demonstrating that fast-dissociating specific antibodies can identify novel biological phenomena.

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.

Incoming news on the F-type ATPase structure and functions in mammalian mitochondria

•Recent findings of cryo-EM structures of mammalian F₁F_O-ATPase.•The membrane-embedded domain of the F₁F_O-ATPase and the permeability transition pore.•The Ca²⁺-activated ₁F_O-ATPase role in the mPTP is consistent with recent cryo-EM findings.•The membrane-embedded FO participates in mPTP formation in mammalian mitochondria.•Conformational changes within FO modify the inner mitochondrial membrane shape.

Resolving cargo-motor-track interactions with bifocal parallax single-particle tracking

Resolving coordinated biomolecular interactions in living cellular environments is vital for understanding the mechanisms of molecular nanomachines. The conventional approach relies on localizing and tracking target biomolecules and/or subcellular organelles labeled with imaging probes. However, it is challenging to gain information on rotational dynamics, which can be more indicative of the work done by molecular motors and their dynamic binding status. Herein, a bifocal parallax single-particle tracking method using half-plane point spread functions has been developed to resolve the full-range azimuth angle (0-360°), polar angle, and three-dimensional (3D) displacement in real time under complex living cell conditions. Using this method, quantitative rotational and translational motion of the cargo in a 3D cell cytoskeleton was obtained. Not only were well-known active intracellular transport and free diffusion observed, but new interactions (tight attachment and tethered rotation) were also discovered for better interpretation of the dynamics of cargo-motor-track interactions at various types of microtubule intersections.

The 3 × 120° rotary mechanism of Paracoccus denitrificans F1-ATPase is different from that of the bacterial and mitochondrial F1-ATPases

The rotation of Paracoccus denitrificans F₁-ATPase (PdF₁) was studied using single-molecule microscopy. At all concentrations of adenosine triphosphate (ATP) or a slowly hydrolyzable ATP analog (ATPγS), above or below K _m, PdF₁ showed three dwells per turn, each separated by 120°. Analysis of dwell time between steps showed that PdF₁ executes binding, hydrolysis, and probably product release at the same dwell. The comparison of ATP binding and catalytic pauses in single PdF₁ molecules suggested that PdF₁ executes both elementary events at the same rotary position. This point was confirmed in an inhibition experiment with a nonhydrolyzable ATP analog (AMP-PNP). Rotation assays in the presence of adenosine diphosphate (ADP) or inorganic phosphate at physiological concentrations did not reveal any obvious substeps. Although the possibility of the existence of substeps remains, all of the datasets show that PdF₁ is principally a three-stepping motor similar to bacterial vacuolar (V₁)-ATPase from Thermus thermophilus This contrasts with all other known F₁-ATPases that show six or nine dwells per turn, conducting ATP binding and hydrolysis at different dwells. Pauses by persistent Mg-ADP inhibition or the inhibitory ζ-subunit were also found at the same angular position of the rotation dwell, supporting the simplified chemomechanical scheme of PdF₁ Comprehensive analysis of rotary catalysis of F₁ from different species, including PdF₁, suggests a clear trend in the correlation between the numbers of rotary steps of F₁ and F_o domains of F-ATP synthase. F₁ motors with more distinctive steps are coupled with proton-conducting F_o rings with fewer proteolipid subunits, giving insight into the design principle the F₁F_o of ATP synthase.

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

In a recent paper entitled "Chemiosmotic misunderstandings", it is claimed that "enough shortcomings in Mitchell's chemiosmotic theory have not been found and that a novel paradigm that offers at least as much explanatory power as chemiosmosis is not ready." This view is refuted by a wealth of molecular-level experimental data and strong new theoretical and computational evidence. It is shown that the chemiosmotic theory was beset with a large number of major shortcomings ever since the time when it was first proposed in the 1960s. These multiple shortcomings and flaws of chemiosmosis were repeatedly pointed out in incisive critiques by biochemical authorities of the late 20th century. All the shortcomings and flaws have been shown to be rectified by a quantitative, unified molecular-level theory that leads to a deeper and far more accurate understanding of biological energy coupling and ATP synthesis. The new theory is shown to be consistent with pioneering X-ray and cryo-EM structures and validated by state-of-the-art single-molecule techniques. Several new biochemical experimental tests are proposed and constructive ways for providing a revitalizing conceptual background and theory for integration of the available experimental information are suggested.

Albumin-based nanoparticles as contrast medium for MRI: vascular imaging, tissue and cell interactions, and pharmacokinetics of second-generation nanoparticles

This multidisciplinary study examined the pharmacokinetics of nanoparticles based on albumin-DTPA-gadolinium chelates, testing the hypothesis that these nanoparticles create a stronger vessel signal than conventional gadolinium-based contrast agents and exploring if they are safe for clinical use. Nanoparticles based on human serum albumin, bearing gadolinium and designed for use in magnetic resonance imaging, were used to generate magnet resonance images (MRI) of the vascular system in rats ("blood pool imaging"). At the low nanoparticle doses used for radionuclide imaging, nanoparticle-associated metals were cleared from the blood into the liver during the first 4 h after nanoparticle application. At the higher doses required for MRI, the liver became saturated and kidney and spleen acted as additional sinks for the metals, and accounted for most processing of the nanoparticles. The multiple components of the nanoparticles were cleared independently of one another. Albumin was detected in liver, spleen, and kidneys for up to 2 days after intravenous injection. Gadolinium was retained in the liver, kidneys, and spleen in significant concentrations for much longer. Gadolinium was present as significant fractions of initial dose for longer than 2 weeks after application, and gadolinium clearance was only complete after 6 weeks. Our analysis could not account quantitatively for the full dose of gadolinium that was applied, but numerous organs were found to contain gadolinium in the collagen of their connective tissues. Multiple lines of evidence indicated intracellular processing opening the DTPA chelates and leading to gadolinium long-term storage, in particular inside lysosomes. Turnover of the stored gadolinium was found to occur in soluble form in the kidneys, the liver, and the colon for up to 3 weeks after application. Gadolinium overload poses a significant hazard due to the high toxicity of free gadolinium ions. We discuss the relevance of our findings to gadolinium-deposition diseases.

How fast are the motions of tertiary-structure elements in proteins?

Protein motions occur on multiple time and distance scales. Large-scale motions of protein tertiary-structure elements, i.e., domains, are particularly intriguing as they are essential for the catalytic activity of many enzymes and for the functional cycles of protein machines and motors. Theoretical estimates suggest that domain motions should be very fast, occurring on the nanosecond or microsecond time scales. Indeed, free-energy barriers for domain motions are likely to involve salt bridges, which can break in microseconds. Experimental methods that can directly probe domain motions on fast time scales have appeared only in recent years. This Perspective discusses briefly some of these techniques, including nuclear magnetic resonance and single-molecule fluorescence spectroscopies. We introduce a few recent studies that demonstrate ultrafast domain motions and discuss their potential roles. Particularly surprising is the observation of tertiary-structure element dynamics that are much faster than the functional cycles in some protein machines. These swift motions can be rationalized on a case-by-case basis. For example, fast domain closure in multi-substrate enzymes may be utilized to optimize relative substrate orientation. Whether a large mismatch in time scales of conformational dynamics vs functional cycles is a general design principle in proteins remains to be determined.

The catalytic dwell in ATPases is not crucial for movement against applied torque

The ATPase-catalysed conversion of ATP to ADP is a fundamental process in biology. During the hydrolysis of ATP, the α₃β₃ domain undergoes conformational changes while the central stalk (γ/D) rotates unidirectionally. Experimental studies have suggested that different catalytic mechanisms operate depending on the type of ATPase, but the structural and energetic basis of these mechanisms remains unclear. In particular, it is not clear how the positions of the catalytic dwells influence the energy transduction. Here we show that the observed dwell positions, unidirectional rotation and movement against the applied torque are reflections of the free-energy surface of the systems. Instructively, we determine that the dwell positions do not substantially affect the stopping torque. Our results suggest that the three resting states and the pathways that connect them should not be treated equally. The current work demonstrates how the free-energy landscape determines the behaviour of different types of ATPases.

Correlation between the numbers of rotation steps in the ATPase and proton-conducting domains of F- and V-ATPases

This letter reports the correlation in the number of distinct rotation steps between the F₁/V₁ and F_o/V_o domains that constitute common rotary F- and V-ATP synthases/ATPases. Recent single-molecule studies on the F₁-ATPase revealed differences in the number of discrete steps in rotary catalysis between different organisms—6 steps per turn in bacterial types and mitochondrial F₁ from yeast, and 9 steps in the mammalian mitochondrial F₁ domains. The number of rotational steps that F_o domain makes is thought to correspond to that of proteolipid subunits within the rotating c-ring present in F_o. Structural studies on F_o and in the whole ATP synthase complex have shown a large diversity in the number of proteolipid subunits. Interestingly, 6 steps in F₁ are always paired with 10 steps in F_o, whereas 9 steps in F₁ are paired with 8 steps in F_o. The correlation in the number of steps has also been revealed for two types of V-ATPases: one having 6 steps in V₁ paired with 10 steps in V_o, and the other one having 3 steps in V₁ paired with 12 steps in V_o. Although the abovementioned correlations await further confirmation, the results suggest a clear trend; ATPase motors with more steps have proton-conducting motors with less steps. In addition, ATPases with 6 steps are always paired with proton-conducting domains with 10 steps.

Efficiencies of molecular motors: a comprehensible overview

Many biological molecular motors can operate specifically and robustly at the highly fluctuating nano-scale. How these molecules achieve such remarkable functions is an intriguing question that requires various notions and quantifications of efficiency associated with the operations and energy transduction of these nano-machines. Here we give a short review of some important concepts of motor efficiencies, including the thermodynamic, Stokes, and generalized and transport efficiencies, as well as some implications provided by the thermodynamic uncertainty relations recently developed in nonequilibrium physics.

Rotary catalysis of bovine mitochondrial F1-ATPase studied by single-molecule experiments

The reaction scheme of rotary catalysis and the torque generation mechanism of bovine mitochondrial F₁ (bMF₁) were studied in single-molecule experiments. Under ATP-saturated concentrations, high-speed imaging of a single 40-nm gold bead attached to the γ subunit of bMF₁ showed 2 types of intervening pauses during the rotation that were discriminated by short dwell and long dwell. Using ATPγS as a slowly hydrolyzing ATP derivative as well as using a functional mutant βE188D with slowed ATP hydrolysis, the 2 pausing events were distinctively identified. Buffer-exchange experiments with a nonhydrolyzable analog (AMP-PNP) revealed that the long dwell corresponds to the catalytic dwell, that is, the waiting state for hydrolysis, while it remains elusive which catalytic state short pause represents. The angular position of catalytic dwell was determined to be at +80° from the ATP-binding angle, mostly consistent with other F₁s. The position of short dwell was found at 50 to 60° from catalytic dwell, that is, +10 to 20° from the ATP-binding angle. This is a distinct difference from human mitochondrial F₁, which also shows intervening dwell that probably corresponds to the short dwell of bMF₁, at +65° from the binding pause. Furthermore, we conducted "stall-and-release" experiments with magnetic tweezers to reveal how the binding affinity and hydrolysis equilibrium are modulated by the γ rotation. Similar to thermophilic F₁, bMF₁ showed a strong exponential increase in ATP affinity, while the hydrolysis equilibrium did not change significantly. This indicates that the ATP binding process generates larger torque than the hydrolysis process.

Method to extract multiple states in F1-ATPase rotation experiments from jump distributions

A method is proposed for analyzing fast (10 μs) single-molecule rotation trajectories in F₁ adenosinetriphosphatase ([Formula: see text]-ATPase). This method is based on the distribution of jumps in the rotation angle that occur in the transitions during the steps between subsequent catalytic dwells. The method is complementary to the "stalling" technique devised by H. Noji et al. [Biophys. Rev. 9, 103-118, 2017], and can reveal multiple states not directly detectable as steps. A bimodal distribution of jumps is observed at certain angles, due to the system being in either of 2 states at the same rotation angle. In this method, a multistate theory is used that takes into account a viscoelastic fluctuation of the imaging probe. Using an established sequence of 3 specific states, a theoretical profile of angular jumps is predicted, without adjustable parameters, that agrees with experiment for most of the angular range. Agreement can be achieved at all angles by assuming a fourth state with an ∼10 μs lifetime and a dwell angle about 40° after the adenosine 5'-triphosphate (ATP) binding dwell. The latter result suggests that the ATP binding in one β subunit and the adenosine 5'-diphosphate (ADP) release from another β subunit occur via a transient whose lifetime is ∼10 μs and is about 6 orders of magnitude smaller than the lifetime for ADP release from a singly occupied [Formula: see text]-ATPase. An internal consistency test is given by comparing 2 independent ways of obtaining the relaxation time of the probe. They agree and are ∼15 μs.

Single-molecule analysis reveals rotational substeps and chemo-mechanical coupling scheme of Enterococcus hirae V1-ATPase

V₁-ATPase (V₁), the catalytic domain of an ion-pumping V-ATPase, is a molecular motor that converts ATP hydrolysis-derived chemical energy into rotation. Here, using a gold nanoparticle probe, we directly observed rotation of V₁ from the pathogen Enterococcus hirae (EhV₁). We found that 120° steps in each ATP hydrolysis event are divided into 40 and 80° substeps. In the main pause before the 40° substep and at low ATP concentration ([ATP]), the time constant was inversely proportional to [ATP], indicating that ATP binds during the main pause with a rate constant of 1.0 × 10⁷ m^-1 s^-1 At high [ATP], we observed two [ATP]-independent time constants (0.5 and 0.7 ms). One of two time constants was prolonged (144 ms) in a rotation driven by slowly hydrolyzable ATPγS, indicating that ATP is cleaved during the main pause. In another subpause before the 80° substep, we noted an [ATP]-independent time constant (2.5 ms). Furthermore, in an ATP-driven rotation of an arginine-finger mutant in the presence of ADP, -80 and -40° backward steps were observed. The time constants of the pauses before -80° backward and +40° recovery steps were inversely proportional to [ADP] and [ATP], respectively, indicating that ADP- and ATP-binding events trigger these steps. Assuming that backward steps are reverse reactions, we conclude that 40 and 80° substeps are triggered by ATP binding and ADP release, respectively, and that the remaining time constant in the main pause represents phosphate release. We propose a chemo-mechanical coupling scheme of EhV₁, including substeps largely different from those of F₁-ATPases.

Insights into the origin of the high energy-conversion efficiency of F1-ATPase

Our understanding of the rotary-coupling mechanism of F₁-ATPase has been greatly enhanced in the last decade by advances in X-ray crystallography, single-molecular imaging, and theoretical models. Recently, Volkán-Kacsó and Marcus [S. Volkán-Kacsó, R. A. Marcus, Proc. Natl. Acad. Sci. U.S.A. 112, 14230 (2015)] presented an insightful thermodynamic model based on the Marcus reaction theory coupled with an elastic structural deformation term to explain the observed γ-rotation angle dependence of the adenosine triphosphate (ATP)/adenosine diphosphate (ADP) exchange rates of F₁-ATPase. Although the model is successful in correlating single-molecule data, it is not in agreement with the available theoretical results. We describe a revision of the model, which leads to consistency with the simulation results and other experimental data on the F₁-ATPase rotor compliance. Although the free energy liberated on ATP hydrolysis by F₁-ATPase is rapidly dissipated as heat and so cannot contribute directly to the rotation, we show how, nevertheless, F₁-ATPase functions near the maximum possible efficiency. This surprising result is a consequence of the differential binding of ATP and its hydrolysis products ADP and P_i along a well-defined pathway.

Insights into the mechanism of ATP-driven rotary motors from direct torque measurement

Motor proteins are molecular machines that convert chemical energy into mechanical work. In addition to existing studies performed on the linear motors found in eukaryotic cells, researchers in biophysics have also focused on rotary motors such as F₁-ATPase. Detailed studies on the rotary F₁-ATPase motor have correlated all chemical states to specific mechanical events at the single-molecule level. Recent studies showed that there exists another ATP-driven protein motor in life: the rotary machinery that rotates archaeal flagella (archaella). Rotation speed, stepwise movement, and variable directionality of the motor of Halobacterium salinarum were described in previous studies. Here we review recent experimental work discerning the molecular mechanism underlying how the archaellar motor protein FlaI drives rotation by generation of motor torque. In combination, those studies found that rotation slows as the viscous drag of markers increases, but torque remains constant at 160 pN·nm independent of rotation speed. Unexpectedly, the estimated work done in a single rotation is twice the expected energy that would come from hydrolysis of six ATP molecules in the FlaI hexamer. To reconcile the apparent contradiction, a new and general model for the mechanism of ATP-driven rotary motors is discussed.

Functional importance of αAsp-350 in the catalytic sites of Escherichia coli ATP synthase

Negatively charged residue αAsp-350 of the highly conserved VISIT-DG sequence is required for Pi binding and maintenance of the phosphate-binding subdomain in the catalytic sites of Escherichia coli F₁F_o ATP synthase. αAsp-350 is situated in close proximity, 2.88 Å and 3.5 Å, to the conserved known phosphate-binding residues αR376 and βR182. αD350 is also in close proximity, 1.3 Å, to another functionally important residue αG351. Mutation of αAsp-350 to Ala, Gln, or Arg resulted in substantial loss of oxidative phosphorylation and reduction in ATPase activity by 6- to 16-fold. The loss of the acidic side chain in the form of αD350A, αD350Q, and αD350R caused loss of Pi binding. While removal of Arg in the form of αR376D resulted in the loss of Pi binding, the addition of Arg in the form of αG351R did not affect Pi binding. Our data demonstrates that αD350R helps in the proper orientation of αR376 and βR182 for Pi binding. Fluoroaluminate, fluoroscandium, and sodium azide caused almost complete inhibition of wild type enzyme and caused variable inhibition of αD350 mutant enzymes. NBD-Cl (4-chloro-7-nitrobenzo-2-oxa-1, 3-diazole) caused complete inhibition of wild type enzyme while some residual activity was left in mutant enzymes. Inhibition characteristics supported the conclusion that NBD-Cl reacts in βE (empty) catalytic sites. Phosphate protected against NBD-Cl inhibition of wild type and αG351R mutant enzymes but not inhibition of αD350A, αD350Q, αD350R, or αR376D mutant enzymes. These results demonstrate that αAsp-350 is an essential residue required for phosphate binding, through its interaction with αR376 and βR182, for normal function of phosphate binding subdomain and for transition state stabilization in ATP synthase catalytic sites.