ATP hydrolysis assists phosphate release and promotes reaction ordering in F1-ATPase

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.

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.

A novel approach to measure complex V ATP hydrolysis in frozen cell lysates and tissue homogenates

Mitochondrial depolarization can initiate reversal activity of ATP synthase, depleting ATP by its hydrolysis. We have recently shown that increased ATP hydrolysis contributes to ATP depletion leading to a maladaptation in mitochondrial disorders, where maximal hydrolytic capacity per CV content is increasing. However, despite its importance, ATP hydrolysis is not a commonly studied parameter because of the limitations of the currently available methods. Methods that measure CV hydrolytic activity indirectly require the isolation of mitochondria and involve the introduction of detergents, preventing their utilization in clinical studies or any high-throughput analyses. Here, we describe a novel approach to assess maximal ATP hydrolytic capacity and maximal respiratory capacity in a single assay in cell lysates, PBMCs, and tissue homogenates that were previously frozen. The methodology described here has the potential to be used in clinical samples to determine adaptive and maladaptive adjustments of CV function in diseases, with the added benefit of being able to use frozen samples in a high-throughput manner and to explore ATP hydrolysis as a drug target for disease treatment.

Elucidating microscopic events driven by GTP hydrolysis reaction in the Ras-GAP system with semi-reactive molecular dynamics simulations: the alternative role of a phosphate binding loop for mechanical energy storage

ATPase and GTPase have been widely found as chemical energy-mechanical work transducers, whereas the physicochemical mechanisms are not satisfactorily understood. We addressed the problem by examining John Ross' conjecture that repulsive Coulomb interaction between ADP/GDP and inorganic phosphate (P_i) does the mechanical work upon the system. We effectively simulated the consequence of a GTP hydrolysis reaction in a complex system of Rat sarcoma (Ras) and GTPase activation protein (GAP) in the framework of classical molecular dynamics by switching force field parameters between the reactant and product systems. We then observed a ca. 5 kcal mol^-1 increase of potential energy about the phosphate-binding loop (P-loop) in the Ras protein, indicating that the mechanical work generated via the GTP hydrolysis is converted into the local interaction energy and stored in the P-loop. Interestingly, this local energy storage in the P-loop depends on neither impulsive nor consecutive collisions of GDP and P_i with the P-loop. Instead, GTP-GDP conversion itself does work on the Ras system, elevating the potential energy. These observations encourage us to challenge a conjecture previously given by Ross. We assert that triphosphate nucleotide hydrolyses do mechanical work by producing emergent steric interaction accompanied by relaxation, namely, a shift of the biomolecular system to the non-equilibrium state on the reshaped potential energy landscape. Recalling the universality of the P-loop motif among GTPases and ATPases, the observations that we obtained through this study would progress the physicochemical understanding of the operating principles of GTP/ATP hydrolysis-driven biological nano-machines.

Scattering-based Light Microscopy: From Metal Nanoparticles to Single Proteins

Our ability to detect, image, and quantify nanoscopic objects and molecules with visible light has undergone dramatic improvements over the past few decades. While fluorescence has historically been the go-to contrast mechanism for ultrasensitive light microscopy due to its superior background suppression and specificity, recent developments based on light scattering have reached single-molecule sensitivity. They also have the advantages of universal applicability and the ability to obtain information about the species of interest beyond its presence and location. Many of the recent advances are driven by novel approaches to illumination, detection, and background suppression, all aimed at isolating and maximizing the signal of interest. Here, we review these developments grouped according to the basic principles used, namely darkfield imaging, interferometric detection, and surface plasmon resonance microscopy.

AutoStepfinder: A fast and automated step detection method for single-molecule analysis

Single-molecule techniques allow the visualization of the molecular dynamics of nucleic acids and proteins with high spatiotemporal resolution. Valuable kinetic information of biomolecules can be obtained when the discrete states within single-molecule time trajectories are determined. Here, we present a fast, automated, and bias-free step detection method, AutoStepfinder, that determines steps in large datasets without requiring prior knowledge on the noise contributions and location of steps. The analysis is based on a series of partition events that minimize the difference between the data and the fit. A dual-pass strategy determines the optimal fit and allows AutoStepfinder to detect steps of a wide variety of sizes. We demonstrate step detection for a broad variety of experimental traces. The user-friendly interface and the automated detection of AutoStepfinder provides a robust analysis procedure that enables anyone without programming knowledge to generate step fits and informative plots in less than an hour.

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Fast, automated, and bias-free detection of steps within single-molecule trajectories

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Robust step detection without any prior knowledge on the data

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A dual-pass strategy for the detection of steps over a wide variety of scales

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A user-friendly interface for a simplified step fitting procedure

Single-molecule techniques have made it possible to track individual protein complexes in real time with a nanometer spatial resolution and a millisecond timescale. Accurate determination of the dynamic states within single-molecule time traces provides valuable kinetic information that underlie the function of biological macromolecules. Here, we present a new automated step detection method called AutoStepfinder, a versatile, robust, and easy-to-use algorithm that allows researchers to determine the kinetic states within single-molecule time trajectories without any bias.

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.

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.

Is F1-ATPase a Rotary Motor with Nearly 100% Efficiency? Quantitative Analysis of Chemomechanical Coupling and Mechanical Slip

We present a chemomechanical network model of the rotary molecular motor F₁-ATPase which quantitatively describes not only the rotary motor dynamics driven by ATP hydrolysis but also the ATP synthesis caused by forced reverse rotations. We observe a high reversibility of F₁-ATPase, that is, the main cycle of ATP synthesis corresponds to the reversal of the main cycle in the hydrolysis-driven motor rotation. However, our quantitative analysis indicates that torque-induced mechanical slip without chemomechanical coupling occurs under high external torque and reduces the maximal efficiency of the free energy transduction to 40-80% below the optimal efficiency. Heat irreversibly dissipates not only through the viscous friction of the probe but also directly from the motor due to torque-induced mechanical slip. Such irreversible heat dissipation is a crucial limitation for achieving a 100% free-energy transduction efficiency with biological nanomachines because biomolecules are easily deformed by external torque.

Effects of non-equilibrium angle fluctuation on F1-ATPase kinetics induced by temperature increase

F₁-ATPase (F₁) is an efficient rotary protein motor, whose reactivity is modulated by the rotary angle to utilize thermal fluctuation. In order to elucidate how its kinetics are affected by the change in the fluctuation, we have extended the reaction-diffusion formalism [R. Watanabe et al., Biophys. J., 2013, 105, 2385] applicable to a wider range of temperatures based on experimental data analysis of F₁ derived from thermophilic Bacillus under high ATP concentration conditions. Our simulation shows that the rotary angle distribution manifests a stronger non-equilibrium feature as the temperature increases, because ATP hydrolysis and P_i release are more accelerated compared with the timescale of rotary angle relaxation. This effect causes the rate coefficient obtained from dwell time fitting to deviate from the Arrhenius relation in P_i release, which has been assumed in the previous activation thermodynamic quantities estimation using linear Arrhenius fitting. Larger negative correlation is also found between hydrolysis and P_i release waiting time in a catalytic dwell with the increase in temperature. This loss of independence between the two successive reactions at the catalytic dwell sheds doubt on the conventional dwell time fitting to obtain rate coefficients with a double exponential function at temperatures higher than 65 °C, which is close to the physiological temperature of the thermophilic Bacillus.

Structure and dynamics of rotary V1 motor

Rotary ATPases are unique rotary molecular motors that function as energy conversion machines. Among all known rotary ATPases, F₁-ATPase is the best characterized rotary molecular motor. There are many high-resolution crystal structures and the rotation dynamics have been investigated in detail by extensive single-molecule studies. In contrast, knowledge on the structure and rotation dynamics of V₁-ATPase, another rotary ATPase, has been limited. However, recent high-resolution structural studies and single-molecule studies on V₁-ATPase have provided new insights on how the catalytic sites in this molecular motor change its conformation during rotation driven by ATP hydrolysis. In this review, we summarize recent information on the structural features and rotary dynamics of V₁-ATPase revealed from structural and single-molecule approaches and discuss the possible chemomechanical coupling scheme of V₁-ATPase with a focus on differences between rotary molecular motors.

Deciphering Intrinsic Inter-subunit Couplings that Lead to Sequential Hydrolysis of F1-ATPase Ring

Rotary sequential hydrolysis of the metabolic machine F₁-ATPase is a prominent manifestation of high coordination among multiple chemical sites in ring-shaped molecular machines, and it is also functionally essential for F₁ to tightly couple chemical reactions and central γ-shaft rotation. High-speed AFM experiments have identified that sequential hydrolysis is maintained in the F₁ stator ring even in the absence of the γ-rotor. To explore the origins of intrinsic sequential performance, we computationally investigated essential inter-subunit couplings on the hexameric ring of mitochondrial and bacterial F₁. We first reproduced in stochastic Monte Carlo simulations the experimentally determined sequential hydrolysis schemes by kinetically imposing inter-subunit couplings and following subsequent tri-site ATP hydrolysis cycles on the F₁ ring. We found that the key couplings to support the sequential hydrolysis are those that accelerate neighbor-site ADP and Pi release upon a certain ATP binding or hydrolysis reaction. The kinetically identified couplings were then examined in atomistic molecular dynamics simulations at a coarse-grained level to reveal the underlying structural mechanisms. To do that, we enforced targeted conformational changes of ATP binding or hydrolysis to one chemical site on the F₁ ring and monitored the ensuing conformational responses of the neighboring sites using structure-based simulations. Notably, we found asymmetrical neighbor-site opening that facilitates ADP release upon enforced ATP binding. We also captured a complete charge-hopping process of the Pi release subsequent to enforced ATP hydrolysis in the neighbor site, confirming recent single-molecule analyses with regard to the role of ATP hydrolysis in F₁. Our studies therefore elucidate both the coordinated chemical kinetics and structural dynamics mechanisms underpinning the sequential operation of the F₁ ring.

Catalytic robustness and torque generation of the F1-ATPase

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

Geometric somersaults of a polymer chain through cyclic twisting motions

This study explores the significance of geometric angle shifts, which we call geometric somersaults, arising from cyclic twisting motions of a polymer chain. A five-bead polymer chain serves as a concise and minimal model of a molecular shaft throughout this study. We first show that this polymer chain can change its orientation about its longitudinal axis largely, e.g., 120^{∘}, under conditions of zero total angular momentum by changing the two dihedral angles in a cyclic manner. This phenomenon is an example of the so-called "falling cat" phenomenon, where a falling cat undergoes a geometric somersault by changing its body shape under conditions of zero total angular momentum. We then extend the geometric somersault of the polymer chain to a noisy and viscous environment, where the polymer chain is steered by external driving forces. This extension shows that the polymer chain can achieve an orientation change keeping its total angular momentum and total external torque fluctuating around zero in a noisy and viscous environment. As an application, we argue that the geometric somersault of the polymer chain by 120^{∘} may serve as a prototypical and coarse-grained model for the rotary motion of the central shaft of ATP synthase (F_{O}F_{1}-ATPase). This geometric somersault is in clear contrast to the standard picture for the rotary motion of the central shaft as a rigid body, which generally incurs nonzero total angular momentum and nonzero total external torque. The power profile of the geometric somersault implies a preliminary mechanism for elastic power transmission. The results of this study may be of fundamental interest in twisting and rotary motions of biomolecules.