An alternative reaction pathway of F1-ATPase suggested by rotation without 80 degrees/40 degrees substeps of a sluggish mutant at low ATP

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.

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.

Graph-theoretical analysis for energy landscape reveals the organization of state transitions in the resting-state human cerebral cortex

The resting-state brain is often considered a nonlinear dynamic system transitioning among multiple coexisting stable states. Despite the increasing number of studies on the multistability of the brain system, the processes of state transitions have rarely been systematically explored. Thus, we investigated the state transition processes of the human cerebral cortex system at rest by introducing a graph-theoretical analysis of the state transition network. The energy landscape analysis of brain state occurrences, estimated using the pairwise maximum entropy model for resting-state fMRI data, identified multiple local minima, some of which mediate multi-step transitions toward the global minimum. The state transition among local minima is clustered into two groups according to state transition rates and most inter-group state transitions were mediated by a hub transition state. The distance to the hub transition state determined the path length of the inter-group transition. The cortical system appeared to have redundancy in inter-group transitions when the hub transition state was removed. Such a hub-like organization of transition processes disappeared when the connectivity of the cortical system was altered from the resting-state configuration. In the state transition, the default mode network acts as a transition hub, while coactivation of the prefrontal cortex and default mode network is captured as the global minimum. In summary, the resting-state cerebral cortex has a well-organized architecture of state transitions among stable states, when evaluated by a graph-theoretical analysis of the nonlinear state transition network of the brain.

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.

Molecular mechanisms of cell death: central implication of ATP synthase in mitochondrial permeability transition

The term mitochondrial permeability transition (MPT) is commonly used to indicate an abrupt increase in the permeability of the inner mitochondrial membrane to low molecular weight solutes. Widespread MPT has catastrophic consequences for the cell, de facto marking the boundary between cellular life and death. MPT results indeed in the structural and functional collapse of mitochondria, an event that commits cells to suicide via regulated necrosis or apoptosis. MPT has a central role in the etiology of both acute and chronic diseases characterized by the loss of post-mitotic cells. Moreover, cancer cells are often relatively insensitive to the induction of MPT, underlying their increased resistance to potentially lethal cues. Thus, intense efforts have been dedicated not only at the understanding of MPT in mechanistic terms, but also at the development of pharmacological MPT modulators. In this setting, multiple mitochondrial and extramitochondrial proteins have been suspected to critically regulate the MPT. So far, however, only peptidylprolyl isomerase F (best known as cyclophilin D) appears to constitute a key component of the so-called permeability transition pore complex (PTPC), the supramolecular entity that is believed to mediate MPT. Here, after reviewing the structural and functional features of the PTPC, we summarize recent findings suggesting that another of its core components is represented by the c subunit of mitochondrial ATP synthase.

Mechanical operation and intersubunit coordination of ring-shaped molecular motors: insights from single-molecule studies

Ring NTPases represent a large and diverse group of proteins that couple their nucleotide hydrolysis activity to a mechanical task involving force generation and some type of transport process in the cell. Because of their shape, these enzymes often operate as gates that separate distinct cellular compartments to control and regulate the passage of chemical species across them. In this manner, ions and small molecules are moved across membranes, biopolymer substrates are segregated between cells or moved into confined spaces, double-stranded nucleic acids are separated into single strands to provide access to the genetic information, and polypeptides are unfolded and processed for recycling. Here we review the recent advances in the characterization of these motors using single-molecule manipulation and detection approaches. We describe the various mechanisms by which ring motors convert chemical energy to mechanical force or torque and coordinate the activities of individual subunits that constitute the ring. We also examine how single-molecule studies have contributed to a better understanding of the structural elements involved in motor-substrate interaction, mechanochemical coupling, and intersubunit coordination. Finally, we discuss how these molecular motors tailor their operation-often through regulation by other cofactors-to suit their unique biological functions.

Characterization of the temperature-sensitive reaction of F1-ATPase by using single-molecule manipulation

F1-ATPase (F1) is a rotary motor protein that couples ATP hydrolysis to mechanical rotation with high efficiency. In our recent study, we observed a highly temperature-sensitive (TS) step in the reaction catalyzed by a thermophilic F1 that was characterized by a rate constant remarkably sensitive to temperature and had a Q10 factor of 6-19. Since reactions with high Q10 values are considered to involve large conformational changes, we speculated that the TS reaction plays a key role in the rotation of F1. To clarify the role of the TS reaction, in this study, we conducted a stall and release experiment using magnetic tweezers, and assessed the torque generated during the TS reaction. The results indicate that the TS reaction generates the same amount of rotational torque as does ATP binding, but more than that generated during ATP hydrolysis. Thus, we confirmed that the TS reaction contributes significantly to the rotation of F1.

Timing of inorganic phosphate release modulates the catalytic activity of ATP-driven rotary motor protein

F₁-ATPase is a rotary motor protein driven by ATP hydrolysis. The rotary motion of F₁-ATPase is tightly coupled to catalysis, in which the catalytic sites strictly obey the reaction sequences at the resolution of elementary reaction steps. This fine coordination of the reaction scheme is thought to be important to achieve extremely high chemomechanical coupling efficiency and reversibility, which is the prominent feature of F₁-ATPase among molecular motor proteins. In this study, we intentionally change the reaction scheme by using single-molecule manipulation, and we examine the resulting effect on the rotary motion of F₁-ATPase. When the sequence of the products released, that is, ADP and inorganic phosphate, is switched, we find that F₁ frequently stops rotating for a long time, which corresponds to inactivation of catalysis. This inactive state presents MgADP inhibition, and thus, we find that an improper reaction sequence of F₁-ATPase catalysis induces MgADP inhibition.

The F1-ATPase is a motor protein which exhibits rotary motion as a result of catalytic hydrolysis of ATP. Here, the authors investigate how the sequence of this reaction influences molecular rotation, showing that premature product release can result in protein inactivation.

Controlled rotation of the F₁-ATPase reveals differential and continuous binding changes for ATP synthesis

F₁-ATPase is an ATP-driven rotary molecular motor that synthesizes ATP when rotated in reverse. To elucidate the mechanism of ATP synthesis, we imaged binding and release of fluorescently labelled ADP and ATP while rotating the motor in either direction by magnets. Here we report the binding and release rates for each of the three catalytic sites for 360° of the rotary angle. We show that the rates do not significantly depend on the rotary direction, indicating ATP synthesis by direct reversal of the hydrolysis-driven rotation. ADP and ATP are discriminated in angle-dependent binding, but not in release. Phosphate blocks ATP binding at angles where ADP binding is essential for ATP synthesis. In synthesis rotation, the affinity for ADP increases by >10⁴, followed by a shift to high ATP affinity, and finally the affinity for ATP decreases by >10⁴. All these angular changes are gradual, implicating tight coupling between the rotor angle and site affinities.

Reverse rotation of the F1-ATPase results in the synthesis, rather than hydrolysis of ATP. Adachi et al. show that the molecular mechanism of ATP synthesis is the reverse of hydrolysis-driven rotation of the motor, and that ADP and ATP are discriminated by angle-dependent binding.

F(1)-ATPase: a prototypical rotary molecular motor

F(1)-ATPase, the soluble portion of ATP synthase, has been shown to be a rotary molecular motor in which the central γ subunit rotates inside the cylinder made of α(3)β(3) subunits. The rotation is powered by ATP hydrolysis in three catalytic sites, and reverse rotation of the γ subunit by an external force leads to ATP synthesis in the catalytic sites. Here I look back how our lab became involved in the study of this marvelous rotary machine, and discuss some aspects of its rotary mechanism while confessing we are far from understanding. This article is a very personal essay, not a scientific review, for this otherwise viral machines book.

Mechanical modulation of catalytic power on F1-ATPase

The conformational fluctuation of enzymes has a crucial role in reaction acceleration. However, the contribution to catalysis enhancement of individual substates with conformations far from the average conformation remains unclear. We studied the catalytic power of the rotary molecular motor F(1)-ATPase from thermophilic Bacillus PS3 as it was stalled in transient conformations far from a stable pausing angle. The rate constants of ATP binding and hydrolysis were determined as functions of the rotary angle. Both rates exponentially increase with rotation, revealing the molecular basis of positive cooperativity among three catalytic sites: elementary reaction steps are accelerated via the mechanical rotation driven by other reactions on neighboring catalytic sites. The rate enhancement induced by ATP binding upon rotation was greater than that brought about by hydrolysis, suggesting that the ATP binding step contributes more to torque generation than does the hydrolysis step. Additionally, 9% of the ATP-driven rotary step was supported by thermal diffusion, suggesting that acceleration of the ATP docking process occurs via thermally agitated conformational fluctuations.

Mechanism of the conformational change of the F1-ATPase β subunit revealed by free energy simulations

F(1)-ATPase is an ATP-driven rotary motor enzyme. The β subunit changes its conformation from an open to a closed form upon ATP binding. The motion in the β subunit is regarded as a major driving force for rotation of the central stalk. In this Article, we explore the conformational change of the β subunit using all-atom free energy simulations with explicit solvent and propose a detailed mechanism for the conformational change. The β subunit conformational change is accomplished roughly in two characteristic steps: changing of the hydrogen-bond network around ATP and the dynamic movement of the C-terminal domain via sliding of the B-helix. The details of the former step agree well with experimental data. In the latter step, sliding of the B-helix enhances the hydrophobic stabilization due to the exclusion of water molecules from the interface and improved packing in the hydrophobic core. This step contributes to a decrease in free energy, leading to the generation of torque in the F(1)-ATPase upon ATP binding.

A model of stepping kinetics for rotary enzymes. Application to the F1-ATPase

Our simple kinetic model, based on the classic "binding change mechanism", describes the stepping kinetics for the rotary enzyme motors. The model shows that the cooperative interactions between active sites in the motor enzyme F1-ATPase induce the stepping product release. This phenomenon results from non-harmonic oscillations in the enzyme forms. The found rate constants, corresponding to the stepping phenomenon, are close to the rate constants known for the F1-ATPase. The duration of dwells during the product release is shown to depend on the ATP concentration in accordance with the known experimental data.

Chemo-mechanical coupling in F(1)-ATPase revealed by catalytic site occupancy during catalysis

F(1)-ATPase is a rotary molecular motor in which the central gamma subunit rotates inside a cylinder made of alpha(3)beta(3) subunits. To clarify how ATP hydrolysis in three catalytic sites cooperate to drive rotation, we measured the site occupancy, the number of catalytic sites occupied by a nucleotide, while assessing the hydrolysis activity under identical conditions. The results show hitherto unsettled timings of ADP and phosphate releases: starting with ATP binding to a catalytic site at an ATP-waiting gamma angle defined as 0 degrees , phosphate is released at approximately 200 degrees , and ADP is released during quick rotation between 240 degrees and 320 degrees that is initiated by binding of a third ATP. The site occupancy remains two except for a brief moment after the ATP binding, but the third vacant site can bind a medium nucleotide weakly.

Normal-mode-based modeling of allosteric couplings that underlie cyclic conformational transition in F(1) ATPase

F(1) ATPase, a rotary motor comprised of a central stalk (gamma subunit) enclosed by three alpha and beta subunits alternately arranged in a hexamer, features highly cooperative binding and hydrolysis of ATP. Despite steady progress in biophysical, biochemical, and computational studies of this fascinating motor, the structural basis for cooperative ATPase involving its three catalytic sites remains not fully understood. To illuminate this key mechanistic puzzle, we have employed a coarse-grained elastic network model to probe the allosteric couplings underlying the cyclic conformational transition in F(1) ATPase at a residue level of detail. We will elucidate how ATP binding and product (ADP and phosphate) release at two catalytic sites are coupled with the rotation of gamma subunit via various domain motions in alpha(3)beta(3) hexamer (including intrasubunit hinge-bending motions in beta subunits and intersubunit rigid-body rotations between adjacent alpha and beta subunits). To this end, we have used a normal-mode-based correlation analysis to quantify the allosteric couplings of these domain motions to local motions at catalytic sites and the rotation of gamma subunit. We have then identified key amino acid residues involved in the above couplings, some of which have been validated against past studies of mutated and gamma-truncated F(1) ATPase. Our finding strongly supports a binding change mechanism where ATP binding to the empty catalytic site triggers a series of intra- and intersubunit domain motions leading to ATP hydrolysis and product release at the other two closed catalytic sites.

Single molecule measurements of F1-ATPase reveal an interdependence between the power stroke and the dwell duration

Increases in the power stroke and dwell durations of single molecules of Escherichia coli F(1)-ATPase were measured in response to viscous loads applied to the motor and inhibition of ATP hydrolysis. The load was varied using different sizes of gold nanorods attached to the rotating gamma subunit and/or by increasing the viscosity of the medium using PEG-400, a noncompetitive inhibitor of ATPase activity. Conditions that increase the duration of the power stroke were found to cause 20-fold increases in the length of the dwell. These results suggest that the order of hydrolysis, product release, and substrate binding may change as the result of external load on the motor or inhibition of hydrolysis.

Temperature dependence of single molecule rotation of the Escherichia coli ATP synthase F1 sector reveals the importance of gamma-beta subunit interactions in the catalytic dwell

The temperature-dependent rotation of F1-ATPase gamma subunit was observed in V(max) conditions at low viscous drag using a 60-nm gold bead (Nakanishi-Matsui, M., Kashiwagi, S., Hosokawa, H., Cipriano, D. J., Dunn, S. D., Wada, Y., and Futai, M. (2006) J. Biol. Chem. 281, 4126-4131). The Arrhenius slopes of the speed of the individual 120 degrees steps and reciprocal of the pause length between rotation steps were very similar, indicating a flat energy pathway followed by the rotationally coupled catalytic cycle. In contrast, the Arrhenius slope of the reciprocal pause length of the gammaM23K mutant F1 was significantly increased, whereas that of the rotation rate was similar to wild type. The effects of the rotor gammaM23K substitution and the counteracting effects of betaE381D mutation in the interacting stator subunits demonstrate that the rotor-stator interactions play critical roles in the utilization of stored elastic energy. The gammaM23K enzyme must overcome an abrupt activation energy barrier, forcing it onto a less favored pathway that results in uncoupling catalysis from rotation.

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

F(1)-ATPase is a rotary molecular motor powered by the torque generated by another rotary motor F(0) to synthesize ATP in vivo. Therefore elucidation of the behavior of F(1) under external torque is very important. Here, we applied controlled external torque by electrorotation and investigated the ATP-driven rotation for the first time. The rotation was accelerated by assisting torque and decelerated by hindering torque, but F(1) rarely showed rotations in the ATP synthesis direction. This is consistent with the prediction by models based on the assumption that the rotation is tightly coupled to ATP hydrolysis and synthesis. At low ATP concentrations (2 and 5 microM), 120 degrees stepwise rotation was observed. Due to the temperature rise during experiment, quantitative interpretation of the data is difficult, but we found that the apparent rate constant of ATP binding clearly decreased by hindering torque and increased by assisting torque.

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

F(1)-ATPase is a rotary molecular motor that proceeds in 120 degrees steps, each driven by ATP hydrolysis. How the chemical reactions that occur in three catalytic sites are coupled to mechanical rotation is the central question. Here, we show by high-speed imaging of rotation in single molecules of F(1) that phosphate release drives the last 40 degrees of the 120 degrees step, and that the 40 degrees rotation accompanies reduction of the affinity for phosphate. We also show, by single-molecule imaging of a fluorescent ATP analog Cy3-ATP while F(1) is forced to rotate slowly, that release of Cy3-ADP occurs at approximately 240 degrees after it is bound as Cy3-ATP at 0 degrees . This and other results suggest that the affinity for ADP also decreases with rotation, and thus ADP release contributes part of energy for rotation. Together with previous results, the coupling scheme is now basically complete.

Dwell time symmetry in random walks and molecular motors

The statistics of steps and dwell times in reversible molecular motors differ from those of cycle completion in enzyme kinetics. The reason is that a step is only one of several transitions in the mechanochemical cycle. As a result, theoretical results for cycle completion in enzyme kinetics do not apply to stepping data. To allow correct parameter estimation, and to guide data analysis and experiment design, a theoretical treatment is needed that takes this observation into account. In this article, we model the distribution of dwell times and number of forward and backward steps using first passage processes, based on the assumption that forward and backward steps correspond to different directions of the same transition. We extend recent results for systems with a single cycle and consider the full dwell time distributions as well as models with multiple pathways, detectable substeps, and detachments. Our main results are a symmetry relation for the dwell time distributions in reversible motors, and a relation between certain relative step frequencies and the free energy per cycle. We demonstrate our results by analyzing recent stepping data for a bacterial flagellar motor, and discuss the implications for the efficiency and reversibility of the force-generating subunits.

Back-stepping, hidden substeps, and conditional dwell times in molecular motors

Processive molecular motors take more-or-less uniformly sized steps, along spatially periodic tracks, mostly forwards but increasingly backwards under loads. Experimentally, the major steps can be resolved clearly within the noise but one knows biochemically that one or more mechanochemical substeps remain hidden in each enzymatic cycle. In order to properly interpret experimental data for back-to-forward step ratios, mean conditional step-to-step dwell times, etc., a first-passage analysis has been developed that takes account of hidden substeps in N -state sequential models. The explicit, general results differ significantly from previous treatments that identify the observed steps with complete mechanochemical cycles; e.g., the mean dwell times tau(+) and tau(-) prior to forward and back steps, respectively, are normally unequal although the dwell times tau(++) and tau(--) between successive forward and back steps are equal. Illustrative (N=2) -state examples display a wide range of behavior. The formulation extends to the case of two or more detectable transitions in a multistate cycle with hidden substeps.

F1-ATPase: a highly coupled reversible rotary motor

F1 (F1-ATPase) is a highly coupled rotary molecular motor and hydrolyses three ATP molecules per turn (3 ATP/turn). Recently, we have developed femtolitre reaction chamber arrays for highly sensitive measurement of biological reactions. By combining this technique with the rotating magnetic tweezers, the coupling ratio of the reverse reaction, ATP synthesis catalysed by single F1 molecules, has been investigated. The low coupling ratio of 10% (0.3 ATP/turn), catalysed by the alpha3beta3gamma subcomplex of F1, was significantly improved to 77% (2.3 ATP/turn) after reconstitution of the epsilon subunit. This result revealed the novel function of the epsilon subunit as a coupling factor of ATP synthesis catalysed by F1. The possible mechanism for highly coupled ATP synthesis supported by the epsilon subunit is discussed.