Reverse engineering a protein: the mechanochemistry of ATP synthase

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.

Oscillatory Motion of an Organic Droplet Reflecting a Reaction Scheme

An organic droplet containing thymol acetate (TA) floating on a sodium dodecyl sulfate aqueous phase was examined to develop a novel self-propelled object based on reaction kinetics. Two types of oscillatory motion, without back-and-forth motion (Osc I) and with back-and-forth motion (Osc II), were observed by varying the pH of the aqueous phase. The oscillation frequency reached its maximum at pH 9.6, coinciding with the occurrence of Osc II. The kinetics of the hydrolysis of TA as a reactant and the acid-base equilibrium between thymol (TOH) and the thymolate ion (TO-) as products were evaluated experimentally. The driving force of motion was discussed on the basis of the interfacial tension. The pH dependence of the oscillation frequency and the selection of Osc I or II were attributed to the equilibrium between the TOH and TO-. These results highlight the possibility of designing self-propulsion systems by considering reaction kinetics and chemical properties.

Life's Mechanism

The multifarious internal workings of organisms are difficult to reconcile with a single feature defining a state of 'being alive'. Indeed, definitions of life rely on emergent properties (growth, capacity to evolve, agency) only symptomatic of intrinsic functioning. Empirical studies demonstrate that biomolecules including ratcheting or rotating enzymes and ribozymes undergo repetitive conformation state changes driven either directly or indirectly by thermodynamic gradients. They exhibit disparate structures, but govern processes relying on directional physical motion (DNA transcription, translation, cytoskeleton transport) and share the principle of repetitive uniplanar conformation changes driven by thermodynamic gradients, producing dependable unidirectional motion: 'heat engines' exploiting thermodynamic disequilibria to perform work. Recognition that disparate biological molecules demonstrate conformation state changes involving directional motion, working in self-regulating networks, allows a mechanistic definition: life is a self-regulating process whereby matter undergoes cyclic, uniplanar conformation state changes that convert thermodynamic disequilibria into directed motion, performing work that locally reduces entropy. 'Living things' are structures including an autonomous network of units exploiting thermodynamic gradients to drive uniplanar conformation state changes that perform work. These principles are independent of any specific chemical environment, and can be applied to other biospheres.

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.

How does a low-magnitude electric field influence anaerobic digestion in wastewater treatment? A review

Anaerobic digestion (AD) is a physio-biochemical process widely used for treating industrial or municipal wastewater with concomitant methane production. Several technologies have been tested to improve AD's efficiency, like pretreatments and co-digestion, among others. Recently the imposition of a low-magnitude electric field (LMEF) has been applied at the AD to improve methane yield. Despite the positive results of imputing an electric field, many gaps are not understood yet. Therefore, this review focuses on the biochemical aspects of AD and electric field for a better understanding of the effect of the LMEF on the metabolisms of the AD during wastewater treatment and its application in methane production enhancement.

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.

The Legend of ATP: From Origin of Life to Precision Medicine

Adenosine triphosphate (ATP) may be the most important biological small molecule. Since it was discovered in 1929, ATP has been regarded as life’s energy reservoir. However, this compound means more to life. Its legend starts at the dawn of life and lasts to this day. ATP must be the basic component of ancient ribozymes and may facilitate the origin of structured proteins. In the existing organisms, ATP continues to construct ribonucleic acid (RNA) and work as a protein cofactor. ATP also functions as a biological hydrotrope, which may keep macromolecules soluble in the primitive environment and can regulate phase separation in modern cells. These functions are involved in the pathogenesis of aging-related diseases and breast cancer, providing clues to discovering anti-aging agents and precision medicine tactics for breast cancer.

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.

Parallel path mechanisms lead to nonmonotonic force-velocity curves and an optimum load for molecular motor function

Molecular motors convert chemical potential energy into mechanical work and perform a great number of critical biological functions. Examples include the polymerization and manipulation of nucleic acids, the generation of cellular motility and contractility, the formation and maintenance of cell shape, and the transport of materials within cells. The mechanisms underlying these molecular machines are varied, but are almost always considered in the context of a single kinetic pathway that describes motor stepping. However, the multidimensional nature of protein energy landscapes suggests the possibility of multiple reaction pathways connecting two states. Here we investigate the properties of a hypothetical molecular motor able to utilize parallel translocation mechanisms. We explore motor velocity and force dependence as a function of the energy landscape of each path and reveal the potential for such a mechanism to result in negative differential conductance. More specifically, regimes exist where increasing opposing force leads to increased velocity and an optimum load for motor function. We explore how the presence of this optimum depends on the rates of the individual paths and show that the distribution of stepping times characterized by the randomness parameter may be used to test for parallel path mechanisms. Last, we caution that experimental data consisting solely of measurements of velocity as a function of ATP concentration and force cannot be used to eliminate the possibility of such a parallel path mechanism.

ATP synthase: Evolution, energetics, and membrane interactions

The synthesis of ATP, life’s “universal energy currency,” is the most prevalent chemical reaction in biological systems and is responsible for fueling nearly all cellular processes, from nerve impulse propagation to DNA synthesis. ATP synthases, the family of enzymes that carry out this endless task, are nearly as ubiquitous as the energy-laden molecule they are responsible for making. The F-type ATP synthase (F-ATPase) is found in every domain of life and has facilitated the survival of organisms in a wide range of habitats, ranging from the deep-sea thermal vents to the human intestine. Accordingly, there has been a large amount of work dedicated toward understanding the structural and functional details of ATP synthases in a wide range of species. Less attention, however, has been paid toward integrating these advances in ATP synthase molecular biology within the context of its evolutionary history. In this review, we present an overview of several structural and functional features of the F-type ATPases that vary across taxa and are purported to be adaptive or otherwise evolutionarily significant: ion channel selectivity, rotor ring size and stoichiometry, ATPase dimeric structure and localization in the mitochondrial inner membrane, and interactions with membrane lipids. We emphasize the importance of studying these features within the context of the enzyme’s particular lipid environment. Just as the interactions between an organism and its physical environment shape its evolutionary trajectory, ATPases are impacted by the membranes within which they reside. We argue that a comprehensive understanding of the structure, function, and evolution of membrane proteins—including ATP synthase—requires such an integrative approach.

Bedaquiline, an FDA-approved drug, inhibits mitochondrial ATP production and metastasis in vivo, by targeting the gamma subunit (ATP5F1C) of the ATP synthase

Here, we provide evidence that high ATP production by the mitochondrial ATP-synthase is a new therapeutic target for anticancer therapy, especially for preventing tumor progression. More specifically, we isolated a subpopulation of ATP-high cancer cells which are phenotypically aggressive and demonstrate increases in proliferation, stemness, anchorage-independence, cell migration, invasion and multi-drug resistance, as well as high antioxidant capacity. Clinically, these findings have important implications for understanding treatment failure and cancer cell dormancy. Using bioinformatic analysis of patient samples, we defined a mitochondrial-related gene signature for metastasis, which features the gamma-subunit of the mitochondrial ATP-synthase (ATP5F1C). The relationship between ATP5F1C protein expression and metastasis was indeed confirmed by immunohistochemistry. Next, we used MDA-MB-231 cells as a model system to functionally validate these findings. Importantly, ATP-high MDA-MB-231 cells showed a nearly fivefold increase in metastatic capacity in vivo. Consistent with these observations, ATP-high cells overexpressed (i) components of mitochondrial complexes I-V, including ATP5F1C, and (ii) markers associated with circulating tumor cells (CTCs) and metastasis, such as EpCAM and VCAM1. Knockdown of ATP5F1C expression significantly reduced ATP-production, anchorage-independent growth, and cell migration, as predicted. Similarly, therapeutic administration of the FDA-approved drug, Bedaquiline, downregulated ATP5F1C expression in vitro and prevented spontaneous metastasis in vivo. In contrast, Bedaquiline had no effect on the growth of non-tumorigenic mammary epithelial cells (MCF10A) or primary tumors in vivo. Taken together, our results suggest that mitochondrial ATP depletion is a new therapeutic strategy for metastasis prophylaxis, to avoid treatment failure. In summary, we conclude that mitochondrial ATP5F1C is a promising new biomarker and molecular target for future drug development, for the prevention of metastatic disease progression.

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 (Kd > 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.

Evolution of mechanical cooperativity among myosin II motors

Myosin II is a biomolecular machine that is responsible for muscle contraction. Myosin II motors act cooperatively: during muscle contraction, multiple motors bind to a single actin filament and pull it against an external load, like people pulling on a rope in a tug-of-war. We model the dynamics of actomyosin filaments in order to study the evolution of motor-motor cooperativity. We find that filament backsliding-the distance an actin slides backward when a motor at the end of its cycle releases-is central to the speed and efficiency of muscle contraction. Our model predicts that this backsliding has been reduced through evolutionary adaptations to the motor's binding propensity, the strength of the motor's power stroke, and the force dependence of the motor's release from actin. These properties optimize the collective action of myosin II motors, which is not a simple sum of individual motor actions. The model also shows that these evolutionary variables can explain the speed-efficiency trade-off observed across different muscle tissues. This is an example of how evolution can tune the microscopic properties of individual proteins in order to optimize complex biological functions.

A protet-based, protonic charge transfer model of energy coupling in oxidative and photosynthetic phosphorylation

Textbooks of biochemistry will explain that the otherwise endergonic reactions of ATP synthesis can be driven by the exergonic reactions of respiratory electron transport, and that these two half-reactions are catalyzed by protein complexes embedded in the same, closed membrane. These views are correct. The textbooks also state that, according to the chemiosmotic coupling hypothesis, a (or the) kinetically and thermodynamically competent intermediate linking the two half-reactions is the electrochemical difference of protons that is in equilibrium with that between the two bulk phases that the coupling membrane serves to separate. This gradient consists of a membrane potential term Δψ and a pH gradient term ΔpH, and is known colloquially as the protonmotive force or pmf. Artificial imposition of a pmf can drive phosphorylation, but only if the pmf exceeds some 150-170mV; to achieve in vivo rates the imposed pmf must reach 200mV. The key question then is 'does the pmf generated by electron transport exceed 200mV, or even 170mV?' The possibly surprising answer, from a great many kinds of experiment and sources of evidence, including direct measurements with microelectrodes, indicates it that it does not. Observable pH changes driven by electron transport are real, and they control various processes; however, compensating ion movements restrict the Δψ component to low values. A protet-based model, that I outline here, can account for all the necessary observations, including all of those inconsistent with chemiosmotic coupling, and provides for a variety of testable hypotheses by which it might be refined.

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.

Opposing Pressures of Speed and Efficiency Guide the Evolution of Molecular Machines

Many biomolecular machines need to be both fast and efficient. How has evolution optimized these machines along the tradeoff between speed and efficiency? We explore this question using optimizable dynamical models along coordinates that are plausible evolutionary degrees of freedom. Data on 11 motors and ion pumps are consistent with the hypothesis that evolution seeks an optimal balance of speed and efficiency, where any further small increase in one of these quantities would come at great expense to the other. For F_oF₁-ATPases in different species, we also find apparent optimization of the number of subunits in the c-ring, which determines the number of protons pumped per ATP synthesized. Interestingly, these ATPases appear to more optimized for efficiency than for speed, which can be rationalized through their key role as energy transducers in biology. The present modeling shows how the dynamical performance properties of biomolecular motors and pumps may have evolved to suit their corresponding biological actions.

On the beneficent thickness of water

In the 1930s, Lars Onsager published his famous 'reciprocal relations' describing free energy conversion processes. Importantly, these relations were derived on the assumption that the fluxes of the processes involved in the conversion were proportional to the forces (free energy gradients) driving them. For chemical reactions, however, this condition holds only for systems operating close to equilibrium-indeed very close; nominally requiring driving forces to be smaller than k B T. Fairly soon thereafter, however, it was quite inexplicably observed that in at least some biological conversions both the reciprocal relations and linear flux-force dependency appeared to be obeyed no matter how far from equilibrium the system was being driven. No successful explanation of how this 'paradoxical' behaviour could occur has emerged and it has remained a mystery. We here argue, however, that this anomalous behaviour is simply a gift of water, of its viscosity in particular; a gift, moreover, without which life almost certainly could not have emerged. And a gift whose appreciation we primarily owe to recent work by Prof. R. Dean Astumian who, as providence has kindly seen to it, was led to the relevant insights by the later work of Onsager himself.

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.

Theory of Nonequilibrium Free Energy Transduction by Molecular Machines

Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared with more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.

Mechanisms for achieving high speed and efficiency in biomolecular machines

How does a biomolecular machine achieve high speed at high efficiency? We explore optimization principles using a simple two-state dynamical model. With this model, we establish physical principles-such as the optimal way to distribute free-energy changes and barriers across the machine cycle-and connect them to biological mechanisms. We find that a machine can achieve high speed without sacrificing efficiency by varying its conformational free energy to directly link the downhill, chemical energy to the uphill, mechanical work and by splitting a large work step into more numerous, smaller substeps. Experimental evidence suggests that these mechanisms are commonly used by biomolecular machines. This model is useful for exploring questions of evolution and optimization in molecular machines.

Generic maps of optimality reveal two chemomechanical coupling regimes for motor proteins: from F1-ATPase and kinesin to myosin and cytoplasmic dynein

Many motor proteins achieve high efficiency for chemomechanical conversion, and single-molecule force-resisting experiments are a major tool to detect the chemomechanical coupling of efficient motors. Here, we introduce several quantitative relations that involve only parameters extracted from force-resisting experiments and offer new benchmarks beyond mere efficiency to judge the chemomechanical optimality or deficit of evolutionary remote motors on the same footing. The relations are verified by the experimental data from F₁-ATPase, kinesin-1, myosin V and cytoplasmic dynein, which are representative members of four motor protein families. A double-fitting procedure yields the chemomechanical parameters that can be cross-checked for consistency. Using the extracted parameters, two generic maps of chemomechanical optimality are constructed on which motors across families can be quantitatively compared. The maps reveal two chemomechanical coupling regimes, one conducive to high efficiency and high directionality, and the other advantageous to force generation. Surprisingly, an F₁ rotor and a kinesin-1 walker belong to the first regime despite their obvious evolutionary gap, while myosin V and cytoplasmic dynein follow the second regime. This analysis also predicts the symmetries of directional biases and heat productions for the motors, which impose constraints on their chemomechanical coupling and are open to future experimental tests. The verified relations, six in total, present a unified fitting framework to analyze force-resisting experiments. The generic maps of optimality, to which many more motors can be added in future, provide a rigorous method for a systematic cross-family comparison of motors to expose their evolutionary connections and mechanistic similarities.

What can be learned about the enzyme ATPase from single-molecule studies of its subunit F1?

We summarize the different types of single molecule experiments on the F1 component of FOF1-ATP Synthase and what has been learned from them. We also describe results from our recent studies on interpreting the experiments using a chemical-mechanical theory for these biological motors.

Mechanochemical coupling and bi-phasic force-velocity dependence in the ultra-fast ring ATPase SpoIIIE

Multi-subunit ring-shaped ATPases are molecular motors that harness chemical free energy to perform vital mechanical tasks such as polypeptide translocation, DNA unwinding, and chromosome segregation. Previously we reported the intersubunit coordination and stepping behavior of the hexameric ring-shaped ATPase SpoIIIE (Liu et al., 2015). Here we use optical tweezers to characterize the motor’s mechanochemistry. Analysis of the motor response to external force at various nucleotide concentrations identifies phosphate release as the likely force-generating step. Analysis of SpoIIIE pausing indicates that pauses are off-pathway events. Characterization of SpoIIIE slipping behavior reveals that individual motor subunits engage DNA upon ATP binding. Furthermore, we find that SpoIIIE’s velocity exhibits an intriguing bi-phasic dependence on force. We hypothesize that this behavior is an adaptation of ultra-fast motors tasked with translocating DNA from which they must also remove DNA-bound protein roadblocks. Based on these results, we formulate a comprehensive mechanochemical model for SpoIIIE.

Allocating dissipation across a molecular machine cycle to maximize flux

Biomolecular machines consume free energy to break symmetry and make directed progress. Nonequilibrium ATP concentrations are the typical free energy source, with one cycle of a molecular machine consuming a certain number of ATP, providing a fixed free energy budget. Since evolution is expected to favor rapid-turnover machines that operate efficiently, we investigate how this free energy budget can be allocated to maximize flux. Unconstrained optimization eliminates intermediate metastable states, indicating that flux is enhanced in molecular machines with fewer states. When maintaining a set number of states, we show that-in contrast to previous findings-the flux-maximizing allocation of dissipation is not even. This result is consistent with the coexistence of both "irreversible" and reversible transitions in molecular machine models that successfully describe experimental data, which suggests that, in evolved machines, different transitions differ significantly in their dissipation.

Theory of long binding events in single-molecule-controlled rotation experiments on F1-ATPase

The theory of elastic group transfer for the binding and release rate constants for nucleotides in F₁-ATPase as a function of the rotor angle is further extended in several respects. (i) A method is described for predicting the experimentally observed lifetime distribution of long binding events in the controlled rotation experiments by taking into account the hydrolysis and synthesis reactions occurring during these events. (ii) A method is also given for treating the long binding events in the experiments and obtaining the rate constants for the hydrolysis and synthesis reactions occurring during these events. (iii) The theory in the previous paper is given in a symmetric form, an extension that simplifies the application of the theory to experiments. It also includes a theory-based correction of the reported "on" and "off" rates by calculating the missed events. A near symmetry of the data about the angle of -40° and a "turnover" in the binding rate data vs. rotor angle for angles greater than [Formula: see text]40° is also discussed.

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.

Mechanochemical Energy Transduction during the Main Rotary Step in the Synthesis Cycle of F1-ATPase

F₁-ATPase is a highly efficient molecular motor that can synthesize ATP driven by a mechanical torque. Its ability to function reversibly in either direction requires tight mechanochemical coupling between the catalytic domain and the rotating central shaft, as well as temporal control of substrate binding and product release. Despite great efforts and significant progress, the molecular details of this synchronized and fine-tuned energy conversion mechanism are not fully understood. Here, we use extensive molecular dynamics simulations to reconcile recent single-molecule experiments with structural data and provide a consistent thermodynamic, kinetic and mechanistic description of the main rotary substep in the synthetic cycle of mammalian ATP synthase. The calculated free energy profiles capture a discrete pattern in the rotation of the central γ-shaft, with a metastable intermediate located-consistently with recent experimental findings-at 70° relative to the X-ray position. We identify this rotary step as the ATP-dependent substep, and find that the associated free energy input supports the mechanism involving concurrent nucleotide binding and release. During the main substep, our simulations show no significant opening of the ATP-bound β subunit; instead, we observe that mechanical energy is transmitted to its nucleotide binding site, thus lowering the affinity for ATP. Simultaneously, the empty subunit assumes a conformation that enables the enzyme to harness the free energy of ADP binding to drive ATP release. Finally, we show that ligand exchange is regulated by a checkpoint mechanism, an apparent prerequisite for high efficiency in protein nanomotors.

Periodic forces trigger knot untying during translocation of knotted proteins

Proteins need to be unfolded when translocated through the pores in mitochondrial and other cellular membranes. Knotted proteins, however, might get stuck during this process, jamming the pore, since the diameter of the pore is smaller than the size of maximally tightened knot. The jamming probability dramatically increases as the magnitude of the driving force exceeds a critical value, F_c. In this numerical study, we show that for deep knots F_c lies below the force range over which molecular import motors operate, which suggest that in these cases the knots will tighten and block the pores. Next, we show how such topological traps might be prevented by using a pulling protocol of a repetitive, on-off character. Such a repetitive pulling is biologically relevant, since the mitochondrial import motor, like other molecular motors transforms chemical energy into directed motions via nucleotide-hydrolysis-mediated conformational changes, which are cyclic in character.

Thermodynamics of proton transport coupled ATP synthesis

The thermodynamic H(+)/ATP ratio of the H(+)-ATP synthase from chloroplasts was measured in proteoliposomes after energization of the membrane by an acid base transition (Turina et al. 2003 [13], 418-422). The method is discussed, and all published data obtained with this system are combined and analyzed as a single dataset. This meta-analysis led to the following results. 1) At equilibrium, the transmembrane ΔpH is energetically equivalent to the transmembrane electric potential difference. 2) The standard free energy for ATP synthesis (reference reaction) is ΔG°(ref)=33.8±1.3kJ/mol. 3) The thermodynamic H(+)/ATP ratio, as obtained from the shift of the ATP synthesis equilibrium induced by changing the transmembrane ΔpH (varying either pH(in) or pH(out)) is 4.0±0.1. The structural H(+)/ATP ratio, calculated from the ratio of proton binding sites on the c-subunit-ring in F(0) to the catalytic nucleotide binding sites on the β-subunits in F(1), is c/β=14/3=4.7. We infer that the energy of 0.7 protons per ATP that flow through the enzyme, but do not contribute to shifting the ATP/(ADP·Pi) ratio, is used for additional processes within the enzyme, such as activation, and/or energy dissipation, due e.g. to internal uncoupling. The ratio between the thermodynamic and the structural H(+)/ATP values is 0.85, and we conclude that this value represents the efficiency of the chemiosmotic energy conversion within the chloroplast H(+)-ATP synthase.

Theory for rates, equilibrium constants, and Brønsted slopes in F1-ATPase single molecule imaging experiments

A theoretical model of elastically coupled reactions is proposed for single molecule imaging and rotor manipulation experiments on F1-ATPase. Stalling experiments are considered in which rates of individual ligand binding, ligand release, and chemical reaction steps have an exponential dependence on rotor angle. These data are treated in terms of the effect of thermodynamic driving forces on reaction rates, and lead to equations relating rate constants and free energies to the stalling angle. These relations, in turn, are modeled using a formalism originally developed to treat electron and other transfer reactions. During stalling the free energy profile of the enzymatic steps is altered by a work term due to elastic structural twisting. Using biochemical and single molecule data, the dependence of the rate constant and equilibrium constant on the stall angle, as well as the Børnsted slope are predicted and compared with experiment. Reasonable agreement is found with stalling experiments for ATP and GTP binding. The model can be applied to other torque-generating steps of reversible ligand binding, such as ADP and Pi release, when sufficient data become available.

ATP Synthesis by Oxidative Phosphorylation

The F1F0-ATP synthase (EC 3.6.1.34) is a remarkable enzyme that functions as a rotary motor. It is found in the inner membranes of Escherichia coli and is responsible for the synthesis of ATP in response to an electrochemical proton gradient. Under some conditions, the enzyme functions reversibly and uses the energy of ATP hydrolysis to generate the gradient. The ATP synthase is composed of eight different polypeptide subunits in a stoichiometry of α3β3γδεab2c10. Traditionally they were divided into two physically separable units: an F1 that catalyzes ATP hydrolysis (α3β3γδε) and a membrane-bound F0 sector that transports protons (ab2c10). In terms of rotary function, the subunits can be divided into rotor subunits (γεc10) and stator subunits (α3β3δab2). The stator subunits include six nucleotide binding sites, three catalytic and three noncatalytic, formed primarily by the β and α subunits, respectively. The stator also includes a peripheral stalk composed of δ and b subunits, and part of the proton channel in subunit a. Among the rotor subunits, the c subunits form a ring in the membrane, and interact with subunit a to form the proton channel. Subunits γ and ε bind to the c-ring subunits, and also communicate with the catalytic sites through interactions with α and β subunits. The eight subunits are expressed from a single operon, and posttranscriptional processing and translational regulation ensure that the polypeptides are made at the proper stoichiometry. Recent studies, including those of other species, have elucidated many structural and rotary properties of this enzyme.

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.

Evidence for an electrostatic mechanism of force generation by the bacteriophage T4 DNA packaging motor

How viral packaging motors generate enormous forces to translocate DNA into viral capsids remains unknown. Recent structural studies of the bacteriophage T4 packaging motor have led to a proposed mechanism wherein the gp17 motor protein translocates DNA by transitioning between extended and compact states, orchestrated by electrostatic interactions between complimentarily charged residues across the interface between the N- and C-terminal subdomains. Here we show that site-directed alterations in these residues cause force dependent impairments of motor function including lower translocation velocity, lower stall force and higher frequency of pauses and slips. We further show that the measured impairments correlate with computed changes in free-energy differences between the two states. These findings support the proposed structural mechanism and further suggest an energy landscape model of motor activity that couples the free-energy profile of motor conformational states with that of the ATP hydrolysis cycle.

A viral packaging motor varies its DNA rotation and step size to preserve subunit coordination as the capsid fills

Multimeric, ring-shaped molecular motors rely on the coordinated action of their subunits to perform crucial biological functions. During these tasks, motors often change their operation in response to regulatory signals. Here, we investigate a viral packaging machine as it fills the capsid with DNA and encounters increasing internal pressure. We find that the motor rotates the DNA during packaging and that the rotation per base pair increases with filling. This change accompanies a reduction in the motor's step size. We propose that these adjustments preserve motor coordination by allowing one subunit to make periodic, specific, and regulatory contacts with the DNA. At high filling, we also observe the downregulation of the ATP-binding rate and the emergence of long-lived pauses, suggesting a throttling-down mechanism employed by the motor near the completion of packaging. This study illustrates how a biological motor adjusts its operation in response to changing conditions, while remaining highly coordinated.

Autonomous synergic control of nanomotors

Control is a hallmark of machines; effective control over a nanoscale system is necessary to turn it into a nanomachine. Nanomotors from biology often integrate a ratchet-like passive control and a power-stroke-like active control, and this synergic active-plus-passive control is critical to efficient utilization of energy. It remains a challenge to integrate the two differing types of control in rationally designed nanomotor systems. Recently a light-powered track-walking DNA nanomotor was developed from a bioinspired design principle that has the potential to integrate both controls. However, it is difficult to separate experimental signals for either control due to a tight coupling of both controls. Here we present a systematic study of the motor and new derivatives using different fluorescence labeling schemes and light operations. The experimental data suggest that the motor achieves the two controls autonomously through a mechanics-mediated symmetry breaking. This study presents an experimental validation for the bioinspired design principle of mechanical breaking of symmetry for synergic ratchet-plus-power stroke control. Augmented by mechanical and kinetic modeling, this experimental study provides mechanistic insights that may help advance molecular control in future nanotechnological systems.

Anatomy of F1-ATPase powered rotation

F1-ATPase, the catalytic complex of the ATP synthase, is a molecular motor that can consume ATP to drive rotation of the γ-subunit inside the ring of three αβ-subunit heterodimers in 120° power strokes. To elucidate the mechanism of ATPase-powered rotation, we determined the angular velocity as a function of rotational position from single-molecule data collected at 200,000 frames per second with unprecedented signal-to-noise. Power stroke rotation is more complex than previously understood. This paper reports the unexpected discovery that a series of angular accelerations and decelerations occur during the power stroke. The decreases in angular velocity that occurred with the lower-affinity substrate ITP, which could not be explained by an increase in substrate-binding dwells, provides direct evidence that rotation depends on substrate binding affinity. The presence of elevated ADP concentrations not only increased dwells at 35° from the catalytic dwell consistent with competitive product inhibition but also decreased the angular velocity from 85° to 120°, indicating that ADP can remain bound to the catalytic site where product release occurs for the duration of the power stroke. The angular velocity profile also supports a model in which rotation is powered by Van der Waals repulsive forces during the final 85° of rotation, consistent with a transition from F1 structures 2HLD1 and 1H8E (Protein Data Bank).

The ClpXP protease unfolds substrates using a constant rate of pulling but different gears

ATP-dependent proteases are vital to maintain cellular protein homeostasis. Here, we study the mechanisms of force generation and intersubunit coordination in the ClpXP protease from E. coli to understand how these machines couple ATP hydrolysis to mechanical protein unfolding. Single-molecule analyses reveal that phosphate release is the force-generating step in the ATP-hydrolysis cycle and that ClpXP translocates substrate polypeptides in bursts resulting from highly coordinated conformational changes in two to four ATPase subunits. ClpXP must use its maximum successive firing capacity of four subunits to unfold stable substrates like GFP. The average dwell duration between individual bursts of translocation is constant, regardless of the number of translocating subunits, implying that ClpXP operates with constant "rpm" but uses different "gears."

pH-dependent regulation of electron transport and ATP synthesis in chloroplasts

This review is focused on pH-dependent mechanisms of regulation of photosynthetic electron transport and ATP synthesis in chloroplasts. The light-induced acidification of the thylakoid lumen is known to decelerate the plastoquinol oxidation by the cytochrome b 6 f complex, thus impeding the electron flow between photosystem II and photosystem I. Acidification of the lumen also triggers the dissipation of excess energy in the light-harvesting antenna of photosystem II, thereby protecting the photosynthetic apparatus against a solar stress. After brief description of structural and functional organization of the chloroplast electron transport chain, our attention is focused on the nature of the rate-limiting step of electron transfer between photosystem II and photosystem I. In the context of pH-dependent mechanism of photosynthetic control in chloroplasts, the mechanisms of plastoquinol oxidation by the cytochrome b 6 f complex have been considered. The light-induced alkalization of stroma is another factor of pH-dependent regulation of electron transport in chloroplasts. Alkalization of stroma induces activation of the Bassham-Benson-Calvin cycle reactions, thereby promoting efflux of electrons from photosystem I to NADP(+). The mechanisms of the light-induced activation of ATP synthase are briefly considered.

Single-molecule analysis of F0F1-ATP synthase inhibited by N,N-dicyclohexylcarbodiimide

N,N-Dicyclohexylcarbodiimide (DCCD) is a classical inhibitor of the F0F1-ATP synthase (F0F1), which covalently binds to the highly conserved carboxylic acid of the proteolipid subunit (c subunit) in F0. Although it is well known that DCCD modification of the c subunit blocks proton translocation in F0 and the coupled ATP hydrolysis activity of F1, how DCCD inhibits the rotary dynamics of F0F1 remains elusive. Here, we carried out single-molecule rotation assays to characterize the DCCD inhibition of Escherichia coli F0F1. Upon the injection of DCCD, rotations irreversibly terminated with first order reaction kinetics, suggesting that the incorporation of a single DCCD moiety is sufficient to block the rotary catalysis of the F0F1. Individual molecules terminated at different angles relative to the three catalytic angles of F1, suggesting that DCCD randomly reacts with one of the 10 c subunits. DCCD-inhibited F0F1 sometimes showed transient activation; molecules abruptly rotated and stopped after one revolution at the original termination angle, suggesting that hindrance by the DCCD moiety is released due to thermal fluctuation. To explore the mechanical activation of DCCD-inhibited molecules, we perturbed inhibited molecules using magnetic tweezers. The probability of transient activation increased upon a forward forcible rotation. Interestingly, during the termination F0F1, showed multiple positional shifts, which implies that F1 stochastically changes the angular position of its rotor upon a catalytic reaction. This effect could be caused by balancing the angular positions of the F1 and the F0 rotors, which are connected via elastic elements.

Large terminase conformational change induced by connector binding in bacteriophage T7

During bacteriophage morphogenesis DNA is translocated into a preformed prohead by the complex formed by the portal protein, or connector, plus the terminase, which are located at an especial prohead vertex. The terminase is a powerful motor that converts ATP hydrolysis into mechanical movement of the DNA. Here, we have determined the structure of the T7 large terminase by electron microscopy. The five terminase subunits assemble in a toroid that encloses a channel wide enough to accommodate dsDNA. The structure of the complete connector-terminase complex is also reported, revealing the coupling between the terminase and the connector forming a continuous channel. The structure of the terminase assembled into the complex showed a different conformation when compared with the isolated terminase pentamer. To understand in molecular terms the terminase morphological change, we generated the terminase atomic model based on the crystallographic structure of its phage T4 counterpart. The docking of the threaded model in both terminase conformations showed that the transition between the two states can be achieved by rigid body subunit rotation in the pentameric assembly. The existence of two terminase conformations and its possible relation to the sequential DNA translocation may shed light into the molecular bases of the packaging mechanism of bacteriophage T7.

Mechanical transduction mechanisms of RecA-like molecular motors

A majority of ATP-dependent molecular motors are RecA-like proteins, performing diverse functions in biology. These RecA-like molecular motors consist of a highly conserved core containing the ATP-binding site. Here I examined how ATP binding within this core is coupled to the conformational changes of different RecA-like molecular motors. Conserved hydrogen bond networks and conformational changes revealed two major mechanical transduction mechanisms: (1) intra-domain conformational changes and (2) inter-domain conformational changes. The intra-domain mechanism has a significant hydrogen bond rearrangement within the domain containing the P-loop, causing relative motion between two parts of the protein. The inter-domain mechanism exhibits little conformational change in the P-loop domain. Instead, the major conformational change is observed between the P-loop domain and an adjacent domain or subunit containing the arginine finger. These differences in the mechanical transduction mechanisms may link to the underlying energy surface governing a Brownian ratchet or a power stroke.

Principal role of the arginine finger in rotary catalysis of F1-ATPase

F(1)-ATPase (F(1)) is an ATP-driven rotary motor wherein the γ subunit rotates against the surrounding α(3)β(3) stator ring. The 3 catalytic sites of F(1) reside on the interface of the α and β subunits of the α(3)β(3) ring. While the catalytic residues predominantly reside on the β subunit, the α subunit has 1 catalytically critical arginine, termed the arginine finger, with stereogeometric similarities with the arginine finger of G-protein-activating proteins. However, the principal role of the arginine finger of F(1) remains controversial. We studied the role of the arginine finger by analyzing the rotation of a mutant F(1) with a lysine substitution of the arginine finger. The mutant showed a 350-fold longer catalytic pause than the wild-type; this pause was further lengthened by the slowly hydrolyzed ATP analog ATPγS. On the other hand, the mutant F(1) showed highly unidirectional rotation with a coupling ratio of 3 ATPs/turn, the same as wild-type, suggesting that cooperative torque generation by the 3 β subunits was not impaired. The hybrid F(1) carrying a single copy of the α mutant revealed that the reaction step slowed by the mutation occurs at +200° from the binding angle of the mutant subunit. Thus, the principal role of the arginine finger is not to mediate cooperativity among the catalytic sites, but to enhance the rate of the ATP cleavage by stabilizing the transition state of ATP hydrolysis. Lysine substitution also caused frequent pauses because of severe ADP inhibition, and a slight decrease in ATP-binding rate.