Dissecting the role of the γ-subunit in the rotary-chemical coupling and torque generation of F1-ATPase

Exploring the activation mechanism of metabotropic glutamate receptor 2

Homomeric dimerization of metabotropic glutamate receptors (mGlus) is essential for the modulation of their functions and represents a promising avenue for the development of novel therapeutic approaches to address central nervous system diseases. Yet, the scarcity of detailed molecular and energetic data on mGlu2 impedes our in-depth comprehension of their activation process. Here, we employ computational simulation methods to elucidate the activation process and key events associated with the mGlu2, including a detailed analysis of its conformational transitions, the binding of agonists, Gi protein coupling, and the guanosine diphosphate (GDP) release. Our results demonstrate that the activation of mGlu2 is a stepwise process and several energy barriers need to be overcome. Moreover, we also identify the rate-determining step of the mGlu2's transition from the agonist-bound state to its active state. From the perspective of free-energy analysis, we find that the conformational dynamics of mGlu2's subunit follow coupled rather than discrete, independent actions. Asymmetric dimerization is critical for receptor activation. Our calculation results are consistent with the observation of cross-linking and fluorescent-labeled blot experiments, thus illustrating the reliability of our calculations. Besides, we also identify potential key residues in the Gi protein binding position on mGlu2, mGlu2 dimer's TM6-TM6 interface, and Gi α5 helix by the change of energy barriers after mutation. The implications of our findings could lead to a more comprehensive grasp of class C G protein-coupled receptor activation.

Rotations of F-ATPase and V-ATPase analyzed by a torque approach

F-type ATP synthase (F-ATPase) and vacuolar ATP hydrolase (V-ATPase) are well-known biomolecular motors, which play significant catalytic roles in ATP synthesis and ATP hydrolysis reactions. Their rotational torques are important factors involved in their rotational behavior that can be measured experimentally but with considerable difficulty. To overcome this difficulty and thereby provide an in-depth understanding of their operation mechanism, we herein carry out simple and fast computer modelling to study the two proteins, using our torque approach that relies on interatomic forces and coordinates of unequilibrated configurations taken from brief molecular dynamics (MD) simulations. As predicted by the torque approach, F-ATPase is demonstrated to be a random rotor, but it prefers to rotate in clockwise direction (as seen from the membrane toward the protein) for ATP synthesis, owing to the predominantly negative angle-averaged torques. By contrast, V-ATPase tends to rotate only in counterclockwise direction for ATP hydrolysis, due to the almost uniform averaged positive torques generated by the unidirectional rotation near the three catalytic sites. The rotational behaviors of both proteins are also affected by the surrounding solvent which can promote or hinder the internal rotation. By combining the torque approach with classic force-field MD simulations, the torques of two biomolecular motors can be calculated economically, and are found to agree with previous experiments and theoretical calculations. This work demonstrates that our torque approach can be extended to the field of biology and can help gain a deeper insight into the mechanistic rotation of biomolecular motors with modest computation time.Communicated by Ramaswamy H. Sarma.

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

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

Long-Time Dynamics of Selected Molecular-Motor Components Using a Physics-Based Coarse-Grained Approach

Molecular motors are essential for the movement and transportation of macromolecules in living organisms. Among them, rotatory motors are particularly efficient. In this study, we investigated the long-term dynamics of the designed left-handed alpha/alpha toroid (PDB: 4YY2), the RBM2 flagellum protein ring from Salmonella (PDB: 6SD5), and the V-type Na+-ATPase rotor in Enterococcus hirae (PDB: 2BL2) using microcanonical and canonical molecular dynamics simulations with the coarse-grained UNRES force field, including a lipid-membrane model, on a millisecond laboratory time scale. Our results demonstrate that rotational motion can occur with zero total angular momentum in the microcanonical regime and that thermal motions can be converted into net rotation in the canonical regime, as previously observed in simulations of smaller cyclic molecules. For 6SD5 and 2BL2, net rotation (with a ratcheting pattern) occurring only about the pivot of the respective system was observed in canonical simulations. The extent and direction of the rotation depended on the initial conditions. This result suggests that rotatory molecular motors can convert thermal oscillations into net rotational motion. The energy from ATP hydrolysis is required probably to set the direction and extent of rotation. Our findings highlight the importance of molecular-motor structures in facilitating movement and transportation within living organisms.

Molecular mechanism and energetics of coupling between substrate binding and product release in the F1-ATPase catalytic cycle

F1-ATPase is a motor protein that couples the rotation of its rotary [Formula: see text] subunit with ATP synthesis or hydrolysis. Single-molecule experiments indicate that nucleotide binding and release events occur almost simultaneously during the synthesis cycle, allowing the energy gain due to spontaneous binding of ADP to one catalytic [Formula: see text] subunit to be directly harnessed for driving the release of ATP from another rather than being dissipated as heat. Here, we examine the unknown mechanism of this coupling that is critical for an exceptionally high mechanochemical efficiency of F1-ATPase by means of all-atom free-energy simulations. We find that nondissipative and kinetically fast progression of the motor in the synthesis direction requires a concerted conformational change involving the closure of the ADP-binding [Formula: see text] subunit followed by the gradual opening of the ATP-releasing [Formula: see text] subunit over the course of the 30 to 40° rotary substep of the [Formula: see text] subunit. This rotary substep, preceding the ATP-dependent metastable state, allows for the recovery of a large portion of the ADP binding energy in the conformation of ATP-bound [Formula: see text] that gradually adopts the low-affinity conformation, captured also by the recent cryo-EM structure of this elusive state. The release of ATP from this nearly open conformation leads to its further opening, which enables the progression of the motor to the next catalytic metastable state. Our simulations explain this energy conversion mechanism in terms of intersubunit and ligand-protein interactions.

F1FO ATP synthase molecular motor mechanisms

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

Application of Coarse-Grained (CG) Models to Explore Conformational Pathway of Large-Scale Protein Machines

Protein machines are clusters of protein assemblies that function in order to control the transfer of matter and energy in cells. For a specific protein machine, its working mechanisms are not only determined by the static crystal structures, but also related to the conformational transition dynamics and the corresponding energy profiles. With the rapid development of crystallographic techniques, the spatial scale of resolved structures is reaching up to thousands of residues, and the concomitant conformational changes become more and more complicated, posing a great challenge for computational biology research. Previously, a coarse-grained (CG) model aiming at conformational free energy evaluation was developed and showed excellent ability to reproduce the energy profiles by accurate electrostatic interaction calculations. In this study, we extended the application of the CG model to a series of large-scale protein machine systems. The spike protein trimer of SARS-CoV-2, ATP citrate lyase (ACLY) tetramer, and P4-ATPases systems were carefully studied and discussed as examples. It is indicated that the CG model is effective to depict the energy profiles of the conformational pathway between two endpoint structures, especially for large-scale systems. Both the energy change and energy barrier between endpoint structures provide reasonable mechanism explanations for the associated biological processes, including the opening of receptor binding domain (RBD) of spike protein, the phospholipid transportation of P4-ATPase, and the loop translocation of ACLY. Taken together, the CG model provides a suitable alternative in mechanistic studies related to conformational change in large-scale protein machines.

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.

Clostridium acetobutylicum atpG-Knockdown Mutants Increase Extracellular pH in Batch Cultures

ATPase, a key enzyme involved in energy metabolism, has not yet been well studied in Clostridium acetobutylicum. Here, we knocked down the atpG gene encoding the ATPase gamma subunit in C. acetobutylicum ATCC 824 using a mobile group II intron system and analyzed the physiological characteristics of the atpG gene knockdown mutant, 824-2866KD. Properties investigated included cell growth, glucose consumption, production of major metabolites, and extracellular pH. Interestingly, in 2-L batch fermentations, 824-2866KD showed no significant difference in metabolite biosynthesis or cell growth compared with the parent ATCC 824. However, the pH value in 824-2866KD cultures at the late stage of the solventogenic phase was abnormally high (pH 6.12), compared with that obtained routinely in the culture of ATCC 824 (pH 5.74). This phenomenon was also observed in batch cultures of another C. acetobutylicum, BEKW-2866KD, an atpG-knockdown and pta-buk double-knockout mutant. The findings reported in this study suggested that ATPase is relatively minor than acid-forming pathway in ATP metabolism in C. acetobutylicum.

Molecular Pumps and Motors

Pumps and motors are essential components of the world as we know it. From the complex proteins that sustain our cells, to the mechanical marvels that power industries, much we take for granted is only possible because of pumps and motors. Although molecular pumps and motors have supported life for eons, it is only recently that chemists have made progress toward designing and building artificial forms of the microscopic machinery present in nature. The advent of artificial molecular machines has granted scientists an unprecedented level of control over the relative motion of components of molecules through the development of kinetically controlled, away-from-thermodynamic equilibrium chemistry. We outline the history of pumps and motors, focusing specifically on the innovations that enable the design and synthesis of the artificial molecular machines central to this Perspective. A key insight connecting biomolecular and artificial molecular machines is that the physical motions by which these machines carry out their function are unambiguously in mechanical equilibrium at every instant. The operation of molecular motors and pumps can be described by trajectory thermodynamics, a theory based on the work of Onsager, which is grounded on the firm foundation of the principle of microscopic reversibility. Free energy derived from thermodynamically non-equilibrium reactions kinetically favors some reaction pathways over others. By designing molecules with kinetic asymmetry, one can engineer potential landscapes to harness external energy to drive the formation and maintenance of geometries of component parts of molecules away-from-equilibrium, that would be impossible to achieve by standard synthetic approaches.

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.

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

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

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.

Consolidation of Nath's torsional mechanism of ATP synthesis and two-ion theory of energy coupling in oxidative phosphorylation and photophosphorylation

In a recent publication, Manoj raises criticisms against consensus views on the ATP synthase. The radical statements and assertions are shown to contradict a vast body of available knowledge that includes i) pioneering single-molecule biochemical and biophysical studies from the respected experimental groups of Kinosita, Yoshida, Noji, Börsch, Dunn, Gräber, Frasch, and Dimroth etc., ii) state-of-the-art X-ray and EM/cryo-EM structural information garnered over the decades by the expert groups of Leslie-Walker, Kühlbrandt, Mueller, Meier, Rubinstein, Sazanov, Duncan, and Pedersen on ATP synthase, iii) the pioneering energy-based computer simulations of Warshel, and iv) the novel theoretical and experimental works of Nath. Valid objections against Mitchell's chemiosmotic theory and Boyer's binding change mechanism put forth by Manoj have been addressed satisfactorily by Nath's torsional mechanism of ATP synthesis and two-ion theory of energy coupling and published 10 to 20 years ago, but these papers are not cited by him. This communication shows conclusively and in great detail that none of his objections apply to Nath's mechanism/theory. Nath's theory is further consolidated based on its previous predictive record, its consistency with biochemical evidence, its unified nature, its application to other related energy transductions and to disease, and finally its ability to guide the design of new experiments. Some constructive suggestions for high-resolution structural experiments that have the power to delve into the heart of the matter and throw unprecedented light on the nature of coupled ion translocation in the membrane-bound F_O portion of F₁F_O-ATP synthase are made.

Revisiting the protomotive vectorial motion of F0-ATPase

The elucidation of the detailed mechanism used by F₀ to convert proton gradient to torque and rotational motion presents a major puzzle despite significant biophysical and structural progress. Although the conceptual model has advanced our understanding of the working principles of such systems, it is crucial to explore the actual mechanism using structure-based models that actually reproduce a unidirectional proton-driven rotation. Our previous work used a coarse-grained (CG) model to simulate the action of F₀ However, the simulations were based on a very tentative structural model of the interaction between subunit a and subunit c. Here, we again use a CG model but with a recent cryo-EM structure of cF₁F₀ and also explore the proton path using our water flooding and protein dipole Langevin dipole semimacroscopic formalism with its linear response approximation version (PDLD/S-LRA) approaches. The simulations are done in the combined space defined by the rotational coordinate and the proton transport coordinate. The study reproduced the effect of the protomotive force on the rotation of the F₀ while establishing the electrostatic origin of this effect. Our landscape reproduces the correct unidirectionality of the synthetic direction of the F₀ rotation and shows that it reflects the combined electrostatic coupling between the proton transport path and the c-ring conformational change. This work provides guidance for further studies in other proton-driven mechanochemical systems and should lead (when combined with studies of F₁) to a complete energy transduction picture of the F₀F₁-ATPase system.

Essential Role of the ε Subunit for Reversible Chemo-Mechanical Coupling in F1-ATPase

F₁-ATPase is a rotary motor protein driven by ATP hydrolysis. Among molecular motors, F₁ exhibits unique high reversibility in chemo-mechanical coupling, synthesizing ATP from ADP and inorganic phosphate upon forcible rotor reversal. The ε subunit enhances ATP synthesis coupling efficiency to > 70% upon rotation reversal. However, the detailed mechanism has remained elusive. In this study, we performed stall-and-release experiments to elucidate how the ε subunit modulates ATP association/dissociation and hydrolysis/synthesis process kinetics and thermodynamics, key reaction steps for efficient ATP synthesis. The ε subunit significantly accelerated the rates of ATP dissociation and synthesis by two- to fivefold, whereas those of ATP binding and hydrolysis were not enhanced. Numerical analysis based on the determined kinetic parameters quantitatively reproduced previous findings of two- to fivefold coupling efficiency improvement by the ε subunit at the condition exhibiting the maximum ATP synthesis activity, a physiological role of F₁-ATPase. Furthermore, fundamentally similar results were obtained upon ε subunit C-terminal domain truncation, suggesting that the N-terminal domain is responsible for the rate enhancement.

Evidence for a Partially Stalled γ Rotor in F1-ATPase from Hydrogen-Deuterium Exchange Experiments and Molecular Dynamics Simulations

F₁-ATPase uses ATP hydrolysis to drive rotation of the γ subunit. The γ C-terminal helix constitutes the rotor tip that is seated in an apical bearing formed by α₃β₃. It remains uncertain to what extent the γ conformation during rotation differs from that seen in rigid crystal structures. Existing models assume that the entire γ subunit participates in every rotation. Here we interrogated E. coli F₁-ATPase by hydrogen-deuterium exchange (HDX) mass spectrometry. Rotation of γ caused greatly enhanced deuteration in the γ C-terminal helix. The HDX kinetics implied that most F₁ complexes operate with an intact rotor at any given time, but that the rotor tip is prone to occasional unfolding. A molecular dynamics (MD) strategy was developed to model the off-axis forces acting on γ. MD runs showed stalling of the rotor tip and unfolding of the γ C-terminal helix. MD-predicted H-bond opening events coincided with experimental HDX patterns. Our data suggest that in vitro operation of F₁-ATPase is associated with significant rotational resistance in the apical bearing. These conditions cause the γ C-terminal helix to get "stuck" (and unfold) sporadically while the remainder of γ continues to rotate. This scenario contrasts the traditional "greasy bearing" model that envisions smooth rotation of the γ C-terminal helix. The fragility of the apical rotor tip in F₁-ATPase is attributed to the absence of a c₁₀ ring that stabilizes the rotation axis in intact F_oF₁. Overall, the MD/HDX strategy introduced here appears well suited for interrogating the inner workings of molecular motors.

Intramolecular Torque Study of a Molecular Rotation Stimulated by Electron Injection and Extraction

Rotation-inducing torque based on interatomic forces is a true indicator of internal molecular rotations. We use the induced intramolecular torque to study the underlying rotational mechanism stimulated by an electron injection or extraction for the rotor molecule 9-(2,4,7-trimethyl-2,3-dihydro-1 H-inden-1-ylidene)-9 H-fluorene, which consists of a "rotator" fragment and a "stator" fragment. The results show that the charged molecule in a quartet spin state can rotate internally, while that in the doublet state cannot. The torque on the rotator in the quartet state always maintains unidirectional rotation. In addition, the attachment/extraction of an electron leads to the reduction of the rotational energy barrier by about 18 kcal/mol, facilitating a more favorable molecular rotation than in the neutral singlet state. Our finding provides a molecular-level understanding of various transformation pathways for experimental designs and further demonstrates the effectiveness of the torque approach.

Elastic coupling power stroke mechanism of the F1-ATPase molecular motor

The angular velocity profile of the 120° F₁-ATPase power stroke was resolved as a function of temperature from 16.3 to 44.6 °C using a Δμ_ATP = -31.25 k_BT at a time resolution of 10 μs. Angular velocities during the first 60° of the power stroke (phase 1) varied inversely with temperature, resulting in negative activation energies with a parabolic dependence. This is direct evidence that phase 1 rotation derives from elastic energy (spring constant, κ = 50 k_BT·rad^-2). Phase 2 of the power stroke had an enthalpic component indicating that additional energy input occurred to enable the γ-subunit to overcome energy stored by the spring after rotating beyond its 34° equilibrium position. The correlation between the probability distribution of ATP binding to the empty catalytic site and the negative E_a values of the power stroke during phase 1 suggests that this additional energy is derived from the binding of ATP to the empty catalytic site. A second torsion spring (κ = 150 k_BT·rad^-2; equilibrium position, 90°) was also evident that mitigated the enthalpic cost of phase 2 rotation. The maximum ΔG^ǂ was 22.6 k_BT, and maximum efficiency was 72%. An elastic coupling mechanism is proposed that uses the coiled-coil domain of the γ-subunit rotor as a torsion spring during phase 1, and then as a crankshaft driven by ATP-binding-dependent conformational changes during phase 2 to drive the power stroke.

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.

The FOF1 ATP synthase: from atomistic three-dimensional structure to the rotary-chemical function

Molecular motors are multi-subunit complexes that are indispensable for accomplishing various tasks of the living cells. One such molecular motor is the F_OF₁ ATP synthase that synthesizes ATP at the expense of the membrane proton gradient. Elucidating the molecular origin of the motor function is challenging despite significant advances in various experimental fields. Currently atomic simulations of whole motor complexes cannot reach to functionally relevant time scales that extend beyond the millisecond regime. Moreover, to reveal the underlying molecular origin of the function, one must model the coupled chemical and conformational events using physically and chemically meaningful multiscaling techniques. In this review, we discuss our approach to model the action of the F₁ and F_O molecular motors, where emphasis is laid on elucidating the molecular origin of the driving force that leads to directional rotation at the expense of ATP hydrolysis or proton gradients. We have used atomic structures of the motors and used hierarchical multiscaling techniques to generate low dimensional functional free energy surfaces of the complete mechano-chemical process. These free energy surfaces were studied further to calculate important characteristics of the motors, such as, rotational torque, temporal dynamics, occurrence of intermittent dwell states, etc. We also studied the result of mutating various parts of the motor domains and our observations correspond very well with the experimental findings. Overall, our studies have generated a cumulative understanding of the motor action, and especially highlight the crucial role of electrostatics in establishing the mechano-chemical coupling.

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.

Methodology for the Simulation of Molecular Motors at Different Scales

Millisecond-scale conformational transitions represent a seminal challenge for traditional molecular dynamics simulations, even with the help of high-end supercomputer architectures. Such events are particularly relevant to the study of molecular motors-proteins or abiological constructs that convert chemical energy into mechanical work. Here, we present a hybrid-simulation scheme combining an array of methods including elastic network models, transition path sampling, and advanced free-energy methods, possibly in conjunction with generalized-ensemble schemes to deliver a viable option for capturing the millisecond-scale motor steps of biological motors. The methodology is already implemented in large measure in popular molecular dynamics programs, and it can leverage the massively parallel capabilities of petascale computers. The applicability of the hybrid method is demonstrated with two examples, namely cyclodextrin-based motors and V-type ATPases.

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.

Chemomechanical Coupling in Hexameric Protein-Protein Interfaces Harnesses Energy within V-Type ATPases

ATP synthase is the most prominent bioenergetic macromolecular motor in all life forms, utilizing the proton gradient across the cell membrane to fuel the synthesis of ATP. Notwithstanding the wealth of available biochemical and structural information inferred from years of experiments, the precise molecular mechanism whereby vacuolar (V-type) ATP synthase fulfills its biological function remains largely fragmentary. Recently, crystallographers provided the first high-resolution view of ATP activity in Enterococcus hirae V1-ATPase. Employing a combination of transition-path sampling and high-performance free-energy methods, the sequence of conformational transitions involved in a functional cycle accompanying ATP hydrolysis has been investigated in unprecedented detail over an aggregate simulation time of 65 μs. Our simulated pathways reveal that the chemical energy produced by ATP hydrolysis is harnessed via the concerted motion of the protein-protein interfaces in the V1-ring, and is nearly entirely consumed in the rotation of the central stalk. Surprisingly, in an ATPase devoid of a central stalk, the interfaces of this ring are perfectly designed for inducing ATP hydrolysis. However, in a complete V1-ATPase, the mechanical property of the central stalk is a key determinant of the rate of ATP turnover. The simulations further unveil a sequence of events, whereby unbinding of the hydrolysis product (ADP + Pi) is followed by ATP uptake, which, in turn, leads to the torque generation step and rotation of the center stalk. Molecular trajectories also bring to light multiple intermediates, two of which have been isolated in independent crystallography experiments.

Theory of single-molecule controlled rotation experiments, predictions, tests, and comparison with stalling experiments in F1-ATPase

A recently proposed chemomechanical group transfer theory of rotary biomolecular motors is applied to treat single-molecule controlled rotation experiments. In these experiments, single-molecule fluorescence is used to measure the binding and release rate constants of nucleotides by monitoring the occupancy of binding sites. It is shown how missed events of nucleotide binding and release in these experiments can be corrected using theory, with F₁-ATP synthase as an example. The missed events are significant when the reverse rate is very fast. Using the theory the actual rate constants in the controlled rotation experiments and the corrections are predicted from independent data, including other single-molecule rotation and ensemble biochemical experiments. The effective torsional elastic constant is found to depend on the binding/releasing nucleotide, and it is smaller for ADP than for ATP. There is a good agreement, with no adjustable parameters, between the theoretical and experimental results of controlled rotation experiments and stalling experiments, for the range of angles where the data overlap. This agreement is perhaps all the more surprising because it occurs even though the binding and release of fluorescent nucleotides is monitored at single-site occupancy concentrations, whereas the stalling and free rotation experiments have multiple-site occupancy.

Rotation of artificial rotor axles in rotary molecular motors

F₁- and V₁-ATPase are rotary molecular motors that convert chemical energy released upon ATP hydrolysis into torque to rotate a central rotor axle against the surrounding catalytic stator cylinder with high efficiency. How conformational change occurring in the stator is coupled to the rotary motion of the axle is the key unknown in the mechanism of rotary motors. Here, we generated chimeric motor proteins by inserting an exogenous rod protein, FliJ, into the stator ring of F₁ or of V₁ and tested the rotation properties of these chimeric motors. Both motors showed unidirectional and continuous rotation, despite no obvious homology in amino acid sequence between FliJ and the intrinsic rotor subunit of F₁ or V₁ These results showed that any residue-specific interactions between the stator and rotor are not a prerequisite for unidirectional rotation of both F₁ and V₁ The torque of chimeric motors estimated from viscous friction of the rotation probe against medium revealed that whereas the F₁-FliJ chimera generates only 10% of WT F₁, the V₁-FliJ chimera generates torque comparable to that of V₁ with the native axle protein that is structurally more similar to FliJ than the native rotor of F₁ This suggests that the gross structural mismatch hinders smooth rotation of FliJ accompanied with the stator ring of F₁.

Torque, chemistry and efficiency in molecular motors: a study of the rotary-chemical coupling in F1-ATPase

Detailed understanding of the action of biological molecular machines must overcome the challenge of gaining a clear knowledge of the corresponding free-energy landscape. An example for this is the elucidation of the nature of converting chemical energy to torque and work in the rotary molecular motor of F₁-ATPase. A major part of the challenge involves understanding the rotary–chemical coupling from a non-phenomenological structure/energy description. Here we focused on using a coarse-grained model of F₁-ATPase to generate a structure-based free-energy landscape of the rotary–chemical process of the whole system. In particular, we concentrated on exploring the possible impact of the position of the catalytic dwell on the efficiency and torque generation of the molecular machine. It was found that the experimentally observed torque can be reproduced with landscapes that have different positions for the catalytic dwell on the rotary–chemical surface. Thus, although the catalysis is undeniably required for torque generation, the experimentally observed position of the catalytic dwell at 80° might not have a clear advantage for the force generation by F₁-ATPase. This further implies that the rotary–chemical couplings in these biological motors are quite robust and their efficiencies do not depend explicitly on the position of the catalytic dwells. Rather, the specific positioning of the dwells with respect to the rotational angle is a characteristic arising due to the structural construct of the molecular machine and might not bear any clear connection to the thermodynamic efficiency for the system.

F1 rotary motor of ATP synthase is driven by the torsionally-asymmetric drive shaft

F₁F₀ ATP synthase (ATPase) either facilitates the synthesis of ATP in a process driven by the proton moving force (pmf), or uses the energy from ATP hydrolysis to pump protons against the concentration gradient across the membrane. ATPase is composed of two rotary motors, F₀ and F₁, which compete for control of their shared γ -shaft. We present a self-consistent physical model of F₁ motor as a simplified two-state Brownian ratchet using the asymmetry of torsional elastic energy of the coiled-coil γ -shaft. This stochastic model unifies the physical concepts of linear and rotary motors, and explains the stepped unidirectional rotary motion. Substituting the model parameters, all independently known from recent experiments, our model quantitatively reproduces the ATPase operation, e.g. the ‘no-load’ angular velocity is ca. 400 rad/s anticlockwise at 4 mM ATP. Increasing the pmf torque exerted by F₀ can slow, stop and overcome the torque generated by F₁, switching from ATP hydrolysis to synthesis at a very low value of ‘stall torque’. We discuss the motor efficiency, which is very low if calculated from the useful mechanical work it produces - but is quite high when the ‘useful outcome’ is measured in the number of H⁺ pushed against the chemical gradient.

The Physics and Physical Chemistry of Molecular Machines

The concept of a "power stroke"-a free-energy releasing conformational change-appears in almost every textbook that deals with the molecular details of muscle, the flagellar rotor, and many other biomolecular machines. Here, it is shown by using the constraints of microscopic reversibility that the power stroke model is incorrect as an explanation of how chemical energy is used by a molecular machine to do mechanical work. Instead, chemically driven molecular machines operating under thermodynamic constraints imposed by the reactant and product concentrations in the bulk function as information ratchets in which the directionality and stopping torque or stopping force are controlled entirely by the gating of the chemical reaction that provides the fuel for the machine. The gating of the chemical free energy occurs through chemical state dependent conformational changes of the molecular machine that, in turn, are capable of generating directional mechanical motions. In strong contrast to this general conclusion for molecular machines driven by catalysis of a chemical reaction, a power stroke may be (and often is) an essential component for a molecular machine driven by external modulation of pH or redox potential or by light. This difference between optical and chemical driving properties arises from the fundamental symmetry difference between the physics of optical processes, governed by the Bose-Einstein relations, and the constraints of microscopic reversibility for thermally activated processes.

Inherent conformational flexibility of F1-ATPase α-subunit

The core of F1-ATPase consists of three catalytic (β) and three noncatalytic (α) subunits, forming a hexameric ring in alternating positions. A wealth of experimental and theoretical data has provided a detailed picture of the complex role played by catalytic subunits. Although major conformational changes have only been seen in β-subunits, it is clear that α-subunits have to respond to these changes in order to be able to transmit information during the rotary mechanism. However, the conformational behavior of α-subunits has not been explored in detail. Here, we have combined unbiased molecular dynamics (MD) simulations and calorimetrically measured thermodynamic signatures to investigate the conformational flexibility of isolated α-subunits, as a step toward deepening our understanding of its function inside the α3β3 ring. The simulations indicate that the open-to-closed conformational transition of the α-subunit is essentially barrierless, which is ideal to accompany and transmit the movement of the catalytic subunits. Calorimetric measurements of the recombinant α-subunit from Geobacillus kaustophilus indicate that the isolated subunit undergoes no significant conformational changes upon nucleotide binding. Simulations confirm that the nucleotide-free and nucleotide-bound subunits show average conformations similar to that observed in the F1 crystal structure, but they reveal an increased conformational flexibility of the isolated α-subunit upon MgATP binding, which might explain the evolutionary conserved capacity of α-subunits to recognize nucleotides with considerable strength. Furthermore, we elucidate the different dependencies that α- and β-subunits show on Mg(II) for recognizing ATP.

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.

Load-dependent destabilization of the γ-rotor shaft in FOF1 ATP synthase revealed by hydrogen/deuterium-exchange mass spectrometry

FoF1 is a membrane-bound molecular motor that uses proton-motive force (PMF) to drive the synthesis of ATP from ADP and Pi. Reverse operation generates PMF via ATP hydrolysis. Catalysis in either direction involves rotation of the γε shaft that connects the α3β3 head and the membrane-anchored cn ring. X-ray crystallography and other techniques have provided insights into the structure and function of FoF1 subcomplexes. However, interrogating the conformational dynamics of intact membrane-bound FoF1 during rotational catalysis has proven to be difficult. Here, we use hydrogen/deuterium exchange mass spectrometry to probe the inner workings of FoF1 in its natural membrane-bound state. A pronounced destabilization of the γ C-terminal helix during hydrolysis-driven rotation was observed. This behavior is attributed to torsional stress in γ, arising from γ⋅⋅⋅α3β3 interactions that cause resistance during γ rotation within the apical bearing. Intriguingly, we find that destabilization of γ occurs only when FoF1 operates against a PMF-induced torque; the effect disappears when PMF is eliminated by an uncoupler. This behavior resembles the properties of automotive engines, where bearings inflict greater forces on the crankshaft when operated under load than during idling.

Intramolecular torque, an indicator of the internal rotation direction of rotor molecules and similar systems

Rotation-inducing torque being ubiquitous in many molecular systems is the driving force of the molecular internal rotation and an indicator of the rotation direction.

Refining the treatment of membrane proteins by coarse-grained models

Obtaining a quantitative description of the membrane proteins stability is crucial for understanding many biological processes. However the advance in this direction has remained a major challenge for both experimental studies and molecular modeling. One of the possible directions is the use of coarse-grained models but such models must be carefully calibrated and validated. Here we use a recent progress in benchmark studies on the energetics of amino acid residue and peptide membrane insertion and membrane protein stability in refining our previously developed coarse-grained model (Vicatos et al., Proteins 2014;82:1168). Our refined model parameters were fitted and/or tested to reproduce water/membrane partitioning energetics of amino acid side chains and a couple of model peptides. This new model provides a reasonable agreement with experiment for absolute folding free energies of several β-barrel membrane proteins as well as effects of point mutations on a relative stability for one of those proteins, OmpLA. The consideration and ranking of different rotameric states for a mutated residue was found to be essential to achieve satisfactory agreement with the reference data.

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.

Elasticity, friction, and pathway of γ-subunit rotation in FoF1-ATP synthase

We combine molecular simulations and mechanical modeling to explore the mechanism of energy conversion in the coupled rotary motors of FoF1-ATP synthase. A torsional viscoelastic model with frictional dissipation quantitatively reproduces the dynamics and energetics seen in atomistic molecular dynamics simulations of torque-driven γ-subunit rotation in the F1-ATPase rotary motor. The torsional elastic coefficients determined from the simulations agree with results from independent single-molecule experiments probing different segments of the γ-subunit, which resolves a long-lasting controversy. At steady rotational speeds of ∼ 1 kHz corresponding to experimental turnover, the calculated frictional dissipation of less than k(B)T per rotation is consistent with the high thermodynamic efficiency of the fully reversible motor. Without load, the maximum rotational speed during transitions between dwells is reached at ∼ 1 MHz. Energetic constraints dictate a unique pathway for the coupled rotations of the Fo and F1 rotary motors in ATP synthase, and explain the need for the finer stepping of the F1 motor in the mammalian system, as seen in recent experiments. Compensating for incommensurate eightfold and threefold rotational symmetries in Fo and F1, respectively, a significant fraction of the external mechanical work is transiently stored as elastic energy in the γ-subunit. The general framework developed here should be applicable to other molecular machines.

Huxley's Model for Muscle Contraction Revisited: The Importance of Microscopic Reversibility

Andrew Huxley's model for muscle contraction is the first mechanistic description of how an energy-providing chemical reaction, ATP hydrolysis, can be coupled by a molecule (myosin) to do work in the environment in a cyclic process. The model was originally used to fit experimentally obtained force vs velocity curves, and has served as a paradigm for understanding mechanochemical coupling ever since. Despite the remarkable success in fitting kinetic data, Huxley's model is thermodynamically inconsistent in several regards, most notably in its failure to include thermal noise in the description of the mechanical transitions by which motion occurs. This inconsistency has led subsequent workers to incorrect conclusions regarding the importance of mechanical transitions for determining the direction of motion, the efficiency of energy conversion, the ratio of forward to backward steps, and the applied force necessary to stop the motion of chemically driven molecular motors. In this chapter an extension of Huxley's model is described where the principle of microscopic reversibility provides a framework for developing a thermodynamically consistent description of a molecular machine. The results show clearly that mechanical strain and the so-called "power stroke" are irrelevant for determining the directionality and thermodynamic properties of any chemically driven molecular motor. Instead these properties are controlled entirely by the chemical specificity that describes how the relative rates of the ATP hydrolysis reaction depend, by allosteric interactions, on the mechanical state of the molecule. This mechanism has been termed an "information ratchet" in the literature. In contrast to the results for chemical driving, a power stroke can be a key component for the operation of an optically driven motor, the transitions of which do not obey microscopic reversibility.