Kinetic modeling of rotary CF0F1-ATP synthase: storage of elastic energy during energy transduction

The ATPase asymmetry: Novel computational insight into coupling diverse FO motors with tripartite F1

ATP synthase, a crucial enzyme for cellular bioenergetics, operates via the coordinated coupling of an FO motor, which presents variable symmetry, and a tripartite F1 motor. Despite extensive research, the understanding of their coupling dynamics, especially with non-10-fold symmetrical FO motors, remains incomplete. This study investigates the coupling patterns between eightfold and ninefold FO motors and the constant threefold F1 motor using coarse-grained molecular dynamics simulations. We unveil that in the case of a ninefold FO motor, a 3-3-3 motion is most likely to occur, whereas a 3-3-2 motion predominates with an eightfold FO motor. Furthermore, our findings propose a revised model for the coupling method, elucidating that the pathways' energy usage is primarily influenced by F1 rotation and conformational changes hindered by the b-subunits. Our results present a crucial step toward comprehending the energy landscape and mechanisms governing ATP synthase operation.

FO-F1 coupling and symmetry mismatch in ATP synthase resolved in every FO rotation step

FOF1 ATP synthase, a ubiquitous enzyme that synthesizes most ATP in living cells, is composed of two rotary motors: a membrane-embedded proton-driven FO motor and a catalytic F1 motor. These motors share both central and peripheral stalks. Although both FO and F1 have pseudo-symmetric structures, their symmetries do not match. How symmetry mismatch is solved remains elusive because of the missing intermediate structures of the rotational steps. Here, for the case of Bacillus PS3 ATP synthases with three- and 10-fold symmetries in F1 and FO, respectively, we uncovered the mechanical couplings between FO and F1 at every 36° rotation step via molecular dynamics simulations and comparative studies of cryoelectron microscopy (cryo-EM) structures from three species. We found that the mismatch could be solved using several elements: 1) the F1 head partially rotates relative to the FO a subunit via elastic distortion of the b subunits, 2) the rotor is twisted, and 3) comparisons of cryo-EM structures further suggest that the c ring rotary angles can deviate from the symmetric ones. In addition, the F1 motor may have non-canonical structures, relieving stronger frustration. Thus, we provide new insights for solving the symmetry mismatch problem.

Magnesium and cell energetics: At the junction of metabolism of adenylate and non-adenylate nucleotides

Free magnesium (Mg²⁺) represents a powerful signal arising from interconversions of adenylates (ATP, ADP and AMP). This is a consequence of the involvement of adenylate kinase (AK) which equilibrates adenylates and uses defined species of Mg-complexed and Mg-free adenylates in both directions of its reaction. However, cells contain also other reversible Mg²⁺-dependent enzymes that equilibrate non-adenylate nucleotides (uridylates, cytidylates and guanylates), i.e. nucleoside monophosphate kinases (NMPKs) and nucleoside diphosphate kinase (NDPK). Here, we propose that AK activity is tightly coupled to activities of NMPK and NDPK, linking adenylate equilibrium to equilibria of other nucleotides, and with [Mg²⁺] controlling the ratios of Mg-chelated and Mg-free nucleotides. This coupling establishes main hubs for adenylate-driven equilibration of non-adenylate nucleotides, with [Mg²⁺] acting as signal arising from all nucleotides rather than adenylates only. Further consequences involve an overall adenylate control of UTP-, GTP- and CTP-dependent pathways and the availability of substrates for RNA and DNA synthesis.

Rotational Mechanism of FO Motor in the F-Type ATP Synthase Driven by the Proton Motive Force

In FOF1 ATP synthase, driven by the proton motive force across the membrane, the FO motor rotates the central rotor and induces conformational changes in the F1 motor, resulting in ATP synthesis. Recently, many near-atomic resolution structural models have been obtained using cryo-electron microscopy. Despite high resolution, however, static information alone cannot elucidate how and where the protons pass through the FO and how proton passage is coupled to FO rotation. Here, we review theoretical and computational studies based on FO structure models. All-atom molecular dynamics (MD) simulations elucidated changes in the protonation/deprotonation of glutamate-the protein-carrier residue-during rotation and revealed the protonation states that form the "water wire" required for long-range proton hopping. Coarse-grained MD simulations unveiled a free energy surface based on the protonation state and rotational angle of the rotor. Hybrid Monte Carlo and MD simulations showed how proton transfer is coupled to rotation.

Structure of ATP synthase under strain during catalysis

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

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

Cryo-EM structures provide insight into how E. coli F1Fo ATP synthase accommodates symmetry mismatch

F₁F_o ATP synthase functions as a biological rotary generator that makes a major contribution to cellular energy production. It comprises two molecular motors coupled together by a central and a peripheral stalk. Proton flow through the F_o motor generates rotation of the central stalk, inducing conformational changes in the F₁ motor that catalyzes ATP production. Here we present nine cryo-EM structures of E. coli ATP synthase to 3.1-3.4 Å resolution, in four discrete rotational sub-states, which provide a comprehensive structural model for this widely studied bacterial molecular machine. We observe torsional flexing of the entire complex and a rotational sub-step of F_o associated with long-range conformational changes that indicates how this flexibility accommodates the mismatch between the 3- and 10-fold symmetries of the F₁ and F_o motors. We also identify density likely corresponding to lipid molecules that may contribute to the rotor/stator interaction within the F_o motor.

Maximum Entropy Production Theorem for Transitions between Enzyme Functional States and Its Applications

Transitions between enzyme functional states are often connected to conformational changes involving electron or proton transport and directional movements of a group of atoms. These microscopic fluxes, resulting in entropy production, are driven by non-equilibrium concentrations of substrates and products. Maximal entropy production exists for any chosen transition, but such a maximal transitional entropy production (MTEP) requirement does not ensure an increase of total entropy production, nor an increase in catalytic performance. We examine when total entropy production increases, together with an increase in the performance of an enzyme or bioenergetic system. The applications of the MTEP theorem for transitions between functional states are described for the triosephosphate isomerase, ATP synthase, for β-lactamases, and for the photochemical cycle of bacteriorhodopsin. The rate-limiting steps can be easily identified as those which are the most efficient in dissipating free-energy gradients and in performing catalysis. The last step in the catalytic cycle is usually associated with the highest free-energy dissipation involving proton nanocurents. This recovery rate-limiting step can be optimized for higher efficiency by using corresponding MTEP requirements. We conclude that biological evolution, leading to increased optimal catalytic efficiency, also accelerated the thermodynamic evolution, the synergistic relationship we named the evolution-coupling hypothesis.

Using a Multi-compartmental Metabolic Model to Predict Carbon Allocation in Arabidopsis thaliana

The molecular mechanism of loading/unloading of sucrose into/from the phloem plays an important role in sucrose translocation among plant tissues. Perturbation of this mechanism results in growth phenotypes of a plant. In order to better understand the coupling of sucrose translocation with metabolic processes a multi-compartmental metabolic network of Arabidopsis thaliana was reconstructed and optimized with respect to biomass growth, both in light and in dark conditions. The model can be used to perform flux balance analysis of metabolic fluxes through the central carbon metabolism and catabolic and anabolic pathways. Balances and turnover of energy (ATP/ADP) and redox metabolites (NAD(P)H/NAD(P)) as well as proton concentrations in different compartments can be estimated. Importantly, the model can be used to quantify the translocation of sucrose from source to sink tissues through phloem in association with an integral balance of protons, which in turn is defined by the operational modes of the energy metabolism (light and dark conditions). This chapter describes how a multi-compartmental model to predict carbon allocation is constructed and used.

Torque-coupled thermodynamic model for F_{o}F_{1}-ATPase

F_{o}F_{1}-ATPase is a motor protein complex that utilizes transmembrane ion flow to drive the synthesis of adenosine triphosphate (ATP) from adenosine diphosphate (ADP) and phosphate (Pi). While many theoretical models have been proposed to account for its rotary activity, most of them focus on the F_{o} or F_{1} portions separately rather than the complex as a whole. Here, we propose a simple but new torque-coupled thermodynamic model of F_{o}F_{1}-ATPase. Solving this model at steady state, we find that the monotonic variation of each portion's efficiency becomes much more robust over a wide range of parameters when the F_{o} and F_{1} portions are coupled together, as compared to cases when they are considered separately. Furthermore, the coupled model predicts the dependence of each portion's kinetic behavior on the parameters of the other. Specifically, the power and efficiency of the F_{1} portion are quite sensitive to the proton gradient across the membrane, while those of the F_{o} portion as well as the related Michaelis constants for proton concentrations respond insensitively to concentration changes in the reactants of ATP synthesis. The physiological proton gradient across the membrane in the F_{o} portion is also shown to be optimal for the Michaelis constants of ADP and phosphate in the F_{1} portion during ATP synthesis. Together, our coupled model is able to predict key dynamic and thermodynamic features of the F_{o}F_{1}-ATPase in vivo semiquantitatively, and suggests that such coupling approach could be further applied to other biophysical systems.

Metabolic model of central carbon and energy metabolisms of growing Arabidopsis thaliana in relation to sucrose translocation

BACKGROUND

Sucrose translocation between plant tissues is crucial for growth, development and reproduction of plants. Systemic analysis of these metabolic and underlying regulatory processes allow a detailed understanding of carbon distribution within the plant and the formation of associated phenotypic traits. Sucrose translocation from 'source' tissues (e.g. mesophyll) to 'sink' tissues (e.g. root) is tightly bound to the proton gradient across the membranes. The plant sucrose transporters are grouped into efflux exporters (SWEET family) and proton-symport importers (SUC, STP families). To better understand regulation of sucrose export from source tissues and sucrose import into sink tissues, there is a need for a metabolic model that takes in account the tissue organisation of Arabidopsis thaliana with corresponding metabolic specificities of respective tissues in terms of sucrose and proton production/utilization. An ability of the model to operate under different light modes ('light' and 'dark') and correspondingly in different energy producing modes is particularly important in understanding regulatory modules.

RESULTS

Here, we describe a multi-compartmental model consisting of a mesophyll cell with plastid and mitochondrion, a phloem cell, as well as a root cell with mitochondrion. In this model, the phloem was considered as a non-growing transport compartment, the mesophyll compartment was considered as both autotrophic (growing on CO₂ under light) and heterotrophic (growing on starch in darkness), and the root was always considered as heterotrophic tissue dependent on sucrose supply from the mesophyll compartment. In total, the model includes 413 balanced compounds interconnected by 400 transformers. The structured metabolic model accounts for central carbon metabolism, photosynthesis, photorespiration, carbohydrate metabolism, energy and redox metabolisms, proton metabolism, biomass growth, nutrients uptake, proton gradient generation and sucrose translocation between tissues. Biochemical processes in the model were associated with gene-products (742 ORFs). Flux Balance Analysis (FBA) of the model resulted in balanced carbon, nitrogen, proton, energy and redox states under both light and dark conditions. The main H⁺-fluxes were reconstructed and their directions matched with proton-dependent sucrose translocation from 'source' to 'sink' under any light condition.

CONCLUSIONS

The model quantified the translocation of sucrose between plant tissues in association with an integral balance of protons, which in turn is defined by operational modes of the energy metabolism.

Characterization of the flexibility of the peripheral stalk of prokaryotic rotary A-ATPases by atomistic simulations

Rotary ATPases are involved in numerous physiological processes, with the three distinct types (F/A/V‐ATPases) sharing functional properties and structural features. The basic mechanism involves the counter rotation of two motors, a soluble ATP hydrolyzing/synthesizing domain and a membrane‐embedded ion pump connected through a central rotor axle and a stator complex. Within the A/V‐ATPase family conformational flexibility of the EG stators has been shown to accommodate catalytic cycling and is considered to be important to function. For the A‐ATPase three EG structures have been reported, thought to represent conformational states of the stator during different stages of rotary catalysis. Here we use long, detailed atomistic simulations to show that those structures are conformers explored through thermal fluctuations, but do not represent highly populated states of the EG stator in solution. We show that the coiled coil tail domain has a high persistence length (∼100 nm), but retains the ability to adapt to different conformational states through the presence of two hinge regions. Moreover, the stator network of the related V‐ATPase has been suggested to adapt to subunit interactions in the collar region in addition to the nucleotide occupancy of the catalytic domain. The MD simulations reported here, reinforce this observation showing that the EG stators have enough flexibility to adapt to significantly different structural re‐arrangements and accommodate structural changes in the catalytic domain whilst resisting the large torque generated by catalytic cycling. These results are important to understand the role the stators play in the rotary‐ATPase mechanism. Proteins 2016; 84:1203–1212. © 2016 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

ATP synthase

Oxygenic photosynthesis is the principal converter of sunlight into chemical energy. Cyanobacteria and plants provide aerobic life with oxygen, food, fuel, fibers, and platform chemicals. Four multisubunit membrane proteins are involved: photosystem I (PSI), photosystem II (PSII), cytochrome b6f (cyt b6f), and ATP synthase (FOF1). ATP synthase is likewise a key enzyme of cell respiration. Over three billion years, the basic machinery of oxygenic photosynthesis and respiration has been perfected to minimize wasteful reactions. The proton-driven ATP synthase is embedded in a proton tight-coupling membrane. It is composed of two rotary motors/generators, FO and F1, which do not slip against each other. The proton-driven FO and the ATP-synthesizing F1 are coupled via elastic torque transmission. Elastic transmission decouples the two motors in kinetic detail but keeps them perfectly coupled in thermodynamic equilibrium and (time-averaged) under steady turnover. Elastic transmission enables operation with different gear ratios in different organisms.

Rotation triggers nucleotide-independent conformational transition of the empty β subunit of F₁-ATPase

F1-ATPase (F1) is the catalytic portion of ATP synthase, a rotary motor protein that couples proton gradients to ATP synthesis. Driven by a proton flux, the F1 asymmetric γ subunit undergoes a stepwise rotation inside the α3β3 headpiece and causes the β subunits' binding sites to cycle between states of different affinity for nucleotides. These concerted transitions drive the synthesis of ATP from ADP and phosphate. Here, we study the coupling between the mechanical progression of γ and the conformations of α3β3. Using molecular dynamics simulations, we show that the nucleotide-free β subunit, initially in the open, low-affinity state, undergoes a spontaneous closing transition to the half-open state in response to the γ rotation in the synthesis direction. We estimate the kinetics of this spontaneous conformational change and analyze its mechanism and driving forces. By computing free energy profiles, we find that the isolated empty β subunit preferentially adopts the half-open conformation and that the transition to this conformation from the fully open state is accompanied by well-defined changes in the structure and interactions of the active site region. These results suggest that ADP binding to F1 occurs via conformational selection and is preceded by the transition of the active site to the half-open conformation, driven by the intrinsic elasticity of β. Our results also indicate that opening of the nucleotide-free β during hydrolysis is not spontaneous, as previously assumed. Rather, the fully open conformation observed in the F1 X-ray structure is enforced sterically by the γ subunit whose orientation is stabilized by interactions with the two other β subunits in the completely closed state. This finding supports the notion that γ acts by coupling the extreme conformational states of β subunits within the α3β3 hexamer and therefore is responsible for high efficiency of the coordinated catalysis.

Combined mathematical methods in the description of the F(o)F(1)-ATP synthase catalytic cycle

The FoF1-ATP synthase is one of the key enzymes in supplying energy production in almost all living systems. In this paper, we provide a theoretical description of its catalytic cycle using combined mathematical methods. These methods include Langevin dynamics for the rotation of the central protein core and the Monte-Carlo method to model nucleotide and proton binding. This model is the first in which ATP synthesis and hydrolysis can occur depending on the nucleotide concentration and system conditions. The main advantage of the presented model is the possibility of obtaining results for both single-molecular protein-machines and large ensembles of proteins. The calculated rates are close to the experimentally measured rates for a single enzyme. The model has been formalised as a computer simulation that allows researchers to evaluate ATP production in different types of living cells.

The torque of rotary F-ATPase can unfold subunit gamma if rotor and stator are cross-linked

During ATP hydrolysis by F₁-ATPase subunit γ rotates in a hydrophobic bearing, formed by the N-terminal ends of the stator subunits (αβ)₃. If the penultimate residue at the α-helical C-terminal end of subunit γ is artificially cross-linked (via an engineered disulfide bridge) with the bearing, the rotary function of F₁ persists. This observation has been tentatively interpreted by the unfolding of the α-helix and swiveling rotation in some dihedral angles between lower residues. Here, we screened the domain between rotor and bearing where an artificial disulfide bridge did not impair the rotary ATPase activity. We newly engineered three mutants with double cysteines farther away from the C-terminus of subunit γ, while the results of three further mutants were published before. We found ATPase and rotary activity for mutants with cross-links in the single α-helical, C-terminal portion of subunit γ (from γ285 to γ276 in E. coli), and virtually no activity when the cross-link was placed farther down, where the C-terminal α-helix meets its N-terminal counterpart to form a supposedly stable coiled coil. In conclusion, only the C-terminal singular α-helix is prone to unwinding and can form a swivel joint, whereas the coiled coil portion seems to resist the enzyme's torque.

Calculating the Na⁺ translocating V-ATPase catalytic site affinity for substrate binding by homology modeled NtpA monomer using molecular dynamics/free energy calculation

Vacuolar ATPase (V-ATPase) of Enterococcus hirae is composed of a soluble catalytic domain (V₁; NtpA₃-B₃-D-G) and an integral membrane domain (V₀; NtpI-K₁₀) connected by a central and two peripheral stalks (NtpC, NtpD-G and NtpE-F). Recently nucleotide binding of catalytic NtpA monomer has been reported (Arai et al.). In the present study, we calculated the nucleotide binding affinity of NtpA by molecular dynamics (MD) simulation/free energy calculation using MM-GBSA approach based on homology modeled structure of NtpA monomer docked with ATP analogue, adenosine 5'-[β, γ-imido] triphosphate (AMP-PNP). The calculated binding free energies showed qualitatively good agreement with experimental data. The calculation was cross-validated further by the rigorous method, thermodynamic integration (TI) simulation. Finally, the interaction between NtpA and nucleotides at the atomic level was investigated by the analyses of components of free energy and the optimized model structures obtained from MD simulations, suggesting that electrostatic contribution is responsible for the difference in nucleotide binding to NtpA monomer. This is the first observation and suggestion to explain the difference of nucleotide binding properties in V-ATPase NtpA subunit, and our method can be a valuable primary step to predict nucleotide binding affinity to other subunits (NtpAB, NtpA₃B₃) and to explore subunit interactions and eventually may help to understand energy transduction mechanism of E. hirae V-ATPase.

Two rotary motors in F-ATP synthase are elastically coupled by a flexible rotor and a stiff stator stalk

ATP is synthesized by ATP synthase (F(O)F(1)-ATPase). Its rotary electromotor (F(O)) translocates protons (in some organisms sodium cations) and generates torque to drive the rotary chemical generator (F(1)). Elastic power transmission between F(O) and F(1) is essential for smoothing the cooperation of these stepping motors, thereby increasing their kinetic efficiency. A particularly compliant elastic domain is located on the central rotor (c(10-15)/ε/γ), right between the two sites of torque generation and consumption. The hinge on the active lever on subunit β adds further compliance. It is under contention whether or not the peripheral stalk (and the "stator" as a whole) also serves as elastic buffer. In the enzyme from Escherichia coli, the most extended component of the stalk is the homodimer b(2), a right-handed α-helical coiled coil. By fluctuation analysis we determined the spring constant of the stator in response to twisting and bending, and compared wild-type with b-mutant enzymes. In both deformation modes, the stator was very stiff in the wild type. It was more compliant if b was elongated by 11 amino acid residues. Substitution of three consecutive residues in b by glycine, expected to destabilize its α-helical structure, further reduced the stiffness against bending deformation. In any case, the stator was at least 10-fold stiffer than the rotor, and the enzyme retained its proton-coupled activity.

Single-molecule fluorescence resonance energy transfer techniques on rotary ATP synthases

Conformational changes of proteins can be monitored in real time by fluorescence resonance energy transfer (FRET). Two different fluorophores have to be attached to those protein domains which move during function. Distance fluctuations between the fluorophores are measured by relative fluorescence intensity changes or fluorescence lifetime changes. The rotary mechanics of the two motors of FoF1-ATP synthase have been studied in vitro by single-molecule FRET. The results are summarized and perspectives for other transport ATPases are discussed.

FoF1-ATPase, rotary motor and biosensor

F(o)F(1)-ATPase is an amazing molecular rotary motor at the nanoscale. Single molecule technologies have contributed much to the understanding of the motor. For example, fluorescence imaging and spectroscopy revealed the physical rotation of isolated F(1) and F(o), or F(o)F(1) holoenzyme. Magnetic tweezers were employed to manipulate the ATP synthesis/hydrolysis in F(1), and proton translation in F(o). Here, we briefly review our recent works including a systematic kinetics study of the holoenzyme, the mechanochemical coupling mechanism, reconstituting the delta-free F(o)F(1)-ATPase, direct observation of F(o) rotation at single molecule level and activity regulation through external links on the stator.

Stiffness of γ subunit of F(1)-ATPase

F(1)-ATPase is a molecular motor in which the γ subunit rotates inside the α(3)β(3) ring upon adenosine triphosphate (ATP) hydrolysis. Recent works on single-molecule manipulation of F(1)-ATPase have shown that kinetic parameters such as the on-rate of ATP and the off-rate of adenosine diphosphate (ADP) strongly depend on the rotary angle of the γ subunit (Hirono-Hara et al. 2005; Iko et al. 2009). These findings provide important insight into how individual reaction steps release energy to power F(1) and also have implications regarding ATP synthesis and how reaction steps are reversed upon reverse rotation. An important issue regarding the angular dependence of kinetic parameters is that the angular position of a magnetic bead rotation probe could be larger than the actual position of the γ subunit due to the torsional elasticity of the system. In the present study, we assessed the stiffness of two different portions of F(1) from thermophilic Bacillus PS3: the internal part of the γ subunit embedded in the α(3)β(3) ring, and the complex of the external part of the γ subunit and the α(3)β(3) ring (and streptavidin and magnetic bead), by comparing rotational fluctuations before and after crosslinkage between the rotor and stator. The torsional stiffnesses of the internal and remaining parts were determined to be around 223 and 73 pNnm/radian, respectively. Based on these values, it was estimated that the actual angular position of the internal part of the γ subunit is one-fourth of the magnetic bead position upon stalling using an external magnetic field. The estimated elasticity also partially explains the accommodation of the intrinsic step size mismatch between F(o) and F(1)-ATPase.

Torque generation and elastic power transmission in the rotary F(O)F(1)-ATPase

Adenosine triphosphate (ATP), the universal fuel of the cell, is synthesized from adenosine diphosphate (ADP) and inorganic phosphate (P(i)) by 'ATP synthase' (F(O)F(1)-ATPase). During respiration or photosynthesis, an electrochemical potential difference of protons is set up across the respective membranes. This powers the enzyme's electrical rotary nanomotor (F(O)), which drives the chemical nanomotor (F(1)) by elastic mechanical-power transmission, producing ATP with high kinetic efficiency. Attempts to understand in detail the mechanisms of torque generation in this simple and robust system have been both aided and complicated by a wealth of sometimes conflicting data.

What is the role of epsilon in the Escherichia coli ATP synthase?

The ATP synthase from Escherichia coli is a prototype of the ATP synthases that are found in many bacteria, in the mitochondria of eukaryotes, and in the chloroplasts of plants. It contains eight different types of subunits that have traditionally been divided into F(1), a water-soluble catalytic sector, and F(o), a membrane-bound ion transporting sector. In the current rotary model for ATP synthesis, the subunits can be divided into rotor and stator subunits. Several lines of evidence indicate that epsilon is one of the three rotor subunits, which rotate through 360 degrees. The three-dimensional structure of epsilon is known and its interactions with other subunits have been explored by several approaches. In light of recent work by our group and that of others, the role of epsilon in the ATP synthase from E. coli is discussed.

Domain compliance and elastic power transmission in rotary F(O)F(1)-ATPase

The 2 nanomotors of rotary ATP synthase, ionmotive F(O) and chemically active F(1), are mechanically coupled by a central rotor and an eccentric bearing. Both motors rotate, with 3 steps in F(1) and 10-15 in F(O). Simulation by statistical mechanics has revealed that an elastic power transmission is required for a high rate of coupled turnover. Here, we investigate the distribution in the F(O)F(1) structure of compliant and stiff domains. The compliance of certain domains was restricted by engineered disulfide bridges between rotor and stator, and the torsional stiffness (kappa) of unrestricted domains was determined by analyzing their thermal rotary fluctuations. A fluorescent magnetic bead was attached to single molecules of F(1) and a fluorescent actin filament to F(O)F(1), respectively. They served to probe first the functional rotation and, after formation of the given disulfide bridge, the stochastic rotational motion. Most parts of the enzyme, in particular the central shaft in F(1), and the long eccentric bearing were rather stiff (torsional stiffness kappa > 750 pNnm). One domain of the rotor, namely where the globular portions of subunits gamma and epsilon of F(1) contact the c-ring of F(O), was more compliant (kappa congruent with 68 pNnm). This elastic buffer smoothes the cooperation of the 2 stepping motors. It is located were needed, between the 2 sites where the power strokes in F(O) and F(1) are generated and consumed.

The proton-translocating a subunit of F0F1-ATP synthase is allocated asymmetrically to the peripheral stalk

The position of the a subunit of the membrane-integral F0 sector of Escherichia coli ATP synthase was investigated by single molecule fluorescence resonance energy transfer studies utilizing a fusion of enhanced green fluorescent protein to the C terminus of the a subunit and fluorescent labels attached to specific positions of the epsilon or gamma subunits. Three fluorescence resonance energy transfer levels were observed during rotation driven by ATP hydrolysis corresponding to the three resting positions of the rotor subunits, gamma or epsilon, relative to the a subunit of the stator. Comparison of these positions of the rotor sites with those previously determined relative to the b subunit dimer indicates the position of a as adjacent to the b dimer on its counterclockwise side when the enzyme is viewed from the cytoplasm. This relationship provides stability to the membrane interface between a and b2, allowing it to withstand the torque imparted by the rotor during ATP synthesis as well as ATP hydrolysis.

The coupled chemomechanics of the F(1)-ATPase molecular motor

The enzyme F(1)-ATPase is a rotary nanomotor in which the central gamma subunit rotates inside the cavity made of alpha(3)beta(3) subunits. The experiments showed that the rotation proceeds in steps of 120 degrees and each 120 degrees step consists of 80 degrees and 40 degrees substeps. Here the Author proposes a stochastic wave mechanics of the F(1)-ATPase motor and combines it with the structure-based kinetics of the F(1)-ATPase to form a chemomechanic coupled model. The model can reproduce quantitatively and explain the experimental observations about the F(1) motor. Using the model, several rate-limited situations about gamma subunit rotation are proposed, the effects of the friction and the load on the substeps are investigated and the chemomechanic coupled time during ATP hydrolysis cycle is determined.

The thermodynamic H+/ATP ratios of the H+-ATPsynthases from chloroplasts and Escherichia coli

The H(+)/ATP ratio is an important parameter for the energy balance of all cells and for the coupling mechanism between proton transport and ATP synthesis. A straightforward interpretation of rotational catalysis predicts that the H(+)/ATP coincides with the ratio of the c-subunits to beta-subunits, implying that, for the chloroplast and Escherichia coli ATPsynthases, numbers of 4.7 and 3.3 are expected. Here, the energetics described by the chemiosmotic theory was used to determine the H(+)/ATP ratio for the two enzymes. The isolated complexes were reconstituted into liposomes, and parallel measurements were performed under identical conditions. The internal phase of the liposomes was equilibrated with the acidic medium during reconstitution, allowing to measure the internal pH with a glass electrode. An acid-base transition was carried out and the initial rates of ATP synthesis or ATP hydrolysis were measured with luciferin/luciferase as a function of DeltapH at constant Q = [ATP]/([ADP][P(i)]). From the shift of the equilibrium DeltapH as a function of Q the standard Gibbs free energy for phosphorylation, DeltaG(p)(0)'; and the H(+)/ATP ratio were determined. It resulted DeltaG(p)(0)' = 38 +/- 3 kJ.mol(-1) and H(+)/ATP = 4.0 +/- 0.2 for the chloroplast and H(+)/ATP = 4.0 +/- 0.3 for the E. coli enzyme, indicating that the thermodynamic H(+)/ATP ratio is the same for both enzymes and that it is different from the subunit stoichiometric ratio.

Cooperativity in the motor activities of the ATP-fueled molecular motors

Kinesin, myosin and F1-ATPase are multi-domain molecular motors with multiple catalytic subunits. The motor mechanochemics are achieved via the conversion of ATP hydrolysis energy into forces and motions. We find that the catalysis of these molecular motors do not follow the simple Michaelis-Menten mechanism. The motor activities, such as the hydrolysis or processive rates, of kinesin, myosin and F1-ATPase have a complex ATP-dependent cooperativity. To understand this complexity in kinetics and mechanochemics, we develop a conformation correlation theory of cooperativity for the ATP-fueled motor proteins. The quantitative analysis and simulations indicate that cooperativity is induced by the conformational coupling of binding states of different subunits and prevails in the motor activities.

Biomolecular motors: the F1-ATPase paradigm

The realization that many essential functions of living cells are performed by nanoscale motors consisting of protein complexes has given rise to an intense effort to understand their mechanisms. Considerable progress has been made in the past two years by a combination of biophysical techniques and theoretical analysis. Single-molecule studies have played a spectacular role for a variety of motors including kinesin, myosin, and polymerases. The understanding of F(1)-ATPase, the smallest biomolecular rotary motor, has made particular progress by the interplay of experimental and theoretical studies; the latter have provided information not available from experiment.

Distances between the b-subunits in the tether domain of F(0)F(1)-ATP synthase from E. coli

The arrangement of the b-subunits in the holo-enzyme F(0)F(1)-ATP synthase from E. coli is investigated by site-directed mutagenesis spin-label EPR. F(0)F(1)-ATP synthases couple proton translocation with the synthesis of ATP from ADP and phosphate. The hydrophilic F(1)-part and the hydrophobic membrane-integrated F(0)-part are connected by a central and a peripheral stalk. The peripheral stalk consists of two b-subunits. Cysteine mutations are introduced in the tether domain of the b-subunit at b-40, b-51, b-53, b-62 or b-64 and labeled with a nitroxide spin label. Conventional (9 GHz), high-field (95 GHz) and pulsed EPR spectroscopy reveal: All residues are in a relatively polar environment, with mobilities consistent with helix sites. The distance between the spin labels at each b-subunit is 2.9 nm in each mutant, revealing a parallel arrangement of the two helices. They can be in-register but separated by a large distance (1.9 nm), or at close contact and displaced along the helix axes by maximally 2.7 nm, which excludes an in-register coiled-coil model suggested previously for the b-subunit. Binding of the non-hydrolysable nucleotide AMPPNP to the spin-labeled enzyme had no significant influence on the distances compared to that in the absence of nucleotides.

Protein structural transitions and their functional role

Living cells are a collection of molecular machines which carry out many of the functions essential for the cell's existence, differentiation and reproduction. Most, though not all, of these machines are made up of proteins. Because of their complexity, an understanding of how they work requires a synergistic combination of experimental and theoretical studies. In this paper we outline our studies of two such protein machines. One is GroEL, the chaperone from Escherichia coli, which aids in protein folding; the other is F(1)-ATPase, a motor protein which synthesizes and hydrolyses ATP.

Complex cooperativity of ATP hydrolysis in the F(1)-ATPase molecular motor

F(1)-ATPase catalyses ATP hydrolysis and converts the cellular chemical energy into mechanical rotation. The hydrolysis reaction in F(1)-ATPase does not follow the widely believed Michaelis-Menten mechanism. Instead, the hydrolysis mechanism behaves in an ATP-dependent manner. We develop a model for enzyme kinetics and hydrolysis cooperativity of F(1)-ATPase which involves the binding-state changes to the coupling catalytic reactions. The quantitative analysis and modeling suggest the existence of complex cooperative hydrolysis between three different catalysis sites of F(1)-ATPase. This complexity may be taken into account to resolve the arguments on the binding change mechanism in F(1)-ATPase.

Binding of the b-subunit in the ATP synthase from Escherichia coli

The rotary mechanism of ATP synthase requires a strong binding within stator subunits. In this work we studied the binding affinity of the b-subunit to F(1)-ATPase of Escherichia coli. The dimerization of the truncated b-subunit without amino acids 1-33, b(34-156)T62C, was investigated by analytical ultracentrifugation, resulting in a dissociation constant of 1.8 microM. The binding of b-subunit monomeric and dimeric forms to the isolated F(1) part was investigated by fluorescence correlation spectroscopy and steady-state fluorescence. The mutants b(34-156)T62C and EF(1)-gammaT106C were labeled with several fluorophores. Fluorescence correlation spectroscopy was used to measure translational diffusion times of the labeled b-subunit, labeled F(1), and a mixture of the labeled b-subunit with unlabeled F(1). Data analysis revealed a dissociation constant of 0.2 nM of the F(1)b(2) complex, yielding a Gibbs free energy of binding of DeltaG(o)= -55 kJ mol(-1). In steady-state fluorescence resonance energy transfer (FRET) measurements it was found that binding of the b-subunit to EF(1)-gammaT106C-Alexa488 resulted in a fluorescence decrease of one-third of the initial FRET donor fluorescence intensity. The decrease of fluorescence was measured as a function of b-concentration, and data were described by a model including equilibria for dimerization of the b-subunit and binding of b and b(2) to F(1). For a quantitative description of fluorescence decrease we used two different models: the binding of the first and the second b-subunit causes the same fluorescence decrease (model 1) or only the binding of the first b-subunit causes fluorescence decrease (model 2). Data evaluation revealed a dissociation constant for the F(1)b(2) complex of 0.6 nM (model 1) or 14 nM (model 2), giving DeltaG(o)= -52 kJ mol(-1) and DeltaG(o)= -45 kJ mol(-1), respectively. The maximal DeltaG observed for ATP synthesis in cells is approximately DeltaG= 55 kJ mol(-1). Therefore, the binding energy of the b-subunit seems to be too low for models in which the free energy for ATP synthesis is accumulated in the elastic strain between rotor and stator subunits and then transduced to the catalytic site in one single step. Models in which energy transduction takes place in at least two steps are favored.

Does F1-ATPase subunit gamma turn in the wrong direction?

Analyzing the direction of F1-ATPase subunit gamma rotation, its shape and non-random distribution of surface residues, a mechanism is proposed for how gamma induces the closing/opening of the catalytic sites at beta/alpha interfaces: by keeping contact with the mobile domain of subunits beta at the 'jaw' (D386, the seven consecutive hydrophobic residues and D394/E395), rotating gamma works as a screw conveyer within the barrel of (alpha,beta)3. Mutations of the conveyer contacts are predicted to inhibit. Rotating wheel cartoons illustrate enzyme turnover and conformational changes. Steric clashes, polar interactions and also substrate limitations lead to specific stops. Because it is constructed as a stepper, gamma prevents uncoupling at high energy charge.

The H+-ATPase from chloroplasts: effect of different reconstitution procedures on ATP synthesis activity and on phosphate dependence of ATP synthesis

The H+-ATP synthase from chloroplasts, CF0F1, was isolated, reconstituted into liposomes and ATP synthesis activity was measured after energization of the proteoliposomes with an acid-base transition. The ATP yield was measured as a function of the reaction time after energization, the data were fitted by an exponential function and the initial rate was calculated from the fit parameters. CF0F1 was reconstituted by detergent dialysis in asolectin liposomes and phosphatidylcholine/phosphatidic acid (PtdCho/PtdAc from egg yolk) liposomes. In asolectin liposomes, high initial rates of ATP synthesis (up to 400 s(-1)) were observed with a rapid decline of the rate; in PtdCho/PtdAc liposomes the initial rate is smaller (up to 200 s(-1)), but the decline of the activity is slower. CF0F1 was reconstituted into PtdCho/PtdAc liposomes either by detergent dialysis or into reverse phase liposomes. The dependence of the rate of ATP synthesis on the phosphate concentration was measured with both types of proteoliposomes. The data can be described by Michaelis-Menten kinetics with a K(M) value of 350 microM for reverse phase liposomes and a K(M) value of 970 microM for dialysis liposomes. Both K(M) values depend neither on the magnitude of DeltapH nor on the electric potential difference, whereas V(max) decreases strongly with decreasing energization. At low phosphate concentration, there are small deviations from Michaelis-Menten kinetics. The measured rates are higher than those calculated from the fitted Michaelis-Menten parameters. This effect is interpreted as evidence that more than one phosphate binding site is involved in ATP synthesis.

Bacterial flagellar motor and H(+)/ATP synthase: two proton-driven rotary molecular devices with different functions

Both the bacterial flagellar motor and the H(+)/ATP synthase are membrane-bound macromolecular complexes in which the movement of protons through channels across the membrane is coupled to the rotation of a part of the complex around an axis perpendicular to the membrane. Despite this similarity, the two devices are designed for quite different functions. The flagellar motor is responsible for a practically smooth rotation of the flagellar filament in order to propel the cell. Smooth rotation is not essential for the H(+)/ATP synthase, which accumulates torque by twisting a rod-shaped structure. Possible mechanisms for generating torque in the two devices are presented, based on the models which have been proposed. The performances of the various mechanisms are discussed.

Viscoelastic dynamics of actin filaments coupled to rotary F-ATPase: angular torque profile of the enzyme

ATP synthase (F(O)F(1)) operates as two rotary motor/generators coupled by a common shaft. Both portions, F(1) and F(O), are rotary steppers. Their symmetries are mismatched (C(3) versus C(10-14)). We used the curvature of fluorescent actin filaments, attached to the rotating c-ring, as a spring balance (flexural rigidity of 8. 10(-26) Nm(2)) to gauge the angular profile of the output torque at F(O) during ATP hydrolysis by F(1) (see theoretical companion article (. Biophys. J. 81:1234-1244.)). The large average output torque (50 +/- 6 pN. nm) proved the absence of any slip. Variations of the torque were small, and the output free energy of the loaded enzyme decayed almost linearly over the angular reaction coordinate. Considering the threefold stepping and high activation barrier of the driving motor proper, the rather constant output torque implied a soft elastic power transmission between F(1) and F(O). It is considered as essential, not only for the robust operation of this ubiquitous enzyme under symmetry mismatch, but also for a high turnover rate of the two counteracting and stepping motor/generators.

Viscoelastic dynamics of actin filaments coupled to rotary F-ATPase: curvature as an indicator of the torque

ATP synthase (F-ATPase) operates as an electrochemical-to-mechanical-to-chemical energy transducer with an astounding 360 degrees rotary motion of subunits epsilongammac(10-14) (rotor) against delta(alphabeta)(3)ab(2) (stator). The enzyme's torque as a function of the angular reaction coordinate in relation to ATP-synthesis/hydrolysis, internal elasticity, and external load has remained an important issue. Fluorescent actin filaments of micrometer length have been used to detect the rotation as driven by ATP hydrolysis. We evaluated the viscoelastic dynamics of actin filaments under the influence of enzyme-generated torque, stochastic Langevin force, and viscous drag. Modeling with realistic parameters revealed the dominance of the lowest normal mode. Because of its slow relaxation (approximately 100 ms), power strokes of the enzyme were expected to appear strongly damped in recordings of the angular velocity of the filament. This article describes the theoretical background for the alternative use of the filament as a spring balance. The enzyme's angular torque profile under load can be gauged by measuring the average curvature and the stochastic fluctuations of actin filaments. Pertinent experiments were analyzed in the companion paper.

Kinetic model of ATP synthase: pH dependence of the rate of ATP synthesis

Recently, a novel molecular mechanism of torque generation in the F(0) portion of ATP synthase was proposed [Rohatgi, Saha and Nath (1998) Curr. Sci. 75, 716-718]. In this mechanism, rotation of the c-subunit was conceived to take place in 12 discrete steps of 30 degrees each due to the binding and unbinding of protons to/from the leading and trailing Asp-61 residues of the c-subunit, respectively. Based on this molecular mechanism, a kinetic scheme has been developed in this work. The scheme considers proton transport driven by a concentration gradient of protons across the proton half-channels, and the rotation of the c-subunit by changes in the electrical potential only. This kinetic scheme has been analyzed mathematically and an expression has been obtained to explain the pH dependence of the rate of ATP synthesis by ATP synthase under steady state operating conditions. For a single set of three enzymological kinetic parameters, this expression predicts the rates of ATP synthesis which agree well with the experimental data over a wide range of pH(in) and pH(out). A logical consequence of our analysis is that DeltapH and Deltapsi are kinetically inequivalent driving forces for ATP synthesis.

F-ATPase: specific observation of the rotating c subunit oligomer of EF(o)EF(1)

The rotary motion in response to ATP hydrolysis of the ring of c subunits of the membrane portion, F(o), of ATP synthase, F(o)F(1), is still under contention. It was studied with EF(o)EF(1) (Escherichia coli) using microvideography with a fluorescent actin filament. To overcome the limited specificity of actin attachment through a Cys-maleimide couple which might have hampered the interpretation of previous work, we engineered a 'strep-tag' sequence into the C-terminal end of subunit c. It served (a) to purify the holoenzyme and (b) to monospecifically attach a fluorescent actin filament to subunit c. EF(o)EF(1) was immobilized on a Ni-NTA-coated glass slide by the engineered His-tag at the N-terminus of subunit beta. In the presence of MgATP we observed up to five counterclockwise rotating actin filaments per picture frame of 2000 microm(2) size, in some cases yielding a proportion of 5% rotating over total filaments. The rotation was unequivocally attributable to the ring of subunit c. The new, doubly engineered construct serves as a firmer basis for ongoing studies on torque and angular elastic distortions between F(1) and F(o).

Molecular architecture of the rotary motor in ATP synthase

Adenosine triphosphate (ATP) synthase contains a rotary motor involved in biological energy conversion. Its membrane-embedded F0 sector has a rotation generator fueled by the proton-motive force, which provides the energy required for the synthesis of ATP by the F1 domain. An electron density map obtained from crystals of a subcomplex of yeast mitochondrial ATP synthase shows a ring of 10 c subunits. Each c subunit forms an alpha-helical hairpin. The interhelical loops of six to seven of the c subunits are in close contact with the gamma and delta subunits of the central stalk. The extensive contact between the c ring and the stalk suggests that they may rotate as an ensemble during catalysis.