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

Mechanical compression enhances ciliary beating through cytoskeleton remodeling in human nasal epithelial cells

Nasal inflammatory diseases, including nasal polyps and acute/chronic sinusitis, are characterized by impaired mucociliary clearance and eventually inflammation and infection. Contact of nasal polyps with adjacent nasal mucosa or stagnated mucus within the maxillary sinus produces compressive mechanical stresses on the apical surface of epithelium which can induce cytoskeleton remodeling in epithelial cells. In this study, we hypothesized that compressive stress modulates ciliary beating by altering the mechanical properties of the cytoskeleton of ciliated cell basal bodies. For the primary human nasal epithelial cells, we found that the applied compressive stress higher than the critical value of 1.0 kPa increased the stroke speed of cilia leading to the enhancement of ciliary beating frequency and mucociliary transportability. Immunostained images of the cytoskeleton showed reorganization and compactness of the actin filaments in the presence of compressive stress. Analysis of beating trajectory with the computational modeling for ciliary beating revealed that the stroke speed of cilium increased as the relative elasticity to viscosity of the surrounding cytoskeleton increases. These results suggest that the compressive stress on epithelial cells increases the ciliary beating speed through cytoskeleton remodeling to prevent mucus stagnation at the early stage of airway obstruction. Our study provides an insight into the defensive mechanism of airway epithelium against pathological conditions. STATEMENT OF SIGNIFICANCE: Cilia dynamics of the nasal epithelium is critical for not only maintaining normal breathing but preventing inflammatory diseases. It has been shown that mechanical compressive stresses can alter the shape and phenotype of epithelial cells. However, the effect of compressive stress on cilia dynamics is unclear. In this study, we demonstrated that the oscillation speed of cilia in human nasal epithelial cells was increased by the applied compressive stress experimentally. The computational simulation revealed that the change of ciliary beating dynamics was attributed to the viscoelastic properties of the reorganized cytoskeleton in response to compressive stress. Our results will be beneficial in understanding the defensive mechanism of airway epithelium against pathological conditions.

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.

Torque transmission mechanism via DELSEED loop of F1-ATPase

F1-ATPase (F1) is an ATP-driven rotary motor in which the three catalytic β subunits in the stator ring sequentially induce the unidirectional rotation of the rotary γ subunit. Many lines of evidence have revealed open-to-closed conformational transitions in the β subunit that swing the C-terminal domain inward. This conformational transition causes a C-terminal protruding loop with conserved sequence DELSEED to push the γ subunit. Previous work, where all residues of DELSEED were substituted with glycine to disrupt the specific interaction with γ and introduce conformational flexibility, showed that F1 still rotated, but that the torque was halved, indicating a remarkable impact on torque transmission. In this study, we conducted a stall-and-release experiment on F1 with a glycine-substituted DELSEED loop to investigate the impact of the glycine substitution on torque transmission upon ATP binding and ATP hydrolysis. The mutant F1 showed a significantly reduced angle-dependent change in ATP affinity, whereas there was no change in the equilibrium for ATP hydrolysis. These findings indicate that the DELSEED loop is predominantly responsible for torque transmission upon ATP binding but not for that upon ATP hydrolysis.

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.

Effects of an ATP analogue, adenosine 5'-[α-thio]-triphosphate, on F1-ATPase rotary catalysis, torque generation, and inhibited intermediated formation

F1-ATPase (F1), an important rotary motor protein, converts the chemical energy of ATP hydrolysis into mechanical energy using rotary motion with extremely high efficiency. The energy-conversion mechanism for this molecular motor has been extensively clarified by previous studies, which indicate that the interactions between the catalytic residues and the β- and γ-phosphates of ATP are indispensable for efficient catalysis and torque generation. However, the role of α-phosphate is largely unknown. In this study, we observed the rotation of F1 fuelled with an ATP analogue, adenosine 5'-[α-thio]-triphosphate (ATPαS), in which the oxygen has been substituted with a sulfur ion to perturb the α-phosphate/F1 interactions. In doing so, we have revealed that ATPαS does not appear to have any impact on the kinetic properties of the motor or on torque generation compared to ATP. On the other hand, F1 was observed to lapse into the ADP-inhibited intermediate states when in the presence of ATPαS more severely than in the presence of ATP, suggesting that the α-phosphate group of ATP contributes to the avoidance of ADP-inhibited intermediate formation.

Catalysis-enhancement via rotary fluctuation of F1-ATPase

Protein conformational fluctuations modulate the catalytic powers of enzymes. The frequency of conformational fluctuations may modulate the catalytic rate at individual reaction steps. In this study, we modulated the rotary fluctuation frequency of F1-ATPase (F1) by attaching probes with different viscous drag coefficients at the rotary shaft of F1. Individual rotation pauses of F1 between rotary steps correspond to the waiting state of a certain elementary reaction step of ATP hydrolysis. This allows us to investigate the impact of the frequency modulation of the rotary fluctuation on the rate of the individual reaction steps by measuring the duration of rotation pauses. Although phosphate release was significantly decelerated, the ATP-binding and hydrolysis steps were less sensitive or insensitive to the viscous drag coefficient of the probe. Brownian dynamics simulation based on a model similar to the Sumi-Marcus theory reproduced the experimental results, providing a theoretical framework for the role of rotational fluctuation in F1 rate enhancement.

Robustness of the rotary catalysis mechanism of F1-ATPase

F1-ATPase (F1) is the rotary motor protein fueled by ATP hydrolysis. Previous studies have suggested that three charged residues are indispensable for catalysis of F1 as follows: the P-loop lysine in the phosphate-binding loop, GXXXXGK(T/S); a glutamic acid that activates water molecules for nucleophilic attack on the γ-phosphate of ATP (general base); and an arginine directly contacting the γ-phosphate (arginine finger). These residues are well conserved among P-loop NTPases. In this study, we investigated the role of these charged residues in catalysis and torque generation by analyzing alanine-substituted mutants in the single-molecule rotation assay. Surprisingly, all mutants continuously drove rotary motion, even though the rotational velocity was at least 100,000 times slower than that of wild type. Thus, although these charged residues contribute to highly efficient catalysis, they are not indispensable to chemo-mechanical energy coupling, and the rotary catalysis mechanism of F1 is far more robust than previously thought.

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

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

Half a century of molecular bioenergetics

Molecular bioenergetics deals with the construction, function and regulation of the powerhouses of life. The present overview sketches scenes and actors, farsighted goals and daring hypotheses, meticulous tool-making, painstaking benchwork, lucky discovery, serious scepticism, emphatic believing and strong characters with weak and others with hard arguments, told from a personal, admittedly limited, perspective. Bioenergetics will blossom further with the search focused on both where there is bright light for ever-finer detail and the obvious dark spots for surprise and discovery.

Mechanical modulation of ATP-binding affinity of V1-ATPase

V(1)-ATPase is a rotary motor protein that rotates the central shaft in a counterclockwise direction hydrolyzing ATP. Although the ATP-binding process is suggested to be the most critical reaction step for torque generation in F(1)-ATPase (the closest relative of V(1)-ATPase evolutionarily), the role of ATP binding for V(1)-ATPase in torque generation has remained unclear. In the present study, we performed single-molecule manipulation experiments on V(1)-ATPase from Thermus thermophilus to investigate how the ATP-binding process is modulated upon rotation of the rotary shaft. When V(1)-ATPase showed an ATP-waiting pause, it was stalled at a target angle and then released. Based on the response of the V(1)-ATPase released, the ATP-binding probability was determined at individual stall angles. It was observed that the rate constant of ATP binding (k(on)) was exponentially accelerated with forward rotation, whereas the rate constant of ATP release (k(off)) was exponentially reduced. The angle dependence of the k(off) of V(1)-ATPase was significantly smaller than that of F(1)-ATPase, suggesting that the ATP-binding process is not the major torque-generating step in V(1)-ATPase. When V(1)-ATPase was stalled at the mean binding angle to restrict rotary Brownian motion, k(on) was evidently slower than that determined from free rotation, showing the reaction rate enhancement by conformational fluctuation. It was also suggested that shaft of V(1)-ATPase should be rotated at least 277° in a clockwise direction for efficient release of ATP under ATP-synthesis conditions.

Structure and flexibility of the C-ring in the electromotor of rotary F(0)F(1)-ATPase of pea chloroplasts

A ring of 8-15 identical c-subunits is essential for ion-translocation by the rotary electromotor of the ubiquitous F(O)F(1)-ATPase. Here we present the crystal structure at 3.4Å resolution of the c-ring from chloroplasts of a higher plant (Pisum sativum), determined using a native preparation. The crystal structure was found to resemble that of an (ancestral) cyanobacterium. Using elastic network modeling to investigate the ring's eigen-modes, we found five dominant modes of motion that fell into three classes. They revealed the following deformations of the ring: (I) ellipsoidal, (II) opposite twisting of the luminal circular surface of the ring against the stromal surface, and (III) kinking of the hairpin-shaped monomers in the middle, resulting in bending/stretching of the ring. Extension of the elastic network analysis to rings of different c(n)-symmetry revealed the same classes of dominant modes as in P. sativum (c(14)). We suggest the following functional roles for these classes: The first and third classes of modes affect the interaction of the c-ring with its counterparts in F(O), namely subunits a and bb'. These modes are likely to be involved in ion-translocation and torque generation. The second class of deformation, along with deformations of subunits γ and ε might serve to elastically buffer the torque transmission between F(O) and F(1).

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

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

Cytoskeletal forces produced by extremely low-frequency electric fields acting on extracellular glycoproteins

The physical mechanism by which cells transduce an applied electric field is not well understood. This article establishes for the first time a direct, quantitative model that links the field to cytoskeletal forces. In a previous article, applied electric fields of physiological strength were shown to produce significant mechanical torques at the cellular level. In this article, the corresponding forces exerted on the cytoskeleton are computed and found to be comparable in magnitude to mechanical forces known to produce physiological effects. In addition to the electrical force, the viscous drag force exerted by the surrounding medium and the restoring force exerted by the neighboring structures are considered in the analysis. For an applied electric field of 10 V/m, the force transmitted to the CD44 receptor of a hyaluronan chain in cartilage is about 1 pN at 10 Hz and 7 pN at 1 Hz. For an applied electric field of 100 V/m, the force transmitted to the cytoskeleton at one focus of the glycocalyx is about 0.5 pN at 10 Hz and 1.3 pN at 1 Hz. Mechanical forces of similar magnitude have been observed to produce physiological effects. Hence, this electromechanical transduction process is a plausible mechanism for the production of physiological effects by such electric fields.

Solution structure, determined by nuclear magnetic resonance, of the b30-82 domain of subunit b of Escherichia coli F1Fo ATP synthase

Subunit b, the peripheral stalk of bacterial F(1)F(o) ATP synthases, is composed of a membrane-spanning and a soluble part. The soluble part is divided into tether, dimerization, and delta-binding domains. The first solution structure of b30-82, including the tether region and part of the dimerization domain, has been solved by nuclear magnetic resonance, revealing an alpha-helix between residues 39 and 72. In the solution structure, b30-82 has a length of 48.07 A. The surface charge distribution of b30-82 shows one side with a hydrophobic surface pattern, formed by alanine residues. Alanine residues 61, 68, 70, and 72 were replaced by single cysteines in the soluble part of subunit b, b22-156. The cysteines at positions 61, 68, and 72 showed disulfide formation. In contrast, no cross-link could be formed for the A70C mutant. The patterns of disulfide bonding, together with the circular dichroism spectroscopy data, are indicative of an adjacent arrangement of residues 61, 68, and 72 in both alpha-helices in b22-156.

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

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

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.

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 mechanical transduction of physiological strength electric fields

In this article it is proposed that electric fields of physiological strength (approximately 100 V/m) are transduced by the mechanical torque they exert on glycoproteins. The resulting mechanical signal is then transmitted to the cytoskeleton and propagated throughout the cell interior. This mechanical coupling is analyzed for transmembrane glycoproteins, such as integrins and the glycocalyx, and for glycoproteins in the extracellular matrix of cartilage. The applied torque is opposed by viscous fluid drag and restoring forces exerted by adjacent molecules in the membrane or cartilage. The resulting system represents a damped, driven harmonic oscillator. The amplitude of oscillation is constant at low frequencies, but falls off rapidly in the range 1-1000 Hz. The transition frequency depends on parameters such as the viscosity of the surrounding fluid and the restoring force exerted by the surrounding structure. The amplitude increases as the fourth power of the length of the transmembrane glycoproteins and as the square of the applied field. This process may operate in concert with other transduction mechanisms, such as the opening of voltage-gated channels and electrodiffusion/osmosis for DC fields.

Functional halt positions of rotary FOF1-ATPase correlated with crystal structures

The F(O)F(1)-ATPase is a rotary molecular motor. Driven by ATP-hydrolysis, its central shaft rotates in 80 degrees and 40 degrees steps, interrupted by catalytic and ATP-waiting dwells. We recorded rotations and halts by means of microvideography in laboratory coordinates. A correlation with molecular coordinates was established by using an engineered pair of cysteines that, under oxidizing conditions, formed zero-length cross-links between the rotor and the stator in an orientation as found in crystals. The fixed orientation coincided with that of the catalytic dwell, whereas the ATP waiting dwell was displaced from it by +40 degrees . In crystals, the convex side of the cranked central shaft faces an empty nucleotide binding site, as if holding it open for arriving ATP. Functional studies suggest that three sites are occupied during a catalytic dwell. Our data imply that the convex side faces a nucleotide-occupied rather than an empty site. The enzyme conformation in crystals seems to differ from the conformation during either dwell of the active enzyme. A revision of current schemes of the mechanism is proposed.

Dynamic and coordinating domain motions in the active subunits of the F1-ATPase molecular motor

F1-ATPase is a rotary molecular motor crucial for various cellular functions. In F1-ATPase, the rotation of the gammadeltaepsilon subunits against the hexameric alpha(3)beta(3) subunits is highly coordinative, driven by ATP hydrolysis and structural changes at three beta subunits. However, the dynamical and coordinating structural transitions in the beta subunits are not fully understood at the molecular level. Here we examine structural transitions and domain motions in the active subunits of F1-ATPase via dynamical domain analysis of the alpha(3)beta(3)gammadeltaepsilon complex. The domain movement and hinge axes and bending residues have been identified and determined for various conformational changes of the beta-subunits. P-loop and the ATP-binding pocket are for the first time found to play essential mechanical functions additional to the catalytic roles. The cooperative conformational changes pertaining to the rotary mechanism of F1-ATPase appears to be more complex than Boyer's 'bi-site' activity. These findings provide unique molecular insights into dynamic and cooperative domain motions in F1-ATPase.

Probing biological interfaces by tracing proton passage across them

The properties of water at the surface, especially at an electrically charged one, differ essentially from those in the bulk phase. Here we survey the traits of surface water as inferred from proton pulse experiments with membrane enzymes. In such experiments, protons that are ejected (or captured) by light-triggered enzymes are traced on their way between the membrane surface and the bulk aqueous phase. In several laboratories it has been shown that proton exchange between the membrane surface and the bulk aqueous phase takes as much as about 1 ms, but could be accelerated by added mobile pH-buffers. Since the accelerating capacity of the latter decreased with increase in their electric charge, it was suggested that the membrane surface is separated from the bulk aqueous phase by a barrier of electrostatic nature. In terms of ordinary electrostatics, the barrier could be ascribed to dielectric saturation of water at a charged surface. In terms of nonlocal electrostatics, the barrier could result from the dielectric overscreening in the surface water layers. It is discussed how the interfacial potential barrier can affect the reactions at interface, especially those coupled with biological energy conversion and membrane transport.

Application of rigid body mechanics to theoretical description of rotation within F0F1-ATP synthase

ATP synthase catalyses the formation of ATP from ADP and P(i) and is powered by the diffusion of protons throughout membranes down the proton electrochemical gradient. The protein consists of a water-soluble F(1) and a transmembrane F(0) proton transporter part. It was previously shown that the ring of membrane subunits rotates past a fixed subunit during catalytic cycle of the enzyme. However, many parameters of this movement are still unknown. In the present study the mutual protein movement in the membrane part of F(0)F(1)-ATP syntase has been analysed within the framework of rigid body mechanics. On the base of available experimental data it was shown that electrostatic interaction of two charged amino acids residues is able to supply quite enough energy for the rotation. The initial torque, which caused the rotation, was estimated as 3.7 pN nm and for this pattern the angular movement of c subunits complex could not physically have a period less than 10(-9)s. If membrane viscosity and elastic resistance were taken into account then the time of a whole turnover could rise up to 6.3 x 10(-3)s. It is remarkable that rotation will take place only under condition when the elasticity (Young's) module of the central stalk (gamma subunit and other minor subunits) is less than 5.0 x 10(7)N/m(2). Thus, for generally accepted structural parameters of ATP synthase, two-charge electrostatic interaction model does not permit rotation of the rotor if elastic properties of the central stalk are tougher than mentioned above. In order to explain the rotation under that condition one should either suppose a shorter distance between subunit a and c subunits complex or assume interaction of more than two charged amino acids residues.

Nature's design of nanomotors

The need for movement is an essential concept of all living organisms. On a macroscopic scale, animals and microbes have to be able to move towards food and away from poison and predators. Plants turn their leaves toward their energy source, the sunlight. But even on a molecular scale, movement is essential for life. It has been known for a long time that enzymes and proteins undergo large conformational changes while performing their biological tasks. The catalytically active regions of enzymes need to sequentially open to bind their respective substrates and close to allow the specific chemical reaction to occur in a defined chemical environment. The active sites finally open up again up to allow the product to be released. Molecular motors are proteins and protein complexes that have evolved in living cells to carry out a variety of functions essential for survival, reproduction and differentiation of the cells and organisms. They use chemical, electrochemical or potential energy and transduce that energy into physical, chemical or mechanical force. In this paper we review some of the molecular motors that were designed by nature to either perform physical work or that contain motor-like movements as part of their catalytic mechanism.

A normal mode analysis of structural plasticity in the biomolecular motor F(1)-ATPase

Normal modes have been used to explore the inherent flexibility of the alpha, beta and gamma subunits of F(1)-ATPase in isolation and as part of the alpha(3)beta(3)gamma complex. It was found that the structural plasticity of the gamma and beta subunits, in particular, correlates with their functions. The N and C-terminal helices forming the coiled-coil domain of the gamma subunit are highly flexible in the isolated subunit, but more rigid in the alpha(3)beta(3)gamma complex due to interactions with other subunits. The globular domain of the gamma subunit is structurally relatively rigid when isolated and in the alpha(3)beta(3)gamma complex; this is important for its functional role in coupling the F(0) and F(1) complex of ATP synthase and in inducing the conformational changes of the beta subunits in synthesis. Most important, the character of the lowest-frequency modes of the beta(E) subunit is highly correlated with the large beta(E) --> beta(TP) transition. This holds for the C-terminal domain and the nucleotide-binding domain, which undergo significant conformational transitions in the functional cycle of F(1)-ATPase. This is most evident in the ligand-free beta(E) subunit; the flexibility in the nucleotide-binding domain is reduced somewhat in the beta(TP) subunit in the presence of Mg(2+).ATP. The low-frequency modes of the alpha(3)beta(3)gamma complex show that the motions of the globular domain of the gamma subunit and of the C-terminal and nucleotide binding domains of the beta(E) subunits are coupled, in accord with their function. Overall, the normal mode analysis reveals that F(1)-ATPase, like other macromolecular assemblies, has the intrinsic structural flexibility required for its function encoded in its sequence and three-dimensional structure. This inherent plasticity is an essential aspect of assuring a small free energy cost for the large-scale conformational transition that occurs in molecular motors.

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.

The proton-driven rotor of ATP synthase: ohmic conductance (10 fS), and absence of voltage gating

The membrane portion of F(0)F(1)-ATP synthase, F(0), translocates protons by a rotary mechanism. Proton conduction by F(0) was studied in chromatophores of the photosynthetic bacterium Rhodobacter capsulatus. The discharge of a light-induced voltage jump was monitored by electrochromic absorption transients to yield the unitary conductance of F(0). The current-voltage relationship of F(0) was linear from 7 to 70 mV. The current was extremely proton-specific (>10(7)) and varied only slightly ( approximately threefold) from pH 6 to 10. The maximum conductance was approximately 10 fS at pH 8, equivalent to 6240 H(+) s(-1) at 100-mV driving force, which is an order-of-magnitude greater than of coupled F(0)F(1). There was no voltage-gating of F(0) even at low voltage, and proton translocation could be driven by deltapH alone, without voltage. The reported voltage gating in F(0)F(1) is thus attributable to the interaction of F(0) with F(1) but not to F(0) proper. We simulated proton conduction by a minimal rotary model including the rotating c-ring and two relay groups mediating proton exchange between the ring and the respective membrane surface. The data fit attributed pK values of approximately 6 and approximately 10 to these relays, and placed them close to the membrane/electrolyte interface.

Protons, proteins and ATP

The machinery of life has been disclosed in the second half of the 20th century to a degree not in the least envisioned previously by even the most daring players in this field. It has been extremely rewarding to start out from the fogs and to enjoy the brightness at the end of one's active career. Perhaps the most astounding lesson to learn is how conservative and modular is the construction of key devices. Oxidative and photophosphorylation are carried out by ATP synthase, which is unique in converting electrochemical, mechanical and chemical forms of energy within one nano-machine. This complex protein consists of more than 20 polypeptides of at least eight different kinds. Still, its activity survives in engineered chimerical constructs joining parts from organisms that underwent billions of years of separate evolution. The path of discovery of its structure and function is sketched here from a personal viewpoint. It has been a long way from before-structure-bioenergetics to the post-structural one (which now dominates the biology textbooks), but there is still a long way to go for a rigorous physical understanding. The author has been privileged to enjoy the friendship, cooperation and competition of excellent scientists from widely different backgrounds and expertise.

The significance of molecular slips in transport systems

The advantage of precision in biological processes is obvious; however, in many cases, deviations from the faithful mechanisms occur. Here, we discuss how in-built operating imperfections in transport systems can actually benefit a cell.

F1-ATPase, the C-terminal end of subunit gamma is not required for ATP hydrolysis-driven rotation

ATP hydrolysis by the isolated F(1)-ATPase drives the rotation of the central shaft, subunit gamma, which is located within a hexagon formed by subunits (alphabeta)(3). The C-terminal end of gamma forms an alpha-helix which properly fits into the "hydrophobic bearing" provided by loops of subunits alpha and beta. This "bearing" is expected to be essential for the rotary function. We checked the importance of this contact region by successive C-terminal deletions of 3, 6, 9, 12, 15, and 18 amino acid residues (Escherichia coli F(1)-ATPase). The ATP hydrolysis activity of a load-free ensemble of F(1) with 12 residues deleted decreased to 24% of the control. EF(1) with deletions of 15 or 18 residues was inactive, probably because it failed to assemble. The average torque generated by a single molecule of EF(1) when loaded by a fluorescent actin filament was, however, unaffected by deletions of up to 12 residues, as was their rotational behavior (all samples rotated during 60 +/- 19% of the observation time). Activation energy analysis with the ensemble revealed a moderate decrease from 54 kJ/mol for EF(1) (full-length gamma) to 34 kJ/mol for EF(1)(gamma-12). These observations imply that the intactness of the C terminus of subunit gamma provides structural stability and/or routing during assembly of the enzyme, but that it is not required for the rotary action under load, proper.

F-ATPase: forced full rotation of the rotor despite covalent cross-link with the stator

In ATP synthase (F(O)F(1)-ATPase) ion flow through the membrane-intrinsic portion, F(O), drives the central "rotor", subunits c(10)epsilongamma, relative to the "stator" ab(2)delta(alphabeta)(3). This converts ADP and P(i) into ATP. Vice versa, ATP hydrolysis drives the rotation backwards. Covalent cross-links between rotor and stator subunits have been shown to inhibit these activities. Aiming at the rotary compliance of subunit gamma we introduced disulfide bridges between gamma (rotor) and alpha or beta (stator). We engineered cysteine residues into positions located roughly at the "top," "center," and "bottom" parts of the coiled-coil portion of gamma and suitable residues on alpha or beta. This part of gamma is located at the center of the (alphabeta)(3) domain with its C-terminal part at the top of F(1) and the bottom part close to the F(O) complex. Disulfide bridge formation under oxidizing conditions was quantitative as shown by SDS-polyacrylamide gel electrophoresis and immunoblotting. As expected both the ATPase activities and the yield of rotating subunits gamma dropped to zero when the cross-link was formed at the center (gammaL262C <--> alphaA334C) and bottom (gammaCys(87) <--> betaD380C) positions. But much to our surprise disulfide bridging impaired neither ATP hydrolysis activity nor the full rotation of gamma and the enzyme-generated torque of oxidized F(1), which had been engineered at the top position (gammaA285C <--> alphaP280C). Apparently the high torque of this rotary engine uncoiled the alpha-helix and forced amino acids at the C-terminal portion of gamma into full rotation around their dihedral (Ramachandran) angles. This conclusion was supported by molecular dynamics simulations: If gammaCys(285)-Val(286) are attached covalently to (alphabeta)(3) and gammaAla(1)-Ser(281) is forced to rotate, gammaGly(282)-Ala(284) can serve as cardan shaft.

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.