Processive Nanostepping of Formin mDia1 Loosely Coupled with Actin Polymerization.

Formins are actin-binding proteins that construct nanoscale machinery with the growing barbed end of actin filaments and serve as key regulators of actin polymerization and depolymerization. To maintain the regulation of actin dynamics, formins have been proposed to processively move at every association or dissociation of a single actin molecule toward newly formed barbed ends. However, the current models for the motile mechanisms were established without direct observation of the elementary processes of this movement. Here, using optical tweezers, we demonstrate that formin mDia1 moves stepwise, observed at a nanometer spatial resolution. The movement was composed of forward and backward steps with unitary step sizes of 2.8 and -2.4 nm, respectively, which nearly equaled the actin subunit length (∼2.7 nm), consistent with the generally accepted models. However, in addition to steps equivalent to the length of a single actin subunit, those equivalent to the length of two or three subunits were frequently observed. Our findings suggest that the coupling between mDia1 stepping and actin polymerization is not tight but loose, which may be achieved by the multiple binding states of mDia1, providing insights into the synergistic functions of biomolecules for the efficient construction and regulation of nanofilaments.

Biphasic Effect of Profilin Impacts the Formin mDia1 Force-Sensing Mechanism in Actin Polymerization.

Formins are force-sensing proteins that regulate actin polymerization dynamics. Here, we applied stretching tension to individual actin filaments under the regulation of formin mDia1 to investigate the mechanical responses in actin polymerization dynamics. We found that the elongation of an actin filament was accelerated to a greater degree by stretching tension for ADP-G-actin than that for ATP-G-actin. An apparent decrease in the critical concentration of G-actin was observed, especially in ADP-G-actin. These results on two types of G-actin were reproduced by a simple kinetic model, assuming the rapid equilibrium between pre- and posttranslocated states of the formin homology domain two dimer. In addition, profilin concentration dramatically altered the force-dependent acceleration of actin filament elongation, which ranged from twofold to an all-or-none response. Even under conditions in which actin depolymerization occurred, applications of a several-piconewton stretching tension triggered rapid actin filament elongation. This extremely high force-sensing mechanism of mDia1 and profilin could be explained by the force-dependent coordination of the biphasic effect of profilin; i.e., an acceleration effect masked by a depolymerization effect became dominant under stretching tension, negating the latter to rapidly enhance the elongation rate. Our findings demonstrate that the biphasic effect of profilin is controlled by mechanical force, thus expanding the function of mDia1 as a mechanosensitive regulator of actin polymerization.

Perfect chemomechanical coupling of FoF1-ATP synthase.

FoF1-ATP synthase (FoF1) couples H+ flow in Fo domain and ATP synthesis/hydrolysis in F1 domain through rotation of the central rotor shaft, and the H+/ATP ratio is crucial to understand the coupling mechanism and energy yield in cells. Although H+/ATP ratio of the perfectly coupling enzyme can be predicted from the copy number of catalytic ß subunits and that of H+ binding c subunits as c/ß, the actual H+/ATP ratio can vary depending on coupling efficiency. Here, we report actual H+/ATP ratio of thermophilic Bacillus FoF1, whose c/ß is 10/3. Proteoliposomes reconstituted with the FoF1 were energized with ΔpH and Δψ by the acid-base transition and by valinomycin-mediated diffusion potential of K+ under various [ATP]/([ADP]⋅[Pi]) conditions, and the initial rate of ATP synthesis/hydrolysis was measured. Analyses of thermodynamically equilibrated states, where net ATP synthesis/hydrolysis is zero, show linear correlation between the chemical potential of ATP synthesis/hydrolysis and the proton motive force, giving the slope of the linear function, that is, H+/ATP ratio, 3.3 ± 0.1. This value agrees well with the c/ß ratio. Thus, chemomechanical coupling between Fo and F1 is perfect.

Torsional stress in DNA limits collaboration among reverse gyrase molecules.

Reverse gyrase is an enzyme that can overwind (introduce positive supercoils into) DNA using the energy obtained from ATP hydrolysis. The enzyme is found in hyperthermophiles, and the overwinding reaction generally requires a temperature above 70 °C. In a previous study using microscopy, we have shown that 30 consecutive mismatched base pairs (a bubble) in DNA serve as a well-defined substrate site for reverse gyrase, warranting the processive overwinding activity down to 50 °C. Here, we inquire how multiple reverse gyrase molecules may collaborate with each other in overwinding one DNA molecule. We introduced one, two, or four bubbles in a linear DNA that tethered a magnetic bead to a coverslip surface. At 40-71 °C in the presence of reverse gyrase, the bead rotated clockwise as viewed from above, to relax the DNA twisted by reverse gyrase. Dependence on the enzyme concentration indicated that each bubble binds reverse gyrase tightly (dissociation constant < 0.1 nm) and that bound enzyme continuously overwinds DNA for > 5 min. Rotation with two bubbles was significantly faster compared with one bubble, indicating that overwinding actions are basically additive, but four bubbles did not show further acceleration except at 40 °C where the activity was very low. The apparent saturation is due to the hydrodynamic friction against the rotating bead, as confirmed by increasing the medium viscosity. When torsional stress in the DNA, determined by the friction, approaches ~ 7 pN·nm (at 71 °C), the overwinding activity of reverse gyrase drops sharply. Multiple molecules of reverse gyrase collaborate additively within this limit.

Simple mechanism whereby the F1-ATPase motor rotates with near-perfect chemomechanical energy conversion.

F1-ATPase is a motor enzyme in which a central shaft γ subunit rotates 120° per ATP in the cylinder made of α3ß3 subunits. During rotation, the chemical energy of ATP hydrolysis (ΔGATP) is converted almost entirely into mechanical work by an elusive mechanism. We measured the force for rotation (torque) under various ΔGATP conditions as a function of rotation angles of the γ subunit with quasi-static, single-molecule manipulation and estimated mechanical work (torque × traveled angle) from the area of the function. The torque functions show three sawtooth-like repeats of a steep jump and linear descent in one catalytic turnover, indicating a simple physical model in which the motor is driven by three springs aligned along a 120° rotation angle. Although the second spring is unaffected by ΔGATP, activation of the first spring (timing of the torque jump) delays at low [ATP] (or high [ADP]) and activation of the third spring delays at high [Pi]. These shifts decrease the size and area of the sawtooth (magnitude of the work). Thus, F1-ATPase responds to the change of ΔGATP by shifting the torque jump timing and uses ΔGATP for the mechanical work with near-perfect efficiency.

Direct observation of DNA overwinding by reverse gyrase.

Reverse gyrase, found in hyperthermophiles, is the only enzyme known to overwind (introduce positive supercoils into) DNA. The ATP-dependent activity, detected at >70 °C, has so far been studied solely by gel electrophoresis; thus, the reaction dynamics remain obscure. Here, we image the overwinding reaction at 71 °C under a microscope, using DNA containing consecutive 30 mismatched base pairs that serve as a well-defined substrate site. A single reverse gyrase molecule processively winds the DNA for >100 turns. Bound enzyme shows moderate temperature dependence, retaining significant activity down to 50 °C. The unloaded reaction rate at 71 °C exceeds five turns per second, which is >10(2)-fold higher than hitherto indicated but lower than the measured ATPase rate of 20 s(-1), indicating loose coupling. The overwinding reaction sharply slows down as the torsional stress accumulates in DNA and ceases at stress of mere ∼ 5 pN ⋅ nm, where one more turn would cost only sixfold the thermal energy. The enzyme would thus keep DNA in a slightly overwound state to protect, but not overprotect, the genome of hyperthermophiles against thermal melting. Overwinding activity is also highly sensitive to DNA tension, with an effective interaction length exceeding the size of reverse gyrase, implying requirement for slack DNA. All results point to the mechanism where strand passage relying on thermal motions, as in topoisomerase IA, is actively but loosely biased toward overwinding.

None of the rotor residues of F1-ATPase are essential for torque generation.

F1-ATPase is a powerful rotary molecular motor that can rotate an object several hundred times as large as the motor itself against the viscous friction of water. Forced reverse rotation has been shown to lead to ATP synthesis, implying that the mechanical work against the motor's high torque can be converted into the chemical energy of ATP. The minimal composition of the motor protein is α3ß3γ subunits, where the central rotor subunit γ turns inside a stator cylinder made of alternately arranged α3ß3 subunits using the energy derived from ATP hydrolysis. The rotor consists of an axle, a coiled coil of the amino- and carboxyl-terminal α-helices of γ, which deeply penetrates the stator cylinder, and a globular protrusion that juts out from the stator. Previous work has shown that, for a thermophilic F1, significant portions of the axle can be truncated and the motor still rotates a submicron sized bead duplex, indicating generation of up to half the wild-type (WT) torque. Here, we inquire if any specific interactions between the stator and the rest of the rotor are needed for the generation of a sizable torque. We truncated the protruding portion of the rotor and replaced part of the remaining axle residues such that every residue of the rotor has been deleted or replaced in this or previous truncation mutants. This protrusionless construct showed an unloaded rotary speed about a quarter of the WT, and generated one-third to one-half of the WT torque. No residue-specific interactions are needed for this much performance. F1 is so designed that the basic rotor-stator interactions for torque generation and control of catalysis rely solely upon the shape and size of the rotor at very low resolution. Additional tailored interactions augment the torque to allow ATP synthesis under physiological conditions.

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

F(1)-ATPase is an ATP-driven rotary molecular motor that synthesizes ATP when rotated in reverse. To elucidate the mechanism of ATP synthesis, we imaged binding and release of fluorescently labelled ADP and ATP while rotating the motor in either direction by magnets. Here we report the binding and release rates for each of the three catalytic sites for 360° of the rotary angle. We show that the rates do not significantly depend on the rotary direction, indicating ATP synthesis by direct reversal of the hydrolysis-driven rotation. ADP and ATP are discriminated in angle-dependent binding, but not in release. Phosphate blocks ATP binding at angles where ADP binding is essential for ATP synthesis. In synthesis rotation, the affinity for ADP increases by >10(4), followed by a shift to high ATP affinity, and finally the affinity for ATP decreases by >10(4). All these angular changes are gradual, implicating tight coupling between the rotor angle and site affinities.

Direct observation of strand passage by DNA-topoisomerase and its limited processivity.

Type-II DNA topoisomerases resolve DNA entanglements such as supercoils, knots and catenanes by passing one segment of DNA duplex through a transient enzyme-bridged double-stranded break in another segment. The ATP-dependent passage reaction has previously been demonstrated at the single-molecule level, showing apparent processivity at saturating ATP. Here we directly observed the strand passage by human topoisomerase IIα, after winding a pair of fluorescently stained DNA molecules with optical tweezers for 30 turns into an X-shaped braid. On average 0.51 ± 0.33 µm (11 ± 6 turns) of a braid was unlinked in a burst of reactions taking 8 ± 4 s, the unlinked length being essentially independent of the enzyme concentration between 0.25-37 pM. The time elapsed before the start of processive unlinking decreased with the enzyme concentration, being ~100 s at 3.7 pM. These results are consistent with a scenario where the enzyme binds to one DNA for a period of ~10 s, waiting for multiple diffusional encounters with the other DNA to transport it across the break ~10 times, and then dissociates from the binding site without waiting for the exhaustion of transportable DNA segments.

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

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

Kinetic equivalence of transmembrane pH and electrical potential differences in ATP synthesis.

ATP synthase is the key player of Mitchell's chemiosmotic theory, converting the energy of transmembrane proton flow into the high energy bond between ADP and phosphate. The proton motive force that drives this reaction consists of two components, the pH difference (ΔpH) across the membrane and transmembrane electrical potential (Δψ). The two are considered thermodynamically equivalent, but kinetic equivalence in the actual ATP synthesis is not warranted, and previous experimental results vary. Here, we show that with the thermophilic Bacillus PS3 ATP synthase that lacks an inhibitory domain of the ε subunit, ΔpH imposed by acid-base transition and Δψ produced by valinomycin-mediated K(+) diffusion potential contribute equally to the rate of ATP synthesis within the experimental range examined (ΔpH -0.3 to 2.2, Δψ -30 to 140 mV, pH around the catalytic domain 8.0). Either ΔpH or Δψ alone can drive synthesis, even when the other slightly opposes. Δψ was estimated from the Nernst equation, which appeared valid down to 1 mm K(+) inside the proteoliposomes, due to careful removal of K(+) from the lipid.

Torque generation and utilization in motor enzyme F0F1-ATP synthase: half-torque F1 with short-sized pushrod helix and reduced ATP Synthesis by half-torque F0F1.

ATP synthase (F(0)F(1)) is made of two motors, a proton-driven motor (F(0)) and an ATP-driven motor (F(1)), connected by a common rotary shaft, and catalyzes proton flow-driven ATP synthesis and ATP-driven proton pumping. In F(1), the central γ subunit rotates inside the α(3)ß(3) ring. Here we report structural features of F(1) responsible for torque generation and the catalytic ability of the low-torque F(0)F(1). (i) Deletion of one or two turns in the α-helix in the C-terminal domain of catalytic ß subunit at the rotor/stator contact region generates mutant F(1)s, termed F(1)(1/2)s, that rotate with about half of the normal torque. This helix would support the helix-loop-helix structure acting as a solid "pushrod" to push the rotor γ subunit, but the short helix in F(1)(1/2)s would fail to accomplish this task. (ii) Three different half-torque F(0)F(1)(1/2)s were purified and reconstituted into proteoliposomes. They carry out ATP-driven proton pumping and build up the same small transmembrane ΔpH, indicating that the final ΔpH is directly related to the amount of torque. (iii) The half-torque F(0)F(1)(1/2)s can catalyze ATP synthesis, although slowly. The rate of synthesis varies widely among the three F(0)F(1)(1/2)s, which suggests that the rate reflects subtle conformational variations of individual mutants.

Torque generation in F1-ATPase devoid of the entire amino-terminal helix of the rotor that fills half of the stator orifice.

F(1)-ATPase is an ATP-driven rotary molecular motor in which the central γ-subunit rotates inside a cylinder made of α(3)ß(3) subunits. The amino and carboxyl termini of the γ rotor form a coiled coil of α-helices that penetrates the stator cylinder to serve as an axle. Crystal structures indicate that the axle is supported by the stator at two positions, at the orifice and by the hydrophobic sleeve surrounding the axle tip. The sleeve contacts are almost exclusively to the longer carboxyl-terminal helix, whereas nearly half the orifice contacts are to the amino-terminal helix. Here, we truncated the amino-terminal helix stepwise up to 50 residues, removing one half of the axle all the way up and far beyond the orifice. The half-sliced axle still rotated with an unloaded speed a quarter of the wild-type speed, with torque nearly half the wild-type torque. The truncations were made in a construct where the rotor tip was connected to a ß-subunit via a short peptide linker. Linking alone did not change the rotational characteristics significantly. These and previous results show that nearly half the normal torque is generated if rotor-stator interactions either at the orifice or at the sleeve are preserved, suggesting that the make of the motor is quite robust.

Efficient ATP synthesis by thermophilic Bacillus FoF1-ATP synthase.

F(o)F(1)-ATP synthase (F(o)F(1)) synthesizes ATP in the F(1) portion when protons flow through F(o) to rotate the shaft common to F(1) and F(o). Rotary synthesis in isolated F(1) alone has been shown by applying external torque to F(1) of thermophilic origin. Proton-driven ATP synthesis by thermophilic Bacillus PS3 F(o)F(1) (TF(o)F(1)), however, has so far been poor in vitro, of the order of 1 s(-1) or less, hampering reliable characterization. Here, by using a mutant TF(o)F(1) lacking an inhibitory segment of the ε-subunit, we have developed highly reproducible, simple procedures for the preparation of active proteoliposomes and for kinetic analysis of ATP synthesis, which was driven by acid-base transition and K(+)-diffusion potential. The synthesis activity reached ∼ 16 s(-1) at 30 °C with a Q(10) temperature coefficient of 3-4 between 10 and 30 °C, suggesting a high level of activity at the physiological temperature of ∼ 60 °C. The Michaelis-Menten constants for the substrates ADP and inorganic phosphate were 13 µM and 0.55 mM, respectively, which are an order of magnitude lower than previous estimates and are suited to efficient ATP synthesis.

Direct observation of the myosin Va recovery stroke that contributes to unidirectional stepping along actin.

Myosins are ATP-driven linear molecular motors that work as cellular force generators, transporters, and force sensors. These functions are driven by large-scale nucleotide-dependent conformational changes, termed "strokes"; the "power stroke" is the force-generating swinging of the myosin light chain-binding "neck" domain relative to the motor domain "head" while bound to actin; the "recovery stroke" is the necessary initial motion that primes, or "cocks," myosin while detached from actin. Myosin Va is a processive dimer that steps unidirectionally along actin following a "hand over hand" mechanism in which the trailing head detaches and steps forward ∼72 nm. Despite large rotational Brownian motion of the detached head about a free joint adjoining the two necks, unidirectional stepping is achieved, in part by the power stroke of the attached head that moves the joint forward. However, the power stroke alone cannot fully account for preferential forward site binding since the orientation and angle stability of the detached head, which is determined by the properties of the recovery stroke, dictate actin binding site accessibility. Here, we directly observe the recovery stroke dynamics and fluctuations of myosin Va using a novel, transient caged ATP-controlling system that maintains constant ATP levels through stepwise UV-pulse sequences of varying intensity. We immobilized the neck of monomeric myosin Va on a surface and observed real time motions of bead(s) attached site-specifically to the head. ATP induces a transient swing of the neck to the post-recovery stroke conformation, where it remains for ∼40 s, until ATP hydrolysis products are released. Angle distributions indicate that the post-recovery stroke conformation is stabilized by ≥ 5 k(B)T of energy. The high kinetic and energetic stability of the post-recovery stroke conformation favors preferential binding of the detached head to a forward site 72 nm away. Thus, the recovery stroke contributes to unidirectional stepping of myosin Va.

Resolving stepping rotation in Thermus thermophilus H(+)-ATPase/synthase with an essentially drag-free probe.

Vacuole-type ATPases (V(o)V1) and F(o)F1 ATP synthases couple ATP hydrolysis/synthesis in the soluble V(1) or F1 portion with proton (or Na(+)) flow in the membrane-embedded V(o) or F(o) portion through rotation of one common shaft. Here we show at submillisecond resolutions the ATP-driven rotation of isolated V1 and the whole V(o)V1 from Thermus thermophilus, by attaching a 40-nm gold bead for which viscous drag is almost negligible. V1 made 120° steps, commensurate with the presence of three catalytic sites. Dwells between the steps involved at least two events other than ATP binding, one likely to be ATP hydrolysis. V(o)V1 exhibited 12 dwell positions per revolution, consistent with the 12-fold symmetry of the V(o) rotor in T. thermophilus. Unlike F1 that undergoes 80°-40° substepping, chemo-mechanical checkpoints in isolated V1 are all at the ATP-waiting position, and V(o) adds further bumps through stator-rotor interactions outside and remote from V1.

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

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

Activation and stiffness of the inhibited states of F1-ATPase probed by single-molecule manipulation.

F(1)-ATPase (F(1)), a soluble portion of F(o)F(1)-ATP synthase (F(o)F(1)), is an ATP-driven motor in which gammaepsilon subunits rotate in the alpha(3)beta(3) cylinder. Activity of F(1) and F(o)F(1) from Bacillus PS3 is attenuated by the epsilon subunit in an inhibitory extended form. In this study we observed ATP-dependent transition of epsilon in single F(1) molecules from extended form to hairpin form by fluorescence resonance energy transfer. The results justify the previous bulk experiments and ensure that fraction of F(1) with hairpin epsilon directly determines the fraction of active F(1) at any ATP concentration. Next, mechanical activation and stiffness of epsilon-inhibited F(1) were examined by the forced rotation of magnetic beads attached to gamma. Compared with ADP inhibition, which is another manner of inhibition, rotation by a larger angle was required for the activation from epsilon inhibition when the beads were forced to rotate to ATP hydrolysis direction, and more torque was required to reach the same rotation angle when beads were forced to rotate to ATP synthesis direction. The results imply that if F(o)F(1) is resting in the epsilon-inhibited state, F(o) motor must transmit to gamma a torque larger than expected from thermodynamic equilibrium to initiate ATP synthesis.

Stimulation of F(1)-ATPase activity by sodium dodecyl sulfate.

F(1)-ATPase is a rotary molecular motor in which the gamma subunit rotates inside the cylinder made of alpha(3)beta(3) subunits. We have studied the effects of sodium dodecyl sulfate (SDS) on the rotational and ATP hydrolysis activities of F(1)-ATPase. Bulk hydrolysis activity at various SDS concentrations was examined at 2mM ATP. Maximal stimulation was obtained at 0.003% (w/v) SDS, the initial (least inhibited) activity being about 1.4 times and the steady-state activity 3-4 times the values in the absence of SDS. Rotation rates observed with a 40-nm gold bead or a 0.29-mum bead duplex as well as the torque were unaffected by the presence of 0.003% SDS. The fraction of beads that rotated, in contrast, tended to increase in the presence of SDS. SDS seems to bring inactive F(1) molecules into an active form but it does not alter or enhance the function of already active F(1) molecules significantly.

A giant liposome for single-molecule observation of conformational changes in membrane proteins.

We present an experimental system that allows visualization of conformational changes in membrane proteins at the single-molecule level. The target membrane protein is reconstituted in a giant liposome for independent control of the aqueous environments on the two sides of the membrane. For direct observation of conformational changes, an extra-liposomal site(s) of the target protein is bound to a glass surface, and a probe that is easily visible under a microscope, such as a micron-sized plastic bead, is attached to another site on the intra-liposomal side. A conformational change, or an angular motion in the tiny protein molecule, would manifest as a visible motion of the probe. The attachment of the protein on the glass surface also immobilizes the liposome, greatly facilitating its manipulation such as the probe injection. As a model system, we reconstituted ATP synthase (F(O)F(1)) in liposomes tens of mum in size, attached the protein specifically to a glass surface, and demonstrated its ATP-driven rotation in the membrane through the motion of a submicron bead.