Theory for rates, equilibrium constants, and Bronsted slopes in F1-ATPase single molecule imaging experiments.
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ABSTRACT:
SUBMITTER: Volkan-Kacso S
PROVIDER: S-EPMC4655567 | biostudies-other | 2015 Nov
REPOSITORIES: biostudies-other
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Project description:The reaction scheme of rotary catalysis and the torque generation mechanism of bovine mitochondrial F1 (bMF1) were studied in single-molecule experiments. Under ATP-saturated concentrations, high-speed imaging of a single 40-nm gold bead attached to the γ subunit of bMF1 showed 2 types of intervening pauses during the rotation that were discriminated by short dwell and long dwell. Using ATPγS as a slowly hydrolyzing ATP derivative as well as using a functional mutant βE188D with slowed ATP hydrolysis, the 2 pausing events were distinctively identified. Buffer-exchange experiments with a nonhydrolyzable analog (AMP-PNP) revealed that the long dwell corresponds to the catalytic dwell, that is, the waiting state for hydrolysis, while it remains elusive which catalytic state short pause represents. The angular position of catalytic dwell was determined to be at +80° from the ATP-binding angle, mostly consistent with other F1s. The position of short dwell was found at 50 to 60° from catalytic dwell, that is, +10 to 20° from the ATP-binding angle. This is a distinct difference from human mitochondrial F1, which also shows intervening dwell that probably corresponds to the short dwell of bMF1, at +65° from the binding pause. Furthermore, we conducted "stall-and-release" experiments with magnetic tweezers to reveal how the binding affinity and hydrolysis equilibrium are modulated by the γ rotation. Similar to thermophilic F1, bMF1 showed a strong exponential increase in ATP affinity, while the hydrolysis equilibrium did not change significantly. This indicates that the ATP binding process generates larger torque than the hydrolysis process.
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Project description:The theory of elastic group transfer for the binding and release rate constants for nucleotides in F1-ATPase as a function of the rotor angle is further extended in several respects. (i) A method is described for predicting the experimentally observed lifetime distribution of long binding events in the controlled rotation experiments by taking into account the hydrolysis and synthesis reactions occurring during these events. (ii) A method is also given for treating the long binding events in the experiments and obtaining the rate constants for the hydrolysis and synthesis reactions occurring during these events. (iii) The theory in the previous paper is given in a symmetric form, an extension that simplifies the application of the theory to experiments. It also includes a theory-based correction of the reported "on" and "off" rates by calculating the missed events. A near symmetry of the data about the angle of -40° and a "turnover" in the binding rate data vs. rotor angle for angles greater than [Formula: see text]40° is also discussed.
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Project description:At scales below micrometers, Brownian motion dictates most of the behaviors. The simple observation of a colloid is striking: a permanent and random motion is seen, whereas inertial forces play a negligible role. This Physics, where velocity is proportional to force, has opened new horizons in biology. The random feature is challenged in living systems where some proteins--molecular motors--have a directed motion whereas their passive behaviors of colloid should lead to a Brownian motion. Individual proteins, polymers of living matter such as DNA, RNA, actin or microtubules, molecular motors, all these objects can be viewed as chains of colloids. They are submitted to shocks from molecules of the solvent. Shapes taken by these biopolymers or dynamics imposed by motors can be measured and modeled from single molecules to their collective effects. Thanks to the development of experimental methods such as optical tweezers, Atomic Force Microscope (AFM), micropipettes, and quantitative fluorescence (such as Förster Resonance Energy Transfer, FRET), it is possible to manipulate these individual biomolecules in an unprecedented manner: experiments allow to probe the validity of models; and a new Physics has thereby emerged with original biological insights. Theories based on statistical mechanics are needed to explain behaviors of these systems. When force-extension curves of these molecules are extracted, the curves need to be fitted with models that predict the deformation of free objects or submitted to a force. When velocity of motors is altered, a quantitative analysis is required to explain the motions of individual molecules under external forces. This lecture will give some elements of introduction to the lectures of the session 'Nanophysics for Molecular Biology'.
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Project description:A method is proposed for analyzing fast (10 μs) single-molecule rotation trajectories in F1 adenosinetriphosphatase ([Formula: see text]-ATPase). This method is based on the distribution of jumps in the rotation angle that occur in the transitions during the steps between subsequent catalytic dwells. The method is complementary to the "stalling" technique devised by H. Noji et al. [Biophys. Rev. 9, 103-118, 2017], and can reveal multiple states not directly detectable as steps. A bimodal distribution of jumps is observed at certain angles, due to the system being in either of 2 states at the same rotation angle. In this method, a multistate theory is used that takes into account a viscoelastic fluctuation of the imaging probe. Using an established sequence of 3 specific states, a theoretical profile of angular jumps is predicted, without adjustable parameters, that agrees with experiment for most of the angular range. Agreement can be achieved at all angles by assuming a fourth state with an ∼10 μs lifetime and a dwell angle about 40° after the adenosine 5'-triphosphate (ATP) binding dwell. The latter result suggests that the ATP binding in one β subunit and the adenosine 5'-diphosphate (ADP) release from another β subunit occur via a transient whose lifetime is ∼10 μs and is about 6 orders of magnitude smaller than the lifetime for ADP release from a singly occupied [Formula: see text]-ATPase. An internal consistency test is given by comparing 2 independent ways of obtaining the relaxation time of the probe. They agree and are ∼15 μs.
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Project description:Despite extensive studies, the structural basis for the mechanochemical coupling in the rotary molecular motor F1-ATPase (F1) is still incomplete. We performed single-molecule FRET measurements to monitor conformational changes in the stator ring-?3?3, while simultaneously monitoring rotations of the central shaft-?. In the ATP waiting dwell, two of three ?-subunits simultaneously adopt low FRET nonclosed forms. By contrast, in the catalytic intermediate dwell, two ?-subunits are simultaneously in a high FRET closed form. These differences allow us to assign crystal structures directly to both major dwell states, thus resolving a long-standing issue and establishing a firm connection between F1 structure and the rotation angle of the motor. Remarkably, a structure of F1 in an ?-inhibited state is consistent with the unique FRET signature of the ATP waiting dwell, while most crystal structures capture the structure in the catalytic dwell. Principal component analysis of the available crystal structures further clarifies the five-step conformational transitions of the ??-dimer in the ATPase cycle, highlighting the two dominant modes: the opening/closing motions of ? and the loosening/tightening motions at the ??-interface. These results provide a new view of tripartite coupling among chemical reactions, stator conformations, and rotary angles in F1-ATPase.
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Project description:Single molecule studies in recent decades have elucidated the full chemo-mechanical cycle of F1-ATPase, mostly based on F1 from thermophilic bacteria. In contrast, high-resolution crystal structures are only available for mitochondrial F1. Here we present high resolution single molecule rotational data on F1 from Saccharomyces cerevisiae, obtained using new high throughput detection and analysis tools. Rotational data are presented for the wild type mitochondrial enzyme, a "liver" isoform, and six mutant forms of yeast F1 that have previously been demonstrated to be less efficient or partially uncoupled. The wild-type and "liver" isoforms show the same qualitative features as F1 from Escherichia coli and thermophilic bacteria. The analysis of the mutant forms revealed a delay at the catalytic dwell and associated decrease in Vmax, with magnitudes consistent with the level of disruption seen in the crystal structures. At least one of the mutant forms shows a previously un-observed dwell at the ATP binding angle, potentially attributable to slowed release of ADP. We discuss the correlation between crystal structures and single molecule results.
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Project description:Mitochondrial F(1)-ATPase contains a hexamer of alternating alpha and beta subunits. The assembly of this structure requires two specialized chaperones, Atp11p and Atp12p, that bind transiently to beta and alpha. In the absence of Atp11p and Atp12p, the hexamer is not formed, and alpha and beta precipitate as large insoluble aggregates. An early model for the mechanism of chaperone-mediated F(1) assembly (Wang, Z. G., Sheluho, D., Gatti, D. L., and Ackerman, S. H. (2000) EMBO J. 19, 1486-1493) hypothesized that the chaperones themselves look very much like the alpha and beta subunits, and proposed an exchange of Atp11p for alpha and of Atp12p for beta; the driving force for the exchange was expected to be a higher affinity of alpha and beta for each other than for the respective chaperone partners. One important feature of this model was the prediction that as long as Atp11p is bound to beta and Atp12p is bound to alpha, the two F(1) subunits cannot interact at either the catalytic site or the noncatalytic site interface. Here we present the structures of Atp11p from Candida glabrata and Atp12p from Paracoccus denitrificans, and we show that some features of the Wang model are correct, namely that binding of the chaperones to alpha and beta prevents further interactions between these F(1) subunits. However, Atp11p and Atp12p do not resemble alpha or beta, and it is instead the F(1) gamma subunit that initiates the release of the chaperones from alpha and beta and their further assembly into the mature complex.
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Project description:F(1)-ATPase is a rotary molecular motor in which the gamma-subunit rotates against the alpha(3)beta(3) cylinder. The unitary gamma-rotation is a 120 degrees step comprising 80 and 40 degrees substeps, each of these initiated by ATP binding and ADP release and by ATP hydrolysis and inorganic phosphate release, respectively. In our previous study on gamma-rotation at low temperatures, a highly temperature-sensitive (TS) reaction step of F(1)-ATPase from thermophilic Bacillus PS3 was found below 9 degrees C as an intervening pause before the 80 degrees substep at the same angle for ATP binding and ADP release. However, it remains unclear as to which reaction step the TS reaction corresponds. In this study, we found that the mutant F(1)(beta E190D) from thermophilic Bacillus PS3 showed a clear pause of the TS reaction below 18 degrees C. In an attempt to identify the catalytic state of the TS reaction, the rotation of the hybrid F(1), carrying a single copy of beta E190D, was observed at 18 degrees C. The hybrid F(1) showed a pause of the TS reaction at the same angle as for the ATP binding of the incorporated beta E190D, although kinetic analysis revealed that the TS reaction is not the ATP binding step. These findings suggest that the TS reaction is a structural rearrangement of beta before or after ATP binding.
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