Trapping the ATP binding state leads to a detailed understanding of the F1-ATPase mechanism

2-Site versus 3-site models of ATP hydrolysis by F1-ATPase: definitive mathematical proof using combinatorics and conservation equations

The F1-ATPase enzyme is the smallest-known molecular motor that rotates in 120° steps, driven by the hydrolysis of ATP. It is a multi-subunit enzyme that contains three catalytic sites. A central question is how the elementary chemical reactions that occur in the three sites are coupled to mechanical rotation. Various models and coupling schemes have been formulated in an attempt to answer this question. They can be classified as 2-site (bi-site) models, exemplified by Boyer's binding change mechanism first proposed 50 years ago, and 3-site (tri-site) models such as Nath's torsional mechanism, first postulated 25 years ago and embellished 1 year back. Experimental data collated using diverse approaches have conclusively shown that steady-state ATP hydrolysis by F1-ATPase occurs in tri-site mode. Hence older models have been continually modified to make them conform to the new facts. Here, we have developed a pure mathematical approach based on combinatorics and conservation laws to test if proposed models are 2-site or 3-site. Based on this novel combinatorial approach, we have proved that older and modified models are effectively bi‒site models in that catalysis and rotation in F1-ATPase occurs in these models with only two catalytic sites occupied by bound nucleotide. Hence these models contradict consensus experimental data. The recent 2023 model of ATP hydrolysis by F1-ATPase has been proved to be a true tri-site model based on our novel mathematical approach. Such pure mathematical proofs constitute an important step forward for ATP mechanism. However, in what must be considered an aspect with great scientific potential, the power of such mathematical proofs has not been fully exploited to solve molecular biological problems, in our opinion. We believe that the creative application of pure mathematical proofs (for another example see Nath in Theory Biosci 141:249-260, 2022) can help resolve with finality various longstanding molecular-level issues that arise as a matter of course in the analysis of fundamental biological problems. Such issues have proved extraordinarily difficult to resolve by standard experimental, theoretical, or computational approaches.

Characterizing ATP processing by the AAA+ protein p97 at the atomic level

The human enzyme p97 regulates various cellular pathways by unfolding hundreds of protein substrates in an ATP-dependent manner, making it an essential component of protein homeostasis and an impactful pharmacological target. The hexameric complex undergoes substantial conformational changes throughout its catalytic cycle. Here we elucidate the molecular motions that occur at the active site in the temporal window immediately before and after ATP hydrolysis by merging cryo-EM, NMR spectroscopy and molecular dynamics simulations. p97 populates a metastable reaction intermediate, the ADP·Pi state, which is poised between hydrolysis and product release. Detailed snapshots reveal that the active site is finely tuned to trap and eventually discharge the cleaved phosphate. Signalling pathways originating at the active site coordinate the action of the hexamer subunits and couple hydrolysis with allosteric conformational changes. Our multidisciplinary approach enables a glimpse into the sophisticated spatial and temporal orchestration of ATP handling by a prototype AAA+ protein.

Perspectives on Computational Enzyme Modeling: From Mechanisms to Design and Drug Development

Understanding enzyme mechanisms is essential for unraveling the complex molecular machinery of life. In this review, we survey the field of computational enzymology, highlighting key principles governing enzyme mechanisms and discussing ongoing challenges and promising advances. Over the years, computer simulations have become indispensable in the study of enzyme mechanisms, with the integration of experimental and computational exploration now established as a holistic approach to gain deep insights into enzymatic catalysis. Numerous studies have demonstrated the power of computer simulations in characterizing reaction pathways, transition states, substrate selectivity, product distribution, and dynamic conformational changes for various enzymes. Nevertheless, significant challenges remain in investigating the mechanisms of complex multistep reactions, large-scale conformational changes, and allosteric regulation. Beyond mechanistic studies, computational enzyme modeling has emerged as an essential tool for computer-aided enzyme design and the rational discovery of covalent drugs for targeted therapies. Overall, enzyme design/engineering and covalent drug development can greatly benefit from our understanding of the detailed mechanisms of enzymes, such as protein dynamics, entropy contributions, and allostery, as revealed by computational studies. Such a convergence of different research approaches is expected to continue, creating synergies in enzyme research. This review, by outlining the ever-expanding field of enzyme research, aims to provide guidance for future research directions and facilitate new developments in this important and evolving field.

Rotary properties of hybrid F1-ATPases consisting of subunits from different species

F₁-ATPase (F₁) is an ATP-driven rotary motor protein ubiquitously found in many species as the catalytic portion of F_oF₁-ATP synthase. Despite the highly conserved amino acid sequence of the catalytic core subunits: α and β, F₁ shows diversity in the maximum catalytic turnover rate V_max and the number of rotary steps per turn. To study the design principle of F₁, we prepared eight hybrid F₁s composed of subunits from two of three genuine F₁s: thermophilic Bacillus PS3 (TF₁), bovine mitochondria (bMF₁), and Paracoccus denitrificans (PdF₁), differing in the V_max and the number of rotary steps. The V_max of the hybrids can be well fitted by a quadratic model highlighting the dominant roles of β and the couplings between α-β. Although there exist no simple rules on which subunit dominantly determines the number of steps, our findings show that the stepping behavior is characterized by the combination of all subunits.

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

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

Common Mechanism of Activated Catalysis in P-loop Fold Nucleoside Triphosphatases-United in Diversity

To clarify the obscure hydrolysis mechanism of ubiquitous P-loop-fold nucleoside triphosphatases (Walker NTPases), we analysed the structures of 3136 catalytic sites with bound Mg-NTP complexes or their analogues. Our results are presented in two articles; here, in the second of them, we elucidated whether the Walker A and Walker B sequence motifs-common to all P-loop NTPases-could be directly involved in catalysis. We found that the hydrogen bonds (H-bonds) between the strictly conserved, Mg-coordinating Ser/Thr of the Walker A motif ([Ser/Thr]WA) and aspartate of the Walker B motif (AspWB) are particularly short (even as short as 2.4 ångströms) in the structures with bound transition state (TS) analogues. Given that a short H-bond implies parity in the pKa values of the H-bond partners, we suggest that, in response to the interactions of a P-loop NTPase with its cognate activating partner, a proton relocates from [Ser/Thr]WA to AspWB. The resulting anionic [Ser/Thr]WA alkoxide withdraws a proton from the catalytic water molecule, and the nascent hydroxyl attacks the gamma phosphate of NTP. When the gamma-phosphate breaks away, the trapped proton at AspWB passes by the Grotthuss relay via [Ser/Thr]WA to beta-phosphate and compensates for its developing negative charge that is thought to be responsible for the activation barrier of hydrolysis.

Simulating a chemically fueled molecular motor with nonequilibrium molecular dynamics

Most computer simulations of molecular dynamics take place under equilibrium conditions-in a closed, isolated system, or perhaps one held at constant temperature or pressure. Sometimes, extra tensions, shears, or temperature gradients are introduced to those simulations to probe one type of nonequilibrium response to external forces. Catalysts and molecular motors, however, function based on the nonequilibrium dynamics induced by a chemical reaction's thermodynamic driving force. In this scenario, simulations require chemostats capable of preserving the chemical concentrations of the nonequilibrium steady state. We develop such a dynamic scheme and use it to observe cycles of a particle-based classical model of a catenane-like molecular motor. Molecular motors are frequently modeled with detailed-balance-breaking Markov models, and we explicitly construct such a picture by coarse graining the microscopic dynamics of our simulations in order to extract rates. This work identifies inter-particle interactions that tune those rates to create a functional motor, thereby yielding a computational playground to investigate the interplay between directional bias, current generation, and coupling strength in molecular information ratchets.

Molecular dynamics free energy simulations of ATP:Mg2+ and ADP:Mg2+ using the polarizable force field AMOEBA

ATPases and GTPases are two important classes of protein that play critical roles in energy transduction, cellular signaling, gene regulation and catalysis. These proteins use cofactors such as nucleoside di and tri-phosphates (NTP, NDP) and can detect the difference between NDP and NTP which then induce different protein conformations. Mechanisms that drive proteins into the NTP or NDP conformation may depend on factors such as ligand structure and how Mg²⁺ coordinates with the ligand, amino acids in the pocket and water molecules. Here, we have used the advanced electrostatic and polarizable force field AMOEBA and molecular dynamics free energy simulations (MDFE) to examine the various binding mechanisms of ATP:Mg²⁺ and ADP:Mg²⁺.We compared the ATP:Mg²⁺ binding with previous studies using non-polarizable force fields and experimental data on the binding affinity. It was found that the total free energy of binding for ATP:Mg²⁺ (-7.00 ± 2.13 kcal/mol) is in good agreement with experimental values (-8.6 ± .2 kcal/mol)¹. In addition, parameters for relevant protonation states of ATP, ADP, GTP and GDP have been derived. These parameters will allow for researchers to investigate biochemical phenomena involving NTP's and NDP's with greater accuracy than previous studies involving non-polarizable force fields.

Rotary catalysis of bovine mitochondrial F1-ATPase studied by single-molecule experiments

The reaction scheme of rotary catalysis and the torque generation mechanism of bovine mitochondrial F₁ (bMF₁) were studied in single-molecule experiments. Under ATP-saturated concentrations, high-speed imaging of a single 40-nm gold bead attached to the γ subunit of bMF₁ showed 2 types of intervening pauses during the rotation that were discriminated by short dwell and long dwell. Using ATPγS as a slowly hydrolyzing ATP derivative as well as using a functional mutant βE188D with slowed ATP hydrolysis, the 2 pausing events were distinctively identified. Buffer-exchange experiments with a nonhydrolyzable analog (AMP-PNP) revealed that the long dwell corresponds to the catalytic dwell, that is, the waiting state for hydrolysis, while it remains elusive which catalytic state short pause represents. The angular position of catalytic dwell was determined to be at +80° from the ATP-binding angle, mostly consistent with other F₁s. The position of short dwell was found at 50 to 60° from catalytic dwell, that is, +10 to 20° from the ATP-binding angle. This is a distinct difference from human mitochondrial F₁, which also shows intervening dwell that probably corresponds to the short dwell of bMF₁, at +65° from the binding pause. Furthermore, we conducted "stall-and-release" experiments with magnetic tweezers to reveal how the binding affinity and hydrolysis equilibrium are modulated by the γ rotation. Similar to thermophilic F₁, bMF₁ showed a strong exponential increase in ATP affinity, while the hydrolysis equilibrium did not change significantly. This indicates that the ATP binding process generates larger torque than the hydrolysis process.

Structural basis for power stroke vs. Brownian ratchet mechanisms of motor proteins

Two mechanisms have been proposed for the function of motor proteins: The power stroke and the Brownian ratchet. The former refers to generation of a large downhill free energy gradient over which the motor protein moves nearly irreversibly in making a step, whereas the latter refers to biasing or rectifying the diffusive motion of the motor. Both mechanisms require input of free energy, which generally involves the processing of an ATP (adenosine 5'-triphosphate) molecule. Recent advances in experiments that reveal the details of the stepping motion of motor proteins, together with computer simulations of atomistic structures, have provided greater insights into the mechanisms. Here, we compare the various models of the power stroke and the Brownian ratchet that have been proposed. The 2 mechanisms are not mutually exclusive, and various motor proteins employ them to different extents to perform their biological function. As examples, we discuss linear motor proteins Kinesin-1 and myosin-V, and the rotary motor F₁-ATPase, all of which involve a power stroke as the essential element of their stepping mechanism.

Insights into the origin of the high energy-conversion efficiency of F1-ATPase

Our understanding of the rotary-coupling mechanism of F₁-ATPase has been greatly enhanced in the last decade by advances in X-ray crystallography, single-molecular imaging, and theoretical models. Recently, Volkán-Kacsó and Marcus [S. Volkán-Kacsó, R. A. Marcus, Proc. Natl. Acad. Sci. U.S.A. 112, 14230 (2015)] presented an insightful thermodynamic model based on the Marcus reaction theory coupled with an elastic structural deformation term to explain the observed γ-rotation angle dependence of the adenosine triphosphate (ATP)/adenosine diphosphate (ADP) exchange rates of F₁-ATPase. Although the model is successful in correlating single-molecule data, it is not in agreement with the available theoretical results. We describe a revision of the model, which leads to consistency with the simulation results and other experimental data on the F₁-ATPase rotor compliance. Although the free energy liberated on ATP hydrolysis by F₁-ATPase is rapidly dissipated as heat and so cannot contribute directly to the rotation, we show how, nevertheless, F₁-ATPase functions near the maximum possible efficiency. This surprising result is a consequence of the differential binding of ATP and its hydrolysis products ADP and P_i along a well-defined pathway.

Structure of F1-ATPase from the obligate anaerobe Fusobacterium nucleatum

The crystal structure of the F₁-catalytic domain of the adenosine triphosphate (ATP) synthase has been determined from the pathogenic anaerobic bacterium Fusobacterium nucleatum. The enzyme can hydrolyse ATP but is partially inhibited. The structure is similar to those of the F₁-ATPases from Caldalkalibacillus thermarum, which is more strongly inhibited in ATP hydrolysis, and in Mycobacterium smegmatis, which has a very low ATP hydrolytic activity. The β_E-subunits in all three enzymes are in the conventional ‘open’ state, and in the case of C. thermarum and M. smegmatis, they are occupied by an ADP and phosphate (or sulfate), but in F. nucleatum, the occupancy by ADP appears to be partial. It is likely that the hydrolytic activity of the F. nucleatum enzyme is regulated by the concentration of ADP, as in mitochondria.

Broadening the horizon: Integrative pharmacophore-based and cheminformatics screening of novel chemical modulators of mitochondria ATP synthase towards interventive Alzheimer's disease therapy

The proven efficacy of J147 in the treatment of Alzheimer's disease (AD) has been emphatic, particularly since its selective modulatory roles towards mitochondrial ATP synthase (mATPase) were defined. This prospect, if methodically probed, could further pave way for the discovery of novel anti-AD drugs with improved pharmacokinetics and therapeutic potential. To this effect, for the first time, we employed a four-step paradigm that integrated our in-house per-residue energy decomposition (PRED) protocol coupled with molecular dynamics, cheminformatics and analytical binding free energy methods. This was geared towards the screening and identification of new leads that exhibit modulatory potentials towards mATPase in a J147-similar pattern. Interestingly, from a large-scale library of compounds, we funnelled down on three potential hits that demonstrated selective and high-affinity binding activities towards α-F1-ATP synthase (ATP5A) relative to J147. Moreover, these compounds exhibited higher binding propensity with a differential ΔGs greater than -1 kcal/mol comparative to J147, and also elicited distinct modulatory effects on ATP5A domain structures. More interestingly, per-residue pharmacophore modeling of these lead compounds revealed similar interactive patterns with crucial residues at the α-site region of ATP5A characterized by high energy contributions based on binding complementarity. Recurrent target residues involved in high-affinity interactions with the hit molecules relative to J147 include Arg1112 and Gln426. Furthermore, assessments of pharmacokinetics revealed that the lead compounds were highly drug-like with minimal violations of the Lipinski's rule of five. As developed in this study, the most extrapolative pharmacophore model of the selected hits encompassed three electron donors and one electron acceptor. We speculate that these findings will be fundamental to the reformation of anti-AD drug discovery procedures.

The structure of the catalytic domain of the ATP synthase from Mycobacterium smegmatis is a target for developing antitubercular drugs

The crystal structure of the F₁-catalytic domain of the adenosine triphosphate (ATP) synthase has been determined from Mycobacterium smegmatis which hydrolyzes ATP very poorly. The structure of the α₃β₃-component of the catalytic domain is similar to those in active F₁-ATPases in Escherichia coli and Geobacillus stearothermophilus However, its ε-subunit differs from those in these two active bacterial F₁-ATPases as an ATP molecule is not bound to the two α-helices forming its C-terminal domain, probably because they are shorter than those in active enzymes and they lack an amino acid that contributes to the ATP binding site in active enzymes. In E. coli and G. stearothermophilus, the α-helices adopt an "up" state where the α-helices enter the α₃β₃-domain and prevent the rotor from turning. The mycobacterial F₁-ATPase is most similar to the F₁-ATPase from Caldalkalibacillus thermarum, which also hydrolyzes ATP poorly. The β_E-subunits in both enzymes are in the usual "open" conformation but appear to be occupied uniquely by the combination of an adenosine 5'-diphosphate molecule with no magnesium ion plus phosphate. This occupation is consistent with the finding that their rotors have been arrested at the same point in their rotary catalytic cycles. These bound hydrolytic products are probably the basis of the inhibition of ATP hydrolysis. It can be envisaged that specific as yet unidentified small molecules might bind to the F₁ domain in Mycobacterium tuberculosis, prevent ATP synthesis, and inhibit the growth of the pathogen.

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

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

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

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

Exploring the selectivity of inhibitor complexes with Bcl-2 and Bcl-XL: A molecular dynamics simulation approach

B-cell lymphoma 2 (Bcl-2) family proteins are potential drug targets in cancer and have a relatively flat and flexible binding site. ABT-199 is one of the most promising selective Bcl-2 inhibitors, and A-1155463 selectively inhibits Bcl-XL. Although the amino acid sequences of the binding sites of these two inhibitors are similar, the inhibitors selectively bind the target protein. In order to determine the origin of the selectivity of these inhibitors, we conducted molecular dynamics simulations using protein-inhibitor modeling. We confirmed that ASP103 of Bcl-2 is a key residue and that hydrogen bonding between ASP103 and ABT-199 confers the Bcl-2 selectivity of this inhibitor. For Bcl-XL selectivity, the secondary structure of α-helix 3 is a key factor. PHE105, SER106, and LEU108 in the loose α-helix 3 interact with A-1155463 to confer Bcl-XL selectivity. These findings provide important insights into the molecular mechanisms of selective inhibitors of Bcl-2 family proteins.

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

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

Mechanochemical Energy Transduction during the Main Rotary Step in the Synthesis Cycle of F1-ATPase

F₁-ATPase is a highly efficient molecular motor that can synthesize ATP driven by a mechanical torque. Its ability to function reversibly in either direction requires tight mechanochemical coupling between the catalytic domain and the rotating central shaft, as well as temporal control of substrate binding and product release. Despite great efforts and significant progress, the molecular details of this synchronized and fine-tuned energy conversion mechanism are not fully understood. Here, we use extensive molecular dynamics simulations to reconcile recent single-molecule experiments with structural data and provide a consistent thermodynamic, kinetic and mechanistic description of the main rotary substep in the synthetic cycle of mammalian ATP synthase. The calculated free energy profiles capture a discrete pattern in the rotation of the central γ-shaft, with a metastable intermediate located-consistently with recent experimental findings-at 70° relative to the X-ray position. We identify this rotary step as the ATP-dependent substep, and find that the associated free energy input supports the mechanism involving concurrent nucleotide binding and release. During the main substep, our simulations show no significant opening of the ATP-bound β subunit; instead, we observe that mechanical energy is transmitted to its nucleotide binding site, thus lowering the affinity for ATP. Simultaneously, the empty subunit assumes a conformation that enables the enzyme to harness the free energy of ADP binding to drive ATP release. Finally, we show that ligand exchange is regulated by a checkpoint mechanism, an apparent prerequisite for high efficiency in protein nanomotors.

Regulation and Plasticity of Catalysis in Enzymes: Insights from Analysis of Mechanochemical Coupling in Myosin

The mechanism of ATP hydrolysis in the myosin motor domain is analyzed using a combination of DFTB3/CHARMM simulations and enhanced sampling techniques. The motor domain is modeled in the pre-powerstroke state, in the post-rigor state, and as a hybrid based on the post-rigor state with a closed nucleotide-binding pocket. The ATP hydrolysis activity is found to depend on the positioning of nearby water molecules, and a network of polar residues facilitates proton transfer and charge redistribution during hydrolysis. Comparison of the observed hydrolysis pathways and the corresponding free energy profiles leads to detailed models for the mechanism of ATP hydrolysis in the pre-powerstroke state and proposes factors that regulate the hydrolysis activity in different conformational states. In the pre-powerstroke state, the scissile P_γ-O_3β bond breaks early in the reaction. Proton transfer from the lytic water to the γ-phosphate through active site residues is an important part of the kinetic bottleneck; several hydrolysis pathways that feature distinct proton transfer routes are found to have similar free energy barriers, suggesting a significant degree of plasticity in the hydrolysis mechanism. Comparison of hydrolysis in the pre-powerstroke state and the closed post-rigor model suggests that optimization of residues beyond the active site for electrostatic stabilization and preorganization is likely important to enzyme design.

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

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

Crystal structures of the ATP-binding and ADP-release dwells of the V1 rotary motor

V1-ATPases are highly conserved ATP-driven rotary molecular motors found in various membrane systems. We recently reported the crystal structures for the Enterococcus hirae A3B3DF (V1) complex, corresponding to the catalytic dwell state waiting for ATP hydrolysis. Here we present the crystal structures for two other dwell states obtained by soaking nucleotide-free V1 crystals in ADP. In the presence of 20 μM ADP, two ADP molecules bind to two of three binding sites and cooperatively induce conformational changes of the third site to an ATP-binding mode, corresponding to the ATP-binding dwell. In the presence of 2 mM ADP, all nucleotide-binding sites are occupied by ADP to induce conformational changes corresponding to the ADP-release dwell. Based on these and previous findings, we propose a V1-ATPase rotational mechanism model.

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

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

A Simple and Accurate Method To Calculate Free Energy Profiles and Reaction Rates from Restrained Molecular Simulations of Diffusive Processes

A method is developed to obtain simultaneously free energy profiles and diffusion constants from restrained molecular simulations in diffusive systems. The method is based on low-order expansions of the free energy and diffusivity as functions of the reaction coordinate. These expansions lead to simple analytical relationships between simulation statistics and model parameters. The method is tested on 1D and 2D model systems; its accuracy is found to be comparable to or better than that of the existing alternatives, which are briefly discussed. An important aspect of the method is that the free energy is constructed by integrating its derivatives, which can be computed without need for overlapping sampling windows. The implementation of the method in any molecular simulation program that supports external umbrella potentials (e.g., CHARMM) requires modification of only a few lines of code. As a demonstration of its applicability to realistic biomolecular systems, the method is applied to model the α-helix ↔ β-sheet transition in a 16-residue peptide in implicit solvent, with the reaction coordinate provided by the string method. Possible modifications of the method are briefly discussed; they include generalization to multidimensional reaction coordinates [in the spirit of the model of Ermak and McCammon (Ermak, D. L.; McCammon, J. A. J. Chem. Phys. 1978, 69, 1352-1360)], a higher-order expansion of the free energy surface, applicability in nonequilibrium systems, and a simple test for Markovianity. In view of the small overhead of the method relative to standard umbrella sampling, we suggest its routine application in the cases where umbrella potential simulations are appropriate.

F1-ATPase conformational cycle from simultaneous single-molecule FRET and rotation measurements

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-α3β3, while simultaneously monitoring rotations of the central shaft-γ. In the ATP waiting dwell, two of three β-subunits simultaneously adopt low FRET nonclosed forms. By contrast, in the catalytic intermediate dwell, two β-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 ε-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 αβ-dimer in the ATPase cycle, highlighting the two dominant modes: the opening/closing motions of β and the loosening/tightening motions at the αβ-interface. These results provide a new view of tripartite coupling among chemical reactions, stator conformations, and rotary angles in F1-ATPase.

Inherent conformational flexibility of F1-ATPase α-subunit

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

A Model for the Molecular Mechanism of an Engineered Light-Driven Protein Machine

Controllable protein-based machines and materials are of considerable interest for diverse biotechnological applications. We previously re-engineered an ATP-driven protein machine, a group II chaperonin, to function as a light-gated nanocage. Here we develop and test a model for the molecular mechanism of the re-engineered chaperonin, which undergoes a large-scale closed to open conformational change triggered by reversible photo-isomerization of a site-specifically attached azobenzene crosslinker. In silico experiments using all-atom simulations suggest that rigid body motions of protein subdomains couple the length changes of the crosslinker to rearrangements of the nucleotide-binding pocket, leading to cage opening. We tested this model by designing a mutant for which the orientation of the two protein subdomains forming the nucleotide-binding pocket is directly controlled by the crosslinker, and confirmed successful reversible photoswitching in vitro. The model probes the conformational cycle of group II chaperonins and offers a design principle for engineering other light-driven protein-based molecular machines.

Operating principles of rotary molecular motors: differences between F1 and V1 motors

Among the many types of bioenergy-transducing machineries, F- and V-ATPases are unique bio- and nano-molecular rotary motors. The rotational catalysis of F₁-ATPase has been investigated in detail, and molecular mechanisms have been proposed based on the crystal structures of the complex and on extensive single-molecule rotational observations. Recently, we obtained crystal structures of bacterial V₁-ATPase (A₃B₃ and A₃B₃DF complexes) in the presence and absence of nucleotides. Based on these new structures, we present a novel model for the rotational catalysis mechanism of V₁-ATPase, which is different from that of F₁-ATPases.

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

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

Molecular dynamics simulations of biological membranes and membrane proteins using enhanced conformational sampling algorithms

This paper reviews various enhanced conformational sampling methods and explicit/implicit solvent/membrane models, as well as their recent applications to the exploration of the structure and dynamics of membranes and membrane proteins. Molecular dynamics simulations have become an essential tool to investigate biological problems, and their success relies on proper molecular models together with efficient conformational sampling methods. The implicit representation of solvent/membrane environments is reasonable approximation to the explicit all-atom models, considering the balance between computational cost and simulation accuracy. Implicit models can be easily combined with replica-exchange molecular dynamics methods to explore a wider conformational space of a protein. Other molecular models and enhanced conformational sampling methods are also briefly discussed. As application examples, we introduce recent simulation studies of glycophorin A, phospholamban, amyloid precursor protein, and mixed lipid bilayers and discuss the accuracy and efficiency of each simulation model and method. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

The Mitochondrial Permeability Transition Pore: Channel Formation by F-ATP Synthase, Integration in Signal Transduction, and Role in Pathophysiology

The mitochondrial permeability transition (PT) is a permeability increase of the inner mitochondrial membrane mediated by a channel, the permeability transition pore (PTP). After a brief historical introduction, we cover the key regulatory features of the PTP and provide a critical assessment of putative protein components that have been tested by genetic analysis. The discovery that under conditions of oxidative stress the F-ATP synthases of mammals, yeast, and Drosophila can be turned into Ca(2+)-dependent channels, whose electrophysiological properties match those of the corresponding PTPs, opens new perspectives to the field. We discuss structural and functional features of F-ATP synthases that may provide clues to its transition from an energy-conserving into an energy-dissipating device as well as recent advances on signal transduction to the PTP and on its role in cellular pathophysiology.

Role of Protein Dynamics in Allosteric Control of the Catalytic Phosphoryl Transfer of Insulin Receptor Kinase

The catalytic and allosteric mechanisms of insulin receptor kinase (IRK) are investigated by a combination of ab initio and semiempirical quantum mechanical and molecular mechanical (QM/MM) methods and classical molecular dynamics (MD) simulations. The simulations reveal that the catalytic reaction proceeds in two steps, starting with the transfer of a proton from substrate Tyr to the catalytic Asp1132, followed by the phosphoryl transfer from ATP to substrate Tyr. The enhancement of the catalytic rate of IRK upon phosphorylations in the enzyme's activation loop is found to occur mainly via changes to the free energy landscape of the proton transfer step, favoring the proton transfer in the fully phosphorylated enzyme. In contrast, the effects of the phosphorylations on the phosphoryl transfer are smaller. Equilibrium MD simulations show that IRK phosphorylations affect the protein dynamics of the enzyme before the proton transfer to Asp1132 with only a minor effect after the proton transfer. This finding is consistent with the large change in the proton transfer free energy and the smaller change in the free energy barrier of phosphoryl transfer found by QM/MM simulations. Taken together, the present results provide details on how IRK phosphorylation exerts allosteric control of the catalytic activity via modifications of protein dynamics and free energy landscape of catalytic reaction. The results also highlight the importance of protein dynamics in connecting protein allostery and catalysis to control catalytic activity of enzymes.

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

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

From ATP to PTP and Back: A Dual Function for the Mitochondrial ATP Synthase

Mitochondria not only play a fundamental role in heart physiology but are also key effectors of dysfunction and death. This dual role assumes a new meaning after recent advances on the nature and regulation of the permeability transition pore, an inner membrane channel whose opening requires matrix Ca(2+) and is modulated by many effectors including reactive oxygen species, matrix cyclophilin D, Pi (inorganic phosphate), and matrix pH. The recent demonstration that the F-ATP synthase can reversibly undergo a Ca(2+)-dependent transition to form a channel that mediates the permeability transition opens new perspectives to the field. These findings demand a reassessment of the modifications of F-ATP synthase that take place in the heart under pathological conditions and of their potential role in determining the transition of F-ATP synthase from and energy-conserving into an energy-dissipating device.

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 α3β3 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.

How release of phosphate from mammalian F1-ATPase generates a rotary substep

ATP, the fuel of life, is produced in the mitochondria of living cells by a molecular machine consisting of two motors linked by a rotor. One motor generates rotation by consuming energy derived from sugars and fats in foodstuffs; the other uses energy transmitted by the rotor to synthesize ATP molecules from their building blocks, ADP and phosphate. The synthetic motor can be uncoupled from the machine, and its rotary action can be studied by driving the motor backward with energy from ATP, releasing ADP and phosphate in the process. Each cycle has three 120° steps, each made of substeps of 65°, 25°, and 30° in humans. We have explained how release of phosphate from the machine generates the 25° rotary substep.

The rotation of the central stalk of F₁-ATPase is driven by energy derived from the sequential binding of an ATP molecule to its three catalytic sites and the release of the products of hydrolysis. In human F₁-ATPase, each 360° rotation consists of three 120° steps composed of substeps of about 65°, 25°, and 30°, with intervening ATP binding, phosphate release, and catalytic dwells, respectively. The F₁-ATPase inhibitor protein, IF₁, halts the rotary cycle at the catalytic dwell. The human and bovine enzymes are essentially identical, and the structure of bovine F₁-ATPase inhibited by IF₁ represents the catalytic dwell state. Another structure, described here, of bovine F₁-ATPase inhibited by an ATP analog and the phosphate analog, thiophosphate, represents the phosphate binding dwell. Thiophosphate is bound to a site in the α_Eβ_E-catalytic interface, whereas in F₁-ATPase inhibited with IF₁, the equivalent site is changed subtly and the enzyme is incapable of binding thiophosphate. These two structures provide a molecular mechanism of how phosphate release generates a rotary substep as follows. In the active enzyme, phosphate release from the β_E-subunit is accompanied by a rearrangement of the structure of its binding site that prevents released phosphate from rebinding. The associated extrusion of a loop in the β_E-subunit disrupts interactions in the α_Eβ_E-catalytic interface and opens it to its fullest extent. Other rearrangements disrupt interactions between the γ-subunit and the C-terminal domain of the α_E-subunit. To restore most of these interactions, and to make compensatory new ones, the γ-subunit rotates through 25°–30°.