Simulating Protein Mediated Hydrolysis of ATP and Other Nucleoside Triphosphates by Combining QM/MM Molecular Dynamics with Advances in Metadynamics

A Mode Evolution Metric to Extract Reaction Coordinates for Biomolecular Conformational Transitions

The complex, multidimensional energy landscape of biomolecules makes the extraction of suitable, nonintuitive collective variables (CVs) that describe their conformational transitions challenging. At present, dimensionality reduction approaches and machine learning (ML) schemes are employed to obtain CVs from molecular dynamics (MD)/Monte Carlo (MC) trajectories or structural databanks for biomolecules. However, minimum sampling conditions to generate reliable CVs that accurately describe the underlying energy landscape remain unclear. Here, we address this issue by developing a Mode evolution Metric (MeM) to extract CVs that can pinpoint new states and describe local transitions in the vicinity of a reference minimum from nonequilibrated MD/MC trajectories. We present a general mathematical formulation of MeM for both statistical dimensionality reduction and machine learning approaches. Application of MeM to MC trajectories of model potential energy landscapes and MD trajectories of solvated alanine dipeptide reveals that the principal components which locate new states in the vicinity of a reference minimum emerge well before the trajectories locally equilibrate between the associated states. Finally, we demonstrate a possible application of MeM in designing efficient biased sampling schemes to construct accurate energy landscape slices that link transitions between states. MeM can help speed up the search for new minima around a biomolecular conformational state and enable the accurate estimation of thermodynamics for states lying on the energy landscape and the description of associated transitions.

Novel Insights into the Catalytic Mechanism of Collagenolysis by Zn(II)-Dependent Matrix Metalloproteinase-1

Collagen hydrolysis, catalyzed by Zn(II)-dependent matrix metalloproteinases (MMPs), is a critical physiological process. Despite previous computational investigations into the catalytic mechanisms of MMP-mediated collagenolysis, a significant knowledge gap in understanding remains regarding the influence of conformational sampling and entropic contributions at physiological temperature on enzymatic collagenolysis. In our comprehensive multilevel computational study, employing quantum mechanics/molecular mechanics (QM/MM) metadynamics (MetD) simulations, we aimed to bridge this gap and provide valuable insights into the catalytic mechanism of MMP-1. Specifically, we compared the full enzyme-substrate complex in solution, clusters in solution, and gas-phase to elucidate insights into MMP-1-catalyzed collagenolysis. Our findings reveal significant differences in the catalytic mechanism when considering thermal effects and the dynamic evolution of the system, contrasting with conventional static potential energy surface QM/MM reaction path studies. Notably, we observed a significant stabilization of the critical tetrahedral intermediate, attributed to contributions from conformational flexibility and entropy. Moreover, we found that protonation of the scissile bond nitrogen occurs via proton transfer from a Zn(II)-coordinated hydroxide rather than from a solvent water molecule. Following C-N bond cleavage, the C-terminus remains coordinated to the catalytic Zn(II), while the N-terminus forms a hydrogen bond with a solvent water molecule. Subsequently, the release of the C-terminus is facilitated by the coordination of a water molecule. Our study underscores the pivotal role of protein conformational dynamics at physiological temperature in stabilizing the transition state of the rate-limiting step and key intermediates, compared to the corresponding reaction in solution. These fundamental insights into the mechanism of collagen degradation provide valuable guidance for the development of MMP-1-specific inhibitors.

Mechanism of phosphate release from actin filaments

After ATP-actin monomers assemble filaments, the ATP's [Formula: see text]-phosphate is hydrolyzedwithin seconds and dissociates over minutes. We used all-atom molecular dynamics simulations to sample the release of phosphate from filaments and study residues that gate release. Dissociation of phosphate from Mg2+ is rate limiting and associated with an energy barrier of 20 kcal/mol, consistent with experimental rates of phosphate release. Phosphate then diffuses within an internal cavity toward a gate formed by R177, as suggested in prior computational studies and cryo-EM structures. The gate is closed when R177 hydrogen bonds with N111 and is open when R177 forms a salt bridge with D179. Most of the time, interactions of R177 with other residues occlude the phosphate release pathway. Machine learning analysis reveals that the occluding interactions fluctuate rapidly, underscoring the secondary role of backdoor gate opening in Pi release, in contrast with the previous hypothesis that gate opening is the primary event.

Mechanism of Phosphate Release from Actin Filaments

After ATP-actin monomers assemble filaments, the ATP's γ-phosphate is hydrolyzed within seconds and dissociates over minutes. We used all-atom molecular dynamics simulations to sample the release of phosphate from filaments and study residues that gate release. Dissociation of phosphate from Mg2+ is rate limiting and associated with an energy barrier of 20 kcal/mol, consistent with experimental rates of phosphate release. Phosphate then diffuses in an internal cavity toward a gate formed by R177 suggested in prior computational studies and cryo-EM structures. The gate is closed when R177 hydrogen bonds with N111 and is open when R177 forms a salt bridge with D179. Most of the time interactions of R177 with other residues occludes the phosphate release pathway. Machine learning analysis reveals that the occluding interactions fluctuate rapidly, underscoring the secondary role of backdoor gate opening in Pi release, in contrast with the previous hypothesis that gate opening is the primary event.

Hybrid Quantum Mechanical/Molecular Mechanical Methods For Studying Energy Transduction in Biomolecular Machines

Hybrid quantum mechanical/molecular mechanical (QM/MM) methods have become indispensable tools for the study of biomolecules. In this article, we briefly review the basic methodological details of QM/MM approaches and discuss their applications to various energy transduction problems in biomolecular machines, such as long-range proton transports, fast electron transfers, and mechanochemical coupling. We highlight the particular importance for these applications of balancing computational efficiency and accuracy. Using several recent examples, we illustrate the value and limitations of QM/MM methodologies for both ground and excited states, as well as strategies for calibrating them in specific applications. We conclude with brief comments on several areas that can benefit from further efforts to make QM/MM analyses more quantitative and applicable to increasingly complex biological problems.

Unveiling the Catalytic Mechanism of GTP Hydrolysis in Microtubules

Microtubules (MTs) are large cytoskeletal polymers, composed of αβ-tubulin heterodimers, capable of stochastically converting from polymerizing to depolymerizing states and vice-versa. Depolymerization is coupled with hydrolysis of GTP within β-tubulin. Hydrolysis is favored in the MT lattice compared to free heterodimer with an experimentally observed rate increase of 500 to 700 fold, corresponding to an energetic barrier lowering of 3.8 to 4.0 kcal/mol. Mutagenesis studies have implicated α-tubulin residues, α:E254 and α:D251, as catalytic residues completing the β-tubulin active site of the lower heterodimer in the MT lattice. The mechanism for GTP hydrolysis in the free heterodimer, however, is not understood. Additionally, there has been debate concerning whether the GTP-state lattice is expanded or compacted relative to the GDP-state and whether a "compacted" GDP-state lattice is required for hydrolysis. In this work, extensive QM/MM simulations with transition-tempered metadynamics free energy sampling of compacted and expanded inter-dimer complexes, as well as free heterodimer, have been carried out to provide clear insight into the GTP hydrolysis mechanism. α:E254 was found to be the catalytic residue in a compacted lattice, while in the expanded lattice disruption of a key salt bridge interaction renders α:E254 less effective. The simulations reveal a barrier decrease of 3.8 ± 0.5 kcal/mol for the compacted lattice compared to free heterodimer, in good agreement with experimental kinetic measurements. Additionally, the expanded lattice barrier was found to be 6.3 ± 0.5 kcal/mol higher than compacted, demonstrating that GTP hydrolysis is variable with lattice state and slower at the MT tip.

Significance Statement

Microtubules (MTs) are large and dynamic components of the eukaryotic cytoskeleton with the ability to stochastically convert from a polymerizing to a depolymerizing state and vice-versa. Depolymerization is coupled to the hydrolysis of guanosine-5'-triphosphate (GTP), which is orders of magnitude faster in the MT lattice than in free tubulin heterodimers. Our results computationally ascertain the catalytic residue contacts in the MT lattice that accelerate GTP hydrolysis compared to the free heterodimer as well as confirm that a compacted MT lattice is necessary for hydrolysis while a more expanded lattice is unable to form the necessary contacts and thereby hydrolyze GTP.

Mechanism of the Early Catalytic Events in the Collagenolysis by Matrix Metalloproteinase-1

Metalloproteinase-1 (MMP-1) catalyzed collagen degradation is essential for a wide variety of normal physiological processes, while at the same time contributing to several diseases in humans. Therefore, a comprehensive understanding of this process is of great importance. Although crystallographic and spectroscopic studies provided fundamental information about the structure and function of MMP-1, the precise mechanism of collagen degradation especially considering the complex and flexible structure of the substrate, remains poorly understood. In addition, how the protein environment dynamically reorganizes at the atomic scale into a catalytically active state capable of collagen hydrolysis remains unknown. In this study, we applied experimentally-guided multiscale molecular modeling methods including classical molecular dynamics (MD), well-tempered (WT) classical metadynamics (MetD), combined quantum mechanics/molecular mechanics (QM/MM) MD and QM/MM MetD simulations to explore and characterize the early catalytic events of MMP-1 collagenolysis. Importantly the study provided a complete atomic and dynamic description of the transition from the open to the closed form of the MMP-1•THP complex. Notably, the formation of catalytically active Michaelis complex competent for collagen cleavage was characterized. The study identified the changes in the coordination state of the catalytic zinc(II) associated with the conformational transformation and the formation of catalytically productive ES complex. Our results confirm the essential role of the MMP-1 catalytic domain's α-helices (hA, hB and hC) and the linker region in the transition to the catalytically competent ES complex. Overall, the results provide unique mechanistic insight into the conformational transformations and associated changes in the coordination state of the catalytic zinc(II) that would be important for the design of effective MMP-1 inhibitors.

Structural basis of actin filament assembly and aging

The dynamic turnover of actin filaments (F-actin) controls cellular motility in eukaryotes and is coupled to changes in the F-actin nucleotide state1–3. It remains unclear how F-actin hydrolyses ATP and subsequently undergoes subtle conformational rearrangements that ultimately lead to filament depolymerization by actin-binding proteins. Here we present cryo-electron microscopy structures of F-actin in all nucleotide states, polymerized in the presence of Mg2+ or Ca2+ at approximately 2.2 Å resolution. The structures show that actin polymerization induces the relocation of water molecules in the nucleotide-binding pocket, activating one of them for the nucleophilic attack of ATP. Unexpectedly, the back door for the subsequent release of inorganic phosphate (Pi) is closed in all structures, indicating that Pi release occurs transiently. The small changes in the nucleotide-binding pocket after ATP hydrolysis and Pi release are sensed by a key amino acid, amplified and transmitted to the filament periphery. Furthermore, differences in the positions of water molecules in the nucleotide-binding pocket explain why Ca2+-actin shows slower polymerization rates than Mg2+-actin. Our work elucidates the solvent-driven rearrangements that govern actin filament assembly and aging and lays the foundation for the rational design of drugs and small molecules for imaging and therapeutic applications.

Bottom-up Coarse-Graining: Principles and Perspectives

Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.

Free Energy Landscape of the Adenylation Reaction of the Aminoacylation Process at the Active Site of Aspartyl tRNA Synthetase

The process of protein biosynthesis is initiated by the aminoacylation process where a transfer ribonucleic acid (tRNA) is charged by the attachment of its cognate amino acid at the active site of the corresponding aminoacyl tRNA synthetase enzyme. The first step of the aminoacylation process, known as the adenylation reaction, involves activation of the cognate amino acid where it reacts with a molecule of adenosine triphosphate (ATP) at the active site of the enzyme to form the aminoacyl adenylate and inorganic pyrophosphate. In the current work, we have investigated the adenylation reaction between aspartic acid and ATP at the active site of the fully solvated aspartyl tRNA synthetase (AspRS) from Escherichia coli in aqueous medium at room temperature through hybrid quantum mechanical/molecular mechanical (QM/MM) simulations combined with enhanced sampling methods of well-tempered and well-sliced metadynamics. The objective of the present work is to study the associated free energy landscape and reaction barrier and also to explore the effects of active site mutation on the free energy surface of the reaction. The current calculations include finite temperature effects on free energy profiles. In particular, apart from contributions of interaction energies, the current calculations also include contributions of conformational, vibrational, and translational entropy of active site residues, substrates, and also the rest of the solvated protein and surrounding water into the free energy calculations. The present QM/MM metadynamics simulations predict a free energy barrier of 23.35 and 23.5 kcal/mol for two different metadynamics methods used to perform the reaction at the active site of the wild type enzyme. The free energy barrier increases to 30.6 kcal/mol when Arg217, which is an important conserved residue of the wild type enzyme at its active site, is mutated by alanine. These free energy results including the effect of mutation compare reasonably well with those of kinetic experiments that are available in the literature. The current work also provides molecular details of structural changes of the reactants and surroundings as the system dynamically evolves along the reaction pathway from reactant to the product state through QM/MM metadynamics simulations.

Assessing the Intestinal Permeability of Small Molecule Drugs via Diffusion Motion on a Multidimensional Free Energy Surface

A protocol that accurately assesses the intestinal permeability of small molecule compounds plays an essential role in decreasing the cost and time in inventing a new drug. This manuscript presents a novel computational method to study the passive permeation of small molecule drugs based on the inhomogeneous solubility-diffusion model. The multidimensional free energy surface of the drug transiting through a lipid bilayer is computed with transition-tempered metadynamics that accurately captures the mechanisms of passive permeation. The permeability is computed by following the diffusion motion of the drug molecules along the minimal free energy path found on the multidimensional free energy surface. This computational method is assessed by studying the permeability of five small molecule drugs (ketoprofen, naproxen, metoprolol, propranolol, and salicylic acid). The results demonstrate a remarkable agreement between the computed permeabilities and those measured with the intestinal assay. The in silico method reported in this manuscript also reproduces the permeability measured from the intestinal assay (in vivo) better than the cell-based assays (e.g., PAMPA and Caco-2) do. In addition, the multidimensional free energy surface reveals the interplay between the structure of the small molecule and its permeability, shedding light on strategies of drug optimization.

Compressive and Tensile Deformations Alter ATP Hydrolysis and Phosphate Release Rates in Actin Filaments

Actin filament networks in eukaryotic cells are constantly remodeled through nucleotide state controlled interactions with actin binding proteins, leading to macroscopic structures such as bundled filaments, branched filaments, and so on. The nucleotide (ATP) hydrolysis, phosphate release, and polymerization/depolymerization reactions that lead to the formation of these structures are correlated with the conformational fluctuations of the actin subunits at the molecular scale. The resulting structures generate and experience varying levels of force and impart cells with several functionalities such as their ability to move, divide, transport cargo, etc. Models that explicitly connect the structure to reactions are essential to elucidate a fundamental level of understanding of these processes. In this regard, a bottom-up Ultra-Coarse-Grained (UCG) model of actin filaments that can simulate ATP hydrolysis, inorganic phosphate release (Pi), and depolymerization reactions is presented in this work. In this model, actin subunits are represented using coarse-grained particles that evolve in time and undergo reactions depending on the conformations sampled. The reactions are represented through state transitions, with each state represented by a unique effective coarse-grained potential. Effects of compressive and tensile strains on the rates of reactions are then analyzed. Compressive strains tend to unflatten the actin subunits, reduce the rate of ATP hydrolysis, and increase the Pi release rate. On the other hand, tensile strain flattens subunits, increases the rate of ATP hydrolysis, and decrease the Pi release rate. Incorporating these predictions into a Markov State Model highlighted that strains alter the steady-state distribution of subunits with ADPPi and ADP nucleotide, thus identifying possible additional factors underlying the cooperative binding of regulatory proteins to actin filaments.

Structural basis for polarized elongation of actin filaments

Actin filaments elongate and shorten much faster at their barbed end than their pointed end, but the molecular basis of this difference has not been understood. We use all-atom molecular dynamics simulations to investigate the properties of subunits at both ends of the filament. The terminal subunits tend toward conformations that resemble actin monomers in solution, while contacts with neighboring subunits progressively flatten the conformation of internal subunits. At the barbed end the terminal subunit is loosely tethered by its DNase-1 loop to the third subunit, because its monomer-like conformation precludes stabilizing contacts with the penultimate subunit. The motions of the terminal subunit make the partially flattened penultimate subunit accessible for binding monomers. At the pointed end, unique contacts between the penultimate and terminal subunits are consistent with existing cryogenic electron microscopic (cryo-EM) maps, limit binding to incoming monomers, and flatten the terminal subunit, which likely promotes ATP hydrolysis and rapid phosphate release. These structures explain the distinct polymerization kinetics of the two ends.

Density Functional Theory-Based Quantum Mechanics/Coarse-Grained Molecular Mechanics: Theory and Implementation

Quantum mechanics/molecular mechanics (QM/MM) is a standard computational tool for describing chemical reactivity in systems with many degrees of freedom, including polymers, enzymes, and reacting molecules in complex solvents. However, QM/MM is less suitable for systems with complex MM dynamics due to associated long relaxation times, the high computational cost of QM energy evaluations, and expensive long-range electrostatics. Recently, a systematic coarse graining of the MM part was proposed to overcome these QM/MM limitations in the form of the quantum mechanics/coarse-grained molecular mechanics (QM/CG-MM) approach. Herein, we recast QM/CG-MM in the density functional theory formalism and, by employing the force-matching variational principle, assess the method performance for the two model systems: QM CCl₄ in the MM CCl₄ liquid and the reaction of tert-butyl hypochlorite with the benzyl radical in the MM CCl₄ solvent. We find that density functional theory (DFT)-QM/CG-MM accurately reproduces DFT-QM/MM radial distribution functions and three-body correlations between the QM and CG-MM subsystems. The free-energy profile of the reaction is also described well, with an error <1-2 kcal/mol. DFT-QM/CG-MM is a general, systematic, and computationally efficient approach to include chemical reactivity in coarse-grained molecular models.

Mycolactone Toxin Membrane Permeation: Atomistic versus Coarse-Grained MARTINI Simulations

Mycolactone, a cytotoxic and immunosuppressive macrolide produced by Mycobacterium ulcerans, is the central virulent factor in the skin disease Buruli ulcer. This multifunctional cytotoxin affects fundamental cellular processes such as cell adhesion, immune response, and cell death by targeting various cellular structures. Developing effective diagnostics that target mycolactone has been challenging, potentially because of suspected interactions with lipophilic architectures, including membranes. To better understand the pathogenesis of Buruli ulcer disease, aid in the development of diagnostics, and learn how amphiphiles in general use lipid trafficking to navigate the host environment, we seek to understand the nature of mycolactone-membrane interactions. Herein, we characterize how the two dominant isomers of mycolactone (A and B) interact with and permeate DPPC membranes with all-atom molecular dynamics simulations employing transition-tempered metadynamics and compare these results to those obtained by MARTINI coarse-grained simulations. Our all-atom simulations reveal that both isomers have a strong preference to associate with the membrane, although their mechanisms and energetics of membrane permeation differ slightly. Water molecules are found to play an important role in the permeation process. Although the MARTINI coarse-grained simulations give the correct free energy of membrane association, they fail to capture the mechanism of permeation and role of water during permeation as seen in all-atom simulations.

Mechanism of actin polymerization revealed by cryo-EM structures of actin filaments with three different bound nucleotides

We used cryo-electron microscopy (cryo-EM) to reconstruct actin filaments with bound AMPPNP (β,γ-imidoadenosine 5'-triphosphate, an ATP analog, resolution 3.1 Å), ADP-Pi (ADP with inorganic phosphate, resolution 3.1 Å), or ADP (resolution 3.6 Å). Subunits in the three filaments have similar backbone conformations, so assembly rather than ATP hydrolysis or phosphate dissociation is responsible for their flattened conformation in filaments. Polymerization increases the rate of ATP hydrolysis by changing the positions of the side chains of Q137 and H161 in the active site. Flattening during assembly also promotes interactions along both the long-pitch and short-pitch helices. In particular, conformational changes in subdomain 3 open up multiple favorable interactions with the DNase-I binding loop in subdomain 2 of the adjacent subunit. Subunits at the barbed end of the filament are likely to be in this favorable conformation, while monomers are not. This difference explains why filaments grow faster at the barbed end than the pointed end. When phosphate dissociates from ADP-Pi-actin through a backdoor channel, the conformation of the C terminus changes so it distorts the DNase binding loop, which allows cofilin binding, and a network of interactions among S14, H73, G74, N111, R177, and G158 rearranges to open the phosphate release site.

Quantum Mechanical/Molecular Mechanical Analysis of the Catalytic Mechanism of Phosphoserine Phosphatase

Phosphoserine phosphatase (PSP), a member of the haloacid dehalogenase (HAD) superfamily that comprises the vast majority of phosphotransferases, is likely a steady-state regulator of the level of d-serine in the brain. The proposed catalytic cycle of PSP consists of a two-step mechanism: formation of a phospho-enzyme intermediate by phosphate transfer to Asp11 and its subsequent hydrolysis. Our combined quantum mechanical/molecular mechanical (QM/MM) calculations of the reaction pathways favour a dissociative mechanism of nucleophilic substitution via a trigonal-planar metaphosphate-like configuration for both steps, associated with proton transfer to the leaving group or from the nucleophile. This proton transfer is facilitated by active site residue Asp13 that acts as both a general base and a general acid. Free energy calculation on the reaction pathways further support the structural role of the enzymatic environment and the active site architecture. The choice of a proper reaction coordinate along which to bias the free energy calculations can be guided by a projection of the canonical reaction coordinate obtained from a chain-of-state optimisation onto important internal coordinates.

Multiscale simulation of actin filaments and actin-associated proteins

Actin is an important cytoskeletal protein that serves as a building block to form filament networks that span across the cell. These networks are orchestrated by a myriad of other cytoskeletal entities including the unbranched filament-forming protein formin and branched network-forming protein complex Arp2/3. Computational models have been able to provide insights into many important structural transitions that are involved in forming these networks, and into the nature of interactions essential for actin filament formation and for regulating the behavior of actin-associated proteins. In this review, we summarize a subset of such models that focus on the atomistic features and those that can integrate atomistic features into a larger picture in a multiscale fashion.

Molecular Mechanism of ATP Hydrolysis in an ABC Transporter

Hydrolysis of nucleoside triphosphate (NTP) plays a key role for the function of many biomolecular systems. However, the chemistry of the catalytic reaction in terms of an atomic-level understanding of the structural, dynamic, and free energy changes associated with it often remains unknown. Here, we report the molecular mechanism of adenosine triphosphate (ATP) hydrolysis in the ATP-binding cassette (ABC) transporter BtuCD-F. Free energy profiles obtained from hybrid quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations show that the hydrolysis reaction proceeds in a stepwise manner. First, nucleophilic attack of an activated lytic water molecule at the ATP γ-phosphate yields ADP + HPO₄ ^2- as intermediate product. A conserved glutamate that is located very close to the γ-phosphate transiently accepts a proton and thus acts as catalytic base. In the second step, the proton is transferred back from the catalytic base to the γ-phosphate, yielding ADP + H₂PO₄ ^-. These two chemical reaction steps are followed by rearrangements of the hydrogen bond network and the coordination of the Mg²⁺ ion. The rate constant estimated from the computed free energy barriers is in very good agreement with experiments. The overall free energy change of the reaction is close to zero, suggesting that phosphate bond cleavage itself does not provide a power stroke for conformational changes. Instead, ATP binding is essential for tight dimerization of the nucleotide-binding domains and the transition of the transmembrane domains from inward- to outward-facing, whereas ATP hydrolysis resets the conformational cycle. The mechanism is likely relevant for all ABC transporters and might have implications also for other NTPases, as many residues involved in nucleotide binding and hydrolysis are strictly conserved.

Insights into the Cooperative Nature of ATP Hydrolysis in Actin Filaments

Actin filaments continually assemble and disassemble within a cell. Assembled filaments "age" as a bound nucleotide ATP within each actin subunit quickly hydrolyzes followed by a slower release of the phosphate Pi, leaving behind a bound ADP. This subtle change in nucleotide state of actin subunits affects filament rigidity as well as its interactions with binding partners. We present here a systematic multiscale ultra-coarse-graining approach that provides a computationally efficient way to simulate a long actin filament undergoing ATP hydrolysis and phosphate-release reactions while systematically taking into account available atomistic details. The slower conformational changes and their dependence on the chemical reactions are simulated with the ultra-coarse-graining model by assigning internal states to the coarse-grained sites. Each state is represented by a unique potential surface of a local heterogeneous elastic network. Internal states undergo stochastic transitions that are coupled to conformations of the underlying molecular system. The model reproduces mechanical properties of the filament and allows us to study whether conformational fluctuations in actin subunits produce cooperative filament aging. We find that the nucleotide states of neighboring subunits modulate the reaction kinetics, implying cooperativity in ATP hydrolysis and Pi release. We further systematically coarse grain the system into a Markov state model that incorporates assembly and disassembly, facilitating a direct comparison with previously published models. We find that cooperativity in ATP hydrolysis and Pi release significantly affects the filament growth dynamics only near the critical G-actin concentration, whereas far from it, both cooperative and random mechanisms show similar growth dynamics. In contrast, filament composition in terms of the bound nucleotide distribution varies significantly at all monomer concentrations studied. These results provide new insights, to our knowledge, into the cooperative nature of ATP hydrolysis and Pi release and the implications it has for actin filament properties, providing novel predictions for future experimental studies.

Mapping Free Energy Pathways for ATP Hydrolysis in the E. coli ABC Transporter HlyB by the String Method

HlyB functions as an adenosine triphosphate (ATP)-binding cassette (ABC) transporter that enables bacteria to secrete toxins at the expense of ATP hydrolysis. Our previous work, based on potential energy profiles from combined quantum mechanical and molecular mechanical (QM/MM) calculations, has suggested that the highly conserved H-loop His residue H662 in the nucleotide binding domain (NBD) of E. coli HlyB may catalyze the hydrolysis of ATP through proton relay. To further test this hypothesis when entropic contributions are taken into account, we obtained QM/MM minimum free energy paths (MFEPs) for the HlyB reaction, making use of the string method in collective variables. The free energy profiles along the MFEPs confirm the direct participation of H662 in catalysis. The MFEP simulations of HlyB also reveal an intimate coupling between the chemical steps and a local protein conformational change involving the signature-loop residue S607, which may serve a catalytic role similar to an Arg-finger motif in many ATPases and GTPases in stabilizing the phosphoryl-transfer transition state.

Structural evidence for the roles of divalent cations in actin polymerization and activation of ATP hydrolysis

Actin polymerization is a divalent cation-dependent process. Here we identify a cation binding site on the surface of actin in a 2.0-Å resolution X-ray structure of actin and find evidence of three additional sites in published high-resolution structures. These cations are stable in molecular dynamics (MD) simulations of the filament, suggesting a functional role in polymerization or filament rigidity. Polymerization activates the ATPase activity of the incorporating actin protomers. Careful analysis of water molecules that approach the ATP in the MD simulations revealed Gln137-activated water to be in a suitable position in F-actin, to initiate attack for ATP hydrolysis, and its occupancy was dependent on bound cations.

The structure of the actin filament is known at a resolution that has allowed the architecture of protein components to be unambiguously assigned. However, fully understanding the chemistry of the system requires higher resolution to identify the ions and water molecules involved in polymerization and ATP hydrolysis. Here, we find experimental evidence for the association of cations with the surfaces of G-actin in a 2.0-Å resolution X-ray structure of actin bound to a Cordon-Bleu WH2 motif and in previously determined high-resolution X-ray structures. Three of four reoccurring divalent cation sites were stable during molecular dynamics (MD) simulations of the filament, suggesting that these sites may play a functional role in stabilizing the filament. We modeled the water coordination at the ATP-bound Mg²⁺, which also proved to be stable during the MD simulations. Using this model of the filament with a hydrated ATP-bound Mg²⁺, we compared the cumulative probability of an activated hydrolytic water molecule approaching the γ-phosphorous of ATP, in comparison with G-actin, in the MD simulations. The cumulative probability increased in F-actin in line with the activation of actin’s ATPase activity on polymerization. However, inclusion of the cations in the filament lowered cumulative probability, suggesting the rate of hydrolysis may be linked to filament flexibility. Together, these data extend the possible roles of Mg²⁺ in polymerization and the mechanism of polymerization-induced activation of actin’s ATPase activity.

Molecular transport through membranes: Accurate permeability coefficients from multidimensional potentials of mean force and local diffusion constants

Estimating the permeability coefficient of small molecules through lipid bilayer membranes plays an important role in the development of effective drug candidates. In silico simulations can produce acceptable relative permeability coefficients for a series of small molecules; however, the absolute permeability coefficients from simulations are usually off by orders of magnitude. In addition to differences between the lipid bilayers used in vitro and in silico, the poor convergence of permeation free energy profiles and over-simplified diffusion models have contributed to these discrepancies. In this paper, we present a multidimensional inhomogeneous solubility-diffusion model to study the permeability of a small molecule drug (trimethoprim) passing through a POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) lipid bilayer. Our approach improves the permeation model in three ways: First, the free energy profile (potential of mean force, PMF) is two-dimensional in two key coordinates rather than simply one-dimensional along the direction normal to the bilayer. Second, the 2-D PMF calculation has improved convergence due to application of the recently developed transition-tempered metadynamics with randomly initialized replicas, while third, the local diffusivity coefficient was calculated along the direction of the minimum free energy path on the two-dimensional PMF. The permeability is then calculated as a line integral along the minimum free energy path of the PMF. With this approach, we report a considerably more accurate permeability coefficient (only 2-5 times larger than the experimental value). We also compare our approach with the common practice of computing permeability coefficients based only on the translation of the center of mass of the drug molecule. Our paper concludes with a discussion of approaches for minimizing the computational cost for the purpose of more rapidly screening a large number of drug candidate molecules.

QM/MM Description of Newly Selected Catalytic Bioscavengers Against Organophosphorus Compounds Revealed Reactivation Stimulus Mediated by Histidine Residue in the Acyl-Binding Loop

Butyrylcholinesterase (BChE) is considered as an efficient stoichiometric antidote against organophosphorus (OP) poisons. Recently we utilized combination of calculations and ultrahigh-throughput screening (uHTS) to select BChE variants capable of catalytic destruction of OP pesticide paraoxon. The purpose of this study was to elucidate the molecular mechanism underlying enzymatic hydrolysis of paraoxon by BChE variants using hybrid quantum mechanical/molecular mechanical (QM/MM) calculations. Detailed analysis of accomplished QM/MM runs revealed that histidine residues introduced into the acyl-binding loop are always located in close proximity with aspartate residue at position 70. Histidine residue acts as general base thus leading to attacking water molecule activation and subsequent SN2 inline hydrolysis resulting in BChE reactivation. This combination resembles canonical catalytic triad found in active centers of various proteases. Carboxyl group activates histidine residue by altering its pK_a, which in turn promotes the activation of water molecule in terms of its nucleophilicity. Observed re-protonation of catalytic serine residue at position 198 from histidine residue at position 438 recovers initial configuration of the enzyme’s active center, facilitating next catalytic cycle. We therefore suggest that utilization of uHTS platform in combination with deciphering of molecular mechanisms by QM/MM calculations may significantly improve our knowledge of enzyme function, propose new strategies for enzyme design and open new horizons in generation of catalytic bioscavengers against OP poisons.

The hydrolysis of 6-phosphogluconolactone in the second step of pentose phosphate pathway occurs via a two-water mechanism

Hydrolysis reaction marks the basis of life yet the mechanism of this crucial biochemical reaction is not completely understood. We recently reported the mechanisms of hydrolysis of nucleoside triphosphate and phosphate monoester. These two reactions hydrolyze P-O-P and P-O-C linkages, respectively. Here, we present the mechanism of hydrolysis of δ-6-phosphogluconolactone, which is an important precursor in the second step of the pentose phosphate pathway. Its hydrolysis requires the cleavage of C-O-C linkage and its mechanism is hitherto unknown. We report three mechanisms of hydrolysis of δ-6-phosphogluconolactone based on density functional computations. In the energetically most favorable mechanism, two water molecules participate in the hydrolysis reaction and the mechanism is sequential, i.e., activation of the attacking water molecule (OH bond breaking) precedes that of the cleavage of the CO bond of the C-O-C linkage. The rate-limiting energy barrier of this mechanism is comparable to the reported experimental free energy barrier. This mechanism has similarities with the mechanism of triphosphate hydrolysis and that of hydrolytic cleavage of DNA in EcoRV enzyme. This two-water sequential hydrolysis mechanism could be the unified mechanism required for the hydrolysis of other hydrolysable species in living cells.

Allostery in the dengue virus NS3 helicase: Insights into the NTPase cycle from molecular simulations

The C-terminus domain of non-structural 3 (NS3) protein of the Flaviviridae viruses (e.g. HCV, dengue, West Nile, Zika) is a nucleotide triphosphatase (NTPase) -dependent superfamily 2 (SF2) helicase that unwinds double-stranded RNA while translocating along the nucleic polymer. Due to these functions, NS3 is an important target for antiviral development yet the biophysics of this enzyme are poorly understood. Microsecond-long molecular dynamic simulations of the dengue NS3 helicase domain are reported from which allosteric effects of RNA and NTPase substrates are observed. The presence of a bound single-stranded RNA catalytically enhances the phosphate hydrolysis reaction by affecting the dynamics and positioning of waters within the hydrolysis active site. Coupled with results from the simulations, electronic structure calculations of the reaction are used to quantify this enhancement to be a 150-fold increase, in qualitative agreement with the experimental enhancement factor of 10–100. Additionally, protein-RNA interactions exhibit NTPase substrate-induced allostery, where the presence of a nucleotide (e.g. ATP or ADP) structurally perturbs residues in direct contact with the phosphodiester backbone of the RNA. Residue-residue network analyses highlight pathways of short ranged interactions that connect the two active sites. These analyses identify motif V as a highly connected region of protein structure through which energy released from either active site is hypothesized to move, thereby inducing the observed allosteric effects. These results lay the foundation for the design of novel allosteric inhibitors of NS3.

Non-structural protein 3 (NS3) is a Flaviviridae (e.g. Hepatitis C, dengue, and Zika viruses) helicase that unwinds double stranded RNA while translocating along the nucleic polymer during viral genome replication. As a member of superfamily 2 (SF2) helicases, NS3 utilizes the free energy of nucleotide triphosphate (NTP) binding, hydrolysis, and product unbinding to perform its functions. While much is known about SF2 helicases, the pathways and mechanisms through which free energy is transduced between the NTP hydrolysis active site and RNA binding cleft remains elusive. Here we present a multiscale computational study to characterize the allosteric effects induced by the RNA and NTPase substrates (ATP, ADP, and P_i) as well as the pathways of short-range, residue-residue interactions that connect the two active sites. Results from this body of molecular dynamics simulations and electronic structure calculations are highlighted in context to the NTPase enzymatic cycle, allowing for development of testable hypotheses for validation of these simulations. Our insights, therefore, provide novel details about the biophysics of NS3 and guide the next generation of experimental studies.

Coarse-Grained Directed Simulation

Many free-energy sampling and quantum mechanics/molecular mechanics (QM/MM) computations on protein complexes have been performed where, by necessity, a single component is studied isolated in solution while its overall configuration is kept in the complex-like state by either rigid restraints or harmonic constraints. A drawback in these studies is that the system's native fluctuations are lost, both due to the change of environment and the imposition of the extra potential. Yet, we know that having both accurate structure and fluctuations is likely crucial to achieving correct simulation estimates for the subsystem within its native larger protein complex context. In this work, we provide a new approach to this problem by drawing on ideas developed to incorporate experimental information into a molecular simulation by relative entropy minimization to a target system. We show that by using linear biases on coarse-grained (CG) observables (such as distances or angles between large subdomains within a protein), we can maintain the protein in a particular target conformation while also preserving the correct equilibrium fluctuations of the subsystem within its larger biomolecular complex. As an application, we demonstrate this algorithm by training a bias that causes an actin monomer (and trimer) in solution to sample the same average structure and fluctuations as if it were embedded within a much larger actin filament. Additionally, we have developed a number of algorithmic improvements that accelerate convergence of the on-the-fly relative entropy minimization algorithms for this type of application. Finally, we have contributed these methods to the PLUMED open source free energy sampling software library.

Effect of protonation on the mechanism of phosphate monoester hydrolysis and comparison with the hydrolysis of nucleoside triphosphate in biomolecular motors

Hydrolysis of phosphate groups is a crucial reaction in living cells. It involves the breaking of two strong bonds, i.e. the O_aH bond of the attacking water molecule, and the PO_l bond of the substrate (O_a and O_l stand for attacking and leaving oxygen atoms). Mechanism of the hydrolysis reaction can proceed either by a concurrent or a sequential mechanism. In the concurrent mechanism, the breaking of O_aH and PO_l bonds occurs simultaneously, whereas in the sequential mechanism, the O_aH and PO_l bonds break at different stages of the reaction. To understand how protonation affects the mechanism of hydrolysis of phosphate monoester, we have studied the mechanism of hydrolysis of protonated and deprotonated phosphate monoester at M06-2X/6-311+G**//M06-2X/6-31+G*+ZPE level of theory (where ZPE stands for zero point energy). Our calculations show that in both protonated and deprotonated cases, the breaking of the water O_aH bond occurs before the breaking of the PO_l bond. Because the two events are not separated by a stable intermediate, the mechanism can be categorized as semi-concurrent. The overall energy barrier is 41kcalmol^-1 in the unprotonated case. Most (5/6th) of this is due to the initial breaking of the water O_aH bond. This component is lowered from 34 to 25kcalmol^-1 by adding one proton to the phosphate. The rest of the overall energy barrier comes from the subsequent breaking of the PO_l bond and is not sensitive to protonation. This is consistent with previous findings about the effect of triphosphate protonation on the hydrolysis, where the equivalent protonation (on the γ-phosphate) was seen to lower the barrier of breaking the water O_aH bond and to have little effect on the PO_l bond breaking. Hydrolysis pathways of phosphate monoester with initial breaking of the PO_l bond could not be found here. This is because the leaving group in phosphate monoester cannot be protonated, unlike in triphosphate hydrolysis, where protonation of the β- and γ-phosphates had been shown to promote a mechanism where the PO_l bond breaks before the O_aH bond does. We also point out that the charge shift due to PO_l bond breaking during sequential ATP hydrolysis in bio-molecular motors onsets the week unbinding of hydrolysis product that finally leads to the product release during power stroke.