Unraveling the mystery of ATP hydrolysis in actin filaments

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.

A tripartite organelle platform links growth factor receptor signaling to mitochondrial metabolism

One open question in the biology of growth factor receptors is how a quantitative input (i.e., ligand concentration) is decoded by the cell to produce specific response(s). Here, we show that an EGFR endocytic mechanism, non-clathrin endocytosis (NCE), which is activated only at high ligand concentrations and targets receptor to degradation, requires a tripartite organelle platform involving the plasma membrane (PM), endoplasmic reticulum (ER) and mitochondria. At these contact sites, EGFR-dependent, ER-generated Ca2+ oscillations are sensed by mitochondria, leading to increased metabolism and ATP production. Locally released ATP is required for cortical actin remodeling and EGFR-NCE vesicle fission. The same biochemical circuitry is also needed for an effector function of EGFR, i.e., collective motility. The multiorganelle signaling platform herein described mediates direct communication between EGFR signaling and mitochondrial metabolism, and is predicted to have a broad impact on cell physiology as it is activated by another growth factor receptor, HGFR/MET.

Quantifying Unbiased Conformational Ensembles from Biased Simulations Using ShapeGMM

Quantifying the conformational ensembles of biomolecules is fundamental to describing mechanisms of processes such as protein folding, interconversion between folded states, ligand binding, and allosteric regulation. Accurate quantification of these ensembles remains a challenge for conventional molecular simulations of all but the simplest molecules due to insufficient sampling. Enhanced sampling approaches, such as metadynamics, were designed to overcome this challenge; however, the nonuniform frame weights that result from many of these approaches present an additional challenge to ensemble quantification techniques such as Markov State Modeling or structural clustering. Here, we present rigorous inclusion of nonuniform frame weights into a structural clustering method entitled shapeGMM. The result of frame-weighted shapeGMM is a high dimensional probability density and generative model for the unbiased system from which we can compute important thermodynamic properties such as relative free energies and configurational entropy. The accuracy of this approach is demonstrated by the quantitative agreement between GMMs computed by Hamiltonian reweighting and direct simulation of a coarse-grained helix model system. Furthermore, the relative free energy computed from a shapeGMM probability density of alanine dipeptide reweighted from a metadynamics simulation quantitatively reproduces the underlying free energy in the basins. Finally, the method identifies hidden structures along the actin globular to filamentous-like structural transition from a metadynamics simulation on a linear discriminant analysis coordinate trained on GMM states, illustrating how structural clustering of biased data can lead to biophysical insight. Combined, these results demonstrate that frame-weighted shapeGMM is a powerful approach to quantifying biomolecular ensembles from biased simulations.

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.

K-Means Clustering Coarse-Graining (KMC-CG): A Next Generation Methodology for Determining Optimal Coarse-Grained Mappings of Large Biomolecules

Coarse-grained (CG) molecular dynamics (MD) has become a method of choice for simulating various large scale biomolecular processes; therefore, the systematic definition of the CG mappings for biomolecules remains an important topic. Appropriate CG mappings can significantly enhance the representability of a CG model and improve its ability to capture critical features of large biomolecules. In this work, we present a systematic and more generalized method called K-means clustering coarse-graining (KMC-CG), which builds on the earlier approach of essential dynamics coarse-graining (ED-CG). KMC-CG removes the sequence-dependent constraints of ED-CG, allowing it to explore a more extensive space and thus enabling the discovery of more physically optimal CG mappings. Furthermore, the implementation of the K-means clustering algorithm can variationally optimize the CG mapping with efficiency and stability. This new method is tested in three cases: ATP-bound G-actin, the HIV-1 CA pentamer, and the Arp2/3 complex. In these examples, the CG models generated by KMC-CG are seen to better capture the structural, dynamic, and functional domains. KMC-CG therefore provides a robust and consistent approach to generating CG models of large biomolecules that can then be more accurately parametrized by either bottom-up or top-down CG force fields.

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.

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.

Structures and mechanisms of actin ATP hydrolysis

A variety of cellular functions are driven by actin, which undergoes cyclic transitions between the monomeric G-form and the filamentous F-form. To gain insights into actin dynamics, the mechanism by which the energy is supplied by the ATP hydrolysis reaction in the F-form actin must be elucidated. This has been hampered by the lack of actin filament structures at atomic resolutions. Here, we have crystallized actin molecules trapped in the F-form without forming filaments, and based upon these structures we determined the reaction path by quantum mechanics calculations. The results are consistent with previous biochemical data. Remarkably, the hydrolysis reaction mechanism is essentially identical to those of motor proteins, while the process of Pi release is distinct.

The major cytoskeleton protein actin undergoes cyclic transitions between the monomeric G-form and the filamentous F-form, which drive organelle transport and cell motility. This mechanical work is driven by the ATPase activity at the catalytic site in the F-form. For deeper understanding of the actin cellular functions, the reaction mechanism must be elucidated. Here, we show that a single actin molecule is trapped in the F-form by fragmin domain-1 binding and present their crystal structures in the ATP analog-, ADP-Pi-, and ADP-bound forms, at 1.15-Å resolutions. The G-to-F conformational transition shifts the side chains of Gln137 and His161, which relocate four water molecules including W1 (attacking water) and W2 (helping water) to facilitate the hydrolysis. By applying quantum mechanics/molecular mechanics calculations to the structures, we have revealed a consistent and comprehensive reaction path of ATP hydrolysis by the F-form actin. The reaction path consists of four steps: 1) W1 and W2 rotations; 2) P^G–O^3B bond cleavage; 3) four concomitant events: W1–PO₃⁻ formation, OH⁻ and proton cleavage, nucleophilic attack by the OH⁻ against P^G, and the abstracted proton transfer; and 4) proton relocation that stabilizes the ADP-Pi–bound F-form actin. The mechanism explains the slow rate of ATP hydrolysis by actin and the irreversibility of the hydrolysis reaction. While the catalytic strategy of actin ATP hydrolysis is essentially the same as those of motor proteins like myosin, the process after the hydrolysis is distinct and discussed in terms of Pi release, F-form destabilization, and global conformational changes.

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.

On Stretching, Bending, Shearing, and Twisting of Actin Filaments I: Variational Models

Mechanochemical simulations of actomyosin networks are traditionally based on one-dimensional models of actin filaments having zero width. Here, and in the follow up paper (arXiv, DOI 10.48550/arXiv.2203.01284), approaches are presented for more efficient modeling that incorporates stretching, shearing, and twisting of actin filaments. Our modeling of a semiflexible filament with a small but finite width is based on the Cosserat theory of elastic rods, which allows for six degrees of freedom at every point on the filament's backbone. In the variational models presented in this paper, a small and discrete set of parameters is used to describe a smooth filament shape having all degrees of freedom allowed in the Cosserat theory. Two main approaches are introduced: one where polynomial spline functions describe the filament's configuration, and one in which geodesic curves in the space of the configurational degrees of freedom are used. We find that in the latter representation the strain energy function can be calculated without resorting to a small-angle expansion, so it can describe arbitrarily large filament deformations without systematic error. These approaches are validated by a dynamical model of a Cosserat filament, which can be further extended by using multiresolution methods to allow more detailed monomer-based resolution in certain parts of the actin filament, as introduced in the follow up paper. The presented framework is illustrated by showing how torsional compliance in a finite-width filament can induce broken chiral symmetry in the structure of a cross-linked bundle.

The Complex Roles of Adenosine Triphosphate in Bioenergetics

ATP is generally defined as the "energy currency" of the cell. Its phosphoanhydride P-O bonds are often considered to be "high energy" linkages that release free energy when broken, and its hydrolysis is described as "strongly exergonic". However, breaking bonds cannot release energy and ATP hydrolysis in motor and active transport proteins is not "strongly exergonic". So, the relevance of ATP resides elsewhere. As important as the nucleotide are the proteins that undergo functionally relevant conformational changes upon both ATP binding and release of ADP and inorganic phosphate. ATP phosphorylates proteins for signaling, active transport, and substrates in condensation reactions. The ensuing dephosphorylation has different consequences in each case. In signaling and active transport the phosphate group is hydrolyzed whereas in condensation reactions the phosphoryl fragment acts as a dehydrating agent. As it will be discussed in this article, ATP does much more than simply contribute free energy to biological processes.

Assembly and architecture of Escherichia coli divisome proteins FtsA and FtsZ

During Escherichia coli cell division, an intracellular complex of cell division proteins known as the Z-ring assembles at midcell during early division and serves as the site of constriction. While the predominant protein in the Z-ring is the widely conserved tubulin homolog FtsZ, the actin homolog FtsA tethers the Z-ring scaffold to the cytoplasmic membrane by binding to FtsZ. While FtsZ is known to function as a dynamic, polymerized GTPase, the assembly state of its partner, FtsA, and the role of ATP are still unclear. We report that a substitution mutation in the FtsA ATP-binding site impairs ATP hydrolysis, phospholipid vesicle remodeling in vitro, and Z-ring assembly in vivo. We demonstrate by transmission electron microscopy and Förster Resonance Energy Transfer that a truncated FtsA variant, FtsA(ΔMTS) lacking a C-terminal membrane targeting sequence, self assembles into ATP-dependent filaments. These filaments coassemble with FtsZ polymers but are destabilized by unassembled FtsZ. These findings suggest a model wherein ATP binding drives FtsA polymerization and membrane remodeling at the lipid surface, and FtsA polymerization is coregulated with FtsZ polymerization. We conclude that the coordinated assembly of FtsZ and FtsA polymers may serve as a key checkpoint in division that triggers cell wall synthesis and division progression.

Zero-mode waveguides visualize the first steps during gelsolin-mediated actin filament formation

Actin filament dynamics underlie key cellular processes. Although the elongation of actin filaments has been extensively studied, the mechanism of nucleation remains unclear. The micromolar concentrations needed for filament formation have prevented direct observation of nucleation dynamics on the single molecule level. To overcome this limitation, we have used the attoliter excitation volume of zero-mode waveguides to directly monitor the early steps of filament assembly. Immobilizing single gelsolin molecules as a nucleator at the bottom of the zero-mode waveguide, we could visualize the actin filament nucleation process. The process is surprisingly dynamic, and two distinct populations during gelsolin-mediated nucleation are observed. The two populations are defined by the stability of the actin dimers and determine whether elongation occurs. Furthermore, by using an inhibitor to block flattening, a conformational change in actin associated with filament formation, elongation was prevented. These observations indicate that a conformational transition and pathway competition determine the nucleation of gelsolin-mediated actin filament formation.

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.

Understanding and Tracking the Excess Proton in Ab Initio Simulations; Insights from IR Spectra

Proton transport in aqueous media is ubiquitously important in chemical and biological processes. Although ab initio molecular dynamics (AIMD) simulations have made great progress in characterizing proton transport, there has been a long-standing challenge in defining and tracking the excess proton, or more properly, the center of excess charge (CEC) created when a hydrogen nucleus distorts the electron distributions of water molecules in a delocalized and highly dynamic nature. Yet, defining (and biasing) such a CEC is essential when combining AIMD with enhanced sampling methods to calculate the relevant macroscopic properties via free-energy landscapes, which is the standard practice for most processes of interest. Several CEC formulas have been proposed and used, but none have yet been systematically tested or rigorously derived. In this paper, we show that the CEC can be used as a computational tool to disentangle IR features of the solvated excess proton from its surrounding solvent, and in turn, how correlating the features in the excess charge spectrum with the behavior of CEC in simulations enables a systematic evaluation of various CEC definitions. We present a new definition of CEC and show how it overcomes the limitations of those currently available both from a spectroscopic point of view and from a practical perspective of performance in enhanced sampling simulations.

Self-organized networks: Darwinian evolution of dynein rings, stalks, and stalk heads

Cytoskeletons are self-organized networks based on polymerized proteins: actin, tubulin, and driven by motor proteins, such as myosin, kinesin, and dynein. Their positive Darwinian evolution enables them to approach optimized functionality (self-organized criticality). Dynein has three distinct titled subunits, but how these units connect to function as a molecular motor is mysterious. Dynein binds to tubulin through two coiled coil stalks and a stalk head. The energy used to alter the head binding and propel cargo along tubulin is supplied by ATP at a ring 1,500 amino acids away. Here, we show how many details of this extremely distant interaction are explained by water waves quantified by thermodynamic scaling. Water waves have shaped all proteins throughout positive Darwinian evolution, and many aspects of long-range water-protein interactions are universal (described by self-organized criticality). Dynein water waves resembling tsunami produce nearly optimal energy transport over 1,500 amino acids along dynein's one-dimensional peptide backbone. More specifically, this paper identifies many similarities in the function and evolution of dynein compared to other cytoskeleton proteins such as actin, myosin, and tubulin.

Charge-dependent interactions of monomeric and filamentous actin with lipid bilayers

The cytoskeletal protein actin polymerizes into filaments that are essential for the mechanical stability of mammalian cells. In vitro experiments showed that direct interactions between actin filaments and lipid bilayers are possible and that the net charge of the bilayer as well as the presence of divalent ions in the buffer play an important role. In vivo, colocalization of actin filaments and divalent ions are suppressed, and cells rely on linker proteins to connect the plasma membrane to the actin network. Little is known, however, about why this is the case and what microscopic interactions are important. A deeper understanding is highly beneficial, first, to obtain understanding in the biological design of cells and, second, as a possible basis for the building of artificial cortices for the stabilization of synthetic cells. Here, we report the results of coarse-grained molecular dynamics simulations of monomeric and filamentous actin in the vicinity of differently charged lipid bilayers. We observe that charges on the lipid head groups strongly determine the ability of actin to adsorb to the bilayer. The inclusion of divalent ions leads to a reversal of the binding affinity. Our in silico results are validated experimentally by reconstitution assays with actin on lipid bilayer membranes and provide a molecular-level understanding of the actin-membrane interaction.

Light-powered and transient peptide two-dimensional assembly driven by trans-to-cis isomerization of azobenzene side chains

A 2D dissipative system is initiated by photo-powered trans-to-cis isomerization of azobenzene, which usually results in the collapse of ordered assemblies.

Mechanistic study of the ATP hydrolysis reaction in dynein motor protein

Dynein, a large and complex motor protein, harnesses energy from adenosine triphosphate (ATP) hydrolysis to regulate essential cellular activities. The ATP hydrolysis mechanism for the dynein motor is still shrouded in mystery. Herein, molecular dynamics simulations of a dynein motor disclosed that two water molecules are present close to the γ-phosphate of ATP and Glu1742 at the AAA1 site of dynein. We have proposed three possible mechanisms for the ATP hydrolysis. We divulge by using a quantum mechanics/molecular mechanics (QM/MM) study that two water molecules and Glu1742 are crucial for facilitating the ATP hydrolysis reaction in dynein. Moreover, the ATP hydrolysis step is initiated by the activation of lytic water (W1) by Glu1742 through relay proton transfers with the help of auxiliary water (W2) yielding HPO₄^2- and ADP, as a product. In the next step, a proton is shifted back from Glu1742 to generate inorganic phosphate (H₂PO₄^-) via another relay proton transfer event. The overall activation barrier for the Glu1742 assisted ATP hydrolysis is found to be the most favourable pathway compared to other plausible pathways. We also unearthed that ATP hydrolysis in dynein follows a so-called associative-like pathway in its rate-limiting step. Our study ascertained the important indirect roles of the two amino acids (such as Arg2109, Asn1792) and Mg²⁺ ion in the ATP hydrolysis of dynein. Additionally, multiple sequence alignment of the different organisms of dynein motors has conveyed the evolutionary importance of the Glu1742, Asn1742, and Arg2109 residues, respectively. As similar mechanisms are also prevalent in other motors, and GTPase and ATPase enzymes, the present finding spells out the definitive requirement of a proton relay process through an extended water-chain as one of the key components in an enzymatic ATP hydrolysis reaction.

Stress relaxation in F-actin solutions by severing

Networks of filamentous actin (F-actin) are important for the mechanics of most animal cells. These cytoskeletal networks are highly dynamic, with a variety of actin-associated proteins that control cross-linking, polymerization and force generation in the cytoskeleton. Inspired by recent rheological experiments on reconstituted solutions of dynamic actin filaments, we report a theoretical model that describes stress relaxation behavior of these solutions in the presence of severing proteins. We show that depending on the kinetic rates of assembly, disassembly, and severing, one can observe both length-dependent and length-independent relaxation behavior.

Atomic view into Plasmodium actin polymerization, ATP hydrolysis, and fragmentation

Plasmodium actins form very short filaments and have a noncanonical link between ATP hydrolysis and polymerization. Long filaments are detrimental to the parasites, but the structural factors constraining Plasmodium microfilament lengths have remained unknown. Using high-resolution crystallography, we show that magnesium binding causes a slight flattening of the Plasmodium actin I monomer, and subsequent phosphate release results in a more twisted conformation. Thus, the Mg-bound monomer is closer in conformation to filamentous (F) actin than the Ca form, and this likely facilitates polymerization. A coordinated potassium ion resides in the active site during hydrolysis and leaves together with the phosphate, a process governed by the position of the Arg178/Asp180-containing A loop. Asp180 interacts with either Lys270 or His74, depending on the protonation state of the histidine, while Arg178 links the inner and outer domains (ID and OD) of the actin protomer. Hence, the A loop acts as a switch between stable and unstable filament conformations, the latter leading to fragmentation. Our data provide a comprehensive model for polymerization, ATP hydrolysis and phosphate release, and fragmentation of parasite microfilaments. Similar mechanisms may well exist in canonical actins, although fragmentation is much less favorable due to several subtle sequence differences as well as the methylation of His73, which is absent on the corresponding His74 in Plasmodium actin I.

A detailed mechanistic study of malaria parasite actins reveals at the atomic level how they polymerize, hydrolyze ATP, and are fragmented to keep actin filament lengths short enough for parasite survival.

Quantifying dissipation in actomyosin networks

Quantifying entropy production in various active matter phases will open new avenues for probing self-organization principles in these far-from-equilibrium systems. It has been hypothesized that the dissipation of free energy by active matter systems may be optimized, leading to system trajectories with histories of large dissipation and an accompanying emergence of ordered dynamical states. This interesting idea has not been widely tested. In particular, it is not clear whether emergent states of actomyosin networks, which represent a salient example of biological active matter, self-organize following the principle of dissipation optimization. In order to start addressing this question using detailed computational modelling, we rely on the MEDYAN simulation platform, which allows simulating active matter networks from fundamental molecular principles. We have extended the capabilities of MEDYAN to allow quantification of the rates of dissipation resulting from chemical reactions and relaxation of mechanical stresses during simulation trajectories. This is done by computing precise changes in Gibbs free energy accompanying chemical reactions using a novel formula and through detailed calculations of instantaneous values of the system's mechanical energy. We validate our approach with a mean-field model that estimates the rates of dissipation from filament treadmilling. Applying this methodology to the self-organization of small disordered actomyosin networks, we find that compact and highly cross-linked networks tend to allow more efficient transduction of chemical free energy into mechanical energy. In these simple systems, we observe that spontaneous network reorganizations tend to result in a decrease in the total dissipation rate to a low steady-state value. Future studies might carefully test whether the dissipation-driven adaptation hypothesis applies in this instance, as well as in more complex cytoskeletal geometries.

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.

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.

Analysis of Phosphoryl-Transfer Enzymes with QM/MM Free Energy Simulations

We discuss the application of quantum mechanics/molecular mechanics (QM/MM) free energy simulations to the analysis of phosphoryl transfers catalyzed by two enzymes: alkaline phosphatase and myosin. We focus on the nature of the transition state and the issue of mechanochemical coupling, respectively, in the two enzymes. The results illustrate unique insights that emerged from the QM/MM simulations, especially concerning the interpretation of experimental data regarding the nature of enzymatic transition states and coupling between global structural transition and catalysis in the active site. We also highlight a number of technical issues worthy of attention when applying QM/MM free energy simulations, and comment on a number of technical and mechanistic issues that require further studies.

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.

Structural transitions of F-actin upon ATP hydrolysis at near-atomic resolution revealed by cryo-EM

The function of actin is coupled to the nucleotide bound to its active site. ATP hydrolysis is activated during polymerization; a delay between hydrolysis and inorganic phosphate (P_i) release results in a gradient of ATP, ADP-P_i and ADP along actin filaments (F-actin). Actin-binding proteins can recognize F-actin's nucleotide state, using it as a local 'age' tag. The underlying mechanism is complex and poorly understood. Here we report six high-resolution cryo-EM structures of F-actin from rabbit skeletal muscle in different nucleotide states. The structures reveal that actin polymerization repositions the proposed catalytic base, His161, closer to the γ-phosphate. Nucleotide hydrolysis and P_i release modulate the conformational ensemble at the periphery of the filament, thus resulting in open and closed states, which can be sensed by coronin-1B. The drug-like toxin jasplakinolide locks F-actin in an open state. Our results demonstrate in detail how ATP hydrolysis links to F-actin's conformational dynamics and protein interaction.

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.

Biomimetic temporal self-assembly via fuel-driven controlled supramolecular polymerization

Temporal control of supramolecular assemblies to modulate the structural and transient characteristics of synthetic nanostructures is an active field of research within supramolecular chemistry. Molecular designs to attain temporal control have often taken inspiration from biological assemblies. One such assembly in Nature which has been studied extensively, for its well-defined structure and programmable self-assembly, is the ATP-driven seeded self-assembly of actin. Here we show, in a synthetic manifestation of actin self-assembly, an ATP-selective and ATP-fuelled, controlled supramolecular polymerization of a phosphate receptor functionalised monomer. It undergoes fuel-driven nucleation and seeded growth that provide length control and narrow dispersity of the resultant assemblies. Furthermore, coupling via ATP-hydrolysing enzymes yielded its transient characteristics. These results will usher investigations into synthetic analogues of important biological self-assembly motifs and will prove to be a significant advancement toward biomimetic temporally programmed materials.

Nanoscale Dynamics and Energetics of Proteins and Protein-Nucleic Acid Complexes in Classical Molecular Dynamics Simulations

The present article describes techniques for classical simulations of proteins and protein-nucleic acid complexes, revealing their dynamics and protein-substrate binding energies. The approach is based on classical atomistic molecular dynamics (MD) simulations of the experimentally determined structures of the complexes. MD simulations can provide dynamics of complexes in realistic solvents on microsecond timescales, and the free energy methods are able to provide Gibbs free energies of binding of substrates, such as nucleic acids, to proteins. The chapter describes methodologies for the preparation of computer models of biomolecular complexes and free energy perturbation methodology for evaluating Gibbs free energies of binding. The applications are illustrated with examples of snapshots of proteins and their complexes with nucleic acids, as well as the precise Gibbs free energies of binding.

Importance of an Orchestrate Participation of each Individual Residue Present at a Catalytic Site

GTP hydrolysis is indispensable to keep a living cell healthy. Nature has evolved so many enzymes to enhance the slow GTP hydrolysis. Rab GTPases are evolved to regulate vesicle trafficking. GTPase activating proteins (GAPs) accelerates their intrinsic slow GTP hydrolysis in order to maintain the sustainability between cellular events. Any malfunction/interference in this hydrolysis disrupts normal cellular events and causes severe diseases. In this study, GTP hydrolysis mechanism of Rab33B catalyzed by TBC-domain GAP protein Gyp1p has been decoded using extensive ab initio QM/MM metadynamics simulations. An organized coupled movement of individual residues present at the catalytic site is found to be the key factor for this reaction. An unorganized coupled movement leads the hydrolysis through very high energy pathways. This also reveals that the chemical transformations occurring at a catalytic site are residue specific.

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.

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

The protein mediated hydrolysis of nucleoside triphosphates such as ATP or GTP is one of the most important and challenging biochemical reactions in nature. The chemical environment (water structure, catalytic metal, and amino acid residues) adjacent to the hydrolysis site contains hundreds of atoms, usually greatly limiting the amount of the free energy sampling that one can achieve from computationally demanding electronic structure calculations such as QM/MM simulations. Therefore, the combination of QM/MM molecular dynamics with the recently developed transition-tempered metadynamics (TTMetaD), an enhanced sampling method that can provide a high-quality free energy estimate at an early stage in a simulation, is an ideal approach to address the biomolecular nucleoside triphosphate hydrolysis problem. In this work the ATP hydrolysis process in monomeric and filamentous actin is studied as an example application of the combined methodology. The performance of TTMetaD in these demanding QM/MM simulations is compared with that of the more conventional well-tempered metadynamics (WTMetaD). Our results show that TTMetaD exhibits much better exploration of the hydrolysis reaction free energy surface in two key collective variables (CVs) during the early stages of the QM/MM simulation than does WTMetaD. The TTMetaD simulations also reveal that a key third degree of freedom, the O-H bond-breaking and proton transfer from the lytic water, must be biased for TTMetaD to converge fully. To perturb the NTP hydrolysis dynamics to the least extent and to properly focus the MetaD free energy sampling, we also adopt here the recently developed metabasin metadynamics (MBMetaD) to construct a self-limiting bias potential that only applies to the lytic water after its nucleophilic attack of the phosphate of ATP. With these new, state-of-the-art enhanced sampling metadynamics techniques, we present an effective and accurate computational strategy for combining QM/MM molecular dynamics simulation with free energy sampling methodology, including a means to analyze the convergence of the calculations through robust numerical criteria.

Distal Proton Shuttle Mechanism of Ribosome Catalysed Peptide Bond Formation-A Theoretical Study

In this work, we have investigated a novel distal proton shuttle mechanism of ribosome catalyzed peptide bond formation reaction. The reaction was found to follow a two-step mechanism. A distal water molecule located about 6.1 Å away from the attacking amine plays as a proton acceptor and results in a charge-separated intermediate that is stabilized by the N terminus of L27 and the A-site A76 5′-phosphate. The ribose A2451 bridges the proton shuttle pathway, thus plays critical role in the reaction. The calculated 27.64 kcal·mol⁻¹ free energy barrier of the distal proton shuttle mechanism is lower than that of eight-membered ring transition state. The distal proton shuttle mechanism studied in this work can provide new insights into the important biological peptide synthesis process.

A Multiscale Description of Biomolecular Active Matter: The Chemistry Underlying Many Life Processes

This Commentary will describe the goal of developing and implementing novel, powerful, and integrated multiscale computer simulation methodology capable of accessing the large length and long time scales inherent in the behavior of biomolecular, multiprotein "active matter" complexes within the context of cellular biology. Examples include those involved in the actin-based cytoskeleton and its mechanochemistry. The primary objective is to connect detailed molecular and chemical properties with the key mesoscopic features manifest at the scales of cellular biology through a transformative theoretical and computer simulation approach, based on real physical and chemical interactions. This multiscale computational work would also make critical contact with rapidly developing experimental techniques such as super-resolution optical imaging, single molecule spectroscopy, and cryo-electron tomography, which are providing remarkable insight into the internal mesoscale self-organization and dynamics of cells.

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.

ATP Hydrolysis Mechanism in a Maltose Transporter Explored by QM/MM Metadynamics Simulation

Translocation of substrates across the cell membrane by adenosine 5'-triphosphate (ATP)-binding cassette (ABC) transporters depends on the energy provided by ATP hydrolysis within the nucleotide-binding domains (NBDs). However, the detailed mechanism remains unclear. In this study, we focused on maltose transporter NBDs (MalK₂) and performed a quantum mechanical/molecular mechanical (QM/MM) well-tempered metadynamics simulation to address this issue. We explored the free-energy profile along an assigned collective variable. As a result, it was determined that the activation free energy is approximately 10.5 kcal/mol, and the reaction released approximately 3.8 kcal/mol of free energy, indicating that the reaction of interest is a one-step exothermic reaction. The dissociation of the ATP γ-phosphate seems to be the rate-limiting step, which supports the so-called dissociative model. Moreover, Glu159, located in the Walker B motif, acts as a base to abstract the proton from the lytic water, but is not the catalytic base, which corresponds to an atypical general base catalysis model. We also observed two interesting proton transfers: transfer from the His192 ε-position nitrogen to the dissociated inorganic phosphate, Pi, and transfer from the Lys42 side chain to adenosine 5'-diphosphate β-phosphate. These proton transfers would stabilize the posthydrolysis state. Our study provides significant insight into the ATP hydrolysis mechanism in MalK₂ from a dynamical viewpoint, and this insight would be applicable to other ABC transporters.

Actin and Actin-Binding Proteins

Organisms from all domains of life depend on filaments of the protein actin to provide structure and to support internal movements. Many eukaryotic cells use forces produced by actin polymerization for their motility, and myosin motor proteins use ATP hydrolysis to produce force on actin filaments. Actin polymerizes spontaneously, followed by hydrolysis of a bound adenosine triphosphate (ATP). Dissociation of the γ-phosphate prepares the polymer for disassembly. This review provides an overview of the properties of actin and shows how dozens of proteins control both the assembly and disassembly of actin filaments. These players catalyze nucleotide exchange on actin monomers, initiate polymerization, promote phosphate dissociation, cap the ends of polymers, cross-link filaments to each other and other cellular components, and sever filaments.

Functional and Proteomic Investigations Reveal Major Royal Jelly Protein 1 Associated with Anti-hypertension Activity in Mouse Vascular Smooth Muscle Cells

Vascular smooth muscle cells (VSMCs) are a major cell type of the arterial wall and their functionality is associated with blood pressure regulation. Although royal jelly (RJ) has reported effects on anti-hypertension, the mechanism of blood pressure regulation by major royal jelly protein 1 (MRJP1), the most abundant RJ protein, is still unknown. The mrjp1 gene was inserted into mouse VSMCs to investigate how MRJP1 influences VSMC functionality by functional and proteomic analysis. The expression of MRJP1 in VSMCs significantly reduced cell contraction, migration, and proliferation, suggesting a potential role in decreasing hypertension via action on VSMCs. These anti-hypertension activities were further observed in the changes of the proteome setting of mouse VSMCs. Among 675 different proteins after MRJP1 expression, 646 were down-regulated and significantly enriched in pathways implicated in VSMC contraction and migration, which suggest MRJP1 lowers VSMC contraction and migration by inhibiting muscle filament movement. The down-regulated proteins also enriched pathways in proliferation, indicating that MRJP1 hinders VSMC proliferation by reducing the supply of energy and genetic material. This is the first report integrating MRJP1 into VSMC, revealing the function and mechanism correlated with anti-hypertensive activity. This offers a therapeutic potential to control hypertension by gene-therapy using bee-products.