Converting conformational changes to electrostatic energy in molecular motors: The energetics of ATP synthase

Identification of Potent siRNA Delivery Peptides Using Computer Modeling

Peptides with suitable aggregation behavior and electrical properties are potential siRNA delivery vectors. However, identifying suitable peptides with ideal delivery and safety features is difficult owing to the variations in amino acid sequences. Here, a holistic program based on computer modeling and single-cell RNA sequencing (scRNA-seq) is used to identify ideal siRNA delivery peptides. Stage one of this program consists of a sequential screening process for candidates with ideal assembly and delivery ability; stage two is a cell subtype-level analysis program that screens for high in vivo tissue safety. The leading candidate peptide selected from a library containing 12 amino acids showed strong lung-targeted siRNA delivery capacity after hydrophobic modification. Systemic administration of these compounds caused the least damage to liver and lung tissues and has little impact on macrophage and neutrophil numbers. By loading STAT3 siRNA, strong anticancer effects are achieved in multiple models, including patient-derived xenografts (PDX). This screening procedure may facilitate the development of peptide-based RNA interference (RNAi) therapeutics.

Simulating the directional translocation of a substrate by the AAA+ motor in the 26S proteasome

This work explored the molecular origin of substrate translocation by the AAA+ motor of the 26S proteasome. This exploration was performed by combining different simulation approaches including calculations of binding free energies, coarse-grained simulations, and considerations of the ATP hydrolysis energy. The simulations were used to construct the free energy landscape for the translocation process. This included the evaluation of the conformational barriers in different translocation steps. Our simulation reveals that the substrate translocation by the AAA+ motor is guided in part by electrostatic interactions. We also validated the experimental observation that bulkier residues in pore loop 1 are responsible for substrate translocation. However, our calculation also reveals that the lysine residues prior to the bulkier residues (conserved along pore loop 1) are also important for the translocation process. We believe that this computational study can help in guiding the ongoing research of the proteasome.

The catalytic dwell in ATPases is not crucial for movement against applied torque

The ATPase-catalysed conversion of ATP to ADP is a fundamental process in biology. During the hydrolysis of ATP, the α₃β₃ domain undergoes conformational changes while the central stalk (γ/D) rotates unidirectionally. Experimental studies have suggested that different catalytic mechanisms operate depending on the type of ATPase, but the structural and energetic basis of these mechanisms remains unclear. In particular, it is not clear how the positions of the catalytic dwells influence the energy transduction. Here we show that the observed dwell positions, unidirectional rotation and movement against the applied torque are reflections of the free-energy surface of the systems. Instructively, we determine that the dwell positions do not substantially affect the stopping torque. Our results suggest that the three resting states and the pathways that connect them should not be treated equally. The current work demonstrates how the free-energy landscape determines the behaviour of different types of ATPases.

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.

A quantum mechanical computational method for modeling electrostatic and solvation effects of protein

An efficient computational approach for modeling protein electrostatic is developed according to static point-charge model distributions based on the linear-scaling EE-GMFCC (electrostatically embedded generalized molecular fractionation with conjugate caps) quantum mechanical (QM) method. In this approach, the Electrostatic-Potential atomic charges are obtained from ab initio calculation of protein, both polarization and charge transfer effect are taken into consideration. This approach shows a significant improvement in the description of electrostatic potential and solvation energy of proteins comparing with current popular molecular mechanics (MM) force fields. Therefore, it has gorgeous prospect in many applications, including accurate calculations of electric field or vibrational Stark spectroscopy in proteins and predicting protein-ligand binding affinity. It can also be applied in QM/MM calculations or electronic embedding method of ONIOM to provide a better electrostatic environment.

Comparing the catalytic strategy of ATP hydrolysis in biomolecular motors

ATP-driven biomolecular motors utilize the chemical energy obtained from the ATP hydrolysis to perform vital tasks in living cells. Understanding the mechanism of enzyme-catalyzed ATP hydrolysis reaction has substantially progressed lately thanks to combined quantum/classical molecular mechanics (QM/MM) simulations. Here, we present a comparative summary of the most recent QM/MM results for myosin, kinesin and F1-ATPase motors. These completely different motors achieve the acceleration of ATP hydrolysis through a very similar catalytic mechanism. ATP hydrolysis has high activation energy because it involves the breaking of two strong bonds, namely the Pγ-Oβγ bond of ATP and the H-O bond of lytic water. The key to the four-fold decrease in the activation barrier by the three enzymes is that the breaking of the Pγ-Oβγ bond precedes the deprotonation of the lytic water molecule, generating a metaphosphate hydrate complex. The resulting singly charged trigonal planar PγO3(-) metaphosphate is a better electrophilic target for attack by an OaH(-) hydroxyl group. The formation of this OaH(-) is promoted by a strong polarization of the lytic water: in all three proteins, this water is forming a hydrogen-bond with a backbone carbonyl group and interacts with the carboxylate group of glutamate (either directly or via an intercalated water molecule). This favors the shedding of one proton by the attacking water. The abstracted proton is transferred to the γ-phosphate via various proton wires, resulting in a H2PγO4(-)/ADP(3-) product state. This catalytic strategy is so effective that most other nucleotide hydrolyzing enzymes adopt a similar approach, as suggested by their very similar triphosphate binding sites.

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

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

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

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

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

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

Methyltransferases do not work by compression, cratic, or desolvation effects, but by electrostatic preorganization

The enzyme catechol O-methyltransferase (COMT) catalyzes the transfer of a methyl group from S-adenosylmethionine to dopamine and related catechols. The search for the origin of COMT catalysis has led to different proposals and hypothesis, including the entropic, the NAC, and the compression proposals as well as the more reasonable electrostatic idea. Thus, it is important to understand the catalytic power of this enzyme and to examine the validity of different proposals and in particular the repeated recent implication of the compression idea. The corresponding analysis should be done by well-defined physically-based considerations that involve computations rather than circular interpretations of experimental results. Thus, we explore here the origin of the catalytic efficiency of COMT by using the empirical valence bond and the linear response approximation approaches. The results demonstrate that the catalytic effect of COMT is mainly due to electrostatic preorganization effects. It is also shown that the compression, NAC and entropic proposals do not account for the catalytic effect.

How valence bond theory can help you understand your (bio)chemical reaction

This Tutorial Review describes modern VB theory, using a didactic example of an S_N2 reaction to illustrate its immediate applications.

Parametrization of DFTB3/3OB for magnesium and zinc for chemical and biological applications

We report the parametrization of the approximate density functional theory, DFTB3, for magnesium and zinc for chemical and biological applications. The parametrization strategy follows that established in previous work that parametrized several key main group elements (O, N, C, H, P, and S). This 3OB set of parameters can thus be used to study many chemical and biochemical systems. The parameters are benchmarked using both gas-phase and condensed-phase systems. The gas-phase results are compared to DFT (mostly B3LYP), ab initio (MP2 and G3B3), and PM6, as well as to a previous DFTB parametrization (MIO). The results indicate that DFTB3/3OB is particularly successful at predicting structures, including rather complex dinuclear metalloenzyme active sites, while being semiquantitative (with a typical mean absolute deviation (MAD) of ∼3–5 kcal/mol) for energetics. Single-point calculations with high-level quantum mechanics (QM) methods generally lead to very satisfying (a typical MAD of ∼1 kcal/mol) energetic properties. DFTB3/MM simulations for solution and two enzyme systems also lead to encouraging structural and energetic properties in comparison to available experimental data. The remaining limitations of DFTB3, such as the treatment of interaction between metal ions and highly charged/polarizable ligands, are also discussed.

Quantitative exploration of the molecular origin of the activation of GTPase

GTPases play a major role in cellular processes, and gaining quantitative understanding of their activation demands reliable free energy surfaces of the relevant mechanistic paths in solution, as well as the interpolation of this information to GTPases. Recently, we generated ab initio quantum mechanical/molecular mechanical free energy surfaces for the hydrolysis of phosphate monoesters in solution, establishing quantitatively that the barrier for the reactions with a proton transfer (PT) step from a single attacking water (1 W) is higher than the one where the PT is assisted by a second water (2 W). The implication of this finding on the activation of GTPases is quantified here, by using the ab initio solution surfaces to calibrate empirical valence bond surfaces and then exploring the origin of the activation effect. It is found that, although the 2 W PT path is a new element, this step is not rate determining, and the catalytic effect is actually due to the electrostatic stabilization of the pre-PT transition state and the subsequent plateau. Thus, the electrostatic catalytic effect found in our previous studies of the Ras GTPase activating protein (RasGAP) and the elongation factor-Tu (EF-Tu) with a 1 W mechanism is still valid for the 2 W path. Furthermore, as found before, the corresponding activation appears to involve a major allosteric effect. Overall, we believe that our finding is general to both GTPases and ATPases. In addition to the biologically relevant finding, we also provide a critical discussion of the requirements from reliable surfaces for enzymatic reactions.

Modeling catalytic promiscuity in the alkaline phosphatase superfamily

In recent years, it has become increasingly clear that promiscuity plays a key role in the evolution of new enzyme function. This finding has helped to elucidate fundamental aspects of molecular evolution. While there has been extensive experimental work on enzyme promiscuity, computational modeling of the chemical details of such promiscuity has traditionally fallen behind the advances in experimental studies, not least due to the nearly prohibitive computational cost involved in examining multiple substrates with multiple potential mechanisms and binding modes in atomic detail with a reasonable degree of accuracy. However, recent advances in both computational methodologies and power have allowed us to reach a stage in the field where we can start to overcome this problem, and molecular simulations can now provide accurate and efficient descriptions of complex biological systems with substantially less computational cost. This has led to significant advances in our understanding of enzyme function and evolution in a broader sense. Here, we will discuss currently available computational approaches that can allow us to probe the underlying molecular basis for enzyme specificity and selectivity, discussing the inherent strengths and weaknesses of each approach. As a case study, we will discuss recent computational work on different members of the alkaline phosphatase superfamily (AP) using a range of different approaches, showing the complementary insights they have provided. We have selected this particular superfamily, as it poses a number of significant challenges for theory, ranging from the complexity of the actual reaction mechanisms involved to the reliable modeling of the catalytic metal centers, as well as the very large system sizes. We will demonstrate that, through current advances in methodologies, computational tools can provide significant insight into the molecular basis for catalytic promiscuity, and, therefore, in turn, the mechanisms of protein functional evolution.

Adenosine triphosphate hydrolysis mechanism in kinesin studied by combined quantum-mechanical/molecular-mechanical metadynamics simulations

Kinesin is a molecular motor that hydrolyzes adenosine triphosphate (ATP) and moves along microtubules against load. While motility and atomic structures have been well-characterized for various members of the kinesin family, not much is known about ATP hydrolysis inside the active site. Here, we study ATP hydrolysis mechanisms in the kinesin-5 protein Eg5 by using combined quantum mechanics/molecular mechanics metadynamics simulations. Approximately 200 atoms at the catalytic site are treated by a dispersion-corrected density functional and, in total, 13 metadynamics simulations are performed with their cumulative time reaching ~0.7 ns. Using the converged runs, we compute free energy surfaces and obtain a few hydrolysis pathways. The pathway with the lowest free energy barrier involves a two-water chain and is initiated by the Pγ-Oβ dissociation concerted with approach of the lytic water to PγO3-. This immediately induces a proton transfer from the lytic water to another water, which then gives a proton to the conserved Glu270. Later, the proton is transferred back from Glu270 to HPO(4)2- via another hydrogen-bonded chain. We find that the reaction is favorable when the salt bridge between Glu270 in switch II and Arg234 in switch I is transiently broken, which facilitates the ability of Glu270 to accept a proton. When ATP is placed in the ADP-bound conformation of Eg5, the ATP-Mg moiety is surrounded by many water molecules and Thr107 blocks the water chain, which together make the hydrolysis reaction less favorable. The observed two-water chain mechanisms are rather similar to those suggested in two other motors, myosin and F1-ATPase, raising the possibility of a common mechanism.

Rate of hydrolysis in ATP synthase is fine-tuned by α-subunit motif controlling active site conformation

Computer-designed artificial enzymes will require precise understanding of how conformation of active sites may control barrier heights of key transition states, including dependence on structure and dynamics at larger molecular scale. F(o)F(1) ATP synthase is interesting as a model system: a delicate molecular machine synthesizing or hydrolyzing ATP using a rotary motor. Isolated F(1) performs hydrolysis with a rate very sensitive to ATP concentration. Experimental and theoretical results show that, at low ATP concentrations, ATP is slowly hydrolyzed in the so-called tight binding site, whereas at higher concentrations, the binding of additional ATP molecules induces rotation of the central γ-subunit, thereby forcing the site to transform through subtle conformational changes into a loose binding site in which hydrolysis occurs faster. How the 1-Å-scale rearrangements are controlled is not yet fully understood. By a combination of theoretical approaches, we address how large macromolecular rearrangements may manipulate the active site and how the reaction rate changes with active site conformation. Simulations reveal that, in response to γ-subunit position, the active site conformation is fine-tuned mainly by small α-subunit changes. Quantum mechanics-based results confirm that the sub-Ångström gradual changes between tight and loose binding site structures dramatically alter the hydrolysis rate.

Why nature really chose phosphate

Phosphoryl transfer plays key roles in signaling, energy transduction, protein synthesis, and maintaining the integrity of the genetic material. On the surface, it would appear to be a simple nucleophile displacement reaction. However, this simplicity is deceptive, as, even in aqueous solution, the low-lying d-orbitals on the phosphorus atom allow for eight distinct mechanistic possibilities, before even introducing the complexities of the enzyme catalyzed reactions. To further complicate matters, while powerful, traditional experimental techniques such as the use of linear free-energy relationships (LFER) or measuring isotope effects cannot make unique distinctions between different potential mechanisms. A quarter of a century has passed since Westheimer wrote his seminal review, 'Why Nature Chose Phosphate' (Science 235 (1987), 1173), and a lot has changed in the field since then. The present review revisits this biologically crucial issue, exploring both relevant enzymatic systems as well as the corresponding chemistry in aqueous solution, and demonstrating that the only way key questions in this field are likely to be resolved is through careful theoretical studies (which of course should be able to reproduce all relevant experimental data). Finally, we demonstrate that the reason that nature really chose phosphate is due to interplay between two counteracting effects: on the one hand, phosphates are negatively charged and the resulting charge-charge repulsion with the attacking nucleophile contributes to the very high barrier for hydrolysis, making phosphate esters among the most inert compounds known. However, biology is not only about reducing the barrier to unfavorable chemical reactions. That is, the same charge-charge repulsion that makes phosphate ester hydrolysis so unfavorable also makes it possible to regulate, by exploiting the electrostatics. This means that phosphate ester hydrolysis can not only be turned on, but also be turned off, by fine tuning the electrostatic environment and the present review demonstrates numerous examples where this is the case. Without this capacity for regulation, it would be impossible to have for instance a signaling or metabolic cascade, where the action of each participant is determined by the fine-tuned activity of the previous piece in the production line. This makes phosphate esters the ideal compounds to facilitate life as we know it.

Addressing open questions about phosphate hydrolysis pathways by careful free energy mapping

The nature and mechanism of phosphate hydrolysis reactions are of great interest in view of the crucial role of these reactions in key biological processes. Although it is becoming clearer that the ultimate way of resolving mechanistic controversies must involve reliable theoretical studies, it is not widely realized that such studies cannot be performed at present by using most existing automated ways and that only careful systematic studies can lead to meaningful conclusions. The present work clarifies the above point by considering the hydrolysis of phosphate monoesters. The clarification starts by defining the actual issues that should be addressed in careful studies and by highlighting the problems with studies that ignore the need for unique mechanistic definitions (e.g., works that confuse associative and dissociative pathways). We then focus on the analysis of the proton transfer (PT) pathways in phosphate hydrolysis and on recent suggestions that PT involves more than one water molecule. Here we point out that most of the studies that found a proton transfer through several water molecules have not involved a sufficient systematic search of the relevant reaction coordinates. This includes both energy minimization approaches as well as a recent metadynamics (MTD) simulation study. To illustrate the crucial need of exploring the potential surfaces reliably, rather than relying on automated approaches, we present here a very careful study of the free energy landscape along a 3D reaction coordinate (RC) exploring both the standard 2D RC, comprised of the attacking and leaving group reaction coordinates, as well as of the proton transfer (PT) coordinate. Our study points out that QM/MM minimization or MTD studies that concluded that the hydrolysis of phosphate monoesters involves a PT through several water molecules, have not explored carefully the single water (1W) path (that involves a direct PT form the attacking water molecule to the phosphate oxygen). Furthermore, we identified the most likely reason for the difficulty in finding the 1W path by QM/MM minimization methods, as well as by the current MTD simulations. We also discuss the problems with current studies that challenge the phosphate as a base mechanism and emphasize that all recent studies found associative/concerted paths (although many have not realized the meaning of their results). Finally, although we clearly do not have the last word about the 1W versus 2W paths we believe that we illustrated that the crucial mechanistic problems with alternative pathways should not be resolved by just running black box search approaches.

Hyperconjugation-mediated solvent effects in phosphoanhydride bonds

Density functional theory and natural bond orbital analysis are used to explore the impact of solvent on hyperconjugation in methyl triphosphate, a model for "energy rich" phosphoanhydride bonds, such as found in ATP. As expected, dihedral rotation of a hydroxyl group vicinal to the phosphoanhydride bond reveals that the conformational dependence of the anomeric effect involves modulation of the orbital overlap between the donor and acceptor orbitals. However, a conformational independence was observed in the rotation of a solvent hydrogen bond. As one lone pair orbital rotates away from an optimal antiperiplanar orientation, the overall magnitude of the anomeric effect is compensated approximately by the other lone pair as it becomes more antiperiplanar. Furthermore, solvent modulation of the anomeric effect is not restricted to the antiperiplanar lone pair; hydrogen bonds involving gauche lone pairs also affect the anomeric interaction and the strength of the phosphoanhydride bond. Both gauche and anti solvent hydrogen bonds lengthen nonbridging O-P bonds, increasing the distance between donor and acceptor orbitals and decreasing orbital overlap, which leads to a reduction of the anomeric effect. Solvent effects are additive with greater reduction in the anomeric effect upon increasing water coordination. By controlling the coordination environment of substrates in an active site, kinases, phosphatases, and other enzymes important in metabolism and signaling may have the potential to modulate the stability of individual phosphoanhydride bonds through stereoelectronic effects.

Molecular mechanism of ATP hydrolysis in F1-ATPase revealed by molecular simulations and single-molecule observations

Enzymatic hydrolysis of nucleotide triphosphate (NTP) plays a pivotal role in protein functions. In spite of its biological significance, however, the chemistry of the hydrolysis catalysis remains obscure because of the complex nature of the reaction. Here we report a study of the molecular mechanism of hydrolysis of adenosine triphosphate (ATP) in F(1)-ATPase, an ATP-driven rotary motor protein. Molecular simulations predicted and single-molecule observation experiments verified that the rate-determining step (RDS) is proton transfer (PT) from the lytic water molecule, which is strongly activated by a metaphosphate generated by a preceding P(γ)-O(β) bond dissociation (POD). Catalysis of the POD that triggers the chain activation of the PT is fulfilled by hydrogen bonds between Walker motif A and an arginine finger, which commonly exist in many NTPases. The reaction mechanism unveiled here indicates that the protein can regulate the enzymatic activity for the function in both the POD and PT steps despite the fact that the RDS is the PT step.

Electrostatic origin of the mechanochemical rotary mechanism and the catalytic dwell of F1-ATPase

Understanding the nature of energy transduction in life processes requires a quantitative description of the energetics of the conversion of ATP to ADP by ATPases. Previous attempts to do so have provided an interesting insight but could not account for the rotary mechanism by a nonphenomenological structure/energy description. In particular it has been very challenging to account for the observations of the 80° and 40° rotational substates, without any prior information about such states in the simulation procedure. Here we use a coarse-grained model of F1-ATPase and generate, without the adjustment of phenomenological parameters, a structure-based free energy landscape that reproduces the energetics of the mechanochemical process. It is found that the landscape along the relevant rotary path is determined by the electrostatic free energy and not by steric effects. Furthermore, the generated surface and the corresponding Langevin dynamics simulations identify a hidden conformational barrier that provides a new fundamental interpretation of the catalytic dwell and illuminate the nature of the energy conversion process.

Catalysis by dihydrofolate reductase and other enzymes arises from electrostatic preorganization, not conformational motions

The proposal that enzymatic catalysis is due to conformational fluctuations has been previously promoted by means of indirect considerations. However, recent works have focused on cases where the relevant motions have components toward distinct conformational regions, whose population could be manipulated by mutations. In particular, a recent work has claimed to provide direct experimental evidence for a dynamical contribution to catalysis in dihydrofolate reductase, where blocking a relevant conformational coordinate was related to the suppression of the motion toward the occluded conformation. The present work utilizes computer simulations to elucidate the true molecular basis for the experimentally observed effect. We start by reproducing the trend in the measured change in catalysis upon mutations (which was assumed to arise as a result of a "dynamical knockout" caused by the mutations). This analysis is performed by calculating the change in the corresponding activation barriers without the need to invoke dynamical effects. We then generate the catalytic landscape of the enzyme and demonstrate that motions in the conformational space do not help drive catalysis. We also discuss the role of flexibility and conformational dynamics in catalysis, once again demonstrating that their role is negligible and that the largest contribution to catalysis arises from electrostatic preorganization. Finally, we point out that the changes in the reaction potential surface modify the reorganization free energy (which includes entropic effects), and such changes in the surface also alter the corresponding motion. However, this motion is never the reason for catalysis, but rather simply a reflection of the shape of the reaction potential surface.

Coarse-grained (multiscale) simulations in studies of biophysical and chemical systems

Recent years have witnessed an explosion in computational power, leading to attempts to model ever more complex systems. Nevertheless, there remain cases for which the use of brute-force computer simulations is clearly not the solution. In such cases, great benefit can be obtained from the use of physically sound simplifications. The introduction of such coarse graining can be traced back to the early usage of a simplified model in studies of proteins. Since then, the field has progressed tremendously. In this review, we cover both key developments in the field and potential future directions. Additionally, particular emphasis is given to two general approaches, namely the renormalization and reference potential approaches, which allow one to move back and forth between the coarse-grained (CG) and full models, as these approaches provide the foundation for CG modeling of complex systems.

Domain motion of individual F1-ATPase β-subunits during unbiased molecular dynamics simulations

F(1)-ATPase is the catalytic domain of F(1)F(o)-ATP synthase and consists of a hexameric arrangement of three noncatalytic α and three catalytic β subunits. We have used unbiased molecular dynamics simulations with a total simulation time of 900 ns to investigate the dynamic relaxation properties of isolated β-subunits as a step toward explaining the function of the integral F(1) unit. To this end, we simulated the open (β(E)) and the closed (β(TP)) conformations under unbiased conditions for up to 120 ns each using several samples. The simulations confirm that nucleotide-free β(E) retains its open configuration over the course of the simulations. The same is true when the neighboring α subunits are included. The nucleotide-depleted as well as the nucleotide-bound isolated β(TP) subunits show a significant trend toward the open conformation during our simulations, with one trajectory per case opening completely. Hence, our simulations suggest that the equilibrium conformation of a nucleotide-free β-subunit is the open conformation and that the transition from the closed to the open conformation can occur on a time scale of a few tens of nanoseconds.

Converting structural information into an allosteric-energy-based picture for elongation factor Tu activation by the ribosome

The crucial process of aminoacyl-tRNA delivery to the ribosome is energized by the GTPase reaction of the elongation factor Tu (EF-Tu). Advances in the elucidation of the structure of the EF-Tu/ribosome complex provide the rare opportunity of gaining a detailed understanding of the activation process of this system. Here, we use quantitative simulation approaches and reproduce the energetics of the GTPase reaction of EF-Tu with and without the ribosome and with several key mutants. Our study provides a novel insight into the activation process. It is found that the critical H84 residue is not likely to behave as a general base but rather contributes to an allosteric effect, which includes a major transition state stabilization by the electrostatic effect of the P loop and other regions of the protein. Our findings have general relevance to GTPase activation, including the processes that control signal transduction.

Double-lock ratchet mechanism revealing the role of alphaSER-344 in FoF1 ATP synthase

In a majority of living organisms, FoF1 ATP synthase performs the fundamental process of ATP synthesis. Despite the simple net reaction formula, ADP+Pi→ATP+H2O, the detailed step-by-step mechanism of the reaction yet remains to be resolved owing to the complexity of this multisubunit enzyme. Based on quantum mechanical computations using recent high resolution X-ray structures, we propose that during ATP synthesis the enzyme first prepares the inorganic phosphate for the γP-OADP bond-forming step via a double-proton transfer. At this step, the highly conserved αS344 side chain plays a catalytic role. The reaction thereafter progresses through another transition state (TS) having a planar ion configuration to finally form ATP. These two TSs are concluded crucial for ATP synthesis. Using stepwise scans and several models of the nucleotide-bound active site, some of the most important conformational changes were traced toward direction of synthesis. Interestingly, as the active site geometry progresses toward the ATP-favoring tight binding site, at both of these TSs, a dramatic increase in barrier heights is observed for the reverse direction, i.e., hydrolysis of ATP. This change could indicate a "ratchet" mechanism for the enzyme to ensure efficacy of ATP synthesis by shifting residue conformation and thus locking access to the crucial TSs.

Conformational consequences of ionization of Lys, Asp, and Glu buried at position 66 in staphylococcal nuclease

The pK(a) values measured previously for the internal Lys-66, Asp-66, and Glu-66 in variants of a highly stable form of staphylococcal nuclease are shifted by as many as 5 pK(a) units relative to normal pK(a) values in water. These shifts cannot be reproduced with continuum electrostatics calculations with static structures unless the protein is treated with high dielectric constants near 10. These high apparent dielectric constants are inconsistent with the highly hydrophobic microenvironments of the ionizable moieties in crystal structures. To examine the origins of these high apparent dielectric constants, we showed that the pK(a) values of these internal residues are sensitive to the global stability of the protein; the shifts tend to be smaller in less stable forms of nuclease. This implies that the apparent dielectric constants reported by these internal ionizable groups are high because they reflect conformational reorganization coupled to their ionization. To detect this directly, acid-base titrations monitored with Trp fluorescence and near-UV and far-UV CD spectroscopy were performed on variants with Lys-66, Glu-66, or Asp-66 in background proteins with different stabilities. Conformational reorganization coupled to the ionization of the internal groups was spectroscopically detectable, especially in the less stable background proteins. The data show that to improve the accuracy of structure-based pK(a) calculations of internal groups the calculations will have to treat explicitly all structural reorganization coupled to ionization. The data also suggest a novel approach to mapping the folding free energy landscape of proteins by using internal ionizable groups to stabilize partially unfolded states.

A binding free energy decomposition approach for accurate calculations of the fidelity of DNA polymerases

DNA polymerase beta (pol beta) is a small eukaryotic enzyme with the ability to repair short single-stranded DNA gaps that has found use as a model system for larger replicative DNA polymerases. For all DNA polymerases, the factors determining their catalytic power and fidelity are the interactions between the bases of the base pair, amino acids near the active site, and the two magnesium ions. In this report, we study effects of all three aspects on human pol beta transition state (TS) binding free energies by reproducing a consistent set of experimentally determined data for different structures. Our calculations comprise the combination of four different base pairs (incoming pyrimidine nucleotides incorporated opposite both matched and mismatched purines) with four different pol beta structures (wild type and three mutants). We generate three fragments of the incoming deoxynucleoside 5'-triphosphate-TS and run separate calculations for the neutral base part and the highly charged triphosphate part, using different dielectric constants in order to account for the specific dielectric response. This new approach improves our ability to predict the effect of matched and mismatched base pairing and of mutations in DNA polymerases on fidelity and may be a useful tool in studying the potential of DNA polymerase mutations in the development of cancer. It also supports our point of view with regards to the origin of the structural control of fidelity, allowing for a quantified description of the fidelity of DNA polymerases.

On the energetics of ATP hydrolysis in solution

ATP hydrolysis is the driving force of many life processes, yet the exact nature of and contributions to the energetics of this reaction are far from being clear. In particular, it is unclear how much of the driving force of this reaction is due to the separation of the already dissociated ADP + P(i) moieties rather than to the chemical event. This fundamental issue is explored here by ab initio calculations that use different solvation models, and it is found that, while the calculations are sensitive to the theoretical approach used, it is quite likely that the dissociation of the charged fragments makes a significant contribution to the energetics of ATP hydrolysis.

F0F1-ATPase activity regulated by external links on beta subunits

F(o)F(1)-ATPase activity is regulated by external links on beta subunits with different molecular weight. It is inhibited when anti-beta subunit antibody, streptavidin and H9 antibody link on the beta subunits successively, but is activated when virus was binded. Western blotting indicated that the employed anti-beta antibody target was on the non-catalytic site of the beta subunit. Furthermore, an ESR study of spin-labeled ATP (SL-ATP) showed that the affinity of ATP to the holoenzyme increases with increasing external links on the beta subunits. This simple regulation method may have great potential in the design of rapid, free labeled, sensitive and selective biosensors.

A computational analysis of ATP binding of SV40 large tumor antigen helicase motor

Simian Virus 40 Large Tumor Antigen (LTag) is an efficient helicase motor that unwinds and translocates DNA. The DNA unwinding and translocation of LTag is powered by ATP binding and hydrolysis at the nucleotide pocket between two adjacent subunits of an LTag hexamer. Based on the set of high-resolution hexameric structures of LTag helicase in different nucleotide binding states, we simulated a conformational transition pathway of the ATP binding process using the targeted molecular dynamics method and calculated the corresponding energy profile using the linear response approximation (LRA) version of the semi-macroscopic Protein Dipoles Langevin Dipoles method (PDLD/S). The simulation results suggest a three-step process for the ATP binding from the initial interaction to the final tight binding at the nucleotide pocket, in which ATP is eventually “locked” by three pairs of charge-charge interactions across the pocket. Such a “cross-locking” ATP binding process is similar to the binding zipper model reported for the F1-ATPase hexameric motor. The simulation also shows a transition mechanism of Mg²⁺ coordination to form the Mg-ATP complex during ATP binding, which is accompanied by the large conformational changes of LTag. This simulation study of the ATP binding process to an LTag and the accompanying conformational changes in the context of a hexamer leads to a refined cooperative iris model that has been proposed previously.

The Large Tumor antigen (LTag) encoded by Simian Virus 40 (SV40) is a marvelous molecule that is not only a viral oncogene, but also an efficient molecular machine as a helicase that unwinds double helix DNA for genome replication, an essential process in all living organisms. LTag hexameric helicase uses the energy of ATP to power its conformational switch for DNA unwinding. Understanding how the LTag conformational switch is coupled to the energy from ATP usage by LTag to do the mechanical work of unwinding DNA is of great interest to biologists, and yet remains to be established. Based on our previous high-resolution structures of LTag helicase in different conformational states, we simulated an LTag conformational transition pathway in the ATP binding process using the targeted molecular dynamics method. Our simulation results suggest a three-step process for the ATP binding to the nucleotide pocket, in which ATP is eventually “locked” into the pocket by three pairs of “locker” interactions. We have also quantitatively evaluated the energy profile of ATP binding using a special computational simulation technique. Additionally, our simulation study of ATP binding by LTag and the accompanying conformational switches in the context of a hexamer leads to a refined cooperative iris model that may be used for DNA unwinding.

The energy gap as a universal reaction coordinate for the simulation of chemical reactions

The selection of a proper reaction coordinate is a major bottleneck in simulations of chemical reactions in complex systems. Increasing the number of variables that are used to bias the reaction largely affects the convergence and leads to an unbearable increase in computational price. This problem can be overcome by employing a complex reaction coordinate that depends on many geometrical variables of the system, such as the energy gap (EGAP) in the empirical valence bond (EVB) method. EGAP depends on all of the coordinates of the system, and its robustness has been demonstrated for a variety of enzymatic reactions. In this work, we demonstrate that EGAP, derived from a classical representation, can be used as a reaction coordinate in systems described with any quantum chemistry Hamiltonian. Benefits of using EGAP as a reaction coordinate as compared to a traditional geometrical variable are illustrated in the case of a symmetric nucleophilic substitution reaction in water solution. EGAP is shown to provide a significantly more efficient sampling and allows a better localization of the transition state as compared to a geometrical reaction coordinate.

Hydrolysis of aspartic acid phosphoramidate nucleotides: a comparative quantum chemical study

L-Aspartic acid has recently been found to be a good leaving group during HIV reverse transcriptase catalyzed incorporation of deoxyadenosine monophosphate (dAMP) in DNA. This showed that L-Asp is a good mimic for the pyrophosphate moiety of deoxyadenosine triphosphate. The present work explores the thermochemistry and mechanism for hydrolysis of several models for L-aspartic-dAMP using B3LYP/DGDZVP, MP2/6-311++G** and G3MP2 level of theory. The effect of the new compound is gradually investigated: starting from a simple methyl amine leaving group up to the aspartic acid leaving group. The enzymatic environment was mimicked by involving two Mg(2+) ions and some important active site residues in the reaction. All reactions are compared to the corresponding O-coupled leaving group, which is methanol for methyl amine and malic acid for aspartic acid. With methyl amine as a leaving group a tautomeric associative or tautomeric dissociative mechanism is preferred and the barrier is lower than the comparable mechanism with methanol as a leaving group. The calculations on the aspartic acid in the enzymatic environment show that qualitatively the mechanism is the same as for triphosphate but the barrier for hydrolysis by the associative mechanism is higher for L-aspartic-dAMP than for L-malic-dAMP and pyrophosphate.

Simulating the electrostatic guidance of the vectorial translocations in hexameric helicases and translocases

The molecular origin of the action of helicases is explored, starting with a model built based on the different X-ray structures of the large tumor antigen (LTag) hexameric helicase and a simplified model containing the ionized phosphate backbones of a single-strand DNA. The coupling between the protein structural changes and the translocation process is quantified using an effective electrostatic free-energy surface for the protein/DNA complex. This surface is then used in Langevin dynamics simulations of the time dependence of the translocation process. Remarkably, the simulated motion along the free-energy surface results in a vectorial translocation of the DNA, consistent with the biological process. The electrostatic energy of the system appears to reproduce the directionality of this process. Thus, we are able to provide a consistent structure-based molecular description of the energetic and dynamics of the translocation process. This analysis may have general implications for relating structural models to translocation directionality in helicases and other DNA translocases.

Progress in ab initio QM/MM free-energy simulations of electrostatic energies in proteins: accelerated QM/MM studies of pKa, redox reactions and solvation free energies

Hybrid quantum mechanical/molecular mechanical (QM/MM) approaches have been used to provide a general scheme for chemical reactions in proteins. However, such approaches still present a major challenge to computational chemists, not only because of the need for very large computer time in order to evaluate the QM energy but also because of the need for proper computational sampling. This review focuses on the sampling issue in QM/MM evaluations of electrostatic energies in proteins. We chose this example since electrostatic energies play a major role in controlling the function of proteins and are key to the structure-function correlation of biological molecules. Thus, the correct treatment of electrostatics is essential for the accurate simulation of biological systems. Although we will be presenting different types of QM/MM calculations of electrostatic energies (and related properties) here, our focus will be on pKa calculations. This reflects the fact that pKa's of ionizable groups in proteins provide one of the most direct benchmarks for the accuracy of electrostatic models of macromolecules. While pKa calculations by semimacroscopic models have given reasonable results in many cases, existing attempts to perform pKa calculations using QM/MM-FEP have led to discrepancies between calculated and experimental values. In this work, we accelerate our QM/MM calculations using an updated mean charge distribution and a classical reference potential. We examine both a surface residue (Asp3) of the bovine pancreatic trypsin inhibitor and a residue buried in a hydrophobic pocket (Lys102) of the T4-lysozyme mutant. We demonstrate that, by using this approach, we are able to reproduce the relevant side chain pKa's with an accuracy of 3 kcal/mol. This is well within the 7 kcal/mol energy difference observed in studies of enzymatic catalysis, and is thus sufficient accuracy to determine the main contributions to the catalytic energies of enzymes. We also provide an overall perspective of the potential of QM/MM calculations in general evaluations of electrostatic free energies, pointing out that our approach should provide a very powerful and accurate tool to predict the electrostatics of not only solution but also enzymatic reactions, as well as the solvation free energies of even larger systems, such as nucleic acid bases incorporated into DNA.

Biomolecular simulation and modelling: status, progress and prospects

Molecular simulation is increasingly demonstrating its practical value in the investigation of biological systems. Computational modelling of biomolecular systems is an exciting and rapidly developing area, which is expanding significantly in scope. A range of simulation methods has been developed that can be applied to study a wide variety of problems in structural biology and at the interfaces between physics, chemistry and biology. Here, we give an overview of methods and some recent developments in atomistic biomolecular simulation. Some recent applications and theoretical developments are highlighted.

The energetics of the primary proton transfer in bacteriorhodopsin revisited: it is a sequential light-induced charge separation after all

The light-induced proton transport in bacteriorhodopsin has been considered as a model for other light-induced proton pumps. However, the exact nature of this process is still unclear. For example, it is not entirely clear what the driving force of the initial proton transfer is and, in particular, whether it reflects electrostatic forces or other effects. The present work simulates the primary proton transfer (PT) by a specialized combination of the EVB and the QCFF/PI methods. This combination allows us to obtain sufficient sampling and a quantitative free energy profile for the PT at different protein configurations. The calculated profiles provide new insight about energetics of the primary PT and its coupling to the protein conformational changes. Our finding confirms the tentative analysis of an earlier work (A. Warshel, Conversion of light energy to electrostatic energy in the proton pump of Halobacterium halobium, Photochem. Photobiol. 30 (1979) 285-290) and determines that the overall PT process is driven by the energetics of the charge separation between the Schiff base and its counterion Asp85. Apparently, the light-induced relaxation of the steric energy of the chromophore leads to an increase in the ion-pair distance, and this drives the PT process. Our use of the linear response approximation allows us to estimate the change in the protein conformational energy and provides the first computational description of the coupling between the protein structural changes and the PT process. It is also found that the PT is not driven by twist-modulated changes of the Schiff base's pKa, changes in the hydrogen bond directionality, or other non-electrostatic effects. Overall, based on a consistent use of structural information as the starting point for converging free energy calculations, we conclude that the primary event should be described as a light-induced formation of an unstable ground state, whose relaxation leads to charge separation and to the destabilization of the ion-pair state. This provides the driving force for the subsequent PT steps.

Identification of the betaTP site in the x-ray structure of F1-ATPase as the high-affinity catalytic site

ATP synthase uses a unique rotary mechanism to couple ATP synthesis and hydrolysis to transmembrane proton translocation. The F(1) subcomplex has three catalytic nucleotide binding sites, one on each beta subunit, with widely differing affinities for MgATP or MgADP. During rotational catalysis, the sites switch their affinities. The affinity of each site is determined by the position of the central gamma subunit. The site with the highest nucleotide binding affinity is catalytically active. From the available x-ray structures, it is not possible to discern the high-affinity site. Using fluorescence resonance energy transfer between tryptophan residues engineered into gamma and trinitrophenyl nucleotide analogs on the catalytic sites, we were able to determine that the high-affinity site is close to the C-terminal helix of gamma, but at considerable distance from its N terminus. Thus, the beta(TP) site in the x-ray structure [Abrahams JP, Leslie AGW, Lutter R, Walker JE (1994) Nature 370:621-628] is the high-affinity site, in agreement with the prediction of Yang et al. [Yang W, Gao YQ, Cui Q, Ma J, Karplus M (2003) Proc Natl Acad Sci USA 100:874-879]. Taking into account the known direction of rotation, the findings establish the sequence of affinities through which each catalytic site cycles during MgATP hydrolysis as low --> high --> medium --> low.

Ammonium Scanning in an Enzyme Active Site

D-amino acids are largely excluded from protein synthesis, yet they are of great interest in biotechnology. Aspartyl-tRNA synthetase (AspRS) can misacylate tRNA(Asp) with D-aspartate instead of its usual substrate, L-Asp. We investigate how the preference for L-Asp arises, using molecular dynamics simulations. Asp presents a special problem, having pseudosymmetry broken only by its ammonium group, and AspRS must protect not only against D-Asp, but against an "inverted" orientation where the two substrate carboxylates are swapped. We compare L-Asp and D-Asp, in both orientations, and succinate, where the ammonium group is removed and the ligand has an additional negative charge. All possible ammonium positions on the ligand are thus scanned, providing information on electrostatic interactions. As controls, we simulate a Q199E mutation, obtaining a reduction in binding free energy in agreement with experiment, and we simulate TyrRS, which can misacylate tRNA(Tyr) with D-Tyr. For both TyrRS and AspRS, we obtain a moderate binding free energy difference DeltaDeltaG between the L- and D-amino acids, in agreement with their known ability to misacylate their tRNAs. In contrast, we predict that AspRS is strongly protected against inverted L-Asp binding. For succinate, kinetic measurements reveal a DeltaDeltaG of over 5 kcal/mol, favoring L-Asp. The simulations show how chiral discriminations arises from the structures, with two AspRS conformations acting in different ways and proton uptake by nearby histidines playing a role. A complex network of charges protects AspRS against most binding errors, making the engineering of its specificity a difficult challenge.

On the mechanism of hydrolysis of phosphate monoesters dianions in solutions and proteins

The nature of the hydrolysis of phosphate monoester dianions in solutions and in proteins is a problem of significant current interest. The present work explores this problem by systematic calculations of the potential surfaces of the reactions of a series of phosphate monoesters with different leaving groups. These calculations involve computational studies ranging from ab initio calculations with implicit solvent models to ab initio QM/MM free energy calculations. The calculations reproduce the observed linear free energy relationship (LFER) for the solution reaction and thus are consistent with the overall experimental trend and can be used to explore the nature of the transition state (TS) region, which is not accessible to direct experimental studies. It is found that the potential surface for the associative and dissociative paths is very flat and that the relative height of the associative and dissociative TS is different in different systems. In general, the character of the TS changes from associative to dissociative upon decrease in the pKa of the leaving group. It is also demonstrated that traditional experimental markers such as isotope effects and the LFER slope cannot be used in a conclusive way to distinguish between the two classes of transition states. In addition it is found that the effective charges of the TS do not follow the previously assumed simple rule. Armed with that experience we explore the free energy surface for the GTPase reaction of the RasGap system. In this case it is found that the surface is flat but that the lowest TS is associative. The present study indicates that the nature of the potential surfaces for the phosphoryl transfer reactions in solution and proteins is quite complicated and cannot be determined in a conclusive way without the use of careful theoretical studies that should, of course, reproduce the available experimental information.