The Hydrolysis Activity of Adenosine Triphosphate in Myosin: A Theoretical Analysis of Anomeric Effects and the Nature of the Transition State

Combined quantum mechanical/molecular mechanical (QM/MM) calculations with density functional theory are employed to analyze two issues related to the hydrolysis activity of adenosine triphosphate (ATP) in myosin. First, we compare the geometrical properties and electronic structure of ATP in the open (post-rigor) and closed (pre-powerstroke) active sites of the myosin motor domain. Compared to both solution and the open active site cases, the scissile Pγ−O3β bond of ATP in the closed active site is shown to be substantially elongated. Natural bond orbital (NBO) analysis clearly shows that this structural feature is correlated with the stronger anomeric effects in the closed active site, which involve charge transfers from the lone pairs in the nonbridging oxygen in the γ-phosphate to the antibonding orbital of the scissile bond. However, an energetic analysis finds that the ATP molecule is not significantly destabilized by the Pγ−O3β bond elongation. Therefore, despite the notable perturbations in the geometry and electronic structure of ATP as its environment changes from solution to the hydrolysis-competent active site, ground-state destabilization is unlikely to play a major role in enhancing the hydrolysis activity in myosin. Second, two-dimensional potential energy maps are used to better characterize the energetic landscape near the hydrolysis transition state. The results indicate that the transition-state region is energetically flat and a range of structures representative of different mechanisms according to the classical nomenclature (e.g., “associative”, “dissociative”, and “concerted”) are very close in energy. Therefore, at least in the case of ATP hydrolysis in myosin, the energetic distinction between different reaction mechanisms following the conventional nomenclature is likely small. This study highlights the importance of (i) explicitly evaluating the relevant energetic properties for determining whether a factor is essential to catalysis and (ii) broader explorations of the energy landscape beyond saddle points (even on free-energy surface) for characterizing the molecular mechanism of catalysis

Activation Mechanism of a Signaling Protein at Atomic Resolution from Advanced Computations

Advanced computational techniques including transition path sampling and free energy calculations are combined synergistically to reveal the activation mechanism at unprecedented resolution for a small signaling protein, chemotaxis protein Y. In the conventional “Y−T coupling” model for response regulators, phosphorylation induces the displacement of the conserved Thr87 residue through hydrogen-bond formation, which in turn makes it sterically possible for Tyr106 to isomerize from a solvent exposed configuration to a buried rotameric state. More than 160 unbiased activation trajectories show, however, that the rotation of Tyr106 does not rely on the displacement of Thr87 per se. Free energy calculations reveal that the Tyr106 rotation is a low-barrier process in the absence of the Thr87-phosphate hydrogen bond, although the rotation is stabilized by the formation of this interaction. The simulations also find that structural change in the β4−α4 loop does not gate the Tyr106 rotation as suggested previously; rather, the rotation of Tyr106 stabilizes the activated configuration of this loop. The computational strategy used and mechanistic insights obtained have an impact on the study of signaling proteins and allosteric systems in general

Does Water Relay Play an Important Role in Phosphoryl Transfer Reactions? Insights from Theoretical Study of a Model Reaction in Water and <i>tert</i>-Butanol

To investigate whether water relay plays an important role in phosphoryl transfer reactions, we have used several theoretical approaches to compare key properties of uridine 3′-m-nitrobenzyl phosphate (UNP) in aqueous and tert-butanol solutions. Previous kinetic experiments found that the isomerization reaction of UNP is abolished in tert-butanol, which was interpreted as the direct evidence that supports the role of water relay in phosphoryl transfer. We have analyzed solute flexibility and solvent structure near the solute using equilibrium molecular dynamics simulations and a combined quantum mechanical/molecular mechanism (QM/MM) potential function for the solute. Snapshots from the simulations are then used in minimum energy path calculations to compare the energetics of direct nucleophilic attack and water-mediated nucleophilic attack pathways. QM/MM simulations are also used to compare the pseudorotation barriers for the pentavalent intermediate formed following the nucleophilic attack, another key step for the isomerization reaction. Combined results from these calculations suggest that water relay does not offer any significant energetic advantage over the direct nucleophilic attack. Unfortunately, the lack of isomerization in tert-butanol solution cannot be straightforwardly explained based on the results we have obtained here and therefore requires additional analysis. This study, nevertheless, has provided new insights into several most commonly discussed possibilities

Is a “Proton Wire” Concerted or Stepwise? A Model Study of Proton Transfer in Carbonic Anhydrase

The energetics of proton transfer reactions in carbonic anhydrase (CA) have been studied with an active site model. Specifically, proton transfer from a zinc-bound water molecule to a histidine residue mediated by a numbers of water molecules was investigated. With two or three bridging water molecules, the proton transfers are fully or nearly fully concerted and only one saddle point exists. With an additional water molecule that forms a ring bridge, an intermediate is formed in which one of the water molecules exists as a hydronium ion. In contrast to previous calculations in which either a low-level of theory was employed or a stepwise mechanism was assumed, the energetics obtained from the current work are approximately consistent with the experimental estimates. In all of the scenarios, the motion of more than one proton is involved in the transition state, which is in agreement with the experimental observation that the reaction rates in H2O/D2O mixture have an exponential dependence on the fraction of D2O in the solvent. For three (W3) or four waters (W4), the proton transfer to the “His 64” model is hardly involved in the transition state, suggesting that the orientation of the proton acceptor is less important than for only two waters (W2). Thus, the W3 and W4 results are consistent with the experimental observation that many kinetic properties of the H64A mutant of CA in well-buffered imidazole solution are similar to the wild type. The barrier height increases, and the barrier frequency (and therefore, the contribution of tunneling) decreases as the number of bridging water molecules increases. Overall, these investigations demonstrate that the proton transfer reaction in CA is sensitive to the nature and structure of the water bridge, which would be influenced by the dynamics of the water molecules and amino acids in the active site of the protein

Coacervation-Induced Remodeling of Nanovesicles

Intrinsically disordered peptides can form biomolecular condensates through liquid–liquid phase separation. These condensates play diverse roles in cells, including inducing large-scale changes in membrane morphology. Here we employ coarse-grained molecular dynamics simulations to identify the most salient physical principles that govern membrane remodeling by condensates. By systematically varying the interaction strengths among the polymers and lipids in our coarse-grained model, we are able to recapitulate various membrane transformations observed in different experiments. Endocytosis and exocytosis of the condensate are observed when the interpolymeric attraction is stronger than polymer–lipid interaction. We find a critical size of the condensate required to exhibit successful endocytosis. Multilamellarity and local gelation are observed when the polymer–lipid attraction is significantly stronger than the interpolymeric attraction. Our insights provide essential guidance to the design of (bio)polymers for the manipulation of membrane morphology in various applications such as drug delivery and synthetic biology

p<i>K</i>_a of Residue 66 in <i>Staphylococal nuclease</i>. I. Insights from QM/MM Simulations with Conventional Sampling

A combined quantum mechanical/molecular mechanical (QM/MM) potential function is used in a thermodynamic integration approach to calculate the pKa of residue 66 in two mutants (V66E, V66D) of Staphylococal nuclease relative to solution. Despite the similarity in chemical nature and experimentally measured pKa of the two buried titritable residues, the behaviors of the two mutants and the computed pKa values vary greatly in the simulations. For Glu66, the side chain is consistently observed to spontaneously flip out from the protein interior during titration, and the overall protein structure remains stable throughout the simulations. The computed pKa shifts using conventional sampling techniques with multiple nanoseconds per λ window (Set A and B) are generally close to the experimental value, therefore indicating that large-scale conformational rearrangements are not as important for V66E as suggested by the recent study of Warshel and co-worker. For Asp66, by contrast, flipping of the shorter side chain is not sufficient for getting adequate solvent stabilization of the ionized state. As a result, more complex behaviors such as partial unfolding of a nearby β-sheet region is observed, and the computed pKa shift is substantially higher than the experimental value unless Asp66 is biased to adopt the similar configurations as Glu66 in the V66E simulations. Collectively, these studies suggest that the lack of electronic polarization is not expected to be the dominant source of error in microscopic pKa shift calculations, while the need of enhanced sampling is more compelling for predicting the pKa of buried residues. Furthermore, the comparison between V66E and V66D also highlights that the microscopic interpretation of similar apparent pKa values and effective “dielectric constants” of proteins can vary greatly in terms of the residues that make key contributions and the scale of structural/hydration response to titration, the latter of which is difficult to predict a priori. Perturbative analyses of interactions that contribute to the titration free energy point to mutants that can be used to verify the microscopic mechanisms of titration in V66E/D SNase proteins

How to Stabilize Carbenes in Enzyme Active Sites without Metal Ions

Carbenes are highly reactive compounds with unique value to synthetic chemistry. However, a small number of natural enzymes have been shown to utilize carbene chemistry, and artificial enzymes engineered with directed evolution required transition metal ions to stabilize the carbene intermediates. To facilitate the design of broader classes of enzymes that can take advantage of the rich carbene chemistry, it is thus important to better understand how to stabilize carbene species in enzyme active sites without metal ions. Motivated by our recent studies of the anaerobic ergothioneine biosynthesis enzyme EanB, we examine carbene–protein interaction with both cluster models and QM/MM simulations. The cluster calculations find that an N-heterocyclic carbene interacts strongly with polar and positively charged protein motifs. In particular, the interaction between a guanidinium group and carbene is as strong as ∼30 kcal/mol, making arginine a great choice for the preferential stabilization of carbenes. We also compare the WT EanB and its mutant in which the key tyrosine was replaced by a non-natural analogue (F2Tyr) using DFTB3/MM simulations. The calculations suggest that the carbene intermediate in the F2Tyr mutant is more stable than that in the WT enzyme by ∼3.5 kcal/mol, due to active site rearrangements that enable a nearby arginine to better stabilize the carbene in the mutant. Overall, the current work lays the foundation for the pursuit of enzyme designs that can take advantage of the unique chemistry offered by carbenes without the requirement of metal ions

Promoting Modes and Demoting Modes in Enzyme-Catalyzed Proton Transfer Reactions: A Study of Models and Realistic Systems

A number of proton transfer reactions have been studied to reveal the identity of modes that influence the rate constant, especially in the context of enzyme catalysis. Results with analytic model potentials confirmed the general notion that the effect of a given mode on the proton transfer rate depends on the symmetry of its coupling with the proton transfer coordinate. Symmetrically coupled modes have promoting effects at both high and low temperatures, although the origin of promotion is largely classical at room temperature and the increase of tunneling is important only at low temperature. Antisymmetric modes have “demoting effects” mainly because the antisymmetric coupling gives rise to asymmetry in the effective potential along the proton transfer coordinate and therefore restricts tunneling to occur effectively only when the mode is vibrationally excited. Thus, vibrational excitation of both types of modes can be important for the proton transfer rate. Calculations on TIM with a QM/MM potential clearly demonstrated that the proton transfer is strongly coupled to a large number of vibrations (including both symmetric and antisymmetric modes), which in general are localized to atoms in the active site. One of the modes is the donor−acceptor stretch, which modulates the effective barrier for the proton transfer and also the effect of tunneling. There are also other modes that are symmetrically or antisymmetrically coupled to the proton-transfer coordinate, and they involve nearby residues such as Ala 212 and Ile 170. Their effect is to adjust the enzyme environment by lowering the effective proton-transfer barrier. We propose procedures to identify motions that are important for the proton transfer based on reaction path curvature and coupling coefficients. We also emphasize that the minimum energy path (MEP) involves changes in environmental variables, such as the donor−acceptor stretch, as the primary part in the reactant and product regions and includes significant proton motion only near the barrier. Thus, there is no fundamental conflict between the MEP description of proton transfers at room temperature and Marcus type of models in the adiabatic regime; that is, both include contributions from change in the zero-point energies

Quantum Mechanics/Molecular Mechanics Studies of Triosephosphate Isomerase-Catalyzed Reactions: Effect of Geometry and Tunneling on Proton-Transfer Rate Constants

The role of tunneling for two proton-transfer steps in the reactions catalyzed by triosephosphate isomerase (TIM) has been studied. One step is the rate-limiting proton transfer from Cα in the substrate to Glu 165, and the other is an intrasubstrate proton transfer proposed for the isomerization of the enediolate intermediate. The latter, which is not important in the wild-type enzyme but is a useful model system because of its simplicity, has also been examined in the gas phase and in solution. Variational transition-state theory with semiclassical ground-state tunneling was used for the calculation with potential energy surface determined by an AM1 method specifically parametrized for the TIM system. The effect of tunneling on the reaction rate was found to be less than a factor of 10 at room temperature; the tunneling becomes more important at lower temperature, as expected. The imaginary frequency (barrier) mode and modes that have large contributions to the reaction path curvature are localized on the atoms in the active site, within 4 Å of the substrate. This suggests that only a small number of atoms that are close to the substrate and their motions (e.g., donor−acceptor vibration) directly determine the magnitude of tunneling. Atoms that are farther away influence the effect of tunneling indirectly by modulating the energetics of the proton transfer. For the intramolecular proton transfer, tunneling was found to be most important in the gas phase, to be similar in the enzyme, and to be the smallest in water. The major reason for this trend is that the barrier frequency is substantially lower in solution than in the gas phase and enzyme; the broader solution barrier is caused by the strong electrostatic interaction between the highly charged solute and the polar solvent molecules. Analysis of isotope effects showed that the conventional Arrenhius parameters are more useful as experimental criteria for determining the magnitude of tunneling than the widely used Swain−Schaad exponent (SSE). For the primary SSE, although values larger than the transition-state theory limit (3.3) occur when tunneling is included, there is no clear relationship between the calculated magnitudes of tunneling and the SSE. Also, the temperature dependence of the primary SSE is rather complex; the value of SSE tends to decrease as the temperature is lowered (i.e., when tunneling becomes more significant). For the secondary SSE, the results suggest that it is more relevant for evaluating the “coupled motion” between the secondary hydrogen and the reaction coordinate than the magnitude of tunneling. Although tunneling makes a significant contribution to the rate of proton transfer, it appears not to be a major aspect of the catalysis by TIM at room temperature; i.e., the tunneling factor of 10 is “small” relative to the overall rate acceleration by 109. For the intramolecular proton transfer, the tunneling in the enzyme is larger by a factor of 5 than in solution

Coacervation-Induced Remodeling of Nanovesicles

Intrinsically disordered peptides can form biomolecular condensates through liquid–liquid phase separation. These condensates play diverse roles in cells, including inducing large-scale changes in membrane morphology. Here we employ coarse-grained molecular dynamics simulations to identify the most salient physical principles that govern membrane remodeling by condensates. By systematically varying the interaction strengths among the polymers and lipids in our coarse-grained model, we are able to recapitulate various membrane transformations observed in different experiments. Endocytosis and exocytosis of the condensate are observed when the interpolymeric attraction is stronger than polymer–lipid interaction. We find a critical size of the condensate required to exhibit successful endocytosis. Multilamellarity and local gelation are observed when the polymer–lipid attraction is significantly stronger than the interpolymeric attraction. Our insights provide essential guidance to the design of (bio)polymers for the manipulation of membrane morphology in various applications such as drug delivery and synthetic biology