An Ab Initio QM/MM Study of the Electrostatic Contribution to Catalysis in the Active Site of Ketosteroid Isomerase

Critical Evaluation of Polarizable and Nonpolarizable Force Fields for Proteins Using Experimentally Derived Nitrile Electric Fields

Molecular dynamics (MD) simulations are frequently carried out for proteins to investigate the role of electrostatics in their biological function. The choice of force field (FF) can significantly alter the MD results, as the simulated local electrostatic interactions lack benchmarking in the absence of appropriate experimental methods. We recently reported that the transition dipole moment (TDM) of the popular nitrile vibrational probe varies linearly with the environmental electric field, overcoming well-known hydrogen bonding (H-bonding) issues for the nitrile frequency and, thus, enabling the unambiguous measurement of electric fields in proteins (J. Am. Chem. Soc. 2022, 144 (17), 7562-7567). Herein, we utilize this new strategy to enable comparisons of experimental and simulated electric fields in protein environments. Specifically, previously determined TDM electric fields exerted onto nitrile-containing o-cyanophenylalanine residues in photoactive yellow protein are compared with MD electric fields from the fixed-charge AMBER FF and the polarizable AMOEBA FF. We observe that the electric field distributions for H-bonding nitriles are substantially affected by the choice of FF. As such, AMBER underestimates electric fields for nitriles experiencing moderate field strengths; in contrast, AMOEBA robustly recapitulates the TDM electric fields. The FF dependence of the electric fields can be partly explained by the presence of additional negative charge density along the nitrile bond axis in AMOEBA, which is due to the inclusion of higher-order multipole parameters; this, in turn, begets more head-on nitrile H-bonds. We conclude by discussing the implications of the FF dependence for the simulation of nitriles and proteins in general.

From random to rational: improving enzyme design through electric fields, second coordination sphere interactions, and conformational dynamics

Enzymes are versatile and efficient biological catalysts that drive numerous cellular processes, motivating the development of enzyme design approaches to tailor catalysts for diverse applications. In this perspective, we investigate the unique properties of natural, evolved, and designed enzymes, recognizing their strengths and shortcomings. We highlight the challenges and limitations of current enzyme design protocols, with a particular focus on their limited consideration of long-range electrostatic and dynamic effects. We then delve deeper into the impact of the protein environment on enzyme catalysis and explore the roles of preorganized electric fields, second coordination sphere interactions, and protein dynamics for enzyme function. Furthermore, we present several case studies illustrating successful enzyme-design efforts incorporating enzyme strategies mentioned above to achieve improved catalytic properties. Finally, we envision the future of enzyme design research, spotlighting the challenges yet to be overcome and the synergy of intrinsic electric fields, second coordination sphere interactions, and conformational dynamics to push the state-of-the-art boundaries.

Assessment of an Electrostatic Energy-Based Charge Model for Modeling the Electrostatic Interactions in Water Solvent

The protein force field based on the restrained electrostatic potential (RESP) charges has limitations in accurately describing hydrogen bonding interactions in proteins. To address this issue, we propose an alternative approach called the electrostatic energy-based charges (EEC) model, which shows improved performance in describing electrostatic interactions (EIs) of hydrogen bonds in proteins. In this study, we further investigate the performance of the EEC model in modeling EIs in water solvent. Our findings demonstrate that the fixed EEC model can effectively reproduce the quantum mechanics/molecular mechanics (QM/MM)-calculated EIs between a water molecule and various water solvent environments. However, to achieve the same level of computational accuracy, the electrostatic potential (ESP) charge model needs to fluctuate according to the electrostatic environment. Our analysis indicates that the requirement for charge adjustments depends on the specific mathematical and physical representation of EIs as a function of the environment for deriving charges. By comparing with widely used empirical water models calibrated to reproduce experimental properties, we confirm that the performance of the EEC model in reproducing QM/MM EIs is similar to that of general purpose TIP4P-like water models such as TIP4P-Ew and TIP4P/2005. When comparing the computed 10,000 distinct EI values within the range of -40 to 0 kcal/mol with the QM/MM results calculated at the MP2/aug-cc-pVQZ/TIP3P level, we noticed that the mean unsigned error (MUE) for the EEC model is merely 0.487 kcal/mol, which is remarkably similar to the MUE values of the TIP4P-Ew (0.63 kcal/mol) and TIP4P/2005 (0.579 kcal/mol) models. However, both the RESP method and the TIP3P model exhibit a tendency to overestimate the EIs, as evidenced by their higher MUE values of 1.761 and 1.293 kcal/mol, respectively. EEC-based molecular dynamics simulations have demonstrated that, when combined with appropriate van der Waals parameters, the EEC model can closely reproduce oxygen-oxygen radial distribution function and density of water, showing a remarkable similarity to the well-established TIP4P-like empirical water models. Our results demonstrate that the EEC model has the potential to build force fields with comparable accuracy to more sophisticated empirical TIP4P-like water models.

Influence of an Oriented External Electric Field on the Mechanism of Double Proton Transfer between Pyrazole and Guanidine: from an Asynchronous Plateau Transition State to a Synchronous or Stepwise Mechanism

The double proton transfer (DPT) reaction between pyrazole and guanidine, a concerted reaction but strongly asynchronous and presenting a "plateau transition region", has been theoretically reinvestigated in the presence of an external uniform electric field. First, we computed the reaction path by DFT and proposed a very detailed description of the constitutive electronic events, based on the ELF topology and the bond evolution theory. Then, we studied the effect of an oriented external electric field (OEEF) on the reaction mechanism, for an OEEF oriented along the proton transfer axis. We observe that in one direction, the DPT reaction can be transformed into a stepwise reaction, going through a stabilized single proton transferred intermediate. Contrarily, the two proton transfers occur simultaneously when the electric field is applied in the opposite direction. In the latter case, the order in which the two protons are transferred in the same elementary step can even be reversed if the OEEF is intense enough. Finally, it has been shown that the evolution of the double proton transfer reaction in the presence of an electric field could be quantitatively anticipated by analyzing the ELF value at the bifurcation point between V(A, H) proton donor and V(B) proton acceptor of the double hydrogen bonded complex in the entrance channel.

Key difference between transition state stabilization and ground state destabilization: increasing atomic charge densities before or during enzyme–substrate binding

The origin of the enormous catalytic power of enzymes has been extensively studied through experimental and computational approaches. Although precise mechanisms are still subject to much debate, enzymes are thought to catalyze reactions by stabilizing transition states (TSs) or destabilizing ground states (GSs). By exploring the catalysis of various types of enzyme–substrate noncovalent interactions, we found that catalysis by TS stabilization and the catalysis by GS destabilization share common features by reducing the free energy barriers (ΔG^‡s) of reactions, but are different in attaining the requirement for ΔG^‡ reduction. Irrespective of whether enzymes catalyze reactions by TS stabilization or GS destabilization, they reduce ΔG^‡s by enhancing the charge densities of catalytic atoms that experience a reduction in charge density between GSs and TSs. Notably, in TS stabilization, the charge density of catalytic atoms is enhanced prior to enzyme–substrate binding; whereas in GS destabilization, the charge density of catalytic atoms is enhanced during the enzyme–substrate binding. Results show that TS stabilization and GS destabilization are not contradictory to each other and are consistent in reducing the ΔG^‡s of reactions. The full mechanism of enzyme catalysis includes the mechanism of reducing ΔG^‡ and the mechanism of enhancing atomic charge densities. Our findings may help resolve the debate between TS stabilization and GS destabilization and assist our understanding of catalysis and the design of artificial enzymes.

Transition state stabilization and ground state destabilization utilize the same molecular mechanism when lowering the free energy barriers (ΔG^‡s) of reactions, but differ in achieving the requirement for ΔG^‡ reduction.

The Interplay of Electrostatics and Chemical Positioning in the Evolution of Antibiotic Resistance in TEM β-Lactamases

The interplay of enzyme active site electrostatics and chemical positioning is important for understanding the origin(s) of enzyme catalysis and the design of novel catalysts. We reconstruct the evolutionary trajectory of TEM-1 β-lactamase to TEM-52 toward extended-spectrum activity to better understand the emergence of antibiotic resistance and to provide insights into the structure-function paradigm and noncovalent interactions involved in catalysis. Utilizing a detailed kinetic analysis and the vibrational Stark effect, we quantify the changes in rates and electric fields in the Michaelis and acyl-enzyme complexes for penicillin G and cefotaxime to ascertain the evolutionary role of electric fields to modulate function. These data are combined with MD simulations to interpret and quantify the substrate-dependent structural changes during evolution. We observe that this evolutionary trajectory utilizes a large preorganized electric field and substrate-dependent chemical positioning to facilitate catalysis. This governs the evolvability, substrate promiscuity, and protein fitness landscape in TEM β-lactamase antibiotic resistance.

A fixed multi-site interaction charge model for an accurate prediction of the QM/MM interactions

A fixed multi-site interaction charge (FMIC) model was proposed for the accurate prediction of intermolecular electrostatic interactions based on the quantum mechanical linear response of a molecule to an external electric field. In such a model, some additional off-center interaction sites were added for capturing multipole interactions for a given molecule. By multivariate least-square fitting analysis of the calculated QM/MM interactions of a given molecule with the electrostatic environment and the electrostatic potentials of the environment at the pre-defined distributed interaction sites, the FMIC of the molecule was obtained. The model system of CO in myoglobin (Mb) was utilized to demonstrate the derivation of the FMIC. The accuracy of FMIC in predicting the electrostatic interactions between CO and the Mb environment was investigated using 10 000 different Mb-CO configurations generated from the 400 ps QM/MM MD simulation. In comparison to the QM/MM calculations at the B3LYP/aug-cc-pVTZ/ff99SB level, the mean unsigned error (MUE) of the results based on the FMIC model was merely 0.10 kcal mol^-1, and the root mean square error (RMSE) was only 0.13 kcal mol^-1, which are significantly lower than the results predicted by the ESP charge model (MUE = 1.45 kcal mol^-1, and RMSE = 1.7 kcal mol^-1, respectively). The transferability of FMIC was tested by applying the obtained FMIC in the wild type Mb-CO system to the mutants of V68F and H64L Mb-CO systems. The MUEs of the obtained results for 10 000 different configurations are both smaller than 0.2 kcal mol^-1 for the V68F and H64L Mb-CO systems in comparison to the B3LYP/aug-cc-pVTZ/ff99SB calculations, and the RMSEs are also lower than 0.2 kcal mol^-1 for both mutants. The applications of FMIC were extended to model the electrostatic interactions between a hydrogen fluoride molecule and 492 waters in a truncated octahedron box; our study showed that the FMIC could give satisfactory results with a MUE of 0.12 kcal mol^-1 and a RMSE of 0.16 kcal mol^-1 in comparison to the B3LYP/aug-cc-pVDZ/TIP3P calculations for 10 000 different configurations generated using the 10 ns classical MD simulation. Therefore, the FMIC method provides an accurate and efficient tool for predicting intermolecular electrostatic interactions, which can be utilized in the future development of molecular force fields.

An electrostatic energy-based charge model for molecular dynamics simulation

The interactions of the polar chemical bonds such as C=O and N-H with an external electric field were investigated, and a linear relationship between the QM/MM interaction energies and the electric field along the chemical bond is established in the range of weak to intermediate electrical fields. The linear relationship indicates that the electrostatic interactions of a polar group with its surroundings can be described by a simple model of a dipole with constant moment under the action of an electric field. This relationship is employed to develop a general approach to generating an electrostatic energy-based charge (EEC) model for molecules containing single or multiple polar chemical bonds. Benchmark test studies of this model were carried out for (CH₃)₂-CO and N-methyl acetamide in explicit water, and the result shows that the EEC model gives more accurate electrostatic energies than those given by the widely used charge model based on fitting to the electrostatic potential (ESP) in direct comparison to the energies computed by the QM/MM method. The MD simulations of the electric field at the active site of ketosteroid isomerase based on EEC demonstrated that EEC gave a better representation of the electrostatic interaction in the hydrogen-bonding environment than the Amber14SB force field by comparison with experiment. The current study suggests that EEC should be better suited for molecular dynamics study of molecular systems with polar chemical bonds such as biomolecules than the widely used ESP or RESP (restrained ESP) charge models.

The Impact of Electron Correlation on Describing QM/MM Interactions in the Attendant Molecular Dynamics Simulations of CO in Myoglobin

The impact of the dispersion and electron correlation effects on describing quantum mechanics/molecular mechanics (QM/MM) interactions in QM/MM molecular dynamics (MD) simulations was explored by performing a series of up to 2 ns QM/MM MD simulations on the B states of the myoglobin-carbon monoxide (MbCO) system. The results indicate that both dispersion and electron correlations play significant roles in the simulation of the ratios of two B states (B₁/B₂), which suggests that the inclusion of the electron correlation effects is essential for accurately modeling the interactions between QM and MM subsystems. We found that the QM/MM interaction energies between the CO and the surroundings statistically present a linear correlation with the electric fields along the CO bond. This indicates that QM/MM interactions can be described by a simple physical model of a dipole with constant moment under the action of the electric fields. The treatment provides us with an accurate and effective approach to account for the electron correlation effects in QM/MM MD simulations.