All Electron Quantum Chemical Calculation of the Entire Enzyme System Confirms a Collective Catalytic Device in the Chorismate Mutase Reaction

Free Energy Profile Decomposition Analysis for QM/MM Simulations of Enzymatic Reactions

In enzyme mechanistic studies and mutant design, it is highly desirable to know the individual residue contributions to the reaction free energy and barrier. In this work, we show that such free energy contributions from each residue can be readily obtained by postprocessing ab initio quantum mechanical molecular mechanical (ai-QM/MM) free energy simulation trajectories. Specifically, through a mean force integration along the minimum free energy pathway, one can obtain the electrostatic, polarization, and van der Waals contributions from each residue to the free energy barrier. Separately, a similar analysis procedure allows us to assess the contribution from different collective variables along the reaction coordinate. The chorismate mutase reaction is used to demonstrate the utilization of these two trajectory analysis tools.

Computational analysis of carbohydrate recognition based on hybrid QM/MM modeling: a case study of norovirus capsid protein in complex with Lewis antigen

Norovirus is a major pathogen of nonbacterial acute gastroenteritis in humans and animals. Carbohydrate recognition between norovirus capsid proteins and Lewis antigens is considered to play a critical role in initiating infection of eukaryotic cells. In this article, we first report a detailed atomistic simulation study of the norovirus capsid protein in complex with the Lewis antigen based on ab initio QM/MM combined with MD-FEP simulations. To understand the mechanistic details of ligand binding, we analyzed and compared the carbohydrate recognition mechanism of the wild-type P domain protein with a mutant protein. Small structural differences between two capsid proteins are observed on the weak interaction site of residue 389, which is located on the solvent exposed surface of the P domain. To further clarify affinity differences in ligand binding, we directly evaluated free energy changes of the ligand binding process. Although the mutant protein loses its interaction energy with the Lewis antigen, this small amount of energy penalty is compensated for by an increase in the solvation stability, which is induced by structural reorganization at the ligand binding site on the protein surface. As a sum of these opposite energy components, the mutant P domain obtains a slightly enhanced binding affinity for the Lewis antigen. The present computational study clearly demonstrated that a detailed free energy balance of the interaction energy between the capsid protein and the surrounding aqueous solvent is the mechanistic basis of carbohydrate recognition in the norovirus capsid protein.

Analysis of Different Fragmentation Strategies on a Variety of Large Peptides: Implementation of a Low Level of Theory in Fragment-Based Methods Can Be a Crucial Factor

We have investigated the performance of two classes of fragmentation methods developed in our group (Molecules-in-Molecules (MIM) and Many-Overlapping-Body (MOB) expansion), to reproduce the unfragmented MP2 energies on a test set composed of 10 small to large biomolecules. They have also been assessed to recover the relative energies of different motifs of the acetyl(ala)18NH2 system. Performance of different bond-cutting environments and the use of Hartree-Fock and different density functionals (as a low level of theory) in conjunction with the fragmentation strategies have been analyzed. Our investigation shows that while a low level of theory (for recovering long-range interactions) may not be necessary for small peptides, it provides a very effective strategy to accurately reproduce the total and relative energies of larger peptides such as the different motifs of the acetyl(ala)18NH2 system. Employing M06-2X as the low level of theory, the calculated mean total energy deviation (maximum deviation) in the total MP2 energies for the 10 molecules in the test set at MIM(d=3.5Å), MIM(η=9), and MOB(d=5Å) are 1.16 (2.31), 0.72 (1.87), and 0.43 (2.02) kcal/mol, respectively. The excellent performance suggests that such fragment-based methods should be of general use for the computation of accurate energies of large biomolecular systems.

Hybrid RHF/MP2 geometry optimizations with the effective fragment molecular orbital method

The frozen domain effective fragment molecular orbital method is extended to allow for the treatment of a single fragment at the MP2 level of theory. The approach is applied to the conversion of chorismate to prephenate by Chorismate Mutase, where the substrate is treated at the MP2 level of theory while the rest of the system is treated at the RHF level. MP2 geometry optimization is found to lower the barrier by up to 3.5 kcal/mol compared to RHF optimzations and ONIOM energy refinement and leads to a smoother convergence with respect to the basis set for the reaction profile. For double zeta basis sets the increase in CPU time relative to RHF is roughly a factor of two.

Exploration of swapping enzymatic function between two proteins: a simulation study of chorismate mutase and isochorismate pyruvate lyase

The enzyme chorismate mutase EcCM from Escherichia coli catalyzes one of the few pericyclic reactions in biology, the transformation of chorismate to prephenate. The isochorismate pyruvate lyase PchB from Pseudomonas aeroginosa catalyzes another pericyclic reaction, the isochorismate to salicylate transformation. Interestingly, PchB possesses weak chorismate mutase activity as well thus being able to catalyze two distinct pericyclic reactions in a single active site. EcCM and PchB possess very similar folds, despite their low sequence identity. Using molecular dynamics simulations of four combinations of the two enzymes (EcCM and PchB) with the two substrates (chorismate and isochorismate) we show that the electrostatic field due to EcCM at atoms of chorismate favors the chorismate to prephenate transition and that, analogously, the electrostatic field due to PchB at atoms of isochorismate favors the isochorismate to salicylate transition. The largest differences between EcCM and PchB in electrostatic field strengths at atoms of the substrates are found to be due to residue side chains at distances between 0.6 and 0.8 nm from particular substrate atoms. Both enzymes tend to bring their non-native substrate in the same conformation as their native substrate. EcCM and to a lower extent PchB fail in influencing the forces on and conformations of the substrate such as to favor the other chemical reaction (isochorismate pyruvate lyase activity for EcCM and chorismate mutase activity for PchB). These observations might explain the difficulty of engineering isochorismate pyruvate lyase activity in EcCM by solely mutating active site residues.

Mapping enzymatic catalysis using the effective fragment molecular orbital method: towards all ab initio biochemistry

We extend the Effective Fragment Molecular Orbital (EFMO) method to the frozen domain approach where only the geometry of an active part is optimized, while the many-body polarization effects are considered for the whole system. The new approach efficiently mapped out the entire reaction path of chorismate mutase in less than four days using 80 cores on 20 nodes, where the whole system containing 2398 atoms is treated in the ab initio fashion without using any force fields. The reaction path is constructed automatically with the only assumption of defining the reaction coordinate a priori. We determine the reaction barrier of chorismate mutase to be kcal mol⁻¹ for MP2/cc-pVDZ and for MP2/cc-pVTZ in an ONIOM approach using EFMO-RHF/6-31G(d) for the high and low layers, respectively.

Analysis of chorismate mutase catalysis by QM/MM modelling of enzyme-catalysed and uncatalysed reactions

Chorismate mutase is at the centre of current controversy about fundamental features of biological catalysts. Some recent studies have proposed that catalysis in this enzyme does not involve transition state (TS) stabilization but instead is due largely to the formation of a reactive conformation of the substrate. To understand the origins of catalysis, it is necessary to compare equivalent reactions in different environments. The pericyclic conversion of chorismate to prephenate catalysed by chorismate mutase also occurs (much more slowly) in aqueous solution. In this study we analyse the origins of catalysis by comparison of multiple quantum mechanics/molecular mechanics (QM/MM) reaction pathways at a reliable, well tested level of theory (B3LYP/6-31G(d)/CHARMM27) for the reaction (i) in Bacillus subtilis chorismate mutase (BsCM) and (ii) in aqueous solvent. The average calculated reaction (potential energy) barriers are 11.3 kcal mol(-1) in the enzyme and 17.4 kcal mol(-1) in water, both of which are in good agreement with experiment. Comparison of the two sets of reaction pathways shows that the reaction follows a slightly different reaction pathway in the enzyme than in it does in solution, because of a destabilization, or strain, of the substrate in the enzyme. The substrate strain energy within the enzyme remains constant throughout the reaction. There is no unique reactive conformation of the substrate common to both environments, and the transition state structures are also different in the enzyme and in water. Analysis of the barrier heights in each environment shows a clear correlation between TS stabilization and the barrier height. The average differential TS stabilization is 7.3 kcal mol(-1) in the enzyme. This is significantly higher than the small amount of TS stabilization in water (on average only 1.0 kcal mol(-1) relative to the substrate). The TS is stabilized mainly by electrostatic interactions with active site residues in the enzyme, with Arg90, Arg7 and Glu78 generally the most important. Conformational effects (e.g. strain of the substrate in the enzyme) do not contribute significantly to the lower barrier observed in the enzyme. The results show that catalysis is mainly due to better TS stabilization by the enzyme.

Protein dynamics and enzyme catalysis: insights from simulations

The role of protein dynamics in enzyme catalysis is one of the most active and controversial areas in enzymology today. Some researchers claim that protein dynamics are at the heart of enzyme catalytic efficiency, while others state that dynamics make no significant contribution to catalysis. What is the biochemist - or student - to make of the ferocious arguments in this area? Protein dynamics are complex and fascinating, as molecular dynamics simulations and experiments have shown. The essential question is: do these complex motions have functional significance? In particular, how do they affect or relate to chemical reactions within enzymes, and how are chemical and conformational changes coupled together? Biomolecular simulations can analyse enzyme reactions and dynamics in atomic detail, beyond that achievable in experiments: accurate atomistic modelling has an essential part to play in clarifying these issues. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.

QM/MM methods for biomolecular systems

Combined quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomolecular systems. Quantum-mechanical (QM) methods are required for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based molecular mechanics (MM) methods. Thus to model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region (e.g., substrates and co-factors in an enzymatic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.

Extending the Power of Quantum Chemistry to Large Systems with the Fragment Molecular Orbital Method

Following the brief review of the modern fragment-based methods and other approaches to perform quantum-mechanical calculations of large systems, the theoretical development of the fragment molecular orbital method (FMO) is covered in detail, with the emphasis on the physical properties, which can be computed with FMO. The FMO-based polarizable continuum model (PCM) for treating the solvent effects in large systems and the pair interaction energy decomposition analysis (PIEDA) are described in some detail, and a range of applications of FMO to biological studies is introduced. The factors determining the relative stability of polypeptide conformers (alpha-helix, beta-turn, and extended form) are elucidated using FMO/PCM and PIEDA, and the interactions in the Trp-cage miniprotein construct (PDB: 1L2Y) are analyzed using PIEDA.

DNA and Estrogen Receptor Interaction Revealed by Fragment Molecular Orbital Calculations

Molecular orbital calculations of the complex between DNA-ERE (estrogen response element) and ER (estrogen receptor)-DBD (DNA-binding domain) were performed using the fragment molecular orbital (FMO) method, which enables large-scale MO (molecular orbital) calculations by reducing the computational cost and by significantly increasing efficiency for parallel computation. Such a large system, which contains 3354 atoms, is impractical via conventional MO methods due to the immense computational cost. Details of the interaction between DNA-ERE and ER-DBD were revealed in this study as follows by using the FMO calculations to analyze the interfragment interaction energies (IFIEs) and the electrostatic potentials (ESPs). An area with a high positive ESP is identified on the DNA-binding side of ER-DBD and is the main driving force behind access to the DNA. The position of the ER-DBD monomer can be fixed on a phosphate group of DNA-ERE by the strong electrostatic interactions, whereas the rotation cannot be fixed. In contrast, both the position and rotation of the ER-DBD dimer can be fixed and can therefore form the stable (ER-DBD)2...DNA-ERE complex. Dimerization of the ER-DBD monomers, each of which have a charge of +5 , is mainly due to large attractive interaction energies of the second Zn fragments. The base pairs in the consensus sequence of DNA-ERE interact only with the recognition helix located in the major groove due to the large shielding effect of the phosphate groups of DNA. The recognition helix has weaker interactions with the base pairs than the electrostatic interactions with the phosphate groups. Thus, the DNA-binding machinery of the ER-DBD dimer, which can secure the recognition helix in the major groove of DNA, is crucial for interactions between the recognition helix and base pairs.

Accuracy of the three-body fragment molecular orbital method applied to Møller-Plesset perturbation theory

The three-body energy expansion in the fragment molecular orbital method (FMO) was applied to the 2nd order Møller-Plesset theory (MP2). The accuracy of both the two and three-body expansions was determined for water clusters, alanine n-mers (alpha-helices and beta-strands) and one synthetic protein, using the 6-31G* and 6-311G* basis sets. At the best level of theory (three-body, two molecules/residues per fragment), the absolute errors in energy relative to ab initio MP2 were at most 1.2 and 5.0 mhartree, for the 6-31G* and 6-311G* basis sets, respectively. The relative accuracy was at worst 99.996% and 99.96%, for 6-31G* and 6-311G*, respectively. A three-body approximation was introduced and the optimum threshold value was determined. The protein calculation (6-31G*) at the production level (FMO2/2) took 3 h on 36 3.2-GHz Pentium 4 nodes and had the absolute error in the MP2 correlation energy of only 2 kcal/mol.

Exhaustive Mutagenesis of Six Secondary Active-Site Residues in Escherichia coli Chorismate Mutase Shows the Importance of Hydrophobic Side Chains and a Helix N-Capping Position for Stability and Catalysis

Secondary active-site residues in enzymes, including hydrophobic amino acids, may contribute to catalysis through critical interactions that position the reacting molecule, organize hydrogen-bonding residues, and define the electrostatic environment of the active site. To ascertain the tolerance of an important model enzyme to mutation of active-site residues that do not directly hydrogen bond with the reacting molecule, all 19 possible amino acid substitutions were investigated in six positions of the engineered chorismate mutase domain of the Escherichia coli chorismate mutase-prephenate dehydratase. The six secondary active-site residues were selected to clarify results of a previous test of computational enzyme design procedures. Five of the positions encode hydrophobic side chains in the wild-type enzyme, and one forms a helix N-capping interaction as well as a salt bridge with a catalytically essential residue. Each mutant was evaluated for its ability to complement an auxotrophic chorismate mutase deletion strain. Kinetic parameters and thermal stabilities were measured for variants with in vivo activity. Altogether, we find that the enzyme tolerated 34% of the 114 possible substitutions, with a few mutations leading to increases in the catalytic efficiency of the enzyme. The results show the importance of secondary amino acid residues in determining enzymatic activity, and they point to strengths and weaknesses in current computational enzyme design procedures.

Molecular recognition mechanism of FK506 binding protein: An all-electron fragment molecular orbital study

The fragment molecular orbital (FMO) method has enabled electronic structure calculations and geometry optimizations of very large molecules with ab initio quality. We applied the method to four FK506 binding protein (FKBP) complexes (denoted by their PDB codes 1fkb, 1fkf, 1fkg, and 1fki) containing rapamycin, FK506, and two synthetic ligands. The geometries of reduced complex models were optimized at the restricted Hartree-Fock (FMO-RHF) level using the 3-21G basis set, and then for a better estimate of binding, the energetics were refined at a higher level of theory (2nd order Møller-Plesset perturbation theory FMO-MP2 with the 6-31G* basis set). Thus, obtained binding energies were -103.9 (-82.0), -102.2 (-69.2), -70.1 (-57.7), and -71.3 (-55.3) kcal/mol for 1fkb, 1fkf, 1fkg, and 1fki, respectively, where the correlation contribution is given in parentheses. The results show that the electron correlation contribution to binding is extremely important, and it accounts for 70-80% of the binding energy. The molecular recognition mechanism of FKBP was analyzed in detail based on the FMO-pair interactions between protein residues and the ligands. Solvation effects on the protein-ligand binding were estimated using the Poisson-Boltzmann/surface area model.

The Fragment Molecular Orbital Method for Geometry Optimizations of Polypeptides and Proteins

The fragment molecular orbital method (FMO) has been used with a large number of wave functions for single-point calculations, and its high accuracy in comparison to ab initio methods has been well established. We have developed the analytic derivative of the electrostatic interaction between far separated fragments and performed a number of restricted Hartree-Fock (RHF) geometry optimizations using FMO and ab initio methods. In particular, the alpha-helix, beta-turn, and extended conformers of a 10-residue polyalanine were studied and the good FMO accuracy was established (the rms deviations for the former two forms were about 0.2 A and for the latter structure about 0.001 A). Met-enkephalin dimer was used as a model for the polypeptide binding and computed at the 3-21G and 6-31G* levels with a similar accuracy achieved; the error in the binding energy predictions (FMO vs ab initio) was 1-3 kcal/mol. Chignolin (PDB: 1uao) and an agonist polypeptide of the erythropoietin receptor protein (emp1) were optimized at the 3-21(+)G level, with the rms deviation from ab initio of about 0.2 A, or 0.5 degrees in terms of bond angles. The effect of solvation on the structure optimization was studied in chignolin and the Trp-cage miniprotein construct (PDB:1l2y), by describing water with TIP3P. The computed structures in gas phase and solution are compared to each other and experiment.

Change in a protein's electronic structure induced by an explicit solvent: Anab initio fragment molecular orbital study of ubiquitin

The effect of solvation on the electronic structure of the ubiquitin protein was analyzed using the ab initio fragment molecular orbital (FMO) method. FMO calculations were performed for the protein in vacuo, and the protein was immersed in an explicit solvent shell as thick as 12 A at the HF or MP2 level by using the 6-31G* basis set. The protein's physical properties examined were the net charge, the dipole moment, the internal energy, and the solvent interaction energy. Comparison of the computational results revealed the following changes in the protein upon solvation. First, the positively charged amino acid residues on the protein surface drew electrons from the solvent, while the negatively charged ones transfer electrons to the solvent. Second, the dipole moment of the protein was enhanced as a result of the polarization. Third, the internal energy of the protein was destabilized, but the destabilization was more than compensated for by the generation of a favorable protein-solvent interaction. Finally, the energetic changes were elicited both by the electron correlation effect of the first solvent shell and by the electrostatic effect of more distant solvent molecules. These findings were consistent with the picture of the solvated protein being a polarizable molecule dissolved in a dielectric media.

Accurate metal-site structures in proteins obtained by combining experimental data and quantum chemistry

The use of molecular mechanics calculations to supplement experimental data in standard X-ray crystallography and NMR refinements is discussed and it is shown that structures can be locally improved by the use of quantum chemical calculations. Such calculations can also be used to interpret the structures, e.g. to decide the protonation state of metal-bound ligands. They have shown that metal sites in crystal structures are frequently photoreduced or disordered, which makes the interpretation of the structures hard. Similar methods can be used for EXAFS refinements to obtain a full atomic structure, rather than a set of metal-ligand distances.

Factors influencing the energetics of electron and proton transfers in proteins. What can be learned from calculations

A protein structure should provide the information needed to understand its observed properties. Significant progress has been made in developing accurate calculations of acid/base and oxidation/reduction reactions in proteins. Current methods and their strengths and weaknesses are discussed. The distribution and calculated ionization states in a survey of proteins is described, showing that a significant minority of acidic and basic residues are buried in the protein and that most of these remain ionized. The electrochemistry of heme and quinones are considered. Proton transfers in bacteriorhodopsin and coupled electron and proton transfers in photosynthetic reaction centers, 5-coordinate heme binding proteins and cytochrome c oxidase are highlighted as systems where calculations have provided insight into the reaction mechanism.

Pair interaction energy decomposition analysis

The energy decomposition analysis (EDA) by Kitaura and Morokuma was redeveloped in the framework of the fragment molecular orbital method (FMO). The proposed pair interaction energy decomposition analysis (PIEDA) can treat large molecular clusters and the systems in which fragments are connected by covalent bonds, such as proteins. The interaction energy in PIEDA is divided into the same contributions as in EDA: the electrostatic, exchange-repulsion, and charge transfer energies, to which the correlation (dispersion) term was added. The careful comparison to the ab initio EDA interaction energies for water clusters with 2-16 molecules revealed that PIEDA has the error of at most 1.2 kcal/mol (or about 1%). The analysis was applied to (H2O)1024, the alpha helix, beta turn, and beta strand of polyalanine (ALA)10, as well as to the synthetic protein (PDB code 1L2Y) with 20 residues. The comparative aspects of the polypeptide isomer stability are discussed in detail.