A quantum chemical method for rapid optimization of protein structures

Quantum Chemical Calculation of Molecular and Periodic Peptide and Protein Structures

Special-purpose classical force fields (FFs) provide good accuracy at very low computational cost, but their application is limited to systems for which potential energy functions are available. This excludes most metal-containing proteins or those containing cofactors. In contrast, the GFN2-xTB semiempirical quantum chemical method is parametrized for almost the entire periodic table. The accuracy of GFN2-xTB is assessed for protein structures with respect to experimental X-ray data. Furthermore, the results are compared with those of two special-purpose FFs, HF-3c, PM6-D3H4X, and PM7. The test sets include proteins without any prosthetic groups as well as metalloproteins. Crystal packing effects are examined for a set of smaller proteins to validate the molecular approach. For the proteins without prosthetic groups, the special purpose FF OPLS-2005 yields the smallest overall RMSD to the X-ray data but GFN2-xTB provides similarly good structures with even better bond-length distributions. For the metalloproteins with up to 5000 atoms, a good overall structural agreement is obtained with GFN2-xTB. The full geometry optimizations of protein structures with on average 1000 atoms in wall-times below 1 day establishes the GFN2-xTB method as a versatile tool for the computational treatment of various biomolecules with a good accuracy/computational cost ratio.

Multilevel X-Pol: a fragment-based method with mixed quantum mechanical representations of different fragments

The explicit polarization (X-Pol) method is a fragment-based quantum mechanical model, in which a macromolecular system or other large or complex system in solution is partitioned into monomeric fragments. The present study extends the original X-Pol method, where all fragments are treated using the same electronic structure theory, to multilevel representations, called multilevel X-Pol, in which different electronic structure methods are used to describe different fragments. The multilevel X-Pol method has been implemented into a locally modified version of Gaussian 09. A key ingredient that is used to couple interfragment electrostatic interactions at different levels of theory is the use of the response density for the post-self-consistent-field energy. (The response density is also called the generalized density.) The method is useful for treating fragments in a small region of the system such as a solute molecule or the substrate and amino acids in the active site of an enzyme with a high-level theory, and the fragments in the rest of the system by a lower-level and computationally more efficient method. Multilevel X-Pol is illustrated here by applications to hydrogen bonding complexes in which one fragment is treated with the hybrid M06 density functional, Møller-Plesset perturbation theory, or coupled cluster theory, and the other fragments are treated by Hartree-Fock theory or the B3LYP or M06 hybrid density functionals.

Structural evolution of protein-biofilms: Simulations and experiments

The control of biofilm formation is a challenging goal that has not been reached yet in many aspects. One unsolved question is the role of van der Waals forces and another is the importance of mutual interactions between the adsorbing and the adsorbed biomolecules ("critical crowding"). In this study, a combined experimental and theoretical approach is presented, which fundamentally probes both aspects. On three model proteins-lysozyme, α-amylase, and bovine serum albumin-the adsorption kinetics is studied experimentally. Composite substrates are used enabling a separation of the short- and the long-range forces. Although usually neglected, experimental evidence is given for the influence of van der Waals forces on the protein adsorption as revealed by in situ ellipsometry. The three proteins were chosen for their different conformational stabilities in order to investigate the influence of conformational changes on the adsorption kinetics. Monte Carlo simulations are used to develop a model for these experimental results by assuming an internal degree of freedom to represent conformational changes. The simulations also provide data on the distribution of adsorption sites. By in situ atomic force microscopy we can also test this distribution experimentally, which opens the possibility to, e.g., investigate the interactions between adsorbed proteins.

An insight into the general relationship between the three dimensional structures of enzymes and their electronic wave functions: Implication for the prediction of functional sites of enzymes

In this study, we explored the general relationship between the three-dimensional (3D) structures of enzymes and their electronic wave functions. Furthermore, we developed a method for the prediction of their functionally important sites. For this purpose, we first performed linear-scaling molecular orbital calculations for 112 nonredundant, non-homologous enzymes with known structure and function. In consequence, we showed that the canonical molecular orbitals (MOs) of the enzymes could be classified into three groups according to the degree of electron delocalization: highly localized orbitals (Group A), highly delocalized orbitals whose electrons are distributed over almost the whole molecule (Group B), and moderately delocalized orbitals (Group C). The MOs belonging to Group A are located near the HOMO-LUMO band gap, and thereby include the frontier orbitals of a given enzyme. We inferred that the MOs of Group B play a role in stabilizing the 3D structure of the enzyme, while those of Group C contribute to constructing the covalent bond framework of the enzyme. Next, we investigated whether the frontier orbitals of enzymes could be used for identifying their potential functional sites. As a result, we found that the frontier orbitals of the 112 enzymes have a high propensity to be colocalized with the known functional sites, especially when the enzymes are hydrated. Such a propensity is shown to be remarkable when Glu or Asp is a functional site residue. On the basis of these results, we finally propose a protocol for the prediction of functional sites of enzymes.

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.

Linear-scaling molecular orbital calculations for the pKa values of ionizable residues in proteins

In this report, we present a computational methodology for the pKa prediction of proteins, based on linear-scaling molecular orbital calculations for their solution-conformations obtained from NMR measurements. The method is used to predict the pKa values of five carboxylic acids (Asp7, Glu10, Glu19, Asp27, and Glu43) in turkey ovomucoid third domain (OMTKY3), and six aspartates residues (Asp 22, Asp 44, Asp 54, Asp 75, Asp 83, and Asp 93) in barnase. For OMTKY3, all the predicted pKa values are within 1 pH units from the available experimental ones, except for the case of Glu 43. For barnase, the root-mean-square deviation from experiment is 1.46 pH units. As a result, the proposed pKa calculation method correctly reproduces the relative order of the pKa values among the carboxylic acids located in different sites of the proteins. The calculated pKa values are decomposed into the contributions of short- and long-range structural difference effects. The results indicate that in both proteins the pKa value of the given carboxylic acid is partially influenced by long-range interactions with distant charged residues, which significantly contribute to determining the relative order of the pKa values. The current methodology based on LSMO provides us useful information about the titration behavior in a protein.

Ab initio QM/MM modelling of acetyl-CoA deprotonation in the enzyme citrate synthase

The first step of the reaction catalysed by the enzyme citrate synthase is studied here with high level combined quantum mechanical/molecular mechanical (QM/MM) methods (up to the MP2/6-31+G(d)//6-31G(d)/CHARMM level). In the first step of the reaction, acetyl-CoA is deprotonated by Asp375, producing an intermediate, which is the nucleophile for attack on the second substrate, oxaloacetate, prior to hydrolysis of the thioester bond of acetyl-CoA and release of the products. A central question has been whether the nucleophilic intermediate is the enolate of acetyl-CoA, the enol, or an 'enolic' intermediate stabilized by a 'low-barrier' hydrogen bond with His274 at the active site. The imidazole sidechain of His274 is neutral, and donates a hydrogen bond to the carbonyl oxygen of acetyl-CoA in substrate complexes. We have investigated the identity of the nucleophilic intermediate by QM/MM calculations on the substrate (keto), enolate, enol and enolic forms of acetyl-CoA at the active site of citrate synthase. The transition states for proton abstraction from acetyl-CoA by Asp375, and for transfer of the hydrogen bonded proton between His274 and acetyl-CoA have been modelled approximately. The effects of electron correlation are included by MP2/6-31G(d) and MP2/6-31+G(d) calculations on active site geometries produced by QM/MM energy minimization. The results do not support the hypothesis that a low-barrier hydrogen bond is involved in catalysis in citrate synthase, in agreement with earlier calculations. The acetyl-CoA enolate is identified as the only intermediate consistent with the experimental barrier for condensation, stabilized by conventional hydrogen bonds from His274 and a water molecule.

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.

Density-functional geometry optimization of the 150 000-atom photosystem-I trimer

We present a linear-scaling method based on the use of density-functional theory (DFT) for the system-wide optimization of x-ray structural coordinates and apply it to optimize the 150,000 atoms of the photosystem-I (PS-I) trimer. The method is based on repetitive applications of a multilevel ONIOM procedure using the PW916-31G(d) DFT calculations for the high level and PM3 for the lower level; this method treats all atoms in the structure equivalently, a structure in which the majority of the atoms can be considered as part of some internal "active site." To obtain a realistic single structure, some changes to the original protein model were necessary but these are kept to a minimum in order that the optimized structure most closely resembles the original x-ray one. Optimization has profound effects on the perceived electronic properties of the cofactors, with, e.g., optimization lowering the internal energy of the chlorophylls by on average 53 kcal mol(-1) and eliminates the enormous 115 kcal mol(-1) energy spread depicted by the original x-ray heavy-atom coordinates. A highly precise structure for PS-I results that is suitable for analysis of device function. Significant qualitative features of the structure are also improved such as correction of an error in the stereochemistry of one of the chlorophylls in the "special pair" of the reaction center, as well as the replacement of a water molecule with a metal cation in a critical region on the C3 axis. The method also reveals other unusual features of the structure, leading both to suggestions concerning device functionality and possible mutations between gene sequencing and x-ray structure determination. The optimization scheme is thus shown to augment the molecular modeling schemes that are currently used to add medium-resolution structural information to the raw scattering data in order to obtain atomically resolved structures. System-wide optimization is now a feasible process and its use within protein x-ray data refinement should be considered.