Interactions of aromatic radicals with water.

The interactions of the benzyl radical (1), the anilinyl radical (2), and the phenoxyl radical (3) with water are investigated using density functional theory (DFT). In addition, we report dispersion-corrected DFT-D molecular dynamics simulations on these three systems and a matrix isolation study on 1-water. The radicals 1-3 form an interesting series with the number of lone pairs increasing from none to two. The anilinyl and benzyl radicals can act as Lewis base through their unpaired electrons, the lone pairs of the heteroatoms, or the doubly occupied π orbitals of the aromatic system. Matrix isolation experiments provide evidence for the formation of a π complex between 1 and water. By combining computational and experimental techniques we identify the possible interactions between the aromatic radicals 1-3 and water, predict the structure and vibrational spectra of the resulting complexes, and analyze the effects of substitution and temperature.

Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation.

The dual Hamiltonian free energy perturbation (DH-FEP) method is designed for accurate and efficient evaluation of the free energy profile of chemical reactions in quantum mechanical/molecular mechanical (QM/MM) calculations. In contrast to existing QM/MM FEP variants, the QM region is not kept frozen during sampling, but all degrees of freedom except for the reaction coordinate are sampled. In the DH-FEP scheme, the sampling is done by semiempirical QM/MM molecular dynamics (MD), while the perturbation energy differences are evaluated from high-level QM/MM single-point calculations at regular intervals, skipping a pre-defined number of MD sampling steps. After validating our method using an analytic model potential with an exactly known solution, we report a QM/MM DH-FEP study of the enzymatic reaction catalyzed by chorismate mutase. We suggest guidelines for QM/MM DH-FEP calculations and default values for the required computational parameters. In the case of chorismate mutase, we apply the DH-FEP approach in combination with a single one-dimensional reaction coordinate and with a two-dimensional collective coordinate (two individual distances), with superior results for the latter choice.

Coupling and uncoupling mechanisms in the methoxythreonine mutant of cytochrome P450cam: a quantum mechanical/molecular mechanical study.

The Thr252 residue plays a vital role in the catalytic cycle of cytochrome P450cam during the formation of the active species (Compound I) from its precursor (Compound 0). We investigate the effect of replacing Thr252 by methoxythreonine (MeO-Thr) on this protonation reaction (coupling) and on the competing formation of the ferric resting state and H2O2 (uncoupling) by combined quantum mechanical/molecular mechanical (QM/MM) methods. For each reaction, two possible mechanisms are studied, and for each of these the residues Asp251 and Glu366 are considered as proton sources. The computed QM/MM barriers indicate that uncoupling is unfavorable in the case of the Thr252MeO-Thr mutant, whereas there are two energetically feasible proton transfer pathways for coupling. The corresponding rate-limiting barriers for the formation of Compound I are higher in the mutant than in the wild-type enzyme. These findings are consistent with the experimental observations that the Thr252MeO-Thr mutant forms the alcohol product exclusively (via Compound I), but at lower reaction rates compared with the wild-type enzyme.

How is the reactivity of cytochrome P450cam affected by Thr252X mutation? A QM/MM study for X = serine, valine, alanine, glycine.

Proton transfer reactions play a vital role in the catalytic cycle of cytochrome P450cam and are responsible for the formation of the iron-oxo species called Compound I (Cpd I) that is supposed to be the active oxidant. Depending on the course of the proton transfer, protonation of the last observable intermediate (ferric hydroperoxo complex, Cpd 0) can lead to either the formation of Cpd I (coupling reaction) or the ferric resting state (uncoupling reaction). The ratio of these two processes is drastically affected by mutation of the Thr252 residue. In this work, we study the effect of Thr252X (X = serine, valine, alanine, glycine) mutations on the formation of Cpd I by means of hybrid quantum mechanical/molecular mechanical (QM/MM) calculations and classical simulations. In the wild-type enzyme, the coupling reaction is favored since its rate-limiting barrier is 13 kcal/mol lower than that for uncoupling. This difference is reduced to 7 kcal/mol in the serine mutant. In the case of valine, alanine, and glycine mutants, an additional water molecule enters the active site and lowers the activation energy of the uncoupling reaction significantly. With the additional water molecule, coupling and uncoupling have similar barriers in the valine mutant, and the uncoupling reaction becomes favored in the alanine and glycine mutants. These findings agree very well with experimental results and thus confirm the assumption that uncontrolled proton delivery by solvent water networks is responsible for the uncoupling reaction. The present study provides a detailed mechanistic understanding of the role of the Thr252 residue.

QM/MM study of the second proton transfer in the catalytic cycle of the D251N mutant of cytochrome P450cam.

Protonation of Compound 0 in the catalytic cycle of cytochrome P450cam may lead to the formation of either the reactive Compound I (coupling) or the ferric resting state (uncoupling). In this work, we investigate the effect of the D251N mutation on the coupling and uncoupling reaction by combined quantum mechanics/molecular mechanics (QM/MM) calculations. The mutated Asn251 residue has two possible orientations, i.e. directed toward the active site (no flip) or away from the active site (flip), with the latter one being preferred in classical molecular dynamics (MD) simulations. The possible proton transfer mechanisms in the coupling and uncoupling reaction were studied for three models of the D251N mutant, i.e. no flip (model I), flip (model II), and flip with an extra water (model III). According to the QM/MM calculations, the uncoupling reaction is always less favorable than the coupling reaction. The coupling reaction in the D251N mutant follows the same mechanism as in the wild-type enzyme, with initial O-O cleavage followed by proton transfer. The barrier for the initial step is similar in all D251N models, but the proton transfer is most facile in model III. The hydroxide anion formed in model III is not reprotonated easily by neighboring residues, while proton delivery from bulk solvent seems possible via a water network that remains intact during 2 ns classical MD simulation. The computational results are consistent with the experimental findings that the coupling reaction dominates the consumption of dioxygen in the D251N mutant, but with lower activity than in the wild-type enzyme.

Semiempirical double-hybrid density functional with improved description of long-range correlation.

The recently proposed new family of "double-hybrid" density functionals [Grimme, S. J. Chem. Phys. 2006, 124, 34108] replaces a fraction of the semi-local correlation energy by a non-local correlation energy expression that employs the Kohn-Sham orbitals in second-order many-body perturbation theory. These functionals have provided results of high accuracy over a wide range of properties but fail to accurately describe long-range van der Waals interactions. In this work, a distance-dependent scaling factor for the non-local correlation energy is introduced to address this problem, and two new double-hybrid density functionals are proposed. The new functionals are optimized with the finite cc-pVTZ basis on training sets of atomization energies and intermolecular interaction energies. They are compared against (scaled) second-order Møller-Plesset perturbation theories and popular density functionals including the hybrid-GGA functional B3-LYP and the first double-hybrid functional (B2-PLYP). Tests are performed on an extensive set including reaction energies, barrier heights, weakly interacting complexes, transition-metal systems, molecular geometries, and harmonic vibrational frequencies. Within the cc-pVTZ atomic orbital basis, we have demonstrated the ability to find a parametrization scheme which is simultaneously able to describe thermochemistry and weakly bound systems with a satisfactory degree of accuracy.

Long-Range Electrostatic Effects in QM/MM Studies of Enzymatic Reactions: Application of the Solvated Macromolecule Boundary Potential.

Long-range electrostatic interactions are important in simulations of enzymatic reactions. They can be divided into the effects due to bulk solvent and those due to the electrostatic potential of the outer macromolecule. We study and quantify the importance of these two effects for two test systems by application of the solvated macromolecule boundary potential (SMBP) [J. Chem. Theory Comput. 2009, 5, 3114-3128]. We validate the accuracy of the SMBP for these test systems and present a transferable protocol for determination of optimal SMBP parameters as well as recommended default values for these parameters. Two enzymatic reactions with different characteristics are studied: the intramolecular Claisen rearrangement in chorismate mutase that is associated with little charge transfer and the hydroxylation reaction in p-hydroxybenzoate hydroxylase that corresponds to a formal "OH(+)" transfer and thus involves significant charge transfer. It is found that the effects of the electrostatic potential of the outer macromolecule and of bulk solvent are only important in the latter case, where their neglect causes deviations in the computed barriers on the order of 1-2 kcal/mol, respectively. Even larger deviations on the order of several kilocalories per mole are observed for the reaction energies in p-hydroxybenzoate hydroxylase if the electrostatic potential of the outer macromolecule is neglected.

A General Boundary Potential for Hybrid QM/MM Simulations of Solvated Biomolecular Systems.

We present a general boundary potential for the efficient and accurate evaluation of electrostatic interactions in hybrid quantum mechanical/molecular mechanical (QM/MM) approaches called solvated macromolecule boundary potential (SMBP), which is designed for QM/MM calculations with any kind of QM method. The SMBP targets QM/MM single-point energy calculations and geometry optimizations. In the SMBP scheme, the outer solvent and macromolecule region is described by a boundary potential obtained with the use of Poisson-Boltzmann calculations (treating the bulk solvent as a dielectric continuum). In the QM calculations, the SMBP is represented by virtual point charges on a surface enclosing the explicitly treated inner region. These charges and their interactions with the QM density are determined through a self-consistent reaction field procedure. The accuracy of the SMBP is evaluated on three diverse test systems: the intramolecular proton transfer of glycine in water, the hydroxylation reaction in p-hydroxybenzoate hydroxylase, and the spin state energy splittings in the pentacoordinated ferric complex of cytochrome P450cam. In the case of solvated glycine, application of the SMBP turns out to be problematic since analogous QM/MM/SMBP and full QM/MM geometry optimizations lead to different close-lying local minima. In both enzymes, the SMBP performs very well and closely reproduces the results from full QM/MM optimizations of these more rigid test systems. Starting from optimized QM/MM/SMBP structures along a reaction path, one can apply the previously implemented generalized solvent boundary potential (GSBP) to sample over MM phase space in QM/MM free energy calculations within the framework of free energy perturbation theory. This reduces the overall computational costs of sampling by 1 order of magnitude while maintaining good accuracy. The combined use of SMBP and GSBP thus allows for efficient QM/MM free energy studies of enzymes.

Efficiency and Accuracy of the Generalized Solvent Boundary Potential for Hybrid QM/MM Simulations: Implementation for Semiempirical Hamiltonians.

We report the implementation of the generalized solvent boundary potential (GSBP) [ Im , W. , Bernèche , S. , and Roux , B. J. Chem. Phys. 2001, 114, 2924 ] in the framework of semiempirical hybrid quantum mechanical/molecular mechanical (QM/MM) methods. Application of the GSBP is connected with a significant overhead that is dominated by numerical solutions of the Poisson-Boltzmann equation for continuous charge distributions. Three approaches are presented that accelerate computation of the values at the boundary of the simulation box and in the interior of the macromolecule and solvent. It is shown that these methods reduce the computational overhead of the GSBP significantly with only minimal loss of accuracy. The accuracy of the GSBP to represent long-range electrostatic interactions is assessed for an extensive set of its inherent parameters, and a set of optimal parameters is defined. On this basis, the overhead and the savings of the GSBP are quantified for model systems of different sizes in the range of 7000 to 40 000 atoms. We find that the savings compensate for the overhead in systems larger than 12 500 atoms. Beyond this system size, the GSBP reduces the computational cost significantly, by 70% and more for large systems (>25 000 atoms).