The influence of solvation and finite temperatures on theWittig reaction: A theoretical study

The effects of the solvent and finite temperature (entropy) on the Wittig reaction are studied by using density functional theory in combination with molecular dynamics and a continuum solvation model. Standard gas-phase zero-temperature calculations are found to give similar results to previous studies. Gas-phase dynamics simulations allow the free energy profile of the reaction to be calculated through thermodynamic integration. The free energy profile is found to have a significant entropic barrier to the addition step of the reaction where only a small barrier was present in the potential energy curve. The introduction of the solvent dimethyl sulfoxide causes a change in the structure of the intermediate from the oxaphosphetane structure to the dipolar betaine structure. The overall reaction energy is changed only slightly. When the effects of both entropy and the solvent are included a significant entropic barrier to the addition reaction is obtained and the predicted intermediate again has the betaine structure.     

Water-assisted oxo mechanism for heme metabolism

A mechanism of heme metabolism by heme oxygenase (HO) is discussed from B3LYP density functional theory calculations. The concerted OH group attack to the alpha-carbon by the iron-hydroperoxo species is investigated using a model with full protoporphyrin IX to confirm our previous conclusion that this species does not have sufficient oxidizing power for heme oxidation (J. Am. Chem. Soc. 2004, 126, 3672). Calculated activation energies and structures of the intermediates and transition state for this process remain unchanged from those for a small model with porphine in the previous study, which shows that the inclusion of the side chain of the porphyrin ring is not essential in describing the OH group transfer. The activation barrier for a direct oxo attack to the alpha-carbon by an iron-oxo model is calculated to be 49.8 kcal/mol, the barrier height of which looks very high for the enzymatic reaction under physiological conditions. This large activation energy is due to a highly bent porphyrin structure in the transition state. However, a bridging water molecule plays an important role in reducing the porphyrin distortion in the transition state, resulting in a remarkable decrease of the activation barrier to 13.9 kcal/mol. A whole-enzyme model with about 4000 atoms is constructed to elucidate functions of the protein environment in this enzymatic reaction using QM/MM calculations. The key water molecule is fixed in the protein environment to ensure the low-barrier and regioselective heme oxidation. A water-assisted oxo mechanism of heme oxidation by heme oxygenase is proposed from these calculational results.     

Implicit versus explicit solvent in free energy calculations of enzyme catalysis: Methyl transfer catalyzed by catechol O-methyltransferase

We compare free energy calculations for the methyl transfer reaction catalyzed by catechol O-methyltransferase using the quantum mechanical/molecular mechanical free energy method with implicit and explicit solvents. An analogous methylation reaction in a solution is also studied. For the explicit solvent model, we use the three-point transferable intermolecular potential model, and for the implicit model, we use the generalized Born molecular volume model as implemented in CHARMM. We find that activation and reaction free energies calculated with the two models are very similar, despite some structural differences that exist. A significant change in the polarization of the environment occurs as the reaction proceeds. This is more pronounced for the reaction in a solution than for the enzymatic reaction. For the enzymatic reaction, most of the changes take place in the protein rather than in the solvent, and, hence, the benefit of having an instantaneous relaxation of the solvent degrees of freedom is less pronounced for the enzymatic reaction than for the reaction in a solution. This is a likely reason why energies of the enzyme reaction are less sensitive to the choice of atomic radii than are energies of the reaction in a solution.     

Activated radiationless decay of rhodamine-3B: nonequilibrium polarization effects in viscous solvents

Nonequilibrium polarization effects that arise in high viscous polar solvents are discussed as regards to the rhodamine-3B-activated radiationless process. Rate constants are interpreted using dipole isomerization theories which enable the recovery of a barrier top region wave number identical to that previously obtained in less viscous solvents [J. Phys Chem. A 104, 11909 (2000)]. The Onsager-frequency-dependent reaction field can model the friction effect on the rate constants that in glycerol were estimated also from an adiabatic charge-transfer model. The cusp barrier height is half the electronic coupling, as expected from the equality found for the frequencies of the reactant well and barrier top in this process. Coupling to solvent polarization modes can control the friction effect on the reactive mode. A two-dimensional reaction surface explains the photophysical features detected in the radiationless decay and a state energy diagram is proposed for rhodamine-3B.     

Modeling the catalysis of anti-cocaine catalytic antibody: competing reaction pathways and free energy barriers

The competing reaction pathways and the corresponding free energy barriers for cocaine hydrolysis catalyzed by an anti-cocaine catalytic antibody, mAb15A10, were studied by using a novel computational strategy based on the binding free energy calculations on the antibody binding with cocaine and transition states. The calculated binding free energies were used to evaluate the free energy barrier shift from the cocaine hydrolysis in water to the antibody-catalyzed cocaine hydrolysis for each reaction pathway. The free energy barriers for the antibody-catalyzed cocaine hydrolysis were predicted to be the corresponding free energy barriers for the cocaine hydrolysis in water plus the calculated free energy barrier shifts. The calculated free energy barrier shift of -6.87 kcal/mol from the dominant reaction pathway of the cocaine benzoyl ester hydrolysis in water to the dominant reaction pathway of the antibody-catalyzed cocaine hydrolysis is in good agreement with the experimentally derived free energy barrier shift of -5.93 kcal/mol. The calculated mutation-caused shifts of the free energy barrier are also reasonably close to the available experimental activity data. The good agreement suggests that the protocol for calculating the free energy barrier shift from the cocaine hydrolysis in water to the antibody-catalyzed cocaine hydrolysis may be used in future rational design of possible high-activity mutants of the antibody as anti-cocaine therapeutics. The general strategy of the free energy barrier shift calculation may also be valuable in studying a variety of chemical reactions catalyzed by other antibodies or proteins through noncovalent bonding interactions with the substrates.     

Multicoordinate driven method for approximating enzymatic reaction paths: automatic definition of the reaction coordinate using a subset of chemical coordinates

We present a generalization of the reaction coordinate driven method to find reaction paths and transition states for complicated chemical processes, especially enzymatic reactions. The method is based on the definition of a subset of chemical coordinates; it is simple, robust, and suitable to calculate one or more alternative pathways, intermediate minima, and transition-state geometries. Though the results are approximate and the computational cost is relatively high, the method works for large systems, where others often fail. It also works when a certain reaction path competes with others having a lower energy barrier. Accordingly, the procedure is appropriate to test hypothetical reaction mechanisms for complicated systems and provides good initial guesses for more accurate methods. We present tests on a number of simple reactions and on several complicated chemical transformations and compare the results with those obtained by other methods. Calculation of the reaction path for the enzymatic hydrolysis of the substrate by dUTPase for an active-site model with 85 atoms, including several loosely bound water molecules, indicates that the method is feasible for the study of enzyme mechanisms.     

Ab initio study of β-lactam antibiotics. II. Potential energy surface for the amidic CN bond breaking in the 3-cephem + OH− reaction and comparison with the β-lactam + OH− reaction

The potential energy surface for the β-lactam amidic CN bond breaking in the 3-cephem + OH^? reaction was investigated by using the ab initio Hartree—Fock method with a 9s6p/7s3p/3s basis set. The investigated reaction is a model of the reaction between an antibiotic cephalosporin and an enzymatic nucleophilic group, this last reaction being related to the mode of action of β-lactam antibiotics. The minimum-energy reaction path is characterized by a tetrahedral intermediate ≈ 116 kcal mol^?1 more stable than the reagents, by a barrier which corresponds to the partial breaking of the amidic bond and is ≈ 7 kcal mol^?1 above the intermediate and by a product ≈ 31 kcal mol^?1 more stable than the intermediate. The analysis of the wavefunction along the reaction path and the comparison with the β-lactam + OH^? reaction pointed out the role of electron-withdrawing groups on the height of the barrier and the role of intramolecular hydrogen bonds on the structure and energy of the product. The calculations suggest a model of the antibiotic activity of cephalosporins which is compared with previous qualitative pictures.     

Crucial role of protein flexibility in formation of a stable reaction transition state in an α-amylase catalysis

Conformational flexibility of proteins provides enzymes with high catalytic activity. Although the conformational flexibility is known to be pivotal for the ligand binding and release, its role in the chemical reaction process of the reactive substrate remains unclear. We determined a transition state of an enzymatic reaction in a psychrophilic α-amylase by a hybrid molecular simulation that allows one to identify the optimal chemical state in an extensive conformational ensemble of protein. The molecular simulation uncovered that formation of the reaction transition state accompanies a large and slow movement of a loop adjacent to the catalytic site. Free energy calculations revealed that, although catalytic electrostatic potentials on the reactive moiety are formed by local and fast reorganization around the catalytic site, reorganization of the large and slow movement of the loop significantly contributes to reduction of the free energy barrier by stabilizing the local reorganization.     

Direct catalytic effect and fine modulation of solvent in the keto-enol isomerization of amides

The modulation of proton transfer reactions by environmental effects has been investigated for the case of keto -enol isomerization of formamide. Formation of long-lived adducts with a single water molecule or of formamide dimers enhances the reaction rate and shifts the equilibrium towards the lactam form. The effect of bulk solvent on these adducts is small, whereas it further stabilizes the keto form of free formamide. Zero point and entropy effects on the thermo-dynamics and kinetics of the reaction are generally negligible and do not modify the above general trends. Significant reaction rates are obtained well under the energy barrier due to tunneling. They are, however, smeared out when going from microcanonical to canonical ensembles.     

Selenocysteine versus cysteine reactivity: a theoretical study of their oxidation by hydrogen peroxide

The cysteine and selenocysteine oxidation by H2O2 in vacuo and in aqueous solution was studied using the integrated molecular orbital + molecular orbital (IMOMO) method combining the quadratic configuration method QCISD(T) and the spin projection of second-order perturbation theory PMP2. It is shown that including in the model system of cysteine (selenocysteine) residue up to 20 atoms has significant consequences upon the calculated reaction energy barrier. On the other hand, it is demonstrated that free cysteine and selenocysteine have very similar reaction energy barriers, 77-79 kJ mol(-1) in aqueous solution. It is thus concluded that the high experimental reaction rate constant reported for the oxidation of the selenocysteine residue in the glutathione peroxidase (GPx) active center is due to an important interaction between selenocysteine and its molecular environment. The sensitivity of the calculated energy barrier to the dielectric constant of the molecular environment observed for both cysteine and selenocysteine as well as the catalytic effect of the NH group emphasized in the case of cysteine supports this hypothesis.     

A Monte Carlo simulation of free energy relationships for the electron transfer reaction between Fe+ and Fe2+ in water

A free energy barrier ΔF^≠ = 174.2 kJ/mol for the self-exchange electron transfer reaction model Fe⁺/Fe²⁺ in water has been calculated by combining Monte Carlo simulations and the statistical perturbation theory. We have shown that, even for those electron transfer reactions that present a very high free energy barrier of activation, the free energy curve behaves parabolically versus the reaction coordinate, which justifies the quadratic expression for the activation free energy done by Marcus.     

Theoretical study of mechanism of forming a silapolycyclic compound between methylenesilylene and acetone

The mechanism of the cycloaddition reaction of forming a silapolycyclic compound between singlet methylenesilylene and acetone has been investigated with MP2/6‐31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated by CCSD(T)//MP2/6‐31G* method. From the potential energy profile, we predict that the cycloaddition reaction of forming a silapolycyclic compound between singlet methylenesilylene and acetone has two competitive dominant reaction pathways. First dominant reaction pathway consists of four steps: (I) the two reactants (R1, R2) first form an intermediate (INT1) through a barrier‐free exothermic reaction of 46.2 kJ/mol; (II) intermediate (INT1) then isomerizes to a planar four‐membered ring product (P3) via transition state (TS3) with an energy barrier of 47.1 kJ/mol; (III) planar four‐membered ring product (P3) further reacts with acetone (R2) to form an intermediate (INT4), which is also a barrier‐free exothermic reaction of 40.0 kJ/mol; (IV) intermediate (INT4) isomerizes to a silapolycyclic compound (P4) via transition state (TS4) with an energy barrier of 57.0 kJ/mol. Second dominant reaction pathway consists of three steps: (I) the two reactants (R1, R2) first form a four‐membered ring intermediate (INT2) through a barrier‐free exothermic reaction of 0.5 kJ/mol; (II) INT2 further reacts with acetone (R2) to form an intermediate (INT5), which is also a barrier‐free exothermic reaction of 45.4 kJ/mol; (III) intermediate (INT5) isomerizes to a silapolycyclic compound (P5) via transition state (TS5) with an energy barrier of 49.3 kJ/mol. P4 and P5 are isomeric compounds. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Hydride transfer in liver alcohol dehydrogenase: quantum dynamics, kinetic isotope effects, and role of enzyme motion.

The quantum dynamics of the hydride transfer reaction catalyzed by liver alcohol dehydrogenase (LADH) are studied with real-time dynamical simulations including the motion of the entire solvated enzyme. The electronic quantum effects are incorporated with an empirical valence bond potential, and the nuclear quantum effects of the transferring hydrogen are incorporated with a mixed quantum/classical molecular dynamics method in which the transferring hydrogen nucleus is represented by a three-dimensional vibrational wave function. The equilibrium transition state theory rate constants are determined from the adiabatic quantum free energy profiles, which include the free energy of the zero point motion for the transferring nucleus. The nonequilibrium dynamical effects are determined by calculating the transmission coefficients with a reactive flux scheme based on real-time molecular dynamics with quantum transitions (MDQT) surface hopping trajectories. The values of nearly unity for these transmission coefficients imply that nonequilibrium dynamical effects such as barrier recrossings are not dominant for this reaction. The calculated deuterium and tritium kinetic isotope effects for the overall rate agree with experimental results. These simulations elucidate the fundamental nature of the nuclear quantum effects and provide evidence of hydrogen tunneling in the direction along the donor-acceptor axis. An analysis of the geometrical parameters during the equilibrium and nonequilibrium simulations provides insight into the relation between specific enzyme motions and enzyme activity. The donor-acceptor distance, the catalytic zinc-substrate oxygen distance, and the coenzyme (NAD(+)/NADH) ring angles are found to strongly impact the activation free energy barrier, while the donor-acceptor distance and one of the coenzyme ring angles are found to be correlated to the degree of barrier recrossing. The distance between VAL-203 and the reactive center is found to significantly impact the activation free energy but not the degree of barrier recrossing. This result indicates that the experimentally observed effect of mutating VAL-203 on the enzyme activity is due to the alteration of the equilibrium free energy difference between the transition state and the reactant rather than nonequilibrium dynamical factors. The promoting motion of VAL-203 is characterized in terms of steric interactions involving THR-178 and the coenzyme.     

How much can an intermediate state influence competing reactive pathways?

A molecule undergoing reaction may form a short-lived intermediate. Under certain conditions, the rate at which the reaction proceeds toward the product state via the intermediate may exceed that of a simple, direct path. The competition of two alternative reactive pathways is analyzed here in terms of a stochastic model. The approach allows one to diagnose this competition as a function of the energy of the intermediate relative to the barrier heights of the potential surface and values of the reactive vibrational modes. The result has applications to a variety of problems in chemical physics, ranging from the "lock-and-key" mechanism for the enzymatic activity to control of temporal evolution of complex systems by optimal laser fields.     

An energy decomposition analysis for intramolecular non-covalent interaction in solvated environment

In this work, the intra-EDA method, which is a recently developed energy decomposition analysis scheme for intramolecular non-covalent interaction is extended from gas phase to solvated environment. It is the first analysis scheme that performs analysis for intramolecular interaction in solution. By fragmentation scheme, a molecule is divided into intramolecular interacting fragments and environmental fragments via single bond homolysis breaking. The solvent effect is taken into account by implicit solvation model. Intramolecular interaction free energy is estimated as the separated treatment of inter-fragment interactions in dielectric environment. The analysis results highlight the importance of solvent effects to intramolecular non-covalent interaction.     

Energy decomposition analysis for intramolecular non-covalent interaction in solvated environment

In this work, the intra-EDA method, which is a recently developed energy decomposition analysis scheme for intramolecular non-covalent interaction is extended from gas phase to solvated environment. It is the first analysis scheme that performs analysis for intramolecular interaction in solution. By fragmentation scheme, a molecule is divided into intramolecular interacting fragments and environmental fragments via single bond homolysis breaking. The solvent effect is taken into account by implicit solvation model. Intramolecular interaction free energy is estimated as the separated treatment of inter-fragment interactions in dielectric environment. The analysis results highlight the importance of solvent effects to intramolecular non-covalent interaction.     

Hybrid QM/MM study of thio effects in transphosphorylation reactions: the role of solvation

Transphosphorylation thio effects in solution are studied using hybrid QM/MM calculations with a d-orbital semiempirical Hamiltonian. Activated dynamics simulations were performed for a 3' ribose-phosphate model in an explicit 20 A sphere of TIP3P water surrounded by a solvent boundary potential, and free energy analysis was performed using the weighted histogram analysis method. Single thio-substitutions at all of the phosphoryl oxygen positions and a double thio-substitution at the nonbridging positions were considered. The reaction free energy profiles are compared with available experimental data, and the role of solvation on the barrier heights and reaction coordinate is discussed. These results provide an important step in the characterization of thio effects in reactions of biological phosphates that may aid in the interpretation of kinetic data and ultimately help to unravel the catalytic mechanisms of ribozymes.