Charge optimization increases the potency and selectivity of a chorismate mutase inhibitor

The highest affinity inhibitor for chorismate mutases, a conformationally constrained oxabicyclic dicarboxylate transition state analogue, was modified as suggested by computational charge optimization methods. As predicted, replacement of the C10 carboxylate in this molecule with a nitro group yields an even more potent inhibitor of a chorismate mutase from Bacillus subtilis (BsCM), but the magnitude of the improvement (roughly 3-fold, corresponding to a DeltaDeltaG of -0.7 kcal/mol) is substantially lower than the gain of 2-3 kcal/mol binding free energy anticipated for the reduced desolvation penalty upon binding. Experiments with a truncated version of the enzyme show that the flexible C terminus, which was only partially resolved in the crystal structure and hence omitted from the calculations, provides favorable interactions with the C10 group that partially compensate for its desolvation. Although truncation diminishes the affinity of the enzyme for both inhibitors, the nitro derivative binds 1.7 kcal/mol more tightly than the dicarboxylate, in reasonable agreement with the calculations. Significantly, substitution of the C10 carboxylate with a nitro group also enhances the selectivity of inhibition of BsCM relative to a chorismate mutase from Escherichia coli (EcCM), which has a completely different fold and binding pocket, by 10-fold. These results experimentally verify the utility of charge optimization methods for improving interactions between proteins and low-molecular weight ligands.     

Investigation of solvent effects for the Claisen rearrangement of chorismate to prephenate: mechanistic interpretation via near attack conformations

Solvent effects on the rate of the Claisen rearrangement of chorismate to prephenate have been examined in water and methanol. The preequilibrium free-energy differences between diaxial and diequatorial conformers of chorismate, which had previously been implicated as the sole basis for the observed 100-fold rate increase in water over methanol, have been reframed using the near attack conformation (NAC) concept of Bruice and co-workers. Using a combined QM/MM Monte Carlo/free-energy perturbation (MC/FEP) method, 82%, 57%, and 1% of chorismate conformers were found to be NAC structures (NACs) in water, methanol, and the gas phase, respectively. As a consequence, the conversion of non-NACs to NACs provides no free-energy contributions to the overall relative reaction rates in water versus methanol. Free-energy perturbation calculations yielded differences in free energies of activation for the two polar protic solvents and the gas phase. The rate enhancement in water over the gas phase arises from preferential hydration of the transition state (TS) relative to the reactants via increased hydrogen bonding and long-range electrostatic interactions, which accompany bringing the two negatively charged carboxylates into closer proximity. More specifically, there is an increase of 1.3 and 0.6 hydrogen bonds to the carboxylate groups and the ether oxygen, respectively, in going from the reactant to the TS in water. In methanol, the corresponding changes in hydrogen bonding with first shell solvent molecules are small; the rate enhancement arises primarily from the enhanced long-range interactions with solvent molecules. Thus, the reaction occurs faster in water than in methanol due to greater stabilization of the TS in water by specific interactions with first shell solvent molecules.     

Enzymes do what is expected (chalcone isomerase versus chorismate mutase)

Madicago sativa chalcone isomerase (CI) catalyzes the isomerization of chalcone to flavanone, whereas E. coli chorismate mutase (CM) catalyzes the pericyclic rearrangement of chorismate to prephenate. Covalent intermediates are not formed in either of the enzyme-catalyzed reactions, K(M) and k(cat) are virtually the same for both enzymes, and the rate constants (k(o)) for the noncatalyzed reactions in water are also the same. This kinetic identity of both the enzymatic and the nonenzymatic reactions is not shared by a similarity in driving forces. The efficiency (DeltaG(o)() - DeltaG(cat)()) for the CI mechanism involves transition-state stabilization through general-acid catalysis and freeing of three water molecules trapped in the E.S species. The contribution to lowering DeltaG(cat)() by an increase in near attack conformer (NAC) formation in E.S as compared to S in water is not so important. In the CM reaction, the standard free energy for NAC formation in water is 8.4 kcal/mol as compared to 0.6 kcal/mol in E.S. Because the value of (DeltaG(o)() - DeltaG(cat)()) is 9 kcal/mol, the greater percentage of NACs accounts for approximately 90% of the kinetic advantage of the CM reaction. There is no discernible transition-state stabilization in the CM reaction. These results are discussed. In anthropomorphic terms, each enzyme has had to do what it must to have a biologically relevant rate of reaction.     

Differential transition-state stabilization in enzyme catalysis: quantum chemical analysis of interactions in the chorismate mutase reaction and prediction of the optimal catalytic field

Chorismate mutase is a key model system in the development of theories of enzyme catalysis. To analyze the physical nature of catalytic interactions within the enzyme active site and to estimate the stabilization of the transition state (TS) relative to the substrate (differential transition state stabilization, DTSS), we have carried out nonempirical variation-perturbation analysis of the electrostatic, exchange, delocalization, and correlation interactions of the enzyme-bound substrate and transition-state structures derived from ab initio QM/MM modeling of Bacillus subtilis chorismate mutase. Significant TS stabilization by approximately -23 kcal/mol [MP2/6-31G(d)] relative to the bound substrate is in agreement with that of previous QM/MM modeling and contrasts with suggestions that catalysis by this enzyme arises purely from conformational selection effects. The most important contributions to DTSS come from the residues, Arg90, Arg7, Glu78, a crystallographic water molecule, Arg116, and Arg63, and are dominated by electrostatic effects. Analysis of the differential electrostatic potential of the TS and substrate allows calculation of the catalytic field, predicting the optimal location of charged groups to achieve maximal DTSS. Comparison with the active site of the enzyme from those of several species shows that the positions of charged active site residues correspond closely to the optimal catalytic field, showing that the enzyme has evolved specifically to stabilize the TS relative to the substrate.     

Transition state stabilization and substrate strain in enzyme catalysis: ab initio QM/MM modelling of the chorismate mutase reaction

To investigate fundamental features of enzyme catalysis, there is a need for high-level calculations capable of modelling crucial, unstable species such as transition states as they are formed within enzymes. We have modelled an important model enzyme reaction, the Claisen rearrangement of chorismate to prephenate in chorismate mutase, by combined ab initio quantum mechanics/molecular mechanics (QM/MM) methods. The best estimates of the potential energy barrier in the enzyme are 7.4-11.0 kcal mol(-1)(MP2/6-31+G(d)//6-31G(d)/CHARMM22) and 12.7-16.1 kcal mol(-1)(B3LYP/6-311+G(2d,p)//6-31G(d)/CHARMM22), comparable to the experimental estimate of Delta H(++)= 12.7 +/- 0.4 kcal mol(-1). The results provide unequivocal evidence of transition state (TS) stabilization by the enzyme, with contributions from residues Arg90, Arg7, and Arg63. Glu78 stabilizes the prephenate product (relative to substrate), and can also stabilize the TS. Examination of the same pathway in solution (with a variety of continuum models), at the same ab initio levels, allows comparison of the catalyzed and uncatalyzed reactions. Calculated barriers in solution are 28.0 kcal mol(-1)(MP2/6-31+G(d)/PCM) and 24.6 kcal mol(-1)(B3LYP/6-311+G(2d,p)/PCM), comparable to the experimental finding of Delta G(++)= 25.4 kcal mol(-1) and consistent with the experimentally-deduced 10(6)-fold rate acceleration by the enzyme. The substrate is found to be significantly distorted in the enzyme, adopting a structure closer to the transition state, although the degree of compression is less than predicted by lower-level calculations. This apparent substrate strain, or compression, is potentially also catalytically relevant. Solution calculations, however, suggest that the catalytic contribution of this compression may be relatively small. Consideration of the same reaction pathway in solution and in the enzyme, involving reaction from a 'near-attack conformer' of the substrate, indicates that adoption of this conformation is not in itself a major contribution to catalysis. Transition state stabilization (by electrostatic interactions, including hydrogen bonds) is found to be central to catalysis by the enzyme. Several hydrogen bonds are observed to shorten at the TS. The active site is clearly complementary to the transition state for the reaction, stabilizing it more than the substrate, so reducing the barrier to reaction.     

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.     

A comparative study of claisen and cope rearrangements catalyzed by chorismate mutase. An insight into enzymatic efficiency: transition state stabilization or substrate preorganization?

In this work we present a detailed analysis of the activation free energies and averaged interactions for the Claisen and Cope rearrangements of chorismate and carbachorismate catalyzed by Bacillus subtilischorismate mutase (BsCM) using quantum mechanics/molecular mechanics (QM/MM) simulation methods. In gas phase, both reactions are described as concerted processes, with the activation free energy for carbachorismate being about 10-15 kcal mol(-)(1) larger than for chorismate, at the AM1 and B3LYP/6-31G levels. Aqueous solution and BsCM active site environments reduce the free energy barriers for both reactions, due to the fact that in these media the two carboxylate groups can be approached more easily than in the gas phase. The enzyme specifically reduces the activation free energy of the Claisen rearrangement about 3 kcal mol(-)(1) more than that for the Cope reaction. This result is due to a larger transition state stabilization associated to the formation of a hydrogen bond between Arg90 and the ether oxygen. When this oxygen atom is changed by a methylene group, the interaction is lost and Arg90 moves inside the active site establishing stronger interactions with one of the carboxylate groups. This fact yields a more intense rearrangement of the substrate structure. Comparing two reactions in the same enzyme, we have been able to obtain conclusions about the relative magnitude of the substrate preorganization and transition state stabilization effects. Transition state stabilization seems to be the dominant effect in this case.     

Conformational effects in enzyme catalysis: QM/MM free energy calculation of the 'NAC' contribution in chorismate mutase

The controversial 'near attack conformation'(NAC) effect in the important model enzyme chorismate mutase is calculated to be 3.8-4.6 kcal mol(-1) by QM/MM free energy perturbation molecular dynamics methods, showing that the NAC effect by itself does not account for catalysis in this enzyme.     

Diphtheria toxin catalyzed hydrolysis of NAD(+): molecular dynamics study of enzyme-bound substrate, transition state, and inhibitor.

The mechanism of the diphtheria toxin-catalyzed hydrolysis of NAD(+) was investigated by quantum chemical calculations and molecular dynamics simulations. Several effects that could explain the 6000-fold rate acceleration (Delta Delta G(++) approximately 5 kcal/mol) by the enzyme were considered. First, the carboxamide arm of the enzyme-bound NAD(+) adopts a trans conformation while the most stable conformation is cis. The most stable conformation for the nicotinamide product has the amide carbonyl trans. The activation energy for the cleavage of the ribosidic bond is reduced by 2 kcal/mol due to the relaxation of this ground state conformational stress in the transition state. Second, molecular dynamics simulations to the nanosecond time range revealed that the carboxylate of Glu148 forms a hydrogen bond to the substrate's 2' hydroxyl group in E.S (approximately 17% of the time) and E.TS (approximately 57% of the time) complexes. This interaction is not seen in crystal structures. The ApUp inhibitor is held more tightly by the enzyme than the transition state and the substrate. Analysis of correlated motions reveals differences in the pattern of anticorrelated motions for protein backbone atoms when the transition state occupies the active site as compared to the E.NAD(+) complex.     

Improved interaction potentials for charged residues in proteins

Electrostatic interactions dominate the structure and free energy of biomolecules. To obtain accurate free energies involving charged groups from molecular simulations, OPLS-AA parameters have been reoptimized using Monte Carlo free energy perturbation. New parameters fit a self-consistent, experimental set of hydration free energies for acetate (Asp), propionate (Glu), 4-methylimidazolium (Hip), n-butylammonium (Lys), and n-propylguanidinium (Arg), all resembling charged residue side chains, including beta-carbons. It is shown that OPLS-AA free energies depend critically on the type of water model, TIP4P or TIP3P; i.e., each water model requires specific water-charged molecule interaction potentials. New models (models 1 and 3) are thus described for both water models. Uncertainties in relative free energies of charged residues are approximately 2 kcal/mol with the new parameters, due to variations in system setup (MAEs of ca. 1 kcal/mol) and noise from simulations (ca. 1 kcal/mol). The latter error of approximately 1 kcal/mol contrasts MAEs from standard OPLS-AA of up to 13 kcal/mol for the entire series of charged residues or up to 5 kcal/mol for the cationic series Lys, Arg, and Hip. The new parameters can be used directly in molecular simulations with no modification of neutral residues needed and are envisioned to be particular important in simulations where charged residues change environment.     

Conformational equilibrium of 1,2-dichloroethane in water: comparison of PCM and RISM-SCF methods

The RISM-SCF and polarizable continuum model (PCM) approaches have been applied to study the conformational equilibrium of 1,2-dichloroethane (DCE) in water. Both the electron correlation effect and basis sets play an important role in the relative energies of the gauche and trans conformers in gas and solution phases. Both PCM and RISM-MP2 methods resulted in a consistent trend with the previous experimental and theoretical studies that the population of the gauche conformer increases in going from the gas phase to the aqueous solution. However, the PCM treatment could not describe the solvent effect completely in that the sign of the relative free energy of the gauche and trans forms is opposite to the most recent experimental and theoretical data, while the RISM-MP2 gives the right sign in the free energy difference. We found that the larger excess chemical potential gain (by ca. -4.1 kcal/mol) for the gauche conformer is large enough to result in the gauche preference of DCE in water, though it has to compensate for more solute reorganization energy (approximately 1.6 kcal/mol) and overcome the energy difference (approximately 1.6 kcal/mol) in the gas phase. The radial distribution functions between DCE and the nearest water shows that the electrostatic repulsion between chlorine and oxygen atoms is higher in the trans conformer than in the gauche one, while the attractive interaction between chlorine and hydrogen of water is higher in the gauche conformer.     

The mechanism of cis-trans isomerization of prolyl peptides by cyclophilin

The mechanism of cis-trans isomerization of prolyl peptides catalyzed by cyclophilin (CyP) was studied computationally via molecular dynamics (MD) simulations of the transition state (TS) and the cis and trans forms of the ground state (GS), when bound to CyP and when free in aqueous solution. The MD simulations include four enzyme-bound species of tetrapeptide (Suc-Ala-XC([double bond]O)-NPro-Phe-pNA; X = Gly, Trp, Ala, and Leu). In water, the prolyl amide bond is favorably planar with the presence of conformers exhibiting +/-20 degrees twist of the C-N dihedral. In the active site a hydrogen bond between the cis-prolyl amide carbonyl O and the backbone amide N-H of Asn102 retains the 20 degrees twist of the C-N dihedral. The TS structure is characterized by a 90 degrees twist of the amide C-N bond and a more favorable interaction with Asn102 due to the shorter distance between Asn102(HN) and the amide carbonyl O. The conformational change of cis --> TS also involves pyramidalization of the amide N, which results in the formation of a hydrogen bond between the amide N and the guanidino group of Arg55. Both Asn102 and Arg55 are held in the same position in CyP.cis-isomer as in CyP.TS. In the ligand-free CyP the Arg55 guanidino group is highly disorganized and Asn102 is displaced 1 A from the position in the ligand-bound CyP. Thus, the organization of Arg55 and Asn102 occurs upon substrate binding. The geometrical complimentarity of the organized enzyme structure to the TS structure is a result of preferential binding of the proline N and the amide carbonyl of the TS compared to that of GS. However, the N-terminal part (Suc-Ala) becomes repositioned in the TS such that two hydrogen bonds disappear, one hydrogen bond appears and two other hydrogen bonds becomes weaker on the conversion of CyP.cis to CyP.TS. During this conversion, total hydrophobic contact between enzyme and the peptide is preserved. Thus, the interaction energies of GS and TS with enzyme are, as a whole, much alike. This does not support the contention that TS is bound more tightly than GS by K(m)/K(TS) = 10(6) in the cis --> trans reaction. Repositioning of the N-terminal part of the peptide on CyP.TS formation becomes more pronounced when the substrate X residue is changed from Gly < Trp < Ala < Leu. We propose that the larger turning of the N-terminus is responsible for the larger value of the experimentally observed Delta S(++) and Delta H(++), which sum up to little change in Delta G(++). The positioning of the Arg55 and the degree of 20 degrees twist of the amide C-N bond are considered as criteria for Near Attack Conformers (NACs) in cis-trans isomerization. NACs account for approximately 30% of the total GS populations of the cis-isomer. Similar NAC populations were observed with four different substrates. This is consistent with the insensitivity of enzymatic activity to the nature of the X residue. Also, the NAC population in CyP.trans-AAPF was comparable to that in CyP.cis-AAPF, in accord with similar experimentally measured rates of the cis --> trans and trans --> cis reaction in CyP. These NACs, found in CyP.cis and CyP.trans, resemble only one of the four possible TS configurations in the water reaction. The identity of this TS structure (syn/exo) is in accord with experimentally determined KIE values in the enzymatic reaction. However, the geometry of the active site was also complementary to another TS structure (anti/exo) that was not detected in the active site by the same KIE measurements, implying that the geometrical fitness of the TS cannot be a single determining factor for enzymatic reactions.     

Entropy of water in the hydration layer of major and minor grooves of DNA

Transport properties (translational and rotational) of water in the two grooves of the B-DNA duplex are known to be different from those in the bulk. Here, we use a recently developed theoretical scheme to compute the entropies of water molecules in both of the grooves of DNA and compare them with that in the bulk. The scheme requires as input both translational and rotational velocity autocorrelation function (C(V)(t) and C(omega)(t), respectively) data. These velocity autocorrelation functions were computed from an atomistic MD simulation of a B-DNA duplex (36 base pairs long) in explicit water (TIP3P). The average values of the entropy of water at 300 K in both of the grooves of DNA (the TS value in the major groove is 6.71 kcal/mol and that in the minor groove is 6.41 kcal/mol) are found to be significantly lower than that in bulk water (the TS value is 7.27 kcal/mol). Thus, the entropic contribution to the free energy change (TDeltaS) of transferring a minor groove water molecule to the bulk is 0.86 kcal/mol and of transferring a major groove water to the bulk is 0.56 kcal/mol at 300 K, which is to be compared with 1.44 kcal/mol for melting of ice at 273 K. We also calculate the energy of interaction of each water molecule with the rest of the atoms in the system and hence calculate the chemical potential (Helmholtz free energy per water molecule, A = E - TS) in the different domains. The identical free energy value of water molecules in the different domains proves the robustness of the scheme. We propose that the configurational entropy of water in the grooves can be used as a measure of the mobility (or microviscosity) of water molecules in a given domain.     

Just a near attack conformer for catalysis (chorismate to prephenate rearrangements in water,antibody, enzymes,and their mutants)

Standard free energies for formation of ground-state reactive conformers (DeltaGN degrees ) and transition states (DeltaG) in the conversion of chorismate to prephenate in water, B. subtilis mutase, E. coli mutase, and their mutants, as well as a catalytic antibody, are related by DeltaG = DeltaGN degrees + 16 kcal/mol. Thus, the differences in the rate constants for the water reaction and catalysts reactions reside in the mole fraction of substrate present as reactive conformers (NACs). These results, and knowledge of the importance of transition state stabilization in other cases, suggest a proposal that enzymes utilize both NAC and transition state stabilization in the mix required for the most efficient catalysis.     

Computational investigation of hydrogen abstraction from 2-aminoethanol by the 1,5-dideoxyribose-5-yl radical: a model study of a reaction occurring in the active site of ethanolamine ammonia lyase

Hydrogen abstraction from 2-aminoethanol by the 5'-deoxyadenosyl radical, which is formed upon Co--C bond homolysis in coenzyme B(12), was investigated by theoretical means with employment of the DFT (B3LYP) and ab initio (MP2) approaches. As a model system for the 5'-deoxyadenosyl moiety the computationally less demanding 1,5-dideoxyribose was employed; two conformers, which differ in ring conformation (C2- and C3-endo), were considered. If hydrogen is abstracted from "free" substrate by the C2-endo conformer of the 1,5-dideoxyribose-5-yl radical, the activation enthalpy is 16.7 kcal mol(-1); with the C3-endo counterpart, the value is 17.3 kcal mol(-1). These energetic requirements are slightly above the activation enthalpy limit (15 kcal mol(-1)) determined experimentally for the rate-determining step of the sequence, that is, hydrogen delivery from 5'-deoxyadenosine to the product radical. The activation enthalpy is lower when the substrate interacts with at least one amino acid from the active site. According to the computations, when a His model system partially protonates the substrate the activation enthalpy is 4.5 kcal mol(-1) for the C3-endo conformer and 5.8 kcal mol(-1) for the C2-endo counterpart. As hydrogen abstraction from the fully as well as the partially protonated substrate is preceded by the formation of quite stable encounter complexes, the actual activation barriers are around 13-15 kcal mol(-1). A synergistic interaction of 2-aminoethanol with two amino acids where His partially protonates the NH(2) group and Asp partially deprotonates the OH group of the substrate results in an activation enthalpy of 12.4 kcal mol(-1) for the C3-endo conformer and 13.2 kcal mol(-1) for the C2-endo counterpart. However, if encounter complexes exist in the active site, the actual activation barriers are much higher (>25 kcal mol(-1)) than that reported for the rate-determining step. These findings together with previous computations suggest that the energetics of the initial hydrogen abstraction decrease with an interaction of the substrate with only a protonating auxiliary, but for the rearrangement of the radical the synergistic effects of two auxiliaries are essential to pull the barrier below the limit of 15 kcal mol(-1).     

Mechanism of the hydration of carbon dioxide: direct participation of H2O versus microsolvation

Thermochemical parameters of carbonic acid and the stationary points on the neutral hydration pathways of carbon dioxide, CO 2 + nH 2O --> H 2CO 3 + ( n - 1)H 2O, with n = 1, 2, 3, and 4, were calculated using geometries optimized at the MP2/aug-cc-pVTZ level. Coupled-cluster theory (CCSD(T)) energies were extrapolated to the complete basis set limit in most cases and then used to evaluate heats of formation. A high energy barrier of approximately 50 kcal/mol was predicted for the addition of one water molecule to CO 2 ( n = 1). This barrier is lowered in cyclic H-bonded systems of CO 2 with water dimer and water trimer in which preassociation complexes are formed with binding energies of approximately 7 and 15 kcal/mol, respectively. For n = 2, a trimeric six-member cyclic transition state has an energy barrier of approximately 33 (gas phase) and a free energy barrier of approximately 31 (in a continuum solvent model of water at 298 K) kcal/mol, relative to the precomplex. For n = 3, two reactive pathways are possible with the first having all three water molecules involved in hydrogen transfer via an eight-member cycle, and in the second, the third water molecule is not directly involved in the hydrogen transfer but solvates the n = 2 transition state. In the gas phase, the two transition states have comparable energies of approximately 15 kcal/mol relative to separated reactants. The first path is favored over in aqueous solution by approximately 5 kcal/mol in free energy due to the formation of a structure resembling a (HCO 3 (-)/H 3OH 2O (+)) ion pair. Bulk solvation reduces the free energy barrier of the first path by approximately 10 kcal/mol for a free energy barrier of approximately 22 kcal/mol for the (CO 2 + 3H 2O) aq reaction. For n = 4, the transition state, in which a three-water chain takes part in the hydrogen transfer while the fourth water microsolvates the cluster, is energetically more favored than transition states incorporating two or four active water molecules. An energy barrier of approximately 20 (gas phase) and a free energy barrier of approximately 19 (in water) kcal/mol were derived for the CO 2 + 4H 2O reaction, and again formation of an ion pair is important. The calculated results confirm the crucial role of direct participation of three water molecules ( n = 3) in the eight-member cyclic TS for the CO 2 hydration reaction. Carbonic acid and its water complexes are consistently higher in energy (by approximately 6-7 kcal/mol) than the corresponding CO 2 complexes and can undergo more facile water-assisted dehydration processes.     

Role of solvation in the reduction of the uranyl dication by water: a density functional study

We have studied the solvation of uranyl, UO(2)(2+), and the reduced species UO(OH)(2+) and U(OH)(2)(2+) systematically using three levels of approximation: direct application of a continuum model (M1); explicit quantum-chemical treatment of the first hydration sphere (M2); a combined quantum-chemical/continuum model approach (M3). We have optimized complexes with varying numbers of aquo ligands (n = 4-6) and compared their free energies of solvation. Models M1 and M2 have been found to recover the solvation energy only partially, underestimating it by approximately 100 kcal/mol or more. With our best model M3, the calculated hydration free energy Delta(h)G degrees of UO(2)(2+) is about -420 kcal/mol, which shifts to about -370 kcal/mol when corrected for the expected error of the model. This value agrees well with the experimentally determined interval, -437 kcal/mol < Delta(h)G degrees < -318 kcal/mol. Complexes with 5 and 6 aquo ligands have been found to be about equally favored with models M2 and M3. The same solvation models have been applied to a two-step reduction of UO(2)(2+) by water, previously theoretically studied in the gas phase. Our results show that the solvation contribution to the reaction free energy, about 60 kcal/mol, dominates the endoergicity of the reduction.     

Secondary Binding Interactions in a Synthetic Receptor for Trimethyllysine

We have systematically studied how secondary interactions with neighboring lysine (Lys) and arginine (Arg) residues influence the binding and selectivity of the synthetic receptor A₂N for trimethyllysine (Kme₃). Multiple secondary binding sites on A₂N are formed by carboxylates rigidly positioned over aromatic rings, a motif that has been shown to stabilize salt bridges. We varied the spacing between Kme_X (X=0, 3) and an ancillary Lys or Arg and measured binding by isothermal titration calorimetry (ITC). These studies revealed that both neighboring residues improve the binding of A₂N to Kme_X by approximately 1 kcal mol^?1, with little influence of the spacing. Nonetheless, the improvement in affinity caused by Arg is enthalpically driven, while for Lys it is entropically driven, suggesting different mechanisms by which the residues interact with the secondary binding site.     

Contributions of conformational compression and preferential transition state stabilization to the rate enhancement by chorismate mutase

The rate enhancement provided by the chorismate mutase (CM) enzyme for the Claisen rearrangement of chorismate to prephenate has been investigated by application of the concept of near attack conformations (NACs). Using a combined QM/MM Monte Carlo/free-energy perturbation (MC/FEP) method, 82% and 100% of chorismate conformers were found to be NAC structures in water and in the CM active site, respectively. Consequently, the conversion of non-NACs to NACs does not contribute to the free energy of activation from preorganization of the substrate into NACs. The FEP calculations yielded differences in free energies of activation that well reproduce the experimental data. Additional calculations indicate that the rate enhancement by CM over the aqueous phase results primarily from conformational compression of NACs by the enzyme and that this process is enthalpically controlled. This suggests that preferential stabilization of the transition state in the enzyme environment relative to water plays a secondary role in the catalysis by CM.     

A computational study of conformational interconversions in 1,4-dithiacyclohexane (1,4-dithiane)

Ab initio molecular orbital theory with the 6-31G(d), 6-31G(d,p), 6-31+G(d), 6-31+G(d,p), 6-31+G(2d,p), 6-311G(d), 6-311G(d,p), and 6-311+G(2d,p) basis sets and density functional theory (BLYP, B3LYP, B3P86, B3PW91) have been used to locate transition states involved in the conformational interconversions of 1,4-dithiacyclohexane (1,4-dithiane) and to calculate the geometry optimized structures, relative energies, enthalpies, entropies, and free energies of the chair and twist conformers. In the chair and 1,4-twist conformers the C-Hax and C-Heq bond lengths are equal at each carbon, which suggest an absence of stereoelectronic hyperconjugative interactions involving carbon-hydrogen bonds. The 1,4-boat transition state structure was 9.53 to 10.5 kcal/mol higher in energy than the chair conformer and 4.75 to 5.82 kcal/mol higher in energy than the 1,4-twist conformer. Intrinsic reaction coordinate (IRC) calculations showed that the 1,4-boat transition state structure was the energy maximum in the interconversion of the enantiomers of the 1,4-twist conformer. The energy difference between the chair conformer and the 1,4-twist conformer was 4.85 kcal/mol and the chair-1,4-twist free energy difference (deltaG degrees (c-t)) was 4.93 kcal/mol at 298.15 K. Intrinsic reaction coordinate (IRC) calculations connected the transition state between the chair conformer and the 1,4-twist conformer. This transition state is 11.7 kcal/mol higher in energy than the chair conformer. The effects of basis sets on the 1,4-dithiane calculations and the relative energies of saturated and unsaturated six-membered dithianes and dioxanes are also discussed.