Molecular dynamics simulations of the catalytic pathway of a cysteine protease: a combined QM/MM study of human cathepsin K

Molecular dynamics simulations using a combined QM/MM potential have been performed to study the catalytic mechanism of human cathepsin K, a member of the papain family of cysteine proteases. We have determined the two-dimensional free energy surfaces of both acylation and deacylation steps to characterize the reaction mechanism. These free energy profiles show that the acylation step is rate limiting with a barrier height of 19.8 kcal/mol in human cathepsin K and of 29.3 kcal/mol in aqueous solution. The free energy of activation for the deacylation step is 16.7 kcal/mol in cathepsin K and 17.8 kcal/mol in aqueous solution. The reduction of free energy barrier is achieved by stabilization of the oxyanion in the transition state. Interestingly, although the "oxyanion hole" has been formed in the Michaelis complex, the amide units do not donate hydrogen bonds directly to the carbonyl oxygen of the substrate, but they stabilize the thiolate anion nucleophile. Hydrogen-bonding interactions are induced as the substrate amide group approaches the nucleophile, moving more than 2 A and placing the oxyanion in contact with Gln19 and the backbone amide of Cys25. The hydrolysis of peptide substrate shares a common mechanism both for the catalyzed reaction in human cathepsin K and for the uncatalyzed reaction in water. Overall, the nucleophilic attack by Cys25 thiolate and the proton-transfer reaction from His162 to the amide nitrogen are highly coupled, whereas a tetrahedral intermediate is formed along the nucleophilic reaction pathway.     

Ab initio quantum mechanical/molecular mechanical molecular dynamics simulation of enzyme catalysis: the case of histone lysine methyltransferase SET7/9

To elucidate enzyme catalysis through computer simulation, a prerequisite is to reliably compute free energy barriers for both enzyme and solution reactions. By employing on-the-fly Born-Oppenheimer molecular dynamics simulations with the ab initio quantum mechanical/molecular mechanical approach and the umbrella sampling method, we have determined free energy profiles for the methyl-transfer reaction catalyzed by the histone lysine methyltransferase SET7/9 and its corresponding uncatalyzed reaction in aqueous solution, respectively. Our calculated activation free energy barrier for the enzyme catalyzed reaction is 22.5 kcal/mol, which agrees very well with the experimental value of 20.9 kcal/mol. The difference in potential of mean force between a corresponding prereaction state and the transition state for the solution reaction is computed to be 30.9 kcal/mol. Thus, our simulations indicate that the enzyme SET7/9 plays an essential catalytic role in significantly lowering the barrier for the methyl-transfer reaction step. For the reaction in solution, it is found that the hydrogen bond network near the reaction center undergoes a significant change, and there is a strong shift in electrostatic field from the prereaction state to the transition state, whereas for the enzyme reaction, such an effect is much smaller and the enzyme SET7/9 is found to provide a preorganized electrostatic environment to facilitate the methyl-transfer reaction. Meanwhile, we find that the transition state in the enzyme reaction is a little more dissociative than that in solution.     

Mechanism of C-terminal intein cleavage in protein splicing from QM/MM molecular dynamics simulations

Protein splicing is a post-translational process in which a biologically inactive protein is activated by the release of a segment denoted as an intein. The process involves four steps. In the third, the scission of the intein takes place after the cyclization of the last amino acid of the segment, an asparagine. Little is known about the chemical reaction necessary for this cyclization. Experiments demonstrate that two histidines (the penultimate amino acid of the intein, and a histidine located 10 amino acids upstream) are relevant in the cyclization of the asparagine. We have investigated the mechanism and determinants of reaction in the GyrA intein focusing on the requirements for asparagine activation for its cyclization. First, the influence that the protonation states of these two histidines have on the orientation of the asparagine side chain is investigated by means of molecular dynamics simulation. Molecular dynamics simulations using the CHARMM27 force field were carried out on the three possible protonation states for each of these two histidines. The results indicate that the only protonation state in which the conformation of the system is suitable for cyclization is when the penultimate histidine is fully protonated (positively charged), and the upstream histidine is in the His(ε) neutral tautomeric form. The free energy profile for the reaction in which the asparagine is activated by a proton transfer to the upstream histidine is presented, computed by hybrid quantum mechanics/molecular mechanics (QM/MM) umbrella sampling molecular dynamics at the SCCDFTB/CHARMM27 level of theory. The calculated free energy barrier for the reaction is 19.0 kcal mol(-1). B3LYP/6-31+G(d) QM/MM single-point calculations give a qualitatively a similar energy profile, although with somewhat higher energy barriers, in good agreement with the value derived from experiment of 25 kcal mol(-1) at 60 °C. QM/MM molecular dynamics simulations of the reactant, activated reactant and intermediate states highlight the importance of the Arg181-Val182-Asp183 segment in catalysing the reaction. Overall, the results indicate that nucleophilic activation of the asparagine for its cyclization by the upstream histidine acting as the base is a plausible mechanism for the C-terminal cleavage in protein splicing.     

Ab initio study of the S(N)2 and E2 mechanisms in the reaction between the cyanide ion and ethyl chloride in dimethyl sulfoxide solution

[reaction: see text] Reliable theoretical calculations predict a free energy barrier for nitrile formation from the reaction between the cyanide ion and ethyl chloride in DMSO solvent of 24.1 kcal/mol, close to the experimental value of 22.6 kcal/mol. We have also predicted that the isonitrile formation is less favorable by 4.7 kcal/mol, while the elimination mechanism is less favorable by more than 10 kcal/mol. These results indicate that isonitrile formation and bimolecular elimination are not significant side reactions for primary alkyl chloride reactions.     

Homology modeling and molecular dynamic simulation of UDP-N-acetylmuramoyl-l-alanine-d-glutamate ligase (MurD) from Mycobacterium tuberculosis H37Rv using in silico approach

The present study aimed to identify the prospective inhibitors of MurD, a cytoplasmic enzyme that catalyzes the addition of d-glutamate to the UDP-N-acetylmuramoyl-l-alanine nucleotide precursor in Mycobacterium tuberculosis (MTB), using virtual screening, docking studies, pharmacokinetic analysis, Molecular Dynamic (MD) simulation, and Molecular Mechanics Generalized Born and Surface Area (MM-GBSA) analyses. The three dimensional (3D) structure was determined based on the homology technique using a template from Streptococcus agalactiae. The modeled structure had three binding sites, namely; substrate binding site (Val18, Thr19, Asp39, Asp40, Gly75, Asn147, Gln171 and His192), the ATP binding site (Gly123, Lys124, Thr125, Thr126, Glu166, Asp283, and Arg314) and the glutamic acid binding site (Arg382, Ser463, and Tyr470). These residues mentioned above play a critical role in the catalytic activity of the enzyme, and their inhibition could serve as a stumbling block to the normal function of the enzyme. A total of 10,344 obtained from virtual screened of Zinc and PubChem databases. These compounds further screened for Lipinski rule of five, docking studies and pharmacokinetic analysis. Four compounds with good binding energies (ZINC11881196 = −10.33 kcal/mol, ZINC12247644 = −8.90 kcal/mol, ZINC14995379 =−8.42 kcal/mol, and PubChem6185 = −8.20 kcal/mol), better than the binding energies of the ATP (−2.31 kcal/mol) and the ligand with known IC₅₀, Aminothiazole (−7.11 kcal/mol) were selected for the MD simulation and MM-GBSA analyses. The result of the analyses showed that all the four ligands formed a stable complex and had the binding free energies better than the binding energy of ATP. Therefore, these ligands considered as suitable prospective inhibitors of the MurD after experimental validation.     

Influence of metal cofactors and water on the catalytic mechanism of creatininase-creatinine in aqueous solution from molecular dynamics simulation and quantum study

The reaction mechanism of creatinine-creatininase binding to form creatine as a final product has been investigated by using a combined ab initio quantum mechanical/molecular mechanical approach and classical molecular dynamics (MD) simulations. In MD simulations, an X-ray crystal structure of the creatininase/creatinine was modified for creatininase/creatinine complexes and the MD simulations were run for free creatininase and creatinine in water. MD results reveal that two X-ray water molecules can be retained in the active site as catalytic water. The binding free energy from Molecular Mechanics Poisson-Boltzmann Surface Area calculation predicted the strong binding of creatinine with Zn²⁺, Asp45 and Glu183. Two step mechanisms via Mn²⁺/Zn²⁺ (as in X-ray structure) and Zn²⁺/Zn²⁺ were proposed for water adding step and ring opening step with two catalytic waters. The pathway using synchronous transit methods with local density approximations with PWC functional for the fragment in the active region were obtained. Preferable pathway Zn²⁺/Zn²⁺ was observed due to lower activation energy in water adding step. The calculated energy in the second step for both systems were comparable with the barrier of 26.03 and 24.44 kcal/mol for Mn²⁺/Zn²⁺ and Zn²⁺/Zn²⁺, respectively.     

Theoretical insight into stereoselective reaction mechanisms of 2,4-pentanediol-tethered ketene-olefin [2 + 2] cycloaddition

We report ab initio molecular dynamics calculations based on density functional theory performed on an intramolecular [2 + 2] cycloaddition between ketene and olefin linked with a 2,4-pentanediol (PD) tether. We find that the encounter of the ketene and olefin moieties could be prearranged in the thermal equilibrated state before the cycloaddition. The reaction mechanism is found to be stepwise, similar to that of intermolecular ketene [2 + 2] cycloadditions with ordinary alkenes. A distinct feature of the reaction pathway for a major diastereoisomer is a differential activation free energy of about 1.5 kcal/mol, including 2.8 kcal/mol as the differential activation entropy, with a transition state consisting of a flexible nine-membered ring in the olefin-PD-ketene moiety. This theoretical study provides a reasonable explanation for the strict stereocontrollability of the PD-tethered ketene-olefin cycloaddition, irrespective of reaction types or conditions.     

A multilayered representation,quantum mechanical and molecular mechanics study of the CH3F + OH− reaction in water

The bimolecular nucleophilic substitution (S_N2) reaction of CH₃F + OH^? in aqueous solution was investigated using a combined quantum mechanical and molecular mechanics approach. Reactant complex, transition state, and product complex along the reaction pathway were analyzed in water. The potentials of mean force were calculated using a multilayered representation with the DFT and CCSD(T) level of theory for the reactive region. The obtained free energy activation barrier for this reaction at the CCSD(T)/MM representation is 18.3 kcal/mol which agrees well with the experimental value at ～21.6 kcal/mol. Both the solvation effect and solute polarization effect play key roles on raising the activation barrier height in aqueous solution, with the former raising the barrier height by 3.1 kcal/mol, the latter 1.5 kcal/mol. © 2013 Wiley Periodicals, Inc.     

A novel quantum mechanical/molecular mechanical approach to the free energy calculation for isomerization of glycine in aqueous solution

The free energy change associated with the isomerization reaction of glycine in water solution has been studied by a hybrid quantum mechanical/molecular mechanical (QM/MM) approach combined with the theory of energy representation (QM/MM-ER) recently developed. The solvation free energies for both neutral and zwitterionic form of glycine have been determined by means of the QM/MM-ER simulation. The contributions of the electronic polarization and the fluctuation of the QM solute to the solvation free energy have been investigated. It has been found that the contribution of the density fluctuation of the zwitterionic solute is estimated as -4.2 kcal/mol in the total solvation free energy of -46.1 kcal/mol, while that of the neutral form is computed as -3.0 kcal/mol in the solvation free energy of -15.6 kcal/mol. The resultant free energy change associated with the isomerization of glycine in water has been obtained as -7.8 kcal/mol, in excellent agreement with the experimental data of -7.3 or -7.7 kcal/mol, implying the accuracy of the QM/MM-ER approach. The results have also been compared with those computed by other methodologies such as the polarizable continuum model and the classical molecular simulation. The efficiency and advantage of the QM/MM-ER method has been discussed.     

Car-Parrinello molecular dynamics study of the rearrangement of the valeramide radical cation

Car-Parrinello molecular dynamics (CPMD) studies of neutral (1) and ionized (1 (+.)) valeramide are performed with the aim of providing a rationalization for the unusual temperature effect on the dissociation pattern of 1(+.) observed in mass spectrometric experiments. According to CPMD simulations of neutral valeramide 1 performed at approximately 500 K, the conformation with the fully relaxed carbon backbone predominates (96 %). Conformational changes involving folding of the carbon backbone into conformers that would allow intramolecular H transfers are predicted not to take place spontaneously at this temperature because of the barrier heights associated with these transitions (3.5 and 6.9 kcal mol(-1)), which cannot be overcome by thermal motion alone. For 1(+.), CPMD simulations performed at approximately 300 K reveal a substantial stability of a conformation in which the carbon backbone is fully relaxed; no reaction is observed even after 7 ps. However, when conformers with already folded carbon-backbones are used as initial geometries in the CPMD simulations, the gamma-hydrogen migration (McLafferty rearrangement resulting in C(3)H(6)) is already completed within 2 ps. For this important process, the free activation energy associated with both a required conformational change and the subsequent H transfer equals 4.5 kcal mol(-1), while for the formally related delta-H shift (which eventually gives rise to the elimination of C(2)H(4)/C(2)H(5.)) it amounts to 7.0 kcal mol(-1). Since the barriers associated with conformational changes are energetically more demanding than those of the corresponding hydrogen transfers, 1(+.) is essentially trapped by conformational barriers and long-lived at approximately 300 K. At elevated temperatures (500 K), the preferred reaction (within 7.3 ps) in the CPMD simulation corresponds to the McLafferty rearrangement. The estimated free activation energy associated with this process amounts to 2.5 kcal mol(-1), while the free activation energy for the delta-H transfer equals 4.4 kcal mol(-1). This relatively small free activation energy for the McLafferty rearrangement might cause dissociation of a substantial fraction of 1(+.) prior to the time-delayed mass selection, which would reduce the C3/C2 ratio in the experiments conducted with metastable ions that have a lifetime in the order of some micros at a source temperature of 500 K.     

A revisited picture of the mechanism of glycerol dehydration

The dehydration mechanism of neutral glycerol in the gas phase was investigated by means of metadynamics simulations. Structures, vibrational frequencies, Gibbs free energy barriers, and rate constants at 800 K were computed for the different steps involved in the pyrolytic process. In this article, we provide a novel mechanism for the dehydration of neutral glycerol, proceeding via formation of glycidol with a barrier of 66.8 kcal/mol. The formation of glycidol is the rate limiting step of the overall decomposition process. Once formed, glycidol converts into 3-hydroxypropanal with a barrier of 49.5 kcal/mol. 3-Hydroxypropanal can decompose further into acrolein or into formaldehyde and vinyl-alcohol with barriers of 53.9 and 35.3 kcal/mol, respectively. These findings offer new insights to available experimental data based on glycerol pyrolysis studies performed with isotopic labeling and on the interpretation of the chemistry of glycerol and sugars in pyrolytic conditions.     

Molecular dynamics and free energy perturbation study of hydride-ion transfer step in dihydrofolate reductase using combined quantum and molecular mechanical model

We used molecular dynamics simulation and free energy perturbation (FEP) methods to investigate the hydride-ion transfer step in the mechanism for the nicotinamide adenine dinucleotide phosphate (NADPH)-dependent reduction of a novel substrate by the enzyme dihydrofolate reductase (DHFR). The system is represented by a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1 semiempirical molecular orbital method for the reacting substrate and NADPH cofactor fragments, the AMBER force field for DHFR, and the TIP3P model for solvent water. The FEP calculations were performed for a number of choices for the QM system. The substrate, 8-methylpterin, was treated quantum mechanically in all the calculations, while the larger cofactor molecule was partitioned into various QM and MM regions with the addition of “link” atoms (F, CH₃, and H). Calculations were also carried out with the entire NADPH molecule treated by QM. The free energies of reaction and the net charges on the NADPH fragments were used to determine the most appropriate QM/MM model. The hydride-ion transfer was also carried out over several FEP pathways, and the QM and QM/MM component free energies thus calculated were found to be state functions (i.e., independent of pathway). A ca. 10 kcal/mol increase in free energy for the hydride-ion transfer with an activation barrier of ca. 30 kcal/mol was calculated. The increase in free energy on the hydride-ion transfer arose largely from the QM/MM component. Analysis of the QM/MM energy components suggests that, although a number of charged residues may contribute to the free energy change through long-range electrostatic interactions, the only interaction that can account for the 10 kcal/mol increase in free energy is the hydrogen bond between the carboxylate side chain of Glu30 (avian DHFR) and the activated (protonated) substrate. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 977–988, 1998     

Rearrangement of 1,3-dipolar cycloadducts derived from bis(phenylazo)stilbene: a DFT level mechanistic investigation

The 1,3-dipolar cycloaddition of bis(phenylazo)stilbene with activated ethene and ethyne derivatives and the subsequent rearrangement of the cycloadducts have been studied using model compounds at the B3LYP/6-31G(d) level of density functional theory (DFT). From the structural and electronic features, a five-membered zwitterionic ring system 9 (1,2,3-triazolium-1-imide system) formed from bis(phenylazo)ethylene is confirmed as the active 1,3-dipole species in the reaction. Formation of the 1,3-dipolar cycloadduct from the alkyne derivative is found to be 26.0 kcal/mol exergonic, and it requires an activation free energy of 19.4 kcal/mol. The 1,3-cycloadduct formed in the reaction undergoes a very facile migration of a nitrogen-bearing fragment, passing through a zwitterionic transition state. A small activation free energy of 8.2 kcal/mol is observed for this step of the reaction, and it is 19.6 kcal/mol exergonic. Further activation of the newly formed rearranged product is possible under elevated temperatures, again passing through a zwitterionic transition state and resulting in the formation of 2,5-dihydro-1,2,3-triazine derivatives. Such derivatives have been recently reported by Butler et al. (J. Org. Chem. 2006, 71, 5679). The charge separation in 9 and the zwitterionic transition states are stabilized through the pi-system of the phenyl rings and the carbonyl groups. Similar structural, electronic, and mechanistic features are obtained for the reaction of 9 with the ethylenic dipolarophile acrylonitrile. Molecular electrostatic potential analyses of the 1,3-dipole and the zwitterionic transitions states are found to be very useful for characterizing their electron delocalization features. The solvation effects can enhance the feasibility of these reactions as they stabilize the zwitterionic transition states to a great extent.     

A theoretical study of radical-only and combined radical/carbocationic mechanisms of arachidonic acid cyclooxygenation by prostaglandin H synthase

Prostaglandin H synthase catalyzes the oxygenation of arachidonic acid into the cyclic endoperoxide, prostaglandin G₂ (PGG₂), and the subsequent reduction of PGG₂ to the corresponding alcohol, prostaglandin H₂ (PGH₂), the precursor of all prostaglandins and thromboxanes. Both radical abstraction by a neighboring tyrosyl radical and combined radical/carbocationic models have been proposed to explain the cyclooxygenase part of this reaction. We have used density functional theory calculations to study the mechanism of the formation of the cyclooxygenated product PGG₂. We found an activation free energy for the initial hydrogen abstraction by the tyrosine radical of 15.6 kcal/mol, and of 14.5 kcal/mol for peroxo bridge formation, in remarkable agreement with the experimental value of 15.0 kcal/mol. Subsequent steps of the radical-based mechanism were found to happen with smaller barriers. A combined radical/carbocation mechanism proceeding through a sigmatropic hydrogen shift was ruled out, owing to its much larger activation free energy of 36.5 kcal/mol. Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s00214-003-0476-9. Electronic Supplementary MaterialSupplementary material is available in the online version of this article at Electronic Supplementary Material: Supplementary material is available in the online version of this article at     

Use of MM-PBSA in reproducing the binding free energies to HIV-1 RT of TIBO derivatives and predicting the binding mode to HIV-1 RT of efavirenz by docking and MM-PBSA.

In this work, a new ansatz is presented that combines molecular dynamics simulations with MM-PBSA (Molecular Mechanics Poisson-Boltzmann/surface area) to rank the binding affinities of 12 TIBO-like HIV-1 RT inhibitors. Encouraging results have been obtained not only for the relative binding free energies, but also for the absolute ones, which have a root-mean-square deviation of 1.0 kcal/mol (the maximum error is 1.89 kcal/mol). Since the root-mean-square error is rather small, this approach can be reliably applied in ranking the ligands from the databases for this important target. Encouraged by the results, we decided to apply MM-PBSA combined with molecular docking to determine the binding mode of efavirenz SUSTIVA(TM) another promising HIV-1 RT inhibitor for which no ligand-protein crystal structure had been published at the time of this work. To proceed, we define the following ansatz: Five hundred picosecond molecular dynamics simulations were first performed for the five binding modes suggested by DOCK 4.0, and then MM-PBSA was carried out for the collected snapshots. MM-PBSA successfully identified the correct binding mode, which has a binding free energy about 7 kcal/mol more favorable than the second best mode. Moreover, the calculated binding free energy (-13.2 kcal/mol) is in reasonable agreement with experiment (-11.6 kcal/mol). In addition, this procedure was also quite successful in modeling the complex and the structure of the last snapshot was quite close to that of the measured 2,3 A resolution crystal (structure the root-mean-square deviation of the 54 C(alpha) around the binding site and the inhibitor is 1.1 A). We want to point out that this result was achieved without prior knowledge of the structure of the efavirenz/RT complex. Therefore, molecular docking combined with MD simulations followed by MM-PBSA analysis is an attractive approach for modeling protein complexes a priori.     

Catalytic mechanism and product specificity of the histone lysine methyltransferase SET7/9: an ab initio QM/MM-FE study with multiple initial structures

Histone lysine methylation is emerging as an important mechanism to regulate chromatin structure and gene activity. To provide theoretical understanding of its reaction mechanism and product specificity, ab initio quantum mechanical/molecular mechanical free energy (QM/MM-FE) calculations and molecular dynamics simulations have been carried out to investigate the histone lysine methyltransferase SET7/9. It is found that the methyl-transfer reaction catalyzed by SET7/9 is a typical in-line S(N)2 nucleophilic substitution reaction with a transition state of 70% dissociative character. The calculated average free energy barrier at the MP2(6-31+G) QM/MM level is 20.4 +/- 1.1 kcal/mol, consistent with the activation barrier of 20.9 kcal/mol estimated from the experimental reaction rate. The barrier fluctuation has a strong correlation with the nucleophilic attack distance and angle in the reactant complex. The calculation results show that the product specificity of SET7/9 as a monomethyltransferase is achieved by disrupting the formation of near-attack conformations for the dimethylation reaction.     

DFT study of the mechanisms of in water Au(I)-catalyzed tandem [3,3]-rearrangement/Nazarov reaction/[1,2]-hydrogen shift of enynyl acetates: a proton-transport catalysis strategy in the water-catalyzed [1,2]-hydrogen shift

A computational study with the Becke3LYP density functional was carried out to elucidate the mechanisms of Au(I)-catalyzed reactions of enynyl acetates involving tandem [3,3]-rearrangement, Nazarov reaction, and [1,2]-hydrogen shift. Calculations indicate that the [3,3]-rearrangement is a two-step process with activation free energies below 10 kcal/mol for both steps. The following Nazarov-type 4pi electrocyclic ring-closure reaction of a Au-containing dienyl cation is also easy with an activation free energy of 3.2 kcal/mol in CH2Cl2. The final step in the catalytic cycle is a [1,2]-hydride shift, and this step is the rate-limiting step (with a computed activation free energy of 20.2 kcal/mol) when dry CH2Cl2 is used as the solvent. When this tandem reaction was conducted in wet CH2Cl2, the [1,2]-hydride shift step in dry solution turned to a very efficient water-catalyzed [1,2]-hydrogen shift mechanism with an activation free energy of 16.4 kcal/mol. Because of this, the tandem reaction of enynyl acetates was found to be faster in wet CH2Cl2 as compared to the reaction in dry CH2Cl2. Calculations show that a water-catalyzed [1,2]-hydrogen shift adopts a proton-transport catalysis strategy, in which the acetoxy group in the substrate is critical because it acts as either a proton acceptor when one water molecule is involved in catalysis or a proton-relay stabilizer when a water cluster is involved in catalysis. Water is found to act as a proton shuttle in the proton-transport catalysis strategy. Theoretical discovery of the role of the acetoxy group in the water-catalyzed [1,2]-hydrogen shift process suggests that a transition metal-catalyzed reaction involving a similar hydrogen shift step can be accelerated in water or on water with only a marginal effect, unless a proton-accepting group such as an acetoxy group, which can form a hydrogen bond network with water, is present around this reaction's active site.     

Mechanism of water exchange in aqueous uranyl(VI) ion. A density functional molecular dynamics study

Constrained Car-Parrinello molecular dynamics simulations and thermodynamic integration have been performed for an associative pathway of water exchange between aqueous [UO2(OH2)5]2+ and bulk water. The simulated free energy of activation for this process, 6.7 kcal mol(-1), is significantly lower than that computed for a purely dissociative mechanism, 10.8 kcal mol(-1). Because the transient hexahydrate is indicated to have no chemically significant lifetime, the exchange mechanism can be classified as associative interchange.     

How the stabilization of INK4 tumor suppressor 3D structure evaluated by quantum chemical and molecular mechanics calculations corresponds well with experimental results: interplay of association enthalpy, entropy, and solvation effects

The folding free energy of the INK4c tumor suppressor core, consisting of 10 helices, was determined as the sum of gas-phase interaction enthalpy, gas-phase interaction entropy, and dehydration and hydration free energy. The interaction energy and the hydration free energy were determined using the nonempirical density functional theory (DFT) method, augmented by a dispersion-energy correction term, the semiempirical density-functional tight-binding method covering the dispersion energy, and the density functional theory/conductor-like screening model (DFT/COSMO) procedure, whereas the interaction entropy was calculated with the empirical Cornell et al. force field. Alternatively, all contributions were evaluated consistently using empirical methods. All the values of the interaction energy of helix pairs are stabilizing, and the dominant stabilizing terms stem from the London dispersion energy and, in the case of charged systems, the electrostatic energy. The stabilization energy of the core, determined as the difference of the energy of the core and 10 separate helices, amounts to approximately 450 kcal/mol. Systematically, the difference in the hydration free energy of a helix pair and its separate components is smaller in magnitude than the interaction energy, and it is negative for some pairs while positive for others. The average total free energy of a core formation amounts to -29.6 kcal/mol (yielded by scaled quantum-chemical methods) and +13.9 kcal/mol (resulting from empirical methods). These values are considerably smaller than their single components, which are dominated by the interaction energy. The computationally predicted interval encloses the experimental value of the folding free energy (-2.8 kcal/mol).