The value of the proton hydration free energy, ΔGhyd(H+), has been quoted in the literature to be from −252.6 to −262.5 kcal/mol. In this article, we present a theoretical model for calculating the hydration free energy of ions in aqueous solvent and use this model to calculate the proton hydration free energy, ΔGhyd(H+), in an effort to resolve the uncertainty concerning its exact value. In the model we define ΔGhyd(H+) as the free energy change associated with the following process: ΔG[H+(gas)+H2nOn(aq)→H+(H2nOn)(aq)], where the solvent is represented by a neutral n-water cluster embedded in a dielectric continuum and the solvated proton is represented by a protonated n-water cluster also in the continuum. All solvated species are treated as quantum mechanical solutes coupled to a dielectric continuum using a self consistent reaction field cycle. We investigated the behavior of ΔGhyd(H+) as the number of explicit waters of hydration is increased from n=1 to n=6. As n increases from 1 to 3, the hydration free energy decreases dramatically. However, for n=4–6 the hydration free energy maintains a relatively constant value of −262.23 kcal/mol. These results indicate that the first hydration shell of the proton is composed of at least four water molecules. The constant value of the hydration free energy for n⩾4 strongly suggests that the proton hydration free energy is at the far lower end of the range of values that have been proposed in the literature.

The structure of the HIV PR/KNI-272 complex illustrates the importance of limiting the conformational degrees of freedom and of using protein-bound water molecules for building potent inhibitors. The binding mode of HIV PR inhibitors can be predicted from the stereochemical relationship between adjacent hydroxyl-bearing and side chain bearing carbon atoms of the P1 substituent. Our structure also provides a framework for designing analogs targeted to drug-resistant mutant enzymes.

We calculate free energy changes of ionization reactions in aqueous solvent using a self-consistent reaction field method. In the calculations all species are treated as quantum mechanical solutes coupled to a solvent dielectric continuum. We show for a series of substituted imidazole compounds that both absolute and relative pK a values for the deprotonation of nitrogen on the imidazole ring can be obtained with an average absolute deviation of 0.8 units from experiment. This degree of accuracy is possible only if the solutes are treated at the correlated level using either G2 type or density functional theory. Inconsistencies in published experimental free energies of hydration that might undermine the reliability of the calculated absolute pK a values are discussed.

The mechanism of the hydrolysis reaction of guanosine triphosphate (GTP) by the protein complex Ras-GAP (p21(ras) - p120(GAP)) has been modeled by the quantum mechanical-molecular mechanical (QM/MM) and ab initio quantum calculations. Initial geometry configurations have been prompted by atomic coordinates of a structural analog (PDBID:1WQ1). It is shown that the minimum energy reaction path is consistent with an assumption of two-step chemical transformations. At the first stage, a unified motion of Arg789 of GAP, Gln61, Thr35 of Ras, and the lytic water molecule results in a substantial spatial separation of the gamma-phosphate group of GTP from the rest of the molecule (GDP). This phase of hydrolysis process proceeds through the low-barrier transition state TS1. At the second stage, Gln61 abstracts and releases protons within the subsystem including Gln61, the lytic water molecule and the gamma-phosphate group of GTP through the corresponding transition state TS2. Direct quantum calculations show that, in this particular environment, the reaction GTP + H(2)O --> GDP + H(2)PO(4) (-) can proceed with reasonable activation barriers of less than 15 kcal/mol at every stage. This conclusion leads to a better understanding of the anticatalytic effect of cancer-causing mutations of Ras, which has been debated in recent years.

The energy of dimerization of two N-methylacetamide (NMA) molecules in vacuum is calculated using density functional theory. Natural orbital analysis suggests that the dimerization energy of -6.6 kcal/mol is predominantly due to the (NsH‚‚‚OdC) donor-acceptor interaction. The gas phase to water hydration free energies and the free energies of transfer from the aqueous phase to liquid alkane of hydrogen bonded, (NsH‚‚‚OdC), and nonbonded, (NsH,OdC), groups are calculated using a continuum solvent model. On the basis of these calculations, we estimate the free energy of forming an amide hydrogen bond in the context of the NMA dimer in water and in liquid alkane as ∼-1 and ∼-5 kcal/mol, respectively. The relevance of these calculations to processes such as protein folding and membrane insertion of proteins is discussed.

The hydrolysis reaction of guanosine triphosphate (GTP) by p21(ras) (Ras) has been modeled by using the ab initio type quantum mechanical-molecular mechanical simulations. Initial geometry configurations have been prompted by atomic coordinates of the crystal structure (PDBID: 1QRA) corresponding to the prehydrolysis state of Ras in complex with GTP. Multiple searches of minimum energy geometry configurations consistent with the hydrogen bond networks have been performed, resulting in a series of stationary points on the potential energy surface for reaction intermediates and transition states. It is shown that the minimum energy reaction path is consistent with an assumption of a two-step mechanism of GTP hydrolysis. At the first stage, a unified action of the nearest residues of Ras and the nearest water molecules results in a substantial spatial separation of the gamma-phosphate group of GTP from the rest of the molecule (GDP). This phase of hydrolysis process proceeds through the low barrier (16.7 kcal/mol) transition state TS1. At the second stage, the inorganic phosphate is formed in consequence of proton transfers mediated by two water molecules and assisted by the Gln61 residue from Ras. The highest transition state at this segment, TS3, is estimated to have an energy 7.5 kcal/mol above the enzyme-substrate complex. The results of simulations are compared to the previous findings for the GTP hydrolysis in the Ras-GAP (p21(ras)-p120(GAP)) protein complex. Conclusions of the modeling lead to a better understanding of the anticatalytic effect of cancer causing mutation of Gln61 from Ras, which has been debated in recent years.

The hydration free energies relative to that of the proton are calculated for a representative set of monatomic ions Z±. These include cationic forms of the alkali earth elements Li, Na, and K, and anionic forms of the halogens F, Cl, and Br. In the current model the relative ion hydration free energy is defined as Δ[ΔGhyd(Z±)]=G(Z±[H2O]n(aq))−G(H+[H2O]n(aq))−G(Z±(gas))−G(H+(gas)), where the solvated ions are represented by ion–water clusters coupled to a dielectric continuum using a self-consistent reaction field cycle. An investigation of the behavior of Δ[ΔGhyd(Z±)] as the number of explicit waters of hydration is increased reveals convergence by n=4. This convergence indicates that the free energy change for the addition of water to a solvated proton–water complex is the same as the free energy change associated with the addition of water to a solvated Z±–water complex. This is true as long as there are four explicitly solvating waters associated with the ion. This convergence is independent of the type of monatomic ion studied and it occurs before the first hydration shell of the ions (typically ⩾6) is satisfied. Structural analysis of the ion–water clusters reveals that the waters within the cluster are more likely to form hydrogen bonds with themselves when clustering around anions than when clustering around cations. This suggests that for small ion–water clusters, anions are more likely to be externally solvated than cations.

The intrinsic chemical reaction of adenosine triphosphate (ATP) hydrolysis catalyzed by myosin is modeled by using a combined quantum mechanics and molecular mechanics (QM/MM) methodology that achieves a near ab initio representation of the entire model. Starting with coordinates derived from the heavy atoms of the crystal structure (Protein Data Bank ID code 1VOM) in which myosin is bound to the ATP analog ADP⅐VO 4 ؊ , a minimum-energy path is found for the transformation ATP ؉ H 2O 3 ADP ؉ Pi that is characterized by two distinct events: (i) a low activation-energy cleavage of the P ␥OO␤␥ bond and separation of the ␥-phosphate from ADP and (ii) the formation of the inorganic phosphate as a consequence of proton transfers mediated by two water molecules and assisted by the Glu-459 -Arg-238 salt bridge of the protein. The minimum-energy model of the enzyme-substrate complex features a stable hydrogen-bonding network in which the lytic water is positioned favorably for a nucleophilic attack of the ATP ␥-phosphate and for the transfer of a proton to stably bound second water. In addition, the P␥OO␤␥ bond has become significantly longer than in the unbound state of the ATP and thus is predisposed to cleavage. The modeled transformation is viewed as the part of the overall hydrolysis reaction occurring in the closed enzyme pocket after ATP is bound tightly to myosin and before conformational changes preceding release of inorganic phosphate.ATP hydrolysis ͉ enzymatic catalysis ͉ energy profile ͉ quantum mechanics and molecular mechanics simulations T he mechanism of hydrolysis of adenosine triphosphate (ATP) by myosin, leading to adenosine diphosphate (ADP) and inorganic phosphate (P i ), which constitutes one of the most important enzymatic reactions responsible for energy transduction into the directed movements of adjoining actin filaments, continues to remain a subject of active debates (1-16), a significant part of which relates to what constitutes the acceptor of the proton that must be released by the ''lytic'' water in its nucleophilic attack on the ATP ␥-phosphate.In terms of the generally accepted kinetic scheme (1-3), the relevant ATP-myosin transformations may be described by the equationin which M* and M** indicate conformers of myosin. As reported (1-3), reaction (Eq. 1) occurs with a near unit equilibrium constant K Ͻ 10 and the estimated rate constants k ϩ Ն 160 s Ϫ1 and k Ϫ Ն 18 s Ϫ1 . The rate constant k ϩ ϭ 160 s Ϫ1 can be converted to the free-energy activation barrier ⌬G # Ϸ 14.6 kcal/mol at room temperature, T ϭ 300 K, by applying a simple transition-state theory formula (17) k Ϸ 6⅐10 12 exp͓Ϫ⌬G # ͞RT͔. [2]However, noting that the experimental rate constants of reaction (Eq. 1) incorporate contributions from conformational changes in the protein from M* to M** leads us to expect that the activation energy of the intrinsic chemical reactionwhich excludes conformational rearrangements, should be considerably Ͻ14.6 kcal/mol. However, previous attempts (13, 15, 16) to simulate the mechanism of react...