Igor A. Topol

CALCULATION OF THE AQUEOUS SOLVATION FREE ENERGY OF THE PROTON

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...

Structure of HIV-1 protease with KNI-272, a tight-binding transition-state analog containing allophenylnorstatine.

BACKGROUND HIV-1 protease (HIV PR), an aspartic protease, cleaves Phe-Pro bonds in the Gag and Gag-Pol viral polyproteins. Substrate-based peptide mimics constitute a major class of inhibitors of HIV PR presently being developed for AIDS treatment. One such compound, KNI-272, which incorporates allophenylnorstatine (Apns)-thioproline (Thp) in place of Phe-Pro, has potent antiviral activity and is undergoing clinical trials. The structure of the enzyme-inhibitor complex should lead to an understanding of the structural basis for its tight binding properties and provide a framework for interpreting the emerging resistance to this drug. RESULTS The three-dimensional crystal structure of KNI-272 bound to HIV PR has been determined to 2.0 A resolution and used to analyze structure-activity data and drug resistance for the Arg8-->Gln and ILe84-->Val mutations in HIV PR. The conformationally constrained Apns-Thp linkage is favorably recognized in its low energy trans conformation, which results in a symmetric mode of binding to the active-site aspartic acids and also explains the unusual preference of HIV PR for the S, or syn, hydroxyl group of the Apns residue. The inhibitor recognizes the enzyme via hydrogen bonds to three bridging water molecules, including one that is coordinated directly to the catalytic Asp125 residue. CONCLUSIONS 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.

On the structure and thermodynamics of solvated monoatomic ions using a hybrid solvation model

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 ty...

QM/MM modeling the Ras–GAP catalyzed hydrolysis of guanosine triphosphate

The mechanism of the hydrolysis reaction of guanosine triphosphate (GTP) by the protein complex Ras–GAP (p21ras – p120GAP) 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 γ‐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 γ‐phosphate group of GTP through the corresponding transition state TS2. Direct quantum calculations show that, in this particular environment, the reaction GTP + H2O → GDP + H2PO  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. Proteins 2005.

Mechanisms of guanosine triphosphate hydrolysis by Ras and Ras-GAP proteins as rationalized by ab initio QM/MM simulations

The hydrolysis reaction of guanosine triphosphate (GTP) by p21ras (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 γ‐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 (p21ras–p120GAP) 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. Proteins 2007.

Mechanism of the myosin catalyzed hydrolysis of ATP as rationalized by molecular modeling

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 ADP·VO4−, a minimum-energy path is found for the transformation ATP + H2O → ADP + Pi that is characterized by two distinct events: (i) a low activation-energy cleavage of the PγOβγ bond and separation of the γ-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 γ-phosphate and for the transfer of a proton to stably bound second water. In addition, the PγOβγ 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.

Peptide models. XXXIII. Extrapolation of low-level Hartree-Fock data of peptide conformation to large basis set SCF, MP2, DFT, and CCSD(T) results. The Ramachandran surface of alanine dipeptide computed at various levels of theory

At the dawn of the new millenium, new concepts are required for a more profound understanding of protein structures. Together with NMR and X‐ray‐based 3D‐stucture determinations in silico methods are now widely accepted. Homology‐based modeling studies, molecular dynamics methods, and quantum mechanical approaches are more commonly used. Despite the steady and exponential increase in computational power, high level ab initio methods will not be in common use for studying the structure and dynamics of large peptides and proteins in the near future. We are presenting here a novel approach, in which low‐ and medium‐level ab initio energy results are scaled, thus extrapolating to a higher level of information. This scaling is of special significance, because we observed previously on molecular properties such as energy, chemical shielding data, etc., determined at a higher theoretical level, do correlate better with experimental data, than those originating from lower theoretical treatments. The Ramachandran surface of an alanine dipeptide now determined at six different levels of theory [RHF and B3LYP 3‐21G, 6‐31+G(d) and 6‐311++G(d,p)] serves as a suitable test. Minima, first‐order critical points and partially optimized structures, determined at different levels of theory (SCF, DFT), were completed with high level energy calculations such as MP2, MP4D, and CCSD(T). For the first time three different CCSD(T) sets of energies were determined for all stable B3LYP/6‐311++G(d,p) minima of an alanine dipeptide. From the simplest ab initio data (e.g., RHF/3‐21G) to more complex results [CCSD(T)/6‐311+G(d,p)//B3LYP/6‐311++G(d,p)] all data sets were compared, analyzed in a comprehensive manner, and evaluated by means of statistics.

Flexible effective fragment QM/MM method: Validation through the challenging tests

A new version of the QM/MM method, which is based on the effective fragment potential (EFP) methodology [Gordon, M. et al., J Phys Chem A 2001, 105, 293] but allows flexible fragments, is verified through calculations of model molecular systems suggested by different authors as challenging tests for QM/MM approaches. For each example, the results of QM/MM calculations for a partitioned system are compared to the results of an all‐electron ab initio quantum chemical study of the entire system. In each case we were able to achieve approximately similar or better accuracy of the QM/MM results compared to those described in original publications. In all calculations we kept the same set of parameters of our QM/MM scheme. A new test example is considered when calculating the potential of internal rotation in the histidine dipeptide around the CαCβ side chain bond.

Electronic Excitations of the Chromophore from the Fluorescent Protein asFP595 in Solutions.

We present the results of modeling spectral properties of the chromophore, 2-acetyl-4-(p-hydroxybenzylidene)-1-methyl-5-imidazolone (AHBMI), from the newly discovered fluorescent protein asFP595 in different solvents and compare computational and recent experimental data. The time-dependent density functional theory (TDDFT) method is used to estimate positions of spectral bands with large oscillator strengths for vertical transitions to excited states following geometry optimizations of chromophore coordinates in vacuo and in solutions. The performance of different TDDFT functionals in computing excitations for a simpler chromophore from the green fluorescent protein was tested at the preliminary stage. Properties of various protonation states (neutral, anionic, zwitterionic) for the cis and trans conformations of AHBMI are compared. By using the polarizable continuum model, the following solvents have been considered for AHBMI:  water, ethanol, acetonitrile, and dimethyl sulfoxide. It is shown that the bands found experimentally in aqueous solution refer to the cis neutral and cis anionic (or trans zwitterionic) conformations. The computed band positions deviate from experimental ones in water by no more than 35 nm (0.23 eV). In accord with experimental studies, the band shifts in different solvents do not show correlation with the dielectric constant or dipole moment; however, the computed values of the shifts are much smaller than those measured experimentally for the ionic species.

Theoretical calculations of glycine and alanine gas-phase acidities

The gas-phase acidities of glycine and alanine were determined by using a variety of high level theoretical methods to establish which of these would give the best results with accessible computational efforts. MP2, MP4, QCISD, G2 ab initio procedures, hybrid Becke3-LYP (B3LYP) and gradient corrected Becke-Perdew (BP) and Perdew-Wang and Perdew (PWP) nonlocal density functionals were used for the calculations. A maximum deviation of approximately 13 and 18 kJ/mol from experimental data was observed for the computed ΔHacid and ΔGacid values, respectively. The best result was obtained at G2 level, but comparable reliability was reached when the considerably less time consuming B3LYP, BP, and PWP density functional approaches were employed.