Transition-state structures for describing the enzyme-catalyzed mechanisms of rubisco

The carboxylation and oxygenation processes of a model substrate, 3,4-dihydroxy-2-pentanone, have been theoreticaly characterized as a set of steps, mimicking the corresponding reactions of D-ribulose-1,5-bisphosphate catalyzed by rubisco. A theoretical characterization is carried out of transition-state structures and possible molecular intermediates represented as saddle points of index 1 and minimum energy structures, respectively. The quantum chemical characterization, at the HF/3-21G calculation level, of these stationary points is used to rationalize and to discuss both catalyzed sequences. The reported set of these stationary points maps out most experimental aspects of the reaction pathways for the real system. Received: 24 March 1998 / Accepted: 3 September 1998 / Published online: 10 December 1998     

META 4. Prediction of the metabolism of polycyclic aromatic hydrocarbons

Polycyclic aromatic hydrocarbons (PAHs) are widely distributed in the environment and are often implicated as potential carcinogens. It is generally believed that the carcinogenic potential of polycyclic aromatic hydrocarbons is linked to the formation of ultimate carcinogens generated by metabolic biotransformations. In this paper we propose a methodology that consists of using both quantum chemical properties and structural features of the reaction sites to predict PAH metabolism. Two essential questions have been answered: at which sites will the reaction take place and does the transformation consist of epoxidation or hydroxylation? This methodology has been successfully implemented into an expert system, META, for the evaluation of metabolic transformations of new chemicals. Received: 3 April 1998 / Accepted: 6 July 1998 / Published online: 7 October 1998     

The search for stationary points on a quantum mechanical/molecular mechanical potential-energy surface

 We propose a methodology to locate stationary points on a quantum mechanical/molecular mechanical potential-energy surface. This algorithm is based on a suitable approximation of an initial full Hessian matrix, either a modified Broyden–Fletcher–Goldfarg–Shanno or a Powell update formula for the location of, respectively, a minimum or a transition state, and the so-called rational function optimization. The latter avoids the Hessian matrix inversion required by a quasi-Newton–Raphson method. Some examples are presented and analyzed. Received: 16 July 2001 / Accepted: 9 October 2001 / Published online: 9 January 2002     

Electron affinities, excitation energies and ionization potentials of the transition metals (I) Sc and Ti

The electron affinities of the Sc and Ti atoms have been obtained by configuration interaction calculations. Energy convergence with respect to the systematic expansion of both the one-electron basis set and the configuration space was investigated for valence electrons, and the inclusion of correlation contributions from core electrons and relativistic effects gave the electron affinities of 0.181 eV and 0.163 eV for Sc and Ti, respectively. These are in excellent agreement with the observed values of 0.189 ± 0.020 eV and 0.080 eV. The same approach was applied for the first excited states and positive ions of both atoms. Excellent agreement with the experimental results was also obtained for these states. Received: 16 February 1998 / Accepted: 2 April 1998 / Published online: 23 June 1998     

Ab initio studies on the mechanism of dimerization reactions of ketene imine and bis(trifluoromethyl)ketene imine

The dimerization reactions of ketene imine and bis(trifluoromethyl)ketene imine were studied theoretically. All the dimerization processes take place in a concerted but asynchronous manner, each proceeding through a four-membered ring transition state. For the ketene imine dimerization reactions, three different processes have almost equal activation barriers, while for the three bis(trifluoromethyl)ketene imine dimerization processes the reaction giving symmetrical a four-membered heterocyclic product has the lowest activation barrier. Received: 15 July 1998 / Accepted 3 September 1998 / Published online: 17 December 1998     

Transition state structure invariance to model system size and calculation levels: a QM/MM study of the carboxylation step catalyzed by Rubisco

The present study elucidates structural features related to the molecular mechanism in the carboxylation step of the reaction catalyzed by Rubisco. Starting from the initial X-ray Protein Data Bank structure of a Rubisco monomer, the reactive subsystem in vacuo is subjected to quantum chemical semiempirical and ab initio studies, while the effects of the protein environments are included by means of a hybrid quantum mechanical/molecular mechanical (QM/MM) approach. The QM/MM is used to characterize the transition structure for carboxylation inside the protein. The calculations were made with the AM1/CHARMM/GRACE scheme. Comparisons between the in vacuo and in situ transition structures show remarkable invariance with respect to geometric parameters, index and transition vector amplitudes. The transition state couples the carbon dioxide attack to the C2 center of the substrate in its dienol form with a simultaneous intramolecular hydrogen transfer from the C2 atom to the hydroxyl group linked to the C3 center. This study suggests that carboxylation may be simultaneously coupled to the activation of the C3 center in the enzyme. Received: 24 March 1998 / Accepted: 3 September 1998 / Published online: 10 December 1998     

An ab initio study of the conformational preferences of Hoechst 33258 in gas-phase and aqueous solution environments

A quantum mechanical study of the conformational preferences of Hoechst 33258, a synthetic minor groove-binding drug, has been performed in both gas-phase and aqueous solution. Gas-phase calculations were performed at the HF/6-31G(d) and MP2/6-31G(d) levels of theory, whereas calculations in the aqueous solution phase were performed using the PCM model with the 6-31G(d) basis set. The molecule was divided into three fragments, which were submitted to a systematic and detailed conformational study. The results clearly indicate that Hoechst 33258 does not adopt a planar conformation in either the gas-phase or aqueous solution. Thus, a folded conformation is not induced by binding of the molecule to DNA, but is an intrinsic property of the compound. Received: 3 March 1998 / Accepted: 29 May 1998 / Published online 19 August 1998     

Periodic orbits and vibrational wave functions for DCP: nonlinear resonances in isotopically substituted molecules

We investigate, by means of classical and quantum mechanics, how isotopic substitution (H/D) affects the vibrational dynamics of HCP. The analysis of periodic orbits, including the location of the principal families as well as saddle node bifurcations, reveals a totally different picture for the phase-space resonance structure for HCP and DCP. While HCP is characterized by a 1:2 resonance between the CP stretch and the bending mode, DCP shows a 1:2 resonance between the two stretching degrees of freedom. Saddle node bifurcations, which are associated with large-amplitude motion of H/D moving from the C- to the P-end, appear at considerably higher energies in DCP than in HCP. These results are in accord with exact quantum mechanical calculations of the vibrational levels. Received: 24 June 1998 / Accepted: 10 August 1998 / Published online: 9 October 1998     

An implementation of the conductor-like screening model of solvation within the Amsterdam density functional package

The conductor-like screening model (COSMO) of solvation has been implemented in the Amsterdam density functional program with maximum flexibility in mind. Four cavity definitions have been incorporated. Several iterative schemes have been tested for solving the COSMO equations. The biconjugate gradient method proves to be both robust and memory-conserving. The interaction between the surface charges and the electron density may be calculated by integrating over either the fitted or exact density, or by calculating the molecular potential. A disk-smearing algorithm is applied in the former case to avoid singularities. Several self-consistent field/COSMO coupling schemes were examined in an attempt to reduce computational effort. A gradient-preserving algorithm for removing outlying charge has been implemented. Preliminary optimized radii are given. Applications to the benzene oxide-oxepin valence tautomerization and to glycine conformation are presented. Received: 13 November 1998 / Accepted: 16 December 1998 / Published online: 16 March 1999     

The generalized hybrid orbital method for combined quantum mechanical/molecular mechanical calculations: formulation and tests of the analytical derivatives

 Hybrid quantum mechanical (QM) and molecular mechanical (MM) potentials are becoming increasingly important for studying condensed-phase systems but one of the outstanding problems in the field has been how to treat covalent bonds between atoms of the QM and MM regions. Recently, we presented a generalized hybrid orbital (GHO) method that was designed to tackle this problem for hybrid potentials using semiempirical QM methods [Gao et al. (1998) J Phys Chem A 102: 4714–4721]. We tested the method on some small molecules and showed that it performed well when compared to the purely QM or MM potentials. In this article, we describe the formalism for the determination of the GHO energy derivatives and then present the results of more tests aimed at validating the model. These tests, involving the calculation of the proton affinities of some model compounds and a molecular dynamics simulation of a protein, indicate that the GHO method will prove useful for the application of hybrid potentials to solution-phase macromolecular systems. Received: 4 October 1999 / Accepted: 18 December 1999 / Published online: 5 June 2000     

Generalized extended empirical bond-order dependent force fields including nonbond interactions

We present a general approach for describing chemical processes (bond breaking and bond formation) in materials using force fields (FF) that properly describe multiple bonds at small distances while describing nonbond (Coulomb and van der Waals) interactions at long distances. This approach is referred to as the generalized extended empirical bond-order dependent FF. In this paper we use the Brenner empirical bond-order dependent FF for the short-range interactions and report applications on the energetics and structures of graphite crystal, dynamics of molecular crystals, and distortions of bucky tubes. Received: 7 August 1998 / Accepted: 26 October 1998 / Published online: 16 March 1999     

Prediction of protein structure using a knowledge-based off-lattice united-residue force field and global optimization methods

A united-residue model of polypeptide chains developed in our laboratories with united side-chains and united peptide groups as interaction sites is presented. The model is designed to work in continuous space; hence efficient global-optimization methods can be applied. In this work, we adopted the distance-scaling method that is based on continuous deformation of the original rugged energy hypersurface to obtain a smoothed surface. The method has been applied successfully to predict the structures of simple motifs, such as the three-helix bundle structure of the 10-58 fragment of staphylococcal protein A in de novo folding simulations and more complicated motifs in inverse-folding simulations. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

Global geometry optimization of small silicon clusters at the level of density functional theory

By an application to small silicon clusters Si _N (with N = 4,5,7,10) it is shown that truly global geometry optimization on an ab initio or density functional theory level can be achieved, at a computational cost of approximately 1–5 traditional local optimization runs (depending on cluster size). This extends global optimization from the limited area of empirical potentials into the realm of ab initio quantum chemistry. Received: 24 February 1998 / Accepted: 6 March 1998 / Published online: 17 June 1998     

Convergence of the density functional one-centre expansion for the molecular continuum: N2 and (CH3)3N

A large-scale one-centre expansion with a radial B-spline basis set is implemented for bound and continuum states. A Kohn-Sham hamiltonian is employed with Hartree and exchange-correlation potentials calculated from the SCF electron density taken from a previous LCAO calculation. An inverse iteration method is used to obtain the continuum wavefunction, from which the cross section and asymmetry parameter are calculated. The convergence with respect to angular momentum and cut-off radius is analysed for N₂. The relevance of multipolar contributions even at large distances is shown and suggestions for further improvements are given. In order to show that the present method is suitable to treat systems of moderate size, the (CH₃)₃N molecule has also been calculated and the results are compared with experiment. Received: 19 May 1998 / Accepted: 20 August 1998 / Published online: 7 December 1998     

Information about the biologically relevant properties of Clostridium pasteurianum rubredoxin obtained from modeling and dynamics simulations of molecular variants

Rubredoxins are small electron transfer proteins containing one iron atom at their active site. The rubredoxin from the anaerobic bacterium Clostridium pasteurianum has been subjected to molecular dynamics studies starting from the minimized solvated structure. The results of the simulations have been compared with identical ones carried out with selected mutated forms of the protein obtained by molecular modeling. Surface residues, which are highly conserved among rubredoxins and close to the cysteine ligands, can be replaced by glutamates, i.e. long chain carboxylates. The main structural consequence is a shift of the protein backbone bearing conserved aromatic residues. Reciprocally, substitution of the aromatic residue closest to the iron atom shifts the cysteine-containing peptide fragments. These observations have been related to the changes in electron transfer and redox properties previously measured for this set of rubredoxin molecular variants. Received: 16 May 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

Diatomic potential well depths from analyses of high-resolution electron energy spectra for autoionizing collision complexes

High-resolution energy spectra of electrons released in Penning ionization collisions of metastable rare gas atoms Rg*(ns) (Rg = He, Ne, Ar, Kr, Xe) with several open-shell and closed-shell atoms are analyzed to determine the well depth of the potential energy curve which describes the respective autoionizing collision complex. We thereby elucidate trends in the chemical interaction of Rg* with closed-shell target atoms A(ns ²) and establish a basis for detailed comparison with the respective interactions involving open-shell, ground state alkali atoms A(ns). From electron energy spectra due to␣associative ionization (RgH⁺ formation) in Rg* + H(1s) collisions, we determine binding energies for the RgH⁺(¹Σ) ground state potential (Rg = Ne, Ar, Kr, Xe) with uncertainties around 0.03 eV. Received: 30 June 1998 / Accepted: 5 August 1998 / Published online: 28 October 1998     

The spin-forbidden reaction CH(2∏) + N2→ HCN + N(4S) revisited I. Ab initio study of the potential energy surfaces

High-level ab initio electronic structure theories have been applied to investigate the detailed reaction mechanism of the spin-forbidden reaction CH(²∏) + N₂ → HCN + N(⁴S). The G2M(RCC) calculations provide accurate energies for the intermediates and transition states involved in the reaction, whereas the B3LYP/6-311G(d,p) method overestimates the stability of some intermediates by as much as about 10 kcal/mol. A few new structures have been found for both the doublet and quartet electronic states, which are mainly involved in the dative pathways. However, due to the higher energies of these structures, the dominant mechanism remains the one involving the C ₂ intersystem-crossing step. The C ₂ minima on the seam of crossing (MSX) structures and the spin-orbit coupling between the doublet and quartet electronic states are rather close to those found in previous studies. Vibrational frequencies orthogonal to the normal of the seam which have been applied in a separate publication to calculate the rate of the CH(²∏) + N₂ → HCN + N(⁴S) reaction with a newly proposed nonadiabatic transition-state theory for spin-forbidden reactions have been calculated at the MSX from first principles. Received: 23 June 1998 / Accepted: 21 September 1998 / Published online: 8 February 1999     

Weighted HOMO-LUMO energy separation as an index of kinetic stability for fullerenes

A very simple but general index of kinetic stability, T, is proposed for π-electron systems, which is defined as a highest occupied molecular orbital (HOMO)- lowest unoccupied molecular orbital (LUMO) energy separation multiplied by the number of conjugated atoms. This new index can be justified by relating it to the approximate form of the superdelocalizability, an index of chemical reactivity defined by Fukui et al. It is best suited for predicting the kinetic stability of fullerenes. All isolable fullerene isomers have T values larger than 13. Received: 24 June 1998 / Accepted: 3 September 1998 / Published online: 17 December 1998     

Visual valence bond rules for chemical reactions

A symmetry-adaptation rule of the valence bond structure for concerted reactions was developed within the bonded tableau valence bond formalism. According to a symmetry analysis of the valence bond structure segments accounting for the reaction, one can predict whether a chemical process is favored or unfavored. This method is based on conceptual resonance theory and the visual valence bond approach, without carrying out any explicitly theoretical calculations to know orbital details. Furthermore, by imposing a phase factor on each bonding pair, namely, the phase alternation postulate, the mechanisms of the concerted reactions can be easily outlined. These rules have been applied to organic and inorganic reactions including the participation of biradicals and species with multi-reference character. Received: 7 September 1998 / Accepted: 9 November 1998 / Published online: 1 February 1999     

Modelling the active site of glyceraldehyde-3 phosphate dehydrogenase with the LSCF formalism

In the framework of a theoretical approach to the relationship between structure and reactivity of the catalytic centers of enzymes, glyceraldehyde-3 phosphate dehydrogenase (GAPDH) has been chosen as a model enzyme. In GAPDH, the proximity of His₁₇₆ increases the reactivity of Cys₁₄₉ at neutral pH; however, its presence alone is not sufficient to explain the reactivity of the catalytic Cys. In order to determine which other interactions play an important role, a study of the geometric and electronic structure of the catalytic site has been made using a hybrid quantum mechanics/molecular mechanics local self-consistent field method. This allows the computation of the electronic properties of amino acid residues in subsystems influenced by other parts of the macromolecule. The quantum subsystem was centered on the Cys₁₄₉ residue of GAPDH. The structures of GAPDH taken from the crystallographic database did not include hydrogen atoms and these had to be added taking into account the fact that, in the active site, His₁₇₆ has three tautomeric forms: δ-His protonated, ε-His protonated and His⁺. The results presented here suggest that the most stable His…Cys system in GAPDH is a strongly hydrogen-bonded Cys₁₄₉ ⁻/His₁₇₆ ⁺ ion pair. Received: 24 March 1998 / Accepted: 3 September 1998 / Published online: 23 November 1998