Sum Of Interactions Between Fragments Ab Research Articles

Could an anisotropic molecular mechanics/dynamics potential account for sigma hole effects in the complexes of halogenated compounds?

Halogenated compounds are gaining an increasing importance in medicinal chemistry and materials science. Ab initio quantum chemistry (QC) has unraveled the existence of a "sigma hole" along the C-X (X = F, Cl, Br, I) bond, namely, a depletion of electronic density prolonging the bond, concomitant with a build-up on its sides, both of which are enhanced along the F < Cl < Br < I series. We have evaluated whether these features were intrinsically built-in in an anisotropic, polarizable molecular mechanics (APMM) procedure such as SIBFA (sum of interactions between fragments ab initio computed). For that purpose, we have computed the interaction energies of fluoro-, chloro-, and bromobenzene with two probes: a divalent cation, Mg(II), and water approaching X through either one H or its O atom. This was done by parallel QC energy-decomposition analyses (EDA) and SIBFA computations. With both probes, the leading QC contribution responsible for the existence of the sigma hole is the Coulomb contribution E(c). For all three halogenated compounds, and with both probes, the in- and out-of-plane angular features of E(c) were closely mirrored by the SIBFA electrostatic multipolar contribution (E(MTP)). Resorting to such a contribution thus dispenses with empirically-fitted "extra", off-centered partial atomic charges as in classical molecular mechanics/dynamics.

Many‐body exchange‐repulsion in polarizable molecular mechanics. I. orbital‐based approximations and applications to hydrated metal cation complexes

We have quantified the extent of the nonadditivity of the short-range exchange-repulsion energy, E(exch-rep), in several polycoordinated complexes of alkali, alkaline-earth, transition, and metal cations. This was done by performing ab initio energy decomposition analyses of interaction energies in these complexes. The magnitude of E(exch-rep(n-body, n > 2)) was found to be strongly cation-dependent, ranging from close to zero for some alkali metal complexes to about 6 kcal/mol for the hexahydrated Zn(2+) complex. In all cases, the cation-water molecules, E(exch-rep(three-body)), has been found to be the dominant contribution to many-body exchange-repulsion effects, higher order terms being negligible. As the physical basis of this effect is discussed, a three-center exponential term was introduced in the SIBFA (Sum of Interactions Between Fragments Ab initio computed) polarizable molecular mechanics procedure to model such effects. The three-body correction is added to the two-center (two-body) overlap-like formulation of the short-range repulsion contribution, E(rep), which is grounded on simplified integrals obtained from localized molecular orbital theory. The present term is computed on using mostly precomputed two-body terms and, therefore, does not increase significantly the computational cost of the method. It was shown to match closely E(three-body) in a series of test cases bearing on the complexes of Ca(2+), Zn(2+), and Hg(2+). For example, its introduction enabled to restore the correct tetrahedral versus square planar preference found from quantum chemistry calculations on the tetrahydrate of Hg(2+) and [Hg(H(2)O)(4)](2+).

Energy Analysis of Zn Polycoordination in a Metalloprotein Environment and of the Role of a Neighboring Aromatic Residue. What Is the Impact of Polarization?

We analyze the intermolecular interaction energies stabilizing the complex of ethanol in the binding site of alcohol dehydrogenase Zn-metalloenzyme (ADH). In this site Zn(II) is ligated by two cysteine and one imidazole residue and by the ethanol substrate. Ethanol is stacked over a phenylalanine residue. The system has been studied by means of SIBFA (Sum of Interactions Between Fragments Ab initio computed) polarizable molecular mechanics (PMM) supplemented by quantum chemical (QC) computations at various levels of theory. The nonadditivities of the QC interaction energies can be traced back by energy-decomposition analyses and are essentially due to polarization, charge-transfer, and electron correlation energies. These contributions can be reproduced by PMM computations. Interestingly, the polarization energy associated with the presence of the benzene ring in the ADH complex is canceled due to many-body/nonadditivity effects. Therefore this ring does not contribute to stabilization prior to including electron correlation/dispersion effects in the QC calculations or in the absence of the PMM dispersion energy contribution. When these effects are taken into account, the stabilization it contributes is in the 3-9 kcal/mol range, reflecting the need for an accurate reproduction of all components of the interaction energy by PMM.

Development, Validation, and Applications of Anisotropic Polarizable Molecular Mechanics to Study Ligand and Drug-Receptor Interactions

A correct representation of intermolecular interaction energies is necessary for reliable drug-receptor docking studies. While ab initio quantum chemistry with extended basis sets is the most accurate tool for that purpose, its use is precluded for very large molecular complexes. This constitutes the incentive for the development of accurate molecular mechanics potentials, in which the first-order electrostatic, and the second-order polarization energy contributions, are of essential importance. In this paper, we review the most important steps in the development of anisotropic, polarizable molecular mechanics (APMM) procedures. Among these, we illustrate validation tests of the ab initio-grounded, polarizable molecular mechanics potential, SIBFA (Sum of Interactions Between Fragments Ab initio computed). These are done by comparisons with parallel quantum-chemical (QC) results on representative multiply hydrogen-bonded complexes and polycoordinated complexes of one, or of two, divalent metal cations. For both kinds of complexes, the need to reproduce the non-additivity of the QC interaction energies is emphasized. One difficulty arises upon handling flexible molecules, due to the need to account simultaneously and consistently for the onset of inter- and intra-molecular polarization and charge-transfer effects. A new approach in the context of SIBFA was recently developed towards this aim, and tested in two cases of conformation-dependent cation-ligand interaction energies. The first relates to the complexes formed between the mecapto-carboxamide anion, an essential building-block of several Zn-metalloenzyme inhibitors, and Zn(II). The second relates to the complexes of the tetra-anionic pyrophosphate anion, a key building-block of ATP and GTP, with one or two divalent Zn(II) cations used as a probe. In the domain of applications, two recent studies are then presented. The first is the docking of the captopril drug to the active site of the binuclear Zn(II)- beta-lactamase enzyme. The second is the complex of a non-hydrolyzable analog of ATP with the active site of a binuclear Mg(II)-dependent kinase. An extension to an open-shell cation, Cu(II), is finally presented. The encouraging results presented in this review show that APMM procedures could be used in large-scale studies of ligand and drug-receptor interactions.

Binding of D- and L-captopril inhibitors to metallo-beta-lactamase studied by polarizable molecular mechanics and quantum mechanics.

The bacterial Zn2+ metallo-beta-lactamase from B. fragilis is a zinc-enzyme with two potential metal ion binding sites. It cleaves the lactam ring of antibiotics, thus contributing to the acquired resistance of bacteria against antibiotics. The present study bears on the binuclear form of the enzyme. We compare several possible binding modes of captopril, a mercaptocarboxamide inhibitor of several zinc-metalloenzymes. Two diastereoisomers of captopril were considered, with either a D- or an L-proline residue. We have used the polarizable molecular mechanics procedure SIBFA (Sum of Interactions Between Fragments ab initio computed). Two beta-lactamase models were considered, encompassing 104 and 188 residues, respectively. The energy balances included the inter and intramolecular interaction energies as well as the contribution from solvation computed using a continuum reaction field procedure. The thiolate ion of the inhibitor is binding to both metal ions, expelling the bridging solvent molecule from the uncomplexed enzyme. Different competing binding modes of captopril were considered, either where the inhibitor binds in a monodentate mode to the zinc cations only with its thiolate ion, or in bidentate modes involving additional zinc binding by its carboxylate or ketone carbonyl groups. The additional coordination by the inhibitor's carboxylate or carbonyl group always occurs at the zinc ion, which is bound by a histidine, a cysteine, and an aspartate side chain. For both diastereomers, the energy balances favor monodentate binding of captopril via S-. The preference over bidentate binding is small. The interaction energies were recomputed in model sites restricted to captopril, the Zn2+ cations, and their coordinating end side chains from beta-lactamase (98 atoms). The interaction energies and their ranking among competing arrangements were consistent with those computed by ab initio HF and DFT procedures.

Theoretical Investigations of the Influence of Pressure on the Selectivity of the Michael Addition of Diphenylmethaneamine to Stereogenic Crotonates.

SIBFA (sum of interactions between fragments ab initio computed) molecular mechanics systematics has been modified to take into account the effect of pressure on intra- and intermolecular energies. The van der Waals radii are related to the pressure, using Bridgman results on the variation of crystal volume, on one hand, and the relation between the volume of an atom and its van der Waals radius on the other. This procedure produces a decrease of the volume of the systems considered. The modified systematics is used for the study of the conformation at 1 atm and 15 kbar of two stereogenic crotonates and of the complexes formed by these two molecules with the diphenylmethaneamine and the three solvent molecules present in the experiment. The results obtained show that in the case of NMECC 1a the diastereoselectivity induced by high pressure and by the presence of methanol proceeds from an important stabilization of the pro-R reactive complex in which the crotonate has a stacked-transoid conformation. This stabilization is mainly due to intermolecular interactions. In the case of the second crotonate considered, NMCC 1b, our results indicate that pressure induces a stabilization of the pro-R and pro-S complexes having the axial conformation for which the reaction exhibits little diastereoselectivity in qualitative agreement with experimental data. This study tends to show that it is possible to account theoretically for the influence of pressure on molecular conformation and/or complex structure, using a molecular mechanics method that is able to take into account the variation of volumes of the different entities present in the system studied.

Conformational properties of a model alanyl dipeptide and of alanine-derived oligopeptides: Effects of solvation in water and in organic solvents—A combined SIBFA/continuum reaction field, ab initio self-consistent field, and density functional theory investigation

A ϕ/ψ conformational energy map of a model alanyl dipeptide is first drawn using the SIBFA (Sum of Interactions Between Fragments Ab initio computed) procedure [N. Gresh, P. Claverie and A. Pullman (1979) International Journal of Quantum Chemistry Symposium, Vol. 13, pp. 243–253; N. Gresh, P. Claverie and A. Pullman (1982) International Journal of Quantum Chemistry, Vol. 22, pp. 199–215; N. Gresh, P. Claverie and A. Pullman (1984) Theoretical Chimica Acta, Vol. 66, pp. 1–20; N. Gresh, P. Claverie and A. Pullman (1985) Theoretical Chimica Acta, Vol. 67, pp. 11–32; N. Gresh, A. Pullman and P. Claverie (1985) International Journal of Quantum Chemistry, Vol. 28, pp. 757–771; N. Gresh, P. Claverie and A. Pullman (1986) International Journal of Quantum Chemistry, Vol. 29, pp. 101–118; N. Gresh (1995) Journal of Computational Chemistry, Vol. 16, pp. 856–882; N. Gresh and D.R. Garmer (1996) Journal of Computational Chemistry, Vol. 17, pp. 1481–1495; N. Gresh, M. Leboeuf and D.R. Salahub (1994) in Modelling the Hydrogen Bond, Vol. 569, American Chemical Society Symposia, Smith, D.A., Ed., pp. 82–112; N. Gresh (1997) Journal de Chim.-Phys. (Paris), Vol. 94, pp. 1365–1416]. A new formulation of the intramolecular (conformational) energy is used, consistent with the refinements that were recently published for the intermolecular interaction energies in joint SIBFA/ab initio supermolecule Self-Consistent Field/Moller-Plesset (SCF/MP2) and Density Functional Theory (DFT) studies of cation-ligand [see Gresh (1995) and Gresh and Garmer (1996) above], and H-bonded [see Gresh et al. (1994) above] complexes. The accuracy of the procedure is assessed, on fourteen conformers selected from the map, by comparing their relative conformational energies with those obtained from SCF/MP2 and DFT computations. Conformational energy maps are then recomputed in the presence of water, dimethyl sulfoxide, chloroform, and carbon tetrachloride, the solvation energies being computed with the Continuum reaction field procedure due to J. Langlet et al. [(1988) Journal of Physical Chemistry, Vol. 92, pp. 1617–1631], and recently integrated into SIBFA [J. Langlet, N. Gresh and C. Giessner-Prettre (1995) Biopolymers, Vol. 36, pp. 765–780]. Such an integrated procedure is next extended to a comparison of the relative stabilities of, on the one hand, the competing types of β-turns (I, I′, II, II′) that are prevalent in Ala/Gly-based model tetrapeptides, and, on the other hand, α- vs 310-helices in alanine oligomers. © 1998 John Wiley & Sons, Inc. Biopoly 45: 405–425, 1998

Modeling of inhibitor–metalloenzyme interactions and selectivity using molecular mechanics grounded in quantum chemistry

We investigated the binding properties of the metalloprotease inhibitors hydroxamate, methanethiolate, and methylphosphoramidate to a model coordination site occurring in several Zn2+ metalloproteases, including thermolysin. This was carried out using both the SIBFA (sum of interactions between fragments ab initio-computed) molecular mechanics and the SCF/MP2 procedures for the purpose of evaluating SIBFA as a metalloenzyme modeling tool. The energy-minimized structures were closely similar to the X-ray crystallographic structures of related thermolysin-inhibitor complexes. We found that selectivity between alternative geometries and between inhibitors usually stemmed from multiple interaction components included in SIBFA. The binding strength sequence is hydroxamate > methanethiolate > or = methylphosphoramidate from multiple interaction components included in SIBFA. The trends in interaction energy components, rankings, and preferences for mono- or bidentate binding were consistent in both computational procedures. We also compared the Zn2+ vs. Mg2+ selectivities in several other polycoordinated sites having various "hard" and "soft" qualities. This included a hexahydrate, a model representing Mg2+/Ca2+ binding sites, a chlorophyll-like structure, and a zinc finger model. The latter three favor Zn2+ over Mg2+ by a greater degree than the hydrated state, but the selectivity varies widely according to the ligand "softness." SIBFA was able to match the ab initio binding energies by < 2%, with the SIBFA terms representing dispersion and charge-transfer contributing the most to Zn2+/Mg2+ selectivity. These results showed this procedure to be a very capable modeling tool for metalloenzyme problems, in this case giving valuable information about details and limitations of "hard" and "soft" selectivity trends.

Model, Multiply Hydrogen-Bonded Water Oligomers (N = 3−20). How Closely Can a Separable, ab Initio-Grounded Molecular Mechanics Procedure Reproduce the Results of Supermolecule Quantum Chemical Computations?

Several high-level quantum chemical calculations have highlighted the prominent weight of nonadditivity within the total stabilization energy of multiply hydrogen-bonded complexes, such as exemplified by water oligomers (reviewed in ref 1). We have evaluated the extent to which the SIBFA (sum of interactions between fragments ab initio computed) molecular mechanics procedure2-4 could account for nonadditivity in such complexes. This takes advantage of the separability of the energy expression into five distinct components, each of which have inherent anisotropic features. For that purpose, we have considered several representative water oligomers encompassing from n = 3 to n = 20 molecules, in cyclic and acyclic, as well as, for n = 6 and beyond, tridimensional cubic arrangements. Single-point ab initio SCF and MP2 supermolecular energy computations were performed in the energy-minimized structures. A decomposition of the SCF intermolecular interaction energy was done, for n = 3−6, using the restricted variational space approximation (RVS) due to Stevens and Fink.5 This enabled the quantification of the relative weights of each of the two individual ab initio second-order terms, polarization and charge-transfer (Epol and Ect, respectively) to nonadditivity. The SIBFA procedure was found to faithfully reproduce the ab initio results, both in terms of the total ΔE's and in terms of the separate nonadditive behaviors of its own Epol and Ect terms. It was also able to match very closely the results of the recent density functional theory computations of Lee et al.6 on cubic arrangements of water as occurring in ice. Thus, upon increasing n from 8 to 20, ΔE(SIBFA) was found to converge asymptotically toward a value of −11.5 kcal per molecule of water, close to the experimental binding energy of ice of −11.4. For n = 20 in this structure, the average dipole moment per water molecule was computed to be 2.74 D, itself very close to the value of 2.70 D in ice.

Inter- and intramolecular interactions. Inception and refinements of the SIBFA, molecular mechanics (SMM) procedure, a separable, polarizable methodology grounded on ab initio SCF/MP2 computations. Examples of applications to molecular recognition problems

In this paper we first summarize the distinctive features of the the SIBFA (Sum of Interactions Between Fragments Ab initio computed) molecular mechanics procedure (1-10). An overview of its applications to molecular recognition problems in complexes of biological or pharmacological interest is presented. Recent refinements and enrichments that took place after 1991 are then exposed, along with ongoing applicatons in cadon-ligand, conformadonal analysis, the study of cooperative interactions in multiply hydrogen-bonded oligomers, and the integration with a Continuum reaction field procedure to study solvation.