Nohad Gresh

Towards a force field based on density fitting

Total intermolecular interaction energies are determined with a first version of the Gaussian electrostatic model (GEM-0), a force field based on a density fitting approach using s-type Gaussian functions. The total interaction energy is computed in the spirit of the sum of interacting fragment ab initio (SIBFA) force field by separately evaluating each one of its components: electrostatic (Coulomb), exchange repulsion, polarization, and charge transfer intermolecular interaction energies, in order to reproduce reference constrained space orbital variation (CSOV) energy decomposition calculations at the B3LYP/aug-cc-pVTZ level. The use of an auxiliary basis set restricted to spherical Gaussian functions facilitates the rotation of the fitted densities of rigid fragments and enables a fast and accurate density fitting evaluation of Coulomb and exchange-repulsion energy, the latter using the overlap model introduced by Wheatley and Price [Mol. Phys. 69, 50718 (1990)]. The SIBFA energy scheme for polarization and charge transfer has been implemented using the electric fields and electrostatic potentials generated by the fitted densities. GEM-0 has been tested on ten stationary points of the water dimer potential energy surface and on three water clusters (n = 16,20,64). The results show very good agreement with density functional theory calculations, reproducing the individual CSOV energy contributions for a given interaction as well as the B3LYP total interaction energies with errors below kBT at room temperature. Preliminary results for Coulomb and exchange-repulsion energies of metal cation complexes and coupled cluster singles doubles electron densities are discussed.

Theoretical studies of molecular conformation. Derivation of an additive procedure for the computation of intramolecular interaction energies. Comparison withab initio SCF computations

An additive procedure (SIBFA) is developed for the rapid computation of conformational energy variations in very large molecules. The macromolecule is built out of constitutive molecular fragments and the intramolecular energy is computed as a sum of interaction energies between the fragments. The electrostatic and the polarization components are calculated using multicenter multipole expansions of theab initio SCF electron density of the fragments. The repulsion component is obtained as a sum of bond and lone pair interactions.Tests of the procedure on a series of model compounds containing ether oxygens and pyridine-like nitrogens are reported and compared with the results of correspondingab initio SCF calculations. The resulting methodology is compatible with the simultaneous computation of intermolecular interactions.

Energetics of Zn2+ binding to a series of biologically relevant ligands: A molecular mechanics investigation grounded on ab initio self-consistent field supermolecular computations

Detailed investigations are performed of the binding energetics of Zn2+ to a series of neutral and anionic ligands making up the sidechains of amino acid residues of proteins, as well as ligands which can be involved in Zn2+ binding during enzymatic activation: imidazole, formamide, methanethiol, methanethiolate, methoxy, and hydroxy. The computations are performed using the SIBFA molecular mechanics procedure (SMM), which expresses the interaction energy under the form of four separate contributions related to the corresponding ab initio supermolecular ones: electrostatic, short‐range repulsion, polarization, and charge transfer. Recent refinements to this procedure are first exposed. To test the reliability of this procedure in large‐scale simulations of inhibitor binding to metalloenzyme cavities, we undertake systematic comparisons of the SMM results with those of recent large basis set ab initio self‐consistent field (SCF) supermolecule computations, in which a decomposition of the total ΔE into its four corresponding components is done (N. Gresh, W. Stevens, and M. Krauss, J. Comp. Chem., 16, 843, 1995). For each complex, the evolution of each individual SMM energy component as a function of radial and in‐ and out‐of‐plane angular variations of the Zn2+ position reproduces with good accuracy the behavior of the corresponding SCF term. Computations performed subsequently on di‐ and oligoligated complexes of Zn2+ show that the SIBFA molecular mechanics (SMM) functionals, Epol and Ect, closely account for the nonadditive behaviors of the corresponding second‐order energy contributions determined from the ab initio SCF calculations on these complexes and their nonlinear dependence on the number of ligands. Thus, the total intermolecular interaction energies computed with this procedure reproduce, with good accuracy, the corresponding SCF ones without the need for additional, extraneous terms in the intermolecular potential of polyligated complexes of divalent cations.

A theoretical investigation on the sequence selective binding of daunomycin to double-stranded polynucleotides.

Theoretical computations are performed on the structural and energetical factors involved in the sequence selective binding of daunomycin (DNM) to six representative self-complementary double-stranded hexanucleotides: d(CGTACG)2,d(CGATCG)2,d(CITACI)2, d(TATATA)2, d(CGCGCG)2 and d(TACGTA)2. The conformational angles of the hexanucleotides are fixed in values found in the representative crystal structure of the d(CGTACG)2-DNM complex. The intermolecular DNM-hexanucleotide interaction energies and the conformational energy changes of DNM upon binding are computed and optimized in the framework of the SIBFA procedure, which uses empirical formulas based on ab initio SCF computations. Among the two regularly alternating hexanucleotides, d(TATATA)2 and d(CGCGCG)2, a stronger binding is predicted for the former, in agreement with experimental results obtained with poly(dA-dT).poly(dA-dT) and poly(dG-dC).poly(dG-dC). Altogether, however, among the six investigated sequences, the strongest complexes are computed for the mixed hexanucleotides d(CGATCG)2 and d(CGTACG)2, containing the intercalation site between two CG base pairs and an adjacent TA base pair. This situation may be related to the increased affinity of DNM for GC rich DNAs and to the situation in the crystal structure of the DNM-d(CGTACG)2 complex. Analysis of the intrinsic base sequence preferences expressed by the individual constituents of DNM, namely the daunosamine side chain, the chromophore ring and its two 9-hydroxyl and 9-acetoxy substituents, reveals that the overall sequence preference found is the result of a rather intricate interplay of intrinsic sequence preferences, in particular at the level of daunosamine and the 9-hydroxyl substituent.(ABSTRACT TRUNCATED AT 250 WORDS)

Interaction of neutral and zwitterionic glycine with Zn2+ in gas phase: ab initio and SIBFA molecular mechanics calculations

The interaction of Zn2+ with glycine (Gly) in the gas phase is studied by a combination of ab initio and molecular mechanics techniques. The structures and energetics of the various isomers of the Gly–Zn2+ complex are first established via high‐level ab initio calculations. Two low‐energy isomers are characterized: one in which the metal ion interacts with the carboxylate end of zwitterionic glycine, and another in which it chelates the amino nitrogen and the carbonyl oygen of neutral glycine. These calculations lead to the first accurate value of the gas‐phase affinity of glycine for Zn2+. Ab initio calculations were also used to evaluate the performance of various implementations of the SIBFA force field. To assess the extent of transferability of the distributed multipoles and polarizabilities used in the SIBFA computations, two approaches are followed. In the first, approach (a), these quantities are extracted from the ab initio Hartree–Fock wave functions of glycine or its zwitterion in its entirety, and for each individual Zn2+‐binding conformation. In the second, approach (b), they are assembled from the appropriate constitutive fragments, namely methylamine and formic acid for neutral glycine, and protonated methylamine and formate for the zwitterion; they undergo the appropriate vector or matrix rotation to be assembled in the conformation studied. The values of the Zn2+–glycine interaction energies are compared to those resulting from ab initio SCF and MP2 computations using both the all‐electron 6‐311+G(2d,2p) basis set and an effective core potential together with the valence CEP 4‐31G(2d) basis set. Approach (a) values closely reproduce the ab initio ones, both in terms of the total interaction energies and of the individual components. Approach (b) can provide a similar match to ab initio interaction energies as does approach (a), provided that the two constitutive Gly building blocks are considered as separate entities having mutual interactions that are computed simultaneously with those occurring with Zn2+. Thus, the supermolecule is treated as a three‐body rather than a two‐body system. These results indicate that the current implementation of the SIBFA force field should be adequate to undertake accurate studies on zinc metallopeptides.

Inclusion of the ligand field contribution in a polarizable molecular mechanics: SIBFA‐LF

To account for the distortion of the coordination sphere that takes place in complexes containing open‐shell metal cations such as Cu(II), we implemented, in sum of interactions between fragments ab initio computed (SIBFA) molecular mechanics, an additional contribution to take into account the ligand field splitting of the metal d orbitals. This term, based on the angular overlap model, has been parameterized for Cu(II) coordinated to oxygen and nitrogen ligands. The comparison of the results obtained from density functional theory computations on the one hand and SIBFA or SIBFA‐LF on the other shows that SIBFA‐LF gives geometric arrangements similar to those obtained from quantum mechanical computations. Moreover, the geometric improvement takes place without downgrading the energetic agreement obtained from SIBFA. The systems considered are Cu(II) interacting with six water molecules, four ammonia or four imidazoles, and four water plus two formate anions.

Parallel ab initio and molecular mechanics investigation of polycoordinated Zn(II) complexes with model hard and soft ligands: Variations of binding energy and of its components with number and charges of ligands

In this study we compare the binding energies of polycoordinated complexes of Zn2+ within cavities composed of model “hard” (H2O, OH−) or “soft” (CH3SH, CH3S−) ligands. Ab initio supermolecule computations are performed at the HF and MP2 levels using extended basis sets to determine the binding energies and their components as a function of: the number of ligands, ranging from three to six; the net charge of the cavity; and the “hard” versus “soft” character of the ligands. These ab initio computations are used to test the reliability of the SIBFA molecular mechanics procedure, originally formulated and calibrated on the basis of ab initio computations, for such charged systems. The SIBFA intermolecular interaction energies match the corresponding ab initio values using a coreless effective potential split‐valence basis set with a relative error of ≤3%. Extensions to binuclear Zn2+ complexes, such as those that occur in the Zn‐binding sites of Gal4 and β‐lactamase proteins, are performed to test the applicability of the methodology for such systems.

Quantum mechanical studies of environmental effects on biomolecules. An ab initio study of the hydration of dimethylphosphate

Abstract STO 3G SCF computations are used to determine the most favorable sites of water fixation and the lability of the binding on the dimethylphosphate anion. A nearly circular region of attraction for water surrounds each of the anionic oxygens and a number of other possible hydration sites are found with very similar binding energies. As a result, many possibilities exist for the constitution of the first hydration shell which is shown to be able to accommodate up to six water molecules.

Comparative binding energetics of Mg2+, Ca2+, Zn2+, and Cd2+ to biologically relevant ligands: Combined ab initio SCF supermolecule and molecular mechanics investigation

A combined ab initio SCF supermolecule and molecular mechanics investigation is carried out on the binding energetics of the divalent cations Mg2+, Ca2+, Zn2+, and Cd2+ to a series of the most common ligand functional groups found in biomolecules. The SCF binding energy components are resolved using the restricted variational space method.1 The results show that the SIBFA molecular mechanics (SMM) procedure2 reproduces the ab initio binding energies and total energy variations as a function of intermolecular variables. The model also reproduces the selectivity energetics for exchange reactions. Thus, the SMM procedure can be used without reparametrization to describe the coordination energetics of complex molecules including those subject to coordination changes. The energetic properties of divalent cation‐hexahydrate complexes are compared as examples of a complete, realistic coordination system. The hexahydrates exhibit strong nonadditive effects typical of dication coordination. Nevertheless, these energetics are satisfactorily reproduced by the SMM procedure.

Polarizable Water Molecules in Ligand−Macromolecule Recognition. Impact on the Relative Affinities of Competing Pyrrolopyrimidine Inhibitors for FAK Kinase

Using polarizable molecular mechanics (PMM), we have compared the complexation energies of the focal adhesion kinase (FAK) kinase by five inhibitors in the pyrrolopyrimidine series. These inhibitors only differ by the substitution position of a carboxylate group on their benzene or pyridine rings, and/or the length of the connecting (CH2)(n) chain (n = 0-2) while their inhibitory properties vary from micromolar to nanomolar. Energy balances in which solvation/desolvation effects are computed by a continuum reaction field procedure failed to rank the inhibitors according to their inhibitory potencies. In marked contrast, including energy-minimizing in the protein-inhibitor binding site limited numbers of structural water molecules, namely five to seven, ranked these energy balances conforming to the experimental ordering. The polarization energy contribution was the most critical energy contribution that stabilized the best-bound inhibitor over the others. These results imply that (a) upon docking charged inhibitors into the active site of kinases such as FAK, the presence of a limited number of structured water molecules is critical to enable meaningful relative energy balances and (b) accounting for an explicit polarization contribution within DeltaE is indispensable.