Thermolysin-inhibitor binding: Effect of the His231 → Ala mutation on the relative affinities of thiolate versus phosphoramidate inhibitors—a model theoretical investigation incorporating acontinuum reaction field hydration model

Modeling Structural Coordination and Ligand Binding in Zinc Proteins with a Polarizable Potential

As the second most abundant cation in human body, zinc is vital for the structures and functions of many proteins. Zinc-containing matrix metalloproteinases (MMPs) have been widely investigated as potential drug targets in a range of diseases ranging from cardiovascular disorders to cancers. However, it remains a challenge in theoretical studies to treat zinc in proteins with classical mechanics. In this study, we examined Zn(2+) coordination with organic compounds and protein side chains using a polarizable atomic multipole based electrostatic model. We find that polarization effect plays a determining role in Zn(2+) coordination geometry in both matrix metalloproteinase (MMP) complexes and in zinc-finger proteins. In addition, the relative binding free energies of selected inhibitors binding with MMP13 have been estimated and compared with experimental results. While not directly interacting with the small molecule inhibitors, the permanent and polarizing field of Zn(2+) exerts a strong influence on the relative affinities of the ligands. The simulation results also reveal the polarization effect on binding is ligand dependent and thus difficult to be incorporated into fixed-charge models implicitly.

The reaction mechanism of type I phosphomannose isomerases: new information from inhibition and polarizable molecular mechanics studies

Type I phosphomannose isomerases (PMIs) are zinc-dependent metalloenzymes involved in the reversible isomerization of D-mannose 6-phosphate (M6P) and D-fructose 6-phosphate (F6P). 5-Phospho-D-arabinonohydroxamic acid (5PAH), an inhibitor endowed with nanomolar affinity for yeast (Type I) and Pseudomonas aeruginosa (Type II) PMIs (Roux et al., Biochemistry 2004; 43:2926-2934), strongly inhibits human (Type I) PMI (for which we report an improved expression and purification procedure), as well as Escherichia coli (Type I) PMI. Its K(i) value of 41 nM for human PMI is the lowest value ever reported for an inhibitor of PMI. 5-Phospho-D-arabinonhydrazide, a neutral analogue of the reaction intermediate 1,2-cis-enediol, is about 15 times less efficient at inhibiting both enzymes, in accord with the anionic nature of the postulated high-energy reaction intermediate. Using the polarizable molecular mechanics, sum of interactions between fragments ab initio computed (SIBFA) procedure, computed structures of the complexes between Candida albicans (Type I) PMI and the cyclic substrate β-D-mannopyranose 6-phosphate (β-M6P) and between the enzyme and the high-energy intermediate analogue inhibitor 5PAH are reported. Their analysis allows us to identify clearly the nature of each individual active site amino acid and to formulate a hypothesis for the overall mechanism of the reaction catalyzed by Type I PMIs, that is, the ring-opening and isomerization steps, respectively. Following enzyme-catalyzed ring-opening of β-M6P by zinc-coordinated water and Gln111 ligands, Lys136 is identified as the probable catalytic base involved in proton transfer between the two carbon atoms C1 and C2 of the substrate D-mannose 6-phosphate.

Synthesis and evaluation of non-hydrolyzable D-mannose 6-phosphate surrogates reveal 6-deoxy-6-dicarboxymethyl-D-mannose as a new strong inhibitor of phosphomannose isomerases

Non-hydrolyzable d-mannose 6-phosphate analogues in which the phosphate group was replaced by a phosphonomethyl, a dicarboxymethyl, or a carboxymethyl group were synthesized and kinetically evaluated as substrate analogues acting as potential inhibitors of type I phosphomannose isomerases (PMIs) from Saccharomyces cerevisiae and Escherichia coli. While 6-deoxy-6-phosphonomethyl-d-mannose and 6-deoxy-6-carboxymethyl-D-mannose did not inhibit the enzymes significantly, 6-deoxy-6-dicarboxymethyl-D-mannose appeared as a new strong competitive inhibitor of both S. cerevisiae and E. coli PMIs with K(m)/K(i) ratios of 28 and 8, respectively. We thus report the first malonate-based inhibitor of an aldose-ketose isomerase to date. Phosphonomethyl mimics of the 1,2-cis-enediolate high-energy intermediate postulated for the isomerization reaction catalyzed by PMIs were also synthesized but behave as poor inhibitors of PMIs. A polarizable molecular mechanics (SIBFA) study was performed on the complexes of d-mannose 6-phosphate and two of its analogues with PMI from Candida albicans, an enzyme involved in yeast infection homologous to S. cerevisiae and E. coli PMIs. It shows that effective binding to the catalytic site occurs with retention of the Zn(II)-bound water molecule. Thus the binding of the hydroxyl group on C1 of the ligand to Zn(II) should be water-mediated. The kinetic study reported here also suggests the dianionic character of the phosphate surrogate as a likely essential parameter for strong binding of the inhibitor to the enzyme active site.

Anisotropic, Polarizable Molecular Mechanics Studies of Inter- and Intramolecular Interactions and Ligand-Macromolecule Complexes. A Bottom-Up Strategy

We present an overview of the SIBFA polarizable molecular mechanics procedure, which is formulated and calibrated on the basis of quantum chemistry (QC). It embodies nonclassical effects such as electrostatic penetration, exchange-polarization, and charge transfer. We address the issues of anisotropy, nonadditivity, and transferability by performing parallel QC computations on multimolecular complexes. These encompass multiply H-bonded complexes and polycoordinated complexes of divalent cations. Recent applications to the docking of inhibitors to Zn-metalloproteins are presented next, namely metallo-beta-lactamase, phosphomannoisomerase, and the nucleocapsid of the HIV-1 retrovirus. Finally, toward third-generation intermolecular potentials based on density fitting, we present the development of a novel methodology, the Gaussian electrostatic model (GEM), which relies on ab initio-derived fragment electron densities to compute the components of the total interaction energy. As GEM offers the possibility of a continuous electrostatic model going from distributed multipoles to densities, it allows an inclusion of short-range quantum effects in the molecular mechanics energies. The perspectives of an integrated SIBFA/GEM/QM procedure are discussed.

Binding of 5-phospho-D-arabinonohydroxamate and 5-phospho-D-arabinonate inhibitors to zinc phosphomannose isomerase from Candida albicans studied by polarizable molecular mechanics and quantum mechanics

Type I phosphomannose isomerase (PMI) is a Zn-dependent metalloenzyme involved in the isomerization of D-fructose 6-phosphate to D-mannose 6-phosphate. One of our laboratories has recently designed and synthesized 5-phospho-D-arabinonohydroxamate (5PAH), an inhibitor endowed with a nanomolar affinity for PMI (Roux et al., Biochemistry 2004, 43, 2926). By contrast, the 5-phospho-D-arabinonate (5PAA), in which the hydroxamate moiety is replaced by a carboxylate one, is devoid of inhibitory potency. Subsequent biochemical studies showed that in its PMI complex, 5PAH binds Zn(II) through its hydroxamate moiety rather than through its phosphate. These results have stimulated the present theoretical investigation in which we resort to the SIBFA polarizable molecular mechanics procedure to unravel the structural and energetical aspects of 5PAH and 5PAA binding to a 164-residue model of PMI. Consistent with the experimental results, our theoretical studies indicate that the complexation of PMI by 5PAH is much more favorable than by 5PAA, and that in the 5PAH complex, Zn(II) ligation by hydroxamate is much more favorable than by phosphate. Validations by parallel quantum-chemical computations on model of the recognition site extracted from the PMI-inhibitor complexes, and totaling up to 140 atoms, showed the values of the SIBFA intermolecular interaction energies in such models to be able to reproduce the quantum-chemistry ones with relative errors < 3%. On the basis of the PMI-5PAH SIBFA energy-minimized structure, we report the first hypothesis of a detailed view of the active site of the zinc PMI complexed to the high-energy intermediate analogue inhibitor, which allows us to identify active site residues likely involved in the proton transfer between the two adjacent carbons of the substrates.

Representation of Zn(II) complexes in polarizable molecular mechanics. Further refinements of the electrostatic and short-range contributions. Comparisons with parallel ab initio computations

We present refinements of the SIBFA molecular mechanics procedure to represent the intermolecular interaction energies of Zn(II). The two first-order contributions, electrostatic (E(MTP)), and short-range repulsion (E(rep)), are refined following the recent developments due to Piquemal et al. (Piquemal et al. J Phys Chem A 2003, 107, 9800; and Piquemal et al., submitted). Thus, E(MTP) is augmented with a penetration component, E(pen), which accounts for the effects of reduction in electronic density of a given molecular fragment sensed by another interacting fragment upon mutual overlap. E(pen) is fit in a limited number of selected Zn(II)-mono-ligated complexes so that the sum of E(MTP) and E(pen) reproduces the Coulomb contribution E(c) from an ab initio Hartree-Fock energy decomposition procedure. Denoting by S, the overlap matrix between localized orbitals on the interacting monomers, and by R, the distance between their centroids, E(rep) is expressed by a S(2)/R term now augmented with an S(2)/R(2) one. It is calibrated in selected monoligated Zn(II) complexes to fit the corresponding exchange repulsion E(exch) from ab initio energy decomposition, and no longer as previously the difference between (E(c) + E(exch)) and E(MTP). Along with the reformulation of the first-order contributions, a limited recalibration of the second-order contributions was carried out. As in our original formulation (Gresh, J Comput Chem 1995, 16, 856), the Zn(II) parameters for each energy contribution were calibrated to reproduce the radial behavior of its ab initio HF counterpart in monoligated complexes with N, O, and S ligands. The SIBFA procedure was subsequently validated by comparisons with parallel ab initio computations on several Zn(II) polyligated complexes, including binuclear Zn(II) complexes as in models for the Gal4 and beta-lactamase metalloproteins. The largest relative error with respect to the RVS computations is 3%, and the ordering in relative energies of competing structures reproduced even though the absolute numerical values of the ab initio interaction energies can be as large as 1220 kcal/mol. A term-to-term identification of the SIBFA contributions to their ab initio counterparts remained possible even for the largest sized complexes.

Conformation-dependent intermolecular interaction energies of the triphosphate anion with divalent metal cations. Application to the ATP-binding site of a binuclear bacterial enzyme. A parallel quantum chemical and polarizable molecular mechanics investigation

We have explored the conformation-dependent interaction energy of the triphosphate moiety, a key constituent of ATP and GTP, with a closed-shell divalent cation, Zn2+, used as a probe. This was done using the SIBFA polarizable molecular mechanics procedure. We have resorted to a previously developed approach in which triphosphate is built out from its elementary constitutive fragments, and the intramolecular, interfragment, interaction energies are computed simultaneously with their intermolecular interactions with the divalent cation. This approach has enabled reproduction of the values of the intermolecular interaction energies from ab initio quantum-chemistry with relative errors <3%. It was extended to the complex of a nonhydrolyzable analog of ATP with the active site of a bacterial enzyme having two Mg2+ cations as cofactors. We obtained following energy-minimization a very close overlap of the ATP analog over its position from X-ray crystallography. For models of the ATP analog-enzyme complex encompassing up to 169 atoms, the values of the SIBFA interaction energies were found to match their DFT counterparts with relative errors of <2%.

Electrostatic properties in the catalytic site of papain: A possible regulatory mechanism for the reactivity of the ion pair

We present an analysis of the electrostatic properties in the catalytic site of papain (EC 3.4.22.2), an archetype enzyme of the C1 cysteine proteinase family, and we investigate their possible role in the formation, stabilization and regulation of the Cys25((-))...His159((+)) catalytic ion pair. The electrostatic properties were computed using a reassociation method based in multicentered multipolar expansions obtained from ab initio quantum calculations of overlapping protein fragments. Solvent effects were introduced by coupling the use of multicentered multipolar expansions to two continuum boundary element methods to solve the Poisson and the linearized Poisson-Boltzmann equations. The electrostatic profile found in the proton transfer region of papain showed that this enzyme has a well-defined electrostatic environment to favor the formation and stabilization of the catalytic ion pair. The papain catalytic site electrostatic profile can be considered as an electrostatic fingerprint of the papain family with the following characteristics: (i) the presence of a net electric field highly aligned in the (Cys25)-SG-->(His159)-ND1 direction; (ii) the electrostatic profile has a saddle-point character; (iii) it is basically a local environmental effect. Furthermore, our analysis describes a possible regulatory mechanism (the E(SG-->ND1) attenuation effect) controlling the ion pair reactivity and permits to infer the Asp57 acidic residue as the most probable candidate to act as the electrostatic modulator.

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.

Polarizable force fields

Standard force fields used in biomolecular computing describe electrostatic interactions in terms of fixed, usually atom-centered, charges. Real physical systems, however, polarize substantially when placed in a high-dielectric medium such as water--or even when a strongly charged system approaches a neutral body in the gas phase. Such polarization strongly affects the geometry and energetics of molecular recognition. First introduced more than 20 years ago, polarizable force fields seek to account for appropriate variations in charge distribution with dielectric environment. Over the past five years, an accelerated pace of development of such force fields has taken place on systems ranging from liquid water to metalloenzymes. Noteworthy progress has been made in better understanding the capabilities and limitations of polarizable models for water and in the formulation and utilization of complete specifically parameterized polarizable force fields for peptides and proteins.

Structural differences of matrix metalloproteinases. Homology modeling and energy minimization of enzyme-substrate complexes

Matrix metalloproteinases are extracellular enzymes taking part in the remodeling of extracellular matrix. The structures of the catalytic domain of MMP1, MMP3, MMP7 and MMP8 are known, but structures of enzymes belonging to this family still remain to be determined. A general approach to the homology modeling of matrix metalloproteinases, exemplified by the modeling of MMP2, MMP9, MMP12 and MMP14 is described. The models were refined using an energy minimization procedure developed for matrix metalloproteinases. This procedure includes incorporation of parameters for zinc and calcium ions in the AMBER 4.1 force field, applying a non-bonded approach and a full ion charge representation. Energy minimization of the apoenzymes yielded structures with distorted active sites, while reliable three-dimensional structures of the enzymes containing a substrate in active site were obtained. The structural differences between the eight enzyme-substrate complexes were studied with particular emphasis on the active site, and possible sites for obtaining selectivity among the MMP's are discussed. Differences in the P1' pocket are well-documented and have been extensively exploited in inhibitor design. The present work indicates that selectivity could be further improved by considering the P2 pocket as well.

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.