Intramolecular interaction energies in model alanine and glycine tetrapeptides. Evaluation of anisotropy, polarization, and correlation effects. A parallel ab initio HF/MP2, DFT, and polarizable molecular mechanics study

Multimolecular complexes of the phosphodiester anion with Zn(II) or Mg(II) and water molecules-Preliminary validations of a polarizable potential by ab initio quantum chemistry

Dimethyl phosphate (DMP^- ) is a model for the phosphodiester backbone of DNA, RNA, and phospholipids. It is central for the binding of divalent cations and water along the backbone of nucleic acids. Significant polarization and charge-transfer contributions and nonadditivity come into play in the multimolecular complexes organized around phosphate. Prior to large-scale molecular dynamics (MD) with advanced polarizable potentials, it is essential to evaluate how well the values and trends of intermolecular interaction energies (ΔE) from ab initio quantum chemistry (QC) and their individual contributions are reproduced in a diversity of such complexes. These differ by the starting binding modes of a divalent cation, Zn(II), namely direct, bi- or mono-dentate to anionic and/or ester oxygens, versus through-water binding. We present first the results from automated refinements of the individual contributions of the SIBFA potential with respect to their QC counterparts using a Zn(II) or a water probe. This is followed by validations on eight relaxed multimolecular complexes of DMP^- with Zn(II) or Mg(II) and seven waters, then on sixteen complexes of DMP^- with Zn(II) and eight waters in arrangements extracted from MD or energy-minimization on a droplet of sixty-four waters. This monitors the compared evolutions of SIBFA and QC ΔE and their individual contributions in the competing arrangements. Some waters, bridging Zn(II) and DMP^- , were found to have exceptionally large dipole moments, of up to 3.8 Debye. The perspectives of extension to a flexible phosphodiester backbone are discussed in the context of the SIBFA potential for DNA and RNA.

Benchmarking of Semiempirical Quantum-Mechanical Methods on Systems Relevant to Computer-Aided Drug Design

The semiempirical quantum mechanical (SQM) methods used in drug design are commonly parametrized and tested on data sets of systems that may not be representative models for drug-biomolecule interactions in terms of both size and chemical composition. This is addressed here with a new benchmark data set, PLF547, derived from protein-ligand complexes, consisting of complexes of ligands with protein fragments (such as amino-acid side chains), with interaction energies based on MP2-F12 and DLPNO-CCSD(T) calculations. From these, composite benchmark interaction energies are also built for complexes of the ligand with the complete active site of the protein (PLA15 data set). These data sets are used to test multiple SQM methods with corrections for noncovalent interactions; the role of the solvation model in the calculations is tested as well.

Efficient minimization of multipole electrostatic potentials in torsion space

The development of models of macromolecular electrostatics capable of delivering improved fidelity to quantum mechanical calculations is an active field of research in computational chemistry. Most molecular force field development takes place in the context of models with full Cartesian coordinate degrees of freedom. Nevertheless, a number of macromolecular modeling programs use a reduced set of conformational variables limited to rotatable bonds. Efficient algorithms for minimizing the energies of macromolecular systems with torsional degrees of freedom have been developed with the assumption that all atom-atom interaction potentials are isotropic. We describe novel modifications to address the anisotropy of higher order multipole terms while retaining the efficiency of these approaches. In addition, we present a treatment for obtaining derivatives of atom-centered tensors with respect to torsional degrees of freedom. We apply these results to enable minimization of the Amoeba multipole electrostatics potential in a system with torsional degrees of freedom, and validate the correctness of the gradients by comparison to finite difference approximations. In the interest of enabling a complete model of electrostatics with implicit treatment of solvent-mediated effects, we also derive expressions for the derivative of solvent accessible surface area with respect to torsional degrees of freedom.

An improved two-rotor function for conformational potential energy surfaces of 20 amino acid diamides

Predicting the three-dimensional structure of a protein from its amino acid sequence requires a complete understanding of the molecular forces that influences the protein folding process. Each possible conformation has its corresponding potential energy, which characterizes its thermodynamic stability. This is needed to identify the primary intra- and inter-molecular interactions, so that we can reduce the dimensionality of the problem, and create a relatively simple representation of the system. Investigating this problem using quantum chemical methods produces accurate results; however, this also entails large computational resources. In this study, an improved two-rotor potential energy function is proposed to represent the backbone interactions in amino acids through a linear combination of a Fourier series and a mixture of Gaussian functions. This function is applied to approximate the 20 amino acid diamide Ramachandran-type PESs, and results yielded an average RMSE of 2.36 kJ mol−1, which suggest that the mathematical model precisely captures the general topology of the conformational potential energy surface. Furthermore, this paper provides insights on the conformational preferences of amino acid diamides through local minima geometries and energy ranges, using the improved mathematical model. The proposed mathematical model presents a simpler representation that attempts to provide a framework on building polypeptide models from individual amino acid functions, and consequently, a novel method for rapid but accurate evaluation of potential energies for biomolecular simulations.

Prediction of Intramolecular Polarization of Aromatic Amino Acids Using Kriging Machine Learning

Present computing power enables novel ways of modeling polarization. Here we show that the machine learning method kriging accurately captures the way the electron density of a topological atom responds to a change in the positions of the surrounding atoms. The success of this method is demonstrated on the four aromatic amino acids histidine, phenylalanine, tryptophan, and tyrosine. A new technique of varying training set sizes to vastly reduce training times while maintaining accuracy is described and applied to each amino acid. Each amino acid has its geometry distorted via normal modes of vibration over all local energy minima in the Ramachandran map. These geometries are then used to train the kriging models. Total electrostatic energies predicted by the kriging models for previously unseen geometries are compared to the true energies, yielding mean absolute errors of 2.9, 5.1, 4.2, and 2.8 kJ mol(-1) for histidine, phenylalanine, tryptophan, and tyrosine, respectively.

Exploring Strong Interactions in Proteins with Quantum Chemistry and Examples of Their Applications in Drug Design

OBJECTIVES

Three strong interactions between amino acid side chains (salt bridge, cation-π, and amide bridge) are studied that are stronger than (or comparable to) the common hydrogen bond interactions, and play important roles in protein-protein interactions.

METHODS

Quantum chemical methods MP2 and CCSD(T) are used in calculations of interaction energies and structural optimizations.

RESULTS

The energies of three types of amino acid side chain interactions in gaseous phase and in aqueous solutions are calculated using high level quantum chemical methods and basis sets. Typical examples of amino acid salt bridge, cation-π, and amide bridge interactions are analyzed, including the inhibitor design targeting neuraminidase (NA) enzyme of influenza A virus, and the ligand binding interactions in the HCV p7 ion channel. The inhibition mechanism of the M2 proton channel in the influenza A virus is analyzed based on strong amino acid interactions.

CONCLUSION

(1) The salt bridge interactions between acidic amino acids (Glu- and Asp-) and alkaline amino acids (Arg+, Lys+ and His+) are the strongest residue-residue interactions. However, this type of interaction may be weakened by solvation effects and broken by lower pH conditions. (2) The cation- interactions between protonated amino acids (Arg+, Lys+ and His+) and aromatic amino acids (Phe, Tyr, Trp and His) are 2.5 to 5-fold stronger than common hydrogen bond interactions and are less affected by the solvation environment. (3) The amide bridge interactions between the two amide-containing amino acids (Asn and Gln) are three times stronger than hydrogen bond interactions, which are less influenced by the pH of the solution. (4) Ten of the twenty natural amino acids are involved in salt bridge, or cation-, or amide bridge interactions that often play important roles in protein-protein, protein-peptide, protein-ligand, and protein-DNA interactions.

Conformational analysis of a polyconjugated protein-binding ligand by joint quantum chemistry and polarizable molecular mechanics. Addressing the issues of anisotropy, conjugation, polarization, and multipole transferability

We investigate the conformational properties of a potent inhibitor of neuropilin-1, a protein involved in cancer processes and macular degeneration. This inhibitor consists of four aromatic/conjugated fragments: a benzimidazole, a methylbenzene, a carboxythiourea, and a benzene-linker dioxane, and these fragments are all linked together by conjugated bonds. The calculations use the SIBFA polarizable molecular mechanics procedure. Prior to docking simulations, it is essential to ensure that variations in the ligand conformational energy upon rotations around its six main-chain torsional bonds are correctly represented (as compared to high-level ab initio quantum chemistry, QC). This is done in two successive calibration stages and one validation stage. In the latter, the minima identified following independent stepwise variations of each of the six main-chain torsion angles are used as starting points for energy minimization of all the torsion angles simultaneously. Single-point QC calculations of the minimized structures are then done to compare their relative energies ΔE conf to the SIBFA ones. We compare three different methods of deriving the multipoles and polarizabilities of the central, most critical moiety of the inhibitor: carboxythiourea (CTU). The representation that gives the best agreement with QC is the one that includes the effects of the mutual polarization energy E pol between the amide and thioamide moieties. This again highlights the critical role of this contribution. The implications and perspectives of these findings are discussed.

The hydration of serine: multipole moments versus point charges

Next-generation force fields must incorporate improved electrostatic potentials in order to increase the reliability of their predictions. A crucial decision toward this goal is to abandon point charges in favour of multipole moments centered on nuclear sites. Here we compare the geometries generated by quantum topological multipole moments with those generated by four popular point charge models (TAFF, OPLS-AA, MMFF94x and PFROSST) for a hydrated serine. A main feature of this study is the dual comparison made, both at static level (geometry optimisation via energy minimisation) and at dynamic level (via molecular dynamics and radial/spatial distribution function analysis). At static level, multipolar electrostatics best reproduces the ab initio reference geometry. At dynamic level, multipolar electrostatics produces more structure than point charge electrostatics does, over the whole range. From our previous work on liquid water [Int. J. Quantum. Chem., 2004, 99, 685], where agreement with experiment only occurs when using multipole moments, we deduce that our predictions for hydrated serine will also be closer to experiment when using multipolar electrostatics. The spatial distribution function shows that only multipolar electrostatics shows pronounced structure at long range. Even at short range there are many regions where waters appear in the system governed by multipolar electrostatics but not in that governed by point charges.

Further refinements of next-generation force fields — Nonempirical localization of off-centered points in molecules

In the present work, we investigate different possibilities for the nonempirical localization of nonatomic centers within the context of the design of new generation polarizable force fields. To do so, the positions of electron localization function (ELF) and electron pair localization function (EPLF) attractors and of Boys orbital centroids are determined for a set of thirteen saturated and conjugated biologically relevant molecules. We consider the similarities and differences in the representations of localized lone pairs and π delocalized systems by these approaches, as well as the effects of the basis sets and of the level of quantum chemistry (QC). All three methods give consistent results upon dealing with the localized lone pairs. Concerning aromatic systems, whereas ELF and EPLF methods give mutually consistent results, the Boys scheme breaks the symmetry by alternating the electron distributions along the C–C bonds providing a different distribution of off-centered points. We then investigate the influence of lone pair localization in the water model of the Gaussian electrostatic model/sum of interactions between fragments ab initio computed (GEM/SIBFA) polarizable force field, which embodies an explicit representation of the lone pairs. This is done, in a series of mono- and poly-hydrated Zn(II) complexes, by comparing the overlap-dependent repulsion (Erep) and charge-transfer (Ect) contributions to their QC counterparts. We resort to either the current GEM/SIBFA water lone pair internal coordinates or to the ones derived from the previously mentioned localization procedures. The latter enables closer reproductions by Erep and Ect (GEM/SIBFA) of their exchange repulsion (Eexch) and Ect QC counterparts. The present preliminary results show that QC localization procedures can be used to derive accurate, nonempirical positions for off-centered points intervening in the formulation of the overlap-dependent contributions of next-generation polarizable force fields.

The multiple roles of histidine in protein interactions

Background

Among the 20 natural amino acids histidine is the most active and versatile member that plays the multiple roles in protein interactions, often the key residue in enzyme catalytic reactions. A theoretical and comprehensive study on the structural features and interaction properties of histidine is certainly helpful.

Results

Four interaction types of histidine are quantitatively calculated, including: (1) Cation-π interactions, in which the histidine acts as the aromatic π-motif in neutral form (His), or plays the cation role in protonated form (His⁺); (2) π-π stacking interactions between histidine and other aromatic amino acids; (3) Hydrogen-π interactions between histidine and other aromatic amino acids; (4) Coordinate interactions between histidine and metallic cations. The energies of π-π stacking interactions and hydrogen-π interactions are calculated using CCSD/6-31+G(d,p). The energies of cation-π interactions and coordinate interactions are calculated using B3LYP/6-31+G(d,p) method and adjusted by empirical method for dispersion energy.

Conclusions

The coordinate interactions between histidine and metallic cations are the strongest one acting in broad range, followed by the cation-π, hydrogen-π, and π-π stacking interactions. When the histidine is in neutral form, the cation-π interactions are attractive; when it is protonated (His⁺), the interactions turn to repulsive. The two protonation forms (and pK_a values) of histidine are reversibly switched by the attractive and repulsive cation-π interactions. In proteins the π-π stacking interaction between neutral histidine and aromatic amino acids (Phe, Tyr, Trp) are in the range from -3.0 to -4.0 kcal/mol, significantly larger than the van der Waals energies.

A water potential based on multipole moments trained by machine learning — Reducing maximum energy errors

A potential that strives to represent the Coulomb interaction realistically must include polarization. In our approach, three decisions were made to accomplish this: (i) define an atom according to quantum chemical topology (QCT), (ii) express the interaction between atoms via their multipole moments, and (iii) use machine learning to capture the response of an atomic multipole moment to a change in this atom’s environment. This approach avoids explicit (distributed) polarizabilities and eliminates the problem of polarization catastrophe. Previously, we showed ( Phys. Chem. Chem. Phys. 2009, 11, 6365 ) that a machine learning method called kriging predicted atomic multipole moments more accurately than competing machine learning methods. This was established for the atoms of a central water molecule in water clusters, from the dimer to the hexamer. The prediction errors in all multipole moments were collectively assessed by errors in total interaction energy, for thousands of clusters configurations. Here, we target the maximum errors, with an eye on reducing the worst predictions that the potential may return. We demonstrate proof-of-principle for the water dimer using local kriging.

Effect of polarization on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins

The explicit treatment of polarization as a many-body interaction in condensed-phase systems represents a current problem in empirical force-field development. Although a variety of efficient models for molecular polarization have been suggested, polarizable force fields are still far from common use nowadays. In this work, we consider interactive polarization models employing Thole's short-range damping scheme and assess them for application on polypeptides. Despite the simplicity of the model, we find mean polarizabilities and anisotropies of amino acid side chains in excellent agreement with MP2/cc-pVQZ benchmark calculations. Combined with restrained electrostatic potential (RESP) derived atomic charges, the models are applied in a quantum-mechanical/molecular-mechanical (QM/MM) approach. An iterative scheme is used to establish a self-consistent mutual polarization between the QM and MM moieties. This ansatz is employed to study the influence of the protein polarizability on calculated optical properties of the protonated Schiff base of retinal in rhodopsin (Rh), bacterio-rhodopsin (bR), and pharaonis sensory rhodopsin II (psRII). The shifts of the excitation energy due to the instantaneous polarization response of the protein to the charge transfer on the retinal chromophore are quantified using the high level ab initio multireference spectroscopy-oriented configuration interaction (SORCI) method. The results are compared with those of previously published QM1/QM2/MM models for bR and psRII.

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.

Physical nature of ethidium and proflavine interactions with nucleic acid bases in the intercalation plane

On the basis of the crystallographic structures of three nucleic acid intercalation complexes involving ethidium and proflavine, we have analyzed the interaction energies between intercalator chromophores and their four nearest bases, using a hybrid variation-perturbation method at the second-order Møller-Plesset theory level (MP2) with a 6-31G(d,p) basis set. A total MP2 interaction energy minimum precisely reproduces the crystallographic position of the ethidium chromophore in the intercalation plane between UA/AU bases. The electrostatic component constitutes the same fraction of the total energy for all three studied structures. The multipole electrostatic interaction energy, calculated from cumulative atomic multipole moments (CAMMs), was found to converge only after including components above the fifth order. CAMM interaction surfaces, calculated on grids in the intercalation planes of these structures, reasonably reproduce the alignment of intercalators in crystal structures; they exhibit additional minima in the direction of the DNA grooves, however, which also need to be examined at higher theory levels if no crystallographic data are given.

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.

The low energy tautomers and conformers of the dipeptides HisGly and GlyHis and of their sodium ion complexes in the gas phase

The low-lying conformers of the dipeptides HisGly and GlyHis, and of their sodium cation complexes, have been studied with a combination of Monte Carlo search with the Amber force field and local geometry optimization at the ab initio HF/6-31G(d) level, completed with MP2(full)/6-311+G(2d,2p) energetics at the HF/6-31G(d) geometries. For each dipeptide, both the N(delta)-H and N(epsilon)-H tautomers of the imidazole side chain of His were considered. For each of the four isomeric dipeptides, 20-30 conformers were fully characterized at the ab initio level. All low energy structures are found to involve H-bonding at the N(delta) position of imidazole, either as a N-H donor or a N acceptor, depending upon the tautomer. In three out of the four species, the most stable conformer involves a C-terminus carboxylic acid in its less favorable trans conformation, in order to maximize intramolecular H bonding. It turns out that the lowest energy tautomer of HisGly is N(epsilon)-H, while that of GlyHis is N(delta)-H. This result argues in favor of the diversity of His tautomeric states in peptides and proteins. The sodium cation complexes of both GlyHis and HisGly have been studied as well, again considering both tautomers in each case. In three out of the four species, the most stable structure involves chelation of sodium by the two carbonyl oxygens and the imidazole ring. On the contrary, the sodium complex of the N(delta)-H tautomer of HisGly favors chelation to the peptidic carbonyl oxygen, the imidazole ring and the amino terminus. In the N(epsilon)-H tautomers of both peptides, the most favorable binding site of imidazole is the N(delta) nitrogen, while in the N(delta)-H tautomers, it is the pi cloud which provides side chain interaction. As a result, both GlyHisNa+ and HisGlyNa+ favor the N(epsilon)-H tautomer of His, in contrast to what was found for the free peptides.

Complexes of thiomandelate and captopril mercaptocarboxylate inhibitors to metallo-β-lactamase by polarizable molecular mechanics. Validation on model binding sites by quantum chemistry

Using the polarizable molecular mechanics method SIBFA, we have performed a search for the most stable binding modes of D- and L-thiomandelate to a 104-residue model of the metallo-beta-lactamase from B. fragilis, an enzyme involved in the acquired resistance of bacteria to antibiotics. Energy balances taking into account solvation effects computed with a continuum reaction field procedure indicated the D-isomer to be more stably bound than the L-one, conform to the experimental result. The most stably bound complex has the S(-) ligand bridging monodentately the two Zn(II) cations and one carboxylate O(-) H-bonded to the Asn193 side chain. We have validated the SIBFA energy results by performing additional SIBFA as well as quantum chemical (QC) calculations on small (88 atoms) model complexes extracted from the 104-residue complexes, which include the residues involved in inhibitor binding. Computations were done in parallel using uncorrelated (HF) as well as correlated (DFT, LMP2, MP2) computations, and the comparisons extended to corresponding captopril complexes (Antony et al., J Comput Chem 2002, 23, 1281). The magnitudes of the SIBFA intermolecular interaction energies were found to correctly reproduce their QC counterparts and their trends for a total of twenty complexes.