Minimal Basis Iterative Stockholder: Atoms in Molecules for Force-Field Development

Atomic partial charges appear in the Coulomb term of many force-field models and can be derived from electronic structure calculations with a myriad of atoms-in-molecules (AIM) methods. More advanced models have also been proposed, using the distributed nature of the electron cloud and atomic multipoles. In this work, an electrostatic force field is defined through a concise approximation of the electron density, for which the Coulomb interaction is trivially evaluated. This approximate "pro-density" is expanded in a minimal basis of atom-centered s-type Slater density functions, whose parameters are optimized by minimizing the Kullback-Leibler divergence of the pro-density from a reference electron density, e.g. obtained from an electronic structure calculation. The proposed method, Minimal Basis Iterative Stockholder (MBIS), is a variant of the Hirshfeld AIM method but it can also be used as a density-fitting technique. An iterative algorithm to refine the pro-density is easily implemented with a linear-scaling computational cost, enabling applications to supramolecular systems. The benefits of the MBIS method are demonstrated with systematic applications to molecular databases and extended models of condensed phases. A comparison to 14 other AIM methods shows its effectiveness when modeling electrostatic interactions. MBIS is also suitable for rescaling atomic polarizabilities in the Tkatchenko-Sheffler scheme for dispersion interactions.Comment: 61 pages, 12 figures, 2 table

Transferable atomic multipole machine learning models for small organic molecules

Accurate representation of the molecular electrostatic potential, which is often expanded in distributed multipole moments, is crucial for an efficient evaluation of intermolecular interactions. Here we introduce a machine learning model for multipole coefficients of atom types H, C, O, N, S, F, and Cl in any molecular conformation. The model is trained on quantum chemical results for atoms in varying chemical environments drawn from thousands of organic molecules. Multipoles in systems with neutral, cationic, and anionic molecular charge states are treated with individual models. The models' predictive accuracy and applicability are illustrated by evaluating intermolecular interaction energies of nearly 1,000 dimers and the cohesive energy of the benzene crystal.Comment: 11 pages, 6 figure

Molecular Modeling of Ions in Biological Systems

Ions are ubiquitous in biological systems. Metal ions contribute to biological function as counter ions, as triggers to cellular response, and as catalytic cofactors. They play structural roles and are part of the catalytic active site of metalloenzymes. NH4+ ions provide a source of nitrogen for amino acid synthesis in plants and bacteria and help maintaining the acid-base balance in mammals. The cationic side chains of amino acids Lys and Arg contribute to the stability of proteins and protein-DNA complexes through cation–π interactions with the π electrons of aromatic amino acids. Developing molecular models for ion-protein interactions is required to investigate and understand the various biological functions of ions and to complement and interpret experimental data. In this regard, the aims of this thesis are to: 1- Investigate the selectivity of alkali ions toward N, O, and S-containing ligands (a step toward understanding protein selectivity to metal ions). 2- Optimize new semiempirical quantum mechanical models for calcium and magnesium metalloproteins. 3- Study the strength and directionality of cation–π interactions involving inorganic and organic cations interacting with model compounds of aromatic amino acid side chains in both gas phase and aqueous solution. 4- Investigate the selectivity and binding affinity of AmtB and RhCG ammonium transport proteins toward various ions and study the function of amino acids that line the transport pathway of these proteins. Proteins bind metal ions through N, O, and S atoms from the side chains of the amino acids His, Asp, Glu, Ser, Tyr, Asn, Gln, Cys, and Met and from main chain carbonyl and amino groups. NH3, H2O, and H2S are used as minimal models for N, O, and S ligands to investigate the selectivity of alkali metal ions. Polarizable potential models for NH3 and H2S that accurately reproduce the experimental properties of the pure and aqueous liquids are developed. The models are used, together with a previously developed model for water, to study the solvation structures and solvation free energies of the ions in the pure liquids and to investigate the selectivity of alkali ions toward the three ligands. The models yield solvation structures and solvation free energies in good agreement with experiments and show a selectivity of alkali ions toward the three ligands that follows the order H2O > NH3 > H2S. Magnesium and Calcium are two of the most bioavailable metals and are known to play roles in signal transduction and in muscular contraction and are cofactors in many enzymes. Semiempirical models are optimized for the two metals based on the ab initio structures and binding energies of complexes formed between Mg2+ and Ca2+ with ligands that model binding groups in biological and chemical systems. Optimized models are tested on the ab initio properties of ~170 ion-ligand binary and ion-water-ligand ternary complexes. Optimized models of Mg underestimate the binding energies of S-containing complexes but give structures and binding energies of other complexes in agreement with ab initio data. Models for Ca reproduce the ab initio properties of all complexes, including S complexes. Cation–π interactions are common among protein structures and are believed to play key roles in stabilizing proteins and protein complexes with ligands and DNA. Polarizable potential models for the interaction of Rb+, Cs+, Tl+, ammonium, tetramethylammonium, and tetraethylammonium with aromatic amino acid side chains are calibrated based on the ab initio properties of the different cation–π complexes. The models are used to study the binding affinity and complexation geometry of the different pairs in water. Results are showing that cation–π interactions persist in aqueous solutions and are stronger than charge-dipole interactions (such as interactions of Rb+, Cs+, Tl+ with ethanol and acetamide). It is also found that cation–π complexes have geometries in aqueous solution similar to gas phase. In addition, results suggest that cation–π interactions influence the solubility of aromatic compounds in aqueous solutions. Proteins of the Amt/Mep/Rh family —ammonium transporters (Amt) in plants and bacteria, methylamine permease (Mep) in yeast, and rhesus (Rh) blood-group associated glycoproteins in animals— facilitate the permeation of ammonium across cell membranes. Crystal structures of AmtB and RhCG proteins reveal structural differences along the transport pathways. Amt proteins are selective toward NH4+ over Na+ and K+, yet their activity can be inhibited by ions such as Cs+ and Tl+. Polarizable potential models for NH3, NH4+, Na+, K+, Rb+, Cs+, and Tl+ interacting with model compounds to side chains of amino acids that line the transport pathway are optimized. The models are used to calculate the binding affinity of both proteins toward the various ligands and to study the functional roles of amino acids along the transport pathway. Results show that among the various ligands, only Cs+ and Tl+ can compete with NH4+ for binding the two proteins and hence inhibit the protein activity. Results also show that the large hydrophobicity of the pore lumen in RhCG protein destabilizes NH4+ and water molecules in the pore which suggests a net NH3 transport mechanism of the protein

Classical And Quantum Mechanical Simulations Of Condensed Systems And Biomolecules

This work describes the fundamental study of two enzymes of Fe(II)/-KG super family enzymes (TET2 and AlkB) by applying MD and QM/MM approaches, as well as the development of multipolar-polarizable force field (AMOEBA/GEM-DM) for condensed systems (ionic liquids and water). TET2 catalytic activity has been studied extensively to identify the potential source of its substrate preference in three iterative oxidation steps. Our MD results along with some experimental data show that the wild type TET2 active site is shaped to enable higher order oxidation. We showed that the scaffold stablished by Y1902 and T1372 is required for iterative oxidation. The mutation of these residues perturbs the alignment of the substrate in the active site, resulting in “5hmC-stalling” phenotype in some of the mutants. We provided more details on 5hmC to 5fC oxidation mechanism for wild type and one of the “5hmC-stallling” mutants (E mutant). We showed that 5hmC oxidizes to 5fC in the wild type via three steps. The first step is the hydrogen atom abstraction from hydroxyl group of 5hmC, while the second hydrogen is transferred from methylene group of 5hmC through the third transition state as a proton. Our results suggest that the oxidation in E mutant is kinetically unfavorable due to its high barrier energy. Many analyses have been performed to qualitatively describe our results and we believed our results can be used as a guide for other researchers. In addition, two MD approaches (explicit ligand sampling and WHAM) are used to study the oxygen molecule diffusion into the active site of AlkB. Our results showed that there are two possible channels for oxygen diffusion, however, diffusion through one of them is thermodynamically favorable. We also applied multipolar-polarizable force field to describe the oxygen diffusion along the preferred tunnel. We showed that the polarizable force field can describe the behavior of the highly polarizable systems accurately. We also developed a new multipolar-polarizable force field (AMOEBA/GEM-DM) to calculate the properties of imidazolium- and pyrrolidinium- based ionic liquids and water in a range of temperature. Our results agree well with the experimental data. The good agreement between our results and experimental data is because our new parameters provide an accurate description of non-bonded interactions. We fit all the non-bonded parameters against QM. We use the multipoles extracted from fitted electron densities (GEM) and we consider both inter- and intra-molecular polarization. We believe this method can accurately calculate the properties of condensed systems and can be helpful for designing new systems such as electrolytes