Monte Carlo Studies on Water in the dCpG/Proflavin Crystal Hydrate

Abstract

The extensive water network identified in the crystallographic studies of the dCpG/Proflavin hydrate by Neidle, Berman and Shieh (Nature 288, 129, 1980) forms an ideal test case for a) assessing the accuracy of theoretical calculations on nucleic acid—water systems based on statistical thermodynamic computer simulation, and b) the possible use of computer simulation in predicting the water positions in crystal hydrates for use in the further refinement and interpretation of diffraction data. Monte Carlo studies have been carried out on water molecules in the unit cell of dCpG/proflavin, with the nucleic acid complex fixed and the condensed phase environment of the system treated by means of periodic boundary conditions. Intermolecular interactions are described by potential functions representative of quantum mechanical calculations developed by Clementi and coworkers, and widely used in recent studies of the aqueous hydration of various forms of DNA fragments. The results are analyzed in terms of hydrogen bond topology, hydrogen bond distances and energies, mean water positions, and water crystal probability density maps. Detailed comparison of calculated and experimentally observed results are given, and the sensitivity of results to choice of potential is determined by comparison with simulation results based on a set of empirical potentials.     

Grand canonical ensemble Monte Carlo simulation of the dCpG/proflavine crystal hydrate.

The grand canonical ensemble Monte Carlo molecular simulation method is used to investigate hydration patterns in the crystal hydrate structure of the dCpG/proflavine intercalated complex. The objective of this study is to show by example that the recently advocated grand canonical ensemble simulation is a computationally efficient method for determining the positions of the hydrating water molecules in protein and nucleic acid structures. A detailed molecular simulation convergence analysis and an analogous comparison of the theoretical results with experiments clearly show that the grand ensemble simulations can be far more advantageous than the comparable canonical ensemble simulations.     

Solvent interactions in nucleic acid crystal hydrates

A detailed knowledge of structural and energetic aspects of water-nucleic acid interactions is essential for understanding the role of solvent in stabilizing the various helical forms of nucleic acids. In this study, computer simulation techniques have been used to predict structural properties of solvent networks in small nucleic acid crystal hydrates. A detailed comparison of predicted and experimental results on the structure of the solvent networks is presented and includes an analysis of both the local environment and hydrogen bond pattern of each water molecule. A correlation between the environment of each unique water molecule and its energetic properties (such a dipole moment and binding energy) is seen. As in the previous studies on small amino acid hydrate crystals, non-pair additive (cooperative) effects are found to be non-negligible. It is concluded that the potential functions used in this initial study lead to simulated solvent networks in reasonable agreement with experimental data. Thus, it is now feasible to use them in studies of hydration of larger helical fragments of nucleic acids of more direct biological interest.     

Monte Carlo simulations of nucleotide crystal hydrates and their counter-ions

A knowledge of structural and energetic aspects of water- and ion-nucleic acid interactions is essential for the understanding of the role of solvent and counterions in stabilising the various helical forms of nucleic acids. In this study, Monte Carlo computer simulation techniques have been used to predict structural properties of solvent networks in small nucleic acid crystal hydrates containing the ions sodium, ammonium and calcium. Appropriate parameters to describe the interaction potentials of the ions are added to those previously developed for water and nucleic acid atoms. A comparison is made between the predicted and experimental results and it is concluded that the potential functions used lead to simulated solvent structure in reasonable agreement with experimental data, at least in the cases of sodium and calcium. It is now feasible to use these functions in studies of hydration of larger helical fragments of nucleic acids of more direct biological interest.     

Ammonium ion representation in Monte Carlo simulations of biomolecular solutions

Monte Carlo computer simulation techniques may be used to predict structural properties of solvent networks in helical fragments of nucleic acids, provided that suitable potential functions are available to describe the interactions between nucleic acid atoms, water and counterions. Previous studies have shown that simple non-bonded and point charge parameters are adequate for mononuclear ions such as sodium and calcium. In this study a model interaction potential for the polynuclear ammonium ion is evaluated. The parameters used take account of the distribution of charge over the constituent atoms in the ion. Simulations are carried out on the ammonium salt of a small nucleic acid crystal hydrate and a comparison is made between the predicted and experimental results. It is shown that the simulated structure is in reasonable agreement with experiment. It is therefore feasible to use this potential in studies of ammonium-containing bimolecular systems.     

Simulation of interactions in the co-planar nucleic acid base pairs using atom-atom potential functions

Calculations of the energy of nucleic acid base interactions as a function of parameters determining mutual position of two bases in a plane have been performed. Atom-atom potential functions used include terms proportional to the first (electrostatic), sixth (or tenth for the atoms of hydrogen bond) and 12th power of interatomic distance. The calculations have shown the existence of 27 energy minima which correspond to the formation of co-planar pairs with two (or three for G : C pair) almost linear N--H...O and N--H...N hydrogen bonds. The positions of nitrogen bases bound by two hydrogen bonds in every crystal of nucleic acid components, in the complexes of polynucleotides and in tRNA are near to the positions in one of these minima. In addition for every pair there exist energy minima which correspond to the formation of one N--H...O or N--H...N and one C--H...O or C--H...N hydrogen bond. Energy behavior near minima have been investigated. The results of our calculations are in agreement with experimental data and with the calculations which employ quantum mechanical results.     

Molecular mechanical studies of proflavine and acridine orange intercalation.

Previous workers have reported that proflavine and acridine orange form various structurally different complexes with the dinucleoside phosphates rCpG and dCpG, with uniform C3'-endo and mixed C3'-endo (3'-5') C2'-endo sugar puckers being observed. We present theoretical calculations, based on the method of molecular mechanics, which support the experimental observations. The results suggest that the mixed C3'-edo (3'-5') C2'-endo pucker conformation isi intrinsically more stable than the uniform C3'-endo conformation, but that the additional stabilisation gained from specific, hydrogen bonding, interactions between nucleic acid and solvent, or intramolecularly within the nucleic acid, can lead to the adoption of the latter conformation, or of variants between the two. The role played by hydrogen bonding between amino-groups and nucleic acid phosphate appears more subtle than previously supposed.     

Polar hydrogen positions in proteins: Empirical energy placement and neutron diffraction comparison

A method for the prediction of hydrogen positions in proteins is presented. The method is based on the knowledge of the heavy atom positions obtained, for instance, from X-ray crystallography. It employs an energy minimization limited to the environment of the hydrogen atoms bound to a common heavy atom or to a single water molecule. The method is not restricted to proteins and can be applied without modification to nonpolar hydrogens and to nucleic acids. The method has been applied to the neutron diffraction structures of trypsin ribonuclease A, and bovine pancreatic trypsin inhibitor. A comparison of the constructed and the observed hydrogen positions shows few deviations except in situations in which several energetically similar conformations are possible. Analysis of the potential energy of rotation of Lys amino and Ser, Thr, Tyr hydroxyl groups reveals that the conformations of lowest intrinsic torsion energies are statistically favored in both the crystal and the constructed structures.     

Hydration of nucleic acid bases studied using novel atom-atom potential functions

New simple atom-atom potential functions for simulating behavior of nucleic acids and their fragments in aqueous solutions are suggested. These functions contains terms which are inversely proportional to the first (electrostatics), sixth (or tenth for the atoms, forming hydrogen bonds) and twelfth (repulsion of all the atoms) powers of interatomic distance. For the refinement of the potential function parameters calculations of ice lattice energy, potential energy and configuration of small clusters consisting of water and nucleic acid base molecules as well as Monte Carlo simulation of liquid water were performed. Calculations using new potential functions give rise to more linear hydrogen bonds between water and base molecules than using other potentials. Sites of preferential hydration of five nucleic bases - uracil, thymine, cytosine, guanine and adenine as well as of 6,6,9-trimethyladenine were found. In the most energetically favourable sites water molecular interacts with two adjacent hydrophilic centres of the base. Studies of interaction of the bases with several water molecules showed that water-water interactions play an important role in the arrangement of the nearest to the base water molecules. Hydrophilic centres are connected by "bridges" formed by hydrogen bonded water molecules. The results obtained are consistent with crystallographic and mass-spectrometric data.     

Solvent structure in vitamin B12 coenzyme crystals

Both the ordered and disordered solvent networks of vitamin B₁₂ coenzyme crystal hydrate have been generated by Monte Carlo simulation techniques. Several different potential functions have been use to model both water-water and water-solute (i.e., water-coenzyme) interactions. The results have been analysed in terms of the structural properties of the water networks, such as mean water oxygen and hydrogen positions, coordination of each water molecule, and maxima of probability density maps in all four asymmetric units of this crystal.The following results were found: (I) Within each asymmetric unit only one hydrogen bonding network was predicted although there were several hydrogen atom positions for any one solvent molecule (defined as maxima in probability density). (II) Reasonable agreement was obtained between predicted and experimental positions in the ordered solvent region, independent of the potential function used. (III) The positions of the calculated probability density maxima for the disordered channel region were different in different asymmetric units; this led to different simulated hydrogen bond networks which were not always consistent with the experimentally determined alternative (lower occupancy) sites.The results suggest that it is advisable to simulate more than one asymmetric unit if one wishes to look at disorder in the solvent regions. Probability density maps were qualitatively very useful for picturing these disordered regions. However, there were no significant differences between quantitative results predicted using either average atomic positions or maxima of the probability density distributions.Problems in quantifying agreement between experimental and predicted disordered solvent networks are discussed. The potential which included hydrogen atoms explicitly (EMPWI) seemed to give the best overall agreement, mainly because it was successful in predicting the unusually short hydrogen bonds which are found in this crystal.     

Hydration of Nucleic Acid Bases Studied Using Novel Atom-Atom Potential Functions

Abstract

New simple atom-atom potential functions for simulating behavior of nucleic acids and their fragments in aqueous solutions are suggested. These functions contain terms which are inversely proportional to the first (electrostatics), sixth (or tenth for the atoms, forming hydrogen bonds) and twelfth (repulsion of all the atoms) powers of interatomic distance. For the refinement of the potential function parameters calculations of ice lattice energy, potential energy and configuration of small clusters consisting of water and nucleic acid base molecules as well as Monte Carlo simulation of liquid water were performed. Calculations using new potential functions give rise to more linear hydrogen bonds between water and base molecules than using other potentials. Sites of preferential hydration of five nucleic bases—uracil, thymine, cytosine, guanine and adenine as well as of 6,6,9-trimethyladenine were found. In the most energetically favourable sites water molecule interacts with two adjacent hydrophilic centres of the base. Studies of interaction of the bases with several water molecules showed that water-water interaction play an important role in the arrangement of the nearest to the base water molecules. Hydrophilic centres are connected by “bridges” formed by hydrogen bonded water molecules. The results obtained are consistent with crystallographic and mass-spectrometric data.     

Display and interpretation of solvent electron density distributions in insulin crystals

In macromolecular crystallography, three-dimensional contour surfaces are useful for interactive computer graphics displays of the protein electron density but are less effective for presenting static images of large volumes of solvent density. A raster-based computer graphics program which displays depth-cued projections of continuous density distributions has been developed to analyze the distribution of solvent atoms in macromolecular crystals. Maps of the water distribution in the cubic insulin crystal show some well-ordered waters, which are bound to surrounding protein atoms by multiple hydrogen bonds, and an ill-defined solvent structure at a greater distance from the protein surface. Molecular dynamics calculations were used to assist in the interpretation of the time-varying solvent structure within two enclosed cavities in the crystal. Two water molecules that ligate a sodium ion were almost immobile during the simulation but the majority of water molecules were found to move rapidly between the density maxima identified from the crystallographic refinement.     

Aqueous Hydration of Nucleic Acid Constituents: Monte Carlo Computer Simulation Studies

Abstract

Monte Carlo computer simulations were performed on dilute aqueous solutions of thymine, cytosine, uracil, adenine, guanine, the dimethyl phosphate anion in the gauche-gauche conformation and a ribose and deoxyribose derivative. The aqueous hydration of each molecule was analysed in terms of quasi-component distribution functions based on the Proximity Criterion, and partitioned into hydrophobic, hydrophilic and ionic contributions. Color stereo views of selected hydration complexes are also presented. A preliminary discussion of the transferability of functional group coordination numbers is given. The results enable to comment on two current problems related to the hydration of nucleic acids: a) the theory of Dickerson and coworkers on the role of water in the relative stability of the A and B forms of DNA and b) the idea of water bridges and filaments emerging from the computer simulation results on the hydration of DNA fragments by Clementi.     

Determination of the positions of bound water molecules in the solution structure of reduced human thioredoxin by heteronuclear three-dimensional nuclear magnetic resonance spectroscopy.

The presence of bound water molecules in the solution structure of reduced human thioredoxin has been investigated using three-dimensional 1H rotating frame Overhauser 1H-15N multiple quantum coherence spectroscopy. It is demonstrated that the backbone amide protons of Lys21, Lys39, Lys82, Gly83 and Asn102, as well as the side-chain amide group of Asn102, are in close proximity to bound water molecules. Examination of the high-resolution solution structure of reduced human thioredoxin reveals that these results are best accounted for by four bound water molecules. Subsequent simulated annealing calculations carried out on the basis of interproton distance and hydrogen bonding restraints to the bound water molecules, supplemented by the original set of experimental restraints used in the calculation of the three-dimensional structure of human thioredoxin, permit a more precise localization of the bound water positions. Potential hydrogen bonds to these water molecules are described and a comparison is made to corresponding bound water molecules in the crystal structure of oxidized Escherichia coli thioredoxin.     

A molecular dynamics simulation of crystalline α-cyclodextrin hexahydrate

The structure of crystalline -cyclodextrin (-CD) hexahydrate, form I (C₃₆H₆₀O₃₀·6H₂O, space group P2₁2₁2₁) is experimentally so well determined by X-ray and by neutron diffraction analyses that the positions of all the hydrogen atoms are available. This provides an opportunity for testing an empirical force field that is currently used in simulations of protein and nucleic acid structures by performing molecular dynamics studies employing the GROMOS program package on a system of 4 unit cells containing 16 -CD molecules and 96 water molecules.A detailed comparison of the simulated and experimentally determined crystal structures shows that the experimental positions of the -CD atoms are reproduced within 0.025 nm, well within the overall experimental accuracy of 0.036 nm; that the water molecules are on average within 0.072 nm from their experimental sites, with two thirds reproduced within experimental accuracy by the calculations; that high correlation is produced, between the occurrence of simulated and experimentally observed hydrogen bonds.The good agreement between simulated and experimental results suggests that the tested force field is reliable.     

Lone pair ··· π interactions between water oxygens and aromatic residues: Quantum chemical studies based on high‐resolution protein structures and model compounds

The π electron cloud of aromatic centers is known to be involved in several noncovalent interactions such as C—H···π, O—H···π, and π···π interactions in biomolecules. Lone-pair (lp) ··· π interactions have gained attention recently and their role in biomolecular structures is being recognized. In this article, we have carried out systematic analysis of high-resolution protein structures and identified more than 400 examples in which water oxygen atoms are in close contact (distance < 3.5 Å) with the aromatic centers of aromatic residues. Three different methods were used to build hydrogen atoms and we used a consensus approach to find out potential candidates for lp···π interactions between water oxygen and aromatic residues. Quantum mechanical calculations at MP2/6-311++G(d,p) level on model systems based on protein structures indicate that majority of the identified examples have energetically favorable interactions. The influence of water hydrogen atoms was investigated by sampling water orientations as a function of two parameters: distance from the aromatic center and the angle between the aromatic plane and the plane formed by the three water atoms. Intermolecular potential surfaces were constructed using six model compounds representing the four aromatic amino acids and 510 different water orientations for each model compound. Ab initio molecular orbital calculations at MP2/6-311++G(d,p) level show that the interaction energy is favorable even when hydrogen atoms are farthest from the aromatic plane while water oxygen is pointing toward the aromatic center. The strength of such interaction depends upon the distance of water hydrogen atoms from the aromatic substituents. Our calculations clearly show that the lp···π interactions due to the close approach of water oxygen and aromatic center are influenced by the positions of water hydrogen atoms and the aromatic substituents.     

The electrostatic potential for the phosphodiester group determined from X-ray diffraction.

The charge density distribution in the crystal structure of ammonium dimethylphosphate at 123 K has been determined from x-ray diffraction data (MoK alpha) using 8437 reflections with sin theta/lambda less than 1.33 A-1 [NH4+.(CH3)2PO4-, M(r) = 143.08, monoclinic, P2(1)/c, a = 10.007(1), b = 6.926(1), c = 9.599(2) A, beta = 105.40(1) degrees, V = 641.4(3) A3, Z = 4, F000 = 304, Dx = 1.4815 g.cm-3, mu = 3.726 cm-1]. Least-squares structure refinement assuming Stewart's rigid pseudoatom model (variables including Slater-type radial exponents and electron populations for multipole terms extending to octapoles for C, N, O, and P, and dipoles for H) gave R(F2) = 0.039 for all reflections. The dimethylphosphate anion is in the gauche-gauche conformation and has approximate twofold symmetry. One phosphoryl O atom forms three hydrogen bonds and the other forms one. Neither of the ester O atoms is hydrogen bonded. For the dimethylphosphate anion isolated from the crystal structure, a map of the electrostatic potential obtained using the pseudoatom charge parameters shows that the phosphoryl O atoms are considerably more electronegative than the ester O atoms. The electrostatic potential distribution obtained in this way has been fitted by least squares to a system of atom-centered point charges. The potential calculated from these point charges agrees with the experimental result. It also agrees reasonably well with potentials obtained from three other systems of point charges that are widely used as part of the semiempirical force field for molecular mechanics and molecular dynamics calculations involving nucleic acids.     

Simulation of interactions between nucleic acid bases by refined atom-atom potential functions

Energy of interaction between nitrogen bases of nucleic acid has been calculated as a function of parameters determining the mutual position of two bases. Refined atom-atom potential functions are suggested. These functions contain terms proportional to the first (electrostatics), sixth (or tenth for the atoms forming a hydrogen bond) and twelfth (repulsion of all atoms) powers of interatomic distance. Calculations have shown that there are two groups of minima of the base interaction energy. The minima of the first group correspond to coplanar arrangement of the base pairs and hydrogen bond formation. The minima of the second group correspond to the position of bases one above the other in almost parallel planes. There are 28 energy minima corresponding to the formation of coplanar pairs with two (three for the G:C pair) almost linear N-H . . . O and (or) N-H . . . N hydrogen bonds. The position of nitrogen bases paired by two such H-bonds in any crystal of nucleic acid component in polynucleotide complexes and in tRNA is close to the position in one of these minima. Besides, for each pair there are energy minima corresponding to the formation of a single N-H . . . O or N-H . . . N and one C-H . . . O or C-H . . . N hydrogen bond. The form of potential surface in the vicinity of minima has been characterized. The results of calculations agree with the experimental data and with more rigorous calculations based on quantum-mechanical approach.     

Simulation of Interactions between Nucleic Acid Bases by Refined Atom-Atom Potential Functions

Abstract

Energy of interaction between nitrogen bases of nucleic acids has been calculated as a function of parameters determining the mutual position of two bases. Refined atom-atom potential functions are suggested. These functions contain terms proportional to the first (electrostatics), sixth (or tenth for the atoms forming a hydrogen bond) and twelfth (repulsion of all atoms) powers of interatomic distance. Calculations have shown that there are two groups of minima of the base interaction energy. The minima of the first group correspond to coplanar arrangement of the base pairs and hydrogen bond formation. The minima of the second group correspond to the position of bases one above the other in almost parallel planes. There are 28 energy minima corresponding to the formation of coplanar pairs with two (three for the G:C pair) almost linear N-H … O and (or) N-H … N hydrogen bonds. The position of nitrogen bases paired by two such H-bonds in any crystal of nucleic acid component, in polynucleotide complexes and in tRNA is close to the position in one of these minima. Besides, for each pair there are energy minima corresponding to the formation of a single N-H … O or N-H … N and one C-H … O or C-H … N hydrogen bond. The form of potential surface in the vicinity of minima has been characterized. The results of calculations agree with the experimental data and with more rigorous calculations based on quantum- mechanical approach.     

Solution Influence on Biomolecular Equilibria: Nucleic Acid Base Associations

Abstract

This paper consists of two parts. In the first part, the general problem of biomolecular equilibria in solution is considered, stressing that molecular interactions ultimately determine the answer to this problem. It is discussed how computer simulation techniques can reliably treat the problem and several pitfalls of computer simulation to be avoided are pointed out. Other approaches based on modeling and conceptual simplifications such as perturbative methods, long-range interaction approximations, surface thermodynamic approaches, and hydration shell models are discussed. In the second part, the results of Monte Carlo calculations on the associations of nucleic acid bases in water and carbon tetrachloride are presented. Stacked self-associations are found to be preferred in water and hydrogen-bonded complexes are favored in nonpolar solutions, in agreement with experimentell data. The influence of the solvent on base associations is explained in terms of solute-solvent and solvent-solvent contributions to the total energy. No enthalpic stabilization of the complexes by the solvent was found. The results are used to examine the validity of various approximations discussed in the first part of the paper.