Molecular dynamics studies of ion distributions for DNA duplexes and DNA clusters: salt effects and connection to DNA melting

We present extensive molecular dynamics simulations of the ion distributions for DNA duplexes and DNA clusters using the Amber force field with implicit water. The distribution of ions and the electrostatic energy of ions around an isolated DNA duplex and clusters of DNA duplexes in different salt (NaCl) concentrations over the range 0.2-1.0 mol/L are determined on the basis of the simulation results. Using the electrostatic energy profile, we determine a local net charge fraction phi, which is found to increase with increasing of salt concentration. For DNA clusters containing two DNA duplexes (DNA pair) or four DNA duplexes, phi increases as the distance between the duplexes decreases. Combining this result with experimental results for the dependence of the DNA melting temperature on bulk salt concentration, we conclude that for a pair of DNA duplexes the melting temperature increases by 5-10 K for interaxis separations of 25-40 A. For a cluster of four DNA duplexes, an even larger melting temperature increase should occur. We argue that this melting temperature increase in dense DNA clusters is responsible for the cooperative melting mechanism in DNA-linked nanoparticle aggregates and DNA-linked polymer aggregates.     

Force fields including charge transfer and local polarization effects: Application to proteins containing multi/heavy metal ions

The question whether molecular dynamics (MD) simulations can yield reliable structural and dynamical properties of metalloproteins depend on the accuracy of the force field, i.e., the potential energy function (PEF) and associated parameters modeling the interactions of the metal ion of interest with water and protein ligands. Previously, we had developed a CTPOL PEF for protein simulations of Zn(2+) bound to Cys(-) and/or His(0) that includes charge transfer and local polarization effects as well as metal van der Waals parameters that reproduce the structural and thermodynamical properties of 22 dications. Here, we evaluate if the CTPOL PEF and the new metal parameters (referred to as the CTPOLa force field) can be applied to proteins containing polynuclear metal-binding sites and heavy toxic metal ions, using the CdZn(2)-Cys(9) beta-domain of rat liver metallothionein-2 and the Hg(2+)-bound 18-residue peptide from MerP as test systems. Using the CTPOLa force field, simulations of the beta-domain of rat liver metallothionein-2 totaling 19 ns could preserve the experimentally observed CdZn(2)-Cys(9) complex geometry and overall protein structure, whereas simulations neglecting charge transfer and local polarization effects could not. However, the CTPOLa force field cannot reproduce the experimentally observed linear bicoordination of Hg(2+) in the MerP peptide without adding an angular restraint to the CTPOL PEF to correct the angle distribution about Hg(2+). Thus, the force fields presented herein for the group IIB metal ions can be applied to simulation studies of proteins containing polynuclear metal-binding sites and heavy metal ions in aqueous solution. PEF neglecting charge transfer and local polarization effects in conjunction with vdW parameters adjusted to reproduce the structural and thermodynamical properties of only the metal ion in question could not yield an accurate representation of the metal-binding site and overall protein structure.     

Ionic liquid near a charged wall: structure and capacitance of electrical double layer

We study the effects of ion size asymmetry and short-range correlations on the electrical double layer in ionic liquids: we perform molecular dynamics simulations of a model ionic liquid between two "electrodes" and calculate the differential capacitance of each as a function of the electrode potential. The capacitance curve has an asymmetric "bell-shape" character, in qualitative agreement with recent experiments and the mean- field theory (MFT) which takes into account the limitation on the maximal local density of ions. The short-range ionic correlations, not included in the MFT, lead to an overscreening effect which changes radically the structure of the double layer at small and moderate charging. With the radius of cations taken to be twice as large as anions, the position of the main capacitance maximum is shifted positively from the potential of zero charge (PZC), as predicted by MFT. An extension of the theory (EMFT), however, reproduces the simulated capacitance curve almost quantitatively. Capacitance curves for real ionic liquids will be affected by nonspherical shape of ions and sophisticated pair potentials, varying from liquid to liquid. But understanding the capacitance behavior of such model system is a basis for rationalizing those more specific features.     

Arsenate incorporation in gypsum probed by neutron, X-ray scattering and density functional theory modeling

The ability of gypsum, a common sulfate mineral, to host arsenic atoms in its crystalline structure, is demonstrated through experimental structural studies of the solid solutions formed upon synthetic coprecipitation of gypsum (CaSO4 x 2 H2O) and arsenic. Neutron and X-ray diffraction methods show an enlargement of the gypsum unit cell proportional to the concentration of arsenic in the solids and to the pH solution value. The substitution of sulfate ions (SO4(2-)) by arsenate ions is shown to be more likely under alkaline conditions, where the HAsO4(2-) species predominates. A theoretical Density Functional Theory model of the arsenic-doped gypsum structure reproduces the experimental volume expansion. Extended X-ray Absorption Fine Structure (EXAFS) measurements of the local structure around the arsenic atom in the coprecipitated solids confirm solid state substitution and allow some refinement of the local structure, corroborating the theoretical structure found in the simulations. The charge redistribution within the structure upon substitutions of either the protonated or the unprotonated arsenate species studied by means of Mulliken Population Analyses demonstrates an increase in the covalency in the interaction between Ca(2+) and AsO4(3-), whereas the interaction between Ca(2+) and HAsO4(2-) remains predominantly ionic.     

Role of ions on structure and stability of a synthetic gramicidin ion channel in solution. A molecular dynamics study

We performed a molecular dynamics (MD) simulation to the investigate structure and stability of a synthetic gramicidin-like peptide in solution with and without ions. The starting structures of the MD simulations were taken from two recently solved NMR structures of this peptide in isotropic solution, which forms stable monomers or dimers in the presence or absence of ions, respectively. The monomeric structure is channel-like and is assumed to be stabilized by the presence of two Cs(+) ions bound in the channel, each one close to one channel entrance. In our MD simulations, we observed how the Cs(+) ions bind in the channel formed by the monomeric gramicidin-like peptide using implicit solvent and explicit ions with a concentration of 2 M. MD simulations were performed with and without explicit ions but with an implicit solvent model defined by the generalized Born approximation, which was used to mimic the dielectric properties of the solvent and to speed up the computations.     

Multiscale modeling of materials based on force and charge density fidelity

The approximate representation of a quantum solid as an equivalent composite semiclassical solid is considered for insulating materials. The composite is comprised of point ions moving on a potential energy surface. In the classical bulk domain this potential energy is represented by potentials constructed to give the same structure and elastic properties as the underlying quantum solid. In a small local quantum domain the potential is determined from a detailed quantum calculation of the electronic structure. The new features of this well-studied problem are (1) a clearly stated theoretical context in which approximations leading to the model are introduced, (2) the representation of the classical domain by potentials focused on reproducing the specific quantum response being studied, (3) development of "pseudoatoms" for a realistic treatment of charge densities where bonds have been broken to define the environment of the quantum domain, and (4) inclusion of polarization effects on the quantum domain due to its distant bulk environment. This formal structure is illustrated in detail for a SiO(2) nanorod. More importantly, each component of the proposed modeling is tested quantitatively for this case, verifying its accuracy as a faithful multiscale model of the original quantum solid. To do so, the charge density of the entire nanorod is calculated quantum mechanically to provide the reference by which to judge the accuracy of the modeling. The construction of the classical potentials, the rod, the pseudoatoms, and the multipoles is discussed and tested in detail. It is then shown that the quantum rod, the rod constructed from the classical potentials, and the composite classical/quantum rod all have the same equilibrium structure and response to elastic strain. In more detail, the charge density and forces in the quantum subdomain are accurately reproduced by the proposed modeling of the environmental effects even for strains beyond the linear domain. The accuracy of the modeling is shown to apply for two quite different choices for the underlying quantum chemical method: transfer Hamiltonian and density functional methods.     

Electron binding energies of aqueous alkali and halide ions: EUV photoelectron spectroscopy of liquid solutions and combined ab initio and molecular dynamics calculations

Photoelectron spectroscopy combined with the liquid microjet technique enables the direct probing of the electronic structure of aqueous solutions. We report measured and calculated lowest vertical electron binding energies of aqueous alkali cations and halide anions. In some cases, ejection from deeper electronic levels of the solute could be observed. Electron binding energies of a given aqueous ion are found to be independent of the counterion and the salt concentration. The experimental results are complemented by ab initio calculations, at the MP2 and CCSD(T) level, of the ionization energies of these prototype ions in the aqueous phase. The solvent effect was accounted for in the electronic structure calculations in two ways. An explicit inclusion of discrete water molecules using a set of snapshots from an equilibrium classical molecular dynamics simulations and a fractional charge representation of solvent molecules give good results for halide ions. The electron binding energies of alkali cations computed with this approach tend to be overestimated. On the other hand, the polarizable continuum model, which strictly provides adiabatic binding energies, performs well for the alkali cations but fails for the halides. Photon energies in the experiment were in the EUV region (typically 100 eV) for which the technique is probing the top layers of the liquid sample. Hence, the reported energies of aqueous ions are closely connected with both structures and chemical reactivity at the liquid interface, for example, in atmospheric aerosol particles, as well as fundamental bulk solvation properties.     

Osmotic coefficients of atomistic NaCl (aq) force fields

Solvated ions are becoming increasingly important for (bio)molecular simulations. But there are not much suitable data to validate the intermediate-range solution structure that ion-water force fields produce. We compare six selected combinations of four biomolecular Na-Cl force fields and four popular water models by means of effective ion-ion potentials. First we derive an effective potential at high dilution from simulations of two ions in explicit water. At higher ionic concentration multibody effects will become important. We propose to capture those by employing a concentration dependent dielectric permittivity. With the so obtained effective potentials we then perform implicit solvent simulations. We demonstrate that our effective potentials accurately reproduce ion-ion coordination numbers and the local structure. They allow us furthermore to calculate osmotic coefficients that can be directly compared with experimental data. We show that the osmotic coefficient is a sensitive and accurate measure for the effective ion-ion interactions and the intermediate-range structure of the solution. It is therefore a suitable and useful quantity for validating and parametrizing atomistic ion-water force fields.     

Collective-variable Monte Carlo simulation of DNA

Monte Carlo simulations have been carried out on DNA oligomers using an internal coordinate model associated with a pseudorotational representation of sugar repuckering. It is shown that when this model is combined with the scaled collective variable approach of Noguti and Go, much more efficient simulations are obtained than with simple single variable steps. Application of this method to a DNA oligomer containing a recognition site for the TATA-box binding protein leads to striking similarities with results recently obtained from a 1-ns molecular dynamics simulation using explicit solvent and counterions. In particular, large amplitude bending fluctuations are observed directed toward the major groove. Conformational analysis of the Monte Carlo simulation shows clear base sequence effects on conformational fluctuations and also that the DNA energy hypersurface, like that of proteins, is complex with many local, conformational substates. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2001–2011, 1997     

Local order in aqueous NaCl solutions and pure water: X-ray scattering and molecular dynamics simulations study

The microstructures of pure water and aqueous NaCl solutions over a wide range of salt concentrations (0-4 m) under ambient conditions are characterized by X-ray scattering and molecular dynamics (MD) simulations. MD simulations are performed with the rigid SPC water model as a solvent, while the ions are treated as charged Lennard-Jones particles. Simulated data show that the first peaks in the O...O and O...H pair correlation functions clearly decrease in height with increasing salt concentration. Simultaneously, the location of the second O...O peak, the signature of the so-called tetrahedral structure of water, gradually disappears. Consequently, the degree of hydrogen bonding in liquid water decreases when compared to pure fluid. MD results also show that the hydration number around the cation decreases as the salt concentration increases, which is most likely because some water molecules in the first hydration shell are occasionally substituted by chlorine. In addition, the fraction of contact ion pairs increases and that of solvent-separated ion pairs decreases. Experimental data are analyzed to deduce the structure factors and the pair correlation functions of each system. X-ray results clearly show a perturbation of the association structure of the solvent and highlight the appearance of new interactions between ions and water. A model of intermolecular arrangement via MD results is then proposed to describe the local order in each system, as deduced from X-ray scattering data.     

Ion condensation behavior and dynamics of water molecules surrounding the sodium poly(methacrylic acid) chain in water: a molecular dynamics study

All-atom molecular dynamics simulations are used to study the condensation behavior of monovalent (Na(+)) and multivalent (Ca(2+)) salt counterions associated with the co-ions (Cl(-)) surrounding the charged poly(methacrylic acid) (PMAA) chain in water. The study is extended to the influences on chain conformation, local arrangement, and dynamics of water in the highly diluted aqueous solutions. We find that even when the salt ions are monovalent, they attract more than one charged monomer and act as a bridging agent within the chain, as the multivalent salt ions. In principle, the salt ions bridge between not only the "non-adjacent" but also the "adjacent" charged monomers, leading to a more coil-like and a locally stretched conformation, respectively. With an increase in the salt concentration, the amount of coiled-type condensed ions increase and reach a maximum when the chain conformation becomes the most collapsed; whereas, the stretched-type shows an opposite trend. Our results show that the attractive interactions through the condensed salt ions between the non-adjacent monomers are responsible for the conformational collapse. When the salt concentration increases high enough, a significant increase for the stretched-type condensed ions makes an expansion effect on the chain. These stretched-type salt ions, followed by the adsorption of the co-ions and water molecules, tend to form a multilayer organization outside surrounding the PMAA chain. Thus, the expansion degree of the chain conformation is greatly limited. When only the monovalent Na(+) ions are present in the solutions, water molecules are primarily adsorbed into either the condensed Na(+) ions or the COO(-) groups. These adsorbed water molecules form hydrogen bonds with each other and enhance the local bridging behavior associated with the Na(+) condensation on the resultant chain conformation. With an increase in the amount of multivalent Ca(2+) salt ions, more water molecules are bonded directly with the condensed Ca(2+) ions. In this case, only the condensed Ca(2+) ions provide a strong bridging effect within the polymer chain. We observe a significant shift towards a higher frequency of the oxygen vibration spectrum and only a slight shift towards a higher frequency of the hydrogen spectrum for the water molecules associated with the ion condensation.     

Solvating,manipulating, damaging,and repairing DNA in a computer

This work highlights four different topics in modeling of DNA: (i) the importance of water and ions together with the structure and function of DNA; the hydration structure around the ions appears to be the determining factor in the ion coordination to DNA, as demonstrated in the results of our MD simulations; (ii) how MD simulations can be used to simulate single molecule manipulation experiments as a complement to reveal the structural dynamics of the studied biomolecules; (iii) how damaged DNA can be studied in computer simulations; and (iv) how repair of damaged DNA can be studied theoretically. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Functionally relevant protein motions: extracting basin-specific collective coordinates from molecular dynamics trajectories

Functionally relevant motion of proteins has been associated with a number of atoms moving in a concerted fashion along so-called "collective coordinates." We present an approach to extract collective coordinates from conformations obtained from molecular dynamics simulations. The power of this technique for differentiating local structural fluctuations between classes of conformers obtained by clustering is illustrated by analyzing nanosecond-long trajectories for the response regulator protein Spo0F of Bacillus subtilis, generated both in vacuo and using an implicit-solvent representation. Conformational clustering is performed using automated histogram filtering of the inter-C(alpha) distances. Orthogonal (varimax) rotation of the vectors obtained by principal component analysis of these interresidue distances for the members of individual clusters is key to the interpretation of collective coordinates dominating each conformational class. The rotated loadings plots isolate significant variation in interresidue distances, and these are associated with entire mobile secondary structure elements. From this we infer concerted motions of these structural elements. For the Spo0F simulations employing an implicit-solvent representation, collective coordinates obtained in this fashion are consistent with the location of the protein's known active sites and experimentally determined mobile regions.     

Packaging of a flexible polyelectrolyte inside a viral capsid: effect of salt concentration and salt valence

The effect of salt on the location and structure of a flexible polyelectrolyte confined inside a viral capsid and the Donnan equilibrium of the salt across the capsid have been examined using a coarse-grained model solved by Monte Carlo simulations. The polyelectrolyte was represented by a linear jointed chain of charged beads, and the capsid was represented by a spherical shell with embedded charges. At low salt concentration, the polyelectrolyte was strongly adsorbed onto the inner capsid surface, whereas at high salt concentration it was located preferentially in the central part of the capsid. Under the condition of equal Debye screening length, the electrostatic screening increased as the valence of the polyelectrolyte counterion was increased. The distribution of the small cations and anions was unequal across the capsid. An excess of polyelectrolyte counterions occurred inside the capsid, and the excess increased with the salt concentration. A simplified representation of the small ions through the use of the screened Coulomb potential provided only a qualitatively correct picture; the electrostatic screening originating from the small ions was exaggerated.     

DNA dynamics in a water drop without counterions

Because of its polyionic character, the DNA double helix is stable and biologically active only in salty aqueous media where its charge is compensated by solvent counterions. Monovalent metal ions are ubiquitous in DNA environment, and they are usually considered as the possible driving force of sequence-dependent modulations of DNA structure that make it recognizable by proteins. In an effort to directly examine this hypothesis, MD simulations of DNA in a water drop surrounded by vacuum were carried out, which relieves the requirement of charge neutrality. Surprisingly, with zero concentration of counterions, a dodecamer DNA duplex appears metastable, and its structure remains similar to that observed in experiment, including the minor groove narrowing in the dodecamer d(CGCGAATTCGCG)(2) often considered as the most evident cation effect. It is suggested that the same computational approach will allow one to simulate dynamics of long DNA chains more efficiently than with periodical boundary conditions.     

Determination of alkali and halide monovalent ion parameters for use in explicitly solvated biomolecular simulations

Alkali (Li(+), Na(+), K(+), Rb(+), and Cs(+)) and halide (F(-), Cl(-), Br(-), and I(-)) ions play an important role in many biological phenomena, roles that range from stabilization of biomolecular structure, to influence on biomolecular dynamics, to key physiological influence on homeostasis and signaling. To properly model ionic interaction and stability in atomistic simulations of biomolecular structure, dynamics, folding, catalysis, and function, an accurate model or representation of the monovalent ions is critically necessary. A good model needs to simultaneously reproduce many properties of ions, including their structure, dynamics, solvation, and moreover both the interactions of these ions with each other in the crystal and in solution and the interactions of ions with other molecules. At present, the best force fields for biomolecules employ a simple additive, nonpolarizable, and pairwise potential for atomic interaction. In this work, we describe our efforts to build better models of the monovalent ions within the pairwise Coulombic and 6-12 Lennard-Jones framework, where the models are tuned to balance crystal and solution properties in Ewald simulations with specific choices of well-known water models. Although it has been clearly demonstrated that truly accurate treatments of ions will require inclusion of nonadditivity and polarizability (particularly with the anions) and ultimately even a quantum mechanical treatment, our goal was to simply push the limits of the additive treatments to see if a balanced model could be created. The applied methodology is general and can be extended to other ions and to polarizable force-field models. Our starting point centered on observations from long simulations of biomolecules in salt solution with the AMBER force fields where salt crystals formed well below their solubility limit. The likely cause of the artifact in the AMBER parameters relates to the naive mixing of the Smith and Dang chloride parameters with AMBER-adapted Aqvist cation parameters. To provide a more appropriate balance, we reoptimized the parameters of the Lennard-Jones potential for the ions and specific choices of water models. To validate and optimize the parameters, we calculated hydration free energies of the solvated ions and also lattice energies (LE) and lattice constants (LC) of alkali halide salt crystals. This is the first effort that systematically scans across the Lennard-Jones space (well depth and radius) while balancing ion properties like LE and LC across all pair combinations of the alkali ions and halide ions. The optimization across the entire monovalent series avoids systematic deviations. The ion parameters developed, optimized, and characterized were targeted for use with some of the most commonly used rigid and nonpolarizable water models, specifically TIP3P, TIP4P EW, and SPC/E. In addition to well reproducing the solution and crystal properties, the new ion parameters well reproduce binding energies of the ions to water and the radii of the first hydration shells.     

Controlling the cohesion of cement paste

The main source of cohesion in cement paste is the nanoparticles of calcium silicate hydrate (C-S-H), which are formed upon the dissolution of the original tricalcium silicate (C(3)S). The interaction between highly charged C-S-H particles in the presence of divalent calcium counterions is strongly attractive because of ion-ion correlations and a negligible entropic repulsion. Traditional double-layer theory based on the Poisson-Boltzmann equation becomes qualitatively incorrect in these systems. Monte Carlo (MC) simulations in the framework of the primitive model of electrolyte solution is then an alternative, where ion-ion correlations are properly included. In addition to divalent calcium counterions, commercial Portland cement contains a variety of other ions (sodium, potassium, sulfate, etc.). The influence of high concentrations of these ionic additives as well as pH on the stability of the final concrete construction is investigated through MC simulations in a grand canonical ensemble. The results show that calcium ions have a strong physical affinity (in opposition to specific chemical adsorption) to the negatively charged silicate particles of interest (C-S-H, C(3)S). This gives concrete surprisingly robust properties, and the cement cohesion is unaffected by the addition of a large variety of additives provided that the calcium concentration and the C-S-H surface charge are high enough. This general phenomenon is also semiquantitatively reproduced from a simple analytical model. The simulations also predict that the affinity of divalent counterions for a highly and oppositely charged surface sometimes is high enough to cause a "charge reversal" of the apparent surface charge in agreement with electrophoretic measurements on both C(3)S and C-S-H particles.     

Modeling and molecular dynamics simulation of the human gonadotropin-releasing hormone receptor in a lipid bilayer

In the present study, a model for the human gonadotropin-releasing hormone receptor embedded in an explicit lipid bilayer was developed. The final conformation was obtained by extensive molecular dynamics simulations of a homology model based on the bovine rhodopsin crystal structure. The analysis of the receptor structure allowed us to detect a number of specific contacts between different amino acid residues, as well as water- and lipid-mediated interactions. These interactions were stable in six additional independent 35 ns long simulations at 310 and 323 K, which used the refined model as the starting structure. All loops, particularly the extracellular loop 2 and the intracellular loop 3, exhibited high fluctuations, whereas the transmembrane helices were more static. Although other models of this receptor have been previously developed, none of them have been subjected to extensive molecular dynamics simulations, and no other three-dimensional structure is publicly available. Our results suggest that the presence of ions as well as explicit solvent and lipid molecules are critical for the structure of membrane protein models, and that molecular dynamics simulations are certainly useful for their refinement.