Computation of ionic distributions around charged biomolecular structures: results for right-handed and left-handed DNA

Texture formation in DNA films with alkali metal chlorides

The formation of textures in DNA films with LiCl, NaCl, KCl, RbCl, and CsCl salts has been studied. The films are prepared by evaporation of water solution with highly polymerized calf thymus DNA and excess salt of specific type. For DNA solution with 10 mM concentration of NaCl, KCl, and RbCl the films with dendritic textures have been obtained, whereas in case of CsCl the textures in the films appear only at 30 mM concentration of excess salt in the initial solution. In the solution with LiCl, the textures in DNA films have not been observed within the whole range of concentration of excess salt under consideration. The analysis of parameters of DNA films with different salts has showed that evaporation of solution leads to crystallization of salt ions on DNA macromolecule and formation of DNA-salt complexes. Electrostatic energy of the system of crystalline ordered ions and charges of DNA chains has been estimated to study the stability of DNA-salt complexes. The results obtained for different salts have been showed that the presence of DNA macromolecule enhances crystallization as compared with solution without DNA. The property of excess salt to form the crystalline structures has been found to decrease in the following order: KCl > NaCl > RbCl > CsCl > LiCl. The results of estimation are in good agreement with the experimentally observed dependence of texture formation on excess salt type.

Solvent-induced free energy landscape and solute-solvent dynamic coupling in a multielement solute

Molecular dynamics simulations using a simple multielement model solute with internal degrees of freedom and accounting for solvent-induced interactions to all orders in explicit water are reported. The potential energy landscape of the solute is flat in vacuo. However, the sole untruncated solvent-induced interactions between apolar (hydrophobic) and charged elements generate a rich landscape of potential of mean force exhibiting typical features of protein landscapes. Despite the simplicity of our solute, the depth of minima in this landscape is not far in size from free energies that stabilize protein conformations. Dynamical coupling between configurational switching of the system and hydration reconfiguration is also elicited. Switching is seen to occur on a time scale two orders of magnitude longer than that of the reconfiguration time of the solute taken alone, or that of the unperturbed solvent. Qualitatively, these results are unaffected by a different choice of the water-water interaction potential. They show that already at an elementary level, solvent-induced interactions alone, when fully accounted for, can be responsible for configurational and dynamical features essential to protein folding and function.

Computer Simulation of the Ionic Atmosphere around Z-DNA

We describe a coarse-grained model for Z-DNA that mimics the DNA shape with a relatively small number of repulsive interaction sites. In addition, negative charges are placed at the phosphate positions. The ionic atmosphere around this grooved Z-DNA model is then investigated with Monte Carlo simulation. Cylindrically averaged concentration profiles as well as the spatial distribution of ions have been calculated. The results are compared to those for other DNA models differing in the repulsive core. This allows the examination of the effect of the DNA shape in the ionic distribution. It is seen that the penetrability of the ions to the DNA groove plays an important role in the ionic distribution. The results are also compared with those reported for B-DNA. In both conformers the ions are structured in alternating layers of positive and negative charge. In Z-DNA the layers are more or less concentric to the molecular axis. Besides, no coions enter into the single groove of this conformer. On the contrary, the alternating layers of B-DNA are also structured along the axial coordinate with some coions penetrating into the major groove. In both cases we have found five preferred locations of the counterions and two for the coions. The concentration of counterions reaches its absolute maximum at the narrow Z-DNA groove and at the minor groove of B-DNA, the value of the maximum being higher in the Z conformer.

Cobalt hexammine induced tautomeric shift in Z-DNA: the structure of d(CGCGCA)*d(TGCGCG) in two crystal forms

We report here the crystal structure of the DNA hexamer duplex d(CGCGCA)*d(TGCGCG) at 1.71 A resolution. The crystals, in orthorhombic space group, were grown in the presence of cobalt hexammine, a known inducer of the left-handed Z form of DNA. The interaction of this ion with the DNA helix results in a change of the adenine base from the common amino tautomeric form to the imino tautomer. Consequently the A:T base pair is disrupted from the normal Watson-Crick base pairing to a 'wobble' like base pairing. This change is accommodated easily within the helix, and the helical parameters are those expected for Z-DNA. When the cobalt hexammine concentration is decreased slightly in the crystallization conditions, the duplex crystallizes in a different, hexagonal space group, with two hexamer duplexes in the asymmetric unit. One of these is situated on a crystallographic 6-fold screw axis, leading to disorder. The tautomeric shift is not observed in this space group. We show that the change in inter-helix interactions that lead to the two different space groups probably arise from the small decrease in ion concentration, and consequently disordered positions for the ion.

Effects of electric charges on hydrophobic forces. II

We study by molecular-dynamics simulations the effect of electric charges of either sign on hydrophobic interactions and on the dynamics of hydration water, using explicit water and very simplified solutes. Results show that the presence of a charged solute can disrupt the "hydrophobic contact bond" between two apolar solutes nearby, by forcing them towards a different configuration. As a consequence of different structural changes of the solvent caused by charges of opposite sign, the effect is markedly charge-sign-dependent. Analogous weaker effects appear to be induced by the presence of one additional apolar element. The dynamics of hydration water around each solute is also seen to be strongly influenced by the presence of other (charged or uncharged) nearby solutes. Comparison between our results on hydration water dynamics around charged solutes and available experimental data allows sorting out the effects of solute charge sign and size. Our results also offer a plain interpretation of the equivalence of the effects on water structure due to solute ions and to high pressures. These results reflect at a basic paradigmatic level the immensely more complex cases of well-known phenomena such as salting-in and salting-out, and of protein conformational changes caused, e.g., by the arrival of a charged or of an apolar group (phosphorilation or methylation). As it will be discussed, they help in the direction of Delbruck's desirable "progress towards a radical physical explanation" for this class of phenomena.

A unified theory of the B-Z transition of DNA in high and low concentrations of multivalent ions

We showed recently that the high-salt transition of poly[d(G-C)]. poly[d(G-C)] between B-DNA and Z-DNA (at [NaCl] = 2.25 M or [MgCl(2)] = 0.7 M) can be ascribed to the lesser electrostatic free energy of the B form, due to better immersion of the phosphates in the solution. This property was incorporated in cylindrical DNA models that were analyzed by Poisson-Boltzmann theory. The results are insensitive to details of the models, and in fair agreement with experiment. In contrast, the Z form of the poly[d(G-m5C)] duplex is stabilized by very small concentrations of magnesium. We now show that this striking difference is accommodated quantitatively by the same electrostatic theory, without any adjustable parameter. The different responses to magnesium of the methylated and nonmethylated polymers do not come from stereospecific cation-DNA interactions: they stem from an experimentally derived, modest difference in the nonelectrostatic component of the free energy difference (or NFED) between the Z and B forms. The NFED is derived from circular DNA measurements. The differences between alkaline earth and transition metal ions are explained by weak coordination of the latter. The theory also explains the induction of the transition by micromolar concentrations of cobalt hexammine, again without specific binding or adjustable parameters. Hence, in the case of the B-Z transition as in others (e.g., the folding of tRNA and of ribozymes), the effect of multivalent cations on nucleic acid structure is mediated primarily by nonspecific ion-polyelectrolyte interactions. We propose this as a general rule for which convincing counter-examples are lacking.

Conformational equilibria of alkanes in aqueous solution: relationship to water structure near hydrophobic solutes

Conformational free energies of butane, pentane, and hexane in water are calculated from molecular simulations with explicit waters and from a simple molecular theory in which the local hydration structure is estimated based on a proximity approximation. This proximity approximation uses only the two nearest carbon atoms on the alkane to predict the local water density at a given point in space. Conformational free energies of hydration are subsequently calculated using a free energy perturbation method. Quantitative agreement is found between the free energies obtained from simulations and theory. Moreover, free energy calculations using this proximity approximation are approximately four orders of magnitude faster than those based on explicit water simulations. Our results demonstrate the accuracy and utility of the proximity approximation for predicting water structure as the basis for a quantitative description of n-alkane conformational equilibria in water. In addition, the proximity approximation provides a molecular foundation for extending predictions of water structure and hydration thermodynamic properties of simple hydrophobic solutes to larger clusters or assemblies of hydrophobic solutes.

Hormonal and dietary regulation of a mammalian gene introduced into rat liver by direct injection

The difficulty of introducing foreign genes into a target tissue such as liver prompted us to explore the method of direct injection of DNA into this organ. In this article we examine whether direct hepatic injection of DNA enables the liver to express a transgene controlled by a mammalian promoter. The construct pS14CAT, composed of the rat S14 gene promoter coupled to CAT, was directly injected into rat liver. Hepatic expression of the pS14CAT transgene mimicked expression of the endogenous S14 gene, characterized by a low level of basal expression that increased markedly after exposure to thyroid hormone or a high sucrose diet. This effect was specific, since similar treatments had no effect on activity of a control transgene, pSV2CAT, which is under the direction of the viral SV40 promoter/enhancer. Dexamethasone treatment enhanced the activity of both pS14CAT or pSV2CAT transgenes, an effect likely mediated by both transcriptional and nontranscriptional pathways. In summary, our study demonstrates the feasibility of using direct DNA injection to study transcriptional regulation of hepatic gene promoters in vivo.

Ion-induced folding of the hammerhead ribozyme: a fluorescence resonance energy transfer study

The ion-induced folding transitions of the hammerhead ribozyme have been analysed by fluorescence resonance energy transfer. The hammerhead ribozyme may be regarded as a special example of a three-way RNA junction, the global structure of which has been studied by comparing the distances (as energy transfer efficiencies) between the ends of pairs of labelled arms for the three possible end-to-end vectors as a function of magnesium ion concentration. The data support two sequential ion-dependent transitions, which can be interpreted in the light of the crystal structures of the hammerhead ribozyme. The first transition corresponds to the formation of a coaxial stacking between helices II and III; the data can be fully explained by a model in which the transition is induced by a single magnesium ion which binds with an apparent association constant of 8000-10 000 M-1. The second structural transition corresponds to the formation of the catalytic domain of the ribozyme, induced by a single magnesium ion with an apparent association constant of approximately 1100 M-1. The hammerhead ribozyme provides a well-defined example of ion-dependent folding in RNA.

Analytical Debye-Huckel model for electrostatic potentials around dissolved DNA

We present an analytical, Green-function-based model for the electric potential of DNA in solution, treating the surrounding solvent with the Debye-Huckel approximation. The partial charge of each atom is accounted for by modeling DNA as linear distributions of atoms on concentric cylindrical surfaces. The condensed ions of the solvent are treated with the Debye-Huckel approximation. The resultant leading term of the potential is that of a continuous shielded line charge, and the higher order terms account for the helical structure. Within several angstroms of the surface there is sufficient information in the electric potential to distinguish features and symmetries of DNA. Plots of the potential and equipotential surfaces, dominated by the phosphate charges, reflect the structural differences between the A, B, and Z conformations and, to a smaller extent, the difference between base sequences. As the distances from the helices increase, the magnitudes of the potentials decrease. However, the bases and sugars account for a larger fraction of the double helix potential with increasing distance. We have found that when the solvent is treated with the Debye-Huckel approximation, the potential decays more rapidly in every direction from the surface than it did in the concentric dielectric cylinder approximation.

Collective properties of hydration: long range and specificity of hydrophobic interactions

We report results of molecular dynamics (MD) simulations of composite model solutes in explicit molecular water solvent, eliciting novel aspects of the recently demonstrated, strong many-body character of hydration. Our solutes consist of identical apolar (hydrophobic) elements in fixed configurations. Results show that the many-body character of PMF is sufficiently strong to cause 1) a remarkable extension of the range of hydrophobic interactions between pairs of solute elements, up to distances large enough to rule out pairwise interactions of any type, and 2) a SIF that drives one of the hydrophobic solute elements toward the solvent rather than away from it. These findings complement recent data concerning SIFs on a protein at single-residue resolution and on model systems. They illustrate new important consequences of the collective character of hydration and of PMF and reveal new aspects of hydrophobic interactions and, in general, of SIFs. Their relevance to protein recognition, conformation, function, and folding and to the observed slight yet significant nonadditivity of functional effects of distant point mutations in proteins is discussed. These results point out the functional role of the configurational and dynamical states (and related statistical weights) corresponding to the complex configurational energy landscape of the two interacting systems: biomolecule + water.

Potential of mean force treatment of salt-mediated protein crystallization

In the initial stages of crystallization of proteins, monomers aggregate rapidly and form nuclei and large fractal clusters, as previously shown by dynamic light scattering experiments (Georgalis, Y., J. Schüler, J. Frank, D. M. Soumpasis, and W. Saenger. 1995. Protein crystallization screening through scattering techniques. Adv. Colloid Interface Sci. 58:57-86). In this communication we initiate an effort to understand the effective interactions controlling charged protein aggregation and crystallization using the potential of mean force (PMF) theory. We compute the PMFs of the system lysozyme-water-NaCl within the framework of the hypernetted chain approximation for a wide range of protein and salt concentrations. We show that the computed effective interactions can rationalize the experimentally observed aggregation behavior of lysozyme under crystallization conditions.

A statistical mechanical description of biomolecular hydration

An efficient and accurate theoretical description of the structural hydration of biological macromolecules is presented. The hydration of molecules of almost arbitrary size (tRNA, antibody-antigen complexes, photosynthetic reaction centre) can be studied in solution and in the crystalline environment. The biomolecular structure obtained from X-ray crystallography, NMR or modelling is required as input information. The structural arrangement of water molecules near a biomolecular surface is represented by the local water density, analogous to the corresponding electron density in an X-ray diffraction experiment. The water-density distribution is approximated in terms of two- and three-particle correlation functions of solute atoms with water using a potentials-of-mean-force expansion.

Hydration of nucleic acid fragments: comparison of theory and experiment for high-resolution crystal structures of RNA, DNA, and DNA-drug complexes

A computationally efficient method to describe the organization of water around solvated biomolecules is presented. It is based on a statistical mechanical expression for the water-density distribution in terms of particle correlation functions. The method is applied to analyze the hydration of small nucleic acid molecules in the crystal environment, for which high-resolution x-ray crystal structures have been reported. Results for RNA [r(ApU).r(ApU)] and DNA [d(CpG).d(CpG) in Z form and with parallel strand orientation] and for DNA-drug complexes [d(CpG).d(CpG) with the drug proflavine intercalated] are described. A detailed comparison of theoretical and experimental data shows positional agreement for the experimentally observed water sites. The presented method can be used for refinement of the water structure in x-ray crystallography, hydration analysis of nuclear magnetic resonance structures, and theoretical modeling of biological macromolecules such as molecular docking studies. The speed of the computations allows hydration analyses of molecules of almost arbitrary size (tRNA, protein-nucleic acid complexes, etc.) in the crystal environment and in aqueous solution.

Analysis of the thermodynamic linkage of DNA binding and ion binding for dimeric and tetrameric forms of the lac repressor

The salt concentration dependences of the observed association constants (Kobs) for the binding of wild-type lac repressor tetramer and the dimeric lacI-18 mutant repressor to lactose operator DNA were compared. For both proteins, the data are consistent with a class of linkage models in which ion binding by the protein is driven by differences in the ionic concentrations in bulk solution and in the volume near the DNA surface. The models that best agree with the data are those in which ion-binding reactions are cooperative. In spite of close agreement between these models and the data, the determination of ion stoichiometries and apparent ion-binding affinities requires additional mechanistic or structural information. The simplest ion-binding mechanism consistent with the data is compatible with a current structural model of the repressor-operator complex. At salt concentrations in excess of 50 mM, at which cation displacement from the DNA and anion displacement from the protein are expected to dominate, similar ion stoichiometries are found for the DNA binding of dimeric and tetrameric repressors. This supports the notion that the DNA contacts of these proteins are homologous. At lower salt concentrations, in which cation binding by the proteins is expected to be significant, the net ion stoichiometry of wild-type repressor binding is slightly greater than that of the lacI-18 mutant. This difference may reflect the availability of ion-binding sites in the distal subunits of tetramer that are not present in the dimer, or may be a consequence of the involvement of ion binding in the dimer/monomer equilibrium.

Ion-exchange reactions of proteins during DNA binding

The equilibrium association constant observed for many DNA/protein interactions in vitro (K(obs)) is strongly dependent on the salt concentration of the reaction buffer ([MX]). This dependence is often used to estimate the number of ionic contacts between protein and DNA by assuming that displacement of cations from the DNA is the predominant form of the involvement of ions in the binding reaction. With this assumption, the graph of log K(obs) versus log [MX] is predicted to have a constant slope proportional to the number of ions displaced from the DNA upon protein binding [Record, M. T., Lohman, T. M. & deHaseth, P. L. (1976) J. Mol. Biol. 107, 145-158]. Experimental data often deviate from linearity, however, at lower salt concentrations. Such deviations can be due to differential cation binding, anion binding or changes in macromolecular hydration, or differential screening effects of the electrolyte on protein and/or DNA charges. Here the theoretical effects on K(obs) of a simple form of ion-protein interaction are examined. A model for binding interactions is used that includes a mass balance of ions bound to both protein and DNA as the protein is transferred from the salt concentration of bulk solvent to the typically higher cation and lower anion concentrations characteristic of the volume adjacent to the DNA. We show that models in which the cation and anion stoichiometries of a protein change as it associates with DNA are consistent with the curvature of plots of log K(obs) versus log [MX]. Such mechanisms could reduce the sensitivity of gene-regulatory interactions to changes in environmental salt concentration.

Composite cylinder models of DNA: application to the electrostatics of the B-Z transition

We develop and test a Poisson-Boltzmann model of the electrostatics of the B-Z transition of DNA. Starting from the detailed geometries of the two forms, we compute at each radius the fractions of DNA matter, of volume forbidden (for nonpoint-like ions), and of volume accessible to the center of ions. These radial distributions are incorporated in a composite cylinder model; availability to ions (porosity) and the dielectric constant at each radial distance are then obtained. The phosphate charge is distributed with cylindrical symmetry on two layers at the appropriate radial distances. The porous sheath, between the axis and the charge distribution, provides much more room for ions in B-DNA than in Z-DNA. By using previously developed methods, the Poisson-Boltzmann problem of such cylinders is easily solved. The computational load is small, so that results can be obtained for a large set of salt concentrations and for a number of ionic radii. The variation of the electrostatic free energy difference with salt concentration compares favorably with the experimental value (it is half as large). There is also qualitative agreement with experiments on supercoiled DNA, including a maximum of the free energy difference at submolar salt concentrations. The results for this cylinder with porous sheath are in line with those of the earlier simple planar model and of a plain cylinder with sheath, which is also presented here. They are thus insensitive to details of the model. They support the proposition that the main electrostatic feature of the B-Z transition is the better immersion of the B-DNA phosphates into the solution. They also give confidence in the validity of the Poisson-Boltzmann approach, despite the large salt concentrations involved. Prior studies using an approach based on the potential of mean force are discussed.

Determination of electrostatic potentials at biological interfaces using electron-electron double resonance

A new general method for the determination of electrostatic potentials at biological surfaces is presented. The approach is based on measurement of the collision frequency of a charged nitroxide in solution with a nitroxide fixed to the surface at the point of interest. The collision frequency is determined with 14N:15N double label electron-electron double resonance (ELDOR). As a test, the method is shown to give values for phospholipid bilayer surface potentials consistent with the Gouy-Chapman theory, a simple model shown by many independent tests to accurately describe charged, planar surfaces. In addition, the method is applied to determine the electrostatic potential near the surface of DNA. The results indicate that the potential is significantly smaller than that predicted from Poisson-Boltzmann analysis, but is in qualitative agreement with that predicted by Manning's theory of counter ion condensation. The method is readily extended to measurement of surface potentials of proteins.

Fluorescence resonance energy transfer analysis of the structure of the four-way DNA junction

We have carried out fluorescence resonance energy transfer (FRET) measurements on four-way DNA junctions in order to analyze the global structure and its dependence on the concentration of several types of ions. A knowledge of the structure and its sensitivity to the solution environment is important for a full understanding of recombination events in DNA. The stereochemical arrangement of the four DNA helices that make up the four-way junction was established by a global comparison of the efficiency of FRET between donor and acceptor molecules attached pairwise in all possible permutations to the 5' termini of the duplex arms of the four-way structure. The conclusions are based upon a comparison between a series of many identical DNA molecules which have been labeled on different positions, rather than a determination of a few absolute distances. Details of the FRET analysis are presented; features of the analysis with particular relevance to DNA structures are emphasized. Three methods were employed to determine the efficiency of FRET: (1) enhancement of the acceptor fluorescence, (2) decrease of the donor quantum yield, and (3) shortening of the donor fluorescence lifetime. The FRET results indicate that the arms of the four-way junction are arranged in an antiparallel stacked X-structure when salt is added to the solution. The ion-related conformational change upon addition of salt to a solution originally at low ionic strength progresses in a continuous noncooperative manner as the ionic strength of the solution increases. The mode of ion interaction at the strand exchange site of the junction is discussed.

Modeling DNA structures

For a molecule of biological importance, one expects a strong correlation between the three-dimensional structure and its biological function(s). Molecular simulations allow the prediction of physical properties of macromolecules. Many of these properties are closely related to the molecular structure. Model-building studies may thus supplement structurally low-resolution experimental data with detailed three-dimensional hypothetical atomic models. Such studies may give a consistent integral view of a wealth of experimental data. In most cases, such models will predict the outcome of certain experiments. Their actual results will often either confirm the model, be used for further refinement, or demand a major revision. Empirical force-fields provide a large amount of physicochemical knowledge concerning structural and other physical properties about various classes of molecules. They give reasonable bond distances and angles and prevent short van der Waals contacts. Difficulties arise for the prediction of large-scale structural elements. These are not only determined by short-range interactions, but also result from long-range electrostatic, hydration, and hydrophobic forces. In the case of the ionically driven DNA B-Z transition, the point of transition as a function of ionic strength and size can be correctly predicted (33). More must be done for a better understanding of the hydration forces (6). What type of questions will be reliably answered by a force-field? Relatively safe answers concern the local geometry of the molecules. If a conformation leads to strong distortions of bond distances or angles or to close van der Waals contacts, it can safely be rejected. Optimizing such unfavorable structures energetically may lead to structures showing how to avoid such distortions. More difficult are energetic questions: Which of two conformers is more stable, or what is the free energy of the substrate in the active site (63)? One cannot always be sure that the force-field provides the correct answers. Therefore, one should concentrate on questions that can be checked experimentally. The application of such concepts to model curved DNA (19, 60) and the DNA four-way junction (61) provides promising results. To explore the knowledge contained in the force-fields, several methods have been proposed. Taking advantage of structural symmetries may improve critically the convergence, while refining the target molecule or its building blocks. A numerically stable derivative for the torsion potential has been proposed. The optimization method of conjugated gradients (see Section II,B) is a powerful tool to find the way downhill toward a local minimum. To surmount barriers and escape local minima requires nonlocal optimization procedures.(ABSTRACT TRUNCATED AT 400 WORDS)