Explicit Ions Research Articles

Explicit Solvent Modeling of Solvatochromic Probes in Ionic Liquids: Implications of Solvation Shell Structure.

Calculations of absorption spectra have been performed for three solvatochromic dyes (para-nitroaniline, N,N-diethyl-para-nitroaniline, and Reichardt's dye) in four ionic liquids based on 1-ethyl-3-methylimidazolium cation. Different variants of explicit solvent model have been used: fully explicit representation of solvent ions, charge embedding method, and mixed approach. Electrostatic solute-solvent interactions have been shown to induce structuring of the solvation shell around dipolar solute, causing significant and nonmonotonic dependence of calculated transition energies on the number of ion pairs included in calculations. A mixed approach with few fully explicit solvent ions embedded in electrostatic field of point charges appears as a promising method of calculations of solvatochromic response, provided that sufficiently large system sizes are used in explicit solvent modeling.

Chromatin Unfolding by Epigenetic Modifications Explained by Dramatic Impairment of Internucleosome Interactions: A Multiscale Computational Study.

Histone tails and their epigenetic modifications play crucial roles in gene expression regulation by altering the architecture of chromatin. However, the structural mechanisms by which histone tails influence the interconversion between active and inactive chromatin remain unknown. Given the technical challenges in obtaining detailed experimental characterizations of the structure of chromatin, multiscale computations offer a promising alternative to model the effect of histone tails on chromatin folding. Here we combine multimicrosecond atomistic molecular dynamics simulations of dinucleosomes and histone tails in explicit solvent and ions, performed with three different state-of-the-art force fields and validated by experimental NMR measurements, with coarse-grained Monte Carlo simulations of 24-nucleosome arrays to describe the conformational landscape of histone tails, their roles in chromatin compaction, and the impact of lysine acetylation, a widespread epigenetic change, on both. We find that while the wild-type tails are highly flexible and disordered, the dramatic increase of secondary-structure order by lysine acetylation unfolds chromatin by decreasing tail availability for crucial fiber-compacting internucleosome interactions. This molecular level description of the effect of histone tails and their charge modifications on chromatin folding explains the sequence sensitivity and underscores the delicate connection between local and global structural and functional effects. Our approach also opens new avenues for multiscale processes of biomolecular complexes.

A coarse-grained simulation study of the structures, energetics, and dynamics of linear and circular DNA with its ions.

We have studied the structural, energetics, and dynamical properties of a variety of linear and circular DNA fragments using a solvent-mediated coarse-grained (CG) model of DNA with explicit ions recently developed by us [Naômé et al., J. Chem. Theory Comput., 2014, 10, 3541-3549]. We particularly examined the treatment of electrostatics and determined that a large cutoff is necessary to properly reproduce the DNA flexibility. Moreover, it is crucial to include long-ranged electrostatic interactions: a Particle Mesh Ewald scheme at low resolution is sufficient to avoid structural artifacts. We calculated the ring closure probabilities, as j-factors, for DNA fragments of different lengths from equilibrium, as well as restrained molecular dynamics (MD) simulations. The latter force integration method provided accurate results without model fitting. We generated topology and energy maps for DNA minicircles of various lengths and helical densities, at low and high ion concentrations. A general trend for structure compaction is observed, driven by an increase in writhing as the ionic concentration increases. Finally, we applied a reconstruction procedure to generate detailed molecular structures from the various superhelical conformations generated by the CG MD of the DNA minicircles. These pre-equilibrated reconstructed atomistic structures can serve as starting material for atomistic simulations.

Multiscale modelling of nucleosome core particle aggregation

The nucleosome core particle (NCP) is the basic building block of chromatin. Under the influence of multivalent cations, isolated mononucleosomes exhibit a rich phase behaviour forming various columnar phases with characteristic NCP–NCP stacking. NCP stacking is also a regular element of chromatin structure in vivo. Understanding the mechanism of nucleosome stacking and the conditions leading to self-assembly of NCPs is still incomplete. Due to the complexity of the system and the need to describe electrostatics properly by including the explicit mobile ions, novel modelling approaches based on coarse-grained (CG) methods at the multiscale level becomes a necessity. In this work we present a multiscale CG computer simulation approach to modelling interactions and self-assembly of solutions of NCPs induced by the presence of multivalent cations. Starting from continuum simulations including explicit three-valent cobalt(III)hexammine (CoHex3+) counterions and 20 NCPs, based on a previously developed advanced CG NCP model with one bead per amino acid and five beads per two DNA base pair unit (Fan et al 2013 PLoS One 8 e54228), we use the inverse Monte Carlo method to calculate effective interaction potentials for a ‘super-CG’ NCP model consisting of seven beads for each NCP. These interaction potentials are used in large-scale simulations of up to 5000 NCPs, modelling self-assembly induced by CoHex3+. The systems of ‘super-CG’ NCPs form a single large cluster of stacked NCPs without long-range order in agreement with experimental data for NCPs precipitated by the three-valent polyamine, spermidine3+.

Predicting proton titration in cationic micelle and bilayer environments.

Knowledge of the protonation behavior of pH-sensitive molecules in micelles and bilayers has significant implications in consumer product development and biomedical applications. However, the calculation of pKa's in such environments proves challenging using traditional structure-based calculations. Here we apply all-atom constant pH molecular dynamics with explicit ions and titratable water to calculate the pKa of a fatty acid molecule in a micelle of dodecyl trimethylammonium chloride and liquid as well as gel-phase bilayers of diethyl ester dimethylammonium chloride. Interestingly, the pKa of the fatty acid in the gel bilayer is 5.4, 0.4 units lower than that in the analogous liquid bilayer or micelle, despite the fact that the protonated carboxylic group is significantly more desolvated in the gel bilayer. This work illustrates the capability of all-atom constant pH molecular dynamics in capturing the delicate balance in the free energies of desolvation and Coulombic interactions. It also shows the importance of the explicit treatment of ions in sampling the protonation states. The ability to model dynamics of pH-responsive substrates in a bilayer environment is useful for improving fabric care products as well as our understanding of the side effects of anti-inflammatory drugs.

Interaction and aggregation of charged platelets in electrolyte solutions: a coarse-graining approach.

A coarse-graining approach has been developed to replace the effect of explicit ions with an effective pair potential between charged sites in anisotropic colloidal particles by optimizing a potential of mean force against the results of simulations of two such colloidal particles with all ions in a cell model. More specifically, effective pair potentials were obtained for charged platelets in electrolyte solutions by simulating two rotating parallel platelets with ions at the primitive model level, enclosed in a cylindrical cell. One-component bulk simulations of many platelets interacting via the effective pair potentials are in excellent agreement with the corresponding bulk simulations with all mobile charges present. The bulk simulations were mainly used to study the effects of platelet size, flexibility, and surface charge density on platelet aggregation in an aqueous 2:1 electrolyte, but systems in a 1:1 electrolyte were also investigated.

A Solvent-Mediated Coarse-Grained Model of DNA Derived with the Systematic Newton Inversion Method.

We present a new class of coarse-grained (CG) force fields (FFs) for B-DNA with explicit ions suited for large-scale mesoscale simulations at microsecond-micrometer scale using a wide spectrum of particle simulation methods from molecular dynamics to dissipative particle dynamics. The effective solvent-mediated pairwise interactions making up the FFs are obtained by inverting radial distribution functions and other particle-particle distributions obtained from all-atom simulations of numbers of octadecamer DNA fragments from the Ascona B-DNA library. The inverse Monte Carlo (IMC) method, later known as Newton inversion (NI) (Lyubartsev, A. P.; Laaksonen, A. Phys. Rev. E, 1995, 52, 3730-3737), was used together with the iterative Boltzmann inversion (IBI) scheme to compute the effective CG potentials. We show that this systematic structure-based approach is capable of providing converged potentials that accurately reproduce the structural features of the underlying atomistic system within a few percents of relative difference. We also show that a simple one-site-per-nucleotide model with 10 intramolecular pair interaction potentials is able to reproduce key features of DNA, for example, the persistence length and its dependence on the ionic concentration, experimentally determined around 50 nm at physiological salt concentration.

A Coarse-Grained DNA Model Parameterized from Atomistic Simulations by Inverse Monte Carlo

Computer modeling of very large biomolecular systems, such as long DNA polyelectrolytes or protein-DNA complex-like chromatin cannot reach all-atom resolution in a foreseeable future and this necessitates the development of coarse-grained (CG) approximations. DNA is both highly charged and mechanically rigid semi-flexible polymer and adequate DNA modeling requires a correct description of both its structural stiffness and salt-dependent electrostatic forces. Here, we present a novel CG model of DNA that approximates the DNA polymer as a chain of 5-bead units. Each unit represents two DNA base pairs with one central bead for bases and pentose moieties and four others for phosphate groups. Charges, intra- and inter-molecular force field potentials for the CG DNA model were calculated using the inverse Monte Carlo method from all atom molecular dynamic (MD) simulations of 22 bp DNA oligonucleotides. The CG model was tested by performing dielectric continuum Langevin MD simulations of a 200 bp double helix DNA in solutions of monovalent salt with explicit ions. Excellent agreement with experimental data was obtained for the dependence of the DNA persistent length on salt concentration in the range 0.1–100 mM. The new CG DNA model is suitable for modeling various biomolecular systems with adequate description of electrostatic and mechanical properties.

Conformation and elasticity of a charged polymer chain bridging two nanoparticles

A complex composed of a charged flexible polymer chain irreversibly attached with its ends to surfaces of two nanoparticles was investigated using the Metropolis Monte Carlo method on a simple cubic lattice. The simulations were performed in the presence of explicit ions. The bridging chain and the nanoparticles bearing the same and the opposite sign charges were considered. Changes in the free energy of the complex upon its stretching or compression, together with the magnitude of the elastic force, were examined. The relative roles of energetic and entropic effects in determining the properties of the complex were identified. Also, the adsorption of charged monomers on the opposite-sign charged nanoparticles and its influence on the examined quantities was studied. Moreover, a simple semi-analytical approach to the thermodynamics of the polymer bridge was derived.

Influence of 8-Oxoguanosine on the Fine Structure of DNA Studied with Biasing-Potential Replica Exchange Simulations

Chemical modification or radiation can cause DNA damage, which plays a crucial role for mutagenesis of DNA, carcinogenesis, and aging. DNA damage can also alter the fine structure of DNA that may serve as a recognition signal for DNA repair enzymes. A new, advanced sampling replica-exchange method has been developed to specifically enhance the sampling of conformational substates in duplex DNA during molecular dynamics (MD) simulations. The approach employs specific biasing potentials acting on pairs of pseudodihedral angles of the nucleic acid backbone that are added in the replica simulations to promote transitions of the most common substates of the DNA backbone. The sampled states can exchange with a reference simulation under the control of the original force field. The application to 7,8-dihydro-8oxo-guanosine, one of the most common oxidative damage in DNA indicated better convergence of sampled states during 10 ns simulations compared to 20 times longer standard MD simulations. It is well suited to study systematically the fine structure and dynamics of large nucleic acids under realistic conditions, including explicit solvent and ions. The biasing potential-replica exchange MD simulations indicated significant differences in the population of nucleic acid backbone substates in the case of 7,8-dihydro-8oxo-guanosine compared to a regular guanosine in the same sequence context. This concerns both the ratio of the B-DNA substates BI and BII associated with the backbone dihedral angles ε and ζ but also coupled changes in the backbone dihedral angles α and γ. Such differences may play a crucial role in the initial recognition of damaged DNA by repair enzymes.

Electrostatic interaction of heterogeneously charged surfaces with semipermeable membranes

In this paper we study the electrostatic interaction of a heterogeneously charged wall with a neutral semipermeable membrane. The wall consists of periodic stripes, where the charge density varies in one direction. The membrane is in contact with a bulk reservoir of an electrolyte solution and separated from the wall by a thin film of salt-free liquid. One type of ions (small counterions) permeates into the gap. This gives rise to a distance-dependent membrane potential, which translates into a repulsive electrostatic disjoining pressure due to an overlap of counterion clouds in the gap. To quantify it we use two complementary approaches. First, we propose a mean-field theory based on a linearized Poisson-Boltzmann equation and Fourier analysis. These calculations allow us to estimate the effect of a heterogeneous charge pattern at the wall on the induced heterogeneous membrane potential, and the value of the disjoining pressure as a function of the gap. Second, we perform Langevin dynamics simulations of the same system with explicit ions. The results of the two approaches are in good agreement with each other at low surface charges and small gaps, but differ due to nonlinearity at higher charges. These results demonstrate that a heterogeneity of the wall charge can lead to a huge reduction in the electrostatic repulsion, which could dramatically facilitate self-assembly in complex synthetic and biological systems.

Extension of Brownian Dynamics for Studying Blockers of Ion Channels

We present new Brownian dynamics techniques for studying blockers of ion channels. By treating the channel as a fixed body, simulating the blocker molecules using rigid bodies, and using an implicit water force field with explicit ions, we are able to carry out fast simulations that can be used to investigate the dynamics of block and unblock, deduce binding modes, and calculate binding affinities. We test our program using the NavAb bacterial sodium channel, whose structure was recently solved (Payandeh et al. Nature, 2011, 475, 353-358) in conjunction with the μ-conotoxin PIIIA blocker. We derive an ohmic current-voltage relationship for channel permeation, calculate potentials of mean force for blocker unbinding, and deduce multiple binding modes for the blocker. Our results are shown to be compatible with other computational and experimental results. Finally, we discuss future improvements such as the inclusion of flexible side chains. After these improvements are carried out, we anticipate our program will be an extremely useful new tool that could be used to help develop new drugs to treat a range of ion-channel related diseases.

Screening for the Location of RNA using the Chloride Ion Distribution in Simulations of Virus Capsids.

The complete structure of the genomic material inside a virus capsid remains elusive, although a limited amount of symmetric nucleic acid can be resolved in the crystal structure of 17 icosahedral viruses. The negatively charged sugar-phosphate backbone of RNA and DNA as well as the large positive charge of the interior surface of the virus capsids suggest that electrostatic complementarity is an important factor in the packaging of the genomes in these viruses. To test how much packing information is encoded by the electrostatic and steric envelope of the capsid interior, we performed extensive all-atom molecular dynamics (MD) simulations of virus capsids with explicit water molecules and solvent ions. The model systems were two small plant viruses in which significant amounts of RNA has been observed by X-ray crystallography: satellite tobacco mosaic virus (STMV, 62% RNA visible) and satellite tobacco necrosis virus (STNV, 34% RNA visible). Simulations of half-capsids of these viruses with no RNA present revealed that the binding sites of RNA correlated well with regions populated by chloride ions, suggesting that it is possible to screen for the binding sites of nucleic acids by determining the equilibrium distribution of negative ions. By including the crystallographically resolved RNA in addition to ions, we predicted the localization of the unresolved RNA in the viruses. Both viruses showed a hot-spot for RNA binding at the 5-fold symmetry axis. The MD simulations were compared to predictions of the chloride density based on nonlinear Poisson-Boltzmann equation (PBE) calculations with mobile ions. Although the predictions are superficially similar, the PBE calculations overestimate the ion concentration close to the capsid surface and underestimate it far away, mainly because protein dynamics is not taken into account. Density maps from chloride screening can be used to aid in building atomic models of packaged virus genomes. Knowledge of the principles of genome packaging might be exploited for both antiviral therapy and technological applications.

BROMOC-D: Brownian Dynamics/Monte-Carlo Program Suite to Study Ion and DNA Permeation in Nanopores.

A theoretical framework is presented to model ion and DNA translocation across a nanopore confinement under an applied electric field. A combined Grand Canonical Monte Carlo Brownian Dynamics (GCMC/BD) algorithm offers a general approach to study ion permeation through wide molecular pores with a direct account of ion–ion and ion–DNA correlations. This work extends previously developed theory by incorporating the recently developed coarse-grain polymer model of DNA by de Pablo and colleagues [Knotts, T. A.; Rathore, N.; Schwartz, D. C.; de Pablo, J. J. J. Chem. Phys. 2007, 126] with explicit ions for simulations of polymer dynamics. Atomistic MD simulations were used to guide model developments. The power of the developed scheme is illustrated with studies of single-stranded DNA (ss-DNA) oligomer translocation in two model cases: a cylindrical pore with a varying radius and a well-studied experimental system, the staphylococcal α-hemolysin channel. The developed model shows good agreement with experimental data for model studies of two homopolymers: ss-poly(dA)n and ss-poly(dC)n. The developed protocol allows for direct evaluation of different factors (charge distribution and pore shape and size) controlling DNA translocation in a variety of nanopores.

Effects of salt on the size and internal structure of PAMAM dendrimers at different pH

G4 and G5 polyamidoamine dendrimers solvated with explicit water, counterions and NaCl ions (0.15, 1 M) were simulated at two levels of protonation, which mimic their electrostatic charges at pH 5 and 7. We used the previously parametrised coarse-grained dendrimer model which had predicted the experimentally measured and theoretically calculated size and internal structure of the dendrimer at different pH values. In this study, addition of ≤ 1 M NaCl does not significantly modulate the dendrimer size, in agreement with experiments and other theoretical studies. In particular, added salt ions do not change the dense-shell and dense-core structures of dendrimers without salt, respectively, at pH 5 and 7. Besides counterions, only a few excess ions penetrate and occupy the dendrimer interior, leading to unchanged volume of the inner cavity in the dendrimer core. These results indicate that addition of ≤ 1 M NaCl does not modulate the efficiency of encapsulating hydrophobic drugs or compounds.

Predicting Nonspecific Ion Binding Using DelPhi

Ions are an important component of the cell and affect the corresponding biological macromolecules either via direct binding or as a screening ion cloud. Although some ion binding is highly specific and frequently associated with the function of the macromolecule, other ions bind to the protein surface nonspecifically, presumably because the electrostatic attraction is strong enough to immobilize them. Here, we test such a scenario and demonstrate that experimentally identified surface-bound ions are located at a potential that facilitates binding, which indicates that the major driving force is the electrostatics. Without taking into consideration geometrical factors and structural fluctuations, we show that ions tend to be bound onto the protein surface at positions with strong potential but with polarity opposite to that of the ion. This observation is used to develop a method that uses a DelPhi-calculated potential map in conjunction with an in-house-developed clustering algorithm to predict nonspecific ion-binding sites. Although this approach distinguishes only the polarity of the ions, and not their chemical nature, it can predict nonspecific binding of positively or negatively charged ions with acceptable accuracy. One can use the predictions in the Poisson-Boltzmann approach by placing explicit ions in the predicted positions, which in turn will reduce the magnitude of the local potential and extend the limits of the Poisson-Boltzmann equation. In addition, one can use this approach to place the desired number of ions before conducting molecular-dynamics simulations to neutralize the net charge of the protein, because it was shown to perform better than standard screened Coulomb canned routines, or to predict ion-binding sites in proteins. This latter is especially true for proteins that are involved in ion transport, because such ions are loosely bound and very difficult to detect experimentally.

Explicit Ions Condensation around Strongly Charged Polyelectrolytes and Spherical Macroions: The Influence of Salt Concentration and Chain Linear Charge Density. Monte Carlo Simulations

The condensation of monovalent counterions and trivalent salt particles around strong rigid and flexible polyelectrolyte chains as well as spherical macroions is investigated by Monte Carlo simulations. The results are compared with the condensation theory proposed by Manning. Considering flexible polyelectrolyte chains, the presence of trivalent salt is found to play an important role by promoting chain collapse. The attraction of counterions and salt particles near the polyelectrolyte chains is found to be strongly dependent on the chain linear charge density with a more important condensation at high values. When trivalent salt is added in a solution containing monovalent salt, the trivalent cations progressively replace the monovalent counterions. Ion condensation around flexible chains is also found to be more efficient compared with rigid rods due to monomer rearrangement around counterions and salt cations. In the case of spherical macroions, it is found that a fraction of their bare charge is neutralized by counterions and salt cations. The decrease of the Debye length, and thus the increase of salt concentration, promotes the attraction of counterions and salt particles at the macroion surface. Excluded volume effects are also found to significantly influence the condensation process, which is found to be more important by decreasing the ion size.

Computer Simulations of Voltage-Gated Cation Channels.

The relentless growth in computational power has seen increasing applications of molecular dynamics (MD) simulation to the study of membrane proteins in realistic membrane environments, which include explicit membrane lipids, water and ions. The concomitant increasing availability of membrane protein structures for ion channels, and transporters -- to name just two examples -- has stimulated many of these MD studies. In the case of voltage-gated cation channels (VGCCs) recent computational works have focused on ion-conduction and gating mechanisms, along with their regulation by agonist/antagonist ligands. The information garnered from these computational studies is largely inaccessible to experiment and is crucial for understanding the interplay between the structure and function as well as providing new directions for experiments. This article highlights recent advances in probing the structure and function of potassium channels and offers a perspective on the challenges likely to arise in making analogous progress in characterizing sodium channels.

RNA and Its Ionic Cloud: Solution Scattering Experiments and Atomically Detailed Simulations

RNA molecules play critical roles in many cellular processes. Traditionally viewed as genetic messengers, RNA molecules were recently discovered to have diverse functions related to gene regulation and expression. RNA also has great potential as a therapeutic and a tool for further investigation of gene regulation. Metal ions are an integral part of RNA structure and should be considered in any experimental or theoretical study of RNA. Here, we report a multidisciplinary approach that combines anomalous small-angle x-ray scattering and molecular-dynamics (MD) simulations with explicit solvent and ions around RNA. From experiment and simulation results, we find excellent agreement in the number and distribution of excess monovalent and divalent ions around a short RNA duplex. Although similar agreement can be obtained from a continuum description of the solvent and mobile ions (by solving the Poisson-Boltzmann equation and accounting for finite ion size), the use of MD is easily extended to flexible RNA systems with thermal fluctuations. Therefore, we also model a short RNA pseudoknot and find good agreement between the MD results and the experimentally derived solution structures. Surprisingly, both deviate from crystal structure predictions. These favorable comparisons of experiment and simulations encourage work on RNA in all-atom dynamic models.

Modeling Polymer Interactions with Nanopores for DNA Sequencing and Proteomics Applications

Protein beta-barrel nanopores have been used to characterize a wide variety of molecules including polyethylene glycol (PEG), deoxyribonucleic acid (DNA) and polypeptides - a potentially significant step in realizing low cost sequencing of DNA, as well as in proteomics. Simulations can improve our understanding of the conformation and dynamics of polymers inside a nanopore, which we believe are significant to properly interpret experimental data. However, in an effort to overcome the limitations of time scales associated with all-atom molecular dynamics simulations we introduce two simplified models for PEG in α-hemolysin. Both represent the nanopore by a grid potential calculated from the Poisson-Boltzmann equation, and contain explicit ions and flexible PEG. One model includes water implicitly with a short-range water mediated potential of mean force to correctly account for ion-ion interactions; the other contains explicit TIP3 water. We also present a third, even simpler model with rigid PEG in the pore, where the ionic current blockade differs from experiment significantly highlighting the importance of the dynamics of PEG inside the pore. We then compare results from the first two simulation models with those from an all-atom simulation. Finally, we compare the depth of the ionic current blockade associated with PEG binding from each model with experimental results.