Efficient sampling of ion motions in molecular dynamics simulations on DNA: Variant Hamiltonian replica exchange method

Predicting RNA-Metal Ion Binding with Ion Dehydration Effects

Metal ions play essential roles in nucleic acids folding and stability. The interaction between metal ions and nucleic acids can be highly complicated because of the interplay between various effects such as ion correlation, fluctuation, and dehydration. These effects may be particularly important for multivalent ions such as Mg²⁺ ions. Previous efforts to model ion correlation and fluctuation effects led to the development of the Monte Carlo tightly bound ion model. Here, by incorporating ion hydration/dehydration effects into the Monte Carlo tightly bound ion model, we develop a, to our knowledge, new approach to predict ion binding. The new model enables predictions for not only the number of bound ions but also the three-dimensional spatial distribution of the bound ions. Furthermore, the new model reveals several intriguing features for the bound ions such as the mutual enhancement/inhibition in ion binding between the fully hydrated (diffuse) ions, the outer-shell dehydrated ions, and the inner-shell dehydrated ions and novel features for the monovalent-divalent ion interplay due to the hydration effect.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Elastic Energy Partitioning in DNA Deformation and Binding to Proteins

We study the elasticity of DNA based on local principal axes of bending identified from over 0.9-μs all-atom molecular dynamics simulations of DNA oligos. The calculated order parameters describe motion of DNA as an elastic rod. In 10 possible dinucleotide steps, bending about the two principal axes is anisotropic yet linearly elastic. Twist about the centroid axis is largely decoupled from bending, but DNA tends to overtwist for unbending beyond the typical range of thermal motion, which is consistent with experimentally observed twist-stretch coupling. The calculated elastic stiffness of dinucleotide steps yield sequence-dependent persistence lengths consistent with previous single-molecule experiments, which is further analyzed by performing coarse-grained simulations of DNA. Flexibility maps of oligos constructed from simulation also match with those from the precalculated stiffness of dinucleotide steps. These support the premise that base pair interaction at the dinucleotide-level is mainly responsible for the elasticity of DNA. Furthermore, we analyze 1381 crystal structures of protein-DNA complexes. In most structures, DNAs are mildly deformed and twist takes the highest portion of the total elastic energy. By contrast, in structures with the elastic energy per dinucleotide step greater than about 4.16 kBT (kBT: thermal energy), the major bending becomes dominant. The extensional energy of dinucleotide steps takes at most 35% of the total elastic energy except for structures containing highly deformed DNAs where linear elasticity breaks down. Such partitioning between different deformational modes provides quantitative insights into the conformational dynamics of DNA as well as its interaction with other molecules and surfaces.

Analyzing ion distributions around DNA: sequence-dependence of potassium ion distributions from microsecond molecular dynamics

Microsecond molecular dynamics simulations of B-DNA oligomers carried out in an aqueous environment with a physiological salt concentration enable us to perform a detailed analysis of how potassium ions interact with the double helix. The oligomers studied contain all 136 distinct tetranucleotides and we are thus able to make a comprehensive analysis of base sequence effects. Using a recently developed curvilinear helicoidal coordinate method we are able to analyze the details of ion populations and densities within the major and minor grooves and in the space surrounding DNA. The results show higher ion populations than have typically been observed in earlier studies and sequence effects that go beyond the nature of individual base pairs or base pair steps. We also show that, in some special cases, ion distributions converge very slowly and, on a microsecond timescale, do not reflect the symmetry of the corresponding base sequence.

Analyzing ion distributions around DNA

We present a new method for analyzing ion, or molecule, distributions around helical nucleic acids and illustrate the approach by analyzing data derived from molecular dynamics simulations. The analysis is based on the use of curvilinear helicoidal coordinates and leads to highly localized ion densities compared to those obtained by simply superposing molecular dynamics snapshots in Cartesian space. The results identify highly populated and sequence-dependent regions where ions strongly interact with the nucleic and are coupled to its conformational fluctuations. The data from this approach is presented as ion populations or ion densities (in units of molarity) and can be analyzed in radial, angular and longitudinal coordinates using 1D or 2D graphics. It is also possible to regenerate 3D densities in Cartesian space. This approach makes it easy to understand and compare ion distributions and also allows the calculation of average ion populations in any desired zone surrounding a nucleic acid without requiring references to its constituent atoms. The method is illustrated using microsecond molecular dynamics simulations for two different DNA oligomers in the presence of 0.15 M potassium chloride. We discuss the results in terms of convergence, sequence-specific ion binding and coupling with DNA conformation.

Fast Analytical Methods for Macroscopic Electrostatic Models in Biomolecular Simulations

We review recent developments of fast analytical methods for macroscopic electrostatic calculations in biological applications, including the Poisson-Boltzmann (PB) and the generalized Born models for electrostatic solvation energy. The focus is on analytical approaches for hybrid solvation models, especially the image charge method for a spherical cavity, and also the generalized Born theory as an approximation to the PB model. This review places much emphasis on the mathematical details behind these methods.

Revisiting the association of cationic groove-binding drugs to DNA using a Poisson-Boltzmann approach

Proper modeling of nonspecific salt-mediated electrostatic interactions is essential to understanding the binding of charged ligands to nucleic acids. Because the linear Poisson-Boltzmann equation (PBE) and the more approximate generalized Born approach are applied routinely to nucleic acids and their interactions with charged ligands, the reliability of these methods is examined vis-à-vis an efficient nonlinear PBE method. For moderate salt concentrations, the negative derivative, SK(pred), of the electrostatic binding free energy, DeltaG(el), with respect to the logarithm of the 1:1 salt concentration, [M(+)], for 33 cationic minor groove drugs binding to AT-rich DNA sequences is shown to be consistently negative and virtually constant over the salt range considered (0.1-0.4 M NaCl). The magnitude of SK(pred) is approximately equal to the charge on the drug, as predicted by counterion condensation theory (CCT) and observed in thermodynamic binding studies. The linear PBE is shown to overestimate the magnitude of SK(pred), whereas the nonlinear PBE closely matches the experimental results. The PBE predictions of SK(pred) were not correlated with DeltaG(el) in the presence of a dielectric discontinuity, as would be expected from the CCT. Because this correlation does not hold, parameterizing the PBE predictions of DeltaG(el) against the reported experimental data is not possible. Moreover, the common practice of extracting the electrostatic and nonelectrostatic contributions to the binding of charged ligands to biopolyelectrolytes based on the simple relation between experimental SK values and the electrostatic binding free energy that is based on CCT is called into question by the results presented here. Although the rigid-docking nonlinear PB calculations provide reliable predictions of SK(pred), at least for the charged ligand-nucleic acid complexes studied here, accurate estimates of DeltaG(el) will require further development in theoretical and experimental approaches.

Using Correlated Monte Carlo Sampling for Efficiently Solving the Linearized Poisson-Boltzmann Equation Over a Broad Range of Salt Concentration

Dielectric continuum or implicit solvent models provide a significant reduction in computational cost when accounting for the salt-mediated electrostatic interactions of biomolecules immersed in an ionic environment. These models, in which the solvent and ions are replaced by a dielectric continuum, seek to capture the average statistical effects of the ionic solvent, while the solute is treated at the atomic level of detail. For decades, the solution of the three-dimensional Poisson-Boltzmann equation (PBE), which has become a standard implicit-solvent tool for assessing electrostatic effects in biomolecular systems, has been based on various deterministic numerical methods. Some deterministic PBE algorithms have drawbacks, which include a lack of properly assessing their accuracy, geometrical difficulties caused by discretization, and for some problems their cost in both memory and computation time. Our original stochastic method resolves some of these difficulties by solving the PBE using the Monte Carlo method (MCM). This new approach to the PBE is capable of efficiently solving complex, multi-domain and salt-dependent problems in biomolecular continuum electrostatics to high precision. Here we improve upon our novel stochastic approach by simultaneouly computating of electrostatic potential and solvation free energies at different ionic concentrations through correlated Monte Carlo (MC) sampling. By using carefully constructed correlated random walks in our algorithm, we can actually compute the solution to a standard system including the linearized PBE (LPBE) at all salt concentrations of interest, simultaneously. This approach not only accelerates our MCPBE algorithm, but seems to have cost and accuracy advantages over deterministic methods as well. We verify the effectiveness of this technique by applying it to two common electrostatic computations: the electrostatic potential and polar solvation free energy for calcium binding proteins that are compared with similar results obtained using mature deterministic PBE methods.

Simultaneous escaping of explicit and hidden free energy barriers: application of the orthogonal space random walk strategy in generalized ensemble based conformational sampling

To overcome the pseudoergodicity problem, conformational sampling can be accelerated via generalized ensemble methods, e.g., through the realization of random walks along prechosen collective variables, such as spatial order parameters, energy scaling parameters, or even system temperatures or pressures, etc. As usually observed, in generalized ensemble simulations, hidden barriers are likely to exist in the space perpendicular to the collective variable direction and these residual free energy barriers could greatly abolish the sampling efficiency. This sampling issue is particularly severe when the collective variable is defined in a low-dimension subset of the target system; then the "Hamiltonian lagging" problem, which reveals the fact that necessary structural relaxation falls behind the move of the collective variable, may be likely to occur. To overcome this problem in equilibrium conformational sampling, we adopted the orthogonal space random walk (OSRW) strategy, which was originally developed in the context of free energy simulation [L. Zheng, M. Chen, and W. Yang, Proc. Natl. Acad. Sci. U.S.A. 105, 20227 (2008)]. Thereby, generalized ensemble simulations can simultaneously escape both the explicit barriers along the collective variable direction and the hidden barriers that are strongly coupled with the collective variable move. As demonstrated in our model studies, the present OSRW based generalized ensemble treatments show improved sampling capability over the corresponding classical generalized ensemble treatments.

Roles of boundary conditions in DNA simulations: analysis of ion distributions with the finite-difference Poisson-Boltzmann method

The wide use of lattice-sum strategies in biomolecular simulations has raised many questions on potential artifacts in these strategies. One interesting question is the artifacts in the counterion distributions of highly charged systems. As one would anticipate, Coulombic interactions under the periodic boundary condition may deviate noticeably from those under the free boundary condition in the highly charged systems, significantly influencing their counterion distributions. On the other hand, the electrostatic screening due to water molecules and mobile ions may effectively damp the possible periodic distortions in Coulombic interactions. Therefore, the magnitude of periodicity-induced artifacts in counterion distributions is not straightforward to dissect without detailed analyses. In this study, we have developed a hybrid explicit counterion/implicit salt representation of mobile ions to address this question. We have chosen a well-studied DNA for easy validation of the minimal hybrid ion representation. Our detailed analysis of continuum ion distributions, explicit ion distributions, radial counterion distribution functions, and sequence-dependent counterion distributions, however, indicates that periodicity artifacts are not apparent at the surface of the tested DNA. Nevertheless, influence of boundary conditions does show up starting at the second solvation shell and becomes apparent at the cell boundary.