Applications of the Cartesian coordinate tensor transfer technique in the simulations of vibrational circular dichroism spectra of oligonucleotides

The application of the Cartesian coordinate tensor transfer (CCT) technique for simulations of the IR absorption and vibrational circular dichroism (VCD) spectra of relatively large nucleic acid fragments is demonstrated on several case studies. The approach is based on direct ab initio calculations of atomic tensors, determining molecular properties, for relatively small fragments, and subsequent transfer of these tensors to the larger systems in Cartesian coordinates. This procedure enables precise computations of vibrational spectra for large biomolecular systems, currently with up to several thousands of atoms. The versatile ability of the CCT methods is emphasized on the examples of VCD and IR absorption spectra calculations for B- and Z-forms of DNA, single-, double-, and triple-stranded RNA helices and DNA structures with different base content and sequences. The development and recent improvements of the methodology are followed, including utilization of the constrained normal mode optimization (NMO) strategy and combined quantum mechanics and molecular dynamics simulations. Advantages, drawbacks, and recommendations for future improvements of the CCT method as applied to nucleic acid spectra calculations are discussed.     

88 Comparison of monovalent and divalent ion distributions around a DNA duplex with molecular dynamic simulation and Poisson–Boltzmann approach

Ion interactions with nucleic acids (both DNA and RNA) are an important and evolving field of investigation. Positively charged cations may interact with highly negatively charged nucleic acids via simple electrostatic interactions to help screen the electrostatic repulsion along the nucleic acids and assist their folding and/or compaction. Cations may also bind at specific sites and become integral parts of the structures, possibly playing important enzymatic roles. Two popular methods for computationally exploring a nucleic acid’s ion atmosphere are atomistic molecular dynamics (MD) simulations and the Poisson–Boltzmann (PB) equation. In general, monovalent ion results obtained from MD simulations and the PB equation agree well with experiment. However, Bai et al. (2007) observed discrepancies between experiment and the PB equation while examining the competitive binding of monovalent and divalent ions, with more significant discrepancies for divalent ions. The goal of this project was to thoroughly investigate monovalent (Na⁺) and divalent (Mg²⁺) ion distributions formed around a DNA duplex with MD simulations and the PB equation. We simulated three different cation concentrations, and matched the equilibrated bulk ion concentration for our theoretical calculations with the PB equation. Based on previous work, our Mg²⁺ ions were fully solvated, the expected state of Mg²⁺ ions when interacting with a duplex, when the production simulations began and remained throughout the simulations (Kirmizialtin, 2010; Robbins, 2012). Na⁺ ion distributions and number of Na⁺ ions within 10?Å of the DNA obtained from our two methods agreed well. However, results differed for Mg²⁺ ions, with a lower number of ions within the cut-off distance obtained from the PB equation when compared to MD simulations. The Mg²⁺ ion distributions around the DNA obtained via the two methods also differed. Based on our results, we conclude that the PB equation will systematically underestimate Mg²⁺ ions bound to DNA, and much of this deviation is attributed to dielectric saturation associated with high valency ions.     

Predicting large-scale conformational changes in proteins using energy-weighted normal modes

We report the development of a method to improve the sampling of protein conformational space in molecular simulations. It is shown that a principal component analysis of energy-weighted normal modes in Cartesian coordinates can be used to extract vectors suitable for describing the dynamics of protein substructures. The method can operate with either atomistic or user-defined coarse-grained models of protein structure. An implicit reverse coarse-graining allows the dynamics of all-atoms to be recovered when a coarse-grained model is used. For an external test set of four proteins, it is shown that the new method is more successful than normal mode analysis in describing the large-scale conformational changes observed on ligand binding. The method has potential applications in protein-ligand and protein-protein docking and in biasing molecular dynamics simulations.     

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.     

Enhanced sampling of molecular dynamics simulation of peptides and proteins by double coupling to thermal bath

Low sampling efficiency in conformational space is the well-known problem for conventional molecular dynamics. It greatly increases the difficulty for molecules to find the transition path to native state, and costs amount of CPU time. To accelerate the sampling, in this paper, we re-couple the critical degrees of freedom in the molecule to environment temperature, like dihedrals in generalized coordinates or nonhydrogen atoms in Cartesian coordinate. After applying to ALA dipeptide model, we find that this modified molecular dynamics greatly enhances the sampling behavior in the conformational space and provides more information about the state-to-state transition, while conventional molecular dynamics fails to do so. Moreover, from the results of 16 independent 100?ns simulations by the new method, it shows that trpzip2 has one-half chances to reach the naive state in all the trajectories, which is greatly higher than conventional molecular dynamics. Such an improvement would provide a potential way for searching the conformational space or predicting the most stable states of peptides and proteins.     

Structure refinement using time-averaged J-coupling constant restraints

Summary We describe a new penalty function for use in restrained molecular dynamics simulations which allows experimental J-coupling information to be enforced as a time-averaged, rather than instantaneous, quantity. The pseudo-energy term has been formulated in terms of a calculated J value (a measured quantity) rather than the relevant dihedral angle (a derived quantity). This accounts for the distinct non-linearity of the coupling constant with respect to either Cartesian coordinates or dihedral angles. Example simulations of the cyclic decapeptide antamanide show the procedure's ability to enforce experimental restraints while exploring a large region of conformational space and producing a relatively small disturbance of the physical force field.Abbreviations MD molecular dynamics - rms root-mean-square - NOE nuclear Overhauser effect     

Partition decoupling for multi-gene analysis of gene expression profiling data

Background

Molecular dynamics (MD) simulations are powerful tools to investigate the conformational dynamics of proteins that is often a critical element of their function. Identification of functionally relevant conformations is generally done clustering the large ensemble of structures that are generated. Recently, Self-Organising Maps (SOMs) were reported performing more accurately and providing more consistent results than traditional clustering algorithms in various data mining problems. We present a novel strategy to analyse and compare conformational ensembles of protein domains using a two-level approach that combines SOMs and hierarchical clustering.

Results

The conformational dynamics of the α-spectrin SH3 protein domain and six single mutants were analysed by MD simulations. The Cα's Cartesian coordinates of conformations sampled in the essential space were used as input data vectors for SOM training, then complete linkage clustering was performed on the SOM prototype vectors. A specific protocol to optimize a SOM for structural ensembles was proposed: the optimal SOM was selected by means of a Taguchi experimental design plan applied to different data sets, and the optimal sampling rate of the MD trajectory was selected. The proposed two-level approach was applied to single trajectories of the SH3 domain independently as well as to groups of them at the same time. The results demonstrated the potential of this approach in the analysis of large ensembles of molecular structures: the possibility of producing a topological mapping of the conformational space in a simple 2D visualisation, as well as of effectively highlighting differences in the conformational dynamics directly related to biological functions.

Conclusions

The use of a two-level approach combining SOMs and hierarchical clustering for conformational analysis of structural ensembles of proteins was proposed. It can easily be extended to other study cases and to conformational ensembles from other sources.     

Metropolis Monte Carlo calculations of DNA structure using internal coordinates and NMR distance restraints: An alternative method for generating a high-resolution solution structure

Summary A new method, a restrained Monte Carlo (rMC) calculation, is demonstrated for generating high-resolution structures of DNA oligonucleotides in solution from interproton distance restraints and bounds derived from complete relaxation matrix analysis of two-dimensional nuclear Overhauser effect (NOE) spectral peak intensities. As in the case of restrained molecular dynamics (rMD) refinement of structures, the experimental distance restraints and bounds are incorporated as a pseudo-energy term (or penalty function) into the mathematical expression for the molecular energy. However, the use of generalized helical parameters, rather than Cartesian coordinates, to define DNA conformation increases efficiency by decreasing by an order of magnitude the number of parameters needed to describe a conformation and by simplifying the potential energy profile. The Metropolis Monte Carlo method is employed to simulate an annealing process. The rMC method was applied to experimental 2D NOE data from the octamer duplex d(GTA-TAATG)·d(CATTATAC). Using starting structures from different locations in conformational space (e.g. A-DNA and B-DNA), the rMC calculations readily converged, with a root-mean-square deviation (RMSD) of <0.3 Å between structures generated using different protocols and starting structures. Theoretical 2D NOE peak intensities were calculated for the rMC-generated structures using the complete relaxation matrix program CORMA, enabling a comparison with experimental intensities via residual indices. Simulation of the vicinal proton coupling constants was carried out for the structures generated, enabling a comparison with the experimental deoxyribose ring coupling constants, which were not utilized in the structure determination in the case of the rMC simulations. Agreement with experimental 2D NOE and scalar coupling data was good in all cases. The rMC structures are quite similar to that refined by a traditional restrained MD approach (RMSD<0.5 Å) despite the different force fields used and despite the fact that MD refinement was conducted with additional restraints imposed on the endocyclic torsion angles of deoxyriboses. The computational time required for the rMC and rMD calculations is about the same. A comparison of structural parameters is made and some limitations of both methods are discussed with regard to the average nature of the experimental restraints used in the refinement.Abbreviations MC Monte Carlo - rMC restrained Monte Carlo - MD molecular dynamics - rMD restrained molecular dynamics - DG distance geometry - EM energy minimization - 2D NOE two-dimensional nuclear Overhauser effect - DQF-COSY double-quantum-filtered correlation spectroscopy - RMSD root-mean-square deviation To whom correspondence should be addressed.     

CORGEN: A FORTRAN-77 generator of standard and non-standard DNA helices from the sequence

An analytical procedure CORGEN generates a variety of DNA double-strandedstructures from user-supplied sequence using a nucleic aciddatabase incorporated into a standard FORTRAN-77 program. Alternatively,the cylindrical polar coordinates of DNA components may be suppliedfrom the external table. An algorithm that performs intercalationsites in DNA is described. This procedure can be used to generatecomplexes of antibiotics with DNA. Non-standard DNA structurescan be built by alternating the global helical twist and globalhelical rise in the regular DNA helix. The procedures describedcan be used for computer generation of a variety of non-standardDNA structures which can be subjected to molecular mechanicsand dynamics simulations. Received on February 20, 1989; accepted on June 27, 1989     

Comparison of monovalent and divalent ion distributions around a DNA duplex with molecular dynamics simulation and a Poisson‐Boltzmann approach

The ion atmosphere created by monovalent (Na⁺) or divalent (Mg²⁺) cations surrounding a B‐form DNA duplex were examined using atomistic molecular dynamics (MD) simulations and the nonlinear Poisson‐Boltzmann (PB) equation. The ion distributions predicted by the two methods were compared using plots of radial and two‐dimensional cation concentrations and by calculating the total number of cations and net solution charge surrounding the DNA. Na⁺ ion distributions near the DNA were more diffuse in PB calculations than in corresponding MD simulations, with PB calculations predicting lower concentrations near DNA groove sites and phosphate groups and a higher concentration in the region between these locations. Other than this difference, the Na⁺ distributions generated by the two methods largely agreed, as both predicted similar locations of high Na⁺ concentration and nearly identical values of the number of cations and the net solution charge at all distances from the DNA. In contrast, there was greater disagreement between the two methods for Mg²⁺ cation concentration profiles, as both the locations and magnitudes of peaks in Mg²⁺ concentration were different. Despite experimental and simulation observations that Mg²⁺ typically maintains its first solvation shell when interacting with nucleic acids, modeling Mg²⁺ as an unsolvated ion during PB calculations improved the agreement of the Mg²⁺ ion atmosphere predicted by the two methods and allowed for values of the number of bound ions and net solution charge surrounding the DNA from PB calculations that approached the values observed in MD simulations. © 2014 Wiley Periodicals, Inc. Biopolymers 101: 834–848, 2014.     

Molecular dynamics simulation of nucleic acids: successes, limitations, and promise.

In the last five years we have witnessed a significant increase in the number publications describing accurate and reliable all-atom molecular dynamics simulations of nucleic acids. This increase has been facilitated by the development of fast and efficient methods for treating the long-range electrostatic interactions, the availability of faster parallel computers, and the development of well-validated empirical molecular mechanical force fields. With these technologies, it has been demonstrated that simulation is not only capable of consistently reproducing experimental observations of sequence specific fine structure of DNA, but also can give detailed insight into prevalent problems in nucleic acid structure, ion association and specific hydration of nucleic acids, polyadenine tract bending, and the subtle environmental dependence of the A-DNA-B-DNA duplex equilibrium. Despite the advances, there are still issues with the methods that need to be resolved through rigorous controlled testing. In general, these relate to deficiencies of the underlying molecular mechanical potentials or applied methods (such as the imposition of true periodicity in Ewald simulations and the need for energy conservation), and significant limits in effective conformational sampling. In this perspective, we provide an overview of our experiences, provide some cautionary notes, and provide recommendations for further study in molecular dynamics simulation of nucleic acids.     

ShapeRotator: An R tool for standardized rigid rotations of articulated three‐dimensional structures with application for geometric morphometrics

The quantification of complex morphological patterns typically involves comprehensive shape and size analyses, usually obtained by gathering morphological data from all the structures that capture the phenotypic diversity of an organism or object. Articulated structures are a critical component of overall phenotypic diversity, but data gathered from these structures are difficult to incorporate into modern analyses because of the complexities associated with jointly quantifying 3D shape in multiple structures. While there are existing methods for analyzing shape variation in articulated structures in two‐dimensional (2D) space, these methods do not work in 3D, a rapidly growing area of capability and research. Here, we describe a simple geometric rigid rotation approach that removes the effect of random translation and rotation, enabling the morphological analysis of 3D articulated structures. Our method is based on Cartesian coordinates in 3D space, so it can be applied to any morphometric problem that also uses 3D coordinates (e.g., spherical harmonics). We demonstrate the method by applying it to a landmark‐based dataset for analyzing shape variation using geometric morphometrics. We have developed an R tool (ShapeRotator) so that the method can be easily implemented in the commonly used R package geomorph and MorphoJ software. This method will be a valuable tool for 3D morphological analyses in articulated structures by allowing an exhaustive examination of shape and size diversity.     

Induced coalescence of cations through low-temperature Poisson-Boltzmann calculations

The computational determination of preferred binding regions of divalent counterions to nucleic acids is either inaccurate (standard Poisson-Boltzmann approaches) or extremely time-consuming (Monte Carlo or molecular dynamics simulations). A novel "selective low-temperature" Poisson-Boltzmann method is introduced that, although approximate in nature, qualitatively accounts for ion correlation and charge-transfer effects and allows for the rapid determination of such regions through an "induced coalescence" of divalent ions. The method is illustrated here for the binding of Mg(2+) to a double-helical sequence of B-form DNA (CGCGAATTCGCG) but the technique is readily applicable to locating divalent cations in other systems such as DNA-endonuclease complexes and ribozymes.     

Enhancing backbone sampling in Monte Carlo simulations using internal coordinates normal mode analysis

Normal mode methods are becoming a popular alternative to sample the conformational landscape of proteins. In this study, we describe the implementation of an internal coordinate normal mode analysis method and its application in exploring protein flexibility by using the Monte Carlo method PELE. This new method alternates two different stages, a perturbation of the backbone through the application of torsional normal modes, and a resampling of the side chains. We have evaluated the new approach using two test systems, ubiquitin and c-Src kinase, and the differences to the original ANM method are assessed by comparing both results to reference molecular dynamics simulations. The results suggest that the sampled phase space in the internal coordinate approach is closer to the molecular dynamics phase space than the one coming from a Cartesian coordinate anisotropic network model. In addition, the new method shows a great speedup (∼5–7×), making it a good candidate for future normal mode implementations in Monte Carlo methods.     

Molecular dynamic simulations of environment and sequence dependent DNA conformations: the development of the BMS nucleic acid force field and comparison with experimental results

Molecular dynamic (MD) simulations using the BMS nucleic acid force field produce environment and sequence dependent DNA conformations that closely mimic experimentally derived structures. The parameters were initially developed to reproduce the potential energy surface, as defined by quantum mechanics, for a set of small molecules that can be used as the building blocks for nucleic acid macromolecules (dimethyl phosphate, cyclopentane, tetrahydrofuran, etc.). Then the dihedral parameters were fine tuned using a series of condensed phase MD simulations of DNA and RNA (in zero added salt, 4M NaCl, and 75% ethanol solutions). In the tuning process the free energy surface for each dihedral was derived from the MD ensemble and fitted to the conformational distributions and populations observed in 87 A- and B-DNA x-ray and 17 B-DNA NMR structures. Over 41 nanoseconds of MD simulations are presented which demonstrate that the force field is capable of producing stable trajectories, in the correct environments, of A-DNA, double stranded A-form RNA, B-DNA, Z-DNA, and a netropsin-DNA complex that closely reproduce the experimentally determined and/or canonical DNA conformations. Frequently the MD averaged structure is closer to the experimentally determined structure than to the canonical DNA conformation. MD simulations of A- to B- and B- to A-DNA transitions are also shown. A-DNA simulations in a low salt environment cleanly convert into the B-DNA conformation and converge into the RMS space sampled by a low salt simulation of the same sequence starting from B-DNA. In MD simulations using the BMS force field the B-form of d(GGGCCC)2 in a 75% ethanol solution converts into the A-form. Using the same methodology, parameters, and conditions the A-form of d(AAATTT)2 correctly converts into the B-DNA conformation. These studies demonstrate that the force field is capable of reproducing both environment and sequence dependent DNA structures. The 41 nanoseconds (nsec) of MD simulations presented in this paper paint a global picture which suggests that the DNA structures observed in low salt solutions are largely due to the favorable internal energy brought about by the nearly uniform screening of the DNA electrostatics. While the conformations sampled in high salt or mixed solvent environments occur from selective and asymmetric screening of the phosphate groups and DNA grooves, respectively, brought about by sequence induced ion and solvent packing.     

Ion Counting from Explicit-Solvent Simulations and 3D-RISM

The ionic atmosphere around nucleic acids remains only partially understood at atomic-level detail. Ion counting (IC) experiments provide a quantitative measure of the ionic atmosphere around nucleic acids and, as such, are a natural route for testing quantitative theoretical approaches. In this article, we replicate IC experiments involving duplex DNA in NaCl_(aq) using molecular dynamics (MD) simulation, the three-dimensional reference interaction site model (3D-RISM), and nonlinear Poisson-Boltzmann (NLPB) calculations and test against recent buffer-equilibration atomic emission spectroscopy measurements. Further, we outline the statistical mechanical basis for interpreting IC experiments and clarify the use of specific concentration scales. Near physiological concentrations, MD simulation and 3D-RISM estimates are close to experimental results, but at higher concentrations (>0.7 M), both methods underestimate the number of condensed cations and overestimate the number of excluded anions. The effect of DNA charge on ion and water atmosphere extends 20–25 Å from its surface, yielding layered density profiles. Overall, ion distributions from 3D-RISMs are relatively close to those from corresponding MD simulations, but with less Na⁺ binding in grooves and tighter binding to phosphates. NLPB calculations, on the other hand, systematically underestimate the number of condensed cations at almost all concentrations and yield nearly structureless ion distributions that are qualitatively distinct from those generated by both MD simulation and 3D-RISM. These results suggest that MD simulation and 3D-RISM may be further developed to provide quantitative insight into the characterization of the ion atmosphere around nucleic acids and their effect on structure and stability.     

Ion Counting from Explicit-Solvent Simulations and 3D-RISM

The ionic atmosphere around nucleic acids remains only partially understood at atomic-level detail. Ion counting (IC) experiments provide a quantitative measure of the ionic atmosphere around nucleic acids and, as such, are a natural route for testing quantitative theoretical approaches. In this article, we replicate IC experiments involving duplex DNA in NaCl_(aq) using molecular dynamics (MD) simulation, the three-dimensional reference interaction site model (3D-RISM), and nonlinear Poisson-Boltzmann (NLPB) calculations and test against recent buffer-equilibration atomic emission spectroscopy measurements. Further, we outline the statistical mechanical basis for interpreting IC experiments and clarify the use of specific concentration scales. Near physiological concentrations, MD simulation and 3D-RISM estimates are close to experimental results, but at higher concentrations (>0.7 M), both methods underestimate the number of condensed cations and overestimate the number of excluded anions. The effect of DNA charge on ion and water atmosphere extends 20–25 Å from its surface, yielding layered density profiles. Overall, ion distributions from 3D-RISMs are relatively close to those from corresponding MD simulations, but with less Na⁺ binding in grooves and tighter binding to phosphates. NLPB calculations, on the other hand, systematically underestimate the number of condensed cations at almost all concentrations and yield nearly structureless ion distributions that are qualitatively distinct from those generated by both MD simulation and 3D-RISM. These results suggest that MD simulation and 3D-RISM may be further developed to provide quantitative insight into the characterization of the ion atmosphere around nucleic acids and their effect on structure and stability.     

Remarks on discrete and continuous large-scale models of DNA dynamics.

We present a comparison of the continuous versus discrete models of large-scale DNA conformation, focusing on issues of relevance to molecular dynamics. Starting from conventional expressions for elastic potential energy, we derive elastic dynamic equations in terms of Cartesian coordinates of the helical axis curve, together with a twist function representing the helical or excess twist. It is noted that the conventional potential energies for the two models are not consistent. In addition, we derive expressions for random Brownian forcing for the nonlinear elastic dynamics and discuss the nature of such forces in a continuous system.     

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 B_I and B_II 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.