Comparison of molecular dynamics and harmonic mode calculations on RNA

DNA Structural Correlation in Short and Long Ranges

Recent single-molecule measurements have revealed the DNA allostery in protein/DNA binding. MD simulations showed that this allosteric effect is associated with the deformation properties of DNA. In this study, we used MD simulations to further investigate the mechanism of DNA structural correlation, its dependence on DNA sequence, and the chemical modification of the bases. Besides a random sequence, poly d(AT) and poly d(GC) are also used as simpler model systems, which show the different bending and twisting flexibilities. The base-stacking interactions and the methyl group on the 5-carbon site of thymine causes local structures and flexibility to be very different for the two model systems, which further lead to obviously different tendencies of the conformational deformations, including the long-range allosteric effects.

Explaining the striking difference in twist-stretch coupling between DNA and RNA: A comparative molecular dynamics analysis

Double stranded helical DNA and RNA are flexible molecules that can undergo global conformational fluctuations. Their bending, twisting and stretching deformabilities are of similar magnitude. However, recent single-molecule experiments revealed a striking qualitative difference indicating an opposite sign for the twist-stretch couplings of dsDNA and dsRNA [Lipfert et al. 2014. Proc. Natl. Acad. Sci. U.S.A. 111, 15408] that is not explained by existing models. Employing unconstrained Molecular Dynamics (MD) simulations we are able to reproduce the qualitatively different twist-stretch coupling for dsDNA and dsRNA in semi-quantitative agreement with experiment. Similar results are also found in simulations that include an external torque to induce over- or unwinding of DNA and RNA. Detailed analysis of the helical deformations coupled to twist indicate that the interplay of helical rise, base pair inclination and displacement from the helix axis upon twist changes are responsible for the different twist-stretch correlations. Overwinding of RNA results in more compact conformations with a narrower major groove and consequently reduced helical extension. Overwinding of DNA decreases the size of the minor groove and the resulting positive base pair inclination leads to a slender and more extended helical structure.

Structural fluctuation of protein in water around its native state: a new statistical mechanics formulation

A new statistical mechanics formulation of characterizing the structural fluctuation of protein correlated with that of water is presented based on the generalized Langevin equation and the 3D-reference interaction site model (RISM)/RISM theory of molecular liquids. The displacement vector of atom positions, and their conjugated momentum, are chosen for the dynamic variables for protein, while the density fields of atoms and their momentum fields are chosen for water. Projection of other degrees of freedom onto those dynamic variables using the standard projection operator method produces essentially two equations, which describe the time evolution of fluctuation concerning the density field of solvent and the conformation of protein around an equilibrium state, which are coupled with each other. The equation concerning the protein dynamics is formally akin to that of the coupled Langevin oscillators, and is a generalization of the latter, to atomic level. The most intriguing feature of the new equation is that it contains the variance-covariance matrix as the "Hessian" term describing the "force" restoring an equilibrium conformation, which is the second moment of the fluctuation of atom positions. The "Hessian" matrix is naturally identified as the second derivative of the free energy surface around the equilibrium. A method to evaluate the Hessian matrix based on the 3D-RISM/RISM theory is proposed. Proposed also is an application of the present formulation to the molecular recognition, in which the conformational fluctuation of protein around its native state becomes an important factor as exemplified by so called "induced fitting."

Toward a consensus view of duplex RNA flexibility

The structure and flexibility of the RNA duplex has been studied using extended molecular dynamics simulations on four diverse 18-mer oligonucleotides designed to contain many copies of the 10 unique dinucleotide steps in different sequence environments. Simulations were performed using the two most popular force fields for nucleic acids simulations (AMBER and CHARMM) in their latest versions, trying to arrive to a consensus picture of the RNA flexibility. Contrary to what was found for DNA duplex (DNA(2)), no clear convergence is found for the RNA duplex (RNA(2)), but one of the force field seems to agree better with experimental data. MD simulations performed with this force field were used to fully characterize, for the first time to our knowledge, the sequence-dependent elastic properties of RNA duplexes at different levels of resolutions. The flexibility pattern of RNA(2) shows similarities with DNA(2), but also surprising differences, which help us to understand the different biological functions of both molecules. A full mesoscopic model of RNA duplex at different resolution levels is derived to be used for genome-wide description of the flexibility of double-helical fragments of RNA.

Molecular dynamics simulations suggest that RNA three-way junctions can act as flexible RNA structural elements in the ribosome

We present extensive explicit solvent molecular dynamics analysis of three RNA three-way junctions (3WJs) from the large ribosomal subunit: the 3WJ formed by Helices 90–92 (H90–H92) of 23S rRNA; the 3WJ formed by H42–H44 organizing the GTPase associated center (GAC) of 23S rRNA; and the 3WJ of 5S rRNA. H92 near the peptidyl transferase center binds the 3′-CCA end of amino-acylated tRNA. The GAC binds protein factors and stimulates GTP hydrolysis driving protein synthesis. The 5S rRNA binds the central protuberance and A-site finger (ASF) involved in bridges with the 30S subunit. The simulations reveal that all three 3WJs possess significant anisotropic hinge-like flexibility between their stacked stems and dynamics within the compact regions of their adjacent stems. The A-site 3WJ dynamics may facilitate accommodation of tRNA, while the 5S 3WJ flexibility appears to be essential for coordinated movements of ASF and 5S rRNA. The GAC 3WJ may support large-scale dynamics of the L7/L12-stalk region. The simulations reveal that H42–H44 rRNA segments are not fully relaxed and in the X-ray structures they are bent towards the large subunit. The bending may be related to L10 binding and is distributed between the 3WJ and the H42–H97 contact.

Molecular recognition of RNA: challenges for modelling interactions and plasticity

There is growing interest in molecular recognition processes of RNA because of RNA's widespread involvement in biological processes. Computational approaches are increasingly used for analysing and predicting binding to RNA, fuelled by encouraging progress in developing simulation, free energy and docking methods for nucleic acids. These developments take into account challenges regarding the energetics of RNA-ligand binding, RNA plasticity, and the presence of water molecules and ions in the binding interface. Accordingly, we will detail advances in force field and scoring function development for molecular dynamics (MD) simulations, free energy computations and docking calculations of nucleic acid complexes. Furthermore, we present methods that can detect moving parts within RNA structures based on graph-theoretical approaches or normal mode analysis (NMA). As an example of the successful use of these developments, we will discuss recent structure-based drug design approaches that focus on the bacterial ribosomal A-site RNA as a drug target.

Elastic properties of ribosomal RNA building blocks: molecular dynamics of the GTPase-associated center rRNA

Explicit solvent molecular dynamics (MD) was used to describe the intrinsic flexibility of the helix 42–44 portion of the 23S rRNA (abbreviated as Kt-42+rGAC; kink-turn 42 and GTPase-associated center rRNA). The bottom part of this molecule consists of alternating rigid and flexible segments. The first flexible segment (Hinge1) is the highly anharmonic kink of Kt-42. The second one (Hinge2) is localized at the junction between helix 42 and helices 43/44. The rigid segments are the two arms of helix 42 flanking the kink. The whole molecule ends up with compact helices 43/44 (Head) which appear to be modestly compressed towards the subunit in the Haloarcula marismortui X-ray structure. Overall, the helix 42–44 rRNA is constructed as a sophisticated intrinsically flexible anisotropic molecular limb. The leading flexibility modes include bending at the hinges and twisting. The Head shows visible internal conformational plasticity, stemming from an intricate set of base pairing patterns including dynamical triads and tetrads. In summary, we demonstrate how rRNA building blocks with contrasting intrinsic flexibilities can form larger architectures with highly specific patterns of preferred low-energy motions and geometries.

Coupling of fast and slow modes in the reaction pathway of the minimal hammerhead ribozyme cleavage

By employing classical molecular dynamics, correlation analysis of coupling between slow and fast dynamical modes, and free energy (umbrella) sampling using classical as well as mixed quantum mechanics molecular mechanics force fields, we uncover a possible pathway for phosphoryl transfer in the self-cleaving reaction of the minimal hammerhead ribozyme. The significance of this pathway is that it initiates from the minimal hammerhead crystal structure and describes the reaction landscape as a conformational rearrangement followed by a covalent transformation. The delineated mechanism is catalyzed by two metal (Mg(2+)) ions, proceeds via an in-line-attack by CYT 17 O2' on the scissile phosphorous (ADE 1.1 P), and is therefore consistent with the experimentally observed inversion configuration. According to the delineated mechanism, the coupling between slow modes involving the hammerhead backbone with fast modes in the cleavage site appears to be crucial for setting up the in-line nucleophilic attack.

B-DNA under stress: over- and untwisting of DNA during molecular dynamics simulations

The twist flexibility of DNA is central to its many biological functions. Explicit solvent molecular dynamics simulations in combination with an umbrella sampling restraining potential have been employed to study induced twist deformations in DNA. Simulations allowed us to extract free energy profiles for twist deformations and were performed on six DNA dodecamer duplexes to cover all 10 possible DNA basepair steps. The shape of the free energy curves was similar for all duplexes. The calculated twist deformability was in good agreement with experiment and showed only modest variation for the complete duplexes. However, the response of the various basepair steps on twist stress was highly nonuniform. In particular, pyrimidine/purine steps were much more flexible than purine/purine steps followed by purine/pyrimidine steps. It was also possible to extract correlations of twist changes and other helical as well as global parameters of the DNA molecules. Twist deformations were found to significantly alter the local as well as global shape of the DNA modulating the accessibility for proteins and other ligands. Severe untwisting of DNA below an average of 25 degrees per basepair step resulted in the onset of a global structural transition with a significantly smaller twist at one end of the DNA compared to the other.

Comparison of mode analyses at different resolutions applied to nucleic acid systems

More than two decades of different types of mode analyses has shown that these techniques can be useful in describing large-scale motions in protein systems. A number of mode analyses are available and include quasiharmonics, classical normal mode, block normal mode, and the elastic network model. Each of these methods has been validated for protein systems and this variety allows researchers to choose the technique that gives the best compromise between computational cost and the level of detail in the calculation. These same techniques have not been systematically tested for nucleic acid systems, however. Given the differences in interactions and structural features between nucleic acid and protein systems, the validity of these techniques in the protein regime cannot be directly translated into validity in the nucleic acid realm. In this work, we investigate the usefulness of the above mode analyses as applied to two RNA systems, i.e., the hammerhead ribozyme and a guanine riboswitch. We show that classical normal-mode analysis can match the magnitude and direction of residue fluctuations from the more detailed, anharmonic technique, quasiharmonic analysis of a molecular dynamics trajectory. The block normal-mode approximation is shown to hold in the nucleic acid systems studied. Only the mode analysis at the lowest level of detail, the elastic network model, produced mixed results in our calculations. We present data that suggest that the elastic network model, with the popular parameterization, is not best suited for systems that do not have a close packed structure; this observation also hints at why the elastic network model has been found to be valid for many globular protein systems. The different behaviors of block normal-mode analysis and the elastic network model, which invoke similar degrees of coarse-graining to the dynamics but use different potentials, suggest the importance of applying a heterogeneous potential function in a robust analysis of the dynamics of biomolecules, especially those that are not closely packed. In addition to these comparisons, we briefly discuss insights into the conformational space available to the hammerhead ribozyme.

Conformational flexibility of the MHC class I alpha1-alpha2 domain in peptide bound and free states: a molecular dynamics simulation study

Major histocompatibility complex class I proteins play a key role in the recognition and presentation of peptide antigens to the host immune system. The structure of various major histocompatibility complex class I proteins has been determined experimentally in complex with several antigenic peptides. However, the structure in the unbound (empty) form is not known. To study the conformational dynamics of the empty major histocompatibility complex class I molecule comparative molecular dynamics simulations have been performed starting from the crystal structure of a peptide bound class I peptide-binding domain in the presence and absence of a peptide ligand. Simulations including the bound peptide stayed close to the experimental start structure at both simulation temperatures (300 and 355 K) during the entire simulation of 26 ns. Several independent simulations in the absence of peptide indicate that the empty domain may not adopt a single defined conformation but is conformationally significantly more heterogeneous in particular within the alpha-helices that flank the peptide binding cleft. The calculated conformational dynamics along the protein chain correlate well with available spectroscopic data and with the observed site-specific sensitivity of the empty class I protein to proteolytic digestion. During the simulations at 300 K the binding region for the peptide N-terminus stayed close to the conformation in the bound state, whereas the anchor region for the C-terminus showed significantly larger conformational fluctuations. This included a segment at the beginning of the second alpha-helix in the domain that is likely to be involved in the interaction with the chaperone protein tapasin during the peptide-loading process. The simulation studies further indicate that peptide binding at the C- and N-terminus may follow different mechanisms that involve different degrees of induced conformational changes in the peptide-binding domain. In particular binding of the peptide C-terminus may require conformational stabilization by chaperone proteins during peptide loading.

Rapid protein-ligand docking using soft modes from molecular dynamics simulations to account for protein deformability: Binding of FK506 to FKBP

Most current docking methods to identify possible ligands and putative binding sites on a receptor molecule assume a rigid receptor structure to allow virtual screening of large ligand databases. However, binding of a ligand can lead to changes in the receptor protein conformation that are sterically necessary to accommodate a bound ligand. An approach is presented that allows relaxation of the protein conformation in precalculated soft flexible degrees of freedom during ligand-receptor docking. For the immunosuppressant FK506-binding protein FKBP, the soft flexible modes are extracted as principal components of motion from a molecular dynamics simulation. A simple penalty function for deformations in the soft flexible mode is used to limit receptor protein deformations during docking that avoids a costly recalculation of the receptor energy by summing over all receptor atom pairs at each step. Rigid docking of the FK506 ligand binding to an unbound FKBP conformation failed to identify a geometry close to experiment as favorable binding site. In contrast, inclusion of the flexible soft modes during systematic docking runs selected a binding geometry close to experiment as lowest energy conformation. This has been achieved at a modest increase of computational cost compared to rigid docking. The approach could provide a computationally efficient way to approximately account for receptor flexibility during docking of large numbers of putative ligands and putative docking geometries.

Modelling ion binding to AA platform motifs in RNA: a continuum solvent study including conformational adaptation

Binding of monovalent and divalent cations to two adenine-adenine platform structures from the Tetrahymena group I intron ribozyme has been studied using continuum solvent models based on the generalised Born and the finite-difference Poisson-Boltzmann approaches. The adenine-adenine platform RNA motif forms an experimentally characterised monovalent ion binding site important for ribozyme folding and function. Qualitative agreement between calculated and experimental ion placements and binding selectivity was obtained. The inclusion of solvation effects turned out to be important to obtain low energy structures and ion binding placements in agreement with the experiment. The calculations indicate that differences in solvation of the isolated ions contribute to the calculated ion binding preference. However, Coulomb attraction and van der Waals interactions due to ion size differences and RNA conformational adaptation also influence the calculated ion binding affinity. The calculated alkali ion binding selectivity for both platforms followed the order K(+) > Na(+) > Rb(+) > Cs(+) > Li(+) (Eisenman series VI) in the case of allowing RNA conformational relaxation during docking. With rigid RNA an Eisenman series V was obtained (K(+) > Rb(+) > Na(+) > Cs(+) > Li(+)). Systematic energy minimisation docking simulations starting from several hundred initial placements of potassium ions on the surface of platform containing RNA fragments identified a coordination geometry in agreement with the experiment as the lowest energy binding site. The approach could be helpful to identify putative ion binding sites in nucleic acid structures determined at low resolution or with experimental methods that do not allow identification of ion binding sites.

Conformational analysis of DNA-trinucleotide-hairpin-loop structures using a continuum solvent model

A number of trinucleotide sequences in DNA can form compact and stable hairpin loops that may have significance for DNA replication and transcription. The conformational analysis of these motifs is important for an understanding of the function and design of nucleic acid structures. Extensive conformational searches have been performed on three experimentally known trinucleotide hairpin loops (AGC, AAA, and GCA) closed by a four-base-pair stem. An implicit solvation model based on the generalized Born method has been employed during energy minimization and conformational search. In addition, energy-minimized conformers were evaluated using a finite-difference Poisson-Boltzmann approach. For all three loop sequences, conformations close to experiment were found as lowest-energy structures among several thousand alternative energy minima. The inclusion of reaction-field contributions was found to be important for a realistic conformer ranking. Most generated hairpin loop structures within approximately 5 kcal x mol(-1) of the lowest-energy structure have a similar topology. Structures within approximately 10 kcal x mol(-1) could be classified into about five structural families representing distinct arrangements of loop nucleotides. Although a large number of backbone torsion angle combinations were compatible with each structural class, some specific patterns could be identified. Harmonic mode analysis was used to account for differences in conformational flexibility of low-energy sub-states. Class-specific differences in the pattern of atomic fluctuations along the sequence were observed; however, inclusion of conformational entropy contributions did not change ranking of structural classes. For an additional loop sequence (AAG) with no available experimental structure, the approach suggests a lowest-energy loop topology overall similar to the other three loop sequences but closed by a different non-canonical base-pairing scheme.