- Email: [email protected]
Simulation of the structure and dynamics of nonhelical RNA motifs
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Simulation of the structure and dynamics of nonhelical RNA motifs Martin Zacharias Computer simulation methods are increasingly being used to study possible conformations and dynamics of structural motifs in RNA. Recent results of molecular dynamics simulations and continuum solvent studies of RNA structures and RNA–ligand complexes show promising agreement with experimental data. Combined with the ongoing progress in the experimental characterization of RNA structure and thermodynamics, these computational approaches can help to better understand the mechanism of RNA structure formation and the binding of ligands. Addresses AG Theoretische Biophysik, Institut für Molekulare Biotechnologie, Beutenbergstrasse 11, D-07745 Jena, Germany; e-mail: [email protected] Current Opinion in Structural Biology 2000, 10:311–317 0959-440X/00/$ — see front matter © 2000 Elsevier Science Ltd. All rights reserved. Abbreviations BD Brownian dynamics FDPB finite-difference Poisson–Boltzmann FMN flavin mononucleotide GB generalized Born MD molecular dynamics NM normal mode PB Poisson–Boltzmann snRNP small nuclear ribonucleoprotein
Introduction RNA molecules play an essential role in many biological processes. To obtain an understanding of the role and function of RNA, knowledge of both its three-dimensional structure and the forces that drive structure formation is important. At the level of secondary structure, RNA consists of base-paired (helical) regions and single-stranded or mispaired sequences that can form hairpin, internal or bulge loop structures. Biologically active RNA is strongly affected by the possible conformations and interactions of the nonhelical motifs that interrupt base-paired RNA. The experimental and theoretical study of the range of conformations accessible to these elements is important for understanding the mechanism of RNA folding. Nonhelical RNA elements do not only play a central role in the folding of RNA molecules. The biological function of the RNA is often directly related to the presence of bulges and loops, which can form recognition sites for ligands or mediate a possible catalytic activity. Some of these elements can even function as isolated structures, without the context of a larger folded RNA structure. As a result of the variety of biological functions, there is also an increasing interest in nonhelical RNA motifs as possible drug targets [1]. During the past several years, a growing number of RNA structures and RNA–protein/ligand complexes have been determined experimentally using X-ray crystallography or
NMR spectroscopy [2,3]. A wealth of information about the conformational preferences of RNA structures and conformational changes upon ligand and protein binding has been obtained. Structural studies, in combination with thermodynamic measurements and site-directed mutagenesis, allowed the analysis of the influence of individual bases and chemical groups on structure stabilization or on interactions with a ligand. Although the forces that drive structure formation are not directly visible in an experimentally determined structure, some of the important molecular interactions can be derived indirectly from observed contacts. In addition to structural and thermodynamic approaches, computer simulation methods, which are based on model energy functions that describe molecular interactions, are increasingly being used to investigate nucleic acids. Provided that the description of the intermolecular interactions is sufficiently accurate, these methods may allow more direct study of the forces that drive structure formation. In addition, simulation approaches can complement structural studies in cases in which the timescales or physical properties of interest are not easily accessible to experimental methods. It is also hoped that computer simulation methods could help to improve structure prediction and model building of nucleic acids. This review describes recent progress in computational studies at the level of a classical atom-centered force field that involve unusual RNA structures. The initial focus is on molecular dynamics (MD) simulations that include surrounding water and ions explicitly. Subsequently, computationally less demanding studies that include solvent effects implicitly are reviewed.
Molecular dynamics simulations of RNA MD simulations involve the stepwise solution of Newton’s equation of motion for the molecule and surrounding water molecules and ions. In most current MD simulations, the Ewald or the particle mesh Ewald (PME) method is employed to account for long-range electrostatic interactions within a periodic system [4,5]. Several simulation studies on RNA and DNA molecules indicate that such a treatment significantly improves the quality of the simulation compared to earlier methods with a cut-off for long-range electrostatic interactions [5–7]. Although the length of MD simulations of nucleic acids has continuously grown over the past few years, the maximum simulation time (tens of nanoseconds) is still considerably less than the time necessary to directly follow large-scale conformational changes, such as RNA folding. Nevertheless, even on the nanosecond timescale, information on the conformational flexibility of structural motifs in nucleic acids and on the lifetime of hydrogen bonds and of nonpolar contacts can be extracted. MD simulations have, for example, been
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successfully applied to study the hydration of nucleic acids. Good agreement between experimentally observed hydration sites and predictions based on MD simulations has been obtained for RNA and DNA [8,9,10••]. In addition to the ordered water molecules that can be seen in high-resolution X-ray diffraction experiments, more mobile hydration sites and hydration kinetics can be studied with the MD method.
the size of the molecule, the simulation time was limited to 0.5 ns. Although the helical stem and tertiary base pairs remained stable during the simulation, a structural rearrangement in the tRNA core that involved the slippage of three consecutive base triples was observed. The increased core flexibility might be attributed to the absence from the simulation of Mg2+ ions known to stabilize and stiffen the tertiary structure of tRNAs [18•].
During the review period, several MD simulations of RNA structures and RNA–ligand complexes that contained nonhelical RNA elements were published. A number of variants of the Escherichia coli tRNAAla acceptor stem helix have been systematically studied by Nagan et al. [11•]. The acceptor stem of tRNAAla contains a G3:U70 wobble pair (numbering corresponds to the tRNA sequence) that is the main identity element for recognition by its cognate aminoacyl-synthetase. The isolated acceptor stem can be specifically aminoacylated in vitro. The observation that some other mismatches, but not canonical base pairs, at the same position support aminoacylation has led to the suggestion that an unusual site-specific structure or flexibility is important for recognition. This view is supported by recent NMR studies [12]. On the 2 ns timescale of the MD simulations, no significant global structural perturbation or enhanced conformational flexibility for mismatch and surrounding base pairs was observed [11•]. However, a characteristic pattern of helix underwinding at the step above (in the 5′ direction) and overwinding at the step below G:U and other purine:pyrimidine wobble pairs was seen during the MD simulation. This has also been observed in NMR [12–14] and crystallographic studies [15] of the acceptor stem. Consistent with suggestions based on the crystal structure analysis [15], the MD simulations indicate that hydration at specific minor groove sites in the case of G:U and other wobble base pairs may contribute to binding specificity. The water residence lifetime at the minor groove near the wobble pair appeared to correlate with the experimentally observed aminoacylation efficiency for the corresponding acceptor stem variant.
Molecular dynamics of RNA in complex with ligands and proteins
Following earlier simulations of the isolated acceptor stem of yeast tRNAAsp [9,16], Auffinger et al. [17•] performed an MD simulation of the entire 76-nucleotide tRNAAsp. The three-dimensional tRNA structure is formed by the complex interplay of base-paired helical stem regions and several nonhelical elements. A number of base triple interactions stabilize the tRNA core structure. In principle, an MD simulation of such a system allows one to study the dynamics of nonhelical RNA elements in the context of a large RNA structure. The study by Auffinger et al. [17•] demonstrated that this is indeed possible using current MD methodology. The simulated structure remained close to the starting crystal structure and the calculated atomic fluctuations were largely compatible with experimental Debye Waller (B) factors. However, significantly larger fluctuations than expected from the experimental B-factors were found for the tRNA anticodon region. Because of
The dynamics of an RNA aptamer in complex with FMN, starting from the known NMR structure, was studied by Schneider and Sühnel [19•]. The simulation preserved all structural features characteristic of the complex, including a base triple, several noncanonical base pairs and the position of the ligand. A number of water-mediated contacts within the RNA and between the RNA and ligand with lifetimes of approximately 0.5 ns have been observed. Interestingly, the MD simulation indicated that water molecules, although having donor as well as acceptor capabilities, act preferably as donors in hydrogen bonding interactions with the 2′-OH group of RNA. The authors described several C2′–H⋅⋅⋅O4′ contacts between riboses of neighboring nucleotides. Such contacts have been found in previous MD simulations and have been proposed to stabilize RNA [16,17•]. Various aspects of RNA–protein interactions have been investigated by three groups studying the U1A–RNA complex. The U1A protein is a component of the U1 small nuclear ribonucleoprotein (snRNP) component, which is involved in RNA splicing. It binds with a picomolar Kd to an eight-nucleotide, nonhelical loop structure. The binding element can be either part of an RNA internal bulge loop (as part of the U1A mRNA) or a hairpin loop in the U1 snRNP itself. Reyes and Kollman [20•] compared the MD of the U1A protein in complex with either the RNA hairpin loop or the internal bulge loop, starting from experimental structures. For both complexes, the experimentally observed interaction pattern between the protein and RNA was largely conserved during the simulations. Overall, the U1A–internal loop complex appeared to be significantly more flexible than the U1A–hairpin loop complex during the simulation. This was manifested in larger average atomic fluctuations and a smaller number of stable intermolecular hydrogen bonds in the simulation of the internal loop complex. In addition, a global conformational change was observed in the case of the internal loop complex that involved a shift in the angular orientation of the loopflanking helices. The observed hinge motion was compatible with experimental (NMR) constraints. Tang and Nilsson [21] focused on comparing the dynamics of the U1A–RNA hairpin complex with that of the free RNA hairpin. The starting structure for the MD simulation
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of the free RNA hairpin was taken from the X-ray structure of the U1A–RNA hairpin complex [22]. The free RNA loop appeared to be much more flexible than in complex with the protein, indicating that it may not adopt a single distinct conformation in the unbound state. Such adaptive conformational transitions upon ligand binding have been observed experimentally in several nonhelical RNA motifs [23]. Most of the hydrogen bonds and van der Waals contacts suggested by the X-ray analysis of the U1A–RNA hairpin complex [22] were stable during the simulation of the complex. The affinity of the U1A protein to the RNA binding region depends strongly on the salt concentration, demonstrating that electrostatic interactions are a major driving force for complex formation. Hermann and Westhof [24] followed the dynamics of the U1A–RNA hairpin complex upon increasing the salt concentration from 0.1 to 1 M in the course of an MD simulation. A significant enhancement of RNA and, to a lesser degree, protein conformational fluctuations was observed following salt addition, which may indicate the onset of RNA–protein dissociation. Although the simulation time (~1.5–1.8 ns at each salt concentration) was orders of magnitude shorter than the expected dissociation time for an RNA–protein complex, such simulations may give hints about the initial events of the process.
Normal mode analysis of RNA In the normal mode approach, information on the flexible degrees of freedom of a molecule is extracted from the curvature of the energy function at an energy minimum. The advantage of this approach is that it can be computationally much less demanding than MD simulations, particularly if an internal coordinate description is used. However, solvent and ions are usually not included explicitly and conformational transitions between conformational substates cannot be considered. A normal mode (NM) analysis of tRNAPhe using torsion angle variables and including sugar pucker flexibility was performed by Matsumoto et al. [25•]. A conclusion from the NM study was that, because of its shape, tRNA is considerably softer than, for example, a globular protein. The calculated harmonic mobility of tRNAPhe was characterized by the motion of three subdomains corresponding to the acceptor stem, anticodon loop and a part consisting of the D arm, variable loop and T arm. The flexibility of tRNA has also been investigated using a very simple model that consisted of one interaction center per nucleotide and assumed an energy function that basically depends on the local packing density [26]. Even this simple model predicted nucleotide mobilities for free tRNAs and a tRNAAsp–aminoacyl-synthetase complex that are close to experimental B-factors. This result suggests that local packing density significantly determines the direction and magnitude of the flexibility of RNA molecules around a stable structure.
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The harmonic deformability of regular duplex RNA and bulge- and mismatch-containing RNA has been compared [27•]. Calculated helical coordinate fluctuations of regular duplex RNA and A-DNA showed reasonable agreement with experimental data from statistics of A-DNA crystal structures [28]. A significant anticorrelation of helical coordinate fluctuations of neighboring base pairs was observed. As a consequence, RNA is predicted to be globally stiffer than expected from the local base pair step flexibility. Most mismatches and bulges slightly increased the calculated harmonic flexibility, with the exception of tandem G:A mismatches in the sheared conformation, which were predicted to stiffen RNA. Similar to NM studies on DNA [29,30], only a few major bending modes were identified, consisting of mainly coupled roll and slide changes of neighboring base pair steps.
Free energies from molecular dynamics and implicit solvent approaches An ultimate goal of computer simulation studies is to calculate conformational preferences and relative conformational stabilities from molecular simulations. Free energy differences between two conformational substates of a molecule can be calculated using thermodynamic integration or perturbation techniques along a reaction path for the conformational transition. Using such an approach, Stofer et al. [31•] studied base pair formation and dissociation in aqueous solution along one direction to separate the bases. The calculated free energies for base pair formation were compatible with an expected hydrogen bond free energy of approximately –2 kcal mol–1. Solvent-separated secondary free energy minima (~1.0 kcal mol–1) were observed for both A:T and G:C base pairs. Such watermediated contacts may stabilize noncanonical base pairs in RNA [32]. Besides gaining insight into the energetics of base pair formation, the free energy simulations can be helpful for developing effective energy functions for calculations that employ implicit solvent models (see below). The definition of an appropriate reaction path can, however, become difficult if several conformational variables change simultaneously to achieve a desired conformational transition. In addition, the calculated free energy difference depends strongly on the relaxation timescales of the structural perturbation and conformational sampling along the selected path. Several recent studies use an approximate approach that applies MD simulations only to generate ensembles of structures compatible with the conformational regions of interest. A free energy estimate is obtained by taking averages of the various intramolecular energy terms over the ensemble. The solvation free energy of the structures is calculated using a mean field approach for solvent and ions that is based on either the finite-difference Poisson–Boltzmann (FDPB) approach or the generalized Born (GB) method. In these approaches, the molecule is treated as a low dielectric cavity surrounded by a high dielectric continuum representing the aqueous environment. Nonpolar solvation
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contributions are calculated from the solvent accessible area of the molecules (see a recent review by Cramer and Truhlar [33•]). Conformational entropy effects can be estimated by quasi-harmonic analysis of the MD trajectory or by harmonic mode analysis of one representative conformation. Although the discrete nature of the solvent is completely neglected in such approaches, experimentally observed trends for the relative stabilities of a number of nucleic acid structures could be reproduced. For example, Jayaram et al. [34•] compared the relative stabilities of ensembles of A-DNA and B-DNA conformations in (salt-containing) aqueous and alcoholic solutions. In agreement with experiment, the calculations predicted B-DNA to be the preferred form in aqueous solution because of its more favorable solvation compared with A-DNA. In alcoholic solution, the overall reduction of solvation effects and a more strongly bound ion atmosphere preferentially stabilized A-DNA. Srinivasan et al. [35•] could reproduce experimentally observed trends for the conformational preferences of B-DNA, A-DNA, RNA and phosphoamidate-modified DNA in aqueous solutions. Using a similar approach, Cheatham et al. [36] calculated a significantly greater ‘A-form-philicity’ for ensembles of poly(G/C) structures than for poly(A/T), in agreement with experiment. The method has also been applied to study the relative stabilities of RNA loop structures. Starting from experimentally known UGAA and UUCG tetraloop structures, MD simulations have been performed to generate ensembles of alternative hairpin loop conformations [37]. On the basis of continuum solvent modeling, the predicted low free energy forms for the two structures agreed with experimentally observed conformational preferences of the corresponding loops. The approach could potentially be useful for several other applications, such as ligand binding to nucleic acids [38].
Simulations and conformational searches of RNA motifs with an implicit solvent representation One limitation of MD simulations that include ions and water molecules explicitly is that conformational transitions often occur on timescales that are large compared with the MD simulation time. Even if one starts from different initial conformations, the convergence to stable structures can be slower than the maximum simulation time, because of various slow relaxing conformational variables. Ultimately, however, the systematic conformational analysis of a given RNA motif is desired in order to get an impression of the range of possible conformations and the energetic order. Conformational searches that neglect solvation effects are computationally rapid, but the calculated structures and energies can be very unrealistic. A number of recent studies have demonstrated that the implicit inclusion of solvation effects, either through solving the PB equation or using the GB model, can significantly improve conformational searches and stochastic dynamics simulations. This was shown for peptide systems [39•] and also for nucleic acids.
Large numbers of sterically possible conformations were systematically generated for single unmatched adenine nucleotides in DNA and RNA [40,41•]. The energetic evaluation based on the FDPB continuum model selected classes of low energy bulge structures that are similar to experimental bulge topologies. The tetraloop sequence GNRA adopts a well-known characteristic fold. Using the MC-SYM (macromolecular conformations by symbolic programming) conformational generator [42], a large variety of sterically possible tetraloop conformations were generated [43•]. The energetic evaluation of these conformations through solving the Poisson equation by atom-centered virtual dipoles picked out structures close to the experimental GNRA loop structure as being those of lowest energy [43•]. In contrast, for both the bulge and the tetraloop systems, treatment of electrostatic interactions with a distance-dependent dielectric constant selected unrealistic structures (in disagreement with experiment) as being those of low energy. Systematic studies on sterically preferred conformations for mononucleotides and dinucleotides can be helpful to reduce the conformational search space in these approaches [44]. A nanosecond stochastic dynamics simulation of the UUCG tetraloop with an implicit solvent model was performed by Williams and Hall [45••]. Treatment of the electrostatic interactions with the GB model lead to trajectories that stayed close to the experimental structure, with conformational fluctuations similar in magnitude to those obtained with an MD simulation with explicit solvent [46]. In addition, starting from an older low-resolution NMRderived structure of the loop that contains an ‘incorrect’ loop closure base pairing scheme led to the formation of the ‘correct’ pairing scheme, compatible with the refined NMR analysis, during the course of the simulation. In contrast, a stochastic simulation with a vacuum treatment of the electrostatic interactions resulted in conformations with significant deviation from the experimental loop structure. Most current protocols for structure determination from NMR data neglect solvation effects [47]. The more realistic treatment of solvation effects in the above-mentioned continuum solvent modeling approaches might be helpful for nucleic acid structure generation from a limited set of experimentally derived constraints.
Modeling ion and ligand binding to RNA The association of ions with RNA plays a key role in the formation of stable three-dimensional structures. Folded conformations of negatively charged RNA are stabilized by a diffuse counterion atmosphere and by specifically bound ions that can be partially dehydrated. Noncanonical base pairs and other nonhelical RNA structures are often part of these ion-binding sites. Ion binding is influenced by the local electrostatic field, the geometry of the binding pocket and also by the degree of ion desolvation upon association [48•]. Theoretical studies of RNA–ion association can be further complicated by the fact that ion binding
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(and the binding of other ligands) may significantly change the conformation or conformational distribution of the RNA molecule. Solutions of the (nonlinear) PB equation can be used to get an impression of the electrostatic field and the mean ion distribution around nucleic acids. Using the PB theory, Misra and Draper [49•] studied the diffusive ion association to cylindrical models of nucleic acids in a mixed salt solution consisting of monovalent co-ions and monovalent and divalent counterions. Good agreement between calculated and experimental magnesium-binding isotherms for DNA and poly(AU) at different sodium concentrations was found. The calculations indicate that added co-ions may also play an important role in the stability of nucleic acids. FDPB calculations, in combination with Brownian dynamics (BD) simulations, were used to study the diffusion of divalent cations around known RNA structures [50]. In the BD simulation, a charged sphere diffuses under the influence of the RNA electrostatic field and settles in binding regions with a negative electrostatic potential. The ion is treated as test charge; ion desolvation effects are not included. Experimentally observed ion-binding positions could be reproduced for several known RNA structures. Chin et al. [51•] looked at isopotential contours and surface potential maps of the electrostatic field (from FDPB calculations) for experimentally determined RNA structures. Known cation-binding sites were observed to correlate with regions of calculated negative electrostatic potential. Interestingly, characteristic holes in the electrostatic surface potential (regions of reduced electrostatic potential) were found close to some nonhelical RNA elements. These sites correspond to known RNA RNA-binding and ligand-binding positions. Although computational approaches are already used extensively to identify possible ligand candidates for proteins, applications to nucleic acids are still very limited (reviewed in [1]). As nonhelical RNA structures play an important role in many biological processes, these are also attractive targets for drug discovery. Methods initially developed for docking ligands to proteins have also been applied to identifying possible RNA-binding ligands [52,53]. Olson and Cuff [54] used a continuum solvent approach to predict the binding of RNA model structures and small ligands to ricin A. Ricin A is a small ribosomeinactivating protein that specifically depurinates an adenine in a GAGA tetraloop. Reasonable agreement between experimental and calculated binding free energies was obtained. Hermann and Westhof [55•] attempted to explain the binding specificity of cationic antibiotics to various nonhelical RNA motifs, speculating that positive charges on the antibiotics replace divalent-ion-binding sites on the RNA. An aminoglycoside antibiotic provides a framework of positively charged groups that fits into regions of negative electrostatic potential normally occupied by ions. On the basis of this model, known
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aminoglycoside-binding sites in experimentally determined complexes could be successfully identified [56]. Putative binding positions for cationic antibiotics in the hammerhead ribozyme [55•] and HIV TAR element have also been suggested [56].
Conclusions MD simulations are now widely used to study regular nucleic acid structures, as well as nonhelical motifs. One of the most important purposes of these studies is to continuously check and improve the simulation model and force field by comparing computational results with available experimental data. Very reasonable agreement between many simulated structures and experimental start structures for RNA and RNA–ligand complexes has already been achieved. It is likely that, in the not too distant future, simulation times of 0.1–1 µs or beyond will be possible for nucleic acids. Such simulations may allow the direct characterization of small conformational rearrangements and, ultimately, certain aspects of RNA folding. The successful prediction of conformational preferences of small experimentally known nucleic acid structural motifs using continuum solvent models indicates that these rapid approaches could improve energy-based prediction methods. At the expense of a less accurate solvent representation compared with MD simulations with explicit solvent, these methods hold the potential for much longer simulation times and a greater variety of sampled conformations. Many applications, ranging from the conformational analysis of RNA motifs to studies of ligand binding, are possible and can contribute to the understanding of RNA structure, function and ligand association.
Acknowledgements I thank Felipe Pineda, Heinz Sklenar and Paul Hagerman for helpful discussions.
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16. Auffinger P, Louise-May S, Westhof E: Molecular dynamics simulations of the anticodon hairpin of tRNAAsp: structuring effects of C-H⋅⋅⋅O hydrogen bonds and long range hydration forces. J Am Chem Soc 1996, 118:1181-1189. 17. Auffinger P, Louise-May S, Westhof E: Molecular dynamics • simulations of solvated yeast tRNAAsp. Biophys J 1999, 76:50-64. The first molecular dynamics simulation of a complete yeast tRNAAsp, including monovalent (NH4+) counterions and explicit water molecules, under periodic boundary conditions and using the particle mesh Ewald (PME) method. Secondary and tertiary base pairs observed in the crystallographic start structure remain stable during the 0.5 ns simulation time. 18. Friederich MW, Vacano E, Hagerman PJ: Global flexibility of tertiary • structure in RNA: yeast tRNAPhe as a model system. Proc Natl Acad Sci USA 1998, 95:3572-3577. This study describes an experimental approach to obtaining quantitative information about the global flexibility of nonhelical RNA structures. On the basis of transient electric birefringence measurements of constructs that contain two tRNAPhe core elements at various distances within an RNA helix, it is possible to separate static from flexible global bending. The presence of Mg2+ ions appears to significantly stiffen the tRNAPhe core elements. 19. Schneider C, Sühnel J: A molecular dynamics simulation of the • flavin mononucleotide-RNA aptamer complex. Biopolymers 1999, 50:287-302. The first nanosecond molecular dynamics simulation of an RNA aptamer–ligand complex. The simulated structure remains close to the experimental start structure and preserves characteristic structural features of the complex. Several water-mediated contacts between the ligand and RNA are observed. 20. Reyes CM, Kollman PA: Molecular dynamics studies of U1A-RNA • complexes. RNA 1999, 5:235-244. A comparative molecular dynamics study of the U1A protein in complex with an RNA hairpin and an internal loop structure. The calculated conformational flexibility of the internal loop complex is larger than for the U1A–RNA hairpin complex. A global hinge motion of the RNA in the internal loop complex compatible with experimental constraints is observed.
32. Brandl M, Meyer M, Sühnel J: Quantum-chemical study of a watermediated uracil-cytosine base pair. J Am Chem Soc 1999, 121:2605-2606 33. Cramer CJ, Truhlar DG: Implicit solvation models: equilibria, • structure, spectra and dynamics. Chem Rev 1999, 99:2161-2200. A detailed review on the use of implicit solvation models in various fields of computational chemistry. 34. Jayaram B, Sprous D, Young MA, Beveridge DL: Free energy • analysis of the conformational preferences of A and B forms of DNA in solution. J Am Chem Soc 1998, 120:10629-10633. A comparison of the relative stability of A-DNA and B-DNA in aqueous and alcoholic solutions on the basis of an analysis of ensembles of DNA structures using a continuum solvent description. The ensembles of structures and surrounding ions were extracted from molecular dynamics simulations. The calculations indicate that favorable hydration stabilizes B-DNA in aqueous solution compared with A-DNA. In alcoholic solutions, a general reduction of solvation effects and a more tightly bound ion atmosphere appear to favor A-DNA over B-DNA. 35. Srinivasan J, Cheatham TE III, Cieplak P, Kollman PA, Case DA: • Continuum solvent studies of the stability of DNA, RNA and phosphoramidate-DNA helices. J Am Chem Soc 1998, 120:9401-9409. Ensembles of DNA, RNA and phosphoramidate-modified DNA generated using nanosecond molecular dynamics simulations were energetically evaluated with a continuum solvent model. The calculated conformational preference of the various nucleic acids is in agreement with experimentally observed trends. 36. Cheatham TE III, Srinivasan J, Case DA, Kollman PA: Molecular dynamics and continuum solvent studies of the stability of
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polyG-polyC and polyA-polyT DNA duplexes in solution. J Biomol Struct Dyn 1998, 16:265-280. 37.
Srinivasan J, Miller J, Kollman PA, Case DA: Continuum solvent studies of the stability of RNA hairpin loops and helices. J Biomol Struct Dyn 1998, 16:671-682.
38. Reyes CM, Kollman PA: Investigating the binding specificity of U1ARNA by computational mutagenesis. J Mol Biol 2000, 295:1-6. 39. Schaefer M, Bartels C, Karplus M: Solution conformations and • thermodynamics of structured peptides: molecular dynamics simulation with an implicit solvation model. J Mol Biol 1998, 284:835-848. This study demonstrates the performance of the ACE continuum solvation model for the folding simulation of two peptides. The resulting peptide conformations and conformational distributions are compatible with experimental results. 40. Zacharias M, Sklenar H: Analysis of the stability of looped-out and stacked-in conformations of an adenine bulge in DNA using a continuum model for solvent and ions. Biophys J 1997, 73:2990-3003. 41. Zacharias M, Sklenar H: Conformational analysis of single-base • bulges in A-form DNA and RNA using a hierarchical approach and energetic evaluation with a continuum solvent model. J Mol Biol 1999, 289:261-275. A systematic conformational search of a single adenine bulge and energetic evaluation using a Poisson–Boltzmann continuum solvent model selects classes of low energy structures compatible with experimentally observed bulge topologies. Unrealistic structures are selected with a distance-dependent dielectric model. 42. Gautheret D, Major F, Cedergren R: Modeling the three-dimensional structure of RNA using discrete nucleotide conformational sets. J Mol Biol 1993, 229:1049-1064. 43. Maier A, Sklenar H, Kratky KF, Renner A, Schuster P: Force field • based conformational analysis of RNA structural motifs: GNRA tetraloops and their pyrimidine relatives. Eur Biophys J 1999, 28:564-573. A variety of sterically possible GNRA tetraloop conformers were evaluated using a continuum solvation model based on a solution of the Poisson equation by atom-centered virtual dipoles. Tetraloop structures close to experimental structures are selected as low energy conformations. 44. Murthy VL, Srinivasan R, Draper DE, Rose GD: A complete conformational map for RNA. J Mol Biol 1999, 291:313-327. 45. Williams DJ, Hall KB: Unrestrained stochastic dynamics •• simulations of the UUCG tetraloop using an implicit solvation model. Biophys J 1999, 76:3192-3205. A stochastic dynamics simulation of the UUCG tetraloop using a generalized Born solvation model leads to stable trajectories. A simulation starting from a misfolded loop structure results in a transition to a conformation close to the experimental topology.
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46. Miller JL, Kollman PA: Theoretical studies of an exceptionally stable RNA tetraloop: observation of convergence from an incorrect NMR structure to the correct one using unrestrained molecular dynamics. J Mol Biol 1997, 270:436-450. 47.
Rife PR, Stallings SC, Correll CC, Dallas A, Steitz TA, Moore PP: Comparison of the crystal and solution structures of two RNA oligonucleotides. Biophys J 1999, 76:65-75.
48. Misra VK, Draper DE: On the role of magnesium ions in RNA • stability. Biopolymers 1998, 48:113-135. A review and extensive discussion of different modes of magnesium binding to RNA. 49. Misra VK, Draper DE: Interpretation of Mg2+ binding isotherms for • nucleic acids using Poisson-Boltzmann theory. J Mol Biol 1999, 294:1135-1147. An application of the Poisson–Boltzmann approach to study diffusive divalent cation binding to a cylindrical model for double-stranded nucleic acids. Good agreement between experimental and calculated magnesium-binding isotherms is observed. The free energy of magnesium binding is partitioned into various salt-dependent ion–ion, ion–DNA and entropic contributions. 50. Hermann T, Westhof E: Exploration of metal ion binding sites in RNA folds by Brownian-dynamics simulations. Structure 1998, 6:1303-1314. 51. Chin K, Sharp KA, Honig B, Pyle AM: Calculating the electrostatic • properties of RNA provides new insights into molecular interactions and functions. Nat Struct Biol 1999, 6:1055-1061. An analysis of the electrostatic potential at the surface of RNA using finitedifference solutions of the nonlinear Poisson–Boltzmann equation. Intermolecular contact regions and ion-binding sites appear to correlate with the magnitude of the electrostatic surface potential. 52. Chen Q, Shafer RH, Kuntz ID: Structure-based discovery of ligands targeted to the RNA double helix. Biochemisty 1997, 36:11402-11407. 53. Leclerc F, Karplus M: MCSS-based predictions of RNA binding sites. Theor Chem Acc 1999, 101:131-137. 54. Olson MA, Cuff L: Free energy determinants of binding the rRNA substrate and small ligands to ricin A-chain. Biophys J 1999, 76:28-39. 55. Hermann T, Westhof E: Aminoglycoside binding to the • hammerhead ribozyme: a general model for the interaction of cationic antibiotics with RNA. J Mol Biol 1998, 276:903-912. This molecular modeling and dynamics study indicates that aminoglycosides can be docked on to the hammerhead ribozyme such that several metalbinding sites are simultaneously replaced by cationic groups of the antibiotics. The result may be important for the identification of RNA ligands. It may give a hint where to place cationic sites on a ligand designed to specifically bind a structural motif in RNA. 56. Hermann T, Westhof E: Docking of cationic antibiotics to negatively charges pockets in RNA folds. J Med Chem 1999, 42:1250-1261.
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Simulation of the structure and dynamics of nonhelical RNA motifs Martin Zacharias Computer simulation methods are increasingly being used to study possible conformations and dynamics of structural motifs in RNA. Recent results of molecular dynamics simulations and continuum solvent studies of RNA structures and RNA–ligand complexes show promising agreement with experimental data. Combined with the ongoing progress in the experimental characterization of RNA structure and thermodynamics, these computational approaches can help to better understand the mechanism of RNA structure formation and the binding of ligands. Addresses AG Theoretische Biophysik, Institut für Molekulare Biotechnologie, Beutenbergstrasse 11, D-07745 Jena, Germany; e-mail: [email protected] Current Opinion in Structural Biology 2000, 10:311–317 0959-440X/00/$ — see front matter © 2000 Elsevier Science Ltd. All rights reserved. Abbreviations BD Brownian dynamics FDPB finite-difference Poisson–Boltzmann FMN flavin mononucleotide GB generalized Born MD molecular dynamics NM normal mode PB Poisson–Boltzmann snRNP small nuclear ribonucleoprotein
Introduction RNA molecules play an essential role in many biological processes. To obtain an understanding of the role and function of RNA, knowledge of both its three-dimensional structure and the forces that drive structure formation is important. At the level of secondary structure, RNA consists of base-paired (helical) regions and single-stranded or mispaired sequences that can form hairpin, internal or bulge loop structures. Biologically active RNA is strongly affected by the possible conformations and interactions of the nonhelical motifs that interrupt base-paired RNA. The experimental and theoretical study of the range of conformations accessible to these elements is important for understanding the mechanism of RNA folding. Nonhelical RNA elements do not only play a central role in the folding of RNA molecules. The biological function of the RNA is often directly related to the presence of bulges and loops, which can form recognition sites for ligands or mediate a possible catalytic activity. Some of these elements can even function as isolated structures, without the context of a larger folded RNA structure. As a result of the variety of biological functions, there is also an increasing interest in nonhelical RNA motifs as possible drug targets [1]. During the past several years, a growing number of RNA structures and RNA–protein/ligand complexes have been determined experimentally using X-ray crystallography or
NMR spectroscopy [2,3]. A wealth of information about the conformational preferences of RNA structures and conformational changes upon ligand and protein binding has been obtained. Structural studies, in combination with thermodynamic measurements and site-directed mutagenesis, allowed the analysis of the influence of individual bases and chemical groups on structure stabilization or on interactions with a ligand. Although the forces that drive structure formation are not directly visible in an experimentally determined structure, some of the important molecular interactions can be derived indirectly from observed contacts. In addition to structural and thermodynamic approaches, computer simulation methods, which are based on model energy functions that describe molecular interactions, are increasingly being used to investigate nucleic acids. Provided that the description of the intermolecular interactions is sufficiently accurate, these methods may allow more direct study of the forces that drive structure formation. In addition, simulation approaches can complement structural studies in cases in which the timescales or physical properties of interest are not easily accessible to experimental methods. It is also hoped that computer simulation methods could help to improve structure prediction and model building of nucleic acids. This review describes recent progress in computational studies at the level of a classical atom-centered force field that involve unusual RNA structures. The initial focus is on molecular dynamics (MD) simulations that include surrounding water and ions explicitly. Subsequently, computationally less demanding studies that include solvent effects implicitly are reviewed.
Molecular dynamics simulations of RNA MD simulations involve the stepwise solution of Newton’s equation of motion for the molecule and surrounding water molecules and ions. In most current MD simulations, the Ewald or the particle mesh Ewald (PME) method is employed to account for long-range electrostatic interactions within a periodic system [4,5]. Several simulation studies on RNA and DNA molecules indicate that such a treatment significantly improves the quality of the simulation compared to earlier methods with a cut-off for long-range electrostatic interactions [5–7]. Although the length of MD simulations of nucleic acids has continuously grown over the past few years, the maximum simulation time (tens of nanoseconds) is still considerably less than the time necessary to directly follow large-scale conformational changes, such as RNA folding. Nevertheless, even on the nanosecond timescale, information on the conformational flexibility of structural motifs in nucleic acids and on the lifetime of hydrogen bonds and of nonpolar contacts can be extracted. MD simulations have, for example, been
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successfully applied to study the hydration of nucleic acids. Good agreement between experimentally observed hydration sites and predictions based on MD simulations has been obtained for RNA and DNA [8,9,10••]. In addition to the ordered water molecules that can be seen in high-resolution X-ray diffraction experiments, more mobile hydration sites and hydration kinetics can be studied with the MD method.
the size of the molecule, the simulation time was limited to 0.5 ns. Although the helical stem and tertiary base pairs remained stable during the simulation, a structural rearrangement in the tRNA core that involved the slippage of three consecutive base triples was observed. The increased core flexibility might be attributed to the absence from the simulation of Mg2+ ions known to stabilize and stiffen the tertiary structure of tRNAs [18•].
During the review period, several MD simulations of RNA structures and RNA–ligand complexes that contained nonhelical RNA elements were published. A number of variants of the Escherichia coli tRNAAla acceptor stem helix have been systematically studied by Nagan et al. [11•]. The acceptor stem of tRNAAla contains a G3:U70 wobble pair (numbering corresponds to the tRNA sequence) that is the main identity element for recognition by its cognate aminoacyl-synthetase. The isolated acceptor stem can be specifically aminoacylated in vitro. The observation that some other mismatches, but not canonical base pairs, at the same position support aminoacylation has led to the suggestion that an unusual site-specific structure or flexibility is important for recognition. This view is supported by recent NMR studies [12]. On the 2 ns timescale of the MD simulations, no significant global structural perturbation or enhanced conformational flexibility for mismatch and surrounding base pairs was observed [11•]. However, a characteristic pattern of helix underwinding at the step above (in the 5′ direction) and overwinding at the step below G:U and other purine:pyrimidine wobble pairs was seen during the MD simulation. This has also been observed in NMR [12–14] and crystallographic studies [15] of the acceptor stem. Consistent with suggestions based on the crystal structure analysis [15], the MD simulations indicate that hydration at specific minor groove sites in the case of G:U and other wobble base pairs may contribute to binding specificity. The water residence lifetime at the minor groove near the wobble pair appeared to correlate with the experimentally observed aminoacylation efficiency for the corresponding acceptor stem variant.
Molecular dynamics of RNA in complex with ligands and proteins
Following earlier simulations of the isolated acceptor stem of yeast tRNAAsp [9,16], Auffinger et al. [17•] performed an MD simulation of the entire 76-nucleotide tRNAAsp. The three-dimensional tRNA structure is formed by the complex interplay of base-paired helical stem regions and several nonhelical elements. A number of base triple interactions stabilize the tRNA core structure. In principle, an MD simulation of such a system allows one to study the dynamics of nonhelical RNA elements in the context of a large RNA structure. The study by Auffinger et al. [17•] demonstrated that this is indeed possible using current MD methodology. The simulated structure remained close to the starting crystal structure and the calculated atomic fluctuations were largely compatible with experimental Debye Waller (B) factors. However, significantly larger fluctuations than expected from the experimental B-factors were found for the tRNA anticodon region. Because of
The dynamics of an RNA aptamer in complex with FMN, starting from the known NMR structure, was studied by Schneider and Sühnel [19•]. The simulation preserved all structural features characteristic of the complex, including a base triple, several noncanonical base pairs and the position of the ligand. A number of water-mediated contacts within the RNA and between the RNA and ligand with lifetimes of approximately 0.5 ns have been observed. Interestingly, the MD simulation indicated that water molecules, although having donor as well as acceptor capabilities, act preferably as donors in hydrogen bonding interactions with the 2′-OH group of RNA. The authors described several C2′–H⋅⋅⋅O4′ contacts between riboses of neighboring nucleotides. Such contacts have been found in previous MD simulations and have been proposed to stabilize RNA [16,17•]. Various aspects of RNA–protein interactions have been investigated by three groups studying the U1A–RNA complex. The U1A protein is a component of the U1 small nuclear ribonucleoprotein (snRNP) component, which is involved in RNA splicing. It binds with a picomolar Kd to an eight-nucleotide, nonhelical loop structure. The binding element can be either part of an RNA internal bulge loop (as part of the U1A mRNA) or a hairpin loop in the U1 snRNP itself. Reyes and Kollman [20•] compared the MD of the U1A protein in complex with either the RNA hairpin loop or the internal bulge loop, starting from experimental structures. For both complexes, the experimentally observed interaction pattern between the protein and RNA was largely conserved during the simulations. Overall, the U1A–internal loop complex appeared to be significantly more flexible than the U1A–hairpin loop complex during the simulation. This was manifested in larger average atomic fluctuations and a smaller number of stable intermolecular hydrogen bonds in the simulation of the internal loop complex. In addition, a global conformational change was observed in the case of the internal loop complex that involved a shift in the angular orientation of the loopflanking helices. The observed hinge motion was compatible with experimental (NMR) constraints. Tang and Nilsson [21] focused on comparing the dynamics of the U1A–RNA hairpin complex with that of the free RNA hairpin. The starting structure for the MD simulation
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of the free RNA hairpin was taken from the X-ray structure of the U1A–RNA hairpin complex [22]. The free RNA loop appeared to be much more flexible than in complex with the protein, indicating that it may not adopt a single distinct conformation in the unbound state. Such adaptive conformational transitions upon ligand binding have been observed experimentally in several nonhelical RNA motifs [23]. Most of the hydrogen bonds and van der Waals contacts suggested by the X-ray analysis of the U1A–RNA hairpin complex [22] were stable during the simulation of the complex. The affinity of the U1A protein to the RNA binding region depends strongly on the salt concentration, demonstrating that electrostatic interactions are a major driving force for complex formation. Hermann and Westhof [24] followed the dynamics of the U1A–RNA hairpin complex upon increasing the salt concentration from 0.1 to 1 M in the course of an MD simulation. A significant enhancement of RNA and, to a lesser degree, protein conformational fluctuations was observed following salt addition, which may indicate the onset of RNA–protein dissociation. Although the simulation time (~1.5–1.8 ns at each salt concentration) was orders of magnitude shorter than the expected dissociation time for an RNA–protein complex, such simulations may give hints about the initial events of the process.
Normal mode analysis of RNA In the normal mode approach, information on the flexible degrees of freedom of a molecule is extracted from the curvature of the energy function at an energy minimum. The advantage of this approach is that it can be computationally much less demanding than MD simulations, particularly if an internal coordinate description is used. However, solvent and ions are usually not included explicitly and conformational transitions between conformational substates cannot be considered. A normal mode (NM) analysis of tRNAPhe using torsion angle variables and including sugar pucker flexibility was performed by Matsumoto et al. [25•]. A conclusion from the NM study was that, because of its shape, tRNA is considerably softer than, for example, a globular protein. The calculated harmonic mobility of tRNAPhe was characterized by the motion of three subdomains corresponding to the acceptor stem, anticodon loop and a part consisting of the D arm, variable loop and T arm. The flexibility of tRNA has also been investigated using a very simple model that consisted of one interaction center per nucleotide and assumed an energy function that basically depends on the local packing density [26]. Even this simple model predicted nucleotide mobilities for free tRNAs and a tRNAAsp–aminoacyl-synthetase complex that are close to experimental B-factors. This result suggests that local packing density significantly determines the direction and magnitude of the flexibility of RNA molecules around a stable structure.
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The harmonic deformability of regular duplex RNA and bulge- and mismatch-containing RNA has been compared [27•]. Calculated helical coordinate fluctuations of regular duplex RNA and A-DNA showed reasonable agreement with experimental data from statistics of A-DNA crystal structures [28]. A significant anticorrelation of helical coordinate fluctuations of neighboring base pairs was observed. As a consequence, RNA is predicted to be globally stiffer than expected from the local base pair step flexibility. Most mismatches and bulges slightly increased the calculated harmonic flexibility, with the exception of tandem G:A mismatches in the sheared conformation, which were predicted to stiffen RNA. Similar to NM studies on DNA [29,30], only a few major bending modes were identified, consisting of mainly coupled roll and slide changes of neighboring base pair steps.
Free energies from molecular dynamics and implicit solvent approaches An ultimate goal of computer simulation studies is to calculate conformational preferences and relative conformational stabilities from molecular simulations. Free energy differences between two conformational substates of a molecule can be calculated using thermodynamic integration or perturbation techniques along a reaction path for the conformational transition. Using such an approach, Stofer et al. [31•] studied base pair formation and dissociation in aqueous solution along one direction to separate the bases. The calculated free energies for base pair formation were compatible with an expected hydrogen bond free energy of approximately –2 kcal mol–1. Solvent-separated secondary free energy minima (~1.0 kcal mol–1) were observed for both A:T and G:C base pairs. Such watermediated contacts may stabilize noncanonical base pairs in RNA [32]. Besides gaining insight into the energetics of base pair formation, the free energy simulations can be helpful for developing effective energy functions for calculations that employ implicit solvent models (see below). The definition of an appropriate reaction path can, however, become difficult if several conformational variables change simultaneously to achieve a desired conformational transition. In addition, the calculated free energy difference depends strongly on the relaxation timescales of the structural perturbation and conformational sampling along the selected path. Several recent studies use an approximate approach that applies MD simulations only to generate ensembles of structures compatible with the conformational regions of interest. A free energy estimate is obtained by taking averages of the various intramolecular energy terms over the ensemble. The solvation free energy of the structures is calculated using a mean field approach for solvent and ions that is based on either the finite-difference Poisson–Boltzmann (FDPB) approach or the generalized Born (GB) method. In these approaches, the molecule is treated as a low dielectric cavity surrounded by a high dielectric continuum representing the aqueous environment. Nonpolar solvation
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contributions are calculated from the solvent accessible area of the molecules (see a recent review by Cramer and Truhlar [33•]). Conformational entropy effects can be estimated by quasi-harmonic analysis of the MD trajectory or by harmonic mode analysis of one representative conformation. Although the discrete nature of the solvent is completely neglected in such approaches, experimentally observed trends for the relative stabilities of a number of nucleic acid structures could be reproduced. For example, Jayaram et al. [34•] compared the relative stabilities of ensembles of A-DNA and B-DNA conformations in (salt-containing) aqueous and alcoholic solutions. In agreement with experiment, the calculations predicted B-DNA to be the preferred form in aqueous solution because of its more favorable solvation compared with A-DNA. In alcoholic solution, the overall reduction of solvation effects and a more strongly bound ion atmosphere preferentially stabilized A-DNA. Srinivasan et al. [35•] could reproduce experimentally observed trends for the conformational preferences of B-DNA, A-DNA, RNA and phosphoamidate-modified DNA in aqueous solutions. Using a similar approach, Cheatham et al. [36] calculated a significantly greater ‘A-form-philicity’ for ensembles of poly(G/C) structures than for poly(A/T), in agreement with experiment. The method has also been applied to study the relative stabilities of RNA loop structures. Starting from experimentally known UGAA and UUCG tetraloop structures, MD simulations have been performed to generate ensembles of alternative hairpin loop conformations [37]. On the basis of continuum solvent modeling, the predicted low free energy forms for the two structures agreed with experimentally observed conformational preferences of the corresponding loops. The approach could potentially be useful for several other applications, such as ligand binding to nucleic acids [38].
Simulations and conformational searches of RNA motifs with an implicit solvent representation One limitation of MD simulations that include ions and water molecules explicitly is that conformational transitions often occur on timescales that are large compared with the MD simulation time. Even if one starts from different initial conformations, the convergence to stable structures can be slower than the maximum simulation time, because of various slow relaxing conformational variables. Ultimately, however, the systematic conformational analysis of a given RNA motif is desired in order to get an impression of the range of possible conformations and the energetic order. Conformational searches that neglect solvation effects are computationally rapid, but the calculated structures and energies can be very unrealistic. A number of recent studies have demonstrated that the implicit inclusion of solvation effects, either through solving the PB equation or using the GB model, can significantly improve conformational searches and stochastic dynamics simulations. This was shown for peptide systems [39•] and also for nucleic acids.
Large numbers of sterically possible conformations were systematically generated for single unmatched adenine nucleotides in DNA and RNA [40,41•]. The energetic evaluation based on the FDPB continuum model selected classes of low energy bulge structures that are similar to experimental bulge topologies. The tetraloop sequence GNRA adopts a well-known characteristic fold. Using the MC-SYM (macromolecular conformations by symbolic programming) conformational generator [42], a large variety of sterically possible tetraloop conformations were generated [43•]. The energetic evaluation of these conformations through solving the Poisson equation by atom-centered virtual dipoles picked out structures close to the experimental GNRA loop structure as being those of lowest energy [43•]. In contrast, for both the bulge and the tetraloop systems, treatment of electrostatic interactions with a distance-dependent dielectric constant selected unrealistic structures (in disagreement with experiment) as being those of low energy. Systematic studies on sterically preferred conformations for mononucleotides and dinucleotides can be helpful to reduce the conformational search space in these approaches [44]. A nanosecond stochastic dynamics simulation of the UUCG tetraloop with an implicit solvent model was performed by Williams and Hall [45••]. Treatment of the electrostatic interactions with the GB model lead to trajectories that stayed close to the experimental structure, with conformational fluctuations similar in magnitude to those obtained with an MD simulation with explicit solvent [46]. In addition, starting from an older low-resolution NMRderived structure of the loop that contains an ‘incorrect’ loop closure base pairing scheme led to the formation of the ‘correct’ pairing scheme, compatible with the refined NMR analysis, during the course of the simulation. In contrast, a stochastic simulation with a vacuum treatment of the electrostatic interactions resulted in conformations with significant deviation from the experimental loop structure. Most current protocols for structure determination from NMR data neglect solvation effects [47]. The more realistic treatment of solvation effects in the above-mentioned continuum solvent modeling approaches might be helpful for nucleic acid structure generation from a limited set of experimentally derived constraints.
Modeling ion and ligand binding to RNA The association of ions with RNA plays a key role in the formation of stable three-dimensional structures. Folded conformations of negatively charged RNA are stabilized by a diffuse counterion atmosphere and by specifically bound ions that can be partially dehydrated. Noncanonical base pairs and other nonhelical RNA structures are often part of these ion-binding sites. Ion binding is influenced by the local electrostatic field, the geometry of the binding pocket and also by the degree of ion desolvation upon association [48•]. Theoretical studies of RNA–ion association can be further complicated by the fact that ion binding
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(and the binding of other ligands) may significantly change the conformation or conformational distribution of the RNA molecule. Solutions of the (nonlinear) PB equation can be used to get an impression of the electrostatic field and the mean ion distribution around nucleic acids. Using the PB theory, Misra and Draper [49•] studied the diffusive ion association to cylindrical models of nucleic acids in a mixed salt solution consisting of monovalent co-ions and monovalent and divalent counterions. Good agreement between calculated and experimental magnesium-binding isotherms for DNA and poly(AU) at different sodium concentrations was found. The calculations indicate that added co-ions may also play an important role in the stability of nucleic acids. FDPB calculations, in combination with Brownian dynamics (BD) simulations, were used to study the diffusion of divalent cations around known RNA structures [50]. In the BD simulation, a charged sphere diffuses under the influence of the RNA electrostatic field and settles in binding regions with a negative electrostatic potential. The ion is treated as test charge; ion desolvation effects are not included. Experimentally observed ion-binding positions could be reproduced for several known RNA structures. Chin et al. [51•] looked at isopotential contours and surface potential maps of the electrostatic field (from FDPB calculations) for experimentally determined RNA structures. Known cation-binding sites were observed to correlate with regions of calculated negative electrostatic potential. Interestingly, characteristic holes in the electrostatic surface potential (regions of reduced electrostatic potential) were found close to some nonhelical RNA elements. These sites correspond to known RNA RNA-binding and ligand-binding positions. Although computational approaches are already used extensively to identify possible ligand candidates for proteins, applications to nucleic acids are still very limited (reviewed in [1]). As nonhelical RNA structures play an important role in many biological processes, these are also attractive targets for drug discovery. Methods initially developed for docking ligands to proteins have also been applied to identifying possible RNA-binding ligands [52,53]. Olson and Cuff [54] used a continuum solvent approach to predict the binding of RNA model structures and small ligands to ricin A. Ricin A is a small ribosomeinactivating protein that specifically depurinates an adenine in a GAGA tetraloop. Reasonable agreement between experimental and calculated binding free energies was obtained. Hermann and Westhof [55•] attempted to explain the binding specificity of cationic antibiotics to various nonhelical RNA motifs, speculating that positive charges on the antibiotics replace divalent-ion-binding sites on the RNA. An aminoglycoside antibiotic provides a framework of positively charged groups that fits into regions of negative electrostatic potential normally occupied by ions. On the basis of this model, known
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aminoglycoside-binding sites in experimentally determined complexes could be successfully identified [56]. Putative binding positions for cationic antibiotics in the hammerhead ribozyme [55•] and HIV TAR element have also been suggested [56].
Conclusions MD simulations are now widely used to study regular nucleic acid structures, as well as nonhelical motifs. One of the most important purposes of these studies is to continuously check and improve the simulation model and force field by comparing computational results with available experimental data. Very reasonable agreement between many simulated structures and experimental start structures for RNA and RNA–ligand complexes has already been achieved. It is likely that, in the not too distant future, simulation times of 0.1–1 µs or beyond will be possible for nucleic acids. Such simulations may allow the direct characterization of small conformational rearrangements and, ultimately, certain aspects of RNA folding. The successful prediction of conformational preferences of small experimentally known nucleic acid structural motifs using continuum solvent models indicates that these rapid approaches could improve energy-based prediction methods. At the expense of a less accurate solvent representation compared with MD simulations with explicit solvent, these methods hold the potential for much longer simulation times and a greater variety of sampled conformations. Many applications, ranging from the conformational analysis of RNA motifs to studies of ligand binding, are possible and can contribute to the understanding of RNA structure, function and ligand association.
Acknowledgements I thank Felipe Pineda, Heinz Sklenar and Paul Hagerman for helpful discussions.
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