Calculations of nucleic acid conformations

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Calculations of nucleic acid conformations Shirley Louise-May, Pascal Auffinger* and Eric Westhoff The present computational power and sophistication of theoretical approaches to nucleic acid structural investigation are sufficient for the realization of static and dynamic models that correlate accurately with current crystallographic, NMR and solution-probing structural data, and consequently are able to provide valuable insights and predictions for a variety of nucleic acid conformational families. In molecular dynamics simulations, the year 1995 was marked by the foray of fast Ewald methods, an accomplishment resulting from several years' work in the search for an adequate treatment of the electrostatic long-range forces so primordial in nucleic acid behavior. In very large systems, and particularly in the RNA-folding field, techniques originating from artificial intelligence research, like constraint satisfaction programming or genetic algorithms, have established their utility and potential.

Addresses Institut de Biologie Moleculaire et Cellulaire du Centre National de la Recherche Scientifique, Modelisations et Simulations des Acides Nucleiques, UPR 9002, 15 rue Rene Descartes, 6?084 Strasbourg Cedex, France * e-mail: [email protected] +e-mail: [email protected] Current Opinion in Structural Biology 1996, 6:289-298

© Current Biology Ltd ISSN 0959-440X Abbreviations bp base pairs CSP constraint satisfaction programming 2D two-dimensional 3D three-dimensional DFT density functional theory GA genetic algorithms HF Hartree-Fock MC Monte Carlo MD molecular dynamics MD-PT molecular dynamics perturbation thermodynamics MM molecular mechanics MMD multiple molecular dynamics MP2 second order Moller-Plesset perturbation theory PME particle mesh Ewald QM quantum mechanical rms root mean square SCF self-consistent field

Introduction Theoretical nucleic acid conformational investigations have, thus far, mainly been concerned with the elucidation of the factors that govern sequence-dependent conformational properties. However, the potential therapeutic applications and growing experimental data on complexes between nucleic acid and small molecule ligands, drugs and proteins, and the effect of carcinogenic modifications on standard nucleosides have widened the focus of current theoretical studies. Perhaps the largest contributions to the

current understanding of nucleic acid conformation come from studies of nucleic acids with unusual conformations or structural motifs: chimeric or R N A - D N A hybrids, parallel-stranded helices, triple helices, quadruplexes, and other telomere-like structures. Computational methods allow for the visualization of large amounts of structural data and the generation of related conformations for statistical and dynamic analyses. The application of thcse methods to systems of biological interest has advanced tremendously in recent years to encompass models that describe local conformational effects with great precision: such as quantum mechanical (QM) studies of the effect of substituent modifications, methods that perform statistical energy-guided conformational searches such as energy minimization, Monte Carlo (MC) and molecular dynamics (MD) simulations, and algorithms that aim to describe the collective structural constraints that influence macromolecular tertiary structure, folding pathways and the energetics of supercoiling. Nucleic acids are highly charged molecular species that interact strongly with their solvent environment and other solutes over potentially long distances. The long-range electrostatic forces greatly influence the delicate balance of structural forces at play in conformations of nucleic acids and their complexes. As such, the correct treatment of these long-range electrostatic forces constitutes a baffling challenge to accurate computational models of nucleic acid conformations. Early theoretical models were limited by computational resources and could neither include an explicit representation of all components of the nucleic acid system nor be calculated for a long enough time to ensure sufficient sampling and system convergcnce. Recent increases in theoretical complexity and computational power allow for more accurate and comprehensive representations of thc nucleic acid environment as well as more extended calculations or longer MD simulations, including multiple or comparative studies as well as the investigation of very large systems. Here we review the methods used for thc calculations of nucleic acid conformations and highlight the most recent studies that push back the limits of the current methodologies or realize highly accurate computational models of nucleic acid systems.

Precise molecular geometries, parameters and interaction energies The geometries and calculated stabilities of normal, tautomeric and novel hydrogen-bonded base pairs generally demonstrate good correlation at the STO-3G and 4-31G level [1,2] with high-resolution cwstallographic structures and thermodynamic data. Such methodologies, combined with a recently developed restrained electrostatic potential (RESP) fitting procedure, have been used in

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the calibration of a new molecular mechanics (MM) force field for nucleic acids [3°,4°]. Although relative interaction energies of hydrogen-bonded base pairs can be sufficiently described at the ab initio Hartree-Fock (HF) self-consistent field (SCF) level, quantitative energies and molecular properties involving conformations in which dispersion energies dominate, such as base stacking, are obtained by using the H F - S C F methods as a first-step geometry optimization before implementing methods that take into account the effect of electron correlation, such as second order Moller-Plesset perturbation theory (MP2) [5]. Density functional theory ( D F T ) is an alternative to conventional quantum mechanical calculations based on calculated wave functions and can yield similar conformational properties as HF and MP2 calculations at a lower computational expense. D F T has been used on small organic molecules of biological interest in an attempt to attain a more accurate parametrization of semi-empirical molecular mechanics potentials by St. Amant et al. [6°]. Conversely, a semi-empirical charge equilibration model was used by Bakowies and Thiel [7] for the parametrization of a combined Q M - M M potential. In combined Q M - M M calculations, the Hamiltonian is partitioned into QM, MM and Q M - M M potentials, with the latter directing the extent of interaction between the former two. These methods have been applied to water-dimer and ion-solvation interactions using an H F - M M potential [8]. Q M - M M coupled potentials have been applied, by Elcock et al. [9°], to the DNA crosslinking reaction of nitrous acid to determine sequence preferences. Relative energy barriers were found to be higher for 5'GC than for 5'CG step cross-linking for six variant sequences ofa B-DNA dodecamer, correlating well with available experimental data. An iterative Q M - M D method was applied by Laughton eta/. [10"] to an all-atom DNA dodecamer in the presence

of counter-ions and water to generate a more accurate partial-charge distribution for the phosphate backbone and to study the counter-ion distribution and geometry around a B-DNA double helix. An initial MD trajectory of a solvated and neutralized DNA dodecamer was used to classify sodium ion positions into 13 subfamilies and compute populations of these subclasses to use in a QM (RHF) calculation of new phosphate backbone charges. T h e new charges were then used in the generation of a new MD trajectory and this process was iterated until no appreciable change was observed in either the ion distribution or the calculated charges. This procedure resulted in distinct charges for the two anionic phosphate oxygens. In two independent free MD runs each of 150 ps, using the final QM-derived phosphate backbone charges, a predominance of indirect counter-ion-DNA interactions was noticed. Furthermore, counter-ions preferred to interact with one phosphate oxygen instead of bridging two adjacent ones around B-DNA.

Potential of mean force calculations were used by Norberg and Nilsson [11",12] to map the free-energy change between stacked and unstacked conformations along a reaction coordinate connecting base glycosidic nitrogens for the 32 solvated and neutralizcd DNA and RNA dinucleoside monophosphates. T h e calculated conformational properties and effect of desolvation in the stacking process was found to be in accord with experimental data, reflecting a delicate balance of solvent and dispersion forces. T h e relative free energies of solvation of thymine and uracil were calculated by Plaxco and Goddard [13"] using molecular dynamics perturbation thermodynamics ( M D - P T ) analysis of explicitly solvatcd A.T and A.U free base pairs and in the context of a full B-DNA turn. T h e results indicate that the energetic cost of solvating the thymine methyl group is the primary factor in the observed sequence specificity of thymines in protein-DNA complexes, and not the direct van der Waals interactions between the methyl group and elements of the protein.

Local c o n f o r m a t i o n a l structure and dynamics A powerful MM technique for mapping the potentialenergy surfaces of user-defined conformations of DNA and RNA double helices, incorporated into the JUMNA program developed by Lavery and co-workers [14], was used to systematically investigate the effect of sequence-dependent local conformational variations in terms of possible B-DNA substates [15]. Their results indicate that a dominant influence is exerted by the sugar pucker conformation on the allowed conformational states and local structural variations. T h e JUMNA programs currently employ an implicit model of the nucleic acid environment through a sigmoidal distance-dependent dielectric function and are therefore ideal for very broad based studies in which a large number of different initial conformations are investigated. T h e y are particularly geared towards the systematic analysis of helical axis bending properties and helical groove dimensions [16] and are therefore useful in the analysis of protein-DNA and d r u g - D N A interactions. For precise dynamical analyses of local structural interactions in nucleic acid systems and especially those involving RNA, it has been found, however, that explicit representation of the counter-ion and solvent environment is necessary [17]. Yet, the increase in the complexity of MD systems has revealed a high level of sensitivity of the structural results to the initial conditions of the system (e.g. starting configuration and equilibration procedure). An extensive comparative study of slightly variant equilibration protocols applied to the same initial configuration [18*], call into question the issue of the stability of current MD protocols, particularly the treatment of long-range electrostatic interactions through truncation methods. The use of multiple molecular dynamics (MMD) trajectories, that is, the generation of a set of t, ncorrelated MD

Calculations of nucleic acid conformations Louise-May,Auffingerand Westhof

trajectories all starting from the same initial configuration, was proposed to evaluate the degree of stability of these MD protocols.

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T h e greatest challenge in the generation of accurate MD trajectories lies in the area of the treatment of long-range electrostatic interactions. T h e considerable computational expense associated with the explicit representation of the nucleic acid environment necessitated the use of truncation methods to bring the interaction energy between two non-bonded atoms beyond a certain distance, typically around 10/~, to zero. However, a variety of documented artefacts emerged from studies employing even very largc truncation distances [19]. With the use of an M M D approach to specifically address the electrostatic model dependence of protocol stability, three sets of 100 ps MD trajectories on the anticodon hairpin and one set on the tRNAAsp thymine hairpin were conducted [20°]. Divergent and unstable trajectories were found as a result of using the application of an 8 ~ cut-off to interactions involving the solvent only (all solute-solute interactions were calculated explicitly; Fig. 1). T h e doubling of these truncation distances to 16/~. demonstrated the structuring effect of long-range solvent interactions on the anticodon hairpin system (Fig. 1; [21°']), and it was proposed that such forces, that is, solvent interactions beyond 8 ~, could play a definite role in folding and recognition processes. However, even 16~ solvent truncation distances led to artefactual counter-ion behavior in the thymine system, preventing the extension of these trajectories to longer timescalcs I20°1. Ewald methods, which impose a crystal-like periodicity to the MD system, can be used to calculate all non-bonded interactions without truncation. Recently, new algorithms have been developed which considerably reduce the amount of computer time needed by such calculations [22,23]. Nucleic acid trajectories generated using fast particle mesh Ewald (PME) methods (implemented in the AMBER 4.1 package [24]) or other adapted Ewald methods have been found to be stable over the nanosecond time regime and to display low root mean square (rms) deviations from the starting configurations of some DNA and RNA systems (Fig. 1): for example, a B-DNA dodecamer and an RNA tetraloop hairpin simulation [25°°]; RNA dinucleotides [26], B-DNA dodecamer [27 °°] and Z - D N A hexamer [28] crystal unit cell simulations; a 200 ps 14-nucleotide RNA hairpin simulation [29]; six 500ps MMD trajectories of the anticodon hairpin fragment [30] and a 500 ps MD trajectory of the 75-nucleotide tRNAAsp molecule ([31°]; P Auffinger, S Louise-May, E Westhof unpublished data). Although the full ramifications of the PME or other Ewald methods have yet to be fully revealed, these theoretical and technical advances have introduced a new level of resolution to MD methods that allow for more quantitative comparison to crystallographic and N M R data. As an example, the level of resolution achieved by these methods can be assessed by the

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characterization of weak but dynamically stable C-H..-O hydrogen-bond interactions in the tRNAAsp anticodon loop system (Fig. 2; [21"*]). Furthermore, structurally important water molecules with residence times longer than 500ps (the length of the MD simulation) have been characterized in a phosphate-bridging position in RNA systems, making additional C-H.-.Ow stabilising hydrogen-bond contacts [31"]. Modified nucleosides, and drug- and protein-binding interactions

Studies of the structural effect of nucleic acid carcinogenic modifications usually begin with an HF-level parametrization of the modified nucleoside followed by MM or MD treatment in a helical structural context and sometimes include a control of the unmodified structure. Such studies

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Two examples of C-H...O hydrogen bonds, (uracil 33)O2..H5-C5 (cytosine 36) and (uracil 33)O2'..H5-C5(uracil 35), observed in the crystallographic structure (hydrogen atom positions have been estimated) are shown together with their time evolution for one MD trajectory of the tRNAAsp anticodon hairpin generated using a 16/~ solvent truncation scheme. The hydrogen bond distances (shown as dotted lines) are given in A. C, cytosine; U, uracil. Reproduced with permission from [20°].

were conducted on UV radiation products of DNA bases [32°]. In agreement with available experimental data, both studies found that the effect of the modification, although marked in some cases, remains structurally and dynamically localized. DNA-drug binding interactions have been modelled recently by several techniques that allow the easy study of variant binding modes or analog variants. All of the following studies conducted an ab initio parametrization of the drug molecules studied. The relative energetics of the possible binding modes of Troeger's bases with eight repeating sequences in the B-form of DNA was systematically explored using the JUMNA suite of programs by Coppel et al. [33]. The difference between the DNA-binding properties of distamycin and an analog of distamycin were studied by molecular dynamics-free energy perturbation (MD-FEP) simulation [34]. The general method of M D - F E P calculations is discussed and an application to the design of anti-HIV drugs is outlined by McCarrick and Kollman [35]. To help direct optimization of elsamicin derivatives, elsamicin parameters derived by ab initio methods were used in combined in vacuo/in aquo MD studies of elsamicin A bound to two DNA decamer sequences [36]. Key drug-DNA interactions were analyzed in detail in MD trajectories containing both explicit water and counter-ions.

DNA-protein complexes provide a rich system for the study of many key structure-mediated biological processes: recognition, binding, water-mediated interactions, desolvation and hydrogen bonding. Because of their size, however, few all-atom dynamic modelling techniques have been applied so far. Zacharias et al. [37] performed conformational searches involving the flexible docking of the DNA and protein combined with Poisson-Boltzmann calculations of the electrostatic contributions to the binding specificity. They investigated the effect of sequence mutations in the DNA lambda repressor-operator complexes. MD simulations of the glucocorticoid receptor protein-DNA complex were reported recently by two groups using the CHARMm force field. Harris et al. [38], starting from NMR-derived coordinates, compared two MD protocols: a 30 ps water-droplet MD trajectory and a 300 ps periodic water-box MD trajectory. Eriksson et al. [39 °] conducted water-droplet simulations starting from the crystallographic coordinates of the dimer protein-DNA complex. Both studies reported the bending of the DNA sequence by protein-DNA interactions and extensive networks of localized water-mediated protein-DNA interactions. However, in the periodic water-box trajectories by Harris et al. [38], the protein-DNA interactions induced the rupturing of Watson-Crick hydrogen bonds and unwinding events in the DNA conformation. U n u s u a l nucleic acid c o n f o r m a t i o n s Chimeric duplex DNA-RNA hybrids

Chimeric duplex DNA-RNA hybrids, key elements in transcription, reverse transcription and replication processes arc being investigated for their potential therapeutic applications in antisense technology. Chimeric systems lend themselves easily to theoretical investigation because the slight chemical difference between ribose and deoxyribose residues, almost too trivial to build by theoretical modeling techniques, produces considerable structural and functional consequences readily measurable by experimental means. Sanghani and Lavery [40] explored the conformational energetics of four possible DNA-RNA hybrid sequences to determine sequence dependencies using JUMNA algorithms. MD simulations of an r(GAlzG)-d(CTIzC) hybrid duplex were compared to the non-hybrid deoxy duplex sequence starting from both the A-form and B-form geometries by Fritsch and Wolf [41]. Both studies conclude that there are very different geometries observed in the two strands of the hybrid, with the RNA strand relatively inflexible and only exhibiting minimal deviation from A-form helical parameters and a DNA strand with greater flexibility which, on average, maintains B-form helical values. Antisense technology is aimed at designing modified oligonucleotides that bind to mRNA in hybrid duplexes with higher affinities than natural oligonucleotides. In addition, the modified oligonucleotides must be nuclease resistant and cell permeable to potentially provide a selective chemotherapeutic strategy. Modifications to the

Calculations of nucleic acid conformations Louise-May, Auffinger and Westhof

backbone that preserve the conformational features of the unmodified phosphate DNA backbone offer some promising leads. In vacuo MD studies of R N A - D N A hybrids with an amide-modified backbone [42 °] reveal that the hydrogen-bonding schemes of the hybrid are preserved. T h e amide-linkage modification slightly affects the sugar conformation of the DNA strand and leaves the RNA strand intact. A thiophosphate-modified backbone D N A - R N A hybrid solution structure was solved by NMR-restrained M D techniques using time-averaged NMR restraints (MD-tar). T h e study by Gonzalez et al. [43 ° ] revealed only minor differences in the backbone conformation of the DNA strand compared to an unmodified B strand. A comparison to standard restrained MD refinement results for this system indicate that the MD-tar description of the sugar-puckering modes in the modified hybrid duplex is a distinct improvement. MD-tar [44] was developed for the dynamic interpretation of NMR data to allow the generation of energetically relevant structures. The method requires that N M R experimental distance and torsion angle constraints need only be satisfied for an ensemble of generated structures thus reflecting that the NMR data sample represents a time-average conformation.

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(170ps), and the analyses of the counter-ion and solvent distribution functions and diffusion constants document well the integrity of this study. T h e reported final rms deviations of 1.5~ with a slight upwards drift indicated local conformational heterogeneity and no severe distortions [48°°]. A similar MD procedure was applied to an antiparallel d(CG-G) 7 triple helix containing a G C - T mismatch at the center of the sequence [49°]. A 1.Sns trajectory was generated. The local conformational effect of the mismatch is discussed in terms of the mobility of the mismatched thymine and local water-DNA interactions. T h e solution structures of mixed sequence purine-purinepyrimidinc and pyrimidine-purine-pyrimidine triple helices formed by single-stranded DNA-containing novel base triple interactions (T-CG, C+-GC and G - T A ) using MD with NMR restraints were determined by Radhakrishnan and Patel [50,51°]. T h e MD refinement protocol included solvent and counterions with 7.5-8.0/~ cut-offs on non-bonded interactions. A small number of final superimposable structures were generated by an iterative process of short MD cycles (1-3ps) starting from multiple initial structures. An analysis of patterns of hydration is also discussed.

Triplex helices of DNA and RNA

In order to generate an RNA triple helix without sterically forbidden short contacts, a linked-atom least squares algorithm without energy reference was employed by Raghunathan et al. [45]. T h e authors hold that constraints due to the addition of the third chain greatly restricts the allowed conformational space. T h e base-pairing scheme attempted for the rU-rA-rA triple helix was Watson-Crick-Hoogsteen and resulted in three identical and symmetry-related chains. The orientation and hydrogen bonding of the third strand of d T - d A - d T triple helices investigated by model building and energy minimization studies by Kiran and Bansal [46] led to the prediction of a parallel orientation. Both A-form and B-form Watson-Crick helices investigated in 200ps AMBER 4.0 in vacuo MD trajectories yielded structures with mixed A- and B-form character: B-form sugar and backbone conformations, but more A-form like base and base-pair parameters. Free energy MM calculations of continuum and explicit solvent models of DNA triple helices conducted by Cheng and Pettitt [47], however, reveal that solvent continuum models cannot differentiate the thermodynamics of the occupied major groove to accurately predict relative stabilities. Backbone and sugar-pucker conformation analyses on 704 starting structures for d(CG-G) 7 and d(TA-T) 7 DNA triple helices (Watson-Crick reverse Hoogsteen pairing) generated by sugar-pucker, twist and rise variations are in agreement with the aforementioned triple-helix studies. Solvated MD studies in the presence of excess salt were continued for the d(CG-G) 7 model for 1.3ns using Ewald summation for the electrostatic calculations, T h e electrostatic model, the prolonged equilibration procedure

DNA telomeric structures

In order to evaluate the conformational polymorphism in telomeric structures, loop orientation and interloop pairing schemes were evaluated by Mohanty and Bansal [52], using model building and energy minimization studies in the presence of explicit solvent. T h e stability of various conformational tetraplexes was discussed in terms of the hydrogen-bonding patterns, the backbone and glycosidic torsions, the stacking interactions, the number of thymines in the loop and the cation binding. A solution-structure model of the dimeric hairpin quadruplcx d(G3T4G3) was refined by MD with NMR restraints techniques and investigated by in vacuo unrestrained MD simulations by Strahan e t a / . [53°]. The conformational features of novel adjacent syn-svn deoxyguanosines are discussed.

Other dynamics techniques Although the problem is much researched, only a few new techniques extending the limits of classical MD protocols in size and timescales have appeared. Briki and Genest [54] used a canonical analysis of the correlated atomic motions on a 200 ps explicitly solvated MD simulation of an octamer DNA duplex. They concluded that the internal dynamics of this oligonucleotide may well be described by rigid-body motions, suggesting the use of a reduced number of degrees of freedom for simulating long-time dynamics of nucleic acid fragments. Such simulations could be useful in the interpretation of N M R data for which sampling on long timescales is required, or for simulations of large macromolecular systems. Classical MD methodology was modified by Harvey and Gabb [55] to allow for conformational transitions

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encountered rarely in free MD simulations. T h e variation of a single monotonic parameter is used to deliver the system from an initial to a final state without imposing any intermediate conformational constraints and can be applied to both small systems, for the induction of rare events, or large systems, for the induction of slow collective motions. As an example, the C O N T R A MD method (conformational transitions via MD) was applied to the simulation of a largescale hinge-bending motion in a tRNA phe molecule. Normal mode calculations express the conformational energy of a molecule in terms of generalized coordinates, typically the dihedral angles of the system, while the bond lengths and angles are held fixed. T h e application of this method to transfer RNA systems was undertaken to help interpret the spectral probing data of conformational changes in protein-tRNA interactions [56].

R N A tertiary structure and folding Secondary and tertiary RNA structure has finally attracted a lot of attention in recent years. Compared to the diverse structural complexity of proteins, its apparent, but deceptive, simplicity (only four bases and base-pairing rules, but complex multiple loops and alternative conformations) makes RNA a valuable study object for theoretical modeling. In addition, the folding hierarchy is pronounced in large RNA systems so that, to a large extent, two-dimensional (2D) and three-dimensional (3D) foldings can be considered separately and in a stepwise fashion following the observation that the 2D structure is energetically the strongest component of the 3D structure (for a discussion, see [57]). T h e two main methods currently employed to deduce RNA 2D structures, comparative sequence analysis and free-energy minimization, are now used more systematically in synergy and several programs allow the identification of consensus secondary structures from homologous sequences [58,59]. Comparisons between foldings derived from free-energy minimizations and from phylogenetic sequence analysis [60,61] show that the agreement depends on the phylogenetic origins (e.g. eubactcrial 16S rRNAs compare better than mitochondrial 16S rRNAs) and on the particular region ofa RNA (some 'well-defined' helices agree up to 80% between the two methods). Genetic algorithms (GA), which simulate competition between intermediate solutions in order to yield improved and optimized solutions, have been applied to the prediction of optimal and suboptimal 2D structures [62] and to the simulation of RNA 2D folding pathways [63°]. Although such computationally intensive methods are not convincing for large and highly structured RNAs, like the Tetrahymena ribozyme, where the folding is thermodynamically controlled, they could be very useful in small functional RNAs with metastable states, some of

which might be under kinetic control, possibly influenced by protein binding. A new procedure that allows the unbiased incorporation of constraints before and during the RNA folding process exploits constraint satisfaction programming (CSP) and user interactivity [64°°]. Any type of constraint, experimental or theoretical, can be introduced at any time during the folding in real time. Following up the partition function folding algorithm pioneered by McCaskill [65], the statistics of energy and sequence landscapes of RNA molecules have been investigated [66,67"1. Such computer simulations yield insights on the features selected during the biological evolution of those macromolecules. For tRNAs, it appears that real sequences have fewer alternative structures close to the ground state than random ones [67°°]. Furthermore, it could be shown that real sequences melt at higher temperatures and with higher cooperativity than random ones [67"]. Such computer experiments are particularly welcome in the present days of in vitro selected RNA molecules [68] and studies of random oligonucleotide binding unto molecular arrays [69]. Accurate statistical thermodynamic theories for nucleic acids, where standard polymer theory breaks down because of the sequence specificity and the numerous intrachain self-contacts, are being actively pursued. Chen and Dill [70 °] described an Ising-like matrix method whereas Yeramian [71 °°] reduces the complexities of the models from O(nk) to O(n) by expressing the length-dependent long-range effects as multiexponential functions. Two main approaches, originally opposed but now merging, dominate RNA 3D modeling. One, applicable at the atomic level to any size molecule, consists of assembling manually and interactively on a graphic terminal selected and preformed elements extracted from a database [72]. Last year, a complete atomic model of 16S rRNA [73*'], incorporating a bewildering amount of biochemical data and especially cross-links between rRNA, tRNA, and mRNA, constitutes the largest assembled system. On the other hand, automatic techniques, not requiring human decision but containing coded expert knowledge, employ various approaches (distance geometry [74], CSP [751 and GA) either at the atomic level, for small systems, or at the pseudo-atom level, for large ones. Even with the use of discrete conformational sets for the nucleotides, such automatic methods require powerful search procedures to sift through the gigantic combinatorial space. Recentlx; the GA technique was applied to the anticodon and thvminc loops of tRNA as target structures. For the thymine loop, an all-atom rms deviation of 1.76~ was obtained [76°]. However, this value applied to the 72nd model among 148 accepted structures. One theoretical drawback in such methods is their reliance on simple in vacuo energy minimization for refinement and selection. As discussed above, such methods are not reliable when applicd to RNA systems.

Calculations of nucleic acid conformations Louise-May, Auffinger and Westhof

DNA supercoiling structure and energetics

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Macromodeling techniques applied to DNA supercoiling are currently in a stage of refinement where bending anisotropies, intrinsic curvature, base sequence and salt dependencies are being added into existing static and dynamic modeling algorithms. Starting from generalized base sequence models and geometry build-up generators, which allow for the most atomic detail, to dynamical models, which allow for the greatest accessibility to generation of physical parameters, the issues remain essentially the s a m e - - t h e addition of the effect of local structural heterogeneity to the present topological and energetic models of DNA supercoiling. A static clash model for B-DNA twisting that correlates to base morphology was formulated by Gorin et el. [77]. T h e sequence dependence of twist angles was analyzed from a set of 38 B-DNA crystal structures and a twist-clash correlation function for the ten common Watson-Crick dimer steps was determined. This model holds when extended to modified bases and is discussed in terms of its effect on DNA-protein interactions and DNA bending. This type of generalized model could be used in the development of sequence dependent bending anisotropy functions or parameters in macromodeling DNA techniques. A method for the generation of curved DNA helices at the atomic level along prescribed 3D curves was reported by Tung and Soumpasis [78"] and was demonstrated for small circular DNA (SI base pairs [bp]), nucleosomal DNA (146bp), knotted superhelical DNAs; trefoil (1S0bp) and ellipsoidal torus (1S0bp; Fig. 3). T h e algorithm is purely geometrical but useful and elegant for the generation of supercoiled structures. T h e base-to-base virtual bond matrix generator methods of Marky and Olson [79,80] have been refined to incorporate sequence-dependent bending and twisting as well as asymmetrical angular and translational residue fluctuations. T h e y applied their new model to investigate alternating A-form and B-form segment-kinked DNA, the B---)A transition and the effect of intercalation on extended chain-bending properties. A Euler-Lagrange numerical analysis of DNA supercoiling using a base-pair level elastic rod model in which base-sequence effects were added via bending parameters was reported bv Westcott et el. [81].

A 150 bp, smoothly-bent DNA ellipsoidal torus knot, generated by the construction algorithm of Tung and Soumpasis [78"]. Reproduced with permission from [78°].

closed circular superhelical DNAs as the superhelical density is approached. T h e families contain multiple minimum-energy conformations and the writhe is found to be discontinuous for some ranges of a change in linking value [86]. MD simulations were also used to determine the salt-concentration influence on the topology and energetics of 1000 and 3000bp supercoiled DNAs. The marked effects observed indicate that the salt concentration may have a possible regulatory role on DNA supercoiling [87°']. Benham [88] has applied a statistical mechanical approach to predict superhelical stress-induced duplex destabilization in genomic DNA sequences and found it to be closely associated with specific transcriptional regulatory elements. Finally, the stationary state configurations of supercoiled DNA could be derived from a generalized one-dimensional time-independent non-linear Schr6dinger equation [89].

Conclusions MC treatments of DNA supercoiling investigated the free energy of supercoiling dependence on the torsional rigidity and linking-number change by Gebe et el. [82] and on the anisotropy of the bending rigidity by Schurr et el. [831. The topology of superhelical DNA loops was investigated with respect to the presence of permanent local curvature by Klenin e t a / . [84°*]. Brownian dynamics was employed by Chirico and Langowski [85] for the introduction of torsional-bending coupling constraints for a bead chain model of closed circular DNA in simulations of up to 401as. MD studies of closed circular DNA were used to study the topological families and dynamics of

The range of computational methods applied to the study of nucleic acid conformation is immense and covers nearly any structural question an investigator might pose. The field is dynamic and enterprising. However, sadly enough and despite the present innovative characteristics of modelling and simulation research, there is a trend in the publishing policy of several journals to severely restrict the access of theoretically oriented papers. Quantum mechanical applications are used for the improved parametrization of molecular potentials and for the development of accurate parameters for modified

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nucleic acid bases, furanose and backbone moieties, or the binding of drugs. T h e coupling of quantum and molecular mechanics potentials should allow, in the near future, the study of a number of localized nucleic acid reactions, such as RNA catalysis, to be addressed. An explicit solvent and counter-ion environment, allowing for the detailed characterization of nucleic acid-water and nucleic acid-ion interactions, can now be (and ought to be) routinely included in MD simulations. As simulation studies increase in length, however, strategies that evaluate the protocol stability (such as MMD) are needed to insure against costly lessons in model and protocol evolvement. Ewald summation techniques, which do not impose non-physical truncations to the long-range electrostatic interactions, are proving their value in nucleic acid systems. Refinement protocols of NMR-derived solution structures of nucleic acids are beginning to include explicit solvent and counter-ions for more realistic models. Several modified MD methods aim to expand the size and/or timescalc currently accessible. T h e field of RNA folding is the subject of intense activity in which sophisticated computer techniques are being tested and developed. DNA macromodeling and supercoiling studies are currently undergoing model improvement and refinement in order to include the effects of sequence variations, bending and salt concentration and are being applied to biologically oriented questions.

"7.

Bakowies D, Thiel W: Semiemperical treatment of electrostatic potentials and partial charges in combined quantum mechanical and molecular mechanical approaches. J Comput Chem 1996, 17:87-108.

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Stanton RV, Little LR, Merz KM-J: An examination of a Hartree-FockJmolecular mechanical coupled potential. J Phys Chem 1995, 99:17344-17348.

9. *

Elcock AH, Lyne PD, Mulholland AJ, Nandra A, Richards WG: Combined quantum and molecular mechanical study of DNA cross-linking by nitrous acid. J Am Chem Soc 1995, 117:4706-4707. This paper constitutes a brief but interesting example of combined QM-MM techniques applied to nucleic acid systems. Laughton CA, Luque FJ, Orozco M: Counterion distribution around DNA studied by molecular dynamics and quantum mechanical simulations. J Phys Chem 1995, 99:11591-11599. QM and MD techniques are applied in an interative manner to achieve a consistent phosphate backbone charge distribution. Detailed statistical analyses of the counterion distribution is reported from two independent MD trajectories using the derived phosphate charges. 10. =,

Norberg J, Nilsson L: Stacking free energy profiles for all 16 natural ribodinucleoside monophosphates in aqueous solution. J Am Chem Soc 1995, 117:10832-10840. This paper describes 30 ns of explicitly solvated MD trajectories for a detailed dynamical characterization of the stacked and unstacked conformations of the GpU dinucleoside. 11. -

12.

13. •

Plaxco KW, Goddard WA Ill: Contributions of the thymine methyl group to the specific recognition of poly- and mononucleotides: an analysis of the relative free energies of solvation of thymine and uracil. Biochemistry 1994, 33:3050-3054. This paper constitutes a thorough study of the effect of desolvation for base pairs both free and within a helical context via MD-PT methods. 14.

Lavery R: Modelling nucleic acids: fine structure, flexibility, and conformational transitions. In Advances in Computational Biology. Edited by Hugo OV. Greenwich, CT: JAI Press Inc; 1994:69-145.

15.

Lavery R, Hartmann B: Modelling DNA conformational mechanics. Biophys Chem 1994, 50:33-45.

16.

Stofer E, Lavery R: Measuring the geometry of DNA grooves. Biopolymers 1994, 34:33?-346. Westhof E, Rubin-Carrez C, Fritsch V: The use of molecular dynamics simulations for modelling nucleic acids. In Computer Modelling in Molecular Biology. Edited by Goodfellow JM New York: VCH; 1995:103-131.

References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted as: • of special interest • o of outstanding interest 1.

Jiang SP, Raghunathan G, Ting KL, Xuan JC, Jernigan RL: Geometries, charges, dipole moments and interaction energies of normal, tautomeric and novel bases. J Biomo/Struct Dyn 1994, 12:367-382.

17.

2.

Gould IR, Kollman PA: Theoretical investigation of the hydrogen bond strengths in guanine-cytosine and adenine-thymine base pairs. J Am Chem Soc 1994, 116:2493-2499.

18. •

3. •

Cieplak P, Comell WD, Bayl C, Kollman PA: Application of the mulUmolecule and multiconfigurational RESP methodology to biopolymers: charge derivation for DNA, RNA, and proteins. J Comput Chem 1995, 16:1357-1377. This paper describes a method to derive electrostatic point charges from ab initio calculations using multiple configurations. It constitutes a step toward more accurate empirical potentials. 4. •

Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM, Ferguson DM, Spellmeyer DC, Fox T, Caldwel JW, Kollman PA: A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J Am Chem Soc 1995, 117:5179-5197. This paper describes the application of the methodology described in [3 °] to the derivation of an improved force field. 5.

6. •

Hobza P, Sponer J, Polasek M: H-bonded and stacked base pairs: cytosine dimer. An ab initio second order Moller-Plesset study. J Am Chem Soc 1995, 117:792-798.

St. Amant A, Comell WD, Kollman PA: Calculation of molecular geometries, relative conformational energies, dipole moments, and molecular electrostatic fitted charges of small organic molecules of biochemical interest by density functional theory. J Comput Chem 1995, 16:1483-1506. This is a very good description of the DFT technique with comparisons to related DFT methods and HF as well as MP2 methods for relevant systems.

Norberg J, Nilsson L: Potential of mean force calculations of the stacking-unstacking process in single stranded deoxyribonucleoside monophosphates. Biophys J 1995, 69:2277-2285.

Auffinger P, Louise-May S, Westhof E: Multiple molecular dynamics simulations of the anticodon loop of tRNAAsp in aqueous solution with counterions. J Am Chem Soc 1995, 117:6720-6726. The MMD approach is introduced and illustrated for a ME) protocol using short solvent interaction truncation distances to demonstrate its level of stability. 19.

Auffinger P, Beveridge DL: A simple test for evaluating the truncation effects in simulation of systems involving charged groups. Chem Phys Lett 1995, 234:413-415.

Louise-May S, Auffinger P, Westhof E: RNA structure from molecular dynamics simulations. In Biological Structure and Dynamics. Proceedings of the Ninth Conversation, State University of New York. Edited by Sarma RH, Sarma MH. Albany, NY: Adenine Press; 1995:1-18. 2.8 ns of MD trajectories on solvated RNA systems using three MD protocols and the MMD techniques are reviewed. 20. •

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 of long-range hydration forces. J Am Chem Soc 1996, 118:1181-1189. This paper constitutes a demonstration of long-range solvent forces and their effect on the structure and dynamics of the anticodon hairpin of tRNAASp using MMD, described in [18"]. From this study, the dynamical stability and structural potential of weak C-H..O interactions could be inferred. 21. ,,

22.

Darden T, York D, Pedersen L: Particle mesh Ewald: an N.Iog(N) method for Ewald sums in large systems. J Chem Phys 1993, 98:1 O089-10092.

Calculations of nucleic acid conformations Louise-May, Auffinger and Westhof

23.

Essmann U, Perera L, Berkowitz ML, Darden 1", Lee H, Pedersen LG: A smooth particle mesh Ewald method. J Chem Phys 1995, 103:8577-8593.

24.

Pearlman DA, Case DA, Caldwell JW, Ross WS, Cheatham TE III, Ferguson DM, Seibel GL, Singh UC, Weiner PK, Kollman PA: AMBER 4.1. San Francisco: 1994.

25. •.

Cheatham TE, Miller JL, Fox T, Darden TA, Kollman PA: Molecular dynamics simulations on solvated biomolecular systems: the particle mesh Ewald method leads to stable trajectories of DNA, RNA and proteins. J Am Chem Soc 1995, 117:4193-4194. The increased stability of a B-DNA, RNA and protein molecule MO trajectory, through accurate treatment of electrostatic long-range interactions using PME methods, marks an important milestone in the generation of accurate MD models (see also [27"']). 26.

Lee H, Darden T, Pedersen L: Accurate crystal molecular dynamics simulations using particle-mesh-Ewald: RNA dinucleotides-ApU and GpC. Chem Phys Lett 1995, 243:229-235.

27. •.

York DM, Yang W, Lee H, Darden T, Pedersen LG: Toward the accurate modeling of DNA: the importance of long-range electrostatics. J Am Chem Soc 1995, 117:5001-5002. This paper describes a solvated MD simulation of a B-DNA dodecamer in its crystal unit cell using Ewald summation (see also [25°°]).

29"7

40.

Sanghani SR, Lavery R: Theoretical studies of DNA-RNA hybrid conformations. Nucleic Acids Res 1994, 22:1444-1449.

41.

Fritsch V, Wolf RM: Molecular dynamics simulations of a r(GA 12G)-d(CT12C) hybrid duplex. J Biomo/Struct Dyn 1994, 11:1161-1174.

42. •

Fritsch V, De Mesmaeker A, Waldner A, Lebreton J, Blommers MJ, Wolf RM: Molecular mechanics and dynamics studies on two structurally related amide-modified DNA backbones for antisense technology. Bioorg Med Chem 1995, 3:321-335. This paper constitutes an example of MD simulations applied to amide-modified oligonucleotides. 43. •

Gonz&lez C, Stec W, Reynolds MA, James TL: Structure and dynamics of a DNA-RNA hybrid duplex with a chiral phosphorothionate moiety: NMR and molecular dynamics with conventional and time-averaged restraints. Biochemistry 1995, 34:4969-4982. This paper describes a comparison of standard NMR-restrained MD techniques with the application of the MD-tar methodology for the generation of NMR solution structures of nucleic acids. 44.

Schmitz U, Ulyanov NB, Kumar A, James TL: Molecular dynamics with weighted time-averaged restraints for a DNA octamer. Dynamic interpretation of nuclear magnetic resonance data. J Mol Biol 1993, 234:373-389.

45.

28.

Lee H, Darden TA, Pedersen LG: Molecular dynamics simulation studies of a high resolution Z-DNA crystal. J Chem Phys 1995, 102:3830-3834.

Raghunathan G, Miles HT, Sasisekharan V: Symmetry and structure of RNA and DNA triple helices. Biopolymers 1994, 36:333-343.

46.

29.

Zichi DA: Molecular dynamics of RNA with the OPLS force field. Aqueous simulation of a hairpin containing a tetranucleotide loop. J Am Chem Soc 1995, 117:2957-2969.

Kiran MR, Bansal M: Structural polymorphism in d(T)t2-d(A)12-d(T)12 triple helices. J Biomol Struct Dyn 1995, 13:493-505.

47.

30.

Auffinger P, Westhof E: H-bond stability in the tRNAAsp anticodon hairpin: three nanoseconds of multiple molecular dynamics trajectories. Biophys J 1g96, in press.

Cheng YK, Pettitt BM: Solvent effects on model d(CG.G)7 and d(TA.T) 7 DNA triple helices. Biopolymers 1995, 35:457-473.

48. De

31. Auffinger P, Louise-May S, Westhof E: Hydration of C-H groups • in tRNA. J Chem Soc Faraday Trans 1996, 103:in press. Extensive hydration analysis from multiple 500 ps solvated MD trajectories of the tRNAAsp molecule reveals the potential structural stabilization of nonclassical C-H..-Ow hydrogen bonds. Characteristic profiles are generated on the basis of multiple analyses and fragment MD results are compared to those of the full molecular context. 32.

Miaskiewicz K, Miller J, Ornstein R, Osman R: Molecular dynamics simulations of the effects of ring-saturated thymine lesions on DNA structure. Biopolymers t995, 35:113-124. Ab initio and solvated MD trajectories of five thymine lesions to a B-DNA dodecamer are compared. •

33.

Coppel Y, Coulombeau C, Lhomme J, Dheu Andries ML, Vatton P: Molecular modelling study of DNA-Troegers bases interactions. J Biomol Struct Dyn 1994, 12:637-653.

Weerasinghe S, Smith PE, Mohan V, Cheng Y-K, Pettitt BM: Nanosecond dynamics and structure of a model DNA triplex helix in saltwater solution. J Am Chem Soc 1995, 117:2147-2158. This paper describes a 1.3 ns solvated MD simulation of a DNA triplex with extensive counter-ion analysis, using an Ewald method for the accurate treatment of electrostatic long-range interactions. 49.

Weerasinghe S, Smith PE, Pettitt M: Structure and stability of a model pyrimidine-purine-purine DNA triple helix with a GC.T mismatch by simulation. Biochemistry 1995, 34:16269-16278. This paper describes a 1.5 ns solvated MD simulation of a DNA triplex containing a GC-T mismatch with extensive counter-ion analysis. •

50.

Radhakrishnan I, Patel DJ: Solution structure of a pyrimidine-purine-pyrimidine DNA triplex containing T.AT, C+.GC and G-TA Triples. Structure 1994, 2:17-32.

51.

Radhakrishnan I, Patel DJ: Solution structure and hydration patterns of a pyrimidine-purine-pyrimidine DNA triplex containing a novel T.CG base-triple. J Mo/BiD/ 1994, 241:600-619. This paper describes the solution structure of a DNA triplex via NMR-restrained MD refinement, which includes explicit solvent and counterions. •

34.

Singh SB, Wemmer DE, Kollman PA: Relative binding affinities of distamycin and its analog to d(CGCAAGTTGGC). d(GCCAACTTGCG): comparison of simulation results with experiment. Proc Natl Acad Sci USA 1994, 91:7673-7677.

35.

McCarrick MA, Kollman P: Use of molecular dynamics and free energy perturbation calculations in anti-human immunodeficiency virus drug design. Methods Enzymol 1994, 241:3?0-384.

53.

Strahan GO, Sharer RH, Keniry MA: Structural properties of

36.

Alhambra C, Luque FJ, Portugal J, Orozco M: Molecular dynamics study of the binding of elsamicin A to DNA. Eur J Biochem 1995, 230:555-566.

•

the [d(G3T4G3)] 2 quadruplex: evidence for sequential syn-syn

37.

Zacharias M, Luty BA, Davis ME, McCammon JA: Combined conformational search and finite-difference poisson-Boltzmann approach for flexible docking. Application to an operator mutation in the lambda repressor-operator complex. J Mol Biol 1994, 238:455-465.

38.

39.

Harris LF, Sullivan MR, Popken Harris PD, Hickok DF: Molecular dynamics simulations in solvent of the glucocorticoid receptor protein in complex with a glucocorticoid response element DNA sequence. J Biomo/Struct Dyn 1994, 12:249-270.

Eriksson MA, Hard T, Nilsson L: Molecular dynamics simulations of the glucocorticoid receptor DNA-binding domain in complex with DNA and free in solution. Biophys J 1995, 68:402-426. The g~ucocorticoid receptor DNA-binding domain, free and complexed, is studied by MD studies in solution. Water molecules with tong residence times are found at the interface of the complex.

52.

Mohanty D, Bansal M: Conformational poiymorphism in telomeric structures: loop orientation and interloop pairing in d(G4TnG4). Biopolymers 1994, 34:1187-1211.

deoxyguanosines. Nucleic Acids Res 1994, 22:5447-5455. Three conformations of the dimeric hairpin quadruplexes formed by d(G3T4G 3) were investigated by unrestrained in vacuo MD simulations to evaluate the stacking energy for comparison to the NMR solution structures of two observed conformations. 54.

Briki F, Genest D: Rigid-body motions of sub-units in DNA: a correlation analysis of a 200 ps molecular dynamics simulation. J Biomol Struct Dyn 1995, 12:1063-1082.

55.

Harvey SC, Gabb HA: Conformational transitions using molecular dynamics with minimum biasing. Biopolymers 1993, 33:1167-1172.

56.

Nakamura S, Doi J: Dynamics of transfer RNAs analyzed by normal mode calculation. Nucleic Acids Res 1994, 22:514-521.

57

Westhof E, Michel F: Prediction and experimental investigation of RNA secondary and tertiary foldings. In RNA-Protein Interactions. Edited by Nagai K, Mattaj tW. Oxford: IRL Press; 1994:25-51.

•

298

Nucleic acids

58.

Kim HJ, Han K: Automated modeling of the RNA folding process. Mol Cells 1995, 5:406-412.

This paper is an extremely well written and clear description of a patiently gathered mountain of data on the next frontier, the ribosome.

59.

Davis JP, Janjic N, Pdbnow D, Zichi DA: Alignment editing and identification of consensus secondary structures for nucleic acid sequences: interactive use of dot matrix representations. Nucleic Acids Res 1995, 23:4471-4479.

74.

Hubbard JM, Hearst JE: Predicting the three-dimensional folding of transfer tRNA with a computer modeling protocol. Biochemistry 1991,30:5458-5465.

60.

Zuker M, Jacobson AB: Well-determined regions in RNA secondary structure prediction: analysis of small subunit ribosomal RNA. Nucleic Acids Res 1995, 23:2791-2798.

?5.

Major F, Turcotte M, Gautheret D, Lapalme G, Fillion E, Cedergren R: The combination of symbolic and numerical computation for three-dimensional modeling of RNA. Science 1991, 253:1255-1260.

61.

Konings DAM, Gutell R: A comparison of thermodynamic foldings with comparatively derived structures of 16S and 16S like rRNAs. RNA 1995, 1:559-574.

62.

Benedetti G, Morosetti S: A genetic algorithm to search for optimal and suboptimal RNA secondary structures. Biophys Chem 1995, 55:253-259.

63.

Gultyaev AP, Van Batenburg FH, Pleij CW: The computer simulation of RNA folding pathways using a genetic algorithm. J Mol Biol 1995, 250:37-51. The authors describe a very stimulating approach, still quite demanding on computer power (60 hours of central processing unit with a 486/33 MHz processor for a 500 nucleotide sequence).

?6.

Ogata H, Akiyama Y, Kanehisa M: A genetic algorithm based molecular modeling technique for RNA stem-loop structures. Nucleic Acids Res 1995, 23:419-426. Like [63*], this paper describes a valuable approach but the calculations were carried out on a supercomputer CRAY Y-MP2E, which is not exactly a bench computer. •

77.

•

64. **

Gaspin C, Westhof E: An interactive framework of RNA secondary structure prediction with a dynamical treatment of constraints. J Mol Bio/1995, 254:163-1 ?4. A referee wrote =This paper represents an important advance in the prediction of RNA secondary structure from single sequences ... the algorithm can compute energetically optimal and suboptimal solutions interactively. In this sense, it is much better than the current Zuker algorithm that does not allow the introduction of variable constraints at the end. The Zuker algorithm is better for the automatic generation of a representative set of foldings".

Gorin AA, Zhurkin VB, Olson WK: B-DNA twisting correlates with base pair morphology. J Mol Bio11995, 247:33-48.

78. •

TungC-S, Soumpasis DM: The construction of DNA helical duplexes along prescribed 3-D curves. J Biomol Struct Dyn 1995, 13:577-582. An extremely efficient and elegant method for the construction of superhelical DNAs of different topologies is presented and illustrated for up to 150 base pairs. 79.

MarkyNL, Olson WK: Configurational statistics of the DNA duplex: extended generator matrices to treat the rotations and translations of adjacent residues. Biopo/ymers 1994, 34:109-120.

80.

Marky NL, Olson WK: Spatial translational motions of base pairs in DNA molecules: application of the extended matrix generator method. Biopo/ymers 1994, 34:121-142.

65.

McCaskill JS: The equilibrium partition function and base pair binding probabilities for RNA secondary structure. Biopo/ymers 1990, 29:1105-1119.

81.

66.

Tacker M, Fontana W, Stadler PF, Schuster P: Statistics of RNA melting. Eur Biophys J 1994, 23:29-38.

Westcott TP, Tobias I, Olson WK: Elasticity theory and numerical analysis of DNA supercoiling: an application to DNA looping. J Phys Chem 1995, 99:1 7926-17935.

82.

Higgs PG: Thermodynamic properties of transfer RNA: a computational study. J Chem Soc Faraday Trans 1995, 91:2531-2540. The author describes a very fine example of computer simulations of the thermodynamic properties of transfer RNAs.

Gebe JA, Allison SA, Clendenning JB, Schurr JM: Monte Carlo simulations of supercoillng free energies for unknotted and trefoil knotted DNAs. Biophys J 1995, 68:619-633.

83.

Schurr JM, Babcock HP, Gebe JA: Effect of anisotropy of the bending rigidity on the supercoiling free energy of small circular DNAs. Biopo/ymers 1995, 36:633-641.

68.

Gold L, Polisky B, Uhlenbeck OC, Yarus M: Diversity of oligonucleoUdes functions. Annu Rev Biochem 1995, 64:763-797.

84. *•

KleninKV, Frank-Kamenetskii MD, Langowski J: Modulation of intramolecular interactions in superhelical DNA by curved sequences: a Monte Carlo simulation study. Biophys J 1995,

69.

Southern EM, Case-Green SC, Eider JK, Johnson M, Mir KU, Wang L, Williams JC: Arrays of complementary oligonucleotides for analysing the hybridisation behaviour of nucleic acids. Nucleic Acids Res 1994, 22:1368-1373.

The authors show that a simple model can ~ead to remarkable agreement between theoretical and experimental data.

67. •*

70. •

Chen S J, Dill KA: Statistical thermodynamics of doublestranded polymer molecules. J Phys Chem 1995, 103:5802-5813. This paper constitutes a courageous attempt at a bafflingly complex problem. The 'firehose' model can treat secondary structures, provided the polymer graph has no linked contacts, while treating excluded volume more suitably than previously. 71. •-

YeramianE: Complexity and tractability. Statistical mechanic of helix-coil transitions in circular DNA as a model-problem. Europhys Lett 1994, 25:49-55. Pioneers are lonely but with the multiexponential representations of lengthdependent long-range effects, calculation times are reduced by factors between 103 and 106 with excellent accuracy. 72.

Westhof E: Modelling the three-dimensional structure of ribonucleic acids. J Mo/Struct 1993, 286:203-21 O.

73. ..

Brimacombe R: The structure of ribosomal RNA: a threedimensional jigsaw puzzle. Eur J Biochem 1995, 230:365-383.

68:81-88.

85.

Chirico G, Langowski J: Kinetics of DNA supercoiling studies by Brownian dynamics simulation. Biopolymers 1994, 34:415-433.

86.

Schlick T, Olson WK, Westcott T, Greenberg JP: On higher buckling transitions in supercoiled DNA. Biopolymers 1994, 34:565-597.

87. *•

Schlick T, Li B, Olson WK: The influence of salt on the structure and energetics of supercoiled DNA. Biophys J 1994, 67:2146-2166. The influence of salt concentration on the energetics and topology of DNA supercoiling via salt-dependent electrostatic coefficients is investigated for supercoiled DNAs of 1000-3000 base pairs. 88.

BenhamC J: Duplex destabilization in superhelical DNA is predicted to occur at specific transcriptional regulatory regions. J Mo/ Bio/1996, 255:425-434.

89,

Shi Y, Borovik AE, Hearst JE: Elastic rod model incorporating shear and extension, generalized nonlinear SchrSdinger equations, and novel closed-form solutions for supercoiled DNA. J Chem Phys 1995, 103:3166-3183.