Spatial configurations of polynucleotide chains. I. Steric interactions in polyribonucleotides: a virtual bond model

Advances in RNA 3D Structure Prediction

RNA molecules carry out various cellular functions, and understanding the mechanisms behind their functions requires the knowledge of their 3D structures. Different types of computational methods have been developed to model RNA 3D structures over the past decade. These methods were widely used by researchers although their performance needs to be further improved. Recently, along with these traditional methods, machine-learning techniques have been increasingly applied to RNA 3D structure prediction and show significant improvement in performance. Here we shall give a brief review of the traditional methods and recent related advances in machine-learning approaches for RNA 3D structure prediction.

Thermodynamics of unfolding mechanisms of mouse mammary tumor virus pseudoknot from a coarse-grained loop-entropy model

Pseudoknotted RNA molecules play important biological roles that depend on their folded structure. To understand the underlying principles that determine their thermodynamics and folding/unfolding mechanisms, we carried out a study on a variant of the mouse mammary tumor virus pseudoknotted RNA (VPK), a widely studied model system for RNA pseudoknots. Our method is based on a coarse-grained discrete-state model and the algorithm of PK3D (pseudoknot structure predictor in three-dimensional space), with RNA loops explicitly constructed and their conformational entropic effects incorporated. Our loop entropy calculations are validated by accurately capturing previously measured melting temperatures of RNA hairpins with varying loop lengths. For each of the hairpins that constitutes the VPK, we identified alternative conformations that are more stable than the hairpin structures at low temperatures and predicted their populations at different temperatures. Our predictions were validated by thermodynamic experiments on these hairpins. We further computed the heat capacity profiles of VPK, which are in excellent agreement with available experimental data. Notably, our model provides detailed information on the unfolding mechanisms of pseudoknotted RNA. Analysis of the distribution of base-pairing probability of VPK reveals a cooperative unfolding mechanism instead of a simple sequential unfolding of first one stem and then the other. Specifically, we find a simultaneous "loosening" of both stems as the temperature is raised, whereby both stems become partially melted and co-exist during the unfolding process.

An RNA-centric historical narrative around the Protein Data Bank

Some of the amazing contributions brought to the scientific community by the Protein Data Bank (PDB) are described. The focus is on nucleic acid structures with a bias toward RNA. The evolution and key roles in science of the PDB and other structural databases for nucleic acids illustrate how small initial ideas can become huge and indispensable resources with the unflinching willingness of scientists to cooperate globally. The progress in the understanding of the molecular interactions driving RNA architectures followed the rapid increase in RNA structures in the PDB. That increase was consecutive to improvements in chemical synthesis and purification of RNA molecules, as well as in biophysical methods for structure determination and computer technology. The RNA modeling efforts from the early beginnings are also described together with their links to the state of structural knowledge and technological development. Structures of RNA and of its assemblies are physical objects, which, together with genomic data, allow us to integrate present-day biological functions and the historical evolution in all living species on earth.

Biophysical Reviews' "Meet the Editors Series"-a profile of Wilma K. Olson

As one of the five Executive Editors of Biophysical Reviews I have been asked to provide this short biographical sketch for the readers of the journal. I have been a member of the Editorial Board since the inception of the journal in 2008 and an Executive Editor since 2014. I hold a B.S. degree in Chemistry from the University of Delaware and a Ph.D. in Physical Chemistry from Stanford University. Except for a year as a Damon Runyon Postdoctoral Fellow at Columbia University, I have spent my entire professional career at Rutgers, the State University of New Jersey, where I am currently the Mary I. Bunting Professor of Chemistry and Chemical Biology. I served for many years as Founding Director of the Rutgers University Center for Molecular Biophysics and Biophysical Chemistry, and have trained undergraduate, graduate, and postdoctoral students from a variety of academic disciplines.

Coarse-grained modeling of RNA 3D structure

Functional RNA molecules depend on three-dimensional (3D) structures to carry out their tasks within the cell. Understanding how these molecules interact to carry out their biological roles requires a detailed knowledge of RNA 3D structure and dynamics as well as thermodynamics, which strongly governs the folding of RNA and RNA-RNA interactions as well as a host of other interactions within the cellular environment. Experimental determination of these properties is difficult, and various computational methods have been developed to model the folding of RNA 3D structures and their interactions with other molecules. However, computational methods also have their limitations, especially when the biological effects demand computation of the dynamics beyond a few hundred nanoseconds. For the researcher confronted with such challenges, a more amenable approach is to resort to coarse-grained modeling to reduce the number of data points and computational demand to a more tractable size, while sacrificing as little critical information as possible. This review presents an introduction to the topic of coarse-grained modeling of RNA 3D structures and dynamics, covering both high- and low-resolution strategies. We discuss how physics-based approaches compare with knowledge based methods that rely on databases of information. In the course of this review, we discuss important aspects in the reasoning process behind building different models and the goals and pitfalls that can result.

Polyelectrolyte properties of single stranded DNA measured using SAXS and single-molecule FRET: Beyond the wormlike chain model

Nucleic acids are highly charged polyelectrolytes that interact strongly with salt ions. Rigid, base-paired regions are successfully described with wormlike chain models, but nonbase-paired single stranded regions have fundamentally different polymer properties because of their greater flexibility. Recently, attention has turned to single stranded nucleic acids due to the growing recognition of their biological importance, as well as the availability of sophisticated experimental techniques sensitive to the conformation of individual molecules. We investigate polyelectrolyte properties of poly(dT), an important and widely studied model system for flexible single stranded nucleic acids, in physiologically important mixed mono- and divalent salt. We report measurements of the form factor and interparticle interactions using SAXS, end-to-end distances using smFRET, and number of excess ions using ASAXS. We present a coarse-grained model that accounts for flexibility, excluded volume, and electrostatic interactions in these systems. Predictions of the model are validated against experiment. We also discuss the state of all-atom, explicit solvent molecular dynamics simulations of poly(dT), the next step in understanding the complexities of ion interactions with these highly charged and flexible polymers.

EK3D: an E. coli K antigen 3-dimensional structure database

A very high rate of multidrug resistance (MDR) seen among Gram-negative bacteria such as Escherichia, Klebsiella, Salmonella, Shigella, etc. is a major threat to public health and safety. One of the major virulent determinants of Gram-negative bacteria is capsular polysaccharide or K antigen located on the bacterial outer membrane surface, which is a potential drug & vaccine target. It plays a key role in host–pathogen interactions as well as host immune evasion and thus, mandates detailed structural information. Nonetheless, acquiring structural information of K antigens is not straightforward due to their innate enormous conformational flexibility. Here, we have developed a manually curated database of K antigens corresponding to various E. coli serotypes, which differ from each other in their monosaccharide composition, linkage between the monosaccharides and their stereoisomeric forms. Subsequently, we have modeled their 3D structures and developed an organized repository, namely EK3D that can be accessed through www.iith.ac.in/EK3D/. Such a database would facilitate the development of antibacterial drugs to combat E. coli infections as it has evolved resistance against 2 major drugs namely, third-generation cephalosporins and fluoroquinolones. EK3D also enables the generation of polymeric K antigens of varying lengths and thus, provides comprehensive information about E. coli K antigens.

Free energy cost of stretching mRNA hairpin loops inhibits small RNA binding

Small RNA-mRNA binding is an essential step in RNA interference, an important cellular regulatory process. Calculations of binding free energy have been used in binding site prediction, but the cost of stretching the mRNA loop when the small RNA-mRNA duplex forms requires further exploration. Here, using both polymer physics theory and simulations, we estimate the free energy of a stretched mRNA loop. We find loop stretching significantly increases the free energy of 3' supplementary/compensatory miRNA binding and siRNA binding to mRNA hairpin loops. We also make the observation that sites where 3' supplementary binding is available may bind at the seed only, and that loop stretching often favors seed-only binding over seed plus 3' supplementary binding in mRNA hairpins.

Coarse-grained prediction of RNA loop structures

One of the key issues in the theoretical prediction of RNA folding is the prediction of loop structure from the sequence. RNA loop free energies are dependent on the loop sequence content. However, most current models account only for the loop length-dependence. The previously developed “Vfold” model (a coarse-grained RNA folding model) provides an effective method to generate the complete ensemble of coarse-grained RNA loop and junction conformations. However, due to the lack of sequence-dependent scoring parameters, the method is unable to identify the native and near-native structures from the sequence. In this study, using a previously developed iterative method for extracting the knowledge-based potential parameters from the known structures, we derive a set of dinucleotide-based statistical potentials for RNA loops and junctions. A unique advantage of the approach is its ability to go beyond the the (known) native structures by accounting for the full free energy landscape, including all the nonnative folds. The benchmark tests indicate that for given loop/junction sequences, the statistical potentials enable successful predictions for the coarse-grained 3D structures from the complete conformational ensemble generated by the Vfold model. The predicted coarse-grained structures can provide useful initial folds for further detailed structural refinement.

Statistical mechanical modeling of RNA folding: from free energy landscape to tertiary structural prediction

In spite of the success of computational methods for predicting RNA secondary structure, the problem of predicting RNA tertiary structure folding remains. Low-resolution structural models show promise as they allow for rigorous statistical mechanical computation for the conformational entropies, free energies, and the coarse-grained structures of tertiary folds. Molecular dynamics refinement of coarse-grained structures leads to all-atom 3D structures. Modeling based on statistical mechanics principles also has the unique advantage of predicting the full free energy landscape, including local minima and the global free energy minimum. The energy landscapes combined with the 3D structures form the basis for quantitative predictions of RNA functions. In this chapter, we present an overview of statistical mechanical models for RNA folding and then focus on a recently developed RNA statistical mechanical model -- the Vfold model. The main emphasis is placed on the physics underpinning the models, the computational strategies, and the connections to RNA biology.

Ionic strength-dependent persistence lengths of single-stranded RNA and DNA

Dynamic RNA molecules carry out essential processes in the cell including translation and splicing. Base-pair interactions stabilize RNA into relatively rigid structures, while flexible non-base-paired regions allow RNA to undergo conformational changes required for function. To advance our understanding of RNA folding and dynamics it is critical to know the flexibility of these un-base-paired regions and how it depends on counterions. Yet, information about nucleic acid polymer properties is mainly derived from studies of ssDNA. Here we measure the persistence lengths (l(p)) of ssRNA. We observe valence and ionic strength-dependent differences in l(p) in a direct comparison between 40-mers of deoxythymidylate (dT(40)) and uridylate (rU(40)) measured using the powerful combination of SAXS and smFRET. We also show that nucleic acid flexibility is influenced by local environment (an adjoining double helix). Our results illustrate the complex interplay between conformation and ion environment that modulates nucleic acid function in vivo.

Loop Entropy Assists Tertiary Order: Loopy Stabilization of Stacking Motifs

The free energy of an RNA fold is a combination of favorable base pairing and stacking interactions competing with entropic costs of forming loops. Here we show how loop entropy, surprisingly, can promote tertiary order. A general formula for the free energy of forming multibranch and other RNA loops is derived with a polymer-physics based theory. We also derive a formula for the free energy of coaxial stacking in the context of a loop. Simulations support the analytic formulas. The effects of stacking of unpaired bases are also studied with simulations.

A new way to see RNA

Unlike proteins, the RNA backbone has numerous degrees of freedom (eight, if one counts the sugar pucker), making RNA modeling, structure building and prediction a multidimensional problem of exceptionally high complexity. And yet RNA tertiary structures are not infinite in their structural morphology; rather, they are built from a limited set of discrete units. In order to reduce the dimensionality of the RNA backbone in a physically reasonable way, a shorthand notation was created that reduced the RNA backbone torsion angles to two (η and θ, analogous to φ and ψ in proteins). When these torsion angles are calculated for nucleotides in a crystallographic database and plotted against one another, one obtains a plot analogous to a Ramachandran plot (the η/θ plot), with highly populated and unpopulated regions. Nucleotides that occupy proximal positions on the plot have identical structures and are found in the same units of tertiary structure. In this review, we describe the statistical validation of the η/θ formalism and the exploration of features within the η/θ plot. We also describe the application of the η/θ formalism in RNA motif discovery, structural comparison, RNA structure building and tertiary structure prediction. More than a tool, however, the η/θ formalism has provided new insights into RNA structure itself, revealing its fundamental components and the factors underlying RNA architectural form.

Computing the conformational entropy for RNA folds

We develop a polymer physics-based method to compute the conformational entropy for RNA tertiary folds, namely, conformations consisting of multiple helices connected through (cross-linked) loops. The theory is based on a virtual bond conformational model for the nucleotide chain. A key issue in the calculation of the entropy is how to treat the excluded volume interactions. The weak excluded volume interference between the different loops leads to the decomposition of the whole structure into a number of three-body building blocks, each consisting of a loop and two helices connected to the two ends of the loop. The simple construct of the three-body system allows an accurate computation for the conformational entropy for each building block. The assembly of the building blocks gives the entropy of the whole structure. This approach enables treatment of molten globule-like folds (partially unfolded tertiary structures) for RNAs. Extensive tests against experiments and exact computer enumerations indicate that the method can give accurate results for the entropy. The method developed here provides a solid first step toward a systematic development of a theory for the entropy and free energy landscape for complex tertiary folds for RNAs and proteins.

A two-length-scale polymer theory for RNA loop free energies and helix stacking

The reliability of RNA secondary structure predictions is subject to the accuracy of the underlying free energy model. Mfold and other RNA folding algorithms are based on the Turner model, whose weakest part is its formulation of loop free energies, particularly for multibranch loops. RNA loops contain single-strand and helix-crossing segments, so we develop an enhanced two-length freely jointed chain theory and revise it for self-avoidance. Our resulting universal formula for RNA loop entropy has fewer parameters than the Turner/Mfold model, and yet simulations show that the standard errors for multibranch loop free energies are reduced by an order of magnitude. We further note that coaxial stacking decreases the effective length of multibranch loops and provides, surprisingly, an entropic stabilization of the ordered configuration in addition to the enthalpic contribution of helix stacking. Our formula is in good agreement with measured hairpin free energies. We find that it also improves the accuracy of folding predictions.

Predicting loop-helix tertiary structural contacts in RNA pseudoknots

Tertiary interactions between loops and helical stems play critical roles in the biological function of many RNA pseudoknots. However, quantitative predictions for RNA tertiary interactions remain elusive. Here we report a statistical mechanical model for the prediction of noncanonical loop-stem base-pairing interactions in RNA pseudoknots. Central to the model is the evaluation of the conformational entropy for the pseudoknotted folds with defined loop-stem tertiary structural contacts. We develop an RNA virtual bond-based conformational model (Vfold model), which permits a rigorous computation of the conformational entropy for a given fold that contains loop-stem tertiary contacts. With the entropy parameters predicted from the Vfold model and the energy parameters for the tertiary contacts as inserted parameters, we can then predict the RNA folding thermodynamics, from which we can extract the tertiary contact thermodynamic parameters from theory-experimental comparisons. These comparisons reveal a contact enthalpy (DeltaH) of -14 kcal/mol and a contact entropy (DeltaS) of -38 cal/mol/K for a protonated C(+)*(G-C) base triple at pH 7.0, and (DeltaH = -7 kcal/mol, DeltaS = -19 cal/mol/K) for an unprotonated base triple. Tests of the model for a series of pseudoknots show good theory-experiment agreement. Based on the extracted energy parameters for the tertiary structural contacts, the model enables predictions for the structure, stability, and folding pathways for RNA pseudoknots with known or postulated loop-stem tertiary contacts from the nucleotide sequence alone.

Predicting structures and stabilities for H-type pseudoknots with interhelix loops

RNA pseudoknots play a critical role in RNA-related biology from the assembly of ribosome to the regulation of viral gene expression. A predictive model for pseudoknot structure and stability is essential for understanding and designing RNA structure and function. A previous statistical mechanical theory allows us to treat canonical H-type RNA pseudoknots that contain no intervening loop between the helices (see S. Cao and S.J. Chen [2006] in Nucleic Acids Research, Vol. 34; pp. 2634-2652). Biologically significant RNA pseudoknots often contain interhelix loops. Predicting the structure and stability for such more-general pseudoknots remains an unsolved problem. In the present study, we develop a predictive model for pseudoknots with interhelix loops. The model gives conformational entropy, stability, and the free-energy landscape from RNA sequences. The main features of this new model are the computation of the conformational entropy and folding free-energy base on the complete conformational ensemble and rigorous treatment for the excluded volume effects. Extensive tests for the structural predictions show overall good accuracy with average sensitivity and specificity equal to 0.91 and 0.91, respectively. The theory developed here may be a solid starting point for first-principles modeling of more complex, larger RNAs.

Contribution of the intrinsic mechanical energy of the phosphodiester linkage to the relative stability of the A, BI, and BII forms of duplex DNA

Canonical forms of duplex DNA are known to sample well-defined regions of the alpha, beta, gamma, epsilon, and zeta dihedral angles that define the conformation of the phosphodiester linkage in the backbone of oligonucleotides. While extensive studies of base composition and base sequence dependent effects on the sampling of the A, B1, and BII canonical forms of duplex DNA have been presented, our understanding of the intrinsic contribution of the five dihedral degrees of freedom associated with the phosphodiester linkage to the conformational properties of duplex DNA is still limited. To better understand this contribution, ab initio quantum mechanical (QM) calculations were performed on a model compound representative of the phosphodiester backbone to systematically sample the energetics about the alpha, beta, gamma, epsilon, and zeta dihedral angles relevant to the conformational properties of duplex DNA. Low-energy regions of dihedral potential energy surfaces are shown to correlate with the regions of dihedral space sampled in experimental crystal structures of the canonical forms of DNA, validating the utility of the model compound and emphasizing the contribution of the intrinsic mechanical properties of the phosphodiester backbone to the conformational properties of duplex DNA. Those contributions include the relative stability of the A, BI, and BII conformations of duplex DNA, where the gas-phase energetics favor the BI form over the A and BII forms. In addition, subtle features of the potential energy surfaces mimic changes in the probability distributions of alpha, beta, gamma, epsilon, and zeta dihedral angles in A, BI, and BII forms of DNA as well as with conformations sampled in single-stranded DNA. These results show that the intrinsic mechanical properties of the phosphodiester backbone make a significant contribution to conformational properties of duplex DNA observed in the condensed phase and allow for the prediction that single-stranded DNA primarily samples folded conformations thereby possibly lowering the entropic barrier to the formation of duplex DNA.

IUPAC-IUB joint commission on biochemical nomenclature abbreviations and symbols for the description of conformations of polynucleotide chains

This appendix presents nomenclature rules that are as close as possible to the originally published version and are reproduced here with permission from the European Journal of Biochemistry. A web-based version prepared by G.P. Moss is also available.

Salt dependence of nucleic acid hairpin stability

Single-stranded junctions/loops are frequently occurring structural motifs in nucleic acid structures. Due to the polyanionic nature of the nucleic acid backbone, metal ions play a crucial role in the loop stability. Here we use the tightly bound ion theory, which can account for the possible ion correlation and ensemble (fluctuation) effects, to predict the ion-dependence of loop and stem-loop (hairpin) free energies. The predicted loop free energy is a function of the loop length, the loop end-to-end distance, and the ion (Na(+) and Mg(2+) in this study) concentrations. Based on the statistical mechanical calculations, we derive a set of empirical formulas for the loop thermodynamic parameters as functions of Na(+) and Mg(2+) concentrations. For three specific types of loops, namely, hairpin, bulge, and internal loops, the predicted free energies agree with the experimental data. Further applications of these empirical formulas to RNA and DNA hairpin stability lead to good agreements with the available experimental data. Our results indicate that the ion-dependent loop stability makes significant contribution to the overall ion-dependence of the hairpin stability.

Polymer properties of polythymine as revealed by translational diffusion

Biopolymers, such as single-stranded DNA (ssDNA), are often described as semiflexible polymers or wormlike chains. We investigated the length dependence of diffusional properties of homogeneous ssDNA (polythymine) with up to 100 nucleotides using fluorescence correlation spectroscopy. We found that the hydrodynamic radius Rh scales according to a power law, with an exponent between 0.5 and 0.7 depending on ionic strength I. With Rh being proportional to the square root of the persistence length Lp, we found that Lp approximately Im, with m=-0.22+/-0.01 for polythymine with 100 residues. For comparison, we performed molecular dynamics (MD) simulations with a force field that accounts for short-range interactions in vacuum, and determined the characteristic polymer properties end-to-end distance R, radius of gyration S, and persistence length Lp of various labeled and nonlabeled polythymine derivatives. We found excellent agreement for the length dependence of simulated S and experimental Rh measured at 100 mM NaCl, revealing that electrostatic interactions are completely shielded in aqueous solution at such ionic strength. MD simulations further showed that polythymine with >approximately 30 residues can be described as a semiflexible polymer with negligible influence of the fluorescent label; and that static flexibility is limited by geometrical and steric constraints as expressed by an intrinsic persistence length of approximately 1.7 nm. These results provide a benchmark for theories and MD simulations describing the influence of electrostatic interactions on polyelectrolyte properties, and thus help to develop a complete and accurate description of ssDNA.

Predicting RNA folding thermodynamics with a reduced chain representation model

Based on the virtual bond representation for the nucleotide backbone, we develop a reduced conformational model for RNA. We use the experimentally measured atomic coordinates to model the helices and use the self-avoiding walks in a diamond lattice to model the loop conformations. The atomic coordinates of the helices and the lattice representation for the loops are matched at the loop-helix junction, where steric viability is accounted for. Unlike the previous simplified lattice-based models, the present virtual bond model can account for the atomic details of realistic three-dimensional RNA structures. Based on the model, we develop a statistical mechanical theory for RNA folding energy landscapes and folding thermodynamics. Tests against experiments show that the theory can give much more improved predictions for the native structures, the thermal denaturation curves, and the equilibrium folding/unfolding pathways than the previous models. The application of the model to the P5abc region of Tetrahymena group I ribozyme reveals the misfolded intermediates as well as the native-like intermediates in the equilibrium folding process. Moreover, based on the free energy landscape analysis for each and every loop mutation, the model predicts five lethal mutations that can completely alter the free energy landscape and the folding stability of the molecule.

Ab initio conformational analysis of nucleic acid components: intrinsic energetic contributions to nucleic acid structure and dynamics

In recent years, the use of high-level ab initio calculations has allowed for the intrinsic conformational properties of nucleic acid building blocks to be revisited. This has provided new insights into the intrinsic conformational energetics of these compounds and its relationship to nucleic acids structure and dynamics. In this article we review recent developments and present new results. New data include comparison of various levels of theory on conformational properties of nucleic acid building blocks, calculations on the abasic sugar, known to occur in vivo in DNA, on the TA conformation of DNA observed in the complex with the TATA box binding protein, and on inosine. Tests of the Hartree-Fock (HF), second-order Møller-Plesset (MP2), and Density Functional Theory/Becke3, Lee, Yang and Par (DFT/B3LYP) levels of theory show the overall shape of backbone torsional energy profiles (for gamma, epsilon, and chi) to be similar for the different levels, though some systematic differences are identified between the MP2 and DFT/B3LYP profiles. The east pseudorotation energy barrier in deoxyribonucleosides is also sensitive to the level of theory, with the HF and DFT/B3LYP east barriers being significantly lower (approximately 2.5 kcal/mol) than the MP2 counterpart (approximately 4.0 kcal/mol). Additional calculations at various levels of theory suggest that the east barrier in deoxyribonucleosides is between 3.0 and 4.0 kcal/mol. In the abasic sugar, the west pseudorotation energy barrier is found to be slightly lower than the east barrier and the south pucker is favored more than in standard nucleosides. Results on the TA conformation suggest that, at the nucleoside level, this conformation is significantly destabilized relative to the global energy minimum, or relative to the A- and B-DNA conformations. Deoxyribocytosine would destabilize the TA conformation more than other bases relative to the A-DNA conformation, but not relative to the B-DNA conformation.

Intrinsic conformational energetics associated with the glycosyl torsion in DNA: a quantum mechanical study

The glycosyl torsion (chi) in nucleic acids has long been recognized to be a major determinant of their conformational properties. chi torsional energetics were systematically mapped in deoxyribonucleosides using high-level quantum mechanical methods, for north and south sugar puckers and with gamma in the g(+) and trans conformations. In all cases, the syn conformation is found higher in energy than the anti. When gamma is changed from g(+) to trans, the anti orientation of the base is strongly destabilized, and the energy difference and barrier between anti and syn are significantly decreased. The barrier between anti and syn in deoxyribonucleosides is found to be less than 10 kcal/mol and tends to be lower with purines than with pyrimidines. With gamma = g(+)/chi = anti, a south sugar yields a significantly broader energy well than a north sugar with no energy barrier between chi values typical of A or B DNA. Contrary to the prevailing view, the syn orientation is not more stable with south puckers than with north puckers. The syn conformation is significantly more energetically accessible with guanine than with adenine in 5-nucleotides but not in nucleosides. Analysis of nucleic acid crystal structures shows that gamma = trans/chi = anti is a minor but not negligible conformation. Overall, chi appears to be a very malleable structural parameter with the experimental chi distributions reflecting, to a large extent, the associated intrinsic torsional energetics.

Structural basis for SRY-dependent 46-X,Y sex reversal: modulation of DNA bending by a naturally occurring point mutation

The HMG-box domain of the human male sex-determining factor SRY, hSRY(HMG) (comprising residues 57-140 of the full-length sequence), binds DNA sequence-specifically in the minor groove, resulting in substantial DNA bending. The majority of point mutations resulting in 46X,Y sex reversal are located within this domain. One clinical de novo mutation, M64I in the full-length hSRY sequence, which corresponds to M9I in the present hSRY(HMG) construct, acts principally by reducing the extent of DNA bending. To elucidate the structural consequences of the M9I mutation, we have solved the 3D solution structures of wild-type and M9I hSRY(HMG) complexed to a DNA 14mer by NMR, including the use of residual dipolar couplings to derive long-range orientational information. We show that the average bend angle (derived from an ensemble of 400 simulated annealing structures for each complex) is reduced by approximately 13 degrees from 54(+/-2) degrees in the wild-type complex to 41(+/-2) degrees in the M9I complex. The difference in DNA bending can be localized directly to changes in roll and tilt angles in the ApA base-pair step involved in interactions with residue 9 and partial intercalation of Ile13. The larger bend angle in the wild-type complex arises as a direct consequence of steric repulsion of the sugar of the second adenine by the bulky S(delta) atom of Met9, whose position is fixed by a hydrogen bond with the guanidino group of Arg17. In the M9I mutant, this hydrogen bond can no longer occur, and the less bulky C(gamma)m methyl group of Ile9 braces the sugar moieties of the two adenine residues, thereby decreasing the roll and tilt angles at the ApA step by approximately 8 degrees and approximately 5 degrees, respectively, and resulting in an overall difference in bend angle of approximately 13 degrees between the two complexes. To our knowledge, this is one of the first examples where the effects of a clinical mutation involving a protein-DNA complex have been visualized at the atomic level.

A-form conformational motifs in ligand-bound DNA structures

Recognition and biochemical processing of DNA requires that proteins and other ligands are able to distinguish their DNA binding sites from other parts of the molecule. In addition to the direct recognition elements embedded in the linear sequence of bases (i.e. hydrogen bonding sites), these molecular agents seemingly sense and/or induce an "indirect" conformational response in the DNA base-pairs that facilitates close intermolecular fitting. As part of an effort to decipher this sequence-dependent structural code, we have analyzed the extent of B-->A conformational conversion at individual base-pair steps in protein and drug-bound DNA crystal complexes. We take advantage of a novel structural parameter, the position of the phosphorus atom in the dimer reference frame, as well as other documented measures of local helical structure, e.g. torsion angles, base-pair step parameters. Our analysis pinpoints ligand-induced conformational changes that are difficult to detect from the global perspective used in other studies of DNA structure. The collective data provide new structural details on the conformational pathway connecting A and B-form DNA and illustrate how both proteins and drugs take advantage of the intrinsic conformational mechanics of the double helix. Significantly, the base-pair steps which exhibit pure A-DNA conformations in the crystal complexes follow the scale of A-forming tendencies exhibited by synthetic oligonucleotides in solution and the known polymorphism of synthetic DNA fibers. Moreover, most crystallographic examples of complete B-to-A deformations occur in complexes of DNA with enzymes that perform cutting or sealing operations at the (O3'-P) phosphodiester linkage. The B-->A transformation selectively exposes sugar-phosphate atoms, such as the 3'-oxygen atom, ordinarily buried within the chain backbone for enzymatic attack. The forced remodeling of DNA to the A-form also provides a mechanism for smoothly bending the double helix, for controlling the widths of the major and minor grooves, and for accessing the minor groove edges of individual base-pairs.

Intrinsic conformational properties of deoxyribonucleosides: implicated role for cytosine in the equilibrium among the A, B, and Z forms of DNA

Structural properties of biomolecules are dictated by their intrinsic conformational energetics in combination with environmental contributions. Calculations using high-level ab initio methods on the deoxyribonucleosides have been performed to investigate the influence of base on the intrinsic conformational energetics of nucleosides. Energy minima in the north and south ranges of the deoxyribose pseudorotation surfaces have been located, allowing characterization of the influence of base on the structures and energy differences between those minima. With all bases, chi values associated with the south energy minimum are lower than in canonical B-DNA, while chi values associated with the north energy minimum are close to those in canonical A-DNA. In deoxycytidine, chi adopts an A-DNA conformation in both the north and south energy minima. Energy differences between the A and B conformations of the nucleosides are <0.5 kcal/mol in the present calculations, except with deoxycytidine, where the A form is favored by 2.3 kcal/mol, leading the intrinsic conformational energetics of GC basepairs to favor the A form of DNA by 1.5 kcal/mol as compared with AT pairs. This indicates that the intrinsic conformational properties of cytosine at the nucleoside level contribute to the A form of DNA containing predominately GC-rich sequences. In the context of a B versus Z DNA equilibrium, deoxycytidine favors the Z form over the B form by 1.6 kcal/mol as compared with deoxythymidine, suggesting that the intrinsic conformational properties of cytosine also contribute to GC-rich sequences occurring in Z DNA with a higher frequency than AT-rich sequences. Results show that the east pseudorotation energy barrier involves a decrease in the furanose amplitude and is systematically lower than the inversion barrier, with the energy differences influenced by the base. Energy barriers going from the south (B form) sugar pucker to the east pseudorotation barrier are lower in pyrimidines as compared with purines, indicating that the intrinsic conformational properties associated with base may also influence the sugar pseudorotational population distribution seen in DNA crystal structures and the kinetics of B to A transitions. The present work provides evidence that base composition, in addition to base sequence, can influence DNA conformation.

Stepping through an RNA structure: A novel approach to conformational analysis

Drawing from the growing database of complex three-dimensional RNA structures, a systematic method has been developed for classifying and analyzing the variety of conformations adopted by nucleic acids. This method is based on the development of a reduced representation for nucleic acid backbone conformation, simplifying the formidable eight-dimensional problem that has long complicated nucleic acid conformational analysis. Two pseudotorsion angles (eta and theta) have been defined, based on the selection of two appropriate pivot points along the RNA backbone, P and C4'. These pseudotorsions, together with a complete library of conventional torsion angles, can be calculated for any RNA structure or all-atom model using a new program called AMIGOS. Having computed eta and theta pseudotorsions for each position on an RNA molecule, they can be represented on a two-dimensional plot similar to the phi-phi plots that have traditionally been used for protein conformational analysis. Like a Ramachandran plot, clusters of residues appear at discrete regions on an eta-theta plot. Nucleotides within these clusters share conformational properties, often belonging to the same type of structural motif such as A-platforms, sheared tandem purine-purine pairs and GNRA tetraloops. An eta-theta plot provides a two-dimensional representation of the conformational properties of an entire RNA molecule, facilitating rapid analysis of structural features. In addition to the utility of eta-theta plots for intuitive visualization of conformational space, the pseudotorsional convention described here should significantly simplify approaches to macromolecular modeling of RNA structure.

Sequence-dependent DNA structure: the role of the sugar-phosphate backbone

A detailed analysis of the coupling between the conformational properties of the sugar-phosphate backbone and the base stacking interactions in dinucleotide steps of double helical DNA is described. In X-ray crystal structures of oligonucleotides, the backbone shows one major degree of freedom, consisting of the torsion angles chi, delta, zeta and the pseudorotation phase angle, P. The remaining torsion angles (beta, epsilon, alpha and gamma) comprise two less important degrees of freedom. The base stacking interactions show three degrees of freedom: slide-roll-twist, shift-tilt, and rise (which is more or less constant). Coupling is observed between the base and backbone degrees of freedom. The major base stacking mode, slide-roll-twist, is coupled to the major backbone mode, chi-P-delta-zeta. The secondary base stacking mode, shift-tilt, is coupled to epsilon and zeta and to a lesser extent to the chi-P-delta-zeta mode. We show that the length of the backbone, C, given by the same strand C1'-C1' separation, is an excellent single parameter descriptor for the conformation of the backbone and the way in which it is coupled to the base stacking geometry. The slide-roll-twist motion relates to changes in the mean backbone length, C, and the shift-tilt motion to the difference between the lengths of the two backbone strands, DeltaC. We use this observation to develop a simple virtual bond model which describes the coupling of the backbone conformations and the base stacking geometry. A semi-flexible bond is used to connect the same strand C1'-C1' atoms. Analysis of the X-ray crystal structure database, simple geometric considerations and model building experiments all show that this bond is flexible with respect to slide, shift and propeller but rigid with respect to the other 14 local base stacking parameters. Using this simple model for the backbone in conjunction with potential energy calculations of the base stacking interactions, we show that it is possible to predict accurately the values of these 14 base step parameters, given values of slide, shift and propeller. We also show that the base step parameters fall into three distinct groups: roll, tilt and rise are determined solely by the base stacking interactions and are independent of the backbone; twist is insensitive to the base stacking interactions and is determined solely by the constraints of a relatively rigid fixed length backbone; slide and shift are the primary degrees of freedom and cannot be predicted accurately at the dinucleotide level because they are influenced by the conformations of neighbouring steps in a sequence. We have found that the context effect on slide is mediated by the chi torsion angles while the context effect on shift results from a BI to BII transition in the backbone. We have therefore reduced the dimensionality of the dinucleotide step problem to two parameters, slide and shift.

A computational approach to modeling nucleic acid hairpin structures

Hairpin is a structural motif frequently observed in both RNA and DNA molecules. This motif is involved specifically in various biological functions (e.g., gene expression and regulation). To understand how these hairpin motifs perform their functions, it is important to study their structures. Compared to protein structural motifs, structures of nucleic acid hairpins are less known. Based on a set of reduced coordinates for describing nucleic acid structures and a sampling algorithm that equilibrates structures using Metropolis Monte Carlo simulation, we developed a method to model nucleic acid hairpin structures. This method was used to predict the structure of a DNA hairpin with a single-guanosine loop. The lowest energy structure from the ensemble of 200 sampled structures has a RMSD of < 1.5 A, from the structure determined using NMR. Additional constraints for the loop bases were introduced for modeling an RNA hairpin with two nucleotides in the loop. The modeled structure of this RNA hairpin has extensive base stacking and an extra hydrogen bond (between the CYT in the loop and a phosphate oxygen), as observed in the NMR structure.

Modeling large RNAs and ribonucleoprotein particles using molecular mechanics techniques

There is a growing body of low-resolution structural data that can be utilized to devise structural models for large RNAs and ribonucleoproteins. These models are routinely built manually. We introduce an automated refinement protocol to utilize such data for building low-resolution three-dimensional models using the tools of molecular mechanics. In addition to specifying the positions of each nucleotide, the protocol provides quantitative estimates of the uncertainties in those positions, i.e., the resolution of the model. In typical applications, the resolution of the models is about 10-20 A. Our method uses reduced representations and allows us to refine three-dimensional structures of systems as big as the 16S and 23S ribosomal RNAs, which are about one to two orders of magnitude larger than nucleic acids that can be examined by traditional all-atom modeling methods. Nonatomic resolution structural data--secondary structure, chemical cross-links, chemical and enzymatic footprinting patterns, protein positions, solvent accessibility, and so on--are combined with known motifs in RNA structure to predict low-resolution models of large RNAs. These structural constraints are imposed on the RNA chain using molecular mechanics-type potential functions with parameters based on the quality of experimental data. Surface potential functions are used to incorporate shape and positional data from electron microscopy image reconstruction experiments into our models. The structures are optimized using techniques of energy refinement to get RNA folding patterns. In addition to providing a consensus model, the method finds the range of models consistent with the data, which allows quantitative evaluation of the resolution of the model. The method also identifies conflicts in the experimental data. Although our protocol is aimed at much larger RNAs, we illustrate these techniques using the tRNA structure as an example and test-bed.

A Monte Carlo method for generating structures of short single-stranded DNA sequences

A Monte Carlo method has been developed for generating the conformations of short single-stranded DNAs from arbitrary starting states. The chain conformers are constructed from energetically favorable arrangements of the constituent mononucleotides. Minimum energy states of individual dinucleotide monophosphate molecules are identified using a torsion angle minimizer. The glycosyl and acyclic backbone torsions of the dimers are allowed to vary, while the sugar rings are held fixed in one of the two preferred puckered forms. A total of 108 conformationally distinct states per dimer are considered in this first stage of minimization. The torsion angles within 5 kcal/mole of the global minimum in the resulting optimized states are then allowed to vary by +/- 10 degrees in an effort to estimate the breadth of the different local minima. The energies of a total of 2187 (3(7)) angle combinations are examined per local conformational minimum. Finally, the energies of all dinucleotide conformers are scaled so that the populations of differently puckered sugar rings in the theoretical sample match those found in nmr solution studies. This last step is necessitated by limitations in the theoretical methods to predict DNA sugar puckering accurately. The conformer populations of the individual acyclic torsion angles in the composite dimer ensembles are found to be in good agreement with the distributions of backbone conformations deduced from nmr coupling constants and the frequencies of glycosyl conformations in x-ray crystal structures, suggesting that the low energy states are reasonable. The low energy dimer forms (consisting of 150-325 conformational states per dimer step) are next used as variables in a Monte Carlo algorithm, which generates the conformations of single-stranded d(CXnG) chains, where X = A, T and n = 3, 4, 5. The oligonucleotides are built sequentially from the 5' end of the chain using random numbers to select the conformations of overlapping dimer units. The simulations are very fast, involving a total of 10(6) conformations per chain sequence. The potential errors in the buildup procedure are minimized by taking advantage of known rotational interdependences in the sugar-phosphate backbone. The distributions of oligonucleotide conformations are examined in terms of the magnitudes, positions, and orientations of the end-to-end vectors of the chains. The differences in overall flexibility and extension of the oligomers are discussed in terms of the conformations of the constituent dinucleotide steps, while the general methodology is discussed and compared with other nucleic acid model building techniques.

DNA associations: packing calculations in A-, B-, and Z-DNA structures

A detailed theoretical study has been carried out to examine the modes of DNA-DNA interactions on the basis of hard-sphere contact criteria. Two helices of identical structure and length are oriented side-by-side and their relative positions are controlled by translations along and rotations about specific axes. Short atomic contacts between pairs of atoms in the structures are assessed and contact-free configurations are compiled. The computed contact-free arrangements of A, B, and Z double helices are found to be remarkably similar to the packing motifs observed in DNA crystals and stretched fibers. Equally interesting in the study are the broad ranges of sterically acceptable arrangements that preserve the overall packing morphology of neighboring duplexes: Among the most notable morphological features in the helical complexes are extended "super" major and minor grooves which might facilitate the wrapping and packaging of DNA chains in supramolecular assemblies. The hard-sphere computations, however, are insufficient for quantitative interpretation of the packing of DNA helices in the solid state. The results are, nevertheless, a useful starting point for energy based studies as well as relevant to the analysis of long-range interactions in DNA supercoils and cruciforms.

Stereochemical studies on nucleic acid analogues. I. Conformations of alpha-nucleosides and alpha-nucleotides: interconversion of sugar puckers via O4'-exo

The preferred conformations of ribo and deoxyribo alpha-nucleosides and alpha-nucleotides, the stereoisomers of the naturally occurring beta-isomers, are worked out by minimizing the conformational energy as a function of all the major parameters including the sugar ring conformations along the pseudorotation path. The results of the studies bring out certain distinct conformational features that are at variance with their beta counterparts. The range of glycosyl conformations are found to be not only quite restricted here but favor predominantly the anti conformation. The syn glycosyl conformation for the entire region of P values are found to be energetically less favorable, with the barrier to anti in equilibrium with syn interconversion being higher especially in alpha-ribonucleosides. The energetically preferred range of pseudorotation phase angles (P) is also considerably restricted and P values corresponding to the C1'-exo range of sugars are highly unfavorable for alpha-nucleosides, in sharp contrast to the broad range of sugar ring conformations favored by beta-isomers. While both trans congruent to 180 degrees and skew congruent to 270 degrees conformations around the C3'-O3' (phi') bond are favored for alpha-3'-nucleotides with deoxyribose sugars, ribose sugars seem to favor only the skew values of phi'. Most interestingly and in sharp contrast to beta-stereoisomers, an energy barrier is encountered at P values corresponding to O4'-endo sugars. This suggests that the possible sugar pucker interconversion between C2'-endo/C3'-exo and C3'-endo/C2'-exo in alpha-anomers could take place only through the O4'-exo region. Likewise the possible path of anti in equilibrium with syn interconversion in alpha-nucleosides is not via high anti, in sharp contrast to beta-nucleosides. These observations should be borne in mind while assigning the sugar ring conformers in alpha-nucleosides and those containing them from nmr investigations. Comparison of the results with beta-anomers seem to suggest on the whole a lack of conformational variability or the restricted nature of alpha-stereoisomers. This could be one of the reasons for its nonselection in the naturally occurring nucleic acids.

Strategies for the use of computational SAR methods in assessing genotoxicity

The relationship between computational SAR studies and relevant data gathering and generation activities is complex. First, the chemical class to be studied is selected on the basis of information requirements for hazard identification and assessment. Membership in the class is determined by consideration of chemical structure and reactivity. Compilation of the existing bioassay data for this chemical class follows immediately from the specification of the class. Bioassay data, qualitative knowledge of general chemical reactivities in this class, and knowledge concerning potential interactions with biomolecular targets all contribute to the derivation of possible mechanisms for biological activity. Computational studies based on modeling the proposed mechanism of action and/or the existing data base can provide a quantitative basis for the differentiation between chemicals. There is the opportunity for continuing feedback between the quantitative computational studies and the development of a relevant bioassay data base for this chemical class. The qualitative and quantitative information on the potential biological responses obtained will provide a rational basis for extrapolation from the extant data base to the chemicals of interest, and to biological responses significant to the assessment for which complete data are unavailable. Knowledge concerning possible mechanisms of action and preexisting data determine the type of computational study that will be most useful.

The B-Z transition in supercoiled DNA depends on sequence beyond nearest-neighbors

In order to examine sequence-dependent structural effects in DNA, the ability of alternating purine-pyrimidine fragments to undergo a B-Z transition when cloned in a supercoiled plasmid was determined solely as a function of sequence, with base and nearest-neighbor composition held constant. Sequences of 22 GC and 2 AT base pairs were synthesized such that the AT base pairs varied between contiguous placement and separation by eight GC base pairs. Results show, surprisingly, that the ease of the B-Z transition varies with the position of the two AT base pairs, occurring at lower superhelical densities when AT base pairs are contiguous, and at higher torsional strain when the AT base pairs are moved further apart.

Conformational studies of nucleic acids: III. Empirical multiple correlation functions for nucleic acid torsion angles

There are seven significantly variable torsion angles in each monomer unit of a polynucleotide. Because of this, it is computationally infeasible to consider the energetics of all conformations available to a nucleic acid without the use of simplifications. In this paper, we develop functions suggested by and regression fit to crystallographic data which allow three of these torsion angles, alpha (O3'-P-O5'-C5'), delta (C5'-C4'-C3'-O3') and epsilon (C4'-C3'-O3'-P), to be calculated as dependent variables of those remaining. Using these functions, the seven independent torsions are reduced to four, a reduction in complexity sufficient to allow an examination of the global conformational energetics of a nucleic acid for the remaining independent torsion angles. These functions are the first to quantitatively relate a dependent nucleic acid torsion angle to several different independent angles. In all three cases the data are fit reasonably well, and in one case, alpha, the fit is exceptionally good, lending support for the suitability of the functions in conformational searches. In addition, an examination of the most significant terms in each of the correlation functions allows insight into the physical basis for the correlations.

Conformational studies of nucleic acids: IV. The conformational energetics of oligonucleotides: d(ApApApA) and ApApApA

Utilizing a new method for modeling furanose pseudorotation (D. A. Pearlman and S.-H. Kim, J. Biomol. Struct. Dyn. 3, 85 (1985)) and the empirical multiple correlations between nucleic acid torsion angles we derived in the previous report (D. A. Pearlman and S.-H. Kim, previous paper in this issue), we have made an energetic examination of the entire conformational spaces available to two nucleic acid oligonucleotides: d(ApApApA) and ApApApA. The energies are calculated using a semi-empirical potential function. From the resulting body of data, energy contour map pairs (one for the DNA molecule, one for the RNA structure) have been created for each of the 21 possible torsion angle pairs in a nucleotide repeating unit. Of the 21 pairs, 15 have not been reported previously. The contour plots are different from those made earlier in that for each point in a particular angle-angle plot, the remaining five variable torsion angles are rotated to the values which give a minimum energy at this point. The contour maps are overall quite consistent with the experimental distribution of oligonucleotide data. A number of these maps are of particular interest: delta (C5'-C4'-C3'-O3')-chi (O4'-C1'-N9-C4), where the energetic basis for an approximately linear delta-chi correlation can be seen: zeta (C3'-O3'-P-O5')-delta, in which the experimentally observed linear correlation between zeta and delta in DNA(220 degrees less than zeta less than 280 degrees) is clearly predicted; zeta-epsilon (C4'-C3'-O3'-P), which shows that epsilon increases with decreasing zeta less than 260 degrees; alpha (O3'-P-O5'-C5')-gamma (O5'-C5'-C4'-C3') where a clear linear correlation between these angles is also apparent, consistent with experiment; and several others. For the DNA molecule studied here, the sugar torsion delta is predicted to be the most flexible, while for the RNA molecule, the greatest amount of flexibility is expected to reside in alpha and gamma. Both the DNA and RNA molecules are predicted to be highly polymorphic. Complete energy minimization has been performed on each of the minima found in the energy searches and the results further support this prediction. Possible pathways for B-form to A-form DNA interconversion suggested by the results of this study are discussed. The results of these calculations support use of the new sugar modeling technique and torsion angle correlations in future conformational studies of nucleic acids.

Conformational studies of (2'-5') polynucleotides: theoretical computations of energy, base morphology, helical structure, and duplex formation

A detailed theoretical analysis has been carried out to probe the conformational characteristics of (2'-5') polynucleotide chains. Semi-empirical energy calculations are used to estimate the preferred torsional combinations of the monomeric repeating unit. The resulting morphology of adjacent bases and the tendency to form regular single-stranded structures are determined by standard computational procedures. The torsional preferences are in agreement with available nmr measurements on model compounds. The tendencies to adopt base stacked and intercalative geometries are markedly depressed compared to those in (3'-5') chains. Very limited families of regular monomerically repeating single-stranded (2'-5') helices are found. Base stacking, however, can be enhanced (but helix formation is at the same time depressed) in mixed puckered chains. Constrained (2'-5') duplex structures have been constructed from a search of all intervening glycosyl and sugar conformations that form geometrically feasible phosphodiester linkages. Both A- and B-type base stacking are found to generate non-standard backbone torsions and mixed glycosyl/sugar combinations. The 2'- and 5'-residues are locked in totally different arrangements and are thereby prevented from generating long helical structures.