Resolving the discrepancies among nucleic acid conformational analyses

FebRNA: An automated fragment-ensemble-based model for building RNA 3D structures

Knowledge of RNA three-dimensional (3D) structures is critical to understanding the important biological functions of RNAs. Although various structure prediction models have been developed, the high-accuracy predictions of RNA 3D structures are still limited to the RNAs with short lengths or with simple topology. In this work, we proposed a new model, namely FebRNA, for building RNA 3D structures through fragment assembly based on coarse-grained (CG) fragment ensembles. Specifically, FebRNA is composed of four processes: establishing the library of different types of non-redundant CG fragment ensembles regardless of the sequences, building CG 3D structure ensemble through fragment assembly, identifying top-scored CG structures through a specific CG scoring function, and rebuilding the all-atom structures from the top-scored CG ones. Extensive examination against different types of RNA structures indicates that FebRNA consistently gives the reliable predictions on RNA 3D structures, including pseudoknots, three-way junctions, four-way and five-way junctions, and RNAs in the RNA-Puzzles. FebRNA is available on the Web site: https://github.com/Tan-group/FebRNA.

Structural Characterization of the Interaction of Hypoxia Inducible Factor-1 with Its Hypoxia Responsive Element at the -964G > A Variation Site of the HLA-G Promoter Region

Human Antigen Leukocyte-G (HLA-G) gene encodes an immune checkpoint molecule that has restricted tissue expression in physiological conditions; however, the gene may be induced in hypoxic conditions by the interaction with the hypoxia inducible factor-1 (HIF1). Hypoxia regulatory elements (HRE) located at the HLA-G promoter region and at exon 2 are the major HIF1 target sites. Since the G allele of the −964G > A transversion induces higher HLA-G expression when compared to the A allele in hypoxic conditions, here we analyzed HIF1-HRE complex interaction at the pair-atom level considering both −964G > A polymorphism alleles. Mouse HIF2 dimer crystal (Protein Data Bank ID: 4ZPK) was used as template to perform homology modelling of human HIF1 quaternary structure using MODELLER v9.14. Two 3D DNA structures were built from 5′GCRTG’3 HRE sequence containing the −964G/A alleles using x3DNA. Protein-DNA docking was performed using the HADDOCK v2.4 server, and non-covalent bonds were computed by DNAproDB server. Molecular dynamic simulation was carried out per 200 ns, using Gromacs v.2019. HIF1 binding in the HRE containing −964G allele results in more hydrogen bonds and van der Waals contact formation than HRE with −964A allele. Protein-DNA complex trajectory analysis revealed that HIF1-HRE-964G complex is more stable. In conclusion, HIF1 binds in a more stable and specific manner at the HRE with G allele.

Carcinogen-induced DNA structural distortion differences in the RAS gene isoforms; the importance of local sequence

BACKGROUND

Local sequence context is known to have an impact on the mutational pattern seen in cancer. The RAS genes and a smoking carcinogen, Benzo[a]pyrene diol epoxide (BPDE), have been utilised to explore these context effects. BPDE is known to form an adduct at the guanines in a number of RAS gene sites, KRAS codons 12, 13 and 14, NRAS codon 12, and HRAS codons 12 and 14.

RESULTS

Molecular modelling techniques, along with multivariate analysis, have been utilised to determine the sequence influenced differences between BPDE-adducted RAS gene sequences as well as the local distortion caused by the adducts.

CONCLUSIONS

We conclude that G:C > T:A mutations at KRAS codon 12 in the tumours of lung cancer patients (who smoke), proposed to be predominantly caused by BPDE, are due to the effect of the interaction methyl group at the C5 position of the thymine base in the KRAS sequence with the BPDE carcinogen investigated causing increased distortion. We further suggest methylated cytosine would have a similar effect, showing the importance of methylation in cancer development.

Intrinsic DNA topology as a prioritization metric in genomic fine-mapping studies

In genomic fine-mapping studies, some approaches leverage annotation data to prioritize likely functional polymorphisms. However, existing annotation resources can present challenges as many lack information for novel variants and/or may be uninformative for non-coding regions. We propose a novel annotation source, sequence-dependent DNA topology, as a prioritization metric for fine-mapping. DNA topology and function are well-intertwined, and as an intrinsic DNA property, it is readily applicable to any genomic region. Here, we constructed and applied Minor Groove Width (MGW) as a prioritization metric. Using an established MGW-prediction method, we generated a MGW census for 199 038 197 SNPs across the human genome. Summarizing a SNP's change in MGW (ΔMGW) as a Euclidean distance, ΔMGW exhibited a strongly right-skewed distribution, highlighting the infrequency of SNPs that generate dissimilar shape profiles. We hypothesized that phenotypically-associated SNPs can be prioritized by ΔMGW. We tested this hypothesis in 116 regions analyzed by a Massively Parallel Reporter Assay and observed enrichment of large ΔMGW for functional polymorphisms (P = 0.0007). To illustrate application in fine-mapping studies, we applied our MGW-prioritization approach to three non-coding regions associated with systemic lupus erythematosus. Together, this study presents the first usage of sequence-dependent DNA topology as a prioritization metric in genomic association studies.

Energy Landscapes of Deoxyxylo- and Xylo-Nucleic Acid Octamers

Artificial analogues of the natural nucleic acids have attracted interest as a diverse class of information storage molecules capable of self-replication. In this study, we use the computational potential energy landscape framework to investigate the structural and dynamical properties of xylo- and deoxyxylo-nucleic acids (XyNA and dXyNA), which are derived from their respective RNA and DNA analogues by inversion of a single chiral center in the sugar moiety of the nucleotides. For an octameric XyNA sequence and the analogue dXyNA, we observe facile conformational transitions between a left-handed helix, which is the free energy global minimum, and a ladder-type structure with approximately zero helicity. The competing ensembles are better separated in the dXyNA, making it a more suitable candidate for a molecular switch, whereas the XyNA exhibits additional flexibility. Both energy landscapes exhibit greater frustration than we observe in RNA or DNA, in agreement with the higher degree of optimization expected from the principle of minimal frustration in evolved biomolecules.

The emergence of sequence-dependent structural motifs in stretched, torsionally constrained DNA

The double-helical structure of DNA results from canonical base pairing and stacking interactions. However, variations from steady-state conformations resulting from mechanical perturbations in cells have physiological relevance but their dependence on sequence remains unclear. Here, we use molecular dynamics simulations showing sequence differences result in markedly different structural motifs upon physiological twisting and stretching. We simulate overextension on different sequences of DNA ((AA)12, (AT)12, (CC)12 and (CG)12) with supercoiling densities at 200 and 50 mM salt concentrations. We find that DNA denatures in the majority of stretching simulations, surprisingly including those with over-twisted DNA. GC-rich sequences are observed to be more stable than AT-rich ones, with the specific response dependent on the base pair order. Furthermore, we find that (AT)12 forms stable periodic structures with non-canonical hydrogen bonds in some regions and non-canonical stacking in others, whereas (CG)12 forms a stacking motif of four base pairs independent of supercoiling density. Our results demonstrate that 20-30% DNA extension is sufficient for breaking B-DNA around and significantly above cellular supercoiling, and that the DNA sequence is crucial for understanding structural changes under mechanical stress. Our findings have important implications for the activities of protein machinery interacting with DNA in all cells.

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.

Web 3DNA 2.0 for the analysis, visualization, and modeling of 3D nucleic acid structures

Web 3DNA (w3DNA) 2.0 is a significantly enhanced version of the widely used w3DNA server for the analysis, visualization, and modeling of 3D nucleic-acid-containing structures. Since its initial release in 2009, the w3DNA server has continuously served the community by making commonly-used features of the 3DNA suite of command-line programs readily accessible. However, due to the lack of updates, w3DNA has clearly shown its age in terms of modern web technologies and it has long lagged behind further developments of 3DNA per se. The w3DNA 2.0 server presented here overcomes all known shortcomings of w3DNA while maintaining its battle-tested characteristics. Technically, w3DNA 2.0 implements a simple and intuitive interface (with sensible defaults) for increased usability, and it complies with HTML5 web standards for broad accessibility. Featurewise, w3DNA 2.0 employs the most recent version of 3DNA, enhanced with many new functionalities, including: the automatic handling of modified nucleotides; a set of 'simple' base-pair and step parameters for qualitative characterization of non-Watson-Crick double-helical structures; new structural parameters that integrate the rigid base plane and the backbone phosphate group, the two nucleic acid components most reliably determined with X-ray crystallography; in silico base mutations that preserve the backbone geometry; and a notably improved module for building models of single-stranded RNA, double-helical DNA, Pauling triplex, G-quadruplex, or DNA structures 'decorated' with proteins. The w3DNA 2.0 server is freely available, without registration, at http://web.x3dna.org.

Effects of Noncanonical Base Pairing on RNA Folding: Structural Context and Spatial Arrangements of G·A Pairs

Noncanonical base pairs play important roles in assembling the three-dimensional structures critical to the diverse functions of RNA. These associations contribute to the looped segments that intersperse the canonical double-helical elements within folded, globular RNA molecules. They stitch together various structural elements, serve as recognition elements for other molecules, and act as sites of intrinsic stiffness or deformability. This work takes advantage of new software (DSSR) designed to streamline the analysis and annotation of RNA three-dimensional structures. The multiscale structural information gathered for individual molecules, combined with the growing number of unique, well-resolved RNA structures, makes it possible to examine the collective features deeply and to uncover previously unrecognized patterns of chain organization. Here we focus on a subset of noncanonical base pairs involving guanine and adenine and the links between their modes of association, secondary structural context, and contributions to tertiary folding. The rigorous descriptions of base-pair geometry that we employ facilitate characterization of recurrent geometric motifs and the structural settings in which these arrangements occur. Moreover, the numerical parameters hint at the natural motions of the interacting bases and the pathways likely to connect different spatial forms. We draw attention to higher-order multiplexes involving two or more G·A pairs and the roles these associations appear to play in bridging different secondary structural units. The collective data reveal pairing propensities in base organization, secondary structural context, and deformability and serve as a starting point for further multiscale investigations and/or simulations of RNA folding.

Molecular Dynamics Simulations of Dna and Its Complexes

This article describes how classical molecular simulation methods are being used to gain a molecular-level understanding of the interaction mechanisms responsible for DNA–ligand recognition, and that govern the response of DNA to ligand binding. Case studies using a variety of different ligands—including small pharmaceutical drugs, proteins and lipids—are used to illustrate the power of modern molecular dynamics simulation methods for understanding how we may control the function and structure of DNA.

Effect of the sulfur atom on S2 and S4 positions of the uracil ring in different DNA:RNA hybrid microhelixes with three nucleotide base pairs

The effect of the sulphur atom on the uracil ring was analyzed in different DNA:RNA microhelixes with three nucleotide base-pairs, including uridine, 2-thiouridine, 4-thiouridine, 2,4-dithiouridine, cytidine, adenosine and guanosine. Distinct backbone and helical parameters were optimized at different density functional (DFT) levels. The Watson-Crick pair with 2-thiouridine appears weaker than with uridine, but its interaction with water molecules appears easier. Two types of microhelixes were found, depending on the H-bond of H2' hydroxyl atom: A-type appears with the ribose ring in ³ E-envelope C_3' -endo, and B-type in ² E-envelope C_2' -endo. B-type is less common but it is more stable and with higher dipole-moment. The sulphur atoms significantly increase the dipole-moment of the microhelix, as well as the rise and propeller twist parameters. Simulations with four Na atoms H-bonded to the phosphate groups, and further hydration with explicit water molecules were carried out. A re-definition of the numerical value calculation of several base-pair and base-stacking parameters is suggested.

Sub-picosecond proton tunnelling in deformed DNA hydrogen bonds under an asymmetric double-oscillator model

We present a model of proton tunnelling across DNA hydrogen bonds, compute the characteristic tunnelling time (CTT) from donor to acceptor and discuss its biological implications. The model is a double oscillator characterised by three geometry parameters describing planar deformations of the H bond, and a symmetry parameter representing the energy ratio between ground states in the individual oscillators. We discover that some values of the symmetry parameter lead to CTTs which are up to 40 orders of magnitude smaller than a previous model predicted. Indeed, if the symmetry parameter is sufficiently far from its extremal values of 1 or 0, then the proton's CTT under any physically realistic planar deformation is guaranteed to be below one picosecond, which is a biologically relevant time-scale. This supports theories of links between proton tunnelling and biological processes such as spontaneous mutation.

Consecutive non-natural PZ nucleobase pairs in DNA impact helical structure as seen in 50 μs molecular dynamics simulations

Z

Little is known about the influence of multiple consecutive 'non-standard' ( , 6-amino-5-nitro-2(1H)-pyridone, and , 2-amino-imidazo[1,2-a]-1,3,5-triazin-4(8H)-one) nucleobase pairs on the structural parameters of duplex DNA. nucleobase pairs follow standard rules for Watson-Crick base pairing but have rearranged hydrogen bonding donor and acceptor groups. Using the X-ray crystal structure as a starting point, we have modeled the motions of a DNA duplex built from a self-complementary oligonucleotide (5΄-CTTATPPPZZZATAAG-3΄) in water over a period of 50 μs and calculated DNA local parameters, step parameters, helix parameters, and major/minor groove widths to examine how the presence of multiple, consecutive nucleobase pairs might impact helical structure. In these simulations, the -containing DNA duplex exhibits a significantly wider major groove and greater average values of stagger, slide, rise, twist and h-rise than observed for a 'control' oligonucleotide in which nucleobase pairs are replaced by . The molecular origins of these structural changes are likely associated with at least two differences between and . First, the electrostatic properties of differ from in terms of density distribution and dipole moment. Second, differences are seen in the base stacking of pairs in dinucleotide steps, arising from energetically favorable stacking of the nitro group in with π-electrons of the adjacent base.

Adaptive resolution simulation of oligonucleotides

Nucleic acids are characterized by a complex hierarchical structure and a variety of interaction mechanisms with other molecules. These features suggest the need of multiscale simulation methods in order to grasp the relevant physical properties of deoxyribonucleic acid (DNA) and RNA using in silico experiments. Here we report an implementation of a dual-resolution modeling of a DNA oligonucleotide in physiological conditions; in the presented setup only the nucleotide molecule and the solvent and ions in its proximity are described at the atomistic level; in contrast, the water molecules and ions far from the DNA are represented as computationally less expensive coarse-grained particles. Through the analysis of several structural and dynamical parameters, we show that this setup reliably reproduces the physical properties of the DNA molecule as observed in reference atomistic simulations. These results represent a first step towards a realistic multiscale modeling of nucleic acids and provide a quantitatively solid ground for their simulation using dual-resolution methods.

Computational 3D Assembling Methods for DNA: A Survey

DNA encodes the genetic information of most living beings, except viruses that use RNA. Unlike other types of molecules, DNA is not usually described by its atomic structure being instead usually described by its base-pair sequence, i.e., the textual sequence of its subsidiary molecules known as nucleotides ( adenine (A), cytosine (C), guanine (G), and thymine (T)). The three-dimensional assembling of DNA molecules based on its base-pair sequence has been, for decades, a topic of interest for many research groups all over the world. In this paper, we survey the major methods found in the literature to assemble and visualize DNA molecules from their base-pair sequences. We divided these methods into three categories: predictive methods, adaptive methods, and thermodynamic methods . Predictive methods aim to predict a conformation of the DNA from its base pair sequence, while the goal of adaptive methods is to assemble DNA base-pairs sequences along previously known conformations, as needed in scenarios such as DNA Monte Carlo simulations. Unlike these two geometric methods, thermodynamic methods are energy-based and aim to predict secondary structural motifs of DNA in cases where hydrogen bonds between base pairs might be broken because of temperature changes. We also present the major software tools that implements predictive, adaptive, and thermodynamic methods.

Aromatic Base Stacking in DNA: From ab initio Calculations to Molecular Dynamics Simulations

Abstract Aromatic stacking of nucleic acid bases is one of the key players in determining the structure and dynamics of nucleic acids. The arrangement of nucleic acid bases with extensive overlap of their aromatic rings gave rise to numerous often contradictory suggestions about the physical origins of stacking and the possible role of delocalized electrons in stacked aromatic π systems, leading to some confusion about the issue. The recent advance of computer hardware and software finally allowed the application of state of the art quantum-mechanical approaches with inclusion of electron correlation effects to study aromatic base stacking, now providing an ultimitate qualitative description of the phenomenon. Base stacking is determined by an interplay of the three most commonly encountered molecular interactions: dispersion attraction, electrostatic interaction, and short-range repulsion. Unusual (aromatic- stacking specific) energy contributions were in fact not evidenced and are not necessary to describe stacking. The currently used simple empirical potential form, relying on atom-centered constant point charges and Lennard-Jones van der Waals terms, is entirely able to reproduce the essential features of base stacking. Thus, we can conclude that base stacking is in principle one of the best described interactions in current molecular modeling and it allows to study base stacking in DNA using large-scale classical molecular dynamics simulations. Neglect of cooperativity of stacking appears to be the most serious approximation of the currently used force field form. This review summarizes recent developments in the field. It is written for an audience that is not necessarily expert in computational quantum chemistry and follows up on our previous contribution (Sponer et. al., J. Biomol. Struct. Dyn. 14, 117, (1997)). First, the applied methodology, its accuracy, and the physical nature of base stacking is briefly overviewed, including a comment on the accuracy of other molecular orbital methods and force fields. Then, base stacking is contrasted with hydrogen bonding, the other dominant force in nucleic acid structure. The sequence dependence and cooperativity of base stacking is commented on, and finally a brief introduction into recent progress in large-scale molecular dynamics simulations of nucleic acids is provided. Using four stranded DNA assemblies as an example, we demonstrate the efficacy of current molecular dynamics techniques that utilize refined and verified force fields in the study of stacking in nucleic acid molecules.

X-ray structure of a lectin-bound DNA duplex containing an unnatural phenanthrenyl pair

DNA duplexes containing unnatural base-pair surrogates are attractive biomolecular nanomaterials with potentially beneficial photophysical or electronic properties.

DSSR: an integrated software tool for dissecting the spatial structure of RNA

Insight into the three-dimensional architecture of RNA is essential for understanding its cellular functions. However, even the classic transfer RNA structure contains features that are overlooked by existing bioinformatics tools. Here we present DSSR (Dissecting the Spatial Structure of RNA), an integrated and automated tool for analyzing and annotating RNA tertiary structures. The software identifies canonical and noncanonical base pairs, including those with modified nucleotides, in any tautomeric or protonation state. DSSR detects higher-order coplanar base associations, termed multiplets. It finds arrays of stacked pairs, classifies them by base-pair identity and backbone connectivity, and distinguishes a stem of covalently connected canonical pairs from a helix of stacked pairs of arbitrary type/linkage. DSSR identifies coaxial stacking of multiple stems within a single helix and lists isolated canonical pairs that lie outside of a stem. The program characterizes 'closed' loops of various types (hairpin, bulge, internal, and junction loops) and pseudoknots of arbitrary complexity. Notably, DSSR employs isolated pairs and the ends of stems, whether pseudoknotted or not, to define junction loops. This new, inclusive definition provides a novel perspective on the spatial organization of RNA. Tests on all nucleic acid structures in the Protein Data Bank confirm the efficiency and robustness of the software, and applications to representative RNA molecules illustrate its unique features. DSSR and related materials are freely available at http://x3dna.org/.

Enhanced sampling simulations of DNA step parameters

A novel approach for the selection of step parameters as reaction coordinates in enhanced sampling simulations of DNA is presented. The method uses three atoms per base and does not require coordinate overlays or idealized base pairs. This allowed for a highly efficient implementation of the calculation of all step parameters and their Cartesian derivatives in molecular dynamics simulations. Good correlation between the calculated and actual twist, roll, tilt, shift, and slide parameters is obtained, while the correlation with rise is modest. The method is illustrated by its application to the methylated and unmethylated 5'-CATGTGACGTCACATG-3' double stranded DNA sequence. One-dimensional umbrella simulations indicate that the flexibility of the central CG step is only marginally affected by methylation.

Coupling between hydrogen atoms transfer and stacking interaction in adenine-thymine/guanine-cytosine complexes: a theoretical study

Four different complexes of two base pairs, an adenine-thymine and a guanine-cytosine one, have been studied in order to understand the modifications induced by the staking interaction between the two base pairs on the hydrogen atoms transfers between the bases in either base pair. The inclusion of these two kinds of interactions allows us to clarify if some properties, as the mechanism of hydrogen transfer, is exclusively a local effect of a base pair or can be modified by a more long-range interaction between the base pairs. The results on these four complexes are compared with those of the monomeric systems, the A-T and G-C base pair, and with those of the A-T and G-C dimers. The specificity of each complex and of each hydrogen bond has been analyzed.

Gold(III) macrocycles: nucleotide-specific unconventional catalytic inhibitors of human topoisomerase I

Topoisomerase IB (Top1) is a key eukaryotic nuclear enzyme that regulates the topology of DNA during replication and gene transcription. Anticancer drugs that block Top1 are either well-characterized interfacial poisons or lesser-known catalytic inhibitor compounds. Here we describe a new class of cytotoxic redox-stable cationic Au³⁺ macrocycles which, through hierarchical cluster analysis of cytotoxicity data for the lead compound, 3, were identified as either poisons or inhibitors of Top1. Two pivotal enzyme inhibition assays prove that the compounds are true catalytic inhibitors of Top1. Inhibition of human topoisomerase IIα (Top2α) by 3 was 2 orders of magnitude weaker than its inhibition of Top1, confirming that 3 is a type I-specific catalytic inhibitor. Importantly, Au³⁺ is essential for both DNA intercalation and enzyme inhibition. Macromolecular simulations show that 3 intercalates directly at the 5′-TA-3′ dinucleotide sequence targeted by Top1 via crucial electrostatic interactions, which include π–π stacking and an Au···O contact involving a thymine carbonyl group, resolving the ambiguity of conventional (drug binds protein) vs unconventional (drug binds substrate) catalytic inhibition of the enzyme. Surface plasmon resonance studies confirm the molecular mechanism of action elucidated by the simulations.

Molecular modeling of nucleic acid structure

This unit is the first in a series of four units covering the analysis of nucleic acid structure by molecular modeling. The unit provides an overview of the computer simulation of nucleic acids. Topics include the static structure model, computational graphics and energy models, the generation of an initial model, and characterization of the overall three-dimensional structure.

Impact of geometry optimization on base-base stacking interaction energies in the canonical A- and B-forms of DNA

Base stacking is known to make an important contribution to the stability of DNA and RNA, and accordingly, significant efforts are ongoing to calculate stacking energies using ab initio quantum mechanical methods. To date, impressive improvements have been made in the model chemistries used to perform stacking energy calculations, including extensions that include robust treatments of electron correlation with extended basis sets, as required to treat interactions where dispersion makes a significant contribution. However, those efforts typically use rigid monomer geometries when calculating the interaction energies. To overcome this, in the present work, we describe a novel internal coordinate definition that allows the relative, intermolecular orientation of stacked base monomers to be constrained during geometry optimizations while allowing full optimization of the intramolecular degrees of freedom. Use of the novel reference frame to calculate the impact of full geometry optimization versus constraining the bases to be planar on base monomer stacking energies, combined with density-fitted, spin-component scaling MP2 treatment of electron correlation, shows that full optimization makes the average stacking energy more favorable by -3.4 and -1.5 kcal/mol for the canonical A and B conformations of the 16 5' to 3' base stacked monomers. Thus, treatment of geometry optimization impacts the stacking energies to an extent similar to or greater than the impact of current state of the art increases in the rigor of the model chemistry itself used to treat base stacking. Results also indicate that stacking favors the B-form of DNA, though the average difference versus the A-form decreases from -2.6 to -0.6 kcal/mol when the intramolecular geometry is allowed to fully relax. However, stacking involving cytosine is shown to favor the A-form of DNA, with that contribution generally larger in the fully optimized bases. The present results show the importance of allowing geometry optimization, as well as properly treating the appropriate model chemistry, in studies of nucleic acid base stacking.

Modeling the mechanical properties of DNA nanostructures

We discuss generalizations of a previously published coarse-grained description [Mergell et al., Phys. Rev. E 68, 021911 (2003)] of double stranded DNA (dsDNA). The model is defined at the base-pair level and includes the electrostatic repulsion between neighbor helices. We show that the model reproduces mechanical and elastic properties of several DNA nanostructures (DNA origamis). We also show that electrostatic interactions are necessary to reproduce atomic force microscopy measurements on planar DNA origamis.

Structure, Stiffness and Substates of the Dickerson-Drew Dodecamer

The Dickerson-Drew dodecamer (DD) d-[CGCGAATTCGCG]₂ is a prototypic B-DNA molecule whose sequence-specific structure and dynamics have been investigated by many experimental and computational studies. Here, we present an analysis of DD properties based on extensive atomistic molecular dynamics (MD) simulations using different ionic conditions and water models. The 0.6-2.4-µs-long MD trajectories are compared to modern crystallographic and NMR data. In the simulations, the duplex ends can adopt an alternative base-pairing, which influences the oligomer structure. A clear relationship between the BI/BII backbone substates and the basepair step conformation has been identified, extending previous findings and exposing an interesting structural polymorphism in the helix. For a given end pairing, distributions of the basepair step coordinates can be decomposed into Gaussian-like components associated with the BI/BII backbone states. The nonlocal stiffness matrices for a rigid-base mechanical model of DD are reported for the first time, suggesting salient stiffness features of the central A-tract. The Riemann distance and Kullback-Leibler divergence are used for stiffness matrix comparison. The basic structural parameters converge very well within 300 ns, convergence of the BI/BII populations and stiffness matrices is less sharp. Our work presents new findings about the DD structural dynamics, mechanical properties, and the coupling between basepair and backbone configurations, including their statistical reliability. The results may also be useful for optimizing future force fields for DNA.

DNA Bending through Roll Angles Is Independent of Adjacent Base Pairs

We have studied DNA bending for a wide range of DNA sequences by two-dimensional adaptive umbrella sampling simulations on adjacent roll angles. Calculated free energy surfaces are largely additive and can be well approximated by the sum of the one-dimensional free energy surfaces. Cooperativity between adjacent roll angles was found to be negligible: less than 1.0 kcal/mol and a small fraction of the overall bending energy. Our calculations validate the assumptions underlying many popular coarse-grained models for DNA bending, and demonstrate their theoretical validity for investigating DNA bending.

DNA Bending through Large Angles Is Aided by Ionic Screening

We used adaptive umbrella sampling on a modified version of the roll angle to simulate the bending of DNA dodecamers. Simulations were carried out with the AMBER and CHARMM force fields for 10 sequences in which the central base pair step was varied. On long length scales, the DNA behavior was found to be consistent with the worm-like chain model. Persistence lengths calculated directly from the simulated structures and indirectly through the use of sequence-independent coarse-grained models based on simulation data were similar to literature values. On short length scales, the free energy cost of bending DNA was found to be consistent with the worm-like chain model for small and intermediate bending angles. At large angles, the bending free energy as a function of the roll angle became linear, suggesting a relative increase in flexibility at larger roll angles. Counterions congregated on the concave side of the highly bent DNA and screened the repulsion of the phosphate groups, facilitating the bending.

Local elasticity of strained DNA studied by all-atom simulations

Genomic DNA is constantly subjected to various mechanical stresses arising from its biological functions and cell packaging. If the local mechanical properties of DNA change under torsional and tensional stress, the activity of DNA-modifying proteins and transcription factors can be affected and regulated allosterically. To check this possibility, appropriate steady forces and torques were applied in the course of all-atom molecular dynamics simulations of DNA with AT- and GC-alternating sequences. It is found that the stretching rigidity grows with tension as well as twisting. The torsional rigidity is not affected by stretching, but it varies with twisting very strongly, and differently for the two sequences. Surprisingly, for AT-alternating DNA it passes through a minimum with the average twist close to the experimental value in solution. For this fragment, but not for the GC-alternating sequence, the bending rigidity noticeably changes with both twisting and stretching. The results have important biological implications and shed light on earlier experimental observations.

Working the kinks out of nucleosomal DNA

Condensation of DNA in the nucleosome takes advantage of its double-helical architecture. The DNA deforms at sites where the base pairs face the histone octamer. The largest so-called kink-and-slide deformations occur in the vicinity of arginines that penetrate the minor groove. Nucleosome structures formed from the 601 positioning sequence differ subtly from those incorporating an AT-rich human α-satellite DNA. Restraints imposed by the histone arginines on the displacement of base pairs can modulate the sequence-dependent deformability of DNA and potentially contribute to the unique features of the different nucleosomes. Steric barriers mimicking constraints found in the nucleosome induce the simulated large-scale rearrangement of canonical B DNA to kink-and-slide states. The pathway to these states shows nonharmonic behavior consistent with bending profiles inferred from AFM measurements.

Molecular dynamics of DNA: comparison of force fields and terminal nucleotide definitions

Despite DNA being a very important target for several proteins and drugs, molecular dynamics simulations with nucleic acids still encompass many challenges, such as the reliability of the chosen force field. In this paper, we carried out molecular dynamics simulations of the Dickerson-Drew dodecamer comparing GROMOS 53A6 and AMBER 03 force fields. While the AMBER force field presents specific topologies for the 5' and 3' terminal nucleotides, the GROMOS force field considers all nucleotides in the same way. To investigate the effects of the terminal nucleotide definitions, both force fields were modified to be applied in the two possible ways: with or without specific terminal nucleotide topologies. The analysis of global stability (rmsd, number of base pairs and hydrogen bonds) showed that both systems simulated with AMBER were stable, while the system simulated with the original GROMOS topologies was very unstable after 5 ns. When specific terminal topologies were included for GROMOS force field, DNA denaturation was delayed until 15 ns, but not avoided. The alpha/gamma transitions also displayed a strong dependence on the force field, but not on the terminal nucleotide definitions: AMBER simulations mainly explored configurations corresponding to the global minimum, while GROMOS simulations exhibited, very early in the simulations, an extensive sampling of local minima that may facilitate transitions to A-DNA isoform. The epsilon/zeta sampling was dependent both on the force field and on the terminal nucleotide definitions: while the AMBER simulations displayed well-defined B-I --> B-II transitions, the GROMOS force field clearly favored the B-I conformation. Also, the system simulated with the original GROMOS topologies displayed uncoupled epsilon/zeta transitions, leading to noncanonical conformations, but this was reverted when the new terminal nucleotide topologies were applied. Finally, the GROMOS force field leads to strong geometrical deformations on the DNA (overestimated groove widths and roll and strongly underestimated twist and slide), which restrict the use of GROMOS force field in long time scale DNA simulations unless a further reparametrization is made.

Nucleic-acid structural deformability deduced from anisotropic displacement parameters

The growing numbers of very well resolved nucleic-acid crystal structures with anisotropic displacement parameters provide an unprecedented opportunity to learn about the natural motions of DNA and RNA. Here we report a new Monte-Carlo approach that takes direct account of this information to extract the distortions of covalent structure, base pairing, and dinucleotide geometry intrinsic to regularly organized double-helical molecules. We present new methods to test the validity of the anisotropic parameters and examine the apparent deformability of a variety of structures, including several A, B, and Z DNA duplexes, an AB helical intermediate, an RNA, a ligand-DNA complex, and an enzyme-bound DNA. The rigid-body parameters characterizing the positions of the bases in the structures mirror the mean parameters found when atomic motion is taken into account. The base-pair fluctuations intrinsic to a single structure, however, differ from those extracted from collections of nucleic-acid structures, although selected base-pair steps undergo conformational excursions along routes suggested by the ensembles. The computations reveal surprising new molecular insights, such as the stiffening of DNA and concomitant separation of motions of contacted nucleotides on opposite strands by the binding of Escherichia coli endonuclease VIII, which suggest how the protein may direct enzymatic action.

Two perspectives on the twist of DNA

Because of the double-helical structure of DNA, in which two strands of complementary nucleotides intertwine around each other, a covalently closed DNA molecule with no interruptions in either strand can be viewed as two interlocked single-stranded rings. Two closed space curves have long been known by mathematicians to exhibit a property called the linking number, a topologically invariant integer, expressible as the sum of two other quantities, the twist of one of the curves about the other, and the writhing number, or writhe, a measure of the chiral distortion from planarity of one of the two closed curves. We here derive expressions for the twist of supercoiled DNA and the writhe of a closed molecule consistent with the modern view of DNA as a sequence of base-pair steps. Structural biologists commonly characterize the spatial disposition of each step in terms of six rigid-body parameters, one of which, coincidentally, is also called the twist. Of interest is the difference in the mathematical properties between this step-parameter twist and the twist of supercoiling associated with a given base-pair step. For example, it turns out that the latter twist, unlike the former, is sensitive to certain translational shearing distortions of the molecule that are chiral in nature. Thus, by comparing the values for the two twists for each step of a high-resolution structure of a protein-DNA complex, we may be able to determine how the binding of various proteins contributes to chiral structural changes of the DNA.

Conformational analysis of nucleic acids revisited: Curves+

We describe Curves+, a new nucleic acid conformational analysis program which is applicable to a wide range of nucleic acid structures, including those with up to four strands and with either canonical or modified bases and backbones. The program is algorithmically simpler and computationally much faster than the earlier Curves approach, although it still provides both helical and backbone parameters, including a curvilinear axis and parameters relating the position of the bases to this axis. It additionally provides a full analysis of groove widths and depths. Curves+ can also be used to analyse molecular dynamics trajectories. With the help of the accompanying program Canal, it is possible to produce a variety of graphical output including parameter variations along a given structure and time series or histograms of parameter variations during dynamics.

Flexibility of Short-Strand RNA in Aqueous Solution as Revealed by Molecular Dynamics Simulation: Are A-RNA and A´-RNA Distinct Conformational Structures?

We use molecular dynamics simulations to compare the conformational structure and dynamics of a 21-base pair RNA sequence initially constructed according to the canonical A-RNA and A′-RNA forms in the presence of counterions and explicit water. Our study aims to add a dynamical perspective to the solid-state structural information that has been derived from X-ray data for these two characteristic forms of RNA. Analysis of the three main structural descriptors commonly used to differentiate between the two forms of RNA – namely major groove width, inclination and the number of base pairs in a helical twist – over a 30 ns simulation period reveals a flexible structure in aqueous solution with fluctuations in the values of these structural parameters encompassing the range between the two crystal forms and more. This provides evidence to suggest that the identification of distinct A-RNA and A′-RNA structures, while relevant in the crystalline form, may not be generally relevant in the context of RNA in the aqueous phase. The apparent structural flexibility observed in our simulations is likely to bear ramifications for the interactions of RNA with biological molecules (e.g. proteins) and non-biological molecules (e.g. non-viral gene delivery vectors).

Analysis and classification of RNA tertiary structures

There is a fast growing interest in noncoding RNA transcripts. These transcripts are not translated into proteins, but play essential roles in many cellular and pathological processes. Recent efforts toward comprehension of their function has led to a substantial increase in both the number and the size of solved RNA structures. With the aim of addressing questions relating to RNA structural diversity, we examined RNA conservation at three structural levels: primary, secondary, and tertiary structure. Additionally, we developed an automated method for classifying RNA structures based on spatial (three-dimensional [3D]) similarity. Applying the method to all solved RNA structures resulted in a classified database of RNA tertiary structures (DARTS). DARTS embodies 1333 solved RNA structures classified into 94 clusters. The classification is hierarchical, reflecting the structural relationship between and within clusters. We also developed an application for searching DARTS with a new structure. The search is fast and its performance was successfully tested on all solved RNA structures since the creation of DARTS. A user-friendly interface for both the database and the search application is available online. We show intracluster and intercluster similarities in DARTS and demonstrate the usefulness of the search application. The analysis reveals the current structural repertoire of RNA and exposes common global folds and local tertiary motifs. Further study of these conserved substructures may suggest possible RNA domains and building blocks. This should be beneficial for structure prediction and for gaining insights into structure-function relationships.

Helical coherence of DNA in crystals and solution

The twist, rise, slide, shift, tilt and roll between adjoining base pairs in DNA depend on the identity of the bases. The resulting dependence of the double helix conformation on the nucleotide sequence is important for DNA recognition by proteins, packaging and maintenance of genetic material, and other interactions involving DNA. This dependence, however, is obscured by poorly understood variations in the stacking geometry of the same adjoining base pairs within different sequence contexts. In this article, we approach the problem of sequence-dependent DNA conformation by statistical analysis of X-ray and NMR structures of DNA oligomers. We evaluate the corresponding helical coherence length--a cumulative parameter quantifying sequence-dependent deviations from the ideal double helix geometry. We find, e.g. that the solution structure of synthetic oligomers is characterized by 100-200 A coherence length, which is similar to approximately 150 A coherence length of natural, salmon-sperm DNA. Packing of oligomers in crystals dramatically alters their helical coherence. The coherence length increases to 800-1200 A, consistent with its theoretically predicted role in interactions between DNA at close separations.

Molecular modeling of nucleic acid structure

This unit is the first in a series of four units covering the analysis of nucleic acid structure by molecular modeling. This unit provides an overview of computer simulation of nucleic acids. Topics include the static structure model, computational graphics and energy models, generation of an initial model, and characterization of the overall three-dimensional structure.

3DNA: a versatile, integrated software system for the analysis, rebuilding and visualization of three-dimensional nucleic-acid structures

We present a set of protocols showing how to use the 3DNA suite of programs to analyze, rebuild and visualize three-dimensional nucleic-acid structures. The software determines a wide range of conformational parameters, including the identities and rigid-body parameters of interacting bases and base-pair steps, the nucleotides comprising helical fragments, the area of overlap of stacked bases and so on. The reconstruction of three-dimensional structure takes advantage of rigorously defined rigid-body parameters, producing rectangular block representations of the nucleic-acid bases and base pairs and all-atom models with approximate sugar-phosphate backbones. The visualization components create vector-based drawings and scenes that can be rendered as raster-graphics images, allowing for easy generation of publication-quality figures. The utility programs use geometric variables to control the view and scale of an object, for comparison of related structures. The commands run in seconds even for large structures. The software and related information are available at http://3dna.rutgers.edu/.

DNA organization and thermodynamics during viral packing

An elastic DNA molecular mechanics model is used to compare DNA structures and packing thermodynamics in two bacteriophage systems, T7 and phi29. A discrete packing protocol allows for multiple molecular dynamics simulations of the entire packing event. In T7, the DNA is coaxially spooled around the cylindrical core protein, whereas the phi29 system, which lacks a core protein, organizes the DNA concentrically, but not coaxially. Two-dimensional projections of the packed structures from T7 simulations are consistent with cryo-electron micrographs of T7 phage DNA. The functional form of the force required to package the phi29 DNA is similar to forces determined experimentally, although the total free energy change is only 40% of the experimental value. Since electrostatics are not included in the simulations, this suggests that electrostatic repulsions are responsible for approximately 60% of the free energy required for packaging. The entropic penalty from DNA confinement has not been computed in previous studies, but it is often assumed to make a negligible contribution to the total work done in packing the DNA. Conformational entropy can be measured in our approach, and it accounts for 70-80% of the total work done in packing the elastic model DNA in both phages. For phi29, this corresponds to an entropic penalty of approximately 35% of the total work observed experimentally.

The ARTS web server for aligning RNA tertiary structures

RNA molecules with common structural features may share similar functional properties. Structural comparison of RNAs and detection of common substructures is, thus, a highly important task. Nevertheless, the current available tools in the RNA community provide only a partial solution, since they either work at the 2D level or are suitable for detecting predefined or local contiguous tertiary motifs only. Here, we describe a web server built around ARTS, a method for aligning tertiary structures of nucleic acids (both RNA and DNA). ARTS receives a pair of 3D nucleic acid structures and searches for a priori unknown common substructures. The search is truly 3D and irrespective of the order of the nucleotides on the chain. The identified common substructures can be large global folds with hundreds and even thousands of nucleotides as well as small local motifs with at least two successive base pairs. The method is highly efficient and has been used to conduct an all-against-all comparison of all the RNA structures in the Protein Data Bank. The web server together with a software package for download are freely accessible at http://bioinfo3d.cs.tau.ac.il/ARTS.

Nature of base stacking: reference quantum-chemical stacking energies in ten unique B-DNA base-pair steps

Base-stacking energies in ten unique B-DNA base-pair steps and some other arrangements were evaluated by the second-order Møller-Plesset (MP2) method, complete basis set (CBS) extrapolation, and correction for triple (T) electron-correlation contributions. The CBS(T) calculations were compared with decade-old MP2/6-31G*(0.25) reference data and AMBER force field. The new calculations show modest increases in stacking stabilization compared to the MP2/6-31G*(0.25) data and surprisingly large sequence-dependent variation of stacking energies. The absolute force-field values are in better agreement with the new reference data, while relative discrepancies between quantum-chemical (QM) and force-field values increase modestly. Nevertheless, the force field provides good qualitative description of stacking, and there is no need to introduce additional pair-additive electrostatic terms, such as distributed multipoles or out-of-plane charges. There is a rather surprising difference of about 0.1 A between the vertical separation of base pairs predicted by quantum chemistry and derived from crystal structures. Evaluations of different local arrangements of the 5'-CG-3' step indicate a sensitivity of the relative stacking energies to the level of calculation. Thus, describing quantitative relations between local DNA geometrical variations and stacking may be more complicated than usually assumed. The reference calculations are complemented by continuum-solvent assessment of solvent-screening effects.

Non-cognate Enzyme–DNA Complex: Structural and Kinetic Analysis of EcoRV Endonuclease Bound to the EcoRI Recognition Site GAATTC

The crystal structure of EcoRV endonuclease bound to non-cognate DNA at 2.0 angstroms resolution shows that very small structural adaptations are sufficient to ensure the extreme sequence specificity characteristic of restriction enzymes. EcoRV bends its specific GATATC site sharply by 50 degrees into the major groove at the center TA step, generating unusual base-base interactions along each individual DNA strand. In the symmetric non-cognate complex bound to GAATTC, the center step bend is relaxed to avoid steric hindrance caused by the different placement of the exocyclic thymine methyl groups. The decreased base-pair unstacking in turn leads to small conformational rearrangements in the sugar-phosphate backbone, sufficient to destabilize binding of crucial divalent metal ions in the active site. A second crystal structure of EcoRV bound to the base-analog GAAUTC site shows that the 50 degrees center-step bend of the DNA is restored. However, while divalent metals bind at high occupancy in this structure, one metal ion shifts away from binding at the scissile DNA phosphate to a position near the 3'-adjacent phosphate group. This may explain why the 10(4)-fold attenuated cleavage efficiency toward GAATTC is reconstituted by less than tenfold toward GAAUTC. Examination of DNA binding and bending by equilibrium and stopped-flow florescence quenching and fluorescence resonance energy transfer (FRET) methods demonstrates that the capacity of EcoRV to bend the GAATTC non-cognate site is severely limited, but that full bending of GAAUTC is achieved at only a threefold reduced rate compared with the cognate complex. Together, the structural and biochemical data demonstrate the existence of distinct mechanisms for ensuring specificity at the bending and catalytic steps, respectively. The limited conformational rearrangements observed in the EcoRV non-cognate complex provide a sharp contrast to the extensive structural changes found in a non-cognate BamHI-DNA crystal structure, thus demonstrating a diversity of mechanisms by which restriction enzymes are able to achieve specificity.

Molecular dynamics simulations of the 136 unique tetranucleotide sequences of DNA oligonucleotides. II: sequence context effects on the dynamical structures of the 10 unique dinucleotide steps

Molecular dynamics (MD) simulations including water and counterions on B-DNA oligomers containing all 136 unique tetranucleotide basepair steps are reported. The objective is to obtain the calculated dynamical structure for at least two copies of each case, use the results to examine issues with regard to convergence and dynamical stability of MD on DNA, and determine the significance of sequence context effects on all unique dinucleotide steps. This information is essential to understand sequence effects on DNA structure and has implications on diverse problems in the structural biology of DNA. Calculations were carried out on the 136 cases embedded in 39 DNA oligomers with repeating tetranucleotide sequences, capped on both ends by GC pairs and each having a total length of 15 nucleotide pairs. All simulations were carried out using a well-defined state-of-the-art MD protocol, the AMBER suite of programs, and the parm94 force field. In a previous article (Beveridge et al. 2004. Biophysical Journal. 87:3799-3813), the research design, details of the simulation protocol, and informatics issues were described. Preliminary results from 15 ns MD trajectories were presented for the d(CpG) step in all 10 unique sequence contexts. The results indicated the sequence context effects to be small for this step, but revealed that MD on DNA at this length of trajectory is subject to surprisingly persistent cooperative transitions of the sugar-phosphate backbone torsion angles alpha and gamma. In this article, we report detailed analysis of the entire trajectory database and occurrence of various conformational substates and its impact on studies of context effects. The analysis reveals a possible direct correspondence between the sequence-dependent dynamical tendencies of DNA structure and the tendency to undergo transitions that "trap" them in nonstandard conformational substates. The difference in mean of the observed basepair step helicoidal parameter distribution with different flanking sequence sometimes differs by as much as one standard deviation, indicating that the extent of sequence effects could be significant. The observations reveal that the impact of a flexible dinucleotide such as CpG could extend beyond the immediate basepair neighbors. The results in general provide new insight into MD on DNA and the sequence-dependent dynamical structural characteristics of DNA.

Protein-DNA Recognition Patterns and Predictions

Structural data on protein-DNA complexes provide clues for understanding the mechanism of protein-DNA recognition. Although the structures of a large number of protein-DNA complexes are known, the mechanisms underlying their specific binding are still only poorly understood. Analysis of these structures has shown that there is no simple one-to-one correspondence between bases and amino acids within protein-DNA complexes; nevertheless, the observed patterns of interaction carry important information on the mechanisms of protein-DNA recognition. In this review, we show how the patterns of interaction, either observed in known structures or derived from computer simulations, confer recognition specificity, and how they can be used to examine the relationship between structure and specificity and to predict target DNA sequences used by regulatory proteins.

Common patterns in type II restriction enzyme binding sites

Restriction enzymes are among the best studied examples of DNA binding proteins. In order to find general patterns in DNA recognition sites, which may reflect important properties of protein–DNA interaction, we analyse the binding sites of all known type II restriction endonucleases. We find a significantly enhanced GC content and discuss three explanations for this phenomenon. Moreover, we study patterns of nucleotide order in recognition sites. Our analysis reveals a striking accumulation of adjacent purines (R) or pyrimidines (Y). We discuss three possible reasons: RR/YY dinucleotides are characterized by (i) stronger H-bond donor and acceptor clusters, (ii) specific geometrical properties and (iii) a low stacking energy. These features make RR/YY steps particularly accessible for specific protein–DNA interactions. Finally, we show that the recognition sites of type II restriction enzymes are underrepresented in host genomes and in phage genomes.

Molecular dynamics simulations of the 136 unique tetranucleotide sequences of DNA oligonucleotides. I. Research design and results on d(CpG) steps

We describe herein a computationally intensive project aimed at carrying out molecular dynamics (MD) simulations including water and counterions on B-DNA oligomers containing all 136 unique tetranucleotide base sequences. This initiative was undertaken by an international collaborative effort involving nine research groups, the "Ascona B-DNA Consortium" (ABC). Calculations were carried out on the 136 cases imbedded in 39 DNA oligomers with repeating tetranucleotide sequences, capped on both ends by GC pairs and each having a total length of 15 nucleotide pairs. All MD simulations were carried out using a well-defined protocol, the AMBER suite of programs, and the parm94 force field. Phase I of the ABC project involves a total of approximately 0.6 mus of simulation for systems containing approximately 24,000 atoms. The resulting trajectories involve 600,000 coordinate sets and represent approximately 400 gigabytes of data. In this article, the research design, details of the simulation protocol, informatics issues, and the organization of the results into a web-accessible database are described. Preliminary results from 15-ns MD trajectories are presented for the d(CpG) step in its 10 unique sequence contexts, and issues of stability and convergence, the extent of quasiergodic problems, and the possibility of long-lived conformational substates are discussed.

Implications of the dependence of the elastic properties of DNA on nucleotide sequence

Recent advances in structural biochemistry have provided evidence that not only the geometric properties but also the elastic moduli of duplex DNA are strongly dependent on nucleotide sequence in a way that is not accounted for by classical rod models of the Kirchhoff type. A theory of sequence-dependent DNA elasticity is employed here to calculate the dependence of the equilibrium configurations of circular DNA on the binding of ligands that can induce changes in intrinsic twist at a single base-pair step. Calculations are presented of the influence on configurations of the assumed values and distribution along the DNA of intrinsic roll and twist and a modulus coupling roll to twist. Among the results obtained are the following. For minicircles formed from intrinsically straight DNA, the distribution of roll-twist coupling strongly affects the dependence of the total elastic energy Psi on the amount alpha of imposed untwisting, and that dependence can be far from quadratic. (In fact, for a periodic distribution of roll-twist coupling with a period equal to the intrinsic helical repeat length, Psi can be essentially independent of alpha for -90 degrees < alpha <90 degrees.) When the minicircle is homogeneous and without roll-twist coupling, but with uniform positive intrinsic roll, the point at which Psi attains its minimum value shifts towards negative values of alpha. It is remarked that there are cases in which one can relate graphs of Psi versus alpha to the 'effective values' of bending and twisting moduli and helical repeat length obtained from measurements of equilibrium distributions of topoisomers and probabilities of ring closure. For a minicircle formed from DNA that has an 'S' shape when stress-free, the graphs of Psi versus alpha have maxima at alpha = 0. As the binding of a twisting agent to such a minicircle results in a net decrease in Psi, the affinity of the twisting agent for binding to the minicircle is greater than its affinity for binding to unconstrained DNA with the same sequence.