DNA stretching and compression: large-scale simulations of double helical structures

Twist-stretch relations in nucleic acids

Nucleic acids are highly deformable helical molecules constantly stretched, twisted and bent in their biological functioning. Single molecule experiments have shown that double stranded (ds)-RNA and standard ds-DNA have opposite twist-stretch patterns and stretching properties when overwound under a constant applied load. The key structural features of the A-form RNA and B-form DNA helices are here incorporated in a three-dimensional mesoscopic Hamiltonian model which accounts for the radial, bending and twisting fluctuations of the base pairs. Using path integral techniques which sum over the ensemble of the base pair fluctuations, I compute the average helical repeat of the molecules as a function of the load. The obtained twist-stretch relations and stretching properties, for short A- and B-helical fragments, are consistent with the opposite behaviors observed in kilo-base long molecules.

Modeling the Homologous Recombination Process: Methods, Successes and Challenges

Homologous recombination (HR) is a fundamental process common to all species. HR aims to faithfully repair DNA double strand breaks. HR involves the formation of nucleoprotein filaments on DNA single strands (ssDNA) resected from the break. The nucleoprotein filaments search for homologous regions in the genome and promote strand exchange with the ssDNA homologous region in an unbroken copy of the genome. HR has been the object of intensive studies for decades. Because multi-scale dynamics is a fundamental aspect of this process, studying HR is highly challenging, both experimentally and using computational approaches. Nevertheless, knowledge has built up over the years and has recently progressed at an accelerated pace, borne by increasingly focused investigations using new techniques such as single molecule approaches. Linking this knowledge to the atomic structure of the nucleoprotein filament systems and the succession of unstable, transient intermediate steps that takes place during the HR process remains a challenge; modeling retains a very strong role in bridging the gap between structures that are stable enough to be observed and in exploring transition paths between these structures. However, working on ever-changing long filament systems submitted to kinetic processes is full of pitfalls. This review presents the modeling tools that are used in such studies, their possibilities and limitations, and reviews the advances in the knowledge of the HR process that have been obtained through modeling. Notably, we will emphasize how cooperative behavior in the HR nucleoprotein filament enables modeling to produce reliable information.

Understanding protein diffusion on force-induced stretched DNA conformation

DNA morphology is subjected to environmental conditions and is closely coupled with its function. For example, DNA experiences stretching forces during several biological processes, including transcription and genome transactions, that significantly alter its conformation from that of B-DNA. Indeed, a well-defined 1.5 times extended conformation of dsDNA, known as Σ-DNA, has been reported in DNA complexes with proteins such as Rad51 and RecA. A striking feature in Σ-DNA is that the nucleobases are partitioned into triplets of three locally stacked bases separated by an empty rise gap of ∼ 5 Å. The functional role of such a DNA base triplet was hypothesized to be coupled with the ease of recognition of DNA bases by DNA-binding proteins (DBPs) and the physical origin of three letters (codon/anti-codon) in the genetic code. However, the underlying mechanism of base-triplet formation and the ease of DNA base-pair recognition by DBPs remain elusive. To investigate, here, we study the diffusion of a protein on a force-induced stretched DNA using coarse-grained molecular dynamics simulations. Upon pulling at the 3' end of DNA by constant forces, DNA exhibits a conformational transition from B-DNA to a ladder-like S-DNA conformation via Σ-DNA intermediate. The resulting stretched DNA conformations exhibit non-uniform base-pair clusters such as doublets, triplets, and quadruplets, of which triplets are energetically more stable than others. We find that protein favors the triplet formation compared to its unbound form while interacting non-specifically along DNA, and the relative population of it governs the ruggedness of the protein-DNA binding energy landscape and enhances the efficiency of DNA base recognition. Furthermore, we analyze the translocation mechanism of a DBP under different force regimes and underscore the significance of triplet formation in regulating the facilitated diffusion of protein on DNA. Our study, thus, provides a plausible framework for understanding the structure-function relationship between triplet formation and base recognition by a DBP and helps to understand gene regulation in complex regulatory processes.

Structure and Dynamics of dsDNA in Cell-like Environments

Deoxyribonucleic acid (DNA) is a fundamental biomolecule for correct cellular functioning and regulation of biological processes. DNA's structure is dynamic and has the ability to adopt a variety of structural conformations in addition to its most widely known double-stranded DNA (dsDNA) helix structure. Stability and structural dynamics of dsDNA play an important role in molecular biology. In vivo, DNA molecules are folded in a tightly confined space, such as a cell chamber or a channel, and are highly dense in solution; their conformational properties are restricted, which affects their thermodynamics and mechanical properties. There are also many technical medical purposes for which DNA is placed in a confined space, such as gene therapy, DNA encapsulation, DNA mapping, etc. Physiological conditions and the nature of confined spaces have a significant influence on the opening or denaturation of DNA base pairs. In this review, we summarize the progress of research on the stability and dynamics of dsDNA in cell-like environments and discuss current challenges and future directions. We include studies on various thermal and mechanical properties of dsDNA in ionic solutions, molecular crowded environments, and confined spaces. By providing a better understanding of melting and unzipping of dsDNA in different environments, this review provides valuable guidelines for predicting DNA thermodynamic quantities and for designing DNA/RNA nanostructures.

Nanoscale structures and mechanics of peptide nucleic acids

Peptide nucleic acids (PNAs) are charge-neutral polyamide oligomers having extremely favorable thermal stability and high affinity to cell membranes when coupled with cationic cell-penetrating peptides (CPPs), as well as the encouraging antisense and antigene activity in cell-free systems. The study of the mechanical properties of short PNA molecules is rare both in experiments and theoretical calculations. Here, we studied the microscopic structures and elastic properties; namely, persistence length, stretch modulus, twist-stretch coupling, and structural crookedness of double-stranded PNA (dsPNA) and their hybrid derivatives using all-atom MD simulation and compared them with those of double-stranded DNA (dsDNA) and double-stranded RNA (dsRNA). The stretch modulus of the dsPNA is found to be ∼160 pN, an order of magnitude lower than that of dsDNA and smaller than dsRNA, respectively. Similarly, the persistence length of dsPNA is found to be ∼35 nm, significantly smaller than those of dsDNA and dsRNA. The PNA-DNA and PNA-RNA hybrid duplexes have elastic properties lying between that of dsPNA and dsDNA/dsRNA. We argue that the neutral backbones of the PNA make it less stiff than dsDNA and dsRNA molecules. Measurement of structural crookedness and principal component analysis additionally support the bending flexibility of dsPNA. Detailed analysis of the helical-rise coupled to helical-twist indicates that the PNA-DNA hybrid over-winds like dsDNA, while PNA-PNA and PNA-RNA unwind like dsRNA upon stretching. Because of the highly flexible nature of PNA, it can bind other biomolecules by adopting a wide range of conformations and is believed to be crucial for future nanobiotechnology research studies.

Elucidating the Role of Topological Constraint on the Structure of Overstretched DNA Using Fluorescence Polarization Microscopy

The combination of DNA force spectroscopy and polarization microscopy of fluorescent DNA intercalator dyes can provide valuable insights into the structure of DNA under tension. These techniques have previously been used to characterize S-DNA-an elongated DNA conformation that forms when DNA overstretches at forces ≥ 65 pN. In this way, it was deduced that the base pairs of S-DNA are highly inclined, relative to those in relaxed (B-form) DNA. However, it is unclear whether and how topological constraints on the DNA may influence the base-pair inclinations under tension. Here, we apply polarization microscopy to investigate the impact of DNA pulling geometry, torsional constraint, and negative supercoiling on the orientations of intercalated dyes during overstretching. In contrast to earlier predictions, the pulling geometry (namely, whether the DNA molecule is stretched via opposite strands or the same strand) is found to have little influence. However, torsional constraint leads to a substantial reduction in intercalator tilting in overstretched DNA, particularly in AT-rich sequences. Surprisingly, the extent of intercalator tilting is similarly reduced when the DNA molecule is negatively supercoiled up to a critical supercoiling density (corresponding to ∼70% reduction in the linking number). We attribute these observations to the presence of P-DNA (an overwound DNA conformation). Our results suggest that intercalated DNA preferentially flanks regions of P-DNA rather than those of S-DNA and also substantiate previous suggestions that P-DNA forms predominantly in AT-rich sequences.

Structural Flexibility of DNA-RNA Hybrid Duplex: Stretching and Twist-Stretch Coupling

DNA-RNA hybrid (DRH) duplexes play essential roles during the replication of DNA and the reverse transcription of RNA viruses, and their flexibility is important for their biological functions. Recent experiments indicated that A-form RNA and B-form DNA have a strikingly different flexibility in stretching and twist-stretch coupling, and the structural flexibility of DRH duplex is of great interest, especially in stretching and twist-stretch coupling. In this work, we performed microsecond all-atom molecular dynamics simulations with new AMBER force fields to characterize the structural flexibility of DRH duplex in stretching and twist-stretch coupling. We have calculated all the helical parameters, stretch modulus, and twist-stretch coupling parameters for the DRH duplex. First, our analyses on structure suggest that the DRH duplex exhibits an intermediate conformation between A- and B-forms and closer to A-form, which can be attributed to the stronger rigidity of the RNA strand than the DNA strand. Second, our calculations show that the DRH duplex has the stretch modulus of 834 ± 34 pN and a very weak twist-stretch coupling. Our quantitative analyses indicate that, compared with DNA and RNA duplexes, the different flexibility of the DRH duplex in stretching and twist-stretch coupling is mainly attributed to its apparently different basepair inclination in the helical structure.

Single-molecule polarization microscopy of DNA intercalators sheds light on the structure of S-DNA

DNA structural transitions facilitate genomic processes, mediate drug-DNA interactions, and inform the development of emerging DNA-based biotechnology such as programmable materials and DNA origami. While some features of DNA conformational changes are well characterized, fundamental information such as the orientations of the DNA base pairs is unknown. Here, we use concurrent fluorescence polarization imaging and DNA manipulation experiments to probe the structure of S-DNA, an elusive, elongated conformation that can be accessed by mechanical overstretching. To this end, we directly quantify the orientations and rotational dynamics of fluorescent DNA-intercalated dyes. At extensions beyond the DNA overstretching transition, intercalators adopt a tilted (θ ~ 54°) orientation relative to the DNA axis, distinct from the nearly perpendicular orientation (θ ~ 90°) normally assumed at lower extensions. These results provide the first experimental evidence that S-DNA has substantially inclined base pairs relative to those of the standard (Watson-Crick) B-DNA conformation.

Radial distribution function of semiflexible oligomers with stretching flexibility

The radial distribution of the end-to-end distance R_ee is crucial for quantifying the global size and flexibility of a linear polymer. For semiflexible polymers, several analytical formulas have been derived for the radial distribution of R_ee ignoring the stretching flexibility. However, for semiflexible oligomers, such as DNA or RNA, the stretching flexibility can be rather pronounced and can significantly affect the radial distribution of R_ee. In this study, we obtained an extended formula that includes the stretch modulus to describe the distribution of R_ee for semiflexible oligomers on the basis of previous formulas for semiflexible polymers without stretching flexibility. The extended formula was validated by extensive Monte Carlo simulations over wide ranges of the stretch modulus and persistence length, as well as all-atom molecular dynamics simulations of short DNAs and RNAs. Additionally, our analyses showed that the effect of stretching flexibility on the distribution of R_ee becomes negligible for DNAs longer than ∼130 base pairs and RNAs longer than ∼240 base pairs.

Lattice Mismatch in Crystalline Nanoparticle Thin Films

For atomic thin films, lattice mismatch during heteroepitaxy leads to an accumulation of strain energy, generally causing the films to irreversibly deform and generate defects. In contrast, more elastically malleable building blocks should be better able to accommodate this mismatch and the resulting strain. Herein, that hypothesis is tested by utilizing DNA-modified nanoparticles as "soft," programmable atom equivalents to grow a heteroepitaxial colloidal thin film. Calculations of interaction potentials, small-angle X-ray scattering data, and electron microscopy images show that the oligomer corona surrounding a particle core can deform and rearrange to store elastic strain up to ±7.7% lattice mismatch, substantially exceeding the ±1% mismatch tolerated by atomic thin films. Importantly, these DNA-coated particles dissipate strain both elastically through a gradual and coherent relaxation/broadening of the mismatched lattice parameter and plastically (irreversibly) through the formation of dislocations or vacancies. These data also suggest that the DNA cannot be extended as readily as compressed, and thus the thin films exhibit distinctly different relaxation behavior in the positive and negative lattice mismatch regimes. These observations provide a more general understanding of how utilizing rigid building blocks coated with soft compressible polymeric materials can be used to control nano- and microstructure.

All-atom molecular dynamics simulations of spin labelled double and single-strand DNA for EPR studies

Prediction of motional EPR spectra of spin labelled DNA structures from fully atomistic MD simulations.

Understanding the mechanical response of double-stranded DNA and RNA under constant stretching forces using all-atom molecular dynamics

Multiple biological processes involve the stretching of nucleic acids (NAs). Stretching forces induce local changes in the molecule structure, inhibiting or promoting the binding of proteins, which ultimately affects their functionality. Understanding how a force induces changes in the structure of NAs at the atomic level is a challenge. Here, we use all-atom, microsecond-long molecular dynamics to simulate the structure of dsDNA and dsRNA subjected to stretching forces up to 20 pN. We determine all of the elastic constants of dsDNA and dsRNA and provide an explanation for three striking differences in the mechanical response of these two molecules: the threefold softer stretching constant obtained for dsRNA, the opposite twist-stretch coupling, and its nontrivial force dependence. The lower dsRNA stretching resistance is linked to its more open structure, whereas the opposite twist-stretch coupling of both molecules is due to the very different evolution of molecules' interstrand distance with the stretching force. A reduction of this distance leads to overwinding in dsDNA. In contrast, dsRNA is not able to reduce its interstrand distance and can only elongate by unwinding. Interstrand distance is directly correlated with the slide base-pair parameter and its different behavior in dsDNA and dsRNA traced down to changes in the sugar pucker angle of these NAs.

Twist-stretch profiles of DNA chains

Helical molecules change their twist number under the effect of a mechanical load. We study the twist-stretch relation for a set of short DNA molecules modeled by a mesoscopic Hamiltonian. Finite temperature path integral techniques are applied to generate a large ensemble of possible configurations for the base pairs of the sequence. The model also accounts for the bending and twisting fluctuations between adjacent base pairs along the molecules stack. Simulating a broad range of twisting conformation, we compute the helix structural parameters by averaging over the ensemble of base pairs configurations. The method selects, for any applied force, the average twist angle which minimizes the molecule's free energy. It is found that the chains generally over-twist under an applied stretching and the over-twisting is physically associated to the contraction of the average helix diameter, i.e. to the damping of the base pair fluctuations. Instead, assuming that the maximum amplitude of the bending fluctuations may decrease against the external load, the DNA molecule first over-twists for weak applied forces and then untwists above a characteristic force value. Our results are discussed in relation to available experimental information albeit for kilo-base long molecules.

Relating the Structure of HIV-1 Reverse Transcriptase to Its Processing Step

Abstract By treating an enzyme as a coarse-grained uniform block of material, utilizing only the α-Carbon positions, the normal modes of motion can be obtained. For reverse transcriptase the slower of these motions are suggestive of being involved in the processing step, where the RNA or DNA strand is copied onto a new DNA strand at a polymerase site, and the RNA strand is subsequently cut up at the distant Ribonuclease H site. The slowest mode of motion involves hinge bending about a site midway between the polymerase and Ribonuclease H sites, suggesting that it can push or pull the RNA strand between these two sites. Pulling the nucleic acid strand would require tight binding to the RNase H site. The next slowest mode involves a hinge that opens and closes the protein like a clamp, which could facilitate the release of the nucleic acids for their step-wise progression. The third mode could rotate the substrate. An overall description of the step-wise processing step would involve close coordination among these steps. Results suggest that the smaller p51 subunit serves only as ballast to support the various modes of motion involving the different parts of the p66 subunit.

A Mechanism for RecA-Promoted Sequence Homology Recognition and Strand Exchange Between Single-Stranded DNA and Duplex DNA, via Triple-Helical Intermediates

Abstract A central function of RecA protein during homologous recombination is to promote sequence recognition and strand exchange between a stretched and unwound single-stranded DNA, to which it is complexed, and a duplex DNA. By studying the properties of DNA under the conditions of deformation imposed by RecA, we propose a model for recognition and strand exchange at the atomic level, via unusual triple-helical intermediates. In this model, association takes place within a stretched and unwound triple helix of a new type, where the invading single strand occupies the minor groove of the duplex in a parallel orientation. Our calculations indicate that strand exchange within this structure is exothermic and results in a triple helix where the third strand interacts in the major groove, the so-called R-DNA triple helix. Preliminary calculations suggest that sequence homology recognition within the triplex of association is partial and that it is completed during strand exchange and product formation.

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

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

The energy of naturally curved elastic rods with an application to the stretching and contraction of a free helical spring as a model for DNA

We give a contemporary and direct derivation of a classical, but insufficiently familiar, result in the theory of linear elasticity-a representation for the energy of a stressed elastic rod with central axis that intrinsically takes the shape of a general space curve. We show that the geometric torsion of the space curve, while playing a crucial role in the bending energy, is physically unrelated to the elastic twist. We prove that the twist energy vanishes in the lowest-energy states of a rod subject to constraints that do not restrict the twist. The stretching and contraction energies of a free helical spring are computed. There are local high-energy minima. We show the possibility of using the spring to model the chirality of DNA. We then compare our results with an available atomic level energy simulation that was performed on DNA unconstrained in the same sense as the free spring. We find some possible reflections of springlike behavior in the mechanics of DNA, but, unsurprisingly, the base pairs lend a material substance to the core of DNA that a spring does not capture.

Equilibrium and kinetics of DNA overstretching modeled with a quartic energy landscape

It is well known that the dsDNA molecule undergoes a phase transition from B-DNA into an overstretched state at high forces. For some time, the structure of the overstretched state remained unknown and highly debated, but recent advances in experimental techniques have presented evidence of more than one possible phase (or even a mixed phase) depending on ionic conditions, temperature, and basepair sequence. Here, we present a theoretical model to study the overstretching transition with the possibility that the overstretched state is a mixture of two phases: a structure with portions of inner strand separation (melted or M-DNA), and an extended phase that retains the basepair structure (S-DNA). We model the double-stranded DNA as a chain composed of n segments of length l, where the transition is studied by means of a Landau quartic potential with statistical fluctuations. The length l is a measure of cooperativity of the transition and is key to characterizing the overstretched phase. By analyzing the different values of l corresponding to a wide spectrum of experiments, we find that for a range of temperatures and ionic conditions, the overstretched form is likely to be a mix of M-DNA and S-DNA. For a transition close to a pure S-DNA state, where the change in extension is close to 1.7 times the original B-DNA length, we find l ? 25 basepairs regardless of temperature and ionic concentration. Our model is fully analytical, yet it accurately reproduces the force-extension curves, as well as the transient kinetic behavior, seen in DNA overstretching experiments.

Double-stranded RNA under force and torque: similarities to and striking differences from double-stranded DNA

RNA plays myriad roles in the transmission and regulation of genetic information that are fundamentally constrained by its mechanical properties, including the elasticity and conformational transitions of the double-stranded (dsRNA) form. Although double-stranded DNA (dsDNA) mechanics have been dissected with exquisite precision, much less is known about dsRNA. Here we present a comprehensive characterization of dsRNA under external forces and torques using magnetic tweezers. We find that dsRNA has a force-torque phase diagram similar to that of dsDNA, including plectoneme formation, melting of the double helix induced by torque, a highly overwound state termed "P-RNA," and a highly underwound, left-handed state denoted "L-RNA." Beyond these similarities, our experiments reveal two unexpected behaviors of dsRNA: Unlike dsDNA, dsRNA shortens upon overwinding, and its characteristic transition rate at the plectonemic buckling transition is two orders of magnitude slower than for dsDNA. Our results challenge current models of nucleic acid mechanics, provide a baseline for modeling RNAs in biological contexts, and pave the way for new classes of magnetic tweezers experiments to dissect the role of twist and torque for RNA-protein interactions at the single-molecule level.

Insights into chromatin fibre structure by in vitro and in silico single-molecule stretching experiments

The detailed structure and dynamics of the chromatin fibre and their relation to gene regulation represent important open biological questions. Recent advances in single-molecule force spectroscopy experiments have addressed these questions by directly measuring the forces that stabilize and alter the folded states of chromatin, and by investigating the mechanisms of fibre unfolding. We present examples that demonstrate how complementary modelling approaches have helped not only to interpret the experimental findings, but also to advance our knowledge of force-induced events such as unfolding of chromatin with dynamically bound linker histones and nucleosome unwrapping.

Denaturation transition of stretched DNA

In the last two decades, single-molecule force measurements using optical and magnetic tweezers and atomic force spectroscopy have dramatically expanded our knowledge of nucleic acids and proteins. These techniques characterize the force on a biomolecule required to produce a given molecular extension. When stretching long DNA molecules, the observed force–extension relationship exhibits a characteristic plateau at approximately 65 pN where the DNA may be extended to almost twice its B-DNA length with almost no increase in force. In the present review, I describe this transition in terms of the Poland–Scheraga model and summarize recent related studies.

Tension induces a base-paired overstretched DNA conformation

Mixed-sequence DNA molecules undergo mechanical overstretching by approximately 70% at 60-70 pN. Since its initial discovery 15 y ago, a debate has arisen as to whether the molecule adopts a new form [Cluzel P, et al. (1996) Science 271:792-794; Smith SB, Cui Y, Bustamante C (1996) Science 271:795-799], or simply denatures under tension [van Mameren J, et al. (2009) Proc Natl Acad Sci USA 106:18231-18236]. Here, we resolve this controversy by using optical tweezers to extend small 60-64 bp single DNA duplex molecules whose base content can be designed at will. We show that when AT content is high (70%), a force-induced denaturation of the DNA helix ensues at 62 pN that is accompanied by an extension of the molecule of approximately 70%. By contrast, GC-rich sequences (60% GC) are found to undergo a reversible overstretching transition into a distinct form that is characterized by a 51% extension and that remains base-paired. For the first time, results proving the existence of a stretched basepaired form of DNA can be presented. The extension observed in the reversible transition coincides with that produced on DNA by binding of bacterial RecA and human Rad51, pointing to its possible relevance in homologous recombination.

Functional specificity of a protein-DNA complex mediated by two arginines bound to the minor groove

A bacteriophage Ø29 transcriptional regulator, protein p4, interacts with its DNA target by employing two mechanisms: by direct readout of the chemical signatures of only one DNA base and by inducing local modification on the topology of short A tracts (indirect readout). p4 binds as a dimer to targets consisting of imperfect inverted repeats. Here we used molecular dynamic simulation to define interactions of a cluster of 12 positively charged amino acids of p4 with DNA and biochemical assays with modified DNA targets and mutated proteins to quantify the contribution of residues in the nucleoprotein complex. Our results show the implication of Arg54, with non-base-specific interaction in the central A tract, in p4 binding affinity. Despite being chemically equivalent and in identical protein monomers, the two Arg54 residues differed in their interactions with DNA. We discuss an indirect-readout mechanism for p4-DNA recognition mediated by dissimilar interaction of arginines penetrating the minor groove and the inherent properties of the A tract. Our findings extend the current understanding of protein-DNA recognition and contribute to the relevance of the sequence-dependent conformational malleability of the DNA, shedding light on the role of arginines in binding affinity. Characterization of mutant p4R54A shows that the residue is required for the activity of the protein as a transcriptional regulator.

SCREW MOTION OF DNA DUPLEX DURING TRANSLOCATION THROUGH PORE I: INTRODUCTION OF THE COARSE-GRAINED MODEL

Based upon the structural properties of DNA duplexes and their counterion-water surrounding in solution, we have introduced here a screw model which may describe translocation of DNA duplexes through artificial nanopores of the proper diameter (where the DNA counterion–hydration shell can be intact) in a qualitatively correct way. This model represents DNA as a kind of "screw," whereas the counterion-hydration shell is a kind of "nut." Mathematical conditions for stable dynamics of the DNA screw model are investigated in detail. When an electrical potential is applied across an artificial membrane with a nanopore, the "screw" and "nut" begin to move with respect to each other, so that their mutual rotation is coupled with their mutual translation. As a result, there are peaks of electrical current connected with the mutual translocation of DNA and its counterion–hydration shell, if DNA is possessed of some non-regular base-pair sequence. The calculated peaks of current strongly resemble those observed in the pertinent experiments. An analogous model could in principle be applied to DNA translocation in natural DNA–protein complexes of biological interest, where the role of "nut" would be played by protein-tailored "channels." In such cases, the DNA screw model is capable of qualitatively explaining chemical-to-mechanical energy conversion in DNA–protein molecular machines via symmetry breaking in DNA–protein friction.

RecA homology search is promoted by mechanical stress along the scanned duplex DNA

A RecA–single-stranded DNA (RecA–ssDNA) filament searches a genome for sequence homology by rapidly binding and unbinding double-stranded DNA (dsDNA) until homology is found. We demonstrate that pulling on the opposite termini (3′ and 5′) of one of the two DNA strands in a dsDNA molecule stabilizes the normally unstable binding of that dsDNA to non-homologous RecA–ssDNA filaments, whereas pulling on the two 3′, the two 5′, or all four termini does not. We propose that the ‘outgoing’ strand in the dsDNA is extended by strong DNA–protein contacts, whereas the ‘complementary’ strand is extended by the tension on the base pairs that connect the ‘complementary’ strand to the ‘outgoing’ strand. The stress resulting from different levels of tension on its constitutive strands causes rapid dsDNA unbinding unless sufficient homology is present.

B-DNA to zip-DNA: simulating a DNA transition to a novel structure with enhanced charge-transport characteristics

The forced extension of a DNA segment is studied in a series of steered molecular dynamics simulations, employing a broad range of pulling forces. Throughout the entire force range, the formation of a zipper-like (zip-) DNA structure is observed. In that structure, first predicted by Lohikoski et al., the bases of the DNA strands interdigitate with each other and form a single-base aromatic stack. Similar motifs, albeit only a few base pairs in extent, have been observed in experimental crystal structures. Analysis of the dynamics of structural changes in pulled DNA shows that S-form DNA, thought to be adopted by DNA under applied force, serves as an intermediate between B-DNA and zip-DNA. Therefore, the phase transition plateau observed in force-extension curves of DNA is suggested to reflect the B-DNA to zip-DNA structural transition. Electronic structure analysis of purine bases in zip-DNA indicates a several-fold to order of magnitude increase in the π-π electronic coupling among nearest-neighbor nucleobases, compared to B-DNA. We further observe that zip-DNA does not require base pair complementarity between DNA strands, and we predict that the increased electronic coupling in zip-DNA will result in a much higher rate of charge transfer through an all-purine zip-DNA compared to B-DNA of equal length.

Anchoring nascent RNA to the DNA template could interfere with transcription

During normal transcription, the nascent RNA product is released from the DNA template. However, in some cases, the RNA remains bound or can become reattached to the template DNA duplex (for example, through R-loop formation). We have analyzed the effect on transcription elongation of nascent RNA anchoring to the template DNA duplex. Because the RNA polymerase follows a helical path along DNA duplex during transcription, the anchoring would result in wrapping the nascent RNA around the DNA in the region between the anchoring point and the translocating polymerase. This wrapping would cause an unfavorable loss of conformation entropy of the nascent RNA. It consequently would create an apparent force to unwrap the RNA by disrupting either the transcription complex or the anchoring structure. We have estimated that this force would be comparable to those required to melt nucleic acid duplexes or to arrest transcription elongation in single-molecule experiments. We predict that this force would create negative supercoiling in the DNA duplex region between the anchoring point and the transcribing RNA polymerase: this can promote the formation of unusual DNA structures and facilitate RNA invasion into the DNA duplex. Potential biological consequences of these effects are discussed.

A three-state model with loop entropy for the overstretching transition of DNA

We introduce a three-state model for a single DNA chain under tension that distinguishes among B-DNA, S-DNA, and M (molten or denatured) segments and at the same time correctly accounts for the entropy of molten loops, characterized by the exponent c in the asymptotic expression S approximately -c ln n for the entropy of a loop of length n. Force extension curves are derived exactly by employing a generalized Poland-Scheraga approach and then compared to experimental data. Simultaneous fitting to force-extension data at room temperature and to the denaturation phase transition at zero force is possible and allows us to establish a global phase diagram in the force-temperature plane. Under a stretching force, the effects of the stacking energy (entering as a domain-wall energy between paired and unpaired bases) and the loop entropy are separated. Therefore, we can estimate the loop exponent c independently from the precise value of the stacking energy. The fitted value for c is small, suggesting that nicks dominate the experimental force extension traces of natural DNA.

Study of force induced melting of dsDNA as a function of length and conformation

We measure the constant force required to melt double-stranded (ds) DNA as a function of length for lengths from 12 to 100,000 base pairs, where the force is applied to the 3'3' or 5'5' ends of the dsDNA. Molecules with 32 base pairs or fewer melt before overstretching. For these short molecules, the melting force is independent of the ends to which the force is applied and the shear force as a function of length is well described by de Gennes theory with a de Gennes length of less than 10 bp. Molecules with lengths of 500 base pairs or more overstretch before melting. For these long molecules, the melting force depends on the ends to which the force is applied. The melting force as a function of length increases even when the length exceeds 1000 bp, where the length dependence is inconsistent with de Gennes theory. Finally, we expand de Gennes melting theory to 3'5' pulling and compare the predictions with experimental results.

Crystal structures of nucleosome core particles containing the '601' strong positioning sequence

Nucleosome positioning plays a key role in genomic regulation by defining histone-DNA context and by modulating access to specific sites. Moreover, the histone-DNA register influences the double-helix structure, which in turn can affect the association of small molecules and protein factors. Analysis of genomic and synthetic DNA has revealed sequence motifs that direct nucleosome positioning in vitro; thus, establishing the basis for the DNA sequence dependence of positioning would shed light on the mechanics of the double helix and its contribution to chromatin structure in vivo. However, acquisition of well-diffracting nucleosome core particle (NCP) crystals is extremely dependent on the DNA fragment used for assembly, and all previous NCP crystal structures have been based on human α-satellite sequences. Here, we describe the crystal structures of Xenopus NCPs containing one of the strongest known histone octamer binding and positioning sequences, the so-called '601' DNA. Two distinct 145-bp 601 crystal forms display the same histone-DNA register, which coincides with the occurrence of DNA stretching-overtwisting in both halves of the particle around five double-helical turns from the nucleosome center, giving the DNA an 'effective length' of 147 bp. As we have found previously with stretching around two turns from the nucleosome center for a centromere-based sequence, the terminal stretching observed in the 601 constructs is associated with extreme kinking into the minor groove at purine-purine (pyrimidine-pyrimidine) dinucleotide steps. In other contexts, these step types display an overall nonflexible behavior, which raises the possibility that DNA stretching in the nucleosome or extreme distortions in general have unique sequence dependency characteristics. Our findings indicate that DNA stretching is an intrinsically predisposed site-specific property of the nucleosome and suggest how NCP crystal structures with diverse DNA sequences can be obtained.

Biophysical characterization of DNA binding from single molecule force measurements

Single molecule force spectroscopy is a powerful method that uses the mechanical properties of DNA to explore DNA interactions. Here we describe how DNA stretching experiments quantitatively characterize the DNA binding of small molecules and proteins. Small molecules exhibit diverse DNA binding modes, including binding into the major and minor grooves and intercalation between base pairs of double-stranded DNA (dsDNA). Histones bind and package dsDNA, while other nuclear proteins such as high mobility group proteins bind to the backbone and bend dsDNA. Single-stranded DNA (ssDNA) binding proteins slide along dsDNA to locate and stabilize ssDNA during replication. Other proteins exhibit binding to both dsDNA and ssDNA. Nucleic acid chaperone proteins can switch rapidly between dsDNA and ssDNA binding modes, while DNA polymerases bind both forms of DNA with high affinity at distinct binding sites at the replication fork. Single molecule force measurements quantitatively characterize these DNA binding mechanisms, elucidating small molecule interactions and protein function.

Structural basis of pathway-dependent force profiles in stretched DNA

Understanding the mechanical properties that determine the flexibility of DNA is important, as DNA must bend and/or stretch in order to function biologically. Recent single-molecule experiments have shown that above a certain loading rate double-stranded DNA is more stable when stretched from the 3' termini than when stretched from the 5' termini. Unfortunately these experiments cannot provide insight into the structural basis for this behavior. We have used molecular dynamics simulations combined with umbrella sampling to study the stability and structural changes of a 30 bp double-stranded DNA oligomer during stretching from either the 3' termini or the 5' termini. At extensions greater than 1.7x the 3' stretched structure is more stable than the 5' stretched structure due to retention of twice the number (80%) of native hydrogen bonds between base pairs and a higher degree of base stacking. This difference results from greater dissipation of the stretch force via conformational flexibility of the phosphate backbone when pulled from the 3' ends, whereas in the 5' stretch the force is borne more directly by the base pair hydrogen bonds leading to rupture. In addition, stretching from the 5' end produces a greater widening of the major groove that increases solvent exposure and hydrolysis of the base pair hydrogen bonds. These results demonstrate that 3' stretching and 5' stretching in DNA are fundamentally different processes.

DNA crunching by a viral packaging motor: Compression of a procapsid-portal stalled Y-DNA substrate

Many large double-stranded DNA viruses employ high force-generating ATP-driven molecular motors to package to high density their genomes into empty procapsids. Bacteriophage T4 DNA translocation is driven by a two-component motor consisting of the procapsid portal docked with a packaging terminase-ATPase. Fluorescence resonance energy transfer and fluorescence correlation spectroscopic (FRET-FCS) studies of a branched (Y-junction) DNA substrate with a procapsid-anchoring leader segment and a single dye molecule situated at the junction point reveal that the "Y-DNA" stalls in proximity to the procapsid portal fused to GFP. Comparable structure Y-DNA substrates containing energy transfer dye pairs in the Y-stem separated by 10 or 14 base pairs reveal that B-form DNA is locally compressed 22-24% by the linear force of the packaging motor. Torsional compression of duplex DNA is thus implicated in the mechanism of DNA translocation.

Protein Structure Hierarchy

The complexity of protein structures requires a description of their structural components. This chapter describes the elements of protein secondary structure — regular local structural patterns — such as helices, sheets, turns, and loops. Helices and sheets tend to fall into specific regions in the {ϕ, ψ} space of the Ramachandran plot (see Figures 28 and 29). The corresponding width and shape of each region reflects the spread of that motif as found in proteins.

Overstretching of a 30 bp DNA duplex studied with steered molecular dynamics simulation: effects of structural defects on structure and force-extension relation

Single-molecule experiments on polymeric DNA show that the molecule can be overstretched at nearly constant force by about 70% beyond its relaxed contour length. In this publication we use steered molecular dynamics (MD) simulation to study the effect of structural defects on force-extension curves and structures at high elongation in a 30 base pair duplex pulled by its torsionally unconstrained 5' -5' ends. The defect-free duplex shows a plateau in the force-extension curve at 120 pN in which large segments with inclined and paired bases ("S-DNA") near both ends of the duplex coexist with a central B-type segment separated from the former by small denaturation bubbles. In the presence of a base mismatch or a nick, force-extension curves are very similar to the ones of the defect-free duplex. For the duplex with a base mismatch, S-type segments with highly inclined base pairs are not observed; rather, the overstretched duplex consists of B-type segments separated by denaturation bubbles. The nicked duplex evolves, via a two-step transition, into a two-domain structure characterized by a large S-type segment coexisting with several short S-type segments which are separated by short denaturation bubbles. Our results suggest that in the presence of nicks the force-extension curve of highly elongated duplex DNA might reflect locally highly inhomogeneous stretching.

The structure of DNA overstretched from the 5'5' ends differs from the structure of DNA overstretched from the 3'3' ends

It has been suggested that the structure that results when double-stranded DNA (dsDNA) is pulled from the 3'3' ends differs from that which results when it is pulled from the 5'5' ends. In this work, we demonstrate, using lambda phage dsDNA, that the overstretched states do indeed show different properties, suggesting that they correspond to different structures. For 3'3' pulling versus 5'5' pulling, the following differences are observed: (i) the forces at which half of the molecules in the ensemble have made a complete force-induced transition to single stranded DNA are 141 +/- 3 pN and 122 +/- 4 pN, respectively; (ii) the extension vs. force curve for overstretched DNA has a marked change in slope at 127 +/- 3 pN for 3'3' and 110 +/- 3 pN for 5'5'; (iii) the hysteresis (H) in the extension vs. force curves at 150 mM NaCl is 0.3 +/- 0.8 pN microm for 3'3' versus 13 +/- 8 pN for 5'5'; and (iv) 3'3' and 5'5' molecules show different changes in hysteresis due to interactions with beta-cyclodextrin, a molecule that is known to form stable host-guest complexes with rotated base pairs, and glyoxal that is known to bind stably to unpaired bases. These differences and additional findings are well-accommodated by the corresponding structures predicted on theoretical grounds.

Optical tweezers experiments resolve distinct modes of DNA-protein binding

Optical tweezers are ideally suited to perform force microscopy experiments that isolate a single biomolecule, which then provides multiple binding sites for ligands. The captured complex may be subjected to a spectrum of forces, inhibiting or facilitating ligand activity. In the following experiments, we utilize optical tweezers to characterize and quantify DNA binding of various ligands. High mobility group type B (HMGB) proteins, which bind to double-stranded DNA, are shown to serve the dual purpose of stabilizing and enhancing the flexibility of double stranded DNA. Unusual intercalating ligands are observed to thread into and lengthen the double-stranded structure. Proteins binding to both double- and single-stranded DNA, such as the alpha polymerase subunit of E. coli Pol III, are characterized, and the subdomains containing the distinct sites responsible for binding are isolated. Finally, DNA binding of bacteriophage T4 and T7 single-stranded DNA (ssDNA) binding proteins is measured for a range of salt concentrations, illustrating a binding model for proteins that slide along double-stranded DNA, ultimately binding tightly to ssDNA. These recently developed methods quantify both the binding activity of the ligand as well as the mode of binding.

Melting of persistent double-stranded polymers

Motivated by recent DNA-pulling experiments, we revisit the Poland-Scheraga model of melting a double-stranded polymer. We include distinct bending rigidities for both the double-stranded segments and the single-stranded segments forming a bubble. There is also bending stiffness at the branch points between the two segment types. The transfer matrix technique for single persistent chains is generalized to describe the branching bubbles. Properties of spherical harmonics are then exploited in truncating and numerically solving the resulting transfer matrix. This allows efficient computation of phase diagrams and force-extension curves (isotherms). While the main focus is on exposition of the transfer matrix technique, we provide general arguments for a reentrant melting transition in stiff double strands. Our theoretical approach can also be extended to study polymers with bubbles of any number of strands, with potential applications to molecules such as collagen.

Remeasuring the double helix

DNA is thought to behave as a stiff elastic rod with respect to the ubiquitous mechanical deformations inherent to its biology. To test this model at short DNA lengths, we measured the mean and variance of end-to-end length for a series of DNA double helices in solution, using small-angle x-ray scattering interference between gold nanocrystal labels. In the absence of applied tension, DNA is at least one order of magnitude softer than measured by single-molecule stretching experiments. Further, the data rule out the conventional elastic rod model. The variance in end-to-end length follows a quadratic dependence on the number of base pairs rather than the expected linear dependence, indicating that DNA stretching is cooperative over more than two turns of the DNA double helix. Our observations support the idea of long-range allosteric communication through DNA structure.

DNA overstretching in the presence of glyoxal: structural evidence of force-induced DNA melting

When a long DNA molecule is stretched beyond its B-form contour length, a transition occurs in which its length increases by a factor of 1.7, with very little force increase. A quantitative model was proposed to describe this transition as force-induced melting, where double-stranded DNA is converted into single-stranded DNA. The force-induced melting model accurately describes the thermodynamics of DNA overstretching as a function of solution conditions and in the presence of DNA binding ligands. An alternative explanation suggests a transformation into S-DNA, a double-stranded form which preserves the interstrand base pairing. To determine the extent to which DNA base pairs are exposed to solution during the transition, we held DNA overstretched to different lengths within the transition in the presence of glyoxal. If overstretching involved strand separation, then force-melted basepairs would be glyoxal-modified, thus essentially permanently single-stranded. Subsequent stretches confirm that a significant fraction of the DNA melted by force is permanently melted. This result demonstrates that DNA overstretching is accompanied by a disruption of the DNA helical structure, including a loss of hydrogen bonding.

B-S transition in short oligonucleotides

Stretching experiments with long double-stranded DNA molecules in physiological ambient revealed a force-induced transition at a force of 65 pN. During this transition between B-DNA and highly overstretched S-DNA the DNA lengthens by a factor of 1.7 of its B-form contour length. Here, we report the occurrence of this so-called B-S transition in short duplexes consisting of 30 basepairs. We employed atomic-force-microscope-based single molecule force spectroscopy to explore the unbinding mechanism of two short duplexes containing 30 or 20 basepairs by pulling at the opposite 5' termini. For a 30-basepair-long DNA duplex the B-S transition is expected to cause a length increase of 6.3 nm and should therefore be detectable. Indeed 30% of the measured force-extension curves exhibit a region of constant force (plateau) at 65 pN, which corresponds to the B-S transition. The observed plateaus show a length between 3 and 7 nm. This plateau length distribution indicates that the dissociation of a 30-basepair duplex mainly occurs during the B-S transition. In contrast, the measured force-extension curves for a 20-basepair DNA duplex exhibited rupture forces below 65 pN and did not show any evidence of a B-S transition.