Helical coherence of DNA in crystals and solution

Single-molecule measurements of double-stranded DNA condensation

Electrostatically driven double-stranded DNA (dsDNA) condensation is critical in regulating many biological processes, including bacteriophage and virus replication and the packaging of chromosomal DNA in sperm heads. Here, we review single-molecule measurements of dsDNA condensed by cationic proteins, polypeptides, and small multivalent cations. Optical tweezers (OT) measurements of dsDNA collapsed by cationic condensing agents reveal a critical condensing force unique to each condensing agent that is tunable with condensing agent concentration and ionic strength. DNA globules visualized via atomic force microscopy, transmission electron microscopy, and cryoelectron microscopy reveal condensed dsDNA adopting several conformations including highly ordered toroids with a measurable central hole and, more recently, the maximally dense, yarn-ball-like structures observed with dsDNA condensed by the HIV-1 nucleocapsid protein. The combination of these approaches provides multifaceted insight into the shape and size of electrostatically condensed dsDNA globules and the kinetics of their formation and dissolution. We also review the physics of dsDNA condensation, including recent studies that show dsDNA globule size is tunable with ionic strength. Overall, this review provides important insights into understanding dsDNA condensate-regulated biological processes, as well as potential uses for gene delivery.

Nonlocal structural effects of water on DNA homology recognition

The mechanism behind mutual recognition of homologous DNA sequences prior to genetic recombination is one of the remaining puzzles in molecular biology. Leading models of homology recognition, based on classical electrostatics, neglect the short-range nonlocal screening effects arising from structured water around DNA, and hence may only provide insight for relatively large separations between interacting DNAs. We elucidate the role of the effects of the nonlocal dielectric response of water on DNA-DNA interaction and show that these can dramatically enhance the driving force for recognition.

Cationic Residues of the HIV-1 Nucleocapsid Protein Enable DNA Condensation to Maintain Viral Core Particle Stability during Reverse Transcription

The HIV-1 nucleocapsid protein (NC) is a multifunctional viral protein necessary for HIV-1 replication. Recent studies have demonstrated that reverse transcription (RT) completes in the intact viral capsid, and the timing of RT and uncoating are correlated. How the small viral core stably contains the ~10 kbp double stranded (ds) DNA product of RT, and the role of NC in this process, are not well understood. We showed previously that NC binds and saturates dsDNA in a non-specific electrostatic binding mode that triggers uniform DNA self-attraction, condensing dsDNA into a tight globule against extending forces up to 10 pN. In this study, we use optical tweezers and atomic force microscopy to characterize the role of NC's basic residues in dsDNA condensation. Basic residue mutations of NC lead to defective interaction with the dsDNA substrate, with the constant force plateau condensation observed with wild-type (WT) NC missing or diminished. These results suggest that NC's high positive charge is essential to its dsDNA condensing activity, and electrostatic interactions involving NC's basic residues are responsible in large part for the conformation, size, and stability of the dsDNA-protein complex inside the viral core. We observe DNA re-solubilization and charge reversal in the presence of excess NC, consistent with the electrostatic nature of NC-induced DNA condensation. Previous studies of HIV-1 replication in the presence of the same cationic residue mutations in NC showed significant defects in both single- and multiple-round viral infectivity. Although NC participates in many stages of viral replication, our results are consistent with the hypothesis that cationic residue mutations inhibit genomic DNA condensation, resulting in increased premature capsid uncoating and contributing to viral replication defects.

Opto-Electrostatic Determination of Nucleic Acid Double-Helix Dimensions and the Structure of the Molecule–Solvent Interface

A DNA molecule is highly electrically charged in solution. The electrical potential at the molecular surface is known to vary strongly with the local geometry of the double helix and plays a pivotal role in DNA–protein interactions. Further out from the molecular surface, the electrical field propagating into the surrounding electrolyte bears fingerprints of the three-dimensional arrangement of the charged atoms in the molecule. However, precise extraction of the structural information encoded in the electrostatic “far field” has remained experimentally challenging. Here, we report an optical microscopy-based approach that detects the field distribution surrounding a charged molecule in solution, revealing geometric features such as the radius and the average rise per basepair of the double helix with up to sub-Angstrom precision, comparable with traditional molecular structure determination techniques like X-ray crystallography and nuclear magnetic resonance. Moreover, measurement of the helical radius furnishes an unprecedented view of both hydration and the arrangement of cations at the molecule–solvent interface. We demonstrate that a probe in the electrostatic far field delivers structural and chemical information on macromolecules, opening up a new dimension in the study of charged molecules and interfaces in solution.

DNA Structure and the Golden Ratio Revisited

B-DNA, the informational molecule for life on earth, appears to contain ratios structured around the irrational number 1.618…, often known as the “golden ratio”. This occurs in the ratio of the length:width of one turn of the helix; the ratio of the spacing of the two helices; and in the axial structure of the molecule which has ten-fold rotational symmetry. That this occurs in the information-carrying molecule for life is unexpected, and suggests the action of some process. What this process might be is unclear, but it is central to any understanding of the formation of DNA, and so life.

Structure and stimuli-responsiveness of all-DNA dendrimers: theory and experiment

We present a comprehensive theoretical and experimental study of the solution phase properties of a DNA-based family of nanoparticles - dendrimer-like DNA molecules (DL-DNA). These charged DNA dendrimers are novel macromolecular aggregates, which hold high promise in targeted self-assembly of soft matter systems in the bulk and at interfaces. To describe the behaviour of this family of dendrimers (with generations ranging from G1 to G7), we use a theoretical model in which base-pairs of a single DL-DNA molecule are modeled by charged monomers, whose interactions are chosen to mimic the equilibrium properties of DNA correctly. Experimental results on the sizes and conformations of DL-DNA are based on static and dynamic light scattering; and molecular dynamics simulations are employed to model the equilibrium properties of DL-DNA, which compare favorably to the findings from experiments while at the same time providing a host of additional information and insight into the molecular structure of the nanostructures. We also examine the salt-responsiveness of these macromolecules, finding that despite the strong screening of electrostatic interactions brought about by the added salt, the macromolecules shrink only slightly, their size robustness stemming from the high bending rigidity of the DNA-segments. The study of these charged dendrimer systems is an important field of research in the area of soft matter due to their potential role for various interdisciplinary applications, ranging from molecular cages and carriers for drug delivery in a living organism to the development of dendrimer- and dendron-based ultra-thin films in the area of nanotechnology. These findings are essential to determine if DL-DNA is a viable candidate for the experimental realization of cluster crystals in the bulk, a novel form of solid with multiple site occupancy.

Introducing a model of pairing based on base pair specific interactions between identical DNA sequences

At present, there have been suggested two types of physical mechanism that may facilitate preferential pairing between DNA molecules, with identical or similar base pair texts, without separation of base pairs. One mechanism solely relies on base pair specific patterns of helix distortion being the same on the two molecules, discussed extensively in the past. The other mechanism proposes that there are preferential interactions between base pairs of the same composition. We introduce a model, built on this second mechanism, where both thermal stretching and twisting fluctuations are included, as well as the base pair specific helix distortions. Firstly, we consider an approximation for weak pairing interactions, or short molecules. This yields a dependence of the energy on the square root of the molecular length, which could explain recent experimental data. However, analysis suggests that this approximation is no longer valid at large DNA lengths. In a second approximation, for long molecules, we define two adaptation lengths for twisting and stretching, over which the pairing interaction can limit the accumulation of helix disorder. When the pairing interaction is sufficiently strong, both adaptation lengths are finite; however, as we reduce pairing strength, the stretching adaptation length remains finite but the torsional one becomes infinite. This second state persists to arbitrarily weak values of the pairing strength; suggesting that, if the molecules are long enough, the pairing energy scales as length. To probe differences between the two pairing mechanisms, we also construct a model of similar form. However, now, pairing between identical sequences solely relies on the intrinsic helix distortion patterns. Between the two models, we see interesting qualitative differences. We discuss our findings, and suggest new work to distinguish between the two mechanisms.

Statistical mechanical model for a closed loop plectoneme with weak helix specific forces

We develop a statistical mechanical framework, based on a variational approximation, to describe closed loop plectonemes. This framework incorporates weak helix structure dependent forces into the determination of the free energy and average structure of a plectoneme. Notably, due to their chiral nature, helix structure dependent forces break the symmetry between left and right handed supercoiling. The theoretical approach, presented here, also provides a systematic way of enforcing the topological constraint of closed loop supercoiling in the variational approximation. At large plectoneme lengths, by considering correlation functions in an expansion in terms of the spatial mean twist density about its thermally averaged value, it can be argued that topological constraint may be approximated by replacing twist and writhe by their thermal averages. A Lagrange multiplier, containing the sum of average twist and writhe, can be added to the free energy to conveniently inforce this result. The average writhe can be calculated through the thermal average of the Gauss' integral in the variational approximation. Furthermore, this approach allows for a possible way to calculate finite size corrections due to the topological constraint. Using interaction energy terms from the mean-field Kornyshev-Leikin theory, for parameter values that correspond to weak helix dependent forces, we calculate the free energy, fluctuation magnitudes and mean geometric parameters for the plectoneme. We see a slight asymmetry, where interestingly, left handed supercoils have a looser structure than right handed ones, although with a lower free energy, unlike what the previous ground state calculations would suggest.

Evidence of protein-free homology recognition in magnetic bead force-extension experiments

Earlier theoretical studies have proposed that the homology-dependent pairing of large tracts of dsDNA may be due to physical interactions between homologous regions. Such interactions could contribute to the sequence-dependent pairing of chromosome regions that may occur in the presence or the absence of double-strand breaks. Several experiments have indicated the recognition of homologous sequences in pure electrolytic solutions without proteins. Here, we report single-molecule force experiments with a designed 60 kb long dsDNA construct; one end attached to a solid surface and the other end to a magnetic bead. The 60 kb constructs contain two 10 kb long homologous tracts oriented head to head, so that their sequences match if the two tracts fold on each other. The distance between the bead and the surface is measured as a function of the force applied to the bead. At low forces, the construct molecules extend substantially less than normal, control dsDNA, indicating the existence of preferential interaction between the homologous regions. The force increase causes no abrupt but continuous unfolding of the paired homologous regions. Simple semi-phenomenological models of the unfolding mechanics are proposed, and their predictions are compared with the data.

Flexibility of short DNA helices with finite-length effect: From base pairs to tens of base pairs

Flexibility of short DNA helices is important for the biological functions such as nucleosome formation and DNA-protein recognition. Recent experiments suggest that short DNAs of tens of base pairs (bps) may have apparently higher flexibility than those of kilo bps, while there is still the debate on such high flexibility. In the present work, we have studied the flexibility of short DNAs with finite-length of 5-50 bps by the all-atomistic molecular dynamics simulations and Monte Carlo simulations with the worm-like chain model. Our microscopic analyses reveal that short DNAs have apparently high flexibility which is attributed to the significantly strong bending and stretching flexibilities of ∼6 bps at each helix end. Correspondingly, the apparent persistence length lp of short DNAs increases gradually from ∼29 nm to ∼45 nm as DNA length increases from 10 to 50 bps, in accordance with the available experimental data. Our further analyses show that the short DNAs with excluding ∼6 bps at each helix end have the similar flexibility with those of kilo bps and can be described by the worm-like chain model with lp ∼ 50 nm.

The intrinsic mechanics of B-DNA in solution characterized by NMR

Experimental characterization of the structural couplings in free B-DNA in solution has been elusive, because of subtle effects that are challenging to tackle. Here, the exploitation of the NMR measurements collected on four dodecamers containing a substantial set of dinucleotide sequences provides new, consistent correlations revealing the DNA intrinsic mechanics. The difference between two successive residual dipolar couplings (ΔRDCs) involving C6/8-H6/8, C3′-H3′ and C4′-H4′ vectors are correlated to the ³¹P chemical shifts (δP), which reflect the populations of the BI and BII backbone states. The δPs are also correlated to the internucleotide distances (D_inter) involving H6/8, H2′ and H2″ protons. Calculations of NMR quantities on high resolution X-ray structures and controlled models of DNA enable to interpret these couplings: the studied ΔRDCs depend mostly on roll, while D_inter are mainly sensitive to twist or slide. Overall, these relations demonstrate how δP measurements inform on key inter base parameters, in addition to probe the BI↔BII backbone equilibrium, and shed new light into coordinated motions of phosphate groups and bases in free B-DNA in solution. Inspection of the 5′ and 3′ ends of the dodecamers also supplies new information on the fraying events, otherwise neglected.

Which way up? Recognition of homologous DNA segments in parallel and antiparallel alignments

Homologous gene shuffling between DNA molecules promotes genetic diversity and is an important pathway for DNA repair. For this to occur, homologous genes need to find and recognize each other. However, despite its central role in homologous recombination, the mechanism of homology recognition has remained an unsolved puzzle of molecular biology. While specific proteins are known to play a role at later stages of recombination, an initial coarse grained recognition step has, however, been proposed. This relies on the sequence dependence of the DNA structural parameters, such as twist and rise, mediated by intermolecular interactions, in particular, electrostatic ones. In this proposed mechanism, sequences that have the same base pair text, or are homologous, have lower interaction energy than those sequences with uncorrelated base pair texts. The difference between the two energies is termed the "recognition energy." Here, we probe how the recognition energy changes when one DNA fragment slides past another, and consider, for the first time, homologous sequences in antiparallel alignment. This dependence on sliding is termed the "recognition well." We find there is a recognition well for anti-parallel, homologous DNA tracts, but only a very shallow one, so that their interaction will differ little from the interaction between two nonhomologous tracts. This fact may be utilized in single molecule experiments specially targeted to test the theory. As well as this, we test previous theoretical approximations in calculating the recognition well for parallel molecules against MC simulations and consider more rigorously the optimization of the orientations of the fragments about their long axes upon calculating these recognition energies. The more rigorous treatment affects the recognition energy a little, when the molecules are considered rigid. When torsional flexibility of the DNA molecules is introduced, we find excellent agreement between the analytical approximation and simulations.

Collapse and coexistence for a molecular braid with an attractive interaction component subject to mechanical forces

Dual mechanical braiding experiments provide a useful tool with which to investigate the nature of interactions between rod-like molecules, for instance actin and DNA. In conditions close to molecular condensation, one would expect an appearance of a local minimum in the interaction potential between the two molecules. We investigate this situation, introducing an attractive component into the interaction potential, using a model developed for describing such experiments. We consider both attractive interactions that do not depend on molecular structure and those which depend on a DNA-like helix structure. In braiding experiments, an attractive term may lead to certain effects. A local minimum may cause molecules to collapse from a loosely braided configuration into a tight one, occurring at a critical value of the moment applied about the axis of the braid. For a fixed number of braid pitches, this may lead to coexistence between the two braiding states, tight and loose. Coexistence implies certain proportions of the braid are in each state, their relative size depending on the number of braid pitches. This manifests itself as a linear dependence in numerically calculated quantities as functions of the number of braid pitches. Also, in the collapsed state, the braid radius stays roughly constant. Furthermore, if the attractive interaction is helix dependent, the left-right handed braid symmetry is broken. For a DNA like charge distribution, using the Kornyshev-Leikin interaction model, our results suggest that significant braid collapse and coexistence only occurs for left handed braids. Regardless of the interaction model, the study highlights the possible qualitative physics of braid collapse and coexistence; and the role helix specific forces might play, if important. The model could be used to connect other microscopic theories of interaction with braiding experiments.

A viral packaging motor varies its DNA rotation and step size to preserve subunit coordination as the capsid fills

Multimeric, ring-shaped molecular motors rely on the coordinated action of their subunits to perform crucial biological functions. During these tasks, motors often change their operation in response to regulatory signals. Here, we investigate a viral packaging machine as it fills the capsid with DNA and encounters increasing internal pressure. We find that the motor rotates the DNA during packaging and that the rotation per base pair increases with filling. This change accompanies a reduction in the motor's step size. We propose that these adjustments preserve motor coordination by allowing one subunit to make periodic, specific, and regulatory contacts with the DNA. At high filling, we also observe the downregulation of the ATP-binding rate and the emergence of long-lived pauses, suggesting a throttling-down mechanism employed by the motor near the completion of packaging. This study illustrates how a biological motor adjusts its operation in response to changing conditions, while remaining highly coordinated.

Effect of undulations on spontaneous braid formation

This paper is an extension of a recent study where it was shown that forces dependent on molecular helical structure may cause two DNA molecules to spontaneously braid [R. Cortini et al., Biophys. J. 101, 875 (2011)]. Here, bending fluctuations of molecular center lines about the braid axis are incorporated into the braiding theory, which may be generalized to other helix-dependent interactions and other helical molecules. The free energy of the pair of molecules is recalculated and compared to its value without incorporating undulations. We find that the loss of configurational entropy due to confinement of the molecules in the braid is quite high. This contribution to the free energy increases the amount of attraction needed for spontaneous braiding due to helix-dependent forces. The theory will be further developed for plectonemes and braids under mechanical forces in later work.

Bullied no more: when and how DNA shoves proteins around

The predominant protein-centric perspective in protein-DNA-binding studies assumes that the protein drives the interaction. Research focuses on protein structural motifs, electrostatic surfaces and contact potentials, while DNA is often ignored as a passive polymer to be manipulated. Recent studies of DNA topology, the supercoiling, knotting, and linking of the helices, have shown that DNA has the capability to be an active participant in its transactions. DNA topology-induced structural and geometric changes can drive, or at least strongly influence, the interactions between protein and DNA. Deformations of the B-form structure arise from both the considerable elastic energy arising from supercoiling and from the electrostatic energy. Here, we discuss how these energies are harnessed for topology-driven, sequence-specific deformations that can allow DNA to direct its own metabolism.

Electrostatic braiding and homologous pairing of DNA double helices

Homologous pairing and braiding (supercoiling) have crucial effects on genome organization, maintenance, and evolution. Generally, the pairing and braiding processes are discussed in different contexts, independently of each other. However, analysis of electrostatic interactions between DNA double helices suggests that in some situations these processes may be related. Here we present a theory of DNA braiding that accounts for the elastic energy of DNA double helices as well as for the chiral nature of the discrete helical patterns of DNA charges. This theory shows that DNA braiding may be affected, stabilized, or even driven by chiral electrostatic interactions. For example, electrostatically driven braiding may explain the surprising recent observation of stable pairing of homologous double-stranded DNA in solutions containing only monovalent salt. Electrostatic stabilization of left-handed braids may stand behind the chiral selectivity of type II topoisomerases and positive plasmid supercoiling in hyperthermophilic bacteria and archea.

Signatures of DNA flexibility, interactions and sequence-related structural variations in classical X-ray diffraction patterns

The theory of X-ray diffraction from ideal, rigid helices allowed Watson and Crick to unravel the DNA structure, thereby elucidating functions encoded in it. Yet, as we know now, the DNA double helix is neither ideal nor rigid. Its structure varies with the base pair sequence. Its flexibility leads to thermal fluctuations and allows molecules to adapt their structure to optimize their intermolecular interactions. In addition to the double helix symmetry revealed by Watson and Crick, classical X-ray diffraction patterns of DNA contain information about the flexibility, interactions and sequence-related variations encoded within the helical structure. To extract this information, we have developed a new diffraction theory that accounts for these effects. We show how double helix non-ideality and fluctuations broaden the diffraction peaks. Meridional intensity profiles of the peaks at the first three helical layer lines reveal information about structural adaptation and intermolecular interactions. The meridional width of the fifth layer line peaks is inversely proportional to the helical coherence length that characterizes sequence-related and thermal variations in the double helix structure. Analysis of measured fiber diffraction patterns based on this theory yields important parameters that control DNA structure, packing and function.

Correlation forces between helical macro-ions in the weak coupling limit

When correlation effects are relatively weak, electrostatic interaction forces between cylindrical macro-ions may be divided into two contributions (Lee 2010 J. Phys.: Condens. Matter 22 414101). Firstly, there is a mean field contribution, described by the theory of Kornyshev and Leikin (1997 J. Chem. Phys. 107 3656) at large separations. Secondly, we have correlation forces, which we analyze by performing an expansion in the number density of condensed ions. We see three distinct contributions, for which analytical expressions are given for both general and helical contributions. Firstly, there is a term (of leading order in the expansion) that is a change in the solvation energies of uncondensed counter-ions due to two macro-molecular interfaces. Secondly, we have a contribution that comes from fluctuations in the condensed ion charge density being repelled by their 'images' in the other molecule. Both of these contributions are repulsive. Lastly, there exists an attractive Oosawa contribution that arises from fluctuations in the condensed ions about one molecule correlating with those about the other molecule. The first two forces do not depend on the orientation of the molecules about their long axes. However, the Oosawa force may do so, depending on the pattern of bound and fixed charges. For a DNA like charge distribution, we see that the strength of this dependence is governed by the relative proportion of bound ions, between two positions that represent the DNA groove centers. We see that, at a Debye screening length equivalent to physiological salt concentrations, the correlation forces can be neglected for univalent ions. For divalent ions, they contribute a small, albeit significant, correction. Our calculations suggest that increasing the salt concentration reduces the size of these forces.

Physics of DNA: unravelling hidden abilities encoded in the structure of ‘the most important molecule’

A comprehensive article “Structure and Interactions of Biological Helices”, published in 2007 in Reviews of Modern Physics, overviewed various aspects of the effect of DNA structure on DNA–DNA interactions in solution and related phenomena, with a thorough analysis of the theory of these effects. Here, an updated qualitative account of this area is presented without any sophisticated ‘algebra’. It overviews the basic principles of the structure-specific interactions between double-stranded DNA and focuses on the physics behind several related properties encoded in the structure of DNA. Among them are (i) DNA condensation and aptitude to pack into small compartments of cells or viral capcids, (ii) the structure of DNA mesophases, and (iii) the ability of homologous genes to recognize each other prior to recombination from a distance. Highlighted are some of latest developments of the theory, including the shape of the ‘recognition well’. The article ends with a brief discussion of the first experimental evidence of the protein-free homology recognition in a ‘test tube’.

Charge renormalization of helical macromolecules

Some time ago a theory of electrostatic interaction between helical macromolecules was proposed (Kornyshev and Leikin 1997 J. Chem. Phys. 107 3656): the Kornyshev-Leikin (KL) theory. We place this theory on a more rigorous statistical mechanical grounding, starting from the free energy that can be derived from a grand partition function. We see that the long range behaviour of the force is indeed given by the KL theory, no matter whether the distributions of 'condensed' ionic charge are at the surface of the macromolecule or extend away from it. Thus, for the limiting behaviour, we need only self-consistently calculate the distribution of the condensed fraction of ions for a single macro-ion. This distribution can be related back to interaction parameters: KL parameters. Furthermore, we are able to see within the formalism where corrections due to the hard core radius of the ion enter. For the adjustment of the 'condensed' ions, we show an expression for the leading order contribution, as well as relevant decay lengths. As a demonstration of the theoretical 'machinery', as well as a study of qualitative effects, we calculate the KL parameters in one instance. We use a DNA-like surface charge distribution, where a fraction of the ions are assumed to be bound in the grooves at the surface of a DNA molecule, whereas the rest of the charge distribution is calculated self-consistently. Also, the electrostatic contribution to the counter-ion binding potentials that ions experience within the grooves can be calculated.

Homology recognition funnel

The recognition of homologous sequences of DNA before strand exchange is considered to be the most puzzling stage of homologous recombination. A mechanism for two homologous dsDNAs to recognize each other from a distance in electrolytic solution without unzipping had been proposed in an earlier paper [A. A. Kornyshev and S. Leikin, Phys. Rev. Lett. 86, 366 (2001)]. In that work, the difference in the electrostatic interaction energy between homologous duplexes and between nonhomologous duplexes, termed the recognition energy, has been calculated. That calculation was later extended in a series of papers to account for torsional elasticity of the molecules. A recent paper [A. A. Kornyshev and A. Wynveen, Proc. Natl. Acad. Sci. U.S.A. 106, 4683 (2009)] investigated the form of the potential well that homologous DNA molecules may feel when sliding along each other. A simple formula for the shape of the well was obtained. However, this latter study was performed under the approximation that the sliding molecules are torsionally rigid. Following on from this work, in the present article we investigate the effect of torsional flexibility of the molecules on the shape of the well. A variational approach to this problem results in a transcendental equation that is easily solved numerically. Its solutions show that at large interaxial separations the recognition well becomes wider and shallower, whereas at closer distances further unexpected features arise related to an abrupt change in the mean azimuthal alignment of the molecules. The energy surface as a function of interaxial separation and the axial shift defines what we call the recognition funnel. We show that it depends dramatically on the patterns of adsorption of counterions on DNA.

Undulations enhance the effect of helical structure on DNA interactions

During the past decade, theory and experiments have provided clear evidence that specific helical patterns of charged groups and adsorbed (condensed) counterions on the DNA surface are responsible for many important features of DNA-DNA interactions in hydrated aggregates. The effects of helical structure on DNA-DNA interactions result from a preferential juxtaposition of the negatively charged sugar phosphate backbone with counterions bound within the grooves of the opposing molecule. Analysis of X-ray diffraction experiments confirmed the mutual alignment of parallel molecules in hydrated aggregates required for such juxtaposition. However, it remained unclear how this alignment and molecular interactions might be affected by intrinsic and thermal fluctuations, which cause structural deviations away from an ideal double helical conformation. We previously argued that the torsional flexibility of DNA allows the molecules to adapt their structure to accommodate a more electrostatically favorable alignment between molecules, partially compensating disruptive fluctuation effects. In the present work, we develop a more comprehensive theory, incorporating also stretching and bending fluctuations of DNA. We found the effects of stretching to be qualitatively and quantitatively similar to those of twisting fluctuations. However, this theory predicts more dramatic and surprising effects of bending. Undulations of DNA in hydrated aggregates strongly amplify rather than weaken the helical structure effects. They enhance the structural adaptation, leading to better alignment of neighboring molecules and pushing the geometry of the DNA backbone closer to that of an ideal helix. These predictions are supported by a quantitative comparison of the calculated and measured osmotic pressures in DNA.

Gel mobilities of linking-number topoisomers and their dependence on DNA helical repeat and elasticity

Agarose-gel electrophoresis has been used for more than thirty years to characterize the linking-number (Lk) distribution of closed-circular DNA molecules. Although the physical basis of this technique remains poorly understood, the gel-electrophoretic behavior of covalently closed DNAs has been used to determine the local unwinding of DNA by proteins and small-molecule ligands, characterize supercoiling-dependent conformational transitions in duplex DNA, and to measure helical-repeat changes due to shifts in temperature and ionic strength. Those results have been analyzed by assuming that the absolute mobility of a particular topoisomer is mainly a function of the integral number of superhelical turns, and thus a slowly varying function of plasmid molecular weight. In examining the mobilities of Lk topoisomers for a series of plasmids that differ incrementally in size over more than one helical turn, we found that the size-dependent agarose-gel mobility of individual topoisomers with identical values of Lk (but different values of the excess linking number, DeltaLk) vary dramatically over a duplex turn. Our results suggest that a simple semi-empirical relationship holds between the electrophoretic mobility of linking-number topoisomers and their average writhe in solution.

Influence of backbone on the charge transport properties of G4-DNA molecules: a model-based calculation

We put forward a model Hamiltonian to describe the influence of backbone energetics on charge transport through guanine-quadruplex DNA (G4-DNA) molecules. Our analytical results show that an energy gap can be produced in the energy spectrum of G4-DNA by hybridization effects between the backbone and the base and by on-site energy difference of the backbone from the base. The environmental effects are investigated by introducing different types of disorder into the backbone sites. Our numerical results suggest that the localization length of G4-DNA can be significantly enhanced by increasing the backbone disorder degree when the environment-induced disorder is sufficiently large. There exists a backbone disorder-induced semiconducting-metallic transition in short G4-DNA molecules, where G4-DNA behaves as a semiconductor if the backbone disorder is weak and behaves as a conductor if the backbone disorder degree surpasses a critical value.

Single molecule detection of direct, homologous, DNA/DNA pairing

Using a parallel single molecule magnetic tweezers assay we demonstrate homologous pairing of two double-stranded (ds) DNA molecules in the absence of proteins, divalent metal ions, crowding agents, or free DNA ends. Pairing is accurate and rapid under physiological conditions of temperature and monovalent salt, even at DNA molecule concentrations orders of magnitude below those found in vivo, and in the presence of a large excess of nonspecific competitor DNA. Crowding agents further increase the reaction rate. Pairing is readily detected between regions of homology of 5 kb or more. Detected pairs are stable against thermal forces and shear forces up to 10 pN. These results strongly suggest that direct recognition of homology between chemically intact B-DNA molecules should be possible in vivo. The robustness of the observed signal raises the possibility that pairing might even be the "default" option, limited to desired situations by specific features. Protein-independent homologous pairing of intact dsDNA has been predicted theoretically, but further studies are needed to determine whether existing theories fit sequence length, temperature, and salt dependencies described here.

Correlation effects, image charge effects and finite size in the macro-ion-electrolyte system: a field-theoretic approach

We consider a model of a macro-ion surrounded by small ions of an electrolyte solution. The finite size of ionic charge distributions of ions, and image charge effects are considered. From such a model it is possible to construct a statistical field theory with a single fluctuating field and derive physical interpretations for both the mean field and two-point correlation function. For point-like charges, at the level of a Gaussian (or saddle point) approximation, we recover the standard Poisson-Boltzmann equation. However, to include ionic correlation effects, as well as image charge effects of individual ions, we must go beyond this. From the field theory considered, it is possible to construct self-consistent approximations. We consider the simplest of these, namely the Hartree approximation. The Hartree equations take the form of two coupled equations. One is a modified Poisson-Boltzmann equation; the other describes both image charge effects on the individual ions, as well as correlations. Such equations are difficult to solve numerically, so we develop an (a WKB-like) approximation for obtaining approximate solutions. This, we apply to a uniformly charged rod in univalent electrolyte solution, for point like ions, as well as for extended spherically symmetric distributions of ionic charge on electrolyte ions. The solutions show how correlation effects and image charge effects modify the Poisson-Boltzmann result. Finite-size charge distributions of the ions reduce both the effects of correlations and image charge effects. For point charges, we test the WKB approximation by calculating a leading-order correction from the exact Hartree result, showing that the WKB-like approximation works reasonably well in describing the full solution to the Hartree equations. From these solutions, we also calculate an effective charge compensation parameter in an analytical formula for the interaction of two charged cylinders.

The homology recognition well as an innate property of DNA structure

Mutual recognition of homologous sequences of DNA before strand exchange is considered to be the most puzzling stage of recombination of genes. In 2001, a mechanism was suggested for a double-stranded DNA molecule to recognize from a distance its homologous match in electrolytic solution without unzipping [Kornyshev AA, Leikin S (2001) Phys Rev Lett 86:3666-3669]. Based on a theory of electrostatic interactions between helical molecules, the difference in the electrostatic interaction energy between homologous duplexes and between nonhomologous duplexes, called the recognition energy, was calculated. Here, we report a theoretical investigation of the form of the potential well that DNA molecules may feel sliding along each other. This well, the bottom of which is determined by the recognition energy, leads to trapping of the molecular tracks of the same homology in direct juxtaposition. A simple formula for the shape of the well is obtained. The well is quasi-exponential. Its half-width is determined by the helical coherence length, introduced first in the same 2001 article, the value of which, as the latest study shows, is approximately 10 nm.

Correlated small polaron hopping transport in 1D disordered systems at high temperatures: a possible charge transport mechanism in DNA

Based on the generalized molecular crystal model (GMCM) and theoretical percolation arguments we investigate small polaron hopping transport in 1D disordered systems at high temperatures. Correlation (cr) effects are taken into account. An analytical expression for the temperature dependence of the electrical conductivity, lnσ(h,cr)∼T(-1/2), is obtained. This result reproduces satisfactorily the experimental data reported for λ-DNA and for poly(dA)-poly(dT) DNA, considering DNA as a one-dimensional disordered molecular wire in which small polarons are the charge carriers. lnσ(h,cr) versus T(-1/2) plots permit the evaluation of the maximum hopping distance. The results indicate that correlation effects are probably responsible for large hopping distances in DNA samples.