DNA-DNA interaction beyond the ground state

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 However, analysis suggests that this approximation is no longer valid at large DNA lengths.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.

Chiral electrostatics breaks the mirror symmetry of DNA supercoiling

DNA supercoiling plays a fundamental role in regulating cellular activity and in the packaging of genetic material. In this communication, we analyse the effect of attractive chiral forces on the conformation of a closed circular DNA molecule, arising due to the helical patterns of charges on the DNA. We propose a model for closed loop DNA which uses the results of the recent theory of electrostatic interactions of a braid of two free-ended DNA molecules. Our model reproduces the known features of DNA supercoiling in an environment of low ionic strength. In high salt conditions, and in the presence of counterions that have high affinity to the DNA grooves, helix-specific forces significantly affect the conformation of the molecule by favouring a state characterized by a central left-handed braided section where there is close contact between distant portions of the loop. In such an environment we predict a previously unexplored possibility that nicked or topologically relaxed DNA molecules adopt a writhed state. This prediction suggests an alternative explanation for experiments in which it was assumed that the most stable topoisomer is always an open circle. Our results also give the first plausible explanation for the occurrence of tightly interwound molecules observed in cryo-electron microscopy and atomic force microscopy in a high ionic strength environment. We suggest several new experiments to test the predictions of this theory.

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.

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.

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.

Helical coherence of DNA in crystals and solution

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

A genomewide survey argues that every zygotic gene product is dispensable for the initiation of somatic homolog pairing in Drosophila

Studies from diverse organisms show that distinct interchromosomal interactions are associated with many developmental events. Despite recent advances in uncovering such phenomena, our understanding of how interchromosomal interactions are initiated and regulated is incomplete. During the maternal-to-zygotic transition (MZT) of Drosophila embryogenesis, stable interchromosomal contacts form between maternal and paternal homologous chromosomes, a phenomenon known as somatic homolog pairing. To better understand the events that initiate pairing, we performed a genomewide assessment of the zygotic contribution to this process. Specifically, we took advantage of the segregational properties of compound chromosomes to generate embryos lacking entire chromosome arms and, thus, all zygotic gene products derived from those arms. Using DNA fluorescence in situ hybridization (FISH) to assess the initiation of pairing at five separate loci, this approach allowed us to survey the entire zygotic genome using just a handful of crosses. Remarkably, we found no defect in pairing in embryos lacking any chromosome arm, indicating that no zygotic gene product is essential for pairing to initiate. From these data, we conclude that the initiation of pairing can occur independently of zygotic control and may therefore be part of the developmental program encoded by the maternal genome.

Disruption of topoisomerase II perturbs pairing in drosophila cell culture

Homolog pairing refers to the alignment and physical apposition of homologous chromosomal segments. Although commonly observed during meiosis, homolog pairing also occurs in nonmeiotic cells of several organisms, including humans and Drosophila. The mechanism underlying nonmeiotic pairing, however, remains largely unknown. Here, we explore the use of established Drosophila cell lines for the analysis of pairing in somatic cells. Using fluorescent in situ hybridization (FISH), we assayed pairing at nine regions scattered throughout the genome of Kc167 cells, observing high levels of homolog pairing at all six euchromatic regions assayed and variably lower levels in regions in or near centromeric heterochromatin. We have also observed extensive pairing in six additional cell lines representing different tissues of origin, different ploidies, and two different species, demonstrating homolog pairing in cell culture to be impervious to cell type or culture history. Furthermore, by sorting Kc167 cells into G1, S, and G2 subpopulations, we show that even progression through these stages of the cell cycle does not significantly change pairing levels. Finally, our data indicate that disrupting Drosophila topoisomerase II (Top2) gene function with RNAi and chemical inhibitors perturbs homolog pairing, suggesting Top2 to be a gene important for pairing.

DNA melting in aggregates: impeded or facilitated?

How does DNA melt in columnar aggregate relative to its melting in diluted solution? Is the melting temperature increased or decreased with the aggregate density? Have DNA-DNA interactions, predominantly of electrostatic nature, an effect on the character of the melting transition? In attempt to answer these questions, we have incorporated the theory of electrostatic interactions between DNA duplexes into the simplest model of DNA melting. The analysis shows that the effect of aggregate density is very different for aggregates built of homologous (or identical) DNA fragments relative to the case of DNA with random base pair sequences. The putative attraction between homologous DNA helices hampers their melting and increases the melting temperature and can even dramatically change the character of the transition. In the aggregate of nonhomologous DNAs, the pattern of electrostatic interactions is more complicated, and their effect could be opposite; in some cases we may even expect electrostatically induced melting. These findings define new directions for melting experiments in dense DNA assemblies.

Electrostatics of DNA Complexes with Cationic Lipid Membranes

We present the exact solutions of the linear Poisson-Boltzmann equation for several problems relevant to electrostatics of DNA complexes with cationic lipids. We calculate the electrostatic potential and electrostatic energy for lamellar and inverted hexagonal phases, concentrating on the effects of dielectric boundaries. We compare our results for the complex energy with the known results of numerical solution of the nonlinear Poisson-Boltzmann equation. Using the solution for the lamellar phase, we calculate the compressibility modulus and compare our findings with the experimental data available. Also, we treat charge-charge interactions across, along, and between two low-dielectric membranes. We obtain an estimate for the strength of electrostatic interactions of one-dimensional DNA smectic layers across the lipid membrane. We discuss in the end some aspects of two-dimensional DNA condensation and DNA-DNA attraction in the DNA-lipid lamellar phase in the presence of di- and trivalent cations. We analyze the equilibrium DNA-DNA separations in lamellar complexes using the recently developed theory of electrostatic interactions of DNA helical charge motifs.

On the physical nature of mesophases of guanosine gels

The unusual columnar aqueous mesophases of self-assembled guanosine stacks, such as 2'-deoxyguanosine 5'-monophosphate and 2'-deoxyguanosine 3'-monophosphate, are analyzed in terms of a general theory of azimuthal correlations between the charged helices. This theory considers forces, specific to the helical structure of each macromolecule, which depend on the azimuthal orientations of the molecules about their long axes. More specifically, in determining the magnitudes and decay lengths of these helix specific forces we utilize the Kornyshev-Leikin theory of electrostatic interaction between helical macromolecules and quantitatively fit experimental data. Together with explaining a number of the observed features of these mesophases, several new effects are predicted. Possible limitations and developments of our theoretical model are discussed, as well as new experiments to test the implications of the theory.

Direct observation of azimuthal correlations between DNA in hydrated aggregates

This study revisits the classical x-ray diffraction patterns from hydrated, noncrystalline fibers originally used to establish the helical structure of DNA. We argue that changes in these diffraction patterns with DNA packing density reveal strong azimuthally dependent interactions between adjacent molecules up to approximately 40 A interaxial or approximately 20 A surface-to-surface separations. These interactions appear to force significant torsional "straightening" of DNA and strong azimuthal alignment of nearest neighbor molecules. The results are in good agreement with the predictions of recent theoretical models relating DNA-DNA interactions to the helical symmetry of their surface charge patterns.

Statistical mechanics of columnar DNA assemblies

Many physical systems can be mapped onto solved or "solvable" models of magnetism. In this work, we have mapped the statistical mechanics of columnar phases of ideally helical rigid DNA--subject to the earlier found unusual, frustrated pair potential (A.A. Kornyshev, S. Leikin, J. Chem. Phys. 107, 3656 (1997))--onto an exotic, unknown variant of the XY model on a fixed or restructurable lattice. Here, the role of the "spin" is played by the azimuthal orientation of the molecules. We have solved this model using a Hartree-Fock approximation, ground-state calculations, and finite-temperature Monte Carlo simulations. We have found peculiar spin order transitions, which may also be accompanied by positional restructuring, from hexagonal to rhombohedric lattices. Some of these have been experimentally observed in dense columnar aggregates. Note that DNA columnar phases are of great interest in biophysical research, not only because they are a useful in vitro tool for the study of DNA condensation, but also since these structures have been detected in living matter. Within the approximations made, our study provides insight into the statistical mechanics of these systems.