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 However, analysis suggests that this approximation is no longer valid at large DNA lengths.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

Single Molecule Trapping and Sensing Using Dual Nanopores Separated by a Zeptoliter Nanobridge.

There is a growing realization, especially within the diagnostic and therapeutic community, that the amount of information enclosed in a single molecule can not only enable a better understanding of biophysical pathways, but also offer exceptional value for early stage biomarker detection of disease onset. To this end, numerous single molecule strategies have been proposed, and in terms of label-free routes, nanopore sensing has emerged as one of the most promising methods. However, being able to finely control molecular transport in terms of transport rate, resolution, and signal-to-noise ratio (SNR) is essential to take full advantage of the technology benefits. Here we propose a novel solution to these challenges based on a method that allows biomolecules to be individually confined into a zeptoliter nanoscale droplet bridging two adjacent nanopores (nanobridge) with a 20 nm separation. Molecules that undergo confinement in the nanobridge are slowed down by up to 3 orders of magnitude compared to conventional nanopores. This leads to a dramatic improvement in the SNR, resolution, sensitivity, and limit of detection. The strategy implemented is universal and as highlighted in this manuscript can be used for the detection of dsDNA, RNA, ssDNA, and proteins.

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.

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.

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.

Self-consistent treatment of electrostatics in molecular DNA braiding through external forces.

In this paper we consider a physical system in which two DNA molecules braid about each other. The distance between the two molecular ends, on either side of the braid, is held at a distance much larger than supercoiling radius of the braid. The system is subjected to an external pulling force, and a moment that induces the braiding. In a model, developed for understanding such a system, we assume that each molecule can be divided into a braided and unbraided section. We also suppose that the DNA is nicked so that there is no constraint of the individual linking numbers of the molecules. Included in the model are steric and electrostatic interactions, thermal fluctuations of the braided and unbraided sections of the molecule, as well as the constraint on the braid linking (catenation) number. We compare two approximations used in estimating the free energy of the braided section. One is where the amplitude of undulations of one molecule with respect to the other is determined only by steric interactions. The other is a self-consistent determination of the mean-squared amplitude of these undulations. In this second approximation electrostatics should play an important role in determining this quantity, as suggested by physical arguments. We see that if the electrostatic interaction is sufficiently large there are indeed notable differences between the two approximations. We go on to test the self-consistent approximation-included in the full model-against experimental data for such a system, and we find good agreement. However, there seems to be a slight left-right-handed braid asymmetry in some of the experimental results. We discuss what might be the origin of this small asymmetry.

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.

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.

The role of electrostatics in the B to A transition of DNA: from solution to assembly.

On the basis of a wealth of published experimental data and computer simulations, we build a simple physical model that allows us to rationalize the A to B transition of DNA in solution and in aggregates. In both cases we find that the electrostatic interactions are strong enough, alone, to induce the transition independently of other energetic contributions, e.g. those related to hydration. On the basis of this analysis we conclude that in ethanol/water mixtures, the effect responsible for the transition is the reduction of dielectric constant in the mixture. This is manifested in electrostatic self-energy terms that include the interaction of phosphate charges with condensed counterions. But in dense aggregates, electrostatics plays a dual role, giving rise to two competing effects. In the absence of groove localized counterions the electrostatic self-energy favours the B form, and the electrostatic interaction energy between neighbouring DNA favours the A form. However, the addition of enough counterions localized in the narrow groove reverses this. In dry aggregates of DNA both terms, in most cases, conspire to keep DNA in the A form. The analysis gives a broad picture of the B to A transition and sets a number of new research goals, particularly concerning simulations that may test our simple model for aggregates.

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.