Undulations enhance the effect of helical structure on DNA interactions

The Effects of Flexibility on dsDNA–dsDNA Interactions

A detailed understanding of the physical mechanism of ion-mediated dsDNA interactions is important in biological functions such as DNA packaging and homologous pairing. We report the potential of mean force (PMF) or the effective solvent mediated interactions between two parallel identical dsDNAs as a function of interhelical separation in 0.15 M NaCl solution. Here, we study the influence of flexibility of dsDNAs on the effective interactions by comparing PMFs between rigid models and flexible ones. The role of flexibility of dsDNA pairs in their association is elucidated by studying the energetic properties of Na⁺ ions as well as the fluctuations of ions around dsDNAs. The introduction of flexibility of dsDNAs softens the vdW contact wall and induces more counterion fluctuations around dsDNAs. In addition, flexibility facilitates the Na⁺ ions dynamics affecting their distribution. The results quantify the extent of attraction influenced by dsDNA flexibility and further emphasize the importance of non-continuum solvation approaches.

Nucleosome-induced homology recognition in chromatin

One of the least understood properties of chromatin is the ability of its similar regions to recognize each other through weak interactions. Theories based on electrostatic interactions between helical macromolecules suggest that the ability to recognize sequence homology is an innate property of the non-ideal helical structure of DNA. However, this theory does not account for the nucleosomal packing of DNA. Can homologous DNA sequences recognize each other while wrapped up in the nucleosomes? Can structural homology arise at the level of nucleosome arrays? Here, we present a theoretical model for the recognition potential well between chromatin fibres sliding against each other. This well is different from the one predicted for bare DNA; the minima in energy do not correspond to literal juxtaposition, but are shifted by approximately half the nucleosome repeat length. The presence of this potential well suggests that nucleosome positioning may induce mutual sequence recognition between chromatin fibres and facilitate the formation of chromatin nanodomains. This has implications for nucleosome arrays enclosed between CTCF-cohesin boundaries, which may form stiffer stem-like structures instead of flexible entropically favourable loops. We also consider switches between chromatin states, e.g. through acetylation/deacetylation of histones, and discuss nucleosome-induced recognition as a precursory stage of genetic recombination.

Interactions between identical DNA double helices

The molecular mechanism of specific interactions between double stranded DNA molecules has been investigated for many years. Problems remain in how confinement, ions, and condensing agents change the interactions. We consider how the orientational alignment of DNAs contributes to the interactions via free energy simulations. Here we report on the effective interactions between two parallel DNA double helices in 150-mM NaCl solution using all atom models. We calculate the potential of mean force (PMF) of DNA-DNA interactions as a function of two coordinates, interhelical separation of parallel double helices and relative rotation of a DNA molecule with respect to the other about the helical axis. We generate the two-dimensional PMF to better understand the effective interactions when a DNA molecule is in juxtaposition with another. The analysis of the ion and solvent distributions around the DNA and particularly in the interface region shows that certain alignments of the DNA pair enhance the interactions. At local free energy minima in distance and alignment, water molecules and Na^{+} ions form a hydrogen bonded network with the phosphates from each DNA. This network contributes an attractive energy component to the DNA-DNA interactions. Our results provide a molecular mechanism whereby local DNA-DNA interactions, depending on the helical orientation, give a potential mechanism for stabilizing pairing of much larger lengths of homologous DNA that have been seen experimentally. The study suggests an atomically detailed local picture of relevance to certain aspects of DNA condensation or aggregation.

The tilt-dependent potential of mean force of a pair of DNA oligomers from all-atom molecular dynamics simulations

Electrostatic interactions between DNA molecules have been extensively studied experimentally and theoretically, but several aspects (e.g. its role in determining the pitch of the cholesteric DNA phase) still remain unclear. Here, we performed large-scale all-atom molecular dynamics simulations in explicit water and 150 mM sodium chloride, to reconstruct the potential of mean force (PMF) of two DNA oligomers 24 base pairs long as a function of their interaxial angle and intermolecular distance. We find that the potential of mean force is dominated by total DNA charge, and not by the helical geometry of its charged groups. The theory of homogeneously charged cylinders fits well all our simulation data, and the fit yields the optimal value of the total compensated charge on DNA to  ≈65% of its total fixed charge (arising from the phosphorous atoms), close to the value expected from Manning's theory of ion condensation. The PMF calculated from our simulations does not show a significant dependence on the handedness of the angle between the two DNA molecules, or its size is on the order of [Formula: see text]. Thermal noise for molecules of the studied length seems to mask the effect of detailed helical charge patterns of DNA. The fact that in monovalent salt the effective interaction between two DNA molecules is independent on the handedness of the tilt may suggest that alternative mechanisms are required to understand the cholesteric phase of DNA.

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.

Continuity of states between the cholesteric → line hexatic transition and the condensation transition in DNA solutions

A new method of finely temperature-tuning osmotic pressure allows one to identify the cholesteric → line hexatic transition of oriented or unoriented long-fragment DNA bundles in monovalent salt solutions as first order, with a small but finite volume discontinuity. This transition is similar to the osmotic pressure-induced expanded → condensed DNA transition in polyvalent salt solutions at small enough polyvalent salt concentrations. Therefore there exists a continuity of states between the two. This finding, together with the corresponding empirical equation of state, effectively relates the phase diagram of DNA solutions for monovalent salts to that for polyvalent salts and sheds some light on the complicated interactions between DNA molecules at high densities.

Undulations in a weakly interacting mechanically generated molecular braid under tension

We consider mechanically generated molecular braids composed of two molecules where long range interactions between them can be considered to be very weak. We describe a model that takes account of the thermal fluctuations of the braid, steric interactions between the molecules, and external mechanical forces. In this model, both sets of ends, of the two molecules, are considered to be separated by a fixed distance much larger than the radius of the braid. One set of ends is rotated to generate a braid of a certain number of pitches (or turns), while the other set remains fixed. This model may describe the situation in which the ends of each molecule are attached to a substrate and a magnetic bead; to the latter a pulling force and rotational torque can be applied. We discuss various aspects of our model. Most importantly, an expression for the free energy is given, from which equations, determining the various geometric parameters of the braid, can be obtained. By numerically solving these equations, we give predictions from the model for the external torque needed to produce a braid with a certain number of turns per bending persistence length, as well as the end to end extension of the two molecules for a given pulling force. Other geometric parameters, as well as the lateral force required to keep the ends of the two molecules apart, are also calculated.

Helical structure determines different susceptibilities of dsDNA, dsRNA, and tsDNA to counterion-induced condensation

Recent studies of counterion-induced condensation of nucleic acid helices into aggregates produced several puzzling observations. For instance, trivalent cobalt hexamine ions condensed double-stranded (ds) DNA oligomers but not their more highly charged dsRNA counterparts. Divalent alkaline earth metal ions condensed triple-stranded (ts) DNA oligomers but not dsDNA. Here we show that these counterintuitive experimental results can be rationalized within the electrostatic zipper model of interactions between molecules with helical charge motifs. We report statistical mechanical calculations that reveal dramatic and nontrivial interplay between the effects of helical structure and thermal fluctuations on electrostatic interaction between oligomeric nucleic acids. Combining predictions for oligomeric and much longer helices, we also interpret recent experimental studies of the role of counterion charge, structure, and chemistry. We argue that an electrostatic zipper attraction might be a major or even dominant force in nucleic acid condensation.

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.

Structure-driven homology pairing of chromatin fibers: the role of electrostatics and protein-induced bridging

Chromatin domains formed in vivo are characterized by different types of 3D organization of interconnected nucleosomes and architectural proteins. Here, we quantitatively test a hypothesis that the similarities in the structure of chromatin fibers (which we call "structural homology") can affect their mutual electrostatic and protein-mediated bridging interactions. For example, highly repetitive DNA sequences in heterochromatic regions can position nucleosomes so that preferred inter-nucleosomal distances are preserved on the surfaces of neighboring fibers. On the contrary, the segments of chromatin fiber formed on unrelated DNA sequences have different geometrical parameters and lack structural complementarity pivotal for stable association and cohesion. Furthermore, specific functional elements such as insulator regions, transcription start and termination sites, and replication origins are characterized by strong nucleosome ordering that might induce structure-driven iterations of chromatin fibers. We propose that shape-specific protein-bridging interactions facilitate long-range pairing of chromatin fragments, while for closely-juxtaposed fibers electrostatic forces can in addition yield fine-tuned structure-specific recognition and pairing. These pairing effects can account for some features observed for mitotic and inter-phase chromatins.

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.

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.