Azimuthal frustration and bundling in columnar DNA aggregates

Local structure of DNA toroids reveals curvature-dependent intermolecular forces

In viruses and cells, DNA is closely packed and tightly curved thanks to polyvalent cations inducing an effective attraction between its negatively charged filaments. Our understanding of this effective attraction remains very incomplete, partly because experimental data is limited to bulk measurements on large samples of mostly uncurved DNA helices. Here we use cryo electron microscopy to shed light on the interaction between highly curved helices. We find that the spacing between DNA helices in spermine-induced DNA toroidal condensates depends on their location within the torus, consistent with a mathematical model based on the competition between electrostatic interactions and the bending rigidity of DNA. We use our model to infer the characteristics of the interaction potential, and find that its equilibrium spacing strongly depends on the curvature of the filaments. In addition, the interaction is much softer than previously reported in bulk samples using different salt conditions. Beyond viruses and cells, our characterization of the interactions governing DNA-based dense structures could help develop robust designs in DNA nanotechnologies.

Role of photoresponse of π electrons in light-driven DNA dissociations

The role of photoresponse of π electrons in light-driven DNA dissociations is theoretically studied. A new model combining the Peyrard-Bishop-Dauxois model and the charge ladder model is first proposed. Then the evolutions of π-electronic states and H-bond stretching in the light-driven DNA dissociations are studied. The results show that light irradiation will induce ultrafast charge redistribution among bases, leading to the precursory insulator-to-metallic transition. This electronic transition will assist DNA to dissociate. Effects of screened Coulomb interactions on dissociation dynamics is emphatically discussed. Finally, it is also found that light-driven DNA dissociation preferentially occurs in the adenine-thymine-rich region rather than the guanine-cytosine-rich region.

Order and interactions in DNA arrays: Multiscale molecular dynamics simulation

While densely packed DNA arrays are known to exhibit hexagonal and orthorhombic local packings, the detailed mechanism governing the associated phase transition remains rather elusive. Furthermore, at high densities the atomistic resolution is paramount to properly account for fine details, encompassing the DNA molecular order, the contingent ordering of counterions and the induced molecular ordering of the bathing solvent, bringing together electrostatic, steric, thermal and direct hydrogen-bonding interactions, resulting in the observed osmotic equation of state. We perform a multiscale simulation of dense DNA arrays by enclosing a set of 16 atomistically resolved DNA molecules within a semi-permeable membrane, allowing the passage of water and salt ions, and thus mimicking the behavior of DNA arrays subjected to external osmotic stress in a bathing solution of monovalent salt and multivalent counterions. By varying the DNA density, local packing symmetry, and counterion type, we obtain osmotic equation of state together with the hexagonal-orthorhombic phase transition, and full structural characterization of the DNA subphase in terms of its positional and angular orientational fluctuations, counterion distributions, and the solvent local dielectric response profile with its order parameters that allow us to identify the hydration force as the primary interaction mechanism at high DNA densities.

Torsional deformation of double helix in interaction and aggregation of DNA

We incorporate sequence-dependent twisting between adjacent base pairs and torsional elasticity of double helix into the theory of DNA-DNA interaction. The results show that pairing and counterion-induced-aggregation of nonhomologous DNA are accompanied by considerable torsional deformation. The deformation tunes negatively charged phosphate strands and positively charged grooves on opposing molecules to stay "in register", substantially reducing nonideality of the helical structure of DNA. Its cost, however, makes interaction between nonhomologous DNA less energetically favorable. In particular, interaction between double helical DNA may result in sequence homology recognition and selective pairing of homologous fragments containing more than 100-200 base pairs. We also find a weak, but potentially measurable, increase in the expected counterion concentration required for aggregation of nonhomologous DNA and slightly higher solubility of such DNA above the critical concentration.

Formation of impeller-like helical DNA-silica complexes by polyamines induced chiral packing

The helicity of DNA and its long-range chiral packing are widespread phenomena; however, the packing mechanism remains poorly understood both in vivo and in vitro. Here, we report the extraordinary DNA chiral self-assembly by silica mineralization, together with circular dichroism measurements and electron microscopy studies on the structure and morphology of the products. Mg(2+) ion and diethylenetriamine were found to induce right- and left-handed chiral DNA packing with two-dimensional-square p4mm mesostructures, respectively, to give corresponding enantiomeric impeller-like helical DNA-silica complexes. Moreover, formation of macroscopic impeller-like helical architectures depends on the types of polyamines and co-structure-directing agents and pH values of reaction solution. It has been suggested that interaction strength between negatively charged DNA phosphate strands and positively charged counterions may be the key factor for the induction of DNA packing handedness.

Salt-induced aggregation of stiff polyelectrolytes

Molecular dynamics simulation techniques are used to study the process of aggregation of highly charged stiff polyelectrolytes due to the presence of multivalent salt. The dominant kinetic mode of aggregation is found to be the case of one end of one polyelectrolyte meeting others at right angles, and the kinetic pathway to bundle formation is found to be similar to that of flocculation dynamics of colloids as described by Smoluchowski. The aggregation process is found to favor the formation of finite bundles of 10-11 filaments at long times. Comparing the distribution of the cluster sizes with the Smoluchowski formula suggests that the energy barrier for the aggregation process is negligible. Also, the formation of long-lived metastable structures with similarities to the raft-like structures of actin filaments is observed within a range of salt concentration.

Creating artificial ice states using vortices in nanostructured superconductors

We demonstrate that it is possible to realize vortex ice states that are analogous to square and kagome ice. With numerical simulations, we show that the system can be brought into a state that obeys either global or local ice rules by applying an external current according to an annealing protocol. We explore the breakdown of the ice rules due to disorder in the nanostructure array and show that in square ice, topological defects appear along grain boundaries, while in kagome ice, individual defects appear. We argue that the vortex system offers significant advantages over other artificial ice systems.

Ground states of colloidal molecular crystals on periodic substrates

Two-dimensional suspensions of spherical colloids subject to periodic external fields exhibit a rich variety of molecular crystalline phases. We study in simulations the ground state configurations of dimeric and trimeric systems, that are realized on square and triangular lattices, when either two or three macroions are trapped in each external potential minimum. Bipartite orders of the checkerboard or stripe types are reported together with more complex quadripartite orderings, and the shortcomings of envisioning the colloids gathered in a single potential minimum as a composite rigid object are discussed. This work also sheds light on simplifying assumptions underlying previous theoretical treatments and that made possible the mapping onto spin models.

Collagen-DNA complex

Previously presented models of collagen-DNA (7) and collagen-siRNA (8) complexes point to a general description of delivery systems and indicate to what specific topology that system should be equipped with to effectively deliver the gene into the living body via in vivo and in vitro injection. We focused our interest on the nature of collagen-DNA complex structure and the molecular and environmental determinants of the self-association processes of collagen with the presence of DNA. In this aspect, the self-association of collagen-DNA complex offers an opportunity to characterize a unique system, which may be related to the general mechanisms of self-association of fiber macromolecules by water bridges. For characterizing the collagen-DNA interaction, we used FTIR-ATR, NMR, and AFM experiments done on a separate collagen film, DNA film, and on the peptide-DNA aqueous solution. We demonstrate that collagen-DNA spontaneously forms self-assembling complex systems in aqueous solution. Such self-association of the complex could be induced by electrostatic interactions between neutral collagen cylinders, having strong dipole moment, and negatively charged DNA cylinders. A final complex could be formed by hydrogen bonds between specified donor groups of collagen and phosphate acceptor groups of DNA. According to FTIR measurements, a collagen triple helix should not change global conformation during collagen-DNA complex formation.

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.

From the double-stranded helix to the chiral nematic phase of B-DNA: A molecular model

B-DNA solutions of suitable concentration form left-handed chiral nematic phases (cholesterics). Such phases have also been observed in solutions of other stiff or semiflexible chiral polymers; magnitude and handedness of the cholesteric pitch are uniquely related to the molecular features. In this work we present a theoretical method and a numerical procedure which, starting from the structure of polyelectrolytes, lead to the prediction of the cholesteric pitch. Molecular expressions for the free energy of the system are obtained on the basis of steric and electrostatic interactions between polymers; the former are described in terms of excluded volume, while a mean field approximation is used for the latter. Calculations have been performed for 130 base pair fragments of B-DNA. The theoretical predictions provide an explanation for the experimental behavior, by showing the counteracting role played by shape and charge chirality of the molecule.

Structural investigations of DNA-polycation complexes

The internal structure of DNA-polycation complexes is investigated by synchrotron small-angle X-ray scattering (SAXS). Hexagonal packing of DNA is observed for DNA complexed with poly-L-lysine (PL), poly-L-arginine (PA), spermine (Sp), and linear and branched polyethyleneimine (lPEI and bPEI, respectively). Variations in the internal spacings and degree of long-range ordering are dependent on both polycation type and concentration of added salt. With increasing concentration of monovalent salt, a discontinuous phase transition is observed from compact to loose bundles and finally to an isotropic network phase. This salt-induced melting transition was found to be universal for all polyplexes studied and is in quantitative agreement with a simple free energy model based solely on electrostatic and entropic contributions. Using the osmotic stress method, bulk modulus (K) is measured for PL-DNA and PA-DNA polyplexes at various salt concentrations. With increasing osmotic force, we show that the salt-induced melting transition is shifted and compression in the loose bundle regime is in qualitative agreement with our model.

DNA-DNA interaction beyond the ground state

The electrostatic interaction potential between DNA duplexes in solution is a basis for the statistical mechanics of columnar DNA assemblies. It may also play an important role in recombination of homologous genes. We develop a theory of this interaction that includes thermal torsional fluctuations of DNA using field-theoretical methods and Monte Carlo simulations. The theory extends and rationalizes the earlier suggested variational approach which was developed in the context of a ground state theory of interaction of nonhomologous duplexes. It shows that the heuristic variational theory is equivalent to the Hartree self-consistent field approximation. By comparison of the Hartree approximation with an exact solution based on the QM analogy of path integrals, as well as Monte Carlo simulations, we show that this easily analytically-tractable approximation works very well in most cases. Thermal fluctuations do not remove the ability of DNA molecules to attract each other at favorable azimuthal conformations, neither do they wash out the possibility of electrostatic "snap-shot" recognition of homologous sequences, considered earlier on the basis of ground state calculations. At short distances DNA molecules undergo a "torsional alignment transition," which is first order for nonhomologous DNA and weaker order for homologous sequences.

Nonlinear effects in the torsional adjustment of interacting DNA

DNA molecules in solution, having negatively charged phosphates and countercations readsorbed on its surface, possess a distinct charge separation motif to interact electrostatically. If their double-helical structure were ideal, duplexes in parallel juxtaposition could choose azimuthal alignment providing attraction, or at least a reduction of repulsion, between them. But duplexes are not perfect staircases and the distortions of their helical structure correlate with their base pair texts. If the patterns of distortions on the opposing molecules are uncorrelated, the mismatch will accumulate as a random walk and attraction vanishes. Based on this idea, a model of recognition of homologous sequences has been proposed [A. A. Kornyshev and S. Leikin, Phys. Rev. Lett. 86, 3666 (2001)]. But DNA has torsional elasticity. How will this help to relax a mismatch between the charge distributions on two nonhomologous DNA's? In the same work, the solution of this problem has been mapped onto a frustrated sine Gordon equation in a nonlocal random field (where the latter represents a pattern of twist angle distortions on the opposing molecules), but the results had been obtained in the limit of torsionally rigid molecules. In the present paper, by solving this equation numerically, we find a strongly nonlinear relaxation mechanism which utilizes static kink-soliton modes triggered by the "random field." In the range of parameters where the solitons do not emerge, we find good agreement with the results of a variational study [A. G. Cherstvy, A. A. Kornyshev, and S. Leikin, J. Phys. Chem. B (to be published)]. We reproduce the first-order transitions in the interaxial separation dependence, but detect also second-order or weak first-order transitions for shorter duplexes. The recognition energy between two nonhomologous DNA sequences is calculated as a function of interaxial separation and the length of juxtaposition. The soliton-caused kinky length dependence is discussed in connection with plots of recombination frequency as a function of the length of homology.