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.

Effects of spatial diffusion on nonequilibrium steady states in a model for prebiotic evolution.

Effects of spatial diffusion in a Kauffman-like model for prebiotic evolution previously studied in a "well-mixed" limit are reported. The previous model was parametrized by a parameter p defined as the probability that a possible reaction in a network of reactions characterizing the artificial chemistry actually appears in the chemical network. In the model reported here, we numerically study a grid of such well-mixed reactors on a two-dimensional spatial lattice in which the model chemical constituents can hop between neighboring reactors at a rate controlled by a second parameter η. We report the frequency of appearance of three distinct types of nonequilibrium steady states, characterized as "diffusively alive locally dead" (DALD), "diffusively dead locally alive" (DDLA) and "diffusively alive locally alive" (DALA). The types are defined according to whether they are chemically equilibrated at each site, diffusively equilibrated between sites, or neither, respectively. With our parametrization of the definitions of these nonequilibrium states, many of the DALA states are growing rapidly in population due to the explosive population growth of a few sites, while their entropy remains well below its equilibrium value. Sharp temporal transitions occur as exploding sites appear. DALD states occur less commonly than the other types and also usually harbor a few explosively growing sites but transitions are less sharp than in DALA systems.

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.

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.

Dynamics of low-energy helium vapor pulses.

We report results of experiments in which pulses of helium vapor are produced by a current pulse in a chromium film covered with superfluid helium at around 0.3 K. The pulses were detected by a titanium bolometer operating at 0.47 K. The shape of the detected signal is a strong function of the power of the initiating current pulse. For low powers the signal from a single current pulse also contains a single peak, but for higher powers, a single current pulse produces two and then at the highest powers, three peak signals. To analyze the origin of these phenomena we report results of hybrid gas-dynamics and hydrodynamics simulations, which demonstrate that the signals arise from shock waves formed in the vapor. The shock waves form due to the presence of a gradient in the small ambient background of helium vapor in the chamber and are extremely sensitive to the pulse power.

Nonequilibrium steady states in a model for prebiotic evolution.

Some statistical features of steady states of a Kauffman-like model for prebiotic evolution are reported from computational studies. We postulate that the interesting "lifelike" states will be characterized by a nonequilibrium distribution of species and a time variable species self-correlation function. Selecting only such states from the population of final states produced by the model yields the probability of the appearance of such states as a function of a parameter p of the model. p is defined as the probability that a possible reaction in the the artificial chemistry actually appears in the network of chemical reactions. Small p corresponds to sparse networks utilizing a small fraction of the available reactions. We find that the probability of the appearance of such lifelike states exhibits a maximum as a function of p: at large p, most final states are in chemical equilibrium and hence are excluded by our criterion. At very small p, the sparseness of the network makes the probability of formation of any nontrivial dynamic final state low, yielding a low probability of production of lifelike states in this limit as well. We also report results on the diversity of the lifelike states (as defined here) that are produced. Repeated starts of the model evolution with different random number seeds in a given reaction network lead to final lifelike states which have a greater than random likelihood of resembling one another. Thus a form of "convergence" is observed. On the other hand, in different reaction networks with the same p, lifelike final states are statistically uncorrelated. In summary, the main results are (1) there is an optimal p or "sparseness" for production of lifelike states in our model-neither very dense nor very sparse networks are optimal--and (2) for a given p or sparseness, the resulting lifelike states can be extremely different. We discuss some possible implications for studies of the origin of life.

Fluctuations and interactions of semi-flexible polyelectrolytes in columnar assemblies.

We have developed a statistical theory for columnar aggregates of semi-flexible polyelectrolytes. The applicability of previous, simplified theories was limited to polyelectrolytes with unrealistically high effective charge and, hence, with strongly suppressed thermal undulations. To avoid this problem, we utilized more consistent approximations for short-range image-charge forces and steric confinement, resulting in new predictions for polyelectrolytes with more practically important, lower effective linear charge densities. In the present paper, we focus on aggregates of wormlike chains with uniform surface charge density, although the same basic ideas may also be applied to structured polyelectrolytes. We find that undulations effectively extend the range of electrostatic interactions between polyelectrolytes upon decreasing aggregate density, in qualitative agreement with previous theories. However, in contrast to previous theories, we demonstrate that steric confinement provides the dominant rather than a negligible contribution at higher aggregate densities and significant quantitative corrections at lower densities, resulting in osmotic pressure isotherms that drastically differ from previous predictions.

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.

Interactions of polarizable media in water: a molecular dynamics approach.

We investigate the interactions of polarizable solutes in water as a function of the solute permittivity. A generic and computationally efficient simulation methodology for the investigation of systems involving dielectric discontinuities is introduced. We report results for interactions between two polarizable cylindrical solutes of nanometer dimensions, which demonstrate that the interactions between the solutes strongly depend on the solute permittivity epsilon. For low permittivity, epsilon approximately 1-2, the interactions are dominated by surface tension forces whose origin lies in the formation of a vapor cavity between the two hydrophobic solutes. This effect leads to a drying transition, where the intersolute force changes discontinuously at a specific solute-solute separation. We find that a moderate permittivity, epsilon approximately 20, enhances the solvation of the polarizable objects inhibiting this drying transition. In the limit of moderately high permittivity, the interactions are dominated by solvation forces. These forces are much larger than those calculated using macroscopic models of dielectrics, which consider water as a continuum dielectric medium. Our results emphasize the importance of including the solvent explicitly to investigate dielectric discontinuities and interactions between polarizable media in water.

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.