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A A Kornyshev

Publications and source records attributed to A A Kornyshev.

11 recordsLinked to original sources
PubMed2005

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.

DNA↗
PubMed2005

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.

Computer Simulation↗
PubMed2004

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.

Base Pairing↗
PubMed2004

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.

Binding Sites↗
PubMed2002

Phase behavior of columnar DNA assemblies.

The interaction between two stiff parallel DNA molecules depends not only on the distance between their axes but also on their azimuthal orientation. The positional and orientational order in columnar B-DNA assemblies in solution is investigated, on the basis of the electrostatic pair potential that takes into account DNA helical symmetry and the amount and distribution of adsorbed counterions. A phase diagram obtained by lattice sums predicts a variety of positionally and azimuthally ordered phases and bundling transitions strongly depending on the counterion adsorption patterns.

DNA↗
PubMed2001

Sequence recognition in the pairing of DNA duplexes.

Pairing of DNA fragments with homologous sequences occurs in gene shuffling, DNA repair, and other vital processes. While chemical individuality of base pairs is hidden inside the double helix, x ray and NMR revealed sequence-dependent modulation of the structure of DNA backbone. Here we show that the resulting modulation of the DNA surface charge pattern enables duplexes longer than approximately 50 base pairs to recognize sequence homology electrostatically at a distance of up to several water layers. This may explain the local recognition observed in pairing of homologous chromosomes and the observed length dependence of homologous recombination.

Base Pairing↗
PubMed2000

Twist in chiral interaction between biological helices.

Using an exact solution for the pair interaction potential, we show that long, rigid, chiral molecules with helical surface charge patterns have a preferential interaxial angle approximately sqrt[RH]/L, where L is the length of the molecules, R is the closest distance between their axes, and H is the helical pitch. Estimates based on this formula suggest a solution for the puzzle of small interaxial angles in alpha-helix bundles and in cholesteric phases of DNA.

DNA↗
PubMed2000

Electrostatic interaction between long, rigid helical macromolecules at all interaxial angles.

We derive formulas for the electrostatic interaction between two long, rigid macromolecules that may have arbitrary surface charge patterns and cross at an arbitrary interaxial angle. We calculate the dependence of the interaction energy on the interaxial angle, on the separation, and on the precise alignment of the charge pattern on one molecule with respect to the other. We focus in particular on molecules with helical charge patterns. We report an exact, explicit expression for the energy of interaction between net-neutral helices in a nonpolar medium as well as an approximate result for charged helices immersed in an electrolyte solution. The latter result becomes exact in the asymptotic limit of large separations. Molecular chirality of helices manifests itself in a torque that tends to twist helices in a certain direction out of parallel alignment and that has a nontrivial behavior at small interaxial angles. We illustrate the theory with the calculation of the torque between layers of idealized, DNA-like double helices in cholesteric aggregates. We propose a mechanism of the observed cholesteric-to-columnar phase transition and suggest an explanation for the observed macroscopic (0.4-5 microm) pitch of the cholesteric phase of B-DNA.

DNA↗
PubMed1998

Electrostatic interaction between helical macromolecules in dense aggregates: an impetus for DNA poly- and meso-morphism.

DNA exhibits a surprising multiplicity of structures when it is packed into dense aggregates. It undergoes various polymorphous transitions (e.g., from the B to A form) and mesomorphous transformations (from hexagonal to orthorhombic or monoclinic packing, changes in the mutual alignment of nearest neighbors, etc). In this report we show that such phenomena may have their origin in the specific helical symmetry of the charge distribution on DNA surface. Electrostatic interaction between neighboring DNA molecules exhibits strong dependence on the patterns of molecular surface groups and adsorbed counter-ions. As a result, it is affected by such structural parameters as the helical pitch, groove width, the number of base pairs per helical turn, etc. We derive expressions which relate the energy of electrostatic interaction with these parameters and with the packing variables characterizing the axial and azimuthal alignment between neighboring macromolecules. We show, in particular, that the structural changes upon the B-to-A transition reduce the electrostatic energy by approximately kcal/mol per base pair, at a random adsorption of counter ions. Ion binding into the narrow groove weakens or inverts this effect, stabilizing B-DNA, as it is presumably the case in Li+-DNA assemblies. The packing symmetry and molecular alignment in DNA aggregates are shown to be affected by the patterns of ion binding.

Animals↗
PubMed1998

Symmetry laws for interaction between helical macromolecules.

The power of symmetry laws is applied in many scientific areas from elementary particle physics to structural biology. The structures of many biological helices, including DNA, were resolved with the use of pertinent symmetry constraints. It was not recognized, however, that similar constraints determine cardinal features of helix-helix interactions vital for many recognition and assembly reactions in living cells. We now formulate such symmetry-determined interaction laws and apply them to explain DNA "over-winding" from 10.5 base pairs per turn in solution to 10 in hydrated fibers, counterion specificity in DNA condensation, and forces observed over the last 15 A of separation between DNA, collagen, and four-stranded guanosine helices.

DNA↗