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 and 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.Comment: 19 pages, 18 figure

Consider again the event space U. Equation (3.1) implicitly tells us the optimal hypothesis function for any training set, as a function of P(f |

this paper, the physical meaning of probabilities is set by their use in error functions: P(d | w) is simply whatever distribution gives the experimentally observed 30 function P(E | s, w) for our hypothesis generalizer substrate P(g | w)

Phase separation in a binary hard-core mixture. An exact result.

We show that certain lattice models for a binary mixture of hard particle mixtures can be mapped onto a one-component lattice gas or, equivalently, onto an Ising model. The repulsive interaction between unlike particles in the mixture leads to an attractive nearest-neighbour interaction in the one-component lattice gas. In particular, we have found a lattice model of a binary hard-core mixture that maps onto the Ising model with nearest neighbor interactions. The existence of a phase transition in the Ising model provides a direct proof of the occurence of a first-order, entropy driven demixing transition in the hard-core mixture on a lattice. The same mapping can be extended to a lattice polymer in solution. The athermal polymer-solvent mixture now maps onto the Flory-Huggins lattice model. This result leads to a very simple interpretation of the entropic contribution to the interaction parameter Ø in the Flory-Huggins theory. In a recent Letter, Biben and Hansen [1] have used an ap..