A lattice polymer study of DNA renaturation dynamics

DNA renaturation is the recombination of two complementary single strands to form a double helix. It is experimentally known that renaturation proceeds through the formation of a double stranded nucleus of several base pairs (the rate limiting step) followed by a much faster zippering. We consider a lattice polymer model undergoing Rouse dynamics and focus on the nucleation of two diffusing strands. We study numerically the dependence of various nucleation rates on the strand lengths and on an additional local nucleation barrier. When the local barrier is sufficiently high, all renaturation rates considered scale with the length as predicted by Kramers' rate theory and are also in agreement with experiments: their scaling behavior is governed by exponents describing equilibrium properties of polymers. When the local barrier is lowered renaturation occurs in a regime of genuine non-equilibrium behavior and the scaling deviates from the rate theory prediction.Comment: 13 pages, 6 figures. To appear in Journal of Statistical Mechanic

Equilibrium shapes and faceting for ionic crystals of body-centered-cubic type

A mean field theory is developed for the calculation of the surface free energy of the staggered BCSOS, (or six vertex) model as function of the surface orientation and of temperature. The model approximately describes surfaces of crystals with nearest neighbor attractions and next nearest neighbor repulsions. The mean field free energy is calculated by expressing the model in terms of interacting directed walks on a lattice. The resulting equilibrium shape is very rich with facet boundaries and boundaries between reconstructed and unreconstructed regions which can be either sharp (first order) or smooth (continuous). In addition there are tricritical points where a smooth boundary changes into a sharp one and triple points where three sharp boundaries meet. Finally our numerical results strongly suggest the existence of conical points, at which tangent planes of a finite range of orientations all intersect each other. The thermal evolution of the equilibrium shape in this model shows strong similarity to that seen experimentally for ionic crystals.Comment: 14 Pages, Revtex and 10 PostScript figures include

Thermodynamic behavior of short oligonucleotides in microarray hybridizations can be described using Gibbs free energy in a nearest-neighbor model

While designing oligonucleotide-based microarrays, cross-hybridization between surface-bound oligos and non-intended labeled targets is probably the most difficult parameter to predict. Although literature describes rules-of-thumb concerning oligo length, overall similarity, and continuous stretches, the final behavior is difficult to predict. The aim of this study was to investigate the effect of well-defined mismatches on hybridization specificity using CodeLink Activated Slides, and to study quantitatively the relation between hybridization intensity and Gibbs free energy (Delta G), taking the mismatches into account. Our data clearly showed a correlation between the hybridization intensity and Delta G of the oligos over three orders of magnitude for the hybridization intensity, which could be described by the Langmuir model. As Delta G was calculated according to the nearest-neighbor model, using values related to DNA hybridizations in solution, this study clearly shows that target-probe hybridizations on microarrays with a three-dimensional coating are in quantitative agreement with the corresponding reaction in solution. These results can be interesting for some practical applications. The correlation between intensity and Delta G can be used in quality control of microarray hybridizations by designing probes and corresponding RNA spikes with a range of Delta G values. Furthermore, this correlation might be of use to fine-tune oligonucleotide design algorithms in a way to improve the prediction of the influence of mismatching targets on microarray hybridizations.Comment: 32 pages on a single pdf fil

Universality in the pair contact process with diffusion

The pair contact process with diffusion is studied by means of multispin Monte Carlo simulations and density matrix renormalization group calculations. Effective critical exponents are found to behave nonmonotonically as functions of time or of system length and extrapolate asymptotically towards values consistent with the directed percolation universality class. We argue that an intermediate regime exists where the effective critical dynamics resembles that of a parity conserving process.Comment: 8 Pages, 9 figures, final version as publishe

Fixed Point of the Finite System DMRG

The density matrix renormalization group (DMRG) is a numerical method that optimizes a variational state expressed by a tensor product. We show that the ground state is not fully optimized as far as we use the standard finite system algorithm, that uses the block structure B**B. This is because the tensors are not improved directly. We overcome this problem by using the simpler block structure B*B for the final several sweeps in the finite iteration process. It is possible to increase the numerical precision of the finite system algorithm without increasing the computational effort.Comment: 6 pages, 4 figure