Denaturation of Heterogeneous DNA

The effect of heterogeneous sequence composition on the denaturation of double stranded DNA is investigated. The resulting pair-binding energy variation is found to have a negligible effect on the critical properties of the smooth second order melting transition in the simplest (Peyrard-Bishop) model. However, sequence heterogeneity is dramatically amplified upon adopting a more realistic treatment of the backbone stiffness. The model yields features of ``multi-step melting'' similar to those observed in experiments.Comment: 4 pages, LaTeX, text and figures also available at http://matisse.ucsd.edu/~hw

Dynamics of Counterion Condensation

Using a generalization of the Poisson-Boltzmann equation, dynamics of counterion condensation is studied. For a single charged plate in the presence of counterions, it is shown that the approach to equilibrium is diffusive. In the far from equilibrium case of a moving charged plate, a dynamical counterion condensation transition occurs at a critical velocity. The complex dynamic behavior of the counterion cloud is shown to lead to a novel nonlinear force-velocity relation for the moving plate.Comment: 5 pages, 1 ps figure included using eps

A new bond fluctuation method for a polymer undergoing gel electrophoresis

We present a new computational methodology for the investigation of gel electrophoresis of polyelectrolytes. We have developed the method initially to incorporate sliding motion of tight parts of a polymer pulled by an electric field into the bond fluctuation method (BFM). Such motion due to tensile force over distances much larger than the persistent length is realized by non-local movement of a slack monomer at an either end of the tight part. The latter movement is introduced stochastically. This new BFM overcomes the well-known difficulty in the conventional BFM that polymers are trapped by gel fibers in relatively large fields. At the same time it also reproduces properly equilibrium properties of a polymer in a vanishing filed limit. The new BFM thus turns out an efficient computational method to study gel electrophoresis in a wide range of the electric field strength.Comment: 15 pages, 11 figure

Formation of helical states in wormlike polymer chains

We propose a potential for wormlike polymer chains which can be used to model the low-temperature conformational structures. We successfully reproduced helix ground states up to 6.5 helical loops, using the multicanonical Monte Carlo simulation method. We demonstrate that the coil-helix transition involves four distinct phases: coil(gaslike), collapsed globular(liquidlike), and two helical phases I and II (both solidlike). The helix I phase is characterized by a helical structure with dangling loose ends, and the helix II phase corresponds to a near perfect helix ordering in the entire crystallized chain.Comment: 5 pages, 2 figures, Submitted to PR

Scaling and Universality in the Counterion-Condensation Transition at Charged Cylinders

We address the critical and universal aspects of counterion-condensation transition at a single charged cylinder in both two and three spatial dimensions using numerical and analytical methods. By introducing a novel Monte-Carlo sampling method in logarithmic radial scale, we are able to numerically simulate the critical limit of infinite system size (corresponding to infinite-dilution limit) within tractable equilibration times. The critical exponents are determined for the inverse moments of the counterionic density profile (which play the role of the order parameters and represent the inverse localization length of counterions) both within mean-field theory and within Monte-Carlo simulations. In three dimensions (3D), correlation effects (neglected within mean-field theory) lead to an excessive accumulation of counterions near the charged cylinder below the critical temperature (condensation phase), while surprisingly, the critical region exhibits universal critical exponents in accord with the mean-field theory. In two dimensions (2D), we demonstrate, using both numerical and analytical approaches, that the mean-field theory becomes exact at all temperatures (Manning parameters), when number of counterions tends to infinity. For finite particle number, however, the 2D problem displays a series of peculiar singular points (with diverging heat capacity), which reflect successive de-localization events of individual counterions from the central cylinder. In both 2D and 3D, the heat capacity shows a universal jump at the critical point, and the energy develops a pronounced peak. The asymptotic behavior of the energy peak location is used to locate the critical temperature, which is also found to be universal and in accordance with the mean-field prediction.Comment: 31 pages, 16 figure

Polymer Induced Bundling of F-actin and the Depletion Force

The inert polymer polyethylene glycol (PEG) induces a "bundling" phenomenon in F-actin solutions when its concentration exceeds a critical onset value C_o. Over a limited range of PEG molecular weight and ionic strength, C_o can be expressed as a function of these two variables. The process is reversible, but hysteresis is also observed in the dissolution of the bundles, with ionic strength having a large influence. Additional actin filaments are able to join previously formed bundles. Little, if any, polymer is associated with the bundle structure. Continuum estimates of the Asakura-Oosawa depletion force, Coulomb repulsion, and van der Waals potential are combined for a partial explanation of the bundling effect and hysteresis. Conjectures are presented concerning the apparent limit in bundle size

Bubbles, clusters and denaturation in genomic DNA: modeling, parametrization, efficient computation

The paper uses mesoscopic, non-linear lattice dynamics based (Peyrard-Bishop-Dauxois, PBD) modeling to describe thermal properties of DNA below and near the denaturation temperature. Computationally efficient notation is introduced for the relevant statistical mechanics. Computed melting profiles of long and short heterogeneous sequences are presented, using a recently introduced reparametrization of the PBD model, and critically discussed. The statistics of extended open bubbles and bound clusters is formulated and results are presented for selected examples.Comment: to appear in a special issue of the Journal of Nonlinear Mathematical Physics (ed. G. Gaeta

Reconstruction of a first-order phase transition from computer simulations of individual phases and subphases

We present a new method for investigating first-order phase transitions using Monte Carlo simulations. It relies on the multiple-histogram method and uses solely histograms of individual phases. In addition, we extend the method to include histograms of subphases. The free energy difference between phases, necessary for attributing the correct statistical weights to the histograms, is determined by a detour in control parameter space via auxiliary systems with short relaxation times. We apply this method to a recently introduced model for structure formation in polypeptides for which other methods fail.Comment: 13 pages in preprint mode, REVTeX, 2 Figures available from the authors ([email protected], [email protected]

Lateral Separation of Macromolecules and Polyelectrolytes in Microlithographic Arrays

A new approach to separation of a variety of microscopic and mesoscopic objects in dilute solution is presented. The approach takes advantage of unique properties of a specially designed separation device (sieve), which can be readily built using already developed microlithographic techniques. Due to the broken reflection symmetry in its design, the direction of motion of an object in the sieve varies as a function of its self-diffusion constant, causing separation transverse to its direction of motion. This gives the device some significant and unique advantages over existing fractionation methods based on centrifugation and electrophoresis.Comment: 4 pages with 3 eps figures, needs RevTeX 3.0 and epsf, also available in postscript form http://cmtw.harvard.edu/~deniz

Gel-Electrophoresis and Diffusion of Ring-Shaped DNA

A model for the motion of ring-shaped DNA in a gel is introduced and studied by numerical simulations and a mean-field approximation. The ring motion is mediated by finger-shaped loops (hernias) that move in an amoeba-like fashion around the gel obstructions. This constitutes an extension of previous reptation tube treatments. It is shown that tension is essential for describing the dynamics in the presence of hernias. It is included in the model as long range interactions over stretched DNA regions. The mobility of ring-shaped DNA is found to saturate much as in the well-studied case of linear DNA. Experiments in polymer gels, however, show that the mobility drops exponentially with the DNA ring size. This is commonly attributed to dangling-ends in the gel that can impale the ring. The predictions of the present model are expected to apply to artificial 2D obstacle arrays (W.D. Volkmuth, R.H. Austin, Nature 358,600 (1992)) which have no dangling-ends. In the zero-field case an exact solution of the model steady-state is obtained, and quantities such as the average ring size are calculated. An approximate treatment of the ring dynamics is given, and the diffusion coefficient is derived. The model is also discussed in the context of spontaneous symmetry breaking in one dimension.Comment: 8 figures, LaTeX, Phys. Rev. E - in pres