Monte Carlo simulation of melting transition on DNA nanocompartment

DNA nanocompartment is a typical DNA-based machine whose function is dependent of molecular collective effect. Fundamental properties of the device have been addressed via electrochemical analysis, fluorescent microscopy, and atomic force microscopy. Interesting and novel phenomena emerged during the switching of the device. We have found that DNAs in this system exhibit a much steep melting transition compared to ones in bulk solution or conventional DNA array. To achieve an understanding to this discrepancy, we introduced DNA-DNA interaction potential to the conventional Ising-like Zimm-Bragg theory and Peyrard-Bishop model of DNA melting. To avoid unrealistic numerical calculation caused by modification of the Peyrard-Bishop nonlinear Hamiltonian with the DNA-DNA interaction, we established coarse-gained Monte Carlo recursion relations by elucidation of five components of energy change during melting transition. The result suggests that DNA-DNA interaction potential accounts for the observed steep transition.Comment: 12 pages, 5 figure

Star polymers: From conformations to interactions to phase diagrams

We review recent progress achieved in the theoretical description of the interactions, correlations, and phase behavior of concentrated solutions of star polymers, sterically stabilized colloids, and micelles. We show that the theoretical prediction of an ultrasoft, logarithmically diverging effective interaction between the star centers, which has been confirmed by SANSexperiments and computer simulations, lies in the core of a host of unusual phenomena encountered in such systems. These include anomalous structure factors, reentrant melting behavior, as well as a variety of exotic crystal phases. Extensions to polydisperse stars and the role of many-body forces are also discussed. A particular ‘mean-field’ character of star polymer fluids is presented and it is shown that it manifests itself in the shape and structure of sedimentation profiles of these systems.Здійснено огляд недавніх досягнень у теоретичному описі взаємодій, кореляцій і фазової поведінки концентрованих розчинів зіркових полімерів, просторово стійких колоїдів і міцел. Ми покажемо, що теоретично передбачена надм’яка логарифмічно розбіжна ефективна взаємодія між центрами зірок, що була підтверджена SANS-експериментами і комп’ютерними симуляціями, потрапляє в множину незвичних явищ, які спостерігаються в таких системах. Сюди відносяться аномальні структурні фактори, поведінка зворотнього плавлення, множини екзотичних кристалічних фаз. Також обговорено узагальнення на випадок полідисперсних зірок і роль сил багатьох тіл. Представлено особливу поведінку типу “cереднього поля” плинів зіркових полімерів і показано, що вона проявляється у формі і структурі профілів осаджування цих систем

Counterion-mediated Electrostatic Interactions between Helical Molecules

We study the interaction of two cylinders with helical charge distribution mediated by neutralizing counterions, by analyzing the separation as well as the azimuthal angle dependence of the interaction force in the weak and strong coupling limit. While the azimuthal dependence of the interaction in the weak coupling limit is overall small and mostly negligible, the strong coupling limit leads to qualitatively new features of the interaction, among others also to an orientationally dependent optimal configuration that is driven by angular dependence of the correlation attraction. We investigate the properties of this azimuthal ordering in detail and compare it to existing results.Comment: 11 pages, 12 figure

Orientationally ordered aggregates of stiff polyelectrolytes in the presence of multivalent salt

Aggregation of stiff polyelectrolytes in solution and angle- and distance-dependent potential of mean force between two like-charged rods are studied in the presence of 3-valent salt using molecular dynamics simulations. In the bulk solution, formation of long-lived metastable structures with similarities to the raft-like structures of actin filaments is observed within a range of salt concentration. The system finally goes to a state with lower free energy in which finite-sized bundles of parallel polyelectrolytes form. Preferred angle and interaction type between two like-charged rods at different separations and salt concentrations are also studied, which shed some light on the formation of orientationally ordered structures.Comment: 18 pages, 8 figures, accepted for publication in Soft Matte

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

Torsional fluctuations in columnar DNA assemblies

In columnar assemblies of helical bio-molecules the azimuthal degrees of freedom, i.e. rotations about the long axes of molecules, may be important in determining the structure of the assemblies especially when the interaction energy between neighbouring molecules explicitly depends on their relative azimuthal orientations. For DNA this leads to a rich variety of mesophases for columnar assemblies, each categorized by a specific azimuthal ordering. In a preceding paper [A. Wynveen, D. J. Lee, and A. A. Kornyshev, Eur. Phys. J. E, 16, 303 (2005)] a statistical mechanical theory was developed for the assemblies of torsionally rigid molecues in order to determine how thermal fluctuations influence the structure of these mesophases. Here we extend this theory by including torsional fluctuations of the molecules, where a DNA molecule may twist about its long axis at the cost of torsional elastic energy. Comparing this with the previous study, we find that inclusion of torsional fluctuations further increases the density at which the transition between the hexagonal structure and the predicted rhombic phase occurs and reduces the level of distortion in the rhombic phase. As X-ray diffraction may probe the 2-D lattice structure of such assemblies and provide information concerning the underlying interaction between molecules, we have also calculated correlation functions for the azimuthal ordering which are manifest in an x-ray scattering intensity profiles.Comment: 33 pages, 8 figure

Phase Transitions in a Two-Component Site-Bond Percolation Model

A method to treat a N-component percolation model as effective one component model is presented by introducing a scaled control variable $p_{+}$. In Monte Carlo simulations on $16^{3}$, $32^{3}$, $64^{3}$ and $128^{3}$ simple cubic lattices the percolation threshold in terms of $p_{+}$ is determined for N=2. Phase transitions are reported in two limits for the bond existence probabilities $p_{=}$ and $p_{\neq}$. In the same limits, empirical formulas for the percolation threshold $p_{+}^{c}$ as function of one component-concentration, $f_{b}$, are proposed. In the limit $p_{=} = 0$ a new site percolation threshold, $f_{b}^{c} \simeq 0.145$, is reported.Comment: RevTeX, 5 pages, 5 eps-figure

Chiral Structure of F-actin Bundle Formed by Multivalent Counterions?

The mechanism of multivalent counterion-induced bundle formation by filamentous actin (F-actin) is studied using a coarse-grained model and molecular dynamics simulation. Real diameter size, helically ordered charge distribution and twist rigidity of F-actin are taken into account in our model. The attraction between parallel F-actins induced by multivalent counterions is studied in detail and it is found that the maximum attraction occurs between their closest charged domains. The model F-actins aggregate due to the like-charge attraction and form closely packed bundles. Counterions are mostly distributed in the narrowest gaps between neighboring F-actins inside the bundles and the channels between three adjacent F-actins correspond to low density of the counterions. Density of the counterions varies periodically with a wave length comparable to the separation between consecutive G-actin monomers along the actin polymers. Long-lived defects in the hexagonal order of F-actins in the bundles are observed that their number increases with increasing the bundles size. Combination of electrostatic interactions and twist rigidity has been found not to change the symmetry of F-actin helical conformation from the native 13/6 symmetry. Calculation of zero-temperature energy of hexagonally ordered model F-actins with the charge of the counterions distributed as columns of charge domains representing counterion charge density waves has shown that helical symmetries commensurate with the hexagonal lattice correspond to local minima of the energy of the system. The global minimum of energy corresponds to 24/11 symmetry with the columns of charge domains arranged in the narrowest gaps between the neighboring F-actins.Comment: 9 pages, 10 figures, Published online in Soft Matter journal: http://pubs.rsc.org/en/content/articlelanding/2012/sm/c2sm07104

Rare isotope production in statistical multifragmentation

Producing rare isotopes through statistical multifragmentation is investigated using the Mekjian method for exact solutions of the canonical ensemble. Both the initial fragmentation and the the sequential decay are modeled in such a way as to avoid Monte Carlo and thus provide yields for arbitrarily scarce fragments. The importance of sequential decay, exact particle-number conservation and the sensitivities to parameters such as density and temperature are explored. Recent measurements of isotope ratios from the fragmentation of different Sn isotopes are interpreted within this picture.Comment: 10 eps figure