DNA condensation and redissolution: Interaction between overcharged DNA molecules

The effective DNA-DNA interaction force is calculated by computer simulations with explicit tetravalent counterions and monovalent salt. For overcharged DNA molecules, the interaction force shows a double-minimum structure. The positions and depths of these minima are regulated by the counterion density in the bulk. Using two-dimensional lattice sum and free energy perturbation theories, the coexisting phases for DNA bundles are calculated. A DNA-condensation and redissolution transition and a stable mesocrystal with an intermediate lattice constant for high counterion concentration are obtained.Comment: 26 pages, 10 figure

Structural Polymorphism of the Cytoskeleton: A Model of Linker-Assisted Filament Aggregation

The phase behavior of charged rods in the presence of inter-rod linkers is studied theoretically as a model for the equilibrium behavior underlying the organization of actin filaments by linker proteins in the cytoskeleton. The presence of linkers in the solution modifies the effective inter-rod interaction and can lead to inter-filament attraction. Depending on the system's composition and physical properties such as linker binding energies, filaments will either orient perpendicular or parallel to each other, leading to network-like or bundled structures. We show that such a system can have one of three generic phase diagrams, one dominated by bundles, another by networks, and the third containing both bundle and network-like phases. The first two diagrams can be found over a wide range of interaction energies, while the third occurs only for a narrow range. These results provide theoretical understanding of the classification of linker proteins as bundling proteins or crosslinking proteins. In addition, they suggest possible mechanisms by which the cell may control cytoskeletal morphology.Comment: 17 pages, 3 figure

Phase diagram of aggregation of oppositely charged colloids in salty water

Aggregation of two oppositely charged colloids in salty water is studied. We focus on the role of Coulomb interaction in strongly asymmetric systems in which the charge and size of one colloid is much larger than the other one. In the solution, each large colloid (macroion) attracts certain number of oppositely charged small colloids ($Z$-ion) to form a complex. If the concentration ratio of the two colloids is such that complexes are not strongly charged, they condense in a macroscopic aggregate. As a result, the phase diagram in a plane of concentrations of two colloids consists of an aggregation domain sandwiched between two domains of stable solutions of complexes. The aggregation domain has a central part of total aggregation and two wings corresponding to partial aggregation. A quantitative theory of the phase diagram in the presence of monovalent salt is developed. It is shown that as the Debye-H\"{u}ckel screening radius $r_s$ decreases, the aggregation domain grows, but the relative size of the partial aggregation domains becomes much smaller. As an important application of the theory, we consider solutions of long double-helix DNA with strongly charged positive spheres (artificial chromatin). We also consider implications of our theory for in vitro experiments with the natural chromatin. Finally, the effect of different shapes of macroions on the phase diagram is discussed.Comment: 10 pages, 9 figures. The text is rewritten, but results are not change

Relative Age Effect in Elite Sports: Methodological Bias or Real Discrimination?

Sport sciences researchers talk about a relative age effect when they observe a biased distribution of elite athletes' birthdates, with an over-representation of those born at the beginning of the competitive year and an under-representation of those born at the end. Using the whole sample of the French male licensed soccer players (n = 1,831,524), our study suggests that there could be an important bias in the statistical test of this effect. This bias could in turn lead to falsely conclude to a systemic discrimination in the recruitment of professional players. Our findings question the accuracy of past results concerning the existence of this effect at the elite level

(k,1)-coloring of sparse graphs

AbstractA graph G is (k,1)-colorable if the vertex set of G can be partitioned into subsets V1 and V2 such that the graph G[V1] induced by the vertices of V1 has maximum degree at most k and the graph G[V2] induced by the vertices of V2 has maximum degree at most 1. We prove that every graph with maximum average degree less than 10k+223k+9 admits a (k,1)-coloring, where k≥2. In particular, every planar graph with girth at least 7 is (2,1)-colorable, while every planar graph with girth at least 6 is (5,1)-colorable. On the other hand, when k≥2 we construct non-(k,1)-colorable graphs whose maximum average degree is arbitrarily close to 14k4k+1

Enhanced Partial Tracking Using Linear Prediction

International audienceIn this paper, we introduce a new partial tracking method suitable for the sinusoidal modeling of mixtures of instrumental sounds with pseudo stationary frequencies. This method, based on the linear prediction of the frequency evolutions of the partials, enables us to track these partials more accurately at the analysis stage, even in complex sound mixtures. This allows our spectral model to better handle polyphonic sound

Symmetries of Electrostatic Interaction between DNA Molecules

We study a model for pair interaction $U$ of DNA molecules generated by the discrete dipole moments of base-pairs and the charges of phosphate groups, and find noncommutative group of eighth order ${\cal S}$ of symmetries that leave $U$ invariant. We classify the minima using group ${\cal S}$ and employ numerical methods for finding them. The minima may correspond to several cholesteric phases, as well as phases formed by cross-like conformations of molecules at an angle close to $\rm{90}^{o}$, "snowflake phase". The results depend on the effective charge $Q$ of the phosphate group which can be modified by the polycations or the ions of metals. The snowflake phase could exist for $Q$ above the threshold $Q_C$. Below $Q_C$ there could be several cholesteric phases. Close to $Q_C$ the snowflake phase could change into the cholesteric one at constant distance between adjacent molecules.Comment: 13 pages, 4 figure

Recursive graphs with small-world scale-free properties

We discuss a category of graphs, recursive clique trees, which have small-world and scale-free properties and allow a fine tuning of the clustering and the power-law exponent of their discrete degree distribution. We determine relevant characteristics of those graphs: the diameter, degree distribution, and clustering parameter. The graphs have also an interesting recursive property, and generalize recent constructions with fixed degree distributions.Comment: 4 pages, 2 figure

DNA folding: structural and mechanical properties of the two-angle model for chromatin

We present a theoretical analysis of the structural and mechanical properties of the 30-nm chromatin fiber. Our study is based on the two-angle model introduced by Woodcock et al. (Woodcock, C. L., S. A. Grigoryev, R. A. Horowitz, and N. Whitaker. 1993. PNAS 90:9021-9025) that describes the chromatin fiber geometry in terms of the entry-exit angle of the nucleosomal DNA and the rotational setting of the neighboring nucleosomes with respect to each other. We explore analytically the different structures that arise from this building principle, and demonstrate that the geometry with the highest density is close to the one found in native chromatin fibers under physiological conditions. On the basis of this model we calculate mechanical properties of the fiber under stretching. We obtain expressions for the stress-strain characteristics which show good agreement with the results of recent stretching experiments (Cui, Y., and C. Bustamante. 2000. PNAS 97:127-132) and computer simulations (Katritch, V., C. Bustamante, and W. K. Olson. 2000. J. Mol. Biol. 295:29-40), and which provide simple physical insights into correlations between the structural and elastic properties of chromatin.Comment: 23 pages, 6 figures, to be published in Biophys.

Attractive Interactions Between Rod-like Polyelectrolytes: Polarization, Crystallization, and Packing

We study the attractive interactions between rod-like charged polymers in solution that appear in the presence of multi-valence counterions. The counterions condensed to the rods exhibit both a strong transversal polarization and a longitudinal crystalline arrangement. At short distances between the rods, the fraction of condensed counterions increases, and the majority of these occupy the region between the rods, where they minimize their repulsive interactions by arranging themselves into packing structures. The attractive interaction is strongest for multivalent counterions. Our model takes into account the hard-core volume of the condensed counterions and their angular distribution around the rods. The hard core constraint strongly suppresses longitudinal charge fluctuations.Comment: 4 figures, uses revtex, psfig and epsf. The new version contains a different introduction, and the bibliography has been expande