Strong and weak adsorptions of polyelectrolyte chains onto oppositely charged spheres

We investigate the complexation of long thin polyelectrolyte (PE) chains with oppositely charged spheres. In the limit of strong adsorption, when strongly charged PE chains adapt a definite wrapped conformation on the sphere surface, we analytically solve the linear Poisson-Boltzmann equation and calculate the electrostatic potential and the energy of the complex. We discuss some biological applications of the obtained results. For weak adsorption, when a flexible weakly charged PE chain is localized next to the sphere in solution, we solve the Edwards equation for PE conformations in the Hulthen potential, which is used as an approximation for the screened Debye-Huckel potential of the sphere. We predict the critical conditions for PE adsorption. We find that the critical sphere charge density exhibits a distinctively different dependence on the Debye screening length than for PE adsorption onto a flat surface. We compare our findings with experimental measurements on complexation of various PEs with oppositely charged colloidal particles. We also present some numerical results of the coupled Poisson-Boltzmann and self-consistent field equation for PE adsorption in an assembly of oppositely charged spheres

Facilitation of polymer looping and giant polymer diffusivity in crowded solutions of active particles

We study the dynamics of polymer chains in a bath of self-propelled particles (SPP) by extensive Langevin dynamics simulations in a two dimensional system. Specifically, we analyse the polymer looping properties versus the SPP activity and investigate how the presence of the active particles alters the chain conformational statistics. We find that SPPs tend to extend flexible polymer chains while they rather compactify stiffer semiflexible polymers, in agreement with previous results. Here we show that larger activities of SPPs yield a higher effective temperature of the bath and thus facilitate looping kinetics of a passive polymer chain. We explicitly compute the looping probability and looping time in a wide range of the model parameters. We also analyse the motion of a monomeric tracer particle and the polymer's centre of mass in the presence of the active particles in terms of the time averaged mean squared displacement, revealing a giant diffusivity enhancement for the polymer chain via SPP pooling. Our results are applicable to rationalising the dimensions and looping kinetics of biopolymers at constantly fluctuating and often actively driven conditions inside biological cells or suspensions of active colloidal particles or bacteria cells.Comment: 15 pages, 9 figures, IOPLaTe

Electrostatic contribution to DNA condensation - application of 'energy minimization' in a simple model in strong Coulomb coupling regime

Bending of DNA from a straight rod to a circular form in presence of any of the mono-, di-, tri- or tetravalent counterions has been simulated in strong Coulomb coupling environment employing a previously developed energy minimization simulation technique. The inherent characteristics of the simulation technique allow monitoring the required electrostatic contribution to the bending. The curvature of the bending has been found to play crucial roles in facilitating electrostatic attractive potential energy. The total electrostatic potential energy has been found to decrease with bending which indicates that bending a straight DNA to a circular form or to a toroidal form in presence of neutralizing counterions is energetically favorable and practically is a spontaneous phenomenon

Regulation of the nucleosome repeat length in vivo by the DNA sequence, protein concentrations and long-range interactions.

The nucleosome repeat length (NRL) is an integral chromatin property important for its biological functions. Recent experiments revealed several conflicting trends of the NRL dependence on the concentrations of histones and other architectural chromatin proteins, both in vitro and in vivo, but a systematic theoretical description of NRL as a function of DNA sequence and epigenetic determinants is currently lacking. To address this problem, we have performed an integrative biophysical and bioinformatics analysis in species ranging from yeast to frog to mouse where NRL was studied as a function of various parameters. We show that in simple eukaryotes such as yeast, a lower limit for the NRL value exists, determined by internucleosome interactions and remodeler action. For higher eukaryotes, also the upper limit exists since NRL is an increasing but saturating function of the linker histone concentration. Counterintuitively, smaller H1 variants or non-histone architectural proteins can initiate larger effects on the NRL due to entropic reasons. Furthermore, we demonstrate that different regimes of the NRL dependence on histone concentrations exist depending on whether DNA sequence-specific effects dominate over boundary effects or vice versa. We consider several classes of genomic regions with apparently different regimes of the NRL variation. As one extreme, our analysis reveals that the period of oscillations of the nucleosome density around bound RNA polymerase coincides with the period of oscillations of positioning sites of the corresponding DNA sequence. At another extreme, we show that although mouse major satellite repeats intrinsically encode well-defined nucleosome preferences, they have no unique nucleosome arrangement and can undergo a switch between two distinct types of nucleosome positioning

Adsorption of mono- and multivalent cat- and anions on DNA molecules

Adsorption of monovalent and multivalent cat- and anions on a deoxyribose nucleic acid (DNA) molecule from a salt solution is investigated by computer simulation. The ions are modelled as charged hard spheres, the DNA molecule as a point charge pattern following the double-helical phosphate strands. The geometrical shape of the DNA molecules is modelled on different levels ranging from a simple cylindrical shape to structured models which include the major and minor grooves between the phosphate strands. The densities of the ions adsorbed on the phosphate strands, in the major and in the minor grooves are calculated. First, we find that the adsorption pattern on the DNA surface depends strongly on its geometrical shape: counterions adsorb preferentially along the phosphate strands for a cylindrical model shape, but in the minor groove for a geometrically structured model. Second, we find that an addition of monovalent salt ions results in an increase of the charge density in the minor groove while the total charge density of ions adsorbed in the major groove stays unchanged. The adsorbed ion densities are highly structured along the minor groove while they are almost smeared along the major groove. Furthermore, for a fixed amount of added salt, the major groove cationic charge is independent on the counterion valency. For increasing salt concentration the major groove is neutralized while the total charge adsorbed in the minor groove is constant. DNA overcharging is detected for multivalent salt. Simulations for a larger ion radii, which mimic the effect of the ion hydration, indicate an increased adsorbtion of cations in the major groove.Comment: 34 pages with 14 figure

Complexation of semiflexible chains with oppositely charged cylinder

We study the complexation of long thin semiflexible polymer chains with an oppositely charged cylinder. Starting from the linear Poisson-Boltzmann equation, we calculate the electrostatic potential and the energy of such a charge distribution. We find that sufficiently flexible chains prefer to wrap around the cylinder in a helical manner, when their charge density is smaller than that of the cylinder. The optimal value of the helical pitch is found by minimization of the sum of electrostatic and bending energies. The dependence of the pitch on the number of chains, their rigidity, and salt concentration in solution is analyzed. We discuss our results in the light of recent experiments on DNA complexation with cylindrical dendronized polymers

Simple Model for Overcharging of a Sphere by a Wrapped Oppositely Charged Asymmetrically Neutralized Polyelectrolyte: Possible Effects of Helical Charge Distribution

We investigate the complexation of a polyelectrolyte bendable rod with an oppositely charged spherical macroion. We take into account electrostatic bending of the rod and its asymmetric charge neutralization by sphere charges. The spontaneous curvature of the rod toward the sphere results in a substantial overcharging of such polyelectrolyte complex with a possible phase transition. Assuming a discrete helical charge distribution on the rod surface, we calculate the electrostatic energy of the helix and the electrostatic contribution to its bending and twisting elasticity. We show that the latter may change sign when the helical pitch is changed. For a DNA-relevant case, these corrections appear to be small compared to the corresponding mechanical elastic moduli. We discuss possible applications of our results to the description of overcharging of the nucleosome core particles