Salt-modulated structure of polyelectrolyte-macroion complex fibers

Abstract

The structure and stability of strongly charged complex fibers, formed by complexation of a single long semi-flexible polyelectrolyte chain and many oppositely charged spherical macroions, are investigated numerically at the ground-state level using a chain-sphere cell model. The model takes into account chain elasticity as well as electrostatic interactions between charged spheres and chain segments. Using a numerical optimization method based on a periodically repeated unit cell, we obtain fiber configurations that minimize the total energy. The optimal fiber configurations exhibit a variety of helical structures for the arrangement of macroions including zig-zag, solenoidal and beads-on-a-string patterns. These structures result from the competition between attraction between spheres and the polyelectrolyte chain (which favors chain wrapping around the spheres), chain bending rigidity and electrostatic repulsion between chain segments (which favor unwrapping of the chain), and the interactions between neighboring sphere-chain complexes which can be attractive or repulsive depending on the system parameters such as salt concentration, macroion charge and chain length per macroion (linker size). At about physiological salt concentration, dense zig-zag patterns are found to be energetically most stable when parameters appropriate for the DNA-histone system in the chromatin fiber are adopted. In fact, the predicted fiber diameter in this regime is found to be around 30 nanometers, which roughly agrees with the thickness observed in in vitro experiments on chromatin. We also find a macroion (histone) density of 5-6 per 11nm which agrees with results from the zig-zag or cross-linker models of chromatin. Since our study deals primarily with a generic chain-sphere model, these findings suggest that structures similar to those found for chromatin should also be observable for polyelectrolyte-macroion complexes formed in solutions of DNA and synthetic nano-colloids of opposite charge. In the ensemble where the mean linear density of spheres on the chain is fixed, the present model predicts a phase separation at intermediate salt concentrations into a densely packed complex phase and a dilute phase.

Structure-driven homology pairing of chromatin fibers: the role of electrostatics and protein-induced bridging

“…A number of experimental [30][31][32][33], theoretical [34][35][36], and computer simulation studies [37][38][39][40][41][42][43][44][45] have emerged on this subject in recent years. Chromatin 30-nm fibers interact electrostatically with each other via "contacting" NCPs positioned on the fiber periphery, both in canonical solenoidal [46,47] and crosslinked [34] fiber models.…”

Global analysis of the ground-state wrapping conformation of a charged polymer on an oppositely charged nano-sphere

“…We shall make use of a numerical minimization scheme that has been employed extensively in previous studies of DNA-histone complexes [32,[37][38][39][40][41]43]. The full details of this scheme can be found in these references and will not be reiterated here and thus we shall delimit our discussion to only a few of the key conceptual elements of our approach.…”

“…The aforementioned optimization procedure can be done most efficiently by numerical methods such as the quasi-Newton numerical minimization algorithm on a properly discretized model of the chain [32,[37][38][39][40][41]43]. In most cases, the symmetries of the numerically obtained optimal configurations already indicate whether the result corresponds to the global minimum of the Hamiltonian but further checks (including a combination of parameter quenching and stochastic perturbation methods) must be done to ensure the global stability of the optimal solutions.…”

“…(see, e.g., Refs. [18,[26][27][28][29][30][31][32] and references therein for the salt-dependent behavior of chromatin which will not be discussed further in this paper). The importance of electrostatic effects in the case of nucleosome core particles is supported by a large body of in vitro experimental observations that have been reviewed elsewhere (see, e.g., Refs.…”

Influence of shear on globule formation in dilute solutions of flexible polymers

“…Equilibrium behavior of dilute solutions of polymers in the presence of monovalent, multivalent salt, and dilute solutions of other particles has been investigated both theoretically and experimentally. [9][10][11][12][13][14][15][16][17] Until recently, few theoretical and experimental studies have been done to understand the interplay of attractive and repulsive interactions in determining their flow behavior. 3,7,8,[18][19][20][21][22][23][24][25][26][27][28] Larson and Hoda 25 used a bead spring chain model of a polymer with bead-bead attractions and spring-spring repulsions, and they found the formation of shear-induced structures.…”