Stability of strong polyelectrolyte-macroion complexes

Abstract

We investigate the thermodynamic stability of complexes formed by one semiflexible charged polymer wrapped around an oppositely charged sphere. Choosing parameters for DNA and histones, we determine all conformational eigen-modes and the corresponding eigen-value spectrum of the complexed chain, from which the free energy of complexation and thus the reaction constant is obtained. The resulting complexation diagram exhibits qualitative agreement with experimental results as a function of salt and DNA/histone concentration.

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

“…This behavior indicates that thermal chain fluctuations [63,71,72,78,88] become relevant at moderately large salt concentrations. These fluctuations can be accounted for within the chain-sphere model as well and lead to a stability diagram that agrees qualitatively with the experimental one [40].…”

“…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.…”

“…It was shown that a minimal chain-sphere model for nucleosome core particles [37][38][39][40][41]51] can closely predict the experimentally observed [79][80][81][82][83][84][85][86][87] salt-induced wrapping-unwrapping behavior of these complexes based on an interplay between two competing mechanisms: the electrostatic attraction of DNA (modeled as a negatively charged worm-like chain) with the histone core (modeled as a positively charged nano-sphere), which favors DNA adsorption and wrapping around the sphere, and the mechanical bending stiffness of the DNA and its electrostatic self-repulsion, which favor unwrapping and even dissociation of the DNA from the complex. The experimental stability diagrams [45] also exhibit an association (or complexation) equilibrium between nucleosome core particles and the free DNA and free histones in an electrolyte solution in the regime of moderately large values of core particle and salt concen-tration.…”

“…Our main objective is to establish structural phase diagrams using a reduced (or dimensionless) description that can be representative of the global (or universal) behavior of the system based on only a few dimensionless parameters (for example, the ratio of the chain length to the sphere radius). This is achieved by employing a primitive chain-sphere model that, as noted above, has proved useful in the context of nucleosome core particles [37][38][39][40][41]51]; its main advantage being its simplicity that enables a systematic investigation of various aspects of charged polymer-sphere complexes especially when specific effects (such as histone tails [19]) are not dominant and the generic properties of these complexes are of interest. We shall make use of a previously established numerical optimization method for strongly coupled complexes [39][40][41] in order to obtain the wrapping conformation of the chain and its symmetry classes (phases) in various parts of the parameter space.…”

“…This is achieved by employing a primitive chain-sphere model that, as noted above, has proved useful in the context of nucleosome core particles [37][38][39][40][41]51]; its main advantage being its simplicity that enables a systematic investigation of various aspects of charged polymer-sphere complexes especially when specific effects (such as histone tails [19]) are not dominant and the generic properties of these complexes are of interest. We shall make use of a previously established numerical optimization method for strongly coupled complexes [39][40][41] in order to obtain the wrapping conformation of the chain and its symmetry classes (phases) in various parts of the parameter space. We shall in particular study the case of a mechanically flexible chain with no mechanical bending rigidity; this latter quantity stiffens the chain and favors unwrapping of the chain from the sphere, and thus competes with the electrostatic self-repulsion of the chain segments, which does the same.…”