Dynamical Clustering of Counterions on Flexible Polyelectrolytes

Abstract

Molecular dynamics simulations are used to study the local dynamics of counterion-charged polymer association at charge densities above and below the counterion condensation threshold. Surprisingly, the counterions form weakly-interacting clusters which exhibit short range orientational order, and which decay slowly due to migration of ions across the diffuse double layer. The cluster dynamics are insensitive to an applied electric field, and qualitatively agree with the available experimental data. The results are consistent with predictions of the classical theory only over much longer time scales.PACS numbers: 82.35. Rs, Many biochemical reactions involve local interactions between small molecules (ligands) and biological macromolecules such as DNA, which are polymers consisting of repeating ionizable groups known as polyelectrolytes [1]. When dissolved in a polar solvent such as water, polyelectrolytes ionize and counterions dissociate from the polymer, leaving an oppositely charged polymer backbone. The highly ionized polyelectrolyte in solution attracts small mobile counterions of opposite charge, partially screening the backbone charge. The approach of the small molecules to a polyelectrolyte is governed to a large degree by electrostatic interactions, which in turn depend on the local molecular environment, and in particular is sensitive to the instantaneous distribution of counterions around the polyelectrolyte. Thus, knowledge of the counterion distribution at atomic resolution is crucial for many aspects of DNA dynamics such as molecular assembly and inter-cellular transport.The difficulty in studying polyelectrolyte solutions resides in the delicate interplay of the long range electrostatic interactions, short range intermolecular interactions, and thermal energy, which are comparable to each other in magnitude. Furthermore, typical polyelectrolytes are highly charged, which precludes straightforward application of the usual Debye-Hückel theory [2] of electrolytic solutions. A key advance in understanding the equilibrium state of counterions associated with a charged polymer was the condensation theory of Manning [3], which treated the polyelectrolyte molecule as an infinite rigid rod of uniform charge density −z p e/b, as an approximation to discrete groups of equal charge −z p e separated by a distance b, and considered independent dissolved counterions of charge z c e placed in a uniform bulk solvent of dielectric constant ǫ r about the molecule. Considering the two-dimensional partition function in the plane normal to the polyelectrolyte axis, Manning found that the free counterion configuration is unstable for sufficiently strong electrostatic interaction, when the dimensionless "Manning parameter" ξ ≡ z p z c l B /b > 1, where l B = e 2 /(ǫ r k B T ) is the "Bjerrum length" at which thermal energy k B T equals electrostatic potential energy. He then hypothesized that counterions would condense uniformly on the polyelectrolyte backbone so as to reduce ξ to unity, while the remaining (dilute) unb...

Solution properties of star polyelectrolytes having a moderate number of arms

“…41–44 Our model incorporates minimal aspects of real polyelectrolyte solution while at the same time it allows for equilibrated molecular dynamics with an explicit solvent. The added cost in computational time required by inclusion of an explicit solvent is necessary to fully capture the polyelectrolyte structural and dynamical behavior, as indicated by a series of studies.…”

Impact of Monovalent Counter-ions on the Conformation of Flexible Polyelectrolytes Having Different Molecular Architectures

“…The existence of a flexible backbone raises basic and theoretically unresolved questions about how the polyelectrolyte conformation affects the distribution of counter-ions distributed these polymers and about how the counter-ions, in turn, influence polymer conformation. Simulation studies [8][9][10][11][12][13][14] of flexible polyelectrolytes in solution have indicated deviations from the theoretical predictions of Manning theory and emphasize that the counter-ions and polymer conformation are coupled. We can also expect this coupling to be altered by chain topology and solvation (i.e., binding by the solvent to the polymer) that competes with ion association with the polymer.…”

Distribution of counterions and interaction between two similarly charged dielectric slabs: Roles of charge discreteness and dielectric inhomogeneity

“…The difference between dielectric constant of water ( 80) and that of organic materials ( 2), silica ( 4) and air ( 1) is an important factor in electrostatic interactions of related systems. The role of such dielectric inhomogeneity has been investigated in systems like ionic channels [10], ions or colloids at the air-water interface [11], copolymers in electric field [12] and polyelectrolytes adsorbed to an interface [13].…”

“…For example, electrostatics plays a key role in proteins structure [1], interaction of DNA and proteins with charged ligands [2], DNA packaging and condensation [3], conformation of polyelectrolytes in solution and their aggregation behavior [4,5] and interaction between charged colloids and their collective behavior in solution [6]. Numerous experimental and theoretical studies have been performed to understand these phenomena and to elucidate the role of electrostatic interactions.…”