Electrostatics in aqueous media is often understood in terms of mean field theories such as the Poisson-Boltzmann formalism, in which like-charged objects such as polyelectrolytes, always repel [1-3]. Indeed, DNA chains in water containing monovalent ions always repel one another. Linearized versions of mean field theory provide the theoretical underpinning for widely employed tools such as Debye-Huckel theory and DLVO (Derjaguin Landau Verwey Overbeek) theory [4,5], which constitute the usual starting point for understanding charged polyelectrolyte or colloidal systems.
In systems with strong electrostatic interactions (containing, for example, high surface charge densities, multivalent ions, etc.), however, the physics is qualitatively different. Polyelectrolytes in aqueous solution are coated by a condensed “Manning” layer of oppositely charged counterions [6,7]. Interactions between polyelectrolytes can be controlled by the structure and dynamics of these condensed ions surrounding the polyelectrolyte. This can lead to counter-intuitive phenomena such as like-charge attraction and overcharging.
It has been recognized for some time that the mean-field Poisson-Boltzmann approach cannot produce attractions unless some form of correlation between the condensed ions is introduced. All proposed theoretical explanations for like-charge attraction introduce some form of positional counterion correlations within the Manning layer. Dynamic “van der Waals”-like correlations of long-wavelength ion fluctuations have been suggested [8-14]. Static mechanisms consisting of ion correlations along the axis of the polyelectrolyte rods in the form of a Wigner lattice have also been considered [15-18].
Like-charge attractions have been experimentally observed in a wide range of polyelectrolyte systems. DNA can be condensed by multivalent ions into dense, ordered states and is one of the most thoroughly studied systems in this context [7,19-32]. The volume fraction occupied by the condensed DNA within the T4 viral capsid is estimated to be approximately a half . This is a remarkable phenomenon if one considers the barriers against such condensation, such as the strongly electrostatic repulsion between the highly charged sugar-phosphate backbone, the large bending modulus of the DNA double helix, and the loss of configurational entropy of the DNA molecule.
Recently, a number of anionic biopolymers have been used as experimental systems for the study of like-charge polyelectrolyte attraction, such as the filamentous bacteriophages, microtubules, and F-actin [33-36]. This has led to a number of interesting new effects. For example, in the presence of divalent ions, F-actin progressively condenses into close-packed bundles via an intermediate state comprised of 1D lamellar stacks of liquid crystalline networks [37-39]. Due to their large persistence lengths (>1 μm), these polyelectrolytes can be thought of as idealized rod-like objects. Since most theoretical approaches employ idealized models for polyelectrolytes, such as infinitely thin lines, or smooth cylinders, or perfect idealized helices, these real polyelectrolyte systems provide a point of contact to proposed analytical models.
Condensation phenomena are important for a wide range of biological and biomedical processes, such as DNA compaction in bacteria and viral capsids, self assembly of synthetic gene delivery systems, nucleic acid-protein interactions, cytoskeletal regulation, as well as industrial processes such as multivalent salt-induced condensation of impurities in water treatment, and cellulosic fiber flocculation in paper making. Additionally, counterion correlations can also have unexpected applications. For example, the nanometer-scale organization of condensed ions by polyelectrolytes such as DNA may have interesting applications in biomineralization and solution templating . The helical sugar-phosphate backbone of DNA creates a spatially periodic anionic ridge that organizes condensed Cd2+ and guides subsequent CdS mineralization.
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