Like-charge attraction between polyelectrolytes induced by counterion charge density waves.

Electrostatics in aqueous media is commonly understood in terms of screened Coulomb interactions, where like-charged objects, such as polyelectrolytes, always repel. These intuitive expectations are based on mean field theories, such as the Poisson-Boltzmann formalism, which are routinely used in colloid science and computational biology [Israelachvili, J. (1992) Intermolecular and Surface Forces (Academic, London), 2nd ed.]. Like-charge attractions, however, have been observed in a variety of systems [Gelbart, W. M., Bruinsma, R. F., Pincus, P. A. & Parsegian, V. A. (2000) Phys. Today 53, 38-44]. Intense theoretical scrutiny over the last 30 years suggests that counterions play a central role, but no consensus exists for the precise mechanism. We have directly observed the organization of multivalent ions on cytoskeletal filamentous actin (a well defined biological polyelectrolyte) by using synchrotron x-ray diffraction and discovered an unanticipated symmetry-breaking collective counterion mechanism for generating attractions. Surprisingly, the counterions do not form a lattice that simply follows actin's helical symmetry; rather, the counterions organize into "frozen" ripples parallel to the actin filaments and form 1D charge density waves. Moreover, this 1D counterion charge density wave couples to twist distortions of the oppositely charged actin filaments. This general cooperative molecular mechanism is analogous to the formation of polarons in ionic solids and mediates attractions by facilitating a "zipper-like" charge alignment between the counterions and the polyelectrolyte charge distribution. We believe these results can fundamentally impinge on our general understanding of electrostatics in aqueous media and are relevant to a wide range of colloidal and biomedical processes.