Colloquium: The physics of charge inversion in chemical and biological systems

The authors review recent advances in the physics of strongly interacting charged systems functioning in water at room temperature. In these systems, many phenomena go beyond the framework of mean-field theories, whether linear Debye-H\"uckel or nonlinear Poisson-Boltzmann, culminating in charge inversion---a counterintuitive phenomenon in which a strongly charged particle, called a macroion, binds so many counterions that its net charge changes sign. The review discusses the universal theory of charge inversion based on the idea of a strongly correlated liquid of adsorbed counterions, similar to a Wigner crystal. This theory has a vast array of applications, particularly in biology and chemistry; for example, in the presence of positive multivalent ions (e.g., polycations), the DNA double helix acquires a net positive charge and drifts as a positive particle in an electric field. This simplifies DNA uptake by the cell as needed for gene therapy, because the cell membrane is negatively charged. Analogies of charge inversion to other fields of physics are also discussed.