Reentrant Condensation of Proteins in Solution Induced by Multivalent Counterions

Negatively charged globular proteins in solution undergo a condensation upon adding trivalent counterions between two critical concentrations ${\mathrm{C}}^{*}$ and ${\mathrm{C}}^{**}$, ${\mathrm{C}}^{*}<{\mathrm{C}}^{**}$. This reentrant condensation behavior above ${\mathrm{C}}^{**}$ is caused by short-ranged electrostatic interactions between multivalent cations and acidic residues, mechanistically different from the case of DNA. Small-angle x-ray scattering indicates a short-ranged attraction between counterion-bound proteins near ${\mathrm{C}}^{*}$ and ${\mathrm{C}}^{**}$. Monte Carlo simulations (under these strong electrostatic coupling conditions) support an effective inversion of charge on surface side chains through binding of the multivalent counterions.