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.

Figure 1

(a) Photograph of sample cells showing the reentrant condensation with increasing salt concentration. BSA $50\mathrm{mg}/\mathrm{mL}$, ${\mathrm{C}}^{*}\sim 4\mathrm{mM}<[{\mathrm{Y}}^{3+}]<{\mathrm{C}}^{**}\sim 25\mathrm{mM}$, gives a phase separated (turbid) solution, outside of this region, it gives a homogeneous solution. (b) Optical transmission as a function of ${\mathrm{Y}}^{3+}$, BSA $20\mathrm{mg}/\mathrm{mL}$, ${\mathrm{C}}^{*}\sim 1.0\mathrm{mM}$, and ${\mathrm{C}}^{**}\sim 11\mathrm{mM}$. (c) Predicted charge of BSA surface residues at specific ${\mathrm{Y}}^{3+}$ concentrations based on a Monte Carlo simulation (see text for details).

Figure 2

Phase diagram of BSA solution as a function of protein and salt concentration. The symbols indicate individual samples in the respective regimes. Note that all data on ${\mathrm{C}}^{*}$ and ${\mathrm{C}}^{**}$ are taken on the time scale of minutes; for very long times (many hours to days) the solution becomes clear again as the aggregate precipitates.

Figure 3

Experimental SAXS data with model fitting for protein solutions with ${\mathrm{Y}}^{3+}$ (a) below and around ${\mathrm{C}}^{*}$ and (c) above ${\mathrm{C}}^{**}$ for BSA $100\mathrm{mg}/\mathrm{mL}$; (b),(d) show the corresponding structure factor evaluated from data fitting.