The stability of aqueous protein solutions is strongly affected by multivalent ions, which induce ion-ion correlations beyond the scope of classical mean-field theory. Using all-atom molecular dynamics (MD) and coarse grained Monte Carlo (MC) simulations, we investigate the interaction between a pair of protein molecules in 3:1 electrolyte solution. In agreement with available experimental findings of "reentrant protein condensation", we observe an anomalous trend in the protein-protein potential of mean force with increasing electrolyte concentration in the order: (i) double-layer repulsion, (ii) ion-ion correlation attraction, (iii) overcharge repulsion, and in excess of 1:1 salt, (iv) non Coulombic attraction. To efficiently sample configurational space we explore hybrid continuum solvent models, applicable to many-protein systems, where weakly coupled ions are treated implicitly, while strongly coupled ones are treated explicitly. Good agreement is found with the primitive model of electrolytes, as well as with atomic models of protein and solvent.

Czech Academy of Sciences Institute of Organic Chemistry and Biochemistry Flemingovo nam 2 16610 Prague 6 Czech Republic

Division of Organic Chemistry and Biochemistry Rudjer Bošković Institute POB 180 HR 10002 Zagreb Croatia

Division of Theoretical Chemistry Lund University POB 124 SE 22100 Lund Sweden

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