(388a) Second Osmotic Virial Coefficients for “Patchy” Proteins

Proteins and anisotropic nanoparticles often have surfaces composed of neutral hydrophilic, hydrophobic, and charged "patches".  In some cases it has been suggested that complementary patch-patch interactions dominate the thermodynamics of protein and nano-particle solutions if the attractive energies are sufficiently large and short-ranged, although criteria for achieving this scenario have not been quantified systematically.  A series of models are used here to evaluate the balance of the favorable energy gain and the entropic penalty for forming such patch-patch contacts, and tested for conditions where experimentally realistic, quantitative values of the second osmotic virial coefficient (B22) are recovered.  Using estimates of the strength of interactions between hydrophobic (HP) patches on proteins and how they scale with patch size, along with a patch-patch model akin to that of Kern and Frenkel (J. Phys. Chem. 118, 9882 (2003)), the results indicate that one of three scenarios is realistic for highly "patchy" proteins or similarly sized nanoparticles: (i) patches are too small, and attractions are not sufficiently strong to overcome the entropic penalty of forming patch-patch pairs; (ii) patches fall within a narrow range of sizes, and contribute significantly to B22; (iii) patches are so large that solutions are effectively unstable (i.e., unphysically large B22 values).  In addition, the models illustrate that repulsive interactions contribute significantly to B22 for only those conditions where the repulsions are long-ranged. Finally, the importance of the balance between energetic and entropic contributions is also highlighted by reformulating B22 in terms of the orientation-space density of states for a given energy and protein-protein distance.  Doing so provides insight into why B22 is indicative of protein phase separation and aggregation propensity for some proteins / solvent conditions but not others.  The results also suggest experimental signatures that can be used to identify whether B22 should be expected to be a useful predictor of aggregation or phase separation for a given protein/solvent system, with examples such as eye lens crystallin(s), antibodies, and model proteins.