Reversible formation of protein oligomers or small clusters is a key step in processes such as protein polymerization and fibril formation, and protein phase separation.  Previously, a cell-based, quasi-chemical (QC) theory to predict colloidal or protein cluster free energies in dilute solution (vol. frac. < ca. 2%) was developed and validated for simple lattice-model systems [1].  The method is generalized here to treat systems interacting via continuous potentials of mean force, and applied to study the effects of anisotropy and competing attractions and repulsions due to electrostatics and weak, nonspecific attractions such as van der Waals and hydrophobic interactions.  Results are obtained under limiting conditions commonly used to induce nonnative aggregation and fibril formation (acidic pH, low or high ionic strength), as well as protein phase separation (pH ~ pI, high ionic strength).  The effects of coarse-graining the potential of mean force (pmf) between proteins are assessed by considering increasingly complex functional forms for the pmf.  The reduced second virial coefficient b₂₂^* is found to provide a useful means of comparing thermodynamic and structural characteristics between different cases.  It is shown that the free energy of cluster formation (ΔA_i) for small clusters (e.g., dimer and trimer) depends weakly on b₂₂^*, independent of whether interactions are strongly anisotropic.  However, as the size of the cluster increases the b₂₂^* dependence becomes much more prominent.  Comparison of ΔA_i, for the isotropic and anisotropic cases shows nearly equivalent results when compared at the same b₂₂^*_, indicating that at the level of free-energy prediction a detailed treatment of anisotropy may be unnecessary if experimental virial coefficient data are available.  However, the results here indicate that the molecular-scale structure of the clusters is sensitive to the anisotropy of the pmf.  The results provide a direct means to quantitatively and qualitatively connect indirect experimental measures of protein-protein interactions to molecular-scale features of the mechanism and kinetics of nonnative aggregation and fibril formation.     

(1) T.M. Young and C.J. Roberts.  “A quasichemical approach for protein-cluster free energies in dilute solution”.  Journal of Chemical Physics 127, p. 165101 (2007).