Models for excluded volume interaction between an unfolded protein and rigid macromolecular cosolutes: Macromolecular crowding and protein stability revisited

Statistical-thermodynamic models for the excluded volume interaction between an unfolded polypeptide chain and a hard sphere or hard rod cosolute are presented, permitting estimation of the free energy of transfer of a polypeptide chain with fixed radius of gyration from a dilute (ideal) solution to a solution containing volume fraction phi of either cosolute. Also presented is a general thermodynamic description of the equilibrium between a unique native state and a manifold of unfolded or partially unfolded states of a protein distinguished by their respective radii of gyration. Together with results of a Monte Carlo calculation of the distribution of radii of gyration of four different unfolded proteins published by Goldenberg in 2003, these models are used to estimate the effect of intermolecular excluded volume upon an experimentally measurable apparent two-state constant for equilibrium between native and nonnative conformations of each of the four proteins, and upon the experimentally measurable root mean-square radius of gyration of the unfolded protein. Model calculations predict that addition of inert cosolutes at volume fractions exceeding 0.1 stabilizes the native state relative to unfolded states by an amount that increases strongly with phi and with the size of the native protein relative to the size of inert cosolute, and results in significant compaction of the manifold of unfolded states. Predicted effects are in qualitative and/or semiquantitative accord with the results of several published experimental studies.