Effects of inert volume-excluding macromolecules on protein fiber formation. I. Equilibrium models

The equilibrium Oosawa-Asakura model for nucleated assembly of rod-like protein fibers is recast in terms of dimensionless (scaled) quantities. The model is then generalized to treat arbitrarily large deviations from thermodynamic ideality arising from high fractional volume occupancy by an inert protein or polymer. Each state of association of the self-associating protein is modeled as an equivalent rigid convex particle (sphere or spherocylinder) and the crowding species is modeled either as an equivalent sphere or cylindrical rod. The resulting conservation of mass relation is readily solved to yield the fractional abundance of monomer, from which the entire equilibrium distribution of oligomeric species can be calculated, either directly or through the use of an additional scaling relationship. Results indicating the potential effect of volume occupancy on the equilibrium solubility of the self-associating protein and upon the equilibrium distribution of polymer size are presented. It is found that the fractional (logarithmic) change in both solubility and in the breadth of the polymer size distribution scale almost linearly with the fractional (logarithmic) change in the thermodynamic activity of monomer.