Theory for the aggregation of proteins and copolymers

We develop mean-field lattice statistical mechanics theory for the equilibrium between denatured and aggregated states of proteins and other random copolymers of hydrophobic and polar monomers in aqueous solution. We suppose that the aggregated state is a mixture of amorphous polymer plus solvent and that the driving forces are the hydrophobic interaction, which favors aggregation, and conformational and translational entropies, which favor disaggregation. The theory predicts that the phase diagram for thermal aggregation is an asymmetric closed loop, and for denaturants (guanidinium hydrochloride or urea) it is asymmetric with an upper consolute point. The theory predicts that a copolymer in a poor solvent will expand with increasing polymer concentration because of "screening" of the solvent interactions by the other chains; the chain ultimately reaches a theta-like state in the absence of solvent. The screening concentration depends strongly on the copolymer composition. We find two striking features of these copolymer phase diagrams. First, they are extraordinarily sensitive to the copolymer composition; a change of one amino acid can substantially change the aggregation behavior. Second, relative to homopolymers, copolymers should be stable against aggregation at concentrations that are higher by many orders of magnitude.