Protein aggregates thermodynamically order regardless of sequence

Proteins can aggregate into disordered aggregates or ordered assemblies such as amyloid fibrils. These two distinct phases serve differing roles in function and disease. How protein sequence determines the preferred phase is unknown. Here we establish a statistical mechanical disorder-to-order transition condition for compact polymer aggregates, including proteins. The theory produces a simple universal equation determining the favored phase as a function of temperature, polymer length, and interaction energy variance. We show that the sequence-dependent energy variance is efficiently calculated using atomistic simulations, so that the theory has no adjustable parameters. The equation accurately predicts experimental length-dependent crystallization temperatures of synthetic polymers. The equation also predicts that all protein sequences that aggregate will also favor ordering. Consequently, energy must be expended to maintain the steady-state disordered phase if it is not kinetically metastable on physiological timescales. More broadly, the theory suggests that aggregates of organic polymers will generally tend to order on habitable planets.