All protein aggregates will thermodynamically order

Proteins can aggregate into disordered liquid droplets or ordered assemblies such as amyloid fibrils. These two distinct phases determine the spatial organization within cells and serve differing roles in a wide range of biological functions including gene regulation, organelle and synapse formation, and memory consolidation. The ordered phase can also give rise to diseases such as Alzheimers. However, how the protein sequence determines aggregation fate is an open question. Here we establish a general statistical mechanical theory of the disordered-to-ordered transition for polymer aggregates, including proteins, thereby completing the phase diagram for this general class of matter. The theory produces a simple universal equation determining the favored phase as a function of the temperature, polymer length, and inter-residue interaction energy variance. We show that the sequence-dependent energy variance can be efficiently calculated from all-atom molecular dynamics simulations, so that the theory has no adjustable parameters. The equation accurately predicts the experimental length-dependent crystallization temperature of synthetic polymers. The theory shows that all protein aggregates, regardless of sequence, will thermodynamically order, even in the most extreme thermophiles. Therefore, energy must be expended to maintain the disordered protein aggregate at steady state. More broadly, the theory establishes a lower bound on the ordering transition temperature for polymers. This bound indicates that condensates of any organic polymer will spontaneously order on all habitable planets.