Origins of Critical Phenomena in the Folding Phase Diagram of Proteins

Proteins are folded polymers that are able to respond to slight environmental perturbations to preformation their biological function while also keeping a quasi-unique conformation. Such properties may be exhibited by a physical system near a critical point. Recent experimental and computational findings demonstrate that protein folding transitions in the temperature (T), pressure (P), and crowding volume-fraction (φ) phase diagram have signatures of criticality, where distinct folding phases merge [A. G. Gasic et al., Phys. Rev. X (2019)]. Here we investigate the origin of this critical behavior using insight from polymer physics. Based on our theory, we show that the separation of T between the folding and collapse transition temperatures (T_F and T_Θ, respectively) lead to a critical transition. We derive the relationship for the correlation length and show divergence approaching the critical regime. Structure-based model simulations of a protein in a crowded environment are used to validate our predictions. Our study illustrates the importance of the crowded cellular environment for a protein biological function.