Inclusion of persistence length-based secondary structure in replica field theoretic models of heteropolymer freezing

The protein folding problem has long represented a "holy grail" in statistical physics due to its physical complexity and its relevance to many human diseases. While past theoretical work has yielded apt descriptions of protein folding landscapes, recent large-scale simulations have provided insights into protein folding that were impractical to obtain from early theories. In particular, the role that non-native contacts play in protein folding, and their relation to the existence of misfolded, β-sheet rich trap states on folding landscapes, has emerged as a topic of interest in the field. In this paper, we present a modified model of heteropolymer freezing that includes explicit secondary structural characteristics which allow observations of "intramolecular amyloid" states to be probed from a theoretical perspective. We introduce a variable persistence length-based energy penalty to a model Hamiltonian, and we illustrate how this modification alters the phase transitions present in the theory. We find, in particular, that inclusion of this variable persistence length increases both generic freezing and folding temperatures in the model, allowing both folding and glass transitions to occur in a more highly optimized fashion. We go on to discuss how these changes might relate to protein evolution, misfolding, and the emergence of intramolecular amyloid states.