Cartoon illustration of energetic components included in the modified heteropolymer freezing Hamiltonian. The model is valid only for maximally compact polymer configurations, and monomers are coarse-grained to remove fine chemical detail. Left: the Hamiltonian contains the standard monomer-monomer contact energies, ε IJ . Right: the modified Hamiltonian now includes a bending energy penalty term, where each component penalty, ε p , is proportional to the persistence length of a given chain link.
Phase diagram for unmodified model for heteropolymer freezing, derived from Eqs. (13) and (14) . Sequence design introduces three distinct phases into the model: a random phase (with relevant conformations); a glassy, misfolded phase (with relevant conformations); and a target, folded phase (also with relevant conformations).
Phase diagram for secondary structure-modified version of our heteropolymer freezing model (derived from Eqs. (11)–(14) ), overlaid on the phase diagram for the unmodified system. Inclusion of persistence length-based secondary structure causes both the freezing temperature, T freeze, and the folding temperature, T fold, to increase, introducing freezing and folding “gaps” in the modified model. The larger extent of the folding gap suggests an evolutionary reason for risking misfolding at higher temperatures.
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