Thermodynamics of ideal proteinogenic homopolymer chains as a function of the energy spectrum E, helical propensity ω and enthalpic energy barrier.

A reformulation and generalization of the Zwanzig model (ZW model) for ideal homopolymer chains poly-X, where X represents any of the twenty naturally occurring proteinogenic amino acid residues is presented. This reformulation and generalization provides a direct connection between coarse-grained parameters originally proposed in the ZW model with variables from the Lifson-Roig (LR) theory, such as the helical propensity per residue ω, and new variables introduced here, such as the energy gap Δ between unfolded and folded structures, as well as the ratio f of the energy scales involved. This enables us to discover the relevance of the energy spectrum E to the onset of configurational phase transitions. From the configurational partition function Q, thermodynamic properties such as the configurational entropy S, specific heat v and average energy <E> are calculated in terms of the number of residues K, temperature T, helical propensity ω and energy barrier ΔH for different poly-X chains in vacuo. Results obtained here provide substantial evidence that configurational phase transitions for ideal poly-X chains correspond to first-order phase transitions. An anomalous behavior of the thermodynamic functions <E>, Cv, S with respect to the number K of residues is also highlighted. On-going methods of solution are outlined.