Exact Solution to the Extended Zwanzig Model for Quasi-Sigmoidal Chemically Induced Denaturation Profiles: Specific Heat and Configurational Entropy

Abstract

Temperature and chemically induced denaturation comprise two of the most characteristic mechanisms to achieve the passage from the native stateNto any of the unstructured statesDjin the denatured ensemble in proteins and peptides. In this work we present a full analytical solution for the configurational partition function𝒵qsof a homopolymer chain poly-X in the extended Zwanzig model (EZM) for a quasisigmoidal denaturation profile. This solution is built up from an EZM exact solution in the case where the fractionαof native contacts follows exact linear dependence on denaturant’s concentrationζ; thus an analytical solution for𝒵Lin the case of an exact linear denaturation profile is also provided. A recently established connection between the numberνof potential nonnative conformations per residue and temperature-independent helical propensityωcomplements the model in order to identify specific proteinogenic poly-X chains, where X represents any of the twenty naturally occurring aminoacid residues. From𝒵qs, equilibrium thermodynamic potentials like entropy𝒮and average internal energy〈E〉and thermodynamic susceptibilities like specific heatC𝓋are calculated for poly-valine (poly-V) and poly-alanine (poly-A) chains. The influence of the rate at which native contacts denature as function ofζon thermodynamic stability is also discussed.