Abstract
Temperature and chemically induced denaturation comprise two of the most characteristic mechanisms to achieve the passage from the native state N to any of the unstructured states Dj in the denatured ensemble in proteins and peptides. In this work we present a full analytical solution for the configurational partition function 𝒵qs of 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 fraction α of native contacts follows exact linear dependence on denaturant’s concentration ζ; thus an analytical solution for 𝒵L in the case of an exact linear denaturation profile is also provided. A recently established connection between the number ν of potential nonnative conformations per residue and temperature-independent helical propensity ω complements the model in order to identify specific proteinogenic poly-X chains, where X represents any of the twenty naturally occurring aminoacid residues. From 𝒵qs, equilibrium thermodynamic potentials like entropy 𝒮 and average internal energy 〈E〉 and thermodynamic susceptibilities like specific heat C𝓋 are calculated for poly-valine (poly-V) and poly-alanine (poly-A) chains. The influence of the rate at which native contacts denature as function of ζ on thermodynamic stability is also discussed.
Highlights
The early recognition that ordered three-dimensional macromolecular structures, later known as the native state, play a fundamental role on biological activity of proteins and peptides led to a large interest in the fundamental mechanisms that drive formation and stabilization of such structures [1,2,3,4]
In particular we focus our attention on thermodynamic susceptibilities like specific heat CV(T, K, ω) and thermodynamic equilibrium potentials as configurational entropy S(T, K, ω) and their connection to the mechanism of chemical denaturation imposed on the chain
A full analytical solution for the extended Zwanzig model (EZM) model in the quasisigmoidal approximation model is presented in order to calculate equilibrium thermodynamic properties of proteinogenic homopolymer poly-X chains under the action of a chemically induced denaturation mechanism
Summary
The early recognition that ordered three-dimensional macromolecular structures, later known as the native state, play a fundamental role on biological activity of proteins and peptides led to a large interest in the fundamental mechanisms that drive formation and stabilization of such structures [1,2,3,4]. The central feature of SMCG methods is the use of a small set of coarse-grained variables to describe average properties of the system instead of a fully detailed atom description Common examples of such sets of variables include, but are not restricted to, pairs of dihedral angles (φj, ψj) for each residue, number of nonnative conformations ] per residue, or intrinsic helical propensity ω among others [27,28,29]. It is possible to extend it to consider the concentration ζ of a chemical denaturant as a contributing factor to unfolding [34] This extended Zwanzig model (EZM) uses the functional dependence of the fraction α of native contacts with respect to ζ to derive an analytical formula for the configurational partition function Z of the polypeptide chain in terms of an integral over microstates whose energy Ej depends on T, ], K, and ζ. A further discussion is included on how thermodynamic equilibrium properties depend on denaturation curve
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