Exploring Flory's isolated-pair hypothesis: Statistical mechanics of helix–coil transitions in polyalanine and the C-peptide from RNase A

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Abstract
To evaluate Flory's isolated-pair hypothesis in the context of helical peptides, we explore equilibrium conformations of alpha-helix-forming polypeptides as a function of temperature by means of replica exchange molecular dynamics in conjunction with the CHARMM/GB implicit solvent force field and the weighted histogram analysis method. From these simulations, Zimm-Bragg parameters, s and sigma, of Ac-Alan-NMe are computed as a function of temperature. The values obtained for s(T) and sigma(T) remain unchanged along the length of the polypeptide except for very short chains and yield results consistent with measurements based on short helix-forming peptides but suggest larger s values than anticipated from polymer-based measurements. From direct estimates of the density of states for Ac-Alan-NMe (n = 3-20) and peptide constructs based on the C peptide from RNase A, the conformational entropy is calculated versus temperature. The calculated S(T) shows a clear proportionality to the chain length over a wide range of temperature. This is observed in polypeptides with both significantly branched and simple methyl (alanine) side chains. These results provide evidence for the validity of Flory's isolated pair hypothesis, at least in the context of helical peptides and helix-to-coil transitions in these peptides.