50 Years of Lifson-Roig Models: Application to Molecular Simulation Data

Simple helix coil transition theories have been indispensable tools in the analysis of data reporting on the reversible folding of alpha-helical polypeptides. They provide a transferable means to not only characterize different systems but to also compare different techniques, viz., experimental probes monitoring helix coil transitions in vitro or biomolecular force fields in silico. This article addresses several issues with the application of Lifson-Roig theory to helix coil transition data. We use computer simulation to generate two sets of ensembles for the temperature-controlled, reversible folding of the 21-residue, alanine-rich FS peptide. Ensembles differ in the rigidity of backbone bond angles and are analyzed using two distinct descriptors of helicity. The analysis unmasks an underlying phase diagram that is surprisingly complex. The complexities give rise to fitted nucleation and propagation parameters that are difficult to interpret and that are inconsistent with the distribution of isolated residues in the alpha-helical basin. We show that enthalpies of helix formation are more robustly determined using van't Hoff analysis of simple measures of helicity rather than fitted propagation parameters. To overcome some of these issues, we design a simple variant of the Lifson-Roig model that recovers physical interpretability of the obtained parameters by allowing bundle formation to be described in simple fashion. The relevance of our results is discussed in relation to the applicability of Lifson-Roig models to both in silico and in vitro data.