Retrospective study for the universal applicability of the residue-based linear free energy relationship in the two-state exchange of protein molecules.

Multiprobe measurements, such as NMR and hydrogen exchange studies, can provide the equilibrium constant, K, and rate constants for forward and backward processes, k and k', of the two-state structural changes of a polypeptide on a per-residue basis. We previously found a linear relationship between log K and log k and between log K and log k' for the topological exchange of a 27-residue bioactive peptide. To test the general applicability of the residue-based linear free energy relationship (rbLEFR), we performed a literature search to collect residue-specific K, k, and k' values in various exchange processes, including folding-unfolding equilibrium, coupled folding and binding of intrinsically disordered peptides, and structural fluctuations of folded proteins. The good linearity in a substantial number of the log-log plots proved that the rbLFER holds for the structural changes in a wide variety of protein-related phenomena. Among the successful cases, the hydrogen exchange study of apomyoglobin folding intermediates is particularly interesting. We found that the residues that deviated from the linear relationship corresponded to the α-helix, for which transient translocation had been identified by other experiments. Thus, the rbLFER is useful for studying the structures and energetics of the dynamic states of protein molecules.