Deviation from the Residue-Based Linear Free Energy Relationship Reveals a Non-Native Structure in Protein Folding

Multiprobe measurements, such as NMR and hydrogen exchange study, can provide the equilibrium constant K and kinetic rate constant k of the structural changes of a polypeptide on a per-residue basis. We previously found a linear relationship between residue-specific log K values and residue-specific log k values for the two-state topological isomerization of a 27-residue peptide. To test the general applicability of the residue-based linear free energy relationship (rbLEFR), we performed a literature search to collect residue-specific equilibrium and kinetic constants in various exchange processes, including protein folding, coupled folding and binding of intrinsically disordered peptides, and structural fluctuations of folded proteins. The good linearity in a substantial number of log-log plots proved that the rbLFER holds for the structural changes in a wide variety of protein-related phenomena. Protein molecules quickly fold into their native structures and change their conformations smoothly. Theoretical studies and molecular simulations advocate that the physicochemical basis is the consistency principle and the minimal frustration principle: Non-native structures/interactions are absent or minimized along the folding pathway. The linearity of the residue-based free energy relationship demonstrates experimentally the absence of non-native structures in transition states. In this context, 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 non-native structure, which had been identified by other experiments. The rbLFER provides a unique and practical method to probe the dynamic aspects of the transition states of protein molecules.