A general multistate model for the analysis of hydrogen-exchange kinetics

In proton nmr, the chemical exchange rates of slowly exchanging labile hydrogens (with lifetimes in the range ～ 10 msec – ～ 1 sec) of peptides, proteins, and nucleic acids can be measured in H₂O by a combination of two separate experiments: (1) the transfer of solvent saturation and (2) saturation-recovery experiments. When these molecules exist in a dynamic equilibrium among different conformations, the experiments cannot be analyzed in a straightforward manner to derive the intrinsic exchange rates. In the present study we have derived analytical expressions for the above two experiments on a biomolecule under certain limiting conditions: (1) the extreme low-motility limit, where each of the conformational transitions is much slower than the corresponding hydrogen exchange rate with the solvent; (2) the high-motility limit (EX₂ mechanism), which is the opposite extreme of the previous limit; and (3) the low-motility limit (EX₁ mechanism), which is a mixture of limits (1) and (2), i.e., for some of the conformations, the exchange rate with the solvent is much faster than their conformational transition rates, while for the remaining conformations the reverse situation is realized. The results may be considered as a generalization to an arbitrary number of states of the two-state model treated by Hvidt. Equations have also been derived that are applicable to the iostope exchange method of measuring very slow exchange rates (with life-times of the order of minutes and longer) in biomolecules. The saturation recovery experiments performed in H₂O on the active pentapeptide fragment of thymopoietin serve to illustrate the high-motility limit. The theoretical formulation presented in this study can be easily adapted to other double-resonance techniques and also to situations where the kinetics of an arbitrary system existing in a multistate equilibrium are of interest.