Estimating the time scale of chemical exchange of proteins from measurements of transverse relaxation rates in solution

Abstract

Chemical (conformational) exchange on the ms-μs time scale is reliably identified by the observation of transverse relaxation rates, R_ex, that depend upon the strength of the effective field (ω_1eff=γB_1eff) used in spin lock or CPMG experiments. In order to determine if the exchange correlation time, τ_ex, is the fast or slow limit, measurements of (i) signal line shape and (ii) temperature dependence of R_ex have been commonly used in studies of stable, small molecules. However, these approaches are often not applicable to proteins, because sample stability and solubility, respectively, limit the temperature range and signal sensitivity of experiments. Herein we use a complex, but general, two-site exchange equation to show when the simple fast exchange equations for R_ex are good approximations, in the case of proteins. We then present a simple empirical equation that approximately predicts R_ex in all exchange regimes, and explains these results in a clear, straightforward manner. Finally we show how one can reliably determine whether τ_ex is in the fast or slow exchange limit.