Protein proton–proton dynamics from amide proton spin flip rates

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Residue-specific amide proton spin-flip rates K were measured for peptide-free and peptide-bound calmodulin. K approximates the sum of NOE build-up rates between the amide proton and all other protons. This work outlines the theory of multi-proton relaxation, cross relaxation and cross correlation, and how to approximate it with a simple model based on a variable number of equidistant protons. This model is used to extract the sums of K-rates from the experimental data. Error in K is estimated using bootstrap methodology. We define a parameter Q as the ratio of experimental K-rates to theoretical K-rates, where the theoretical K-rates are computed from atomic coordinates. Q is 1 in the case of no local motion, but decreases to values as low as 0.5 with increasing domination of sidechain protons of the same residue to the amide proton flips. This establishes Q as a monotonous measure of local dynamics of the proton network surrounding the amide protons. The method is applied to the study of proton dynamics in Ca(2+)-saturated calmodulin, both free in solution and bound to smMLCK peptide. The mean Q is 0.81 +/- 0.02 for free calmodulin and 0.88 +/- 0.02 for peptide-bound calmodulin. This novel methodology thus reveals the presence of significant interproton disorder in this protein, while the increase in Q indicates rigidification of the proton network upon peptide binding, confirming the known high entropic cost of this process.