Detection of nano-second internal motion and determination of overall tumbling times independent of the time scale of internal motion in proteins from NMR relaxation data

Abstract

The usual analysis of ¹⁵N relaxation data of proteins is straightforward as long as the assumption can be made that the backbone of most residues only undergoes fast (ps), small amplitude internal motions. If this assumption cannot be made, as for example for proteins which undergo domain motions or for unfolded or partially folded proteins, one needs a method to establish for each residue whether it undergoes fast (ps) or slow (ns) internal motion. Even then it is impossible to determine the correct overall tumbling time, τ_m ⁰, via the usual method from the ratio of the longitudinal and transverse relaxation times, if the majority of residues do not undergo fast, small amplitude internal motions. The latter problem is solved when τ_m ⁰ can be determined independent of the time scale, τ_i, or the amplitude, S², of the internal motion. We propose a new protocol, called PINATA, for analyzing ¹⁵N relaxation data acquired at minimally two field strengths, where no a priori assumption about time scales or amplitude of internal motions needs to be made, and overall tumbling can either be isotropic or anisotropic. The protocol involves four steps. First, for each residue, it is detected whether it undergoes ps- or ns-internal motion, via the combination of the ratio of the longitudinal relaxation time at two fields and the hetero-nuclear NOE. Second, for each residue τ_m ⁰ and the exchange broadening, Rex, are iteratively determined. The accuracy of the determination of τ_m ⁰ is ca. ±0.5 ns and of Rex ca ± 0.7 s⁻¹, when the relaxation data are of good quality and τ_m ⁰>5 ns, S²>0.3, and τ_i<≈3 ns. Third, given τ_m ⁰ and Rex, step 1 is repeated to iteratively improve on the internal motion and obtain better estimates of the internal parameter values. Fourth, final time scales and amplitudes for internal motions are determined via grid search based fitting and χ²-analysis. The protocol was successfully tested on synthetic and experimental data sets. The synthetic dataset mimics internal motions on either fast or slow time scales, or a combination of both, of either small- or large amplitude, superimposed onto anisotropic overall motion. The procedures are incorporated into MATLAB scripts, which are available on request.