Paramagnetic relaxation enhancements in unfolded proteins: theory and application to drkN SH3 domain.

Site-directed spin labeling in combination with paramagnetic relaxation enhancement (PRE) measurements is one of the most promising techniques for studying unfolded proteins. Since the pioneering work of Gillespie and Shortle (J Mol Biol 1997;268:158), PRE data from unfolded proteins have been interpreted using the theory that was originally developed for rotational spin relaxation. At the same time, it can be readily recognized that the relative motion of the paramagnetic tag attached to the peptide chain and the reporter spin such as (1)H(N) is best described as a translation. With this notion in mind, we developed a number of models for the PRE effect in unfolded proteins: (i) mutual diffusion of the two tethered spheres, (ii) mutual diffusion of the two tethered spheres subject to a harmonic potential, (iii) mutual diffusion of the two tethered spheres subject to a simulated mean-force potential (Smoluchowski equation); (iv) explicit-atom molecular dynamics simulation. The new models were used to predict the dependences of the PRE rates on the (1)H(N) residue number and static magnetic field strength; the results are appreciably different from the Gillespie-Shortle model. At the same time, the Gillespie-Shortle approach is expected to be generally adequate if the goal is to reconstruct the distance distributions between (1)H(N) spins and the paramagnetic center (provided that the characteristic correlation time is known with a reasonable accuracy). The theory has been tested by measuring the PRE rates in three spin-labeled mutants of the drkN SH3 domain in 2M guanidinium chloride. Two modifications introduced into the measurement scheme-using a reference compound to calibrate the signals from the two samples (oxidized and reduced) and using peak volumes instead of intensities to determine the PRE rates-lead to a substantial improvement in the quality of data. The PRE data from the denatured drkN SH3 are mostly consistent with the model of moderately expanded random-coil protein, although part of the data point toward a more compact structure (local hydrophobic cluster). At the same time, the radius of gyration reported by Choy et al. (J Mol Biol 2002;316:101) suggests that the protein is highly expanded. This seemingly contradictory evidence can be reconciled if one assumes that denatured drkN SH3 forms a conformational ensemble that is dominated by extended conformations, yet also contains compact (collapsed) species. Such behavior is apparently more complex than predicted by the model of a random-coil protein in good solvent/poor solvent.