Model-free extraction of spin label position distributions from pseudocontact shift data

Abstract

A significant problem with paramagnetic tags attached to proteins and nucleic acids is their conformational mobility. Each tag is statistically distributed within a volume between 5 and 10 Angstroms across; structural biology conclusions from NMR and EPR work are necessarily diluted by this uncertainty. The problem is solved in electron spin resonance, but remains open in the other major branch of paramagnetic resonance - pseudocontact shift (PCS) NMR spectroscopy, where structural biologists have so far been reluctantly using the point paramagnetic centre approximation. Here we describe a new method for extracting probability densities of lanthanide tags from PCS data. The method relies on Tikhonov-regularised 3D reconstruction and opens a new window into biomolecular structure and dynamics because it explores a very different range of conditions from those accessible to double electron resonance work on paramagnetic tags: a room-temperature solution rather than a glass at cryogenic temperatures. The method is illustrated using four different Tm³⁺ DOTA-M8 tagged mutants of human carbonic anhydrase II; the results are in good agreement with rotamer library and DEER data. The wealth of high-quality pseudocontact shift data accumulated by the biological magnetic resonance community over the last 30 years, and so far only processed using point models, could now become a major source of useful information on conformational distributions of paramagnetic tags in biomolecules.

Fig. 1. Evolution of the probability density of the Tm³⁺ ion attached to C220 of the S220C mutant of human carbonic anhydrase II with a DOTA-M8 tag during the error functional optimisation process. The initial guess is a uniform distribution within the volume that is at least 2.0 Å from all atoms of the protein itself and at most 12 Å from any of its atoms, corresponding to the region of the space realistically accessible by the Tm³⁺ ion in a tag attached anywhere on the protein surface. As the optimisation proceeds, the probability density gradually becomes zero in the locations that are not consistent with the experimental PCS data. At the end of the optimisation, the probability density is localised, subject to the standard accuracy conditions associated with Tikhonov regularisation, in the region of space actually accessible to the Tm³⁺ ion.

Fig. 2. Diagnostic information and the outcome of a typical paramagnetic centre probability density reconstruction run. After the initial localisation stage (Fig. 1), the region of space in which the probability density is allowed to vary is chosen (right panel, red cube). Multiple reconstruction runs with different values of the regularisation parameter are performed to obtain the L-curve (left panel, cut-in). The optimum regularisation parameter is extracted as the maximum curvature point on the L-curve (middle panel). The final reconstruction is performed to obtain the probability density (right panel, red cloud) and the fitting plot (left panel). Blue circles in the left panel correspond to the point model fit and the red dots to the probability density fit.

Fig. 3. Tm³⁺ ion position distributions in DOTA-M8 tagged human carbonic anhydrase II, extracted from PCS data (the translucent coloured bubbles enclose 50% of the total probability) and overlaid with rotamer library predictions (swarms of coloured spheres with volumes proportional to the Boltzmann populations of the corresponding rotamers). The locations of Tm³⁺ ions predicted by the point model fits are indicated with dark grey three-dimensional crosses. The protein is visualized as a translucent grey ribbon model with the labelled positions (SER to CYS mutation followed by DOTA-M8 tagging) coloured.

Fig. 4. Distance distributions extracted from the PCS-based probability densities obtained in this work (red lines), compared with DEER-based distance distributions measured in the structurally identical Gd³⁺ tagged proteins (grey lines), compared with the same distributions extracted from the rotamer library results (blue lines).