Theory and practice of using solvent paramagnetic relaxation enhancement to characterize protein conformational dynamics

Abstract

Paramagnetic relaxation enhancement (PRE) has been established as a powerful tool in NMR for investigating protein structure and dynamics. The PRE is usually measured with a paramagnetic probe covalently attached at a specific site of an otherwise diamagnetic protein. The present work provides the numerical formulation for probing protein structure and conformational dynamics based on the solvent PRE (sPRE) measurement, using two alternative approaches. An inert paramagnetic cosolute randomly collides with the protein, and the resulting sPRE manifests the relative solvent exposure of protein nuclei. To make the back-calculated sPRE values most consistent with the observed values, the protein structure is either refined against the sPRE, or an ensemble of conformers is selected from a pre-generated library using a Monte Carlo algorithm. The ensemble structure comprises either N conformers of equal occupancy, or two conformers with different relative populations. We demonstrate the sPRE method using GB1, a structurally rigid protein, and calmodulin, a protein comprising two domains and existing in open and closed states. The sPRE can be computed with a stand-alone program for rapid evaluation, or with the invocation of a module in the latest release of the structure calculation software Xplor-NIH. As a label-free method, the sPRE measurement can be readily integrated with other biophysical techniques. The current limitations of the sPRE method are also discussed, regarding accurate measurement and theoretical calculation, model selection and suitable timescale.

Keywords: Molecular dynamics simulation; Monte Carlo algorithm; Paramagnetic relaxation enhancement; Protein cosolute; Structure refinement; Xplor-NIH.

Fig. 1. Structure of the three paramagnetic cosolute molecules

A) diethylenetriamine pentaacetate bismethylamide gadolinium chelate (Gd(III)-DTPA-BMA). B) triethylenetetraamine hexaacetate trimethylamide gadolinium chelate (Gd(III)-TTHA-TMA), which provides full coordination to Gd³⁺ and eliminates the need for an inner-sphere water. C) diethylenetriamine pentacetate bishydroxyethylamide gadolinium chelate (Gd(III)-DTPA-BEA), which is similar to compound B but less hydrophobic.

Fig. 2. Methods for evaluating theoretical sPRE

(A) For protein GB1 (PDB code 2GB1), the theoretical sPRE values for protein backbone amide protons can be calculated with lattice point model of different spacing or with surface integral model. Comparing to the experimental data, the correlation coefficient R is 0.866 for 1.0-Å spacing, 0.931 for 0.5-Å spacing, 0.917 for 0.1-Å spacing, and 0.927 for the values calculated with the PSol module in Xplor-NIH. (B) Evaluation of sPRE Q-factor by scaling the calculated sPRE values. The Q-factor can be as low as 0.16 for values calculated with lattice point model with 0.5 Å spacing. (C) The values calculated with the two alternative approaches are highly consistent. The experimental data was collected with 2 mM Gd³⁺-TTHA-TMA, and the error bars stand for 1 standard deviation in the measurement.

Fig. 3. Flowchart for visualizing protein structure and dynamics using the sPRE

Protein structure can be directly refined, or selected from a library of conformers. Evaluation of the agreement between the observed and calculated sPRE values are based on correlation coefficient R at a certain cutoff.

Fig. 4. Evaluation of the robustness of the Monte Carlo ensemble selection algorithm

Different number of conformers (from 1 to 10) was selected from a sPRE library of apo AdK protein, derived from a pool of many different conformers, to construct a reference ensemble. The same set of conformers can be repeatedly identified in the working ensemble using our selection algorithm, affording a perfect correlation (dashed diagonal line).

Fig. 5. Protein structure refinement against sPRE restraints

A) Superposition of 20 lowest-energy structures for GB1 protein refined with only dihedral angle restraints. The r.m.s. deviation for backbone heavy atoms is 5.14±1.79 Å. B) Superposition of 20 lowest energy structures with the sPRE restraints using the sPRE PsolPot term incorporated. The r.m.s. deviation for backbone heavy atoms is now improved to 1.67±0.34 Å. C) Comparison between the structure refined with PsolPot term (cyan) and the NMR structure previously determined (PDB code 2GB1, green). D) Correlation between back-calculated sPRE values for the GB1 structure in panel C and the observed values. The error bar in the x-axis is 1 standard deviation in sPRE measurement uncertainty. The correlation coefficient R is 0.86, and the sPRE Q-factor can be as low as 0.22 after appropriate scaling of the calculated values.

Fig. 6. Characterization of protein dynamic domain movement based on sPRE

A) Correlation between the sPRE collected for ligand-free Ca²⁺-CaM in the presence of 2 mM and 4 mM paramagnetic cosolute, Gd³⁺-TTHA-TMA. PRE values and errors are both multiplied by 2 for the 2 mM dataset. B) Correlation between observed and calculated sPRE values based on the open structure of the protein (PDB code 1CLL). The sPRE values are colored by NTD (residues 1-74), linker region (residues 75-86), and CTD (residues 87-148). C) Comparison of the observed sPRE profile (red dots) and back-calculated sPRE profiles for the known crystal structure in the open conformation (blue line) and the ensemble structure identified in this study (orange line). Residues with large improvement in the agreement between observed and calculated sPRE values are color-shaded. The error bars stand for 1 standard deviation in sPRE measurement uncertainty.

Fig. 7. A two-conformer ensemble structure identified for ligand-free Ca²⁺-CaM

A) The open state selected from MD library with a population of 60%. B) The close state selected from MD library with a population of 40%. The two domains, with the NTD and CTD colored in different shades of gray, bury solvent accessible surface area of ~1255 Ų, while at the same time, the linker residues improve their solvent exposure at one side of the protein. C) Comparison of the closed-state structure identified based on the sPRE data (colored blue) and previously determined based on the PRE data with a nitroxide probe covalently attached at S17C site (colored light orange). The backbone r.m.s. difference between the two structures is as low as 1.50 Å. D) Comparison of the closed-state structure based on the sPRE (marine) and the crystal structure of the ligand-bound Ca²⁺-CaM (PDB code 1CDL, colored orange). The backbone r.m.s. difference between the two structures is as low as 3.50 Å.