Exploring Nanosecond Motions at Atomic Resolution in Proteins with High-Resolution Relaxometry

Auther: Fabien Ferrage

Issue No.7, May, 2021

Figure 1. Spectral density function for the dipole-dipole interaction in an 15N-1H pair in a protein with a correlation time for isotropic overall diffusion τc = 5 ns.

     Internal motions in proteins are essential for their functions, but how do proteins move? NMR relaxation is an invaluable method to probe local motions in proteins [1]. NMR relaxation in proteins has been measured and analyzed for several decades. The most popular approach consists in recording nitrogen-15 relaxation rates in an isotopically labeled protein and analyze these rates with the model-free formalism [2]. One obtains order parameters that describe the equilibrium distribution of orientations and an effective timescale for local motions.

     However, high-field measurements of relaxation only probe motions at the resonance frequencies of the system, leaving broad gaps where no information is gathered (see Fig. 1). To fill these gaps, relaxation measurements have to be performed at lower magnetic fields, where the sensitivity and resolution are insufficient for protein NMR. Several groups (R. G. Bryant, A. G. Redfield, H. M. Vieth, K. L. Ivanov, T. H. Huang) and companies (Field Cycling Technology Ltd., Bruker Biospin) have worked on a technological solution: designing fast sample shuttle systems that make it possible to measure relaxation at low fields in the stray field of a commercial magnet, while polarization and detection take place at high field.

Figure 2. Dynamics of the side chain of isoleucine 13 in ubiquitin from 13C relaxation. (a) Nuclear magnetic relaxation dispersion profile for the 13Cδ1 carbon nucleus; (b) 1H-13C dipolar cross-relaxation rate measured at four high magnetic fields; (c) transverse 13C relaxation rates measured at four high magnetic fields; (d) Distribution of probabilities for the parameters of our model from a Monte Carlo Markov Chain analysis: order parameters for fast and slow motions, S2f and S2s, as well as accompanying effective correlation times τf and τs; correlation time for the rotation of the methyl group and chemical shift anisotropy for the 13C nucleus ΔσC. [3]
Figure 3. Interpreting results of high-resolution relaxometry with molecular dynamics simulations. (a) Comparison of the correlation functions for the auto-correlation of the Cγ1Cδ1 vector in Ile36; (b) depiction of dihedral angles in an isoleucine side-chain; (c) auto-correlation of the χ1 angle in isoleucine 36; (d) Ramachandran plot for the side-chain of Ile36 from MD simulations. [3]

Figure 4. Detector sensitivities obtained from a relaxation dataset that include low-field relaxation rates down to 0.33 T. The non-zero sensitivities for the detector ρ5 identify motions on low nanosecond timescales for Ile13, Ile36, and Ile44. The non-zero sensitivity for ρ4 in Ile44 confirms the model-free analysis showing that this motion takes place on correlation times slightly shorter than the other two.[4]

     The first investigation of site-specific dynamics in a protein by high-resolution relaxometry was performed by the groups of Al Redfield and Dorothee Kern [5]. Using the sample shuttle system built by Al Redfield[6], they measured 15N longitudinal relaxation rates down to 4 T (17.3 MHz resonance frequency for 15N) on the nucleocapsid protein of virus SARS-CoV (before there was a need to give a number to the SARS-CoV…). The motion of an entire β-haipin was identified, with an effective correlation time around 0.8 ns.

     We have investigated site-specific motions on nanosecond timescales in the protein ubiquitin using a prototype developed by Bruker Biospin [7]. In particular, we have recently investigated motions in methyl-bearing side chains through measurements of 13C relaxation in 13C1H2H2 methyl groups from 0.33 T to 22.3 T. We found, for 3 out of 7 isoleucine sidechains, that significant motions on low nanosecond timescales could be identified from relaxometry data[3].

    The model-free analysis of such relaxation datasets is convenient and instructive, yet, it does not provide a mechanistic description of the motions detected. To gain additional insight into the nature of these motions, the combination of molecular dynamics (MD) simulations and experimental approaches is essential. The results of the analysis of relaxometry and MD simulations (carried by the group of Rafael Brüschweiler) agreed well for the side chain of isoleucine 36 in ubiquitin, which gave us an opportunity to explore the nature of nanosecond motions. In this case, nanosecond motions are dominated by the dynamics of rotamer jumps around the χ1 dihedral angle.

     A recent investigation of this set of thirty relaxation rates per methyl group, based on the detectors approach [8], confirmed that low-field relaxation rates were essential to characterize the nanosecond motions of two of these methyl groups: those of Ile13 and Ile36, that are characterized by effective correlation times between 2 and 4 ns [4]. Importantly, the optimization of detectors for small and medium-sized proteins highlights the increase of resolution expected in the determination of slow, nanosecond-timescale motion achieved by high-resolution relaxometry, in particular for larger proteins, showing the way for further investigations.