Accurate Determination of Motional Amplitudes in Biomolecules by Solid-State NMR

Abstract

Protein dynamics are an intrinsically important factor when considering a protein's biological function. Understanding these motions is often limited through the use of static structure determination methods, namely, X-ray crystallography and cryo-EM. Molecular simulations have allowed for the prediction of global and local motions of proteins from these static structures. Nevertheless, determining local dynamics at residue-specific resolution through direct measurement remains crucial. Solid-state nuclear magnetic resonance (NMR) is a powerful tool for studying dynamics in rigid or membrane-bound biomolecules without prior structural knowledge with the help of relaxation parameters such as T ₁ and T _1ρ. However, these provide only a combined result of amplitude and correlation times in the nanosecond-millisecond frequency range. Thus, direct and independent determination of the amplitude of motions might considerably improve the accuracy of dynamics studies. In an ideal situation, the use of cross-polarization would be the optimal method for measuring the dipolar couplings between chemically bound heterologous nuclei. This would unambiguously provide the amplitude of motion per residue. In practice, however, the inhomogeneity of the applied radio-frequency fields across the sample leads to significant errors. Here, we present a novel method to eliminate this issue through including the radio-frequency distribution map in the analysis. This allows for direct and accurate measurement of residue-specific amplitudes of motion. Our approach has been applied to the cytoskeletal protein BacA in filamentous form, as well as to the intramembrane protease GlpG in lipid bilayers.

Figure 1

Pseudo-3D pulse scheme employed to measure ¹H–¹⁵N dipolar couplings. Representation of RF irradiation elements follows conventional notations—see also detailed description in the text.

Figure 2

Representative examples of ¹⁵N magnetization evolution as a function of the CP contact time for a few ¹H–¹⁵N pairs in BacA. The experimental data (open circles) were recorded on a 600 MHz spectrometer and shown along with best-fit curves (continuous lines).

Figure 3

(A) Experimental ¹H,¹⁵N order parameters as a function of residue for BacA. The right axis represents a full-open angle of the ¹H–¹⁵N vector’s diffusion cone. (B) Order parameter values are residuewise mapped onto the BacA structure (PDB ID: 2N3D) with a yellow to a red color gradient.

Figure 4

(A) Experimental ¹H–¹⁵N order parameters as a function of residue number of GlpG. The right axis represents a full-open angle of the ¹H–¹⁵N vector’s diffusion cone. (B) Order parameter values are residuewise mapped onto the structure of the “closed” conformation of GlpG (PDB ID: 2IC8) with a yellow to a red color gradient.