Using NMR to study fast dynamics in proteins: methods and applications

Abstract

Proteins exist not as singular structures with precise coordinates, but rather as fluctuating bodies that move rapidly through an enormous number of conformational substates. These dynamics have important implications for understanding protein function and for structure-based drug design. NMR spectroscopy is particularly well suited to characterize the dynamics of proteins and other molecules in solution at atomic resolution. Here, NMR relaxation methods for characterizing thermal motions on the picosecond-nanosecond (ps-ns) timescale are reviewed. Motion on this timescale can be conveniently captured by the Lipari-Szabo order parameter, S², a bond-specific measure of restriction of motion. Approaches for determining order parameters are discussed, as are recent examples from the literature that link ps-ns dynamics with conformational entropy, allostery, and protein function in general.

Figure 1

Basic flow-chart for characterization of ps-ns dynamics by NMR. A pictorial representation of T₂ relaxation is presented in the first quadrant. The presence of a static magnetic field (B₀) results in a bulk magnetization (grey arrow) aligned with B₀. An RF pulse rotates the bulk magnetization into the xy plane. The individual spins de-phase during the relaxation time (T), leading to the exponential decrease in the bulk magnetization as a function of T. The rate of loss of spin coherence is referred to as the spin-spin relaxation rate (R₂). Molecular tumbling and internal fluctuations affect this rate of relaxation. Relaxation is monitored by acquisition of 2D HSQC type spectra with variable times of T (upper right quadrant). The spectra are ¹H-¹⁵N and ¹H-¹³C for ¹⁵N and ²H relaxation, respectively. ¹⁵N relaxation typically involves measurement of two rates, R₁ and R₂, and the {¹H}-¹⁵N heteronuclear NOE; ²H relaxation involves measurement of R₁ and R_1p. To obtain relaxation rates, the decays in resonance intensities are fit to single exponential equations (lower right quadrant). These raw relaxation parameters are subsequently fit to Lipari-Szabo model-free equations in order to obtain parameters describing amplitude (the order parameter, S²), and characteristic time (τ_e) of bond vector motion (lower left quadrant). Note that the model-free parameters report on the amide ¹H-¹⁵N bond vector (black) and the C-CH₃ symmetry axis (alanine example in red) for ¹⁵N and ²H relaxation, respectively.

Figure 2

Side-chain flexibility is more heterogeneously distributed than main-chain flexibility. Backbone amide S² values (black) and side-chain methyl S²_axis values (red) for Ca²⁺-bound calmodulin are plotted. Note that the backbone values are tightly clustered around 0.9 with the exceptions of loops and the central helix (α-helices and β-sheets are depicted by cylinders and arrows respectively at the top of the figure). The side-chain methyl order parameters are more heterogeneous and have no relation to the protein secondary structure. Data were obtained from the Biological Magnetic Resonance Data Bank (accession number 15188).