Figure 1. Chemical exchange lineshapes. (a) Symmetric exchange with p _A = p _B = 0.5. (b) Exchange with skewed populations p _A = 0.9 and p _B = 0.1. Values of k _ex (in s ⁻¹) are indicated on the left. The spectra are simulated with R ₂ = 10 s ⁻¹ and Δω = 500 s ⁻¹. Spectra were calculated using the solution of Equation 3. (c) Simulation of ligand binding in fast (K _d = 10 µM) and slow exchange (K _d = 100 nM) using theory reviewed in Felding [ 17].

Figure 2. Outline of the approach for structure determination of protein complexes in solution by NMR. Starting from the three‐dimensional structures of the individual domains/subunits (represented as sphere, ellipsoid, and line), the structure of the protein complex is constructed in several steps. Commonly used methods to determine the interdomain/subunit interfaces and domain/subunit arrangement are listed, indicated schematically (on the right), and further described in the text.

Figure 3. Sample preparation strategies for structural studies of protein complexes. The three panels show the most efficient strategies to reduce spectral complexity and for optimal signal‐to‐noise in large protein complexes. The strategies are described in detail in the text.

Figure 4. (a) Principle of the cross‐saturation experiment. The protein with residues to be identified in the complex interface is of low density. Saturation caused by irradiation of protons of the unlabeled protein (high density) is transferred to the protein with low ‐density and is limited to the molecular interface. r.f., radiofrequency. (b) Lineshape simulations generated by using the solution of Equation 3. The transverse relaxation rates of the free and bound states are 10 and 100 s ⁻¹, respectively. The change in chemical shift that occurs upon binding is varied. In all cases, p _A = p _B = 0.5. Chemical shift changes (Δω) upon binding are labeled.

Figure 5. General principle of solvent PREs. (a) Paramagnetic centers of Gd(DTPA‐BMA) are shown as spheres. The arrow indicates increasing PREs from the interior to solvent‐accessible areas of the protein (i.e., the surface, flexible loops/linkers). (b) Measurement of solvent PREs. Relaxation rates (e.g., ‐R ₁/R ₂, ‐R ₁/R ₂) are measured for different concentrations of the paramagnetic cosolvent (Gd(DTPA‐BMA)). The slope of the linear relationship determines the solvent PRE. (c) Detection of interaction surfaces by solvent PREs. Solvent PREs are measured for the domains/subunits that are free and in the complex. Residues that show lower solvent PREs in the complex compared to the free domain/subunit are located in the interface. Solid and dotted lines represent the solvent PRE pattern in the free and complex‐bound domain/subunit, respectively.

Figure 6. Experimental solvent PRE data for the 42‐kDa MBP in complex with β‐cyclodextrin. (a) – HSQC spectrum of MBP at 0 (black) and 10 mM Gd(DTPA‐BMA) (red). Selected residues are labeled. (b) – TOCSY spectrum of MBP at 10 (black) and 50 mM Gd(DTPA‐BMA) (red). Selected residues are labeled. (c) Ribbon of the crystal structure of MBP colored according to the strength of the experimental solvent PRE of backbone amide protons. Residues for which no PREs were available due to spectral overlap are shown in gray. Residues shown in (a) and (b) are labeled.

Figure 7. Paramagnetic restraints. Several types of restraints are available for paramagnetic spin labels. Provided that the magnetic susceptibility tensor (χ) is anisotropic (Δχ _ax,rh axial/rhombic components of the anisotropy component of the χ tensor), PCSs are detected as differences in chemical shifts between the paramagnetic and the diamagnetic state. PCSs depend on the distance (r ⁻³) and the orientation (θ/ϕ) of the spins with respect to the paramagnetic center. PREs are observed as line broadening and depend only on the distance (r ⁻⁶). Provided that the χ tensor is anisotropic, RDCs can be measured and depend on the orientation of the bond vector (angles θ, ϕ) with respect to the internal reference frame (χ tensor).

Figure 8. General scheme for structure determination of protein complexes. Details are discussed in the text.