Protein structure determination

Proteins are biopolymers characterized by four structural levels [83]: (1) primary structure given by the amino acid sequence, (2) secondary structure defined by the local conformation of the backbone, (3) tertiary structure represented by the spatial proximity of the secondary elements and (4) quaternary structure that specifies the packing of several polypeptide chains.

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Figure 2.8: Structural levels of proteins: primary, secondary, tertiary and quaternary.

Assuming that sample and measured data are available, there are three main steps [84] in the strategy of protein structure determination by NMR: (1) sequential as-signment, (2) collection of structural constraints and (3) structure calculation (see Figure 2.9).

During sequential assignment each of the resonances in the NMR spectra are attributed to residues from the primary sequence of the protein (see conventions in [85]

and BMRB). Assigning the resonances is the critical step in the strategy of Figure 2.9 due to limited resolution and spectral overlap. In the end, the quality of the determined structures depends on the number of correct assignments.

Figure 2.9: Strategy of NMR protein structure determination and the parameters associated with structural constraints, particularly for solid-state NMR [20, 57] which is the aim of this thesis.

Structural constraints (e.g., angles or distances) are obtained from measured parameters via theoretical or empirical relationships and they define in the context of solid-state NMR: (1) the local structure (such as ¹³Cα and ¹³Cβ chemical shifts [86], see Figure 2.10, or NHHC [30]) and (2) the global 3D fold (such as CHHC [87]). Structure calculation uses the determined constraints together with the known covalent topology of each residue most often in restrained molecular dynamics protocols (CNS [88], XPLOR [89]) containing NMR specific force fields. For example, restrained potential energy used in XPLOR is defined as a sum of covalent (first four terms) and non-covalent (the last two terms contain NMR restrains) contribution:

Epot = P

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Starting from an extended polypeptide chain, potential energy (Equation 2.14) is minimized and the ensemble of 10-20 lowest energy conformations are selected to represent the NMR derived protein structure. Refinement and validation of the structure can be done iteratively [90, 91].

Figure 2.10: Elements of protein secondary structure (α-helix and β-sheet) defined by the backbone torsion angles (φ and ψ) and empirical correlations with ¹³Cα and ¹³Cβ secondary chemical shifts [92, 93, 86].

Liquid-state NMR has constantly developed methods since the first protein struc-ture determination in 1985 by W¨uthrich [94] and currently, a large toolbox of multidimen-sional NMR experiments [39, 95], labeling schemes [96], automated or semi-automated programs [84, 90, 97, 91] exist for sequential assignment and structure calculation. Pro-teins up to 30 kDa can be routinely studied by liquid-state NMR and successful

appli-cations have been demonstrated for proteins with molecular weights up to 100 kDa [98].

This limitation in liquid-state NMR appears due to the increase of the correlation time (τc, see Figure 2.12) with the molecular weight (’correlation-time problem’) that shortens the transverse relaxation time (T₂ ∝ τ_c⁻¹) and degrades spectral resolution. The prob-lem becomes even more apparent in the case of membrane proteins where the size of the lipid-protein assemblies (micelles, bicelles, liposomes) can easily reach or exceed the above limits even for small proteins.

The situation is different in solid-state NMR. Here, the proteins are often im-mobilized on the NMR time scale. As a result, solid-state NMR is less sensitive to the correlation-time problem and the resolution will not degrade with increasing molecular weights. Instead it will be determined by the available MAS rate (T2 ∝ ωr2, see Equa-tions 2.15-2.16), the structural heterogeneity (static disorder) and the degree of spectral overlap. In addition, fast internal dynamics (see § 2.5.2 and Chapter 4 ) may improve resolution. Although, a routine methodology for solid-state NMR does not exist yet as in the case of liquid-state NMR, much progress has been recently realized.

The current strategy for uniformly labeled proteins in MAS solid-state NMR re-lies heavily on ¹³C (detected) and ¹⁵N nuclei, making isotope labeling mandatory [99].

The residues type are identified in (¹³C,¹³C) homonuclear correlation spectra (SQ/SQ or DQ/SQ) based on the unique spin connectivities and distinct ¹³C chemical shifts of each residue, while sequential assignment is obtained from combination of het-eronuclear NCACX and NCOCX spectra that link neighbour residues via the common amide¹⁵N nucleus [62, 20] (see Figure 2.11). Sequential assignments can be probed also in CC correlation spectra under specific, so called’weak coupling conditions’ [100], or in NN correlations when possible [101]. To improve resolution and obtain long range constraints in spin diffusion [102, 103] spectra, special¹³C labeling schemes have been proposed [26].

Most often, protons are used in solid-state NMR for signal enhancement via cross-polarization as opposed to liquid-state NMR where ¹H is the detect nucleus and provides important distance constraints and assignments from NOESY experiments [104].

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ever, a variety of methods have been developed to obtain more information from the protons either by indirect detection of the ¹H−¹H distances in CHHC [105, 87] (probe 3D structure) and NHHC [30] (probe secondary structure and molecular interfaces) ex-periments, or by decoupling sequences that improve proton resolution [48, 54].

Figure 2.11: Correlation experiments for uniformly labeled proteins in MAS solid-state NMR:

(a) CC residue type (black) or sequential (dashed) assignment, intra-residue NCACX (blue) and sequential inter-residue NCOCX (red), (b) indirect detected non-trivial ¹H-¹H distances in CHHC, or (c) NHHC experiments.

MAS experiments on uniformly [¹³C,¹⁵N] labeled proteins in different prepara-tions, including (1) microcrystals [106, 107, 108, 109, 27, 110], (2) proteoliposomes [111], or (3) fibrils [112, 113] have shown that sufficient resolution can be obtained in 2D and 3D spectroscopy for the assignment of proteins up to 150 residues. In addition to MAS, the use of oriented samples has proven to be helpful for structure determination of mem-brane proteins reconstituted in macroscopically aligned lipid bilayers [114, 115, 22]. Here, separated-local-fields experiments such as PISEMA [116, 117, 118] on ¹⁵N labeled mem-brane proteins correlate¹⁵N CSA and¹⁵N−¹H dipolar-coupling interactions and produce peak patterns that are diagnostic of secondary structure and orientation.