Characterization of Amyloid Structures at the Molecular Level by Solid State Nuclear Magnetic Resonance Spectroscopy

Abstract

Solid state nuclear magnetic resonance (NMR) spectroscopy is particularly useful in structural studies of amyloid fibrils because solid state NMR techniques have unique capabilities as site-specific, molecular-level structural probes of noncrystalline materials. These techniques provide experimental data that strongly constrain the secondary, tertiary, and quaternary structures of amyloid fibrils, permitting the development of experimentally-based structural models. Examples of techniques that are applicable to amyloid samples prepared with isotopic labeling of specific sites and to samples prepared with uniform isotopic labeling of selected residues are presented, illustrating the utility of the various techniques and labeling schemes. Information regarding the preparation of amyloid samples for solid state NMR measurements is also included.

I. Introduction

The phrase “solid state NMR” simply means nuclear magnetic resonance (NMR) techniques that are applicable to samples that are solids (crystalline or noncrystalline) or solid-like (e.g., phospholipid bilayer membranes, precipitated protein aggregates). As demonstrated by recent studies in our laboratory (Antzutkin et al., 2000; Antzutkin et al., 2003; Antzutkin et al., 2002; Balbach et al., 2000; Balbach et al., 2002; Gordon et al., 2004; Oyler and Tycko, 2004; Petkova et al., 2004; Petkova et al., 2002; Petkova et al., 2005; Tycko and Ishii, 2003) and in other laboratories (Benzinger et al., 1998; Benzinger et al., 2000; Burkoth et al., 2000; Gregory et al., 1998; Heller et al., 1996; Jaroniec et al., 2002b; Jaroniec et al., 2004; Kammerer et al., 2004; Lansbury et al., 1995; Laws et al., 2001; Naito et al., 2004; Siemer et al., 2005), amyloid fibrils are excellent systems for solid state NMR investigations. This is because (i) amyloid fibrils, although noncrystalline, do have well-defined molecular structures and therefore yield solid state NMR data that are of high quality and have clear interpretations, (ii) amyloid fibrils can be prepared with selective or uniform isotopic labeling in the multimilligram quantities required for most solid state NMR measurements, (iii) amyloid fibrils can be prepared in high concentrations by lyophilization or centrifugation, leading to good signal-to-noise ratios in the solid state NMR data, (iv) the structural information available from solid state NMR measurements is arguably more direct and specific than information available from other measurements, and (v) the molecular structures of amyloid fibrils are of great current interest in the biomedical, biophysical, and biochemical research communities.

Based on x-ray fiber diffraction data, we know that the principal structural motifs in amyloid fibrils are cross-β motifs, i.e., ribbon-like β-sheets extending over the length of the fibrils, comprised of β-strand peptide segments oriented approximately perpendicular to the long fibril axis and linked by backbone hydrogen bonds oriented approximately parallel to the long axis (Sunde and Blake, 1998; Tycko, 2004). The reality of the cross-β motif in fibrils formed by the β-amyloid peptide associated with Alzheimer's disease (Aβ) has been confirmed by electron microscopy (EM) (Serpell and Smith, 2000) and by recent solid state NMR measurements on oriented fibrils (Oyler and Tycko, 2004). Given that amyloid fibrils are constructed from β-sheets, the molecular structures of amyloid fibrils can be discussed at the levels of primary, secondary, tertiary, and quaternary structure, in analogy to the classification of structure in globular proteins and protein complexes. Primary structure refers to the amino acid sequence. For amyloid fibrils, secondary structure refers to the locations of β-strand and non-β-strand segments and of ordered and disordered segments. Tertiary structure refers to the arrangement of β-strands into parallel or antiparallel β-sheets. Quaternary structure refers to the relative orientation of and contacts between β-sheets. As explained below, solid state NMR data can be used to determine or place strong constraints on secondary, tertiary, and quaternary structure in amyloid fibrils. These constraints permit the development of complete structural models based entirely on experimental data (Burkoth et al., 2000; Jaroniec et al., 2004; Kammerer et al., 2004; Lansbury et al., 1995; Petkova et al., 2002).

II. Determination of secondary structure

Constraints on secondary structure come from at least two types of solid state NMR measurements. One approach is simply to measure isotropic ¹³C NMR chemical shifts in fibrils that are prepared with ¹³C labels at specific carbonyl, α-carbon, or β-carbon si tes (Balbach et al., 2002; Heller et al., 1996; Laws et al., 2001; Naito et al., 2004) or with uniformly ¹³C-labeled residues (Balbach et al., 2000; Jaroniec et al., 2002b; Jaroniec et al., 2004; Petkova et al., 2004; Petkova et al., 2002; Petkova et al., 2005; Siemer et al., 2005). In β-strand segments, carbonyl and α-carbon lines are shifted upfield relative to “random coil” chemical shift values, while β-carbon lines are shifted downfield (Balbach et al., 2000; Petkova et al., 2002; Saito, 1986; Spera and Bax, 1991; Wishart et al., 1991). Observation of β-strand-like ¹³C chemical shifts for several sequential residues provides strong evidence for a β-strand encompassing these residues. As an example, ¹³C chemical shift data for Aβ_16-22 fibrils (where Aβ_n-m means residues n through m of the Aβ peptide) are plotted in Fig. 1 as “secondary shifts”, or the differences between observed chemical shifts and the corresponding random coil shifts.

Figure 1:

¹³C NMR secondary shifts (i.e., differences between observed chemical shifts and random coil shifts) for amyloid fibrils formed by Aβ_16-22 (N-acetyl-KLVFFAE-amide). Negative secondary shifts for β-carbons and carbonyl carbons and positive secondary shifts for β-carbons indicate a β-strand containing residues 17-21 (Balbach et al., 2000).

The chemical shift measurements are carried out with magic-angle spinning (MAS), a standard solid state NMR technique in which samples are placed in cylindrical capsules (called MAS rotors) and spun rapidly about an axis that makes an angle ${\theta }_m\equiv {\cos }^{-1}\left(1∕\sqrt{3}\right)$ with the magnetic field of the NMR spectrometer, using a pneumatic turbine system. MAS at 5-25 kHz frequencies averages out both chemical shift anisotropies (CSA) and nuclear magnetic dipole-dipole couplings (e.g., between ¹³C-¹³C and ¹⁵N-¹³C pairs), resulting in relatively sharp NMR lines at the isotropic chemical shift positions. Dipole-dipole couplings to protons are not removed efficiently by MAS at readily achievable spinning frequencies and therefore must be removed by high-power proton decoupling. In the case of samples with uniformly labeled residues, two-dimensional (2D) spectroscopy (or higher-dimensional spectroscopy) is usually required for resolution and assignment of the ¹³C MAS NMR lines (Balbach et al., 2000; Jaroniec et al., 2002b; Jaroniec et al., 2004; Petkova et al., 2004; Petkova et al., 2002; Petkova et al., 2005; Siemer et al., 2005). Fig. 2 shows examples of 2D solid state ¹³C-¹³C NMR spectra of Aβ_1-40 fibrils, synthesized with uniform ¹⁵N and ¹³C labeling of selected residues.

Figure 2:

Two-dimensional ¹³C NMR spectra of Aβ_1-40 fibrils in lyophilized form, obtained with magic-angle spinning under conditions that produce strong crosspeaks for directly bonded ¹³C pairs (Ishii, 2001; Petkova et al., 2002). Full spectra (a,c) and expansions of the aliphatic regions (b,d) are shown for fibrils that are uniformly ¹⁵N,¹³C-labeled at A2, D7, G9, Y10, V12, and M35 (a,b) or F10, D23, V24, K28, G29, A30, and I31 (c,d). Solid and dashed lines indicate crosspeak connectivities used for resonance assignment. Note the broad crosspeaks for A2 and D7, which support the existence of a disordered N-terminal segment in Aβ_1-40 fibrils. Spectra were recorded in a 9.4 T field, with magic-angle spinning at approximately 23 kHz.

A more sophisticated and potentially more powerful approach is to use a class of solid state NMR techniques that are collectively called “tensor correlation methods” (Blanco and Tycko, 2001; Chan and Tycko, 2003; Costa et al., 1997a; Costa et al., 1997b; Dabbagh et al., 1994; Feng et al., 1997; Feng et al., 1996; Ishii et al., 1996; McDermott et al., 1994; Reif et al., 2000; SchmidtRohr, 1996a; SchmidtRohr, 1996b; Takegoshi et al., 2000; Tycko and Dabbagh, 1991; Weliky et al., 1993; Weliky and Tycko, 1996). These techniques provide quantitative constraints on the relative orientations of pairs of chemical bonds (e.g., the relative orientation of a ¹⁵N-H bond and a ¹³C_α-H bond within one residue, which depends on the backbone ϕ torsion angle for this residue) or pairs of functional groups (e.g., the relative orientation of sequential ¹³C-labeled backbone carbonyl sites, which depends on the backbone ϕ and ψ torsion angles between the labeled sites). Tensor correlation methods are particularly useful for determining sidechain conformations or backbone conformations at residues where the chemical shift data suggest a non-β-strand conformation (Antzutkin et al., 2003).

Structurally ordered segments in amyloid fibrils can be distinguished from disordered segments by measurements of ¹³C MAS NMR linewidths. In lyophilized samples, ordered segments exhibit linewidths of roughly 2 ppm or less for backbone sites, while disordered segments exhibit linewidths greater than 3 ppm (Balbach et al., 2000; Petkova et al., 2004; Petkova et al., 2002). For comparison, solid state ¹³C MAS NMR linewidths for peptides that are tightly bound to antibodies, and are therefore structurally ordered, are 1.5-2.5 ppm in noncrystalline frozen solutions (Sharpe et al., 2004; Weliky et al., 1999). Fully hydrated amyloid samples may exhibit narrower lines for ordered segments (although not necessarily), and may exhibit missing signals for disordered segments that undergo large-amplitude motions when hydrated (Jaroniec et al., 2002b; Jaroniec et al., 2004; Petkova et al., 2004; Siemer et al., 2005). Fig. 3 shows ¹³C NMR linewidth data extracted from 2D spectra of Aβ_1-40 fibrils.

Figure 3:

¹³C NMR linewidths (full width at half maximum) extracted from two-dimensional spectra as in Fig. 2. These data indicate conformational disorder in the N-terminal segment, in the vicinity of Q15, and (to a lesser extent) in residues 35-39. Other residues are well ordered.

To date, helical secondary structure has not been observed in amyloid fibrils by solid state NMR, although helical segments in peptides and proteins can be identified by either ¹³C NMR chemical shift measurements (Havlin and Tycko, 2005) or tensor correlation methods (Blanco et al., 2001; Blanco and Tycko, 2001; Chan and Tycko, 2003; Long and Tycko, 1998). Solid state NMR can also be used to characterize β-turn conformations (Ashida et al., 2002; Sharpe et al., 2004; Weliky et al., 1999; Yao and Hong, 2004). Recent models for amyloid fibrils derived from solid state NMR and other data (Guo et al., 2004; Jimenez et al., 2002; Petkova et al., 2002; Williams et al., 2004) assign the observed non-β-strand segments to “bend” or “loop” structures, rather than the standard β-turns invoked in some earlier models (George and Howlett, 1999; Lazo and Downing, 1998; Li et al., 1999).

III. Determination of tertiary structure

As reflected in structural models for Aβ fibrils published before 2000 (Chaney et al., 1998; George and Howlett, 1999; Lazo and Downing, 1998; Li et al., 1999), a consensus once existed that the cross-β motifs in amyloid fibrils were comprised of antiparallel β-sheets. This belief was overturned by solid state NMR studies of Aβ_10-35 fibrils by Lynn, Meredith, Botto, and coworkers (Benzinger et al., 1998; Benzinger et al., 2000; Burkoth et al., 2000; Gregory et al., 1998), which showed that Aβ_10-35 fibrils contain only in-register parallel β-sheets (i.e., β-sheets in which residue k in one β-strand forms backbone hydrogen bonds with residues k-1 and k+1 of a neighboring β-strand). Subsequently, in-register parallel β-sheets have been discovered in other amyloid fibrils, including full-length Aβ fibrils (Antzutkin et al., 2000; Antzutkin et al., 2002; Balbach et al., 2002; Petkova et al., 2005; Torok et al., 2002), by solid state NMR (Antzutkin et al., 2000; Antzutkin et al., 2002; Balbach et al., 2002; Gordon et al., 2004) and other techniques (Der-Sarkissian et al., 2003; Jayasinghe and Langen, 2004; Torok et al., 2002). However, certain amyloid fibrils have been shown to contain antiparallel β-sheets, particularly fibrils formed by relatively short peptides (Balbach et al., 2000; Gordon et al., 2004; Kammerer et al., 2004; Lansbury et al., 1995; Petkova et al., 2004), implying that there is no truly universal molecular structure for amyloid fibrils. Results obtained to date suggest that parallel β-sheets are favored in amyloid fibrils because parallel alignment of β-strand segments maximizes hydrophobic contacts (Antzutkin et al., 2000; Petkova et al., 2002) and permits favorable interactions among polar sidechains, dubbed “polar zippers” by M.F. Perutz (Perutz et al., 1994), within a single β-sheet. Antiparallel β-sheets can be favored by electrostatic interactions, but have been found in amyloid fibrils comprised of peptides with hydrophobic segments only when the requirement for optimal hydrophobic contacts can also be met with antiparallel alignment of β-strand segments (Balbach et al., 2000; Gordon et al., 2004; Lansbury et al., 1995; Petkova et al., 2004).

Constraints on tertiary structure are obtained from measurements of nuclear magnetic dipole-dipole couplings, whose strength is proportional to $\raisebox{1ex}{${\gamma }_I{\gamma }_S$}\!\left/ \!\raisebox{-1ex}{${R_{IS}}^3$}\right.$, where γ_I and γ_S are the gyromagnetic ratios of coupled nuclei I and S and R_IS is the internuclear distance. For a ¹³C-¹³C pair at R_IS = 4.8 Å (the interstrand distance in a β-sheet), the coupling strength is 69 Hz, implying a 15 ms time scale for evolution of NMR signals from ¹³ C nuclei with 4.8 Å separations. For a ¹⁵N-¹³C pair at R_IS = 4.1 Å (the approximate distance between an amide nitrogen and a carbonyl carbon in an interstrand hydrogen bond), the coupling strength is 45 Hz, implying a 22 ms time scale.

In-register parallel β-sheets can be identified by synthesizing a series of peptide samples with single ¹³C labels at backbone or sidechain sites (Antzutkin et al., 2000; Balbach et al., 2002; Benzinger et al., 1998; Gregory et al., 1998). Because carbonyl and methyl carbon sites have relatively weak dipole-dipole couplings to proteins and hence exhibit relatively long transverse spin relaxation times (T₂ values) under typical experimental conditions, it has proven most useful to label backbone carbonyl and alanine methyl sites. Measurements of intermolecular ¹³C-¹³C dipole-dipole couplings, as in Fig. 4 for Aβ_1-40 fibrils, permit intermolecular distances up to at least 6 Å to be measured with approximately ±10% accuracy (limited by effects of T₂ relaxation and pulse sequence imperfections). Measurements of intermolecular distances between backbone carbonyl sites alone may be incapable of distinguishing in-register alignment of β-strands from a one-residue shift in alignment, as examination of molecular models for parallel β-sheets shows that a one-residue shift only increases the nearest-neighbor intermolecular distances for backbone carbonyl labels from 4.8 Å to approximately 5.2 Å. However, nearest-neighbor intermolecular distances for alanine methyl carbon labels increase from 4.8 Å to approximately 6.7 Å with a one-residue shift. Therefore, data such as those in Fig. 4 can only be explained by an in-register parallel β-sheet structure.

Figure 4:

Experimental constraints on intermolecular distances in Aβ_1-40 fibrils, using the fpRFDR-CT technique (Balbach et al., 2002; Ishii et al., 2001) to measure ¹³C-¹³C nuclear magnetic dipole-dipole couplings in samples that are ¹³C labeled at single sites in V12, A30, or V39. Simulations for linear chains of ¹³C nuclei with nearest-neighbor spacings from 4.0 Å to 7.0 Å are shown. These data indicate that the labeled residues participate in in-register parallel β-sheets. Data were obtained in 9.4 T field, with magic-angle spinning at 20.0 kHz.

Data in Fig. 4 were obtained under MAS, using a pulse sequence technique called “constant-time finite-pulse radiofrequency-driven recoupling” (fpRFDR-CT) (Balbach et al., 2002; Ishii et al., 2001). This technique is one example of a class of solid state NMR methods called “recoupling” techniques, in which radiofrequency pulses are applied in synchrony with sample rotation to restore dipole-dipole couplings or other nuclear spin interactions that would otherwise be averaged out by MAS (Bennett et al., 1998; Gullion and Schaefer, 1989; Gullion and Vega, 1992; Hohwy et al., 1998; Ishii, 2001; Mehta et al., 1996; Meier and Earl, 1986; Tycko and Dabbagh, 1990; Tycko et al., 1989). The fpRFDR-CT technique has the advantages of being relatively insensitive to T₂ effects, compatible with high-speed MAS, and effective even in the presence of the large ¹³C CSA characteristic of carbonyl carbons.

NMR signal decay curves recorded under fpRFDR-CT or other dipolar recoupling techniques are primarily determined by the shortest internuclear distances, i.e., the strongest dipole-dipole couplings. Thus, these data do not readily distinguish a propagating in-register parallel β-sheet structure from, for example, a structure that alternates between in-register parallel and antiparallel (or shifted) alignment of neighboring β-strands. Multiple quantum ¹³C NMR measurements, which are sensitive to the entire network of dipole-dipole couplings among many ¹³C spins, can distinguish among these and other structures (Antzutkin et al., 2000). Multiple quantum ¹³C NMR data show that the in-register parallel alignment of peptide chains in Aβ_1-40 fibrils extends over at least four successive peptide chains in the β-sheets (and probably hundreds of β-strands).

Antiparallel β-sheets have also been demonstrated by solid state NMR to exist in amyloid fibrils. Measurements of either ¹³C-¹³C (Lansbury et al., 1995) or ¹⁵N-¹³C (Balbach et al., 2000; Gordon et al., 2004; Kammerer et al., 2004; Petkova et al., 2004) intermolecular dipole-dipole couplings can be used to identify antiparallel β-sheets in samples with selective isotopic labeling. Measurements of intermolecular couplings between ¹⁵N-labeled backbone amide sites and ¹³C-labeled backbone carbonyl sites, using the rotational echo double resonance (REDOR) recoupling technique (Anderson et al., 1995; Gullion and Schaefer, 1989), are particularly powerful because the 4.1 Å internuclear distance for hydrogen bonded backbone amide and carbonyl sites is significantly shorter than other intermolecular distances in β-sheets. REDOR data such as those in Fig. 5 establish the registry of hydrogen bonds unambiguously.

Figure 5:

Measurements of intermolecular dipole-dipole couplings between ¹⁵N labels at backbone amide sites and ¹³C labels at backbone carbonyl sites in amyloid fibrils formed by Aβ_16-22 with either acetyl (circles, downward triangles) or octanoyl (upward triangles, squares) groups at the N-terminus. These measurements use the REDOR solid state NMR technique (Anderson et al., 1995; Gullion and Schaefer, 1989). Fibrils are formed from mixtures of molecules that are ¹⁵N-labeled at A21 and molecules that are ¹³C-labeled at L17 (circles, squares) or F20 (triangles), with an approximate 1.6:1.0 ratio of ¹⁵N-labeled to ¹³C-labeled molecules. Curves are simulations in which the labeled residues are hydrogen bonded in parallel (solid line) or antiparallel (dashed line) β-sheets, or shifted from hydrogen bonded positions by one residue in parallel (dash-dotted line) or antiparallel (dotted line) β-sheets. These data indicate an antiparallel β-sheet structure with hydrogen bonds between residues 17+k and 21-k (k = 0, 1, 2, 3) for the acetyl peptide, and an in-register parallel β-sheet structure for the octanoyl peptide (Gordon et al., 2004). Data were obtained in a 9.4 T field, with magic-angle spinning at 5.00 kHz.

Constraints on secondary and tertiary structure from fpRFDR-CT, multiple quantum NMR, REDOR, and related solid state NMR measurements can be analyzed quantitatively by comparison of experimental data with accurate numerical simulations of the solid state NMR measurements. Such simulations contain no adjustable parameters other than the geometric parameters that describe the molecular structure, such as internuclear distances.

In samples with multiple uniformly labeled residues (or multiple residues ¹³C-labeled at α-carbons), the hydrogen bond registry in antiparallel β-sheets can also be established from 2D solid state ¹³C NMR spectra in which transfer of nuclear spin polarization between ¹³C-labeled sites occurs in three steps: (i) transfer from ¹³C nuclei to directly bonded protons; (ii) transfer among protons that are within approximately 3 Å of one another; (iii) transfer from protons to directly bonded ¹³C nuclei. Such “proton-mediated” transfers are particularly efficient for α-carbons that are directly opposite one another in antiparallel β-sheets, because the corresponding interstrand β-proton distances are approximately 2.1 Å. Proton-mediated 2D ¹³C-¹³C exchange spectra of antiparallel β-sheet structures therefore show strong, nonsequential crosspeaks connecting NMR lines of α-carbons that align with one another (Petkova et al., 2004; Tycko and Ishii, 2003). Fig. 6 shows examples of proton-mediated 2D spectra for Aβ_11-25 fibrils prepared at pH 2.4 and pH 7.4. These spectra reveal that the hydrogen bond registry is pH-dependent, presumably due to variations in electrostatic interactions.

Figure 6:

Proton-mediated two-dimensional ¹³C-¹³C exchange spectra of Aβ_11-25 fibrils grown at pH 7.4 (a) or pH 2.4 (b), with uniform ¹⁵N and ¹³C labeling of V18, F19, F20, and A21. Strong crosspeaks between α-carbon chemical shifts of V18 and α-carbon chemical shifts of either F19 (a) or A21 (b) indicate the hydrogen bond registry in antiparallel β-sheets (Petkova et al., 2004; Tycko and Ishii, 2003). At pH 7.4, residue 17+k is hydrogen bonded to residue 20-k. At pH 2.4, residue 17+k is hydrogen bonded to residue 22-k. Spectra were recorded in a 14.1 T field, with magic-angle spinning at 21.40 kHz.

IV. Determination of quaternary structure

Experimental constraints on quaternary structure from solid state NMR take the form of measurements of approximate distances, or “contacts”, between sidechains that project above or below the β-sheets, or between sidechain and backbone sites. Because the shortest distances between backbone atoms in different β-sheets are roughly 8 Å or more, corresponding to ¹³C-¹³C dipole-dipole couplings of 15 Hz or less, constraints on quaternary structure can not be obtained readily from backbone-backbone couplings.

Semi-quantitative information about sidechain-sidechain distances can be obtained from 2D ¹³C-¹³C exchange spectra of amyloid fibril samples with multiple uniformly labeled residues, obtained under MAS and with exchange periods greater than 100 ms. An example is shown in Fig. 7. Under these conditions, all possible intraresidue crosspeaks are observed (rather than only the one-bond or two-bond crosspeaks that appear with shorter exchange periods, as in Fig. 2), and many inter-residue crosspeaks are observed for sequential pairs of labeled residues. In addition, nonsequential crosspeaks that can only arise from quaternary contacts may be observed. Because of the complexity of the dipole-dipole coupling networks in such measurements, internuclear distances can not be determined precisely from the crosspeak intensities. However, basic principles of nuclear spin interactions (Tycko and Dabbagh, 1992) imply that detectable crosspeaks in 2D ¹³C exchange spectra with exchange periods less than one second can only occur if the internuclear distances are less than 10 Å.

Figure 7:

(a) Two-dimensional ¹³C-¹³C exchange spectra of Aβ_1-40 fibrils, prepared with uniform ¹⁵N and ¹³C labeling of K16, F19, A21, E22, I32, and V36, obtained with a 500 ms exchange period. (b) One-dimensional slices taken at positions indicated by the dashed lines in the two-dimensional spectrum. The slice at the chemical shift of F19 aromatic carbons shows crosspeaks at the chemical shifts of V36 aliphatic carbons (dotted lines) and I32 aliphatic carbons (dotdashed lines). These crosspeaks indicate contacts between aromatic and aliphatic sidechains, placing constraints on quaternary structure. The spectrum was recorded in a 14.1 T field, with magic-angle spinning at 18.00 kHz.

Constraints on quaternary structure in amyloid fibrils can also be obtained from measurements of ¹⁵N-¹³C dipole-dipole couplings. Two-dimensional ¹⁵N-¹³C transferred echo double resonance (TEDOR) techniques (Hing et al., 1992; Jaroniec et al., 2002a; Michal and Jelinski, 1997) are particularly useful for detecting the proximity of specific sidechain carbon sites to specific backbone nitrogen sites in samples with multiple uniformly labeled residues. An example is shown in Fig. 8. By comparing 2D ¹⁵N-¹³C TEDOR spectra of samples in which all molecules are isotopically labeled with spectra of samples in which labeled molecules are diluted in unlabeled molecules (prior to fibril formation), one can distinguish intermolecular ¹⁵N-¹³C contacts from intramolecular contacts.

Figure 8:

(a) Two-dimensional ¹⁵N-¹³C TEDOR spectrum of Aβ_1-40 fibrils, prepared with uniform ¹⁵N and ¹³C labeling of I31, G33, M35, G37, and V39, obtained with 5.745 ms ¹⁵N-¹³C recoupling periods (Jaroniec et al., 2002a). Crosspeaks indicate the proximity of particular ¹³C-labeled backbone and sidechain sites to ¹⁵N-labeled backbone amide sites. (b) One-dimensional slices taken at the ¹⁵N chemical shift of G33, indicated by the dashed line in the two-dimensional spectrum, for samples grown from labeled Aβ_1-40 (top) and from a 2:1 mixture of unlabeled and labeled Aβ_1-40. The reduced amplitude of the M35 methyl crosspeak relative to the G33 carbonyl crosspeak in the isotopically diluted sample indicates that the M35 methyl/G33 amide contact is primarily intermolecular and therefore represents a quaternary constraint. Spectra were recorded in a 14.1 T field, with magic-angle spinning at 11.140 kHz.

V. Construction of molecular models based on solid state NMR data

In principle, the molecular structures of amyloid fibrils can be determined completely from solid state NMR data, with no assistance from other experimental techniques, in analogy to approaches commonly employed to determined complete structures of soluble proteins from solution NMR data. However, this approach would require solid state NMR constraints on many torsion angles and many internuclear distances (both intramolecular and intermolecular) for each residue in the amyloid-forming peptide or protein. The limited resolution and signal-to-noise in solid state NMR spectra and the difficulty of preparing fibril samples with arbitrary isotopic labeling patterns make this approach impractical, except possibly in the case of fibrils formed by relatively short peptides (Jaroniec et al., 2004).

Fortunately, information from other experimental techniques greatly simplifies the task of constructing realistic models for amyloid fibril structures. The fact that amyloid fibrils contain cross-β motifs implies that the number of possible quaternary structures is not large, once solid state NMR data that constrain the secondary and tertiary structures are available. This is because the cross-β motif requires that all β-strand segments be approximately perpendicular to a single axis (the long axis of the fibrils), with their backbone carbonyl and amide groups orientated to permit hydrogen bonds that are approximately parallel to the same axis. The number of possible quaternary structures is also strongly restricted by measurements of fibril dimensions in EM or atomic force microscope (AFM) images and by measurements of the mass-per-length of amyloid fibrils by scanning transmission electron microscopy (Antzutkin et al., 2002; Goldsbury et al., 2000; Petkova et al., 2005). In addition, the structural model should make sense from the standpoint of physical chemistry (e.g., exposure of hydrophobic groups to aqueous solvent should be minimized and burial of unpaired charges in the fibril core should be avoided). Detection of a small number of unambiguous contacts between β-sheets by solid state NMR may then be sufficient to determine the correct quaternary structure and hence the principal features of the full molecular structure. The precise details of sidechain conformations and backbone conformations at certain sites may remain undetermined, but these can be constrained by subsequent solid state NMR measurements as required.

These remarks apply to the determination of structural models for the cores of amyloid fibrils. As demonstrated definitively by biochemical experiments on yeast prion protein fibrils (Baxa et al., 2002), amyloid fibrils formed by large proteins can contain highly structured globular domains outside the fibril core. Determination of the structures of these domains in the context of amyloid fibrils would depend on solid state NMR strategies demonstrated recently in studies of microcrystalline globular proteins (Castellani et al., 2003; Lange et al., 2005).

Atomic coordinates for molecular models derived from solid state NMR constraints can be generated with molecular modeling and molecular dynamics (MD) software (Petkova et al., 2002). A relatively simple approach to the generation of atomic coordinates that reflect the experimental information consists of three steps: (i) construction of a peptide in a conformation that is approximately consistent with available data by manual assignment of backbone torsion angles, using molecular modeling software; (ii) construction of an initial model for a segment of the amyloid structure by manual combination of multiple copies of this peptide with appropriate translations and rotations; (iii) refinement of the model by alternating cycles of energy minimization and MD simulations, using appropriate software. In the energy minimization and MD simulations, experimental constraints on internuclear distances and on backbone and sidechain torsion angles are enforced by artificial harmonic potential functions. If the simulations are performed without explicit solvent, electrostatic interactions are turned off or attenuated by setting the dielectric constant to an artificially large value. To identify aspects of the structural model that are not restricted by experimental constraints, the MD simulations can be run at elevated temperatures and the results of multiple independent refinement attempts can be compared. Portions of the structure that are not constrained by experiments will appear to be disordered.

VI. Sample preparation for solid state NMR

Amyloid fibrils are typically prepared by incubation of peptides or proteins in aqueous or mixed solvents under controlled conditions of concentration, pH, ionic strength, and temperature. Formation of fibrils can be monitored by EM or AFM imaging of aliquots of the incubating solution. However, it is important to recognize that EM and AFM images do not necessarily show all aggregated structures (nonfibrillar as well as fibrillar) in the solution. Ultimately, only the absence of signals attributable to nonfibrillar components in the solid state NMR spectra themselves is proof that the sample is fully fibrillized. Complete conversion to fibrils is essential because all immobilized molecules in the sample will contribute approximately equally to the solid state NMR signals. Unlike EM and AFM, solid state NMR sees the entire sample.

Structural studies of amyloid fibrils using the techniques discussed above require roughly 1 μmole of isotopically labeled molecules to achieve an adequate signal-to-noise ratio in the data. With 1 μmole samples, 2D spectra are typically obtained in 0.5-10 days (depending on the details of the measurements) when the experiments are performed at room temperature and in 9.4 T or 14.1 T magnetic fields. Solid state NMR measurements can be performed either on centrifuged pellets of fibrils or on lyophilized samples. We find that pelleted and lyophilized samples have identical chemical shifts in ¹³C MAS NMR spectra (Petkova et al., 2004), indicating that lyophilization does not perturb the structures of amyloid fibrils. Certain sidechain ¹³C NMR linewidths are reduced in hydrated samples (either pelleted or lyophilized and subsequently rehydrated) relative to the linewidths in dry lyophilized samples, most likely reflecting sidechain motions in hydrated samples that are quenched in dry samples. Lyophilization permits a denser packing of fibrils into the MAS rotors, increasing the signal-to-noise ratio and facilitating high-speed MAS. Lyophilization also minimizes sample heating by radiofrequency pulses during NMR experiments.

EM images often show several distinct morphologies for fibrils that are formed by a single peptide or protein (Goldsbury et al., 2000; Jimenez et al., 2002). The distinct morphologies may differ in diameter, twist periodicity, and apparent propensity for lateral association. The sensitivity of ¹³C NMR chemical shifts to subtle variations in molecular structure has allowed us to demonstrate that distinct fibril morphologies have different underlying molecular structures (Petkova et al., 2005). The molecular structure propagates with the morphology when sonicated fibril fragments are used to seed the growth of new fibrils. Existing data suggest that fibrils with different morphologies have different quaternary structures and different conformations in non-β-strand segments. These findings imply that careful attention must be paid to fibril growth conditions, which can affect the relative abundances of various fibril polymorphs, and to the detailed appearance of fibrils in EM images before comparisons of structural data from different research groups are made. The most definitive proof that two different groups are studying the same fibril structure would be that the two groups observe the same sets of NMR chemical shifts in their samples.