Kinetics of Amyloid β monomer to oligomer exchange by NMR Relaxation

Abstract

Recent studies implicating non-fibrillar oligomers of the amyloid β (Aβ) peptide as the primary toxic species in Alzheimer’s disease have made Aβ oligomers the subject of intense study. Detailed structural and kinetic characterization of these states, however, has been difficult. Here we use NMR relaxation measurements to address the kinetics of exchange between monomeric and large, polymorphic oligomeric species of Aβ (1–40). ¹⁵N-R₂ and ¹H_N-R₂ data at multiple magnetic fields were recorded for several peptide concentrations subsequent to the establishment of a stable pseudo-equilibrium between monomeric and NMR invisible soluble oligomeric species. The increase in ¹⁵N- and ¹H_N-R₂ rates as a function of protein concentration is independent of nucleus and magnetic field and shows only a small degree of variation along the peptide chain. This phenomenon is due to a lifetime broadening effect arising from the unidirectional conversion of monomer to the NMR invisible oligomeric species (‘dark’ state). At a total Aβ(1–40) concentration of 300 µM, the apparent first order rate constant for this process is ~3 s⁻¹. Fitting the McConnell equations for two dipolar-coupled spins in two-site exchange to transfer-of-saturation profiles at two radiofrequency field strengths gives an estimate for k_off of 73 s⁻¹ and transiently-bound-monomer ¹H_N-R₂ rates of up to 42,000 s⁻¹ in the tightly bound central hydrophobic region and ~300 s⁻¹ in the disordered regions such as the first nine residues. The fraction of peptide within the ‘dark’ oligomeric state undergoing exchange with free monomer is calculated to be ~3%. The relatively rapid exchange between the monomer and the polymorphic oligomeric form suggests that therapeutic efforts aimed at altering the equilibrium distribution between these species may be more successful than for the extremely stable fibril form.

A hallmark of Alzheimer’s disease (AD) is the formation of plaques composed of amyloid-β (Aβ) fibrils characterized by an elongated highly ordered β-sheet structure.¹ The link, however, between amyloid fibrils and the etiology of the disease is not well understood.² Recent evidence suggests that smaller, less ordered oligomers of Aβ may be primarily responsible for neurotoxicity,³ and the presence of non-fibrillar Aβ oligomers (ranging from 40 to 200 kDa) in the cerebrospinal fluid correlates with AD.⁴ Elucidating the mechanism of conversion of non-toxic monomers to toxic oligomers or fibrils may be critical to the design of therapeutic interventions that steer the equilibrium away from the buildup of toxic species.⁵ While Aβ amyloid fibrils have been studied at the atomic level by fiber diffraction,⁶ solid state NMR,⁷ electron microscopy,⁸ and H/D exchange combined with mutagenesis,⁹ characterization of the non-fibrillar oligomeric states has proven difficult due to their heterogeneous nature.⁵ Recent work has provided some structural information on Aβ oligomers,¹⁰ but the chemical cross-linking reagents, ionization conditions, and organic solvents and detergents used in these studies make comparison with oligomers formed in their absence difficult.^5,11 Several fundamental questions concerning the nature of Aβ oligomers remain to be answered, including whether the oligomers are permanently stable, or if they are constantly forming from and dissociating back into monomers in a dynamic equilibrium preceding the formation of the extremely stable amyloid fibrils.¹² In this study, we make use of solution NMR relaxation measurements to directly observe rapid exchange under pseudo-equilibrium conditions between monomeric Aβ peptide and non-fibrillar oligomers formed spontaneously in a standard buffer without organic solvents or detergents. These data provide significant details concerning the pre-fibrillar equilibrium that are difficult to probe by other biophysical techniques.

Samples of uniformly ¹⁵N-labeled Aβ(1–40) peptide, were prepared from NaOH treated stocks to remove fibril seeds.¹³ NMR samples comprised 60, 150 and 300 µM Aβ(1–40) in 50 mM HEPES, pH 6.8 and 90% H₂O/10% D₂O. All solutions were pre-filtered in the presence of the chelating agent Chelex 100 (Sigma-Aldrich) to remove any potential trace metal contamination.¹⁴ Samples were prepared and maintained between 4 and 10°C, and all NMR experiments were conducted at 10°C. Under these conditions, Aβ(1–40) at a concentration of 60 µM remains stable for many weeks as monitored by following the ¹H_N/¹⁵N cross-peak intensities in ¹H-¹⁵N HSQC correlation spectra (Figures 1A,B) over time. At peptide concentrations of 150 and 300 µM, however, the signal intensities decay uniformly across the peptide over a period of about one week after which a pseudo-equilibrium is established with integrated intensities for the backbone amide (¹H_N) envelope (measured from the first t₁ increment of an HSQC spectrum) of 70 and 40% of their original values, corresponding to monomer concentrations of 105 and 130 µM, respectively (Figure 1B). Since the ¹H_N/¹⁵N observed cross-peaks arise solely from monomeric peptide^13,15,16 and no new cross-peaks appear, the decrease in signal intensity must arise from the conversion of monomer to a species whose NMR signals are broadened beyond detection due to large oligomer size and correspondingly long rotational correlation times. These large species remain in solution as the samples are clear. Once equilibrated, the presence of large polydisperse aggregates was confirmed by dynamic light scattering, and transmision EM revealed the presence of elongated morphologically disordered non-fibrillar aggregates with possibly some small needle-like fibrils present (Figure 2) similar to those observed for other proteins.¹⁷

Figure 1.

(A) 900 MHz ¹H-¹⁵N HSQC correlation spectrum of 60 µM Aβ(1–40) at 10°C. (B) Time dependence of the integrated intensity of the ¹H_N envelope (measured from the first t₁ increment of a ¹H-¹⁵N HSQC spectrum) for 60 (black), 150 (red) and 300 (blue) µM Aβ(1–40) samples. The solid lines represent single or double exponential fits to the 150 or 300 µM Aβ(1–40) data, respectively. The double exponential fitting function is given by I (t) / I₀ = A₁e^{− t/τ₁}+ A₂e^−t/τ₂ + (1 − A₁ − A₂), where τ₁ and τ₂ are characteristic time constants, and A₁ and A₂ are the associated amplitudes. The parameter A₂ is set to 0 for the single exponential fit. For the 150 µM sample, τ₁ = 51 h and A₁ = 0.31; for the 300 µM sample, τ₁ = 6 h, τ₂ = 93 h, A₁ = 0.36 and A₂ = 0.21. At both 150 and 300 µM total concentrations, the samples reach pseudo-equilibrium after about 100 h, after which the signal intensity does not change more than a few percent on the timescale of a complete NMR experiment (4 to 12 h). (C) ¹⁵N-R₂ (top) and ¹H_N-R₂ (bottom) relaxation data for the 60 µM Aβ(1–40) sample recorded at 900 MHz. The solid lines are single exponential best-fits.

Figure 2.

Transmission EM images of negatively stained (A) 150 and (b) 300 µM Aβ(1–40) NMR samples after >3 weeks of equilibration.

¹⁵N and ¹H_N transverse relaxation (R₂) rates (Figure 1C) were measured for the equilibrated Aβ(1–40) samples using 2D ¹H-¹⁵N HSQC-based experiments.^14,18 The R₂ rates increase as a function of total peptide concentration (Figure 3). The difference in R₂ rates, ΔR₂, between high (150 or 300 µM) and low (60 µM) concentration samples is independent of nucleus or magnetic field (Figure 3B and 3C), as evidenced by the linear ΔR₂ correlation plots with a slope of ~1 (Figure 4). In addition, the variation in ΔR₂ across the peptide chain is small with average ΔR₂(150 µM - 60 µM) and ΔR₂(300 µM - 60 µM) values of 0.7 ± 0.3 and 2.4 ± 0.5 s⁻¹, respectively. The ΔR₂ values are slightly higher for the hydrophobic (green lettering) segments spanning Leu17 to Ala21 and Ala30 to Val40 with the former being systematically elevated relative to the latter. These two regions correspond to the exterior and interior in-register parallel β-strands, respectively, of the cross-β core of Aβ(1–40) amyloid fibrils.7a,b

Figure 3.

Transverse relaxation rates (R₂) measured on equilibrated samples of Aβ(1–40). (A) ¹⁵N-R₂ at 900MHz for 60 µM Aβ(1–40). Cross-peaks for Ala2, His6 and His14 are not sufficiently resolved to permit accurate determination of R₂ rates. The difference in R₂ relaxation rates, ΔR₂, between 300 (blue) or 150 (red) µM samples and the 60 µM sample for (B) ¹⁵N (top, 900 MHz; bottom, 600 MHz) and (C) ¹H_N (top, 900 MHz; bottom, 600 MHz). Large R₂ rates and uncertainties in their values preclude reliable determination of ΔR₂ for His13, Gln15 and Asn27 (A, open circles), and hence are excluded in (B) and (C). The peptide sequence, with hydrophobic residues colored in green, is presented at the top of the figure. (Error bars, 1 s.d.)

Figure 4.

ΔR₂ is independent of nucleus and magnetic field. Correlation plots of ¹⁵N-ΔR₂ at 900 MHz vs. ¹H_N-ΔR₂ at 900 MHz (left panel) and ¹⁵N-ΔR₂ at 600 MHz (right panel). The ΔR₂(300 µM - 60 µM) and ΔR₂(150 µM - 60 µM) rates are colored in blue and red, respectively. A line with slope of unity is displayed for comparison. A histogram of the distribution of ¹⁵N-ΔR₂ rates is shown as an inset.

The observation that the R₂ rate enhancements as a function of total Aβ(1–40) concentration are independent of nucleus and magnetic field and, in addition, vary only slightly along the peptide, indicates that the R₂ rate increases cannot be due to exchange line broadening on the fast/intermediate chemical shift time scale. The latter is dependent on the difference in the resonance frequencies of the spins involved and therefore strongly affected by the nucleus’ chemical environment and the external magnetic field used in the measurements.¹⁹ It is also important to stress that the observed resonances arise only from the monomeric Aβ(1–40) peptide and not from any aggregates present. Indeed, intermolecular paramagnetic relaxation enhancement (PRE) measurements, which provide a highly sensitive probe for the presence of low populations of self-associated species in fast (µs to ms) exchange with monomer,20a,b showed no transverse PRE rate enhancements above a reliable detection limit of ~5 s⁻¹ for mixtures of ¹⁵N-labeled Aβ(1–40) and nitroxide spin-labeled Aβ(1–40) at natural isotopic abundance (Figure 5). Thus, either the population of lower order, transient, self-associated states, if present, is less than 1–2%,^20c or such exchange is slow on the PRE time scale (< ca. 1 ms). We conclude that the observed R₂ rate enhancements must be due to a lifetime broadening effect arising from direct incorporation of the NMR visible monomer into NMR invisible oligomers (i.e. a ‘dark’ state).

Figure 5.

Intermolecular PRE profiles for Aβ(1–40). Transverse ¹H_N-PRE rates, ¹H_N-Γ₂, were determined from the difference in transverse relaxation rates, ¹H_N-R₂, between paramagnetic and diamagnetic samples. The samples comprised 100 µM U-[¹⁵N]-labeled Aβ(1–40) and 170 µM single-cysteine variant Aβ(1–40) peptides at natural isotopic abundance conjugated to either a nitroxide spin-label or a diamagnetic analogue. A Cys residue was introduced preceding the N-terminal Asp residue (Cys-Aβ, black) or as a F20C mutation in the center of the peptide (red). For the Cys-Aβ variant only small intermolecular PREs (¹H_N-Γ₂ < 5 s⁻¹) were observed, while essentially no intermolecular PREs were observed for the F20C sample.

The transverse magnetizations of any large oligomeric species will decay very rapidly owing to the very large R₂ rates associated with their high molecular weights. Hence, the observed increase in R₂ rates at high concentration of Aβ(1–40) can be interpreted as the unidirectional monomer to oligomer conversion rate under pseudo-equilibrium conditions. The maximum observed ¹⁵N ΔR₂ rates of 1.1 and 3.1 s⁻¹ at total Aβ(1–40) concentrations of 150 and 300 µM, respectively, provide estimates of the apparent first order association rate constants, $k_{\mathit{\text{on}}}^{\mathit{\text{app}}}$, for this process. A similar phenomenon has been observed for the equilibrium between monomeric and lipid bound α-synuclein.²¹

To probe the invisible oligomeric state, we carried out a series of ¹H saturation transfer experiments. Using 1 s off-resonance continuous wave (CW) pulses with radiofrequency (RF) field strengths of 180 Hz or 350 Hz at a series of offsets (ranging from +35 kHz to −35 kHz) from the water resonance, the underlying broad resonances of the large oligomers were partially saturated and transfer of saturation from the ‘dark’ oligomeric states to the monomer was measured from the overall decrease in intensity of the ¹H_N backbone amide envelope (7.8 to 9 ppm) of the monomer in a one-dimensional ¹H-NMR spectrum relative to that in a reference spectrum obtained without saturation.

For the 60 µM Aβ(1–40) sample, the off-resonance saturation pulse has no effect on the signal intensity of the amide resonances until the saturation pulse approaches resonances of the protein (Figure 6, black), as expected for a monomeric peptide or protein. For the 300 µM Aβ(1–40) sample, however, the amide resonances are uniformly attenuated by the CW pulse at RF offsets far off-resonance (Figure 6, orange and blue), due to transfer of saturation from the invisible ‘dark’ state with large R₂.

Figure 6.

Attenuation of the integrated intensity of the ¹H_N envelope of monomeric Aβ(1–40) by transfer of saturation from the ‘dark’ state following application of an off-resonance radio-frequency (RF) field as a function of offset from the water resonance. Black circles, 60 µM total concentration and 350 Hz RF field; orange and blue circles, 300 µM total concentration with 180 and 350 Hz RF fields, respectively. The simultaneous best-fits to the experimental saturation profiles for the 300 µM sample at the two RF fields, using the McConnell equations for a dipolar-coupled two spin, two-site exchange model, are significantly better with two distinct ${\mathrm{R}}_2^{\text{dark}}$ rates (bold orange and blue lines) than with a single ${\mathrm{R}}_2^{\text{dark}}$ rate (thin orange and blue lines). Dotted blue and orange lines indicate the region near-resonance where saturation is not well represented by the model due to the many-spin nature of the experimental system. Plots of the residuals (observed minus calculated) between the experimental saturation profiles and the best-fit curves are shown in the top panel. The model with the single ${\mathrm{R}}_2^{\text{dark}}$ underestimates the attenuation between 5 kHz < |RF offset| < 20 kHz at the lower (180 Hz) RF field, while overestimating the attenuation between −15 kHz < RF offset < −5 kHz and between +5 kHz < RF offset < +10 kHz at the higher (350 Hz) RF field. The best-fit parameters for the model with a single ${\mathrm{R}}_2^{\text{dark}}$ rate are ${\mathrm{R}}_2^{\text{dark}}=66,000\pm 9000{\mathrm{s}}^{-1}$ and k_off = 320 ± 20 s⁻¹. The best-fit parameters for the model with two ${\mathrm{R}}_2^{\text{dark}}$ rates are k_off = 73 ± 6 s⁻¹, ${\mathrm{R}}_2^{\text{dark}}(\text{large})=42,000\pm 3000{\mathrm{s}}^{-1}$ and ${\mathrm{R}}_2^{\text{dark}}$ (small) ≤300 s⁻¹ with population weights of 0.40±0.03 and 0.60±0.03, respectively.

Exchange between free monomer (M_free) and transiently bound monomer (M_bound) in the NMR invisible ‘dark’ state, can be represented phenomenologically by a pseudo-first order process (see Supplementary):

(Scheme 1)

The values of the dissociation rate constant, k_off, and the ${\mathrm{R}}_2^{\text{dark}}$ rate for the ‘dark’ state can be obtained by simultaneously fitting the experimental saturation profiles for the 300 µM sample at the two RF field strengths to a solution of the McConnell equations²² for two dipolar-coupled spins in two-site exchange in the presence of a CW saturation field (see Supplementary). Inclusion of two dipolar-coupled spins with different resonance frequencies was necessary to account for the ~5 kHz width of the saturation profile observed for the 60 µM sample (black circles in Figure 6) where the fraction of oligomers is negligible (Figure 1B): the width of the saturation profile spans the ¹H chemical shift range of the monomer and is ascribed to saturation transfer arising from cross-relaxation among protons in the monomer.

Given measured values of ¹H_N-R₁ = 1 s⁻¹ and ¹H_N-R₂ = 10 s⁻¹ for the Aβ(1–40) monomer, $k_{\mathit{\text{on}}}^{\mathit{\text{app}}}=3.1{\mathrm{s}}^{-1}$, and assuming the cross-relaxation rates are small in the monomer (−0.5 to −3 s⁻¹) but large in the oligomer (~ −500 s⁻¹), the saturation profiles for the 300 µM sample can be fit with k_off = 73 ± 6 s⁻¹ and two distinct values of ${\mathrm{R}}_2^{\text{dark}}$: 42,000 ± 3000 s⁻¹ and ~300 s⁻¹ with weights of 0.40±0.03 and 0.60±0.03, respectively (Figure 6, thick orange and blue lines). The saturation profiles for the 300 µM sample cannot be adequately fit by a model with only a single ${\mathrm{R}}_2^{\text{dark}}$ rate (Figure 6, thin orange and blue lines), but are not inconsistent with a distribution of larger and smaller ${\mathrm{R}}_2^{\text{dark}}$ rates.

If ${\mathrm{R}}_2^{\text{dark}}$ varies along the peptide chain, ranging from ~300 to ~40,000 s⁻¹, the residues with the largest ${\mathrm{R}}_2^{\text{dark}}$ rates would have broad saturation profiles while those with smaller ${\mathrm{R}}_2^{\text{dark}}$ rates would experience saturation profiles close to that of the free monomer. Because only a small fraction of monomer is involved in transient interactions with the oligomer (k_off ≫ $k_{\mathit{\text{on}}}^{\mathit{\text{app}}}$), ¹H_N resonances with smaller ${\mathrm{R}}_2^{\text{dark}}$ rates will make a negligible contribution to a standard 1D ¹H-NMR spectrum such that only signals of the free monomer are observed. Further, because k_off is large, the lifetime broadening effect (ΔR₂) will be smaller in the case of residues having smaller ${\mathrm{R}}_2^{\text{dark}}$ rates (Figure 7), thereby explaining the small variation in ΔR₂ as a function of residue (Figure 3). Thus, the lower observed ΔR₂ rates for the first nine N-terminal residues (which are disordered in Aβ fibrils^6a,23), as well as for residues 24–29 (which form a turn between the two hydrophobic segments in Aβ fibrils^7a,24), can be attributed to their higher mobility in the oligomer-bound state. Regions in intimate contact with the oligomer exhibit maximal ΔR₂ rates equal to the unidirectional on-rate $k_{\mathit{\text{on}}}^{\mathit{\text{app}}}$, as exemplified by the central hydrophobic region. The optimized weights of 40 and 60% for the large and small ${\mathrm{R}}_2^{\text{dark}}$ rates obtained from the fits to the saturation profiles (Figure 6) are fully consistent with the number of residues exhibiting larger and smaller ΔR₂ values, respectively (Figures 3 and 4).

Figure 7.

Simulation of the dependence of the monomer ΔR₂ rates arising from exchange with an NMR invisible, oligomer bound species as a function of the R₂ rate in the bound state obtained by numerical solution of the McConnell equations. The blue curve is calculated using the experimentally determined values of 3.1 and 73 s⁻¹ for $k_{\mathit{\text{on}}}^{\mathit{\text{app}}}$ and k_off, respectively, obtained for the 300 µM Aβ (1–40) sample. The ΔR₂ predicted for k_off ±6 s⁻¹ (the 68% confidence interval, representing ±1 s.d) is represented by the gray region. Calculated ΔR₂ rates as a function of the R₂ rate in the oligomeric state for k_off values of 2 (black), 20 (red) and 200 (green) s⁻¹ are also shown for comparison. The effect of ¹H chemical shift differences, between free and oligomer-bound monomers, on the observed ΔR₂ is assumed to be negligible. Residue positions tightly interacting with the oligomer, such as the central hydrophobic region, may have large chemical shift deviations upon binding, but these effects are far exceeded by the large R₂ (ca. 40,000 s⁻¹) at those positions, which causes complete decay of transverse magnetization of these residues in the oligomer-bound monomer. In contrast, residue positions retaining significant mobility in the oligomer-bound form have much lower R₂ values (ca. 300 s⁻¹); hence, their chemical shift changes are likely to be small since the average environment of these highly disordered residues is likely to be very similar to that in the unstructured free state. Further, the ¹⁵N CPMG R₂ experiment with a 180° pulse separation time of 900 µs should suppress the effects arising from chemical exchange for moderate shift differences (<200 Hz). The correspondence of the ΔR₂ measured on two different nuclei (¹H_N and ¹⁵N R₂ relaxation) at two different fields (600 MHz and 900 MHz) (Figure 3) further supports this assumption of negligible effects of shift differences upon chemical exchange.

The fraction, f_ex, of peptide within the oligomeric ‘dark’ state that exchanges with free monomer, is given by the ratio of [M_bound] to total peptide sample concentration. f_ex is readily calculated from the values of k_off, $k_{\mathit{\text{on}}}^{\mathit{\text{app}}}$ and [M_free], and found to be 3.5 and 3.3% for the 150 and 300 µM Aβ(1–40) samples, respectively, indicating that the data at the two sample concentrations are self-consistent. Thus, only 1 in about 30 peptides within the oligomer undergoes exchange with free monomer suggesting that exchange occurs predominantly from the ends of the oligomers.

In conclusion, we have demonstrated that large oligomers of the Aβ(1–40) peptide are in dynamic equilibrium with the monomeric state on a timescale of 10 to 15 ms, and that monomers are constantly binding and being released from NMR invisible oligomers. This process is slower than the fast transient (µs to ms time scale) self-association of monomers that gives rise to sizeable intermolecular PREs observed for α-synuclein.²⁴ The small regional specificity for ΔR₂ indicates that the N-terminal 9 residues remain highly mobile while the central and C-terminal hydrophobic regions are largely immobilized upon association of monomer onto the surface of the oligomeric species. Rapid exchange between monomeric and polymorphous oligomeric forms suggests that therapeutic efforts aimed at altering the equilibrium between these species may be more successful than for highly stable amyloid fibrils.