Dynamics studies of side-chains and hydration shells in amyloid-beta fibrils using deuterium and oxygen-17 solid-state NMR

Abstract

This review focuses on deuterium and oxygen-17 solid-state NMR methods for studies of dynamics in amyloid-beta fibrils in rehydrated lyophilized states. For both nuclei NMR spectroscopic properties are dominated by the quadrupolar interaction. Deuterium NMR methods for studies of side-chain dynamics cover line shape analysis, longitudinal Zeeman and Quadrupolar order relaxation, transverse relaxation using Qudrupolar Carr Purcell Meiboom Gill scheme real-time detection, rotating frame relaxation (including off-resonance and quadrupolar order locking), and Chemical Exchange Saturation Transfer methods. Examples are chosen based on the results obtained for native and post-translationally modified fibrils under static and magic-angle spinning conditions. Oxygen-17 laboratory and rotating frame relaxation methods focusing on detection of the central transition under static conditions are presented for hydration shell dynamics in pyroglutateme-3 modified fibrils. Experimental methodology is supplemented with description of explicit motional modeling approaches to arrive at quantitative description of dynamical modes and their corresponding parameters. Special emphasis is placed on the complementarity of different approaches to obtain a fuller picture of motions.

Introduction

Quadrupolar solid-state NMR has been long recognized to be a sensitive tool in studies of molecular dynamics. In this review we focus on the application of deuterium and oxygen-17 solid-state NMR for studies of dynamics in amyloid-β(Aβ) fibrils’ side-chains as well as in the hydration shells. We first present a brief overview of methodology, followed by examples of applications.

For both nuclei, the dominant interaction governing spectroscopic properties is the quadrupolar interaction, which is the interaction between the electric quadrupole moment associated with nuclear spin greater than ½ and the electric field gradient caused by an asymmetric distribution of electron density around the nucleus.(Abragam, 1961) Deuterium has a spin of 1, and oxygen-17 has a spin of 5/2. For studies using deuterium nuclei, in the vast majority of cases it is sufficient to assume that the quadrupolar interaction is the only relevant mechanism, thus rendering it essentially a single particle case in terms of theoretical treatment. For oxygen-17 nuclei, the situation is more complex as the effects of proton dipolar network and/or chemical shift anisotropy have to be taken into account. Without the account of motions, the quadrupolar interaction coupling constant ($C_q$) of deuterons is in about 175-250 kHz range, and is reduced to the effective value of 53-60 kHz for methyl groups undergoing fast rotation about the threefold axis.(Perera et al., 2018; Shi & Rienstra, 2016; Vold & Vold, 1991) The quadrupolar coupling constant for ¹⁷O nuclei for water in frozen hydration shells is on the order of 6.5 to 9 MHz. (Michaelis et al., 2015; Spiess et al., 1969) For the case of deuterium, second order quadrupolar interaction can be ignored. In contrast, the effects of the second order quadrupolar interactions on oxygen-17 nuclei, arising as the first perturbation term in the Magnus expansion, can be considerable.(Man, 2011; Vold & Vold, 1991)

Distortions in quadrupolar NMR line shapes induced by motions can be used to quantify the mechanisms and time scales of motions.(Beerwerth et al., 2018; Hung et al., 2017; Keeler et al., 2016; Wu, 2019) In addition, relaxation measurements can provide useful complementary information on a variety of time scales.(Vold & Vold, 1991; L. Vugmeyster et al., 2024; Vugmeyster & Ostrovsky, 2019; Wu, 2019) It is well-known that covering multiple measurements and relaxation rates and including a broad-temperature range as well as magnetic field dependence permits for most precise determination of motional mechanisms and the corresponding parameters of motions.

In the following we will outline several NMR methods, for each one focusing on practical considerations necessary for their implementation. We will provide examples of how each technique can help to reveal a specific aspect of the dynamics, while underscoring complementarities with other techniques leading to fuller pictures of the dynamics. We will also provide brief commentaries on the computational modeling methods necessary for the quantitative assessment of the underlying motional parameters. The goal of this review is thus to present the diversity and possibilities involved in different techniques as applied to amyloid fibrils and their hydration shells, while referring the reader to publications in which further technical descriptions can be found.

1. Studies of side-chain dynamics in Aβ fibrils using deuterium solid-state NMR.

We will focus on singly labeled samples of Aβ_1-40 fibrils, which are generated using solid-phase peptide synthesis. These samples can be studied using static (non-spinning) solid-state NMR spectroscopy, however magic-angle spinning (MAS) or multiple echo acquisition schemes (QCPMG)(Larsen et al., 1997; Vold et al., 2009) can be employed for sensitivity enhancement and to obtain further insight into dynamics. All the techniques described below are extendable to multiply-labeled samples. However, due to limited chemical shift range of deuterium, they need to incorporate polarization transfer steps to other nuclei such as carbon to obtain site-specific resolution. Polarization transfer steps between ²H and ¹³C nuclei are not as straightforward as more traditional transfers between spin ½ nuclei and a number of approaches were developed to maximize the sensitivity and cover the maximum range of quadrupolar frequencies.(Akbey et al., 2014; Hodgkinson et al., 1998; Jain et al., 2014; Marks et al., 1996; Wei et al., 2011) Several of such studies have been recently presented in the literature. (Akbey, 2021, 2023; Gelenter et al., 2021; Gelenter et al., 2017; Hologne et al., 2006; Shi & Rienstra, 2016; Zhou et al., 2007)

Hydration of protein samples is important to retain functional dynamics, with the water content of 25-60% by weight sufficient for this purpose.(Roh et al., 2005) Amyloid aggregates in general are not soluble, and to ensure homogeneity of the hydration, the levels from 50 to 100% w/w usually must be employed. Homogeneous hydration can be achieved by pipetting the desired amount of water and thorough mixing in the NMR container, followed by equilibration for at least 24 hours. Alternatively, exposure to water in a controlled humidity environment such as in a desiccator can be used. In our experience, water content beyond 35-40% w/w is difficult to achieve in a desiccator and direct pipetting is preferable. For samples that can withstand freezing and thawing cycles, flash-freezing and thawing in liquid nitrogen speeds up homogenization. For deuterium studies of side-chain dynamics it is optimal to use deuterium depleted water, so that residual HOD signals are minimized. The amount of peptide required for deuterium studies under static conditions depends on the labeling sites: for methyl groups with the CD₃ labeling pattern one can get by with about 5-7 mg of sample, while for groups that don’t undergo fast rotations, such as aromatic side chains, at least 10-15 mg of sample is required.

Side-chain sites of Aβ_1-40 that will be discussed in this review are shown in Figure 1. We will present examples for the wild-type fibrils, as well as several naturally occurring post-translational modifications (PTM): truncation at the residue E3 (ΔE3), pyroglutamate substation in this truncated variant (pyro-E3), and phosphorylation at serine 8 (pS8).

Figure 1.

Ribbon diagram of Aβ_1-40 monomer unit of the 2-fold symmetric Aβ fibrils (PDB ID 2LMN(Paravastu et al., 2008)). The N-terminal domain (residues 1–16) is extended schematically in the solid line toward residues 1–8, as the structure starts at residue 9. Residues discussed in this work are labeled in black, and post-translational modification sites are shown in orange.

1.1. ²H NMR line shape using quadrupolar echo and multiple echo acquisition schemes, applications to dependence of dynamics on solvation and temperature for the wild-type Aβ fibrils

The simplest measurement that has been used for decades to obtain dynamical information is the line shape, which probes times scales on the order of $1∕C_q$. It provides a good initial estimate of the dynamics, even if additional more complicated techniques discussed in sections below may be needed for a fuller picture of the motional models and parameters, especially when the dynamics spans multiple motional modes. This technique is a pre-requisite for more advanced applications, as it provides quantitative information on the overall averaging of the quadrupolar tensor by the motional processes as well as the extent of changes with temperature, hydration, and other variables.

²H line shapes under static (non-spinning) conditions are usually collected using the quadrupolar echo (QE) pulse sequence [${{90}^{°}}_{\mathrm{x}}\text{-}\tau \text{-}{{90}^{°}}_{\mathrm{y}}\text{-}\tau$],(Antonijevic & Wimperis, 2003; Duer, 2004; Mananga et al., 2007) in which the $\tau$ delay needs to be long enough to minimize acoustical probe ringing but short enough not to lead to substantial losses due to transverse relaxation, thus usually falling in the range between 20 to 50 μs.(Vold, 1994) The power of the 90° pulses must be high enough to cover the broad excitation region of the quadrupolar pattern (i.e., the width of the solid-state NMR spectrum arising due to quadrupolar interaction). The optimal length is 2 μs, however for methyl groups this can be increased to 3 μs, if needed due to the probe’s radio frequency (RF) field strength limits. Alternatively, composite pulses can be employed. (Brown et al., 2007; Mananga et al., 2006) ²H static line shape methodology is extensively reviewed in the literature and includes extensions that utilize dependence on the $\tau$ delay length.(Molugu et al., 2017; Vold, 1994; Vugmeyster & Ostrovsky, 2017)

If the signal is too weak, one can employ MAS with rates low enough not to average quadrupolar interactions substantially, usually falling in 7 to 20 kHz MAS range.(Akbey, 2023; Shi & Rienstra, 2016) Another interesting application of MAS-based method is performing the measurements off-magic angle.(Huang et al., 2006) An additional option is to retain the static conditions and employ the multiple-echo acquisition scheme, also referred to as Quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG).(Larsen et al., 1997) The scheme employs several loops of QE cycles. Unlike MAS that modulates the spatial part of the interaction, this scheme acts on the spin part, but the resulting pattern looks similar to MAS in terms of breaking the powder pattern into a series of spikes. The level of the enhancement depends on the number of echo cycles employed, counteracted by the effects of transverse relaxation. For hydrated amyloid fibrils samples another factor to consider is the effect of RF heating, which needs to be minimized to maintain sample integrity and hydration level. This constrains the number of echo cycles to around 15.

Figure 2A displays the simulated Pake (powder) pattern for a methyl group undergoing fast methyl rotations, reducing the effective $C_q$ to 53.3 kHz, but otherwise participating in no other motions. Motions that fall within the time scale of $C_q$ modify this powder pattern. Figure 2B shows examples for core methyl groups in Aβ_1-40 fibrils in the 2-fold symmetric polymorph in the dry lyophilized state and in hydrated state of 100% by weight, using deuterium depleted water.(Au et al., 2019; Vugmeyster, Clark, et al., 2016) The line shape measurements enabled to assess the effect of hydration, which is minimal for V36 and rather substantial for the M35-CD₃ site, indicating that hydration enhances dynamics at this site.

Figure 2.

A) Deuteron solid-state NMR Pake pattern with the effective quadrupolar constant of $C_q=53.3\text{kHz}$, simulated using EXPRESS.(Vugmeyster et al., 2009) B) ²H static NMR line shapes in hydrated (red) and dry (black) Aβ_1-40 fibrils deuterated at either M35 (at 310 K) or V36 (at 294 K) methyl groups, collected using the QE pulse sequence at 17.6 T.(Vugmeyster, Clark, et al., 2016) C) ²H static NMR line shapes at different temperatures for the G9-CD₂ and M35-CD₃ sites of Aβ_1-40 fibrils, collected at 17.6 T.(Au et al., 2019; Vugmeyster, Clark, et al., 2016) D) ²H static NMR spectrum with the use of QCPMG detection scheme, for the G9-CD₂ site of Aβ_1-40 fibrils generated in the presence of synaptic plasma vesicles.(Liliya Vugmeyster et al., 2024) The data were collected at 310 K and 9.4 T using the echo period of 63 μs and utilizing 15 echo cycles.

Further, as illustrated in Figure 2C for the hydrated M35 and G9 sites temperature dependence of the line shape can illuminate the reduction of motions with temperature. While for the M35 site the motions were attributed to rotameric interconversion, for the G9-CD₂ site belonging to the flexible N-terminal domain, the motions stem from the concerted fluctuations of the entire domain.(Au et al., 2019) G9-CD₂ site is a challenging to probe due to the wide powder pattern. Unlike the case of methyl groups, the ${\mathrm{C}}^{\alpha }{\mathrm{D}}_2$ site does not possess motional narrowing due to fast motions, thus for this site the $C_q$ value is around 175 kHz. Additionally, the label is CD₂ in comparison to the CD₃ for the methyl group, which leads to further reduction in sensitivity, and thus this group is a good candidate for the employment of sensitivity enhancement methods. An example of QCPMG detection is shown in Figure 2D, applied to the G9-CD₂ group in Aβ fibrils generated in the presence of synaptic plasma vesicles which required to work with a smaller amount of peptide.(Liliya Vugmeyster et al., 2024)

Modeling of deuteron line shapes is relatively straightforward as it involves evolution of a single coherence during the acquisition time.(Greenfield et al., 1987) The simulations of dynamics are based on setting up motional frames with discrete orientations and specifying the parameters of exchange between these orientations. Each orientation is characterized by the value of the quadrupolar frequency, which is calculated from the transformation of the components of the quadrupolar tensor from its principal-axis system to the axes associated with the given orientation. The exchange is described as a matrix of Markovian jumps between the orientations. Special care must be taken to ensure accurate representation of possible orientations of C─D bonds in the molecular frame. The procedure involves assigning weights (occupation numbers) for each orientation and specifying connections between orientations, which correspond to non-zero terms in the exchange matrix. In cases where multiple nested motions are involved, their mutual orientations with respect to each other need to be considered, with faster smaller-angle motions usually set up as an initial subframe within a frame representing larger amplitude motions. A detailed example of Euler’s angle needed to set up nested frame simulations for the case of methyl fast jumps, restricted motions within rotameric wells, and large-angle rotameric jumps can be found in Vugmeyster et al.(Vugmeyster et al., 2009; Vugmeyster et al., 2011) Unless the spectra are substantially narrowed, a large number of crystallite orientations (tiles) is required to produce smooth simulated spectra, sometimes reaching tens of thousands. EXPRESS program by Vold and Hoatson(Vold & Hoatson, 2009) was created in Matlab to model the dynamics of quadrupolar nuclei in the presence of nested frames. It handles line shape simulations, as well as laboratory frame relaxation in the Redfield approximation. The Redfield approach assumes that the exchange is efficient enough to make relaxation uniform for all orientations. (Abragam, 1961)

1.2. Zeeman order longitudinal relaxation with Quadrupolar CPMG signal-enhancement scheme – application to aromatic ring flips motions.

Zeeman order ($T_1$) relaxation is a well-known tool for studies of motions, with highest sensitivity to motions that fall on time-scales in the vicinity of the Larmor frequency (${\omega }_0$).(Brown, 1982; Vold & Vold, 1991) ²H $T_1$ relaxation can be usually treated in the Redfield limit,(Abragam, 1961) simplifying simulation approaches. Techniques such as inversion or saturation recovery can be coupled with signal-enhancement approaches, such as MAS and QCPMG detection. Unlike MAS, QCPMG retains relaxation anisotropy, which can be useful in differentiating motional mechanisms.(Vold et al., 2009)

The analytical expressions for the Zeeman ($T_1$) and Quadrupolar ($T_{1Q}$) order relaxation (discussed below) are the following in case of the axially symmetric tensor:

$$\begin{gathered} \frac{1}{T_1}=\frac{3{\pi }^2}{2}{C}_q^2(J_1({\omega }_0)+4J_2(2{\omega }_0)) \\ \frac{1}{T_{1Q}}=\frac{9{\pi }^2}{2}{C}_q^2{J}_1({\omega }_0) \end{gathered}$$ Eq. 1

in which $J_1$ and $J_2$ are the spectral density functions.(Duer, 2004)

Temperature dependence of the longitudinal relaxation times reveals motional regime with respect to the Larmor frequency: if the relaxation times increase with the decrease in temperature, the corresponding motions are slower than the Larmor frequency. The relaxation time minimum occurs roughly when the motions are on the order of the Larmor frequency. If the motions are slow, techniques geared to slower time scale dynamics such as rotating frame relaxation (i.e., relaxation in the presence of RF irradiation during the relaxation period(Palmer, 2014) ) and saturation transfer, discussed below, can be in order. If the motions are very fast, they are expected to average the effective value of $C_q$ and narrow the line shapes but otherwise will be difficult to capture from the line shape and rotating frame relaxation approaches.

When multiple modes of motions constitute the dynamics, the temperature dependence of the relaxation times can also aid in pinpointing the regimes in which these modes dominate as well as the transition region. An example of such a study is shown in Figure 3, in which the side-chain dynamics of F19 ring in the Aβ_1-40 fibrils is presented.(Vugmeyster et al., 2017) One can observe the changes in the slope in the graph of $\text{ln}{T}_1$ versus the inverse temperature, in which the high temperature regime is dominated by aromatic flips, and the low temperature regime is dominated by small-angle fluctuations of the χ₂ angle, when the large-amplitude flips become too slow. In the hydrated sample (red line) the transition region is around 240 K, while in the dry sample (black line) it is shifted to a much higher temperature around 278 K. Using this approach, the activation energies of the motions can be determined, as well as the distribution of the rate constants. The distributions are reflected in the non-exponentiality of the magnetization build up curves $M(t)$ (Figure 3C), which can be fitted with the stretched exponential function. $T_1^{eff}$ shown in Figure 3A is a characteristic time constant used in fitting the stretched exponential function, and $\beta$ is the non-exponentiality parameter: $M(t)=M_{\infty }\left(1-e^{-{(t∕T_1^{eff})}^{\beta }}\right)$.

Figure 3.

²H $T_1$ longitudinal relaxation under static conditions for the F19-ring-D₅ side-chain of Aβ_1-40 fibrils.(Vugmeyster et al., 2017) A) $T_1^{eff}$ times versus inverse temperature for the wild-type fibrils in the 3-fold symmetric polymorph in either the hydrated state (red) or dry state (black), collected at 17.6 T magnetic field strength. The arrows point to the transition in the dominance of the relaxation mechanisms from the ring-flips (high temperatures) to the small angle fluctuations (lower temperatures). B) An example of the spectrum obtained with the use of the QCPMG detection, at 252 K and 17.6 T. C) An example of the non-exponential saturation recovery build-up curve, shown for the ±60 kHz spikelet positions, normalized intensity versus time, collected at 220 K and 17.6 T. The solid line indicates the fit to the stretched exponential function. D) Activation energies for the ring-flipping motions in F19 residues, obtained from the temperature dependence of $T_1$ relaxation times for the wild-type (wt) 2-fold fibrils, ΔE3 truncated fibrils, and those with pS8 modification. The black lines show the ranges within the Gaussian distribution model around the central values.(Vugmeyster, Fai Au, et al., 2021)

In this case nested frames for the small angle jumps and the aromatic flips could not be invoked, as the motions were found to be in the strong-collision limit, implying that the ring flip is accompanied by simultaneous change of the smaller-angle adjustment, meaning that the flips occur at 180°-$\alpha$ angle, where the amplitude $\alpha$ is in the 5° to 10° range. To describe the distribution of rate constants quantitatively one needs to postulate the shape of the distribution (log-normal is a natural choice), generate relaxation curves for a wide range of rates and select the central value and the width of the distribution for which simulated curves produce the same values of $T_1^{eff}$ and $\beta$ as obtained from the experimental magnetization decay curves.(Vugmeyster et al., 2013) The log-normal distribution in the rate constants corresponds to Gaussian distribution in the activation energy space, assuming the Arrhenius dependence. In case of strong non-exponentiality, it is very important to use the same relaxation times for both experimental and simulated curves. It is also necessary to make a full simulation of the experiment, including the acquisition scheme, due of the dynamical suppression of signal intensity by motions on the order of quadrupolar coupling.(Wittebort et al., 1987)

An example of the comparison of activation energies of the aromatic ring flips in the F19 side chain in the hydrated wild-type 2-fold symmetric Aβ_1-40 fibrils and two PTM variants, ΔE3 modification (truncation for the first two residues) and pS8,(Kummer & Heneka, 2014) are shown in Figure 3D(Vugmeyster, Fai Au, et al., 2021), showing a higher central value of the activation energy for the pS8 fibrils variant.

1.3. Quadrupolar order relaxation with quadrupolar CPMG enhancement – applications to detection of differences in methyl group dynamics in different polymorphs of Aβ fibrils.

Quadrupolar order relaxation has a different functional dependence on Larmor frequency compared with the Zeeman order, as can be seen from Eq. 1. Therefore, it has a somewhat different sensitivity to the motional rate constants. Due to these properties, the two types of relaxation times are complementary.

The gist of the $T_{1Q}$ pulse sequence is the creation of the quadrupolar order. The broad-band Jeener-Broekaert [${{90}^{°}}_{\mathrm{x}}-2{\tau }_{\mathrm{e}}-{{67.5}^{°}}_{-\mathrm{y}}-2{\tau }_{\mathrm{e}}-{{45}^{°}}_{\mathrm{y}}-\tau -{{45}^{°}}_{\mathrm{y}}-\text{acq}$] sequence(Hoatson, 1991; Wimperis, 1990) can be used for the excitation of the quadrupolar order in the hydrated fibrils. The value of ${\tau }_{\mathrm{e}}$ should not exceed 5 μs to minimize losses due to the transverse relaxation. An interesting example in which $T_{1Q}$ detects differences between the motions while $T_1$ does not is shown in Figure 4C. Specifically, we probed the M35-CD₃ site, which is particularly sensitive to the interface contacts between the Aβ subunits, in either the 2-fold or the 3-fold symmetric polymorphs of hydrated Aβ fibrils.(Vugmeyster, Ostrovsky, et al., 2016) $T_1$ and $T_{1Q}$ relaxation measurements were coupled with the QCPMG detection scheme for signal enhancement. Based on the comparison of the line shape and relaxation data in the 2-polymorphs, as well as the field-dependence of relaxation, we concluded that the main relaxation mechanisms driving the differences between the polymorphs in this case is diffusion within the rotameric wells, in contrast to large-angle rotameric jumps that were found similar in the two polymorphs.

Figure 4.

Quadrupolar order relaxation under static conditions at the M35-CD₃ site of Aβ fibrils.(Vugmeyster, Ostrovsky, et al., 2016) A) The most relaxed spectrum resulting from the $T_{1Q}$ series, employing the broad-band Jeener-Broekaert scheme,(Hoatson, 1991; Wimperis, 1990) collected for the 3-fold symmetric polymorph of hydrated Aβ_1-40 fibrils at 17.6 T and 253 K and utilizing the QCPMG detection block with 52 μs echo period and 15 echo cycles. B) Corresponding relaxation decay curve at the major singularities, normalized intensity versus time. C) $T_{1Q}$ times versus inverse temperature for the 2-fold (squares) and 3-fold (circles) symmetric polymorphs.

1.4. Rotating frame relaxation $T_{1\rho }$ under static and MAS conditions – applications to detection of conformational exchange of the flexible N-terminal domain of Aβ fibrils, as well as rotameric exchange.

Rotating frame relaxation can be especially sensitive to motions in μs to ms time scale range due to its dependence on spectral densities at zero frequencies.(Palmer, 2014; van der Maarel) ²H $T_{1\rho }$ experiments involve spin-locking fields (i.e., RF irradiation applied along the direction of magnetization in the rotating frame), which must be high enough to be effective for all frequencies of the line shape, but not so high as to cause RF-induced heating that can cause probe damage and/or sample damage and dehydration.(Vugmeyster & Ostrovsky, 2019) Additionally, to keep RF-induced heating controlled, larger inter-scan delays and/or heat compensation blocks can be employed. Full powder patterns of 200 kHz are difficult to lock, while those of methyl groups, with the width between the horns of the powder pattern at 40 kHz or smaller, can be locked with the RF field, ${\omega }_{RF}∕2\pi$, of about 45 kHz. If the linewidth is further reduced due to large-scale rearrangements, smaller spin-locking fields of 15-30 kHz can be employed. In this regards two variations of this experiment may provide an alternative pathway to reducing the spin-locking field: performing the measurements off-resonance(Vugmeyster, Rodgers, et al., 2023) or locking the quadrupolar order magnetization.(Vugmeyster & Ostrovsky, 2021) For the quadrupolar order relaxation measurements, it is important to ensure an adequate excitation profile with the pulse sequence blocks such as Jeener-Broekart,(Hoatson, 1991; Wimperis, 1990) as discussed in section 1.3. Rotating frame relaxation measurements are possible under MAS conditions,(Vugmeyster et al., 2022; Vugmeyster, Rodgers, et al., 2023) but it is important to select an appropriate spinning rate (${\omega }_{MAS}$) and the spin-locking field strength in such a way as to avoid rotary resonances, occurring at ${\omega }_{RF}=\frac{n}{2}{\omega }_{MAS}$. When $C_q$ is greater than the MAS rate, this condition is modified due to the incomplete averaging of the quadrupolar coupling during the rotor period: the resonance values of ${\omega }_{RF}$ shift to values smaller than $\frac{n}{2}{\omega }_{MAS}$. We have also shown that the rotating frame relaxation measurements under MAS can be coupled to the ¹³C-²H polarization transfer schemes to enable site-specific resolution in multiply labeled samples. However, special care needs to be taken to implement adiabatic transfer schemes.(Akbey et al., 2014; Jain et al., 2014; L. Vugmeyster et al., 2024)

In case of off-resonance experiment ${\omega }_{RF}$ is replaced by the effective field aligned along the tilted axis, given by ${\omega }_{eff}=\sqrt{{\omega }_{RF}^2+{\Omega }^2}$, where $\Omega$ is the resonance offset. The initial magnetization has to be aligned along the effective field using adiabatic pulses.(Vugmeyster, Rodgers, et al., 2023) Modeling of $T_{1\rho }$ experiment requires the numerical solution of the Liouville – von Neumann equations for the full set of basis coherences rather than a simpler Redfield approach. The Redfield approach is valid when the relaxation rate remains significantly smaller than the rate of motions that cause it.(Abragam, 1961) This assumption doesn’t normally hold for the rotating frame relaxation, which arises from the transitions not involving different Zeeman levels. We also found that inclusion of RF inhomogeneity profiles explicitly into the simulations significantly enhances their accuracy. In the presence of MAS, quadrupolar frequency in each site becomes time-dependent, making it necessary to calculate evolution operator for the Liouville – von Neumann equations over a rotor period. The number of time points per period depends on relative time scales of MAS rates, jump rates, and quadrupolar couplings and can be found by successive approximations with increasing number of points until convergence is reached. For constructing simulated relaxation decay curves, relaxation delay times are matched to those employed in the experiment.

One of the examples of applications of $T_{1\rho }$ measurements is shown in Figure 6, which includes cases of on and off resonances spin-locking in the static sample, as well as an investigation under MAS conditions. The method was applied to one of the most flexible sites in the N-terminal domain of Aβ_1-40 fibrils, A2-CD₃ methyl group, which has an effective quadrupolar coupling constant of 3 kHz, averaged by fast isotropic motions from its rigid methyl group value of 53-55 kHz.(Au et al., 2019; Vugmeyster, Au, Ostrovsky, & Fu, 2019; Vugmeyster et al., 2022; Vugmeyster, Rodgers, et al., 2023) Thus, under static conditions the spin lock of ${\omega }_{RF}=10\text{kHz}$ is sufficient. The maximum sampling time of 30 ms was employed as the limiting value of the relaxation delay to avoid the RF-induced heating. The resulting magnetization decay curve for the on-resonance spin-lock application, obtained via integration of the entire powder pattern, was bi-exponential in that case and the fast-relaxing component was used to simulate the dynamics (green line in panel B, Figure 6). The slow-relaxing component contribution was not well defined within the sampling time, but as we will discuss below, information on the dynamics governing the slow component could be obtained from the complementary quadrupolar CPMG measurements. The relaxation dispersion profile of the fast-relaxing component, $T_{1\rho }$ versus spin-lock field strength, is shown in Figure 6C. The relaxation dispersion profile was fitted to the 2-state exchange model. The model was interpreted as an exchange between a highly mobile state in which the N-terminal domain undergoes near isotropic diffusive motions and the more rigid state, arising likely due to transient interaction with the rigid core. The exchange rate constant, the relative population of the states, and the effective diffusion coefficient of the mobile state can be determined in this fashion.

Figure 6.

Left column: Data for A2-CD₃ site of wild-type Aβ_1-40 fibrils in the 3-fold symmetric polymorph, belonging to the flexible N-terminal region, at 310 K. Right column: Data for $\mathrm{V}12\text{-}{({\mathrm{C}}^{\gamma }{\mathrm{D}}_3)}_2$ sites of pyro-E3 fibrils, belonging to the flexible N-terminal region, at 310 K. A) ²H line shape at either static conditions (blue line) recorded at 14.1 T with the QE pulse sequence or at 8 kHz MAS recorded at 17.6 T (black line). B) An example of magnetization decay curves for ²H $T_{1\rho }$ measurements for several conditions, normalized intensity versus time: static on-resonance measurements at ${\omega }_{RF}=10\text{kHz}$ and at 14.1 T (green circles), static off-resonance measurements at ${\omega }_{RF}=15\text{kHz}$ and 35 kHz resonance offset and at 14.1 T (blue circles), and MAS measurements at 8 kHz spinning rate, and ${\omega }_{RF}=22\text{kHz}$ and at 17.6 T (black circles). For the static case the integration of the entire powder pattern was used, while for the MAS case the integration over the center-band intensity was taken. The lines represent either the mono-exponential fits (black and blue lines), or the double-exponential fits (green line). C) Relaxation dispersion profiles, $T_{1\rho }$ times versus effective spin-lock field, for the on-resonance static case depicting the fast components of the bi-exponential fits (green circles), the off-resonance static case (blue circles), and the on-resonance 8 kHz MAS case (black circles). The lines represent the best-fit simulations to the data within the 2-state model described in the text.(Au et al., 2019; Vugmeyster, Au, Ostrovsky, & Fu, 2019; Vugmeyster et al., 2022; Vugmeyster, Rodgers, et al., 2023) D) ²H line shapes under static conditions at 9.4 T collected with the quadrupolar echo sequence (black) and with the broad-band Jeener-Broekart excitation of the quadrupolar order coherence (blue). E) Corresponding $T_{1Q,\rho }$ magnetization decay curves, intensity versus time, obtained from the sum of the 5 kHz-width regions around the major singularities of the powder pattern, with the spin-locking RF field strength of 5 kHz.(Vugmeyster & Ostrovsky, 2021) The line represents the fit of the mono-exponential function with the baseline.

An example of the off-resonance $T_{1\rho }$ measurement is presented for ${\omega }_{RF}=10\text{kH}$ and the off-resonance offset of 35 kHz (blue symbols in panel B, Figure 6), displaying a much slower decay than the on-resonance case. The mono-exponential fit with the baseline needs to be used to account for the slow-relaxing components, which are not covered entirely by the limitations of the sampling times. The resulting dispersion profile (blue data in panel C, Figure 6) extends to much higher values of effective fields compared to the on-resonance case. Finally, the third example is presented for the on-resonance case performed under 8 kHz MAS spinning rate. The spinning rate is slow enough to avoid major rotary resonance conditions other than ${\omega }_{RF}∕2\pi =8\text{kHz}$. Thus, the relaxation dispersion profile can be obtained at ${\omega }_{RF}∕2\pi >8\text{kHz}$, but avoiding values of ${\omega }_{RF}∕2\pi =12$, 16, 20, and 24 kHz. With the effective quadrupolar coupling constant of 3 kHz employing a much faster MAS rate for the $T_{1\rho }$ measurements can lead to significant reduction of the effective quadrupolar contribution, which would decrease the precision of these measurements. The magnetization decay curve (black symbols in panel B, Figure 6) indicates much faster decay compared to the static case, which can be sampled with shorter relaxation delays up to 7 ms and fitted with the single exponent.

All $T_{1\rho }$ measurements led to the values of $D$ in 1.9-3.5·10⁶ rad²/s range and $k_{ex}$ in the 3·10⁴-1·10⁵ s^-1 range, using the population of the rigid state of 8% based on the static line shape analysis. Confirmation of the exchange process and quantification of $k_{ex}$ value was not possible from the line shape analysis alone. In terms of the modeling procedure, isotropic diffusion can be simulated using discreet jumps between the nearest neighbors on a grid of sites covering orientations on the two-dimensional sphere approximately uniformly, provided that the coverage is sufficiently dense (in practice, ~100 grid points is sufficient) and the jump rate between the sites is adjusted to approximate the diffusion coefficient.(Persson & Strang, 2004) The exchange with a rigid state can be modeled as jumps between the spherical sites and a fixed orientation.(Au et al., 2019)

Quadrupolar order coherence requires smaller value of RF field strength for efficient locking of the magnetization in the rotating frame.(Vugmeyster & Ostrovsky, 2021) In fact, the optimal condition for the quadrupolar order is given by ${\omega }_Q∕2\sqrt{2}<{\omega }_{RF}<{\omega }_Q∕\sqrt{2}$, in which ${\omega }_Q$ is the chosen value of the quadrupolar frequency. For methyl groups the focus is often placed on the major singularities of the powder patterns (occurring at around ±20 kHz spectral frequencies for $C_q$ in the range of 53-55 kHz), leading to the optimal value of ${\omega }_{RF}∕2\pi$ in 5 to 10 kHz range.

An example of spin-locking applied to the quadrupolar order, created with the broad-band Jeener-Broekart sequence, is shown in panels D and E of Figure 6 for the methyl groups of the V12 residue of the Aβ_1-40 fibrils with the pyro-E3 modification, performed under static conditions.(Vugmeyster & Ostrovsky, 2021) The relatively wide powder pattern (Figure 6D) can be efficiently locked with either 5 or 10 kHz spin-lock. The resulting magnetization decay curves can be fitted with the single exponential function with the baseline (Figure 6E). V12 residue is situated toward the rigid end of the N-terminal domain, and the dominant state becomes the “bound” state of Figure 8. Based on the QE line shape decomposition, there is a residual mobile free-state fraction of under 10%. However, the quadrupolar order excitation in this case is only effective for the rigid state fraction due to low effective $C_q$ value for the mobile state. The dynamics of the bound state for V12 is dominated by the rotameric exchange. The rotameric exchange constant obtained on the basis of the $T_{1\rho ,\mathrm{Q}}$ measurements is three times larger in comparison with what one obtains from the lineshape fits, underscoring the complementarity of the two approaches. These discrepancies pointed to the fact that the V12 side-chain may span a range of rotameric exchange rates and that the $T_{1\rho ,\mathrm{Q}}$ measurement could sense a somewhat different subset of these time scales compared with the line shape measurements.

Figure 8.

Motional model for the dynamics of the A2-CD₃ site (orange dot), dominated by the overall motion of the N-terminal domain.(Vugmeyster, Au, Ostrovsky, & Fu, 2019) The disordered N-terminal domain (curved line) transiently interacts with the structured C-terminal domain (blue rectangle). In the two free states, the N-terminal domain is assumed to undergo isotropic diffusion represented by the gray spheres, while in the single bound state intra- or inter-molecular interactions quench this mode. The free and bound states undergo conformational exchange on the order of 3·10⁵ s^-1 (the free state with fast diffusion) and 3·10⁴ s^-1 (the free state with slower diffusion). ²H $T_{1\rho }$ measurements were most sensitive to the slow diffusion state and its exchange with the bound state, while ²H QCPMG measurements primarily probed the faster diffusion state and its exchange process.

1.5. QCPMG time domain $T_2$ measurements – applications to the detection of conformational exchange of the flexible N-terminal domain.

Besides its application as a signal enhancement scheme, the time domain quadrupolar CPMG can be used for studies of the dynamics, as it permits the measurements of the transverse relaxation times as a function of echo spacing, yielding dispersion profiles conceptually similar to those discussed for the $T_{1\rho }$ measurements, but probing somewhat different motional time scales.(Vugmeyster, Au, Ostrovsky, & Fu, 2019) The lower limit on the spacing, ${\tau }_{qcpmg}$ is given by the RF heating considerations as well as the receiver dead times and acoustical ringing, while the upper limit is governed only by the magnitude of the $T_2$ time itself.

An example of the time-domain QCPMG signal is shown in Figure 7A for the A2-CD₃ site of Aβ_1-40 fibrils discussed above, using the echo spacing of 53 μs.(Vugmeyster, Au, Ostrovsky, & Fu, 2019) $T_2$ times were then obtained for different ${\tau }_{qcpmg}$ values, and a well-pronounced dispersion can be seen in Figure 7B. The trend of the dispersion profile is reversed from the more traditional decrease in the relaxation time with the increase in ${\tau }_{qcpmg}$ and arises due to the anisotropic nature of the quadrupolar interaction. When the experimental dispersion profile is fitted to the 2-state model above, very different values of the parameters are obtained in comparison with the $T_{1\rho }$ measurements, $D=1\cdot {10}^8{\text{rad}}^2∕\mathrm{s}$ and $k_{ex}=3\cdot {10}^5{\mathrm{s}}^{\text{-}}$. Both values of $D$ and $k_{ex}$ are orders of magniute larger, indicating that QCPMG measurements probe a different and even more mobile free state of the N-terminal domain. This example underscores the complementarity of the two techniques. Interestingly, for the G9 site we have noted that the QCPMG measurement is most sensitive to the presence of the slower free state of the domain, while the $T_{1\rho }$ measurement is most sensitive to the fast one. Simulations show that this is due to the differences in the effective quadrupolar tensor parameters (without taking the averaging due to diffusion into account): $C_q=55\text{kHz}$ and $\eta =0$ for A2-CD₃ and $C_q=78\text{kHz}$ and $\eta =1$ for G9-CD₂, where $\eta$ is the asymmetry parameter. The generalized model with two different mobile states is shown in Figure 8.

Figure 7.

All data shown for the A2-CD₃ site of wild-type Aβ_1-40 fibrils in the 3-fold symmetric polymorph, belonging to the flexible N-terminal region, at 310 K. A) An example of the time-domain ²H QCPMG profile collected under static conditions with the 53 μs echo spacing and at 14.1 T magnetic field strength, normalized FID signal versus time. B) ²H QCPMG dispersion profile, $T_2$ versus the echo spacing ${\tau }_{qcpmg}$. The lines indicate the fit to the 2-state motional model discussed in the text.(Vugmeyster, Au, Ostrovsky, & Fu, 2019) C) ²H quadrupolar CEST profiles, intensity versus resonance offset $\Omega ∕2\pi$, employing the saturation field strength of 1.3 kHz and 20 ms saturation time, collected either under the static conditions at 14.1 T and using integration over the entire powder pattern (blue circles), or under spinning conditions of 25 kHz MAS rate and at 17.6 T (red circles) and using integrated intensity of all bands.(Vugmeyster et al., 2020; Vugmeyster, Ostrovsky, et al., 2021) The lines represent the best fit simulations to the 2-state model for the MAS case and the 3-state exchange model for the static case, illustrated in Figure 8. The upper trace shows the corresponding ²H NMR line shape at 25 kHz MAS rate.

1.6. CEST – applications to the detection of conformational exchange of the flexible N-terminal domain, as well as differences in the rotameric exchange between wild-type and chemically modified fibrils.

²H Quadrupolar CEST is another useful technique for assessing μs-ms time scale dynamics, and is complementary to other approaches in terms of probing somewhat different time scales and sub-states.(Vugmeyster et al., 2020; Vugmeyster, Ostrovsky, et al., 2021) The basis of this technique is applying a weak RF irradiation along the x-direction to the equilibrium magnetization. The RF field, usually in the 1 to 5 kHz range, is scanned across the range of resonance offsets spanning the entire powder pattern. This yields the so-called ²H CEST profiles, intensity versus resonance offsets. The intensities can be taken either from the integration of the entire powder pattern or selected regions for the static conditions. Either all or selected spinning bands can be used in the case of MAS. It is desirable to perform the measurements for several values of the RF fields and saturation times. The CEST profiles are then matched with simulations to deduce the motional models and their parameters. As the initial magnetization is along the z-axis, the saturation pulse should be shorter than $T_1$ time. $T_1$ relaxation can also be directly included into the simulations for increased accuracy of the resulting parameters. Similarly to the $T_{1\rho }$ simulations, including RF inhomogeneity profiles into simulations increases the accuracy. Performing measurements under MAS can lead to rotary resonances that modulate the CEST profiles around the $\Omega =\frac{n}{2}{\omega }_{MAS}$ conditions. Thus, low MAS rates can lead to significant modulations of the profiles and complicate the analysis. However, high MAS rates (${\omega }_{MAS}∕2\pi \gg C_q$) will significantly average quadrupolar interaction over the rotor period and may render the method less effective. Therefore, a balance between the two effects of the MAS rates needs to be considered. The existence of the rotary resonance in the CEST profiles is not trivial and can serve as a confirmation of the existence of the exchange process itself, similar to the NERD effects observed for the dipolar interactions in spin ½ systems.(Marion et al., 2019)

An example of the ²H CEST profiles under static and 25 kHz MAS spin rate conditions is shown in Figure 7C for the A2-CD₃ site of Aβ_1-40 fibrils. In this case the saturation field was 1.3 kHz and the saturation time was 20 ms. The $T_1$ time for the methyl group is 55 ms, thus it was important to include longitudinal relaxation effects into the simulations. Interestingly, the CEST experiment can sense the two different free states detected by ²H $R_{1\rho }$ and QCPMG measurements. In fact, based on all the available data, one can observe an ensemble of free state undergoing isotropic diffusion in the range of 3·10⁶ to 1·10⁸ rad²/s and participating in the conformational exchange with the bound state, likely arising from transient inter and intra-molecular interactions. The rate constants of the exchange processes span the 2·10⁴ to 3·10⁶ s^-1 range.

Another interesting application of the ²H CEST measurements relates to the rotameric exchange at the M35-CD₃ site of Aβ fibrils. As we have seen in section 1.3, this site is sensitive to the contacts between different Aβ subunits. ²H CEST measurements were conducted for the wild-type Aβ fibrils in the 2-fold symmetric polymorph, as well as for the ΔE3 truncated and pS8 Aβ fibrils. The CEST measurements indicated that the rotameric exchange rate is increased at the physiological temperature in both types of the post-translationally modified fibrils in comparison to the wild-type, while the line shape analysis could not detect these differences.(Vugmeyster, Fai Au, et al., 2021) Additionally, the ²H CEST measurements permitted for refinement of rotameric distribution of states in comparison to the line shape measurements.

All the methods described above are sensitive to the residue positions in the Aβ fibrils, polymorphs of Aβ, post-translational modifications and mutations. The immediate environment of the primary sequence, the overall flexibility of the domains and inter-chain contacts play important roles in defining mobilities at different sites. The choice of the method depends largely on the time scales of the motions. For example, the flexibility of the N-terminal domain leads to concerted slower fluctuations, which are most amenable to methods described in sections 1.4-1.6 while more local motions such as fast methyl rotations can be probed by methods of sections 1.2-1.3. Thus, the site-dependent flexibility of the N-terminal domain and the influence of mutations and PTM was assessed by ²H $R_{1\rho }$, QCPMG, and CEST approaches,(Au et al., 2019; Vugmeyster, Au, Ostrovsky, Kierl, et al., 2019; Vugmeyster, Fai Au, et al., 2021; Vugmeyster, Ostrovsky, et al., 2021; Vugmeyster et al., 2022; Vugmeyster, Rodgers, et al., 2023) while phenylalanine aromatic ring flips and methyl group rotations and their comparisons in different polymorphs of the wild-type Aβ or in the presence of PTM were assessed by laboratory frame relaxation.(Vugmeyster, Clark, et al., 2016; Vugmeyster, Ostrovsky, et al., 2016; Vugmeyster et al., 2017) In some cases, the combination of longitudinal and rotating frame relaxation or CEST can provide the most precise view, as was the case for assessment of rotameric jumps in M35 and V12 residues in the wild-type Aβ and its various PTM.(Vugmeyster & Ostrovsky, 2021; Vugmeyster et al., 2020; Vugmeyster, Ostrovsky, et al., 2023)

2. ¹⁷O static solid-state $T_1$ and $T_{1\rho }$ relaxation methods for determination of hydration shell dynamics in Aβ fibrils.

In this section we will demonstrate how ¹⁷O nuclei can be used for studies of dynamics in hydration shells of amyloid fibrils, when ¹⁷O-enriched H₂O is used for rehydration of lyophilized fibrils. For static samples about 8-15 mg of protein lead to optimal sensitivity, if the ¹⁷O isotopical enrichment of water is about 70%. Lower enrichments can be used at the expense of larger amounts of peptide.

In analogy to ²H nucleus methodology, the studies of dynamics using ¹⁷O nuclei can utilize line shapes and multiple relaxation measurements, which are sensitive to different motional regimes.(Dai et al., 2025; L. Vugmeyster et al., 2024) For probing hydration shells dynamics using $T_2$ and $T_{1\rho }$ measurements, one needs to include proton decoupling during the relaxation time period to remove at least the heterogeneous ¹H-¹⁷O coupling. Further, for $T_{1\rho }$ measurements the decoupling needs to be in continuous wave (cw) mode to exclude additional phase modulation of ¹⁷O coherence during the spin-locking period.(Jaroniec et al., 2001)

When the temperature of the rehydrated fibrillar/oligomeric samples is below the bulk freezing point, one expects a heterogeneous distribution of water layers in terms of their mobility, in which some layers can retain large-scale isotropic reorientations leading to effective averaging of ¹⁷O $C_q$ to values close to zero. Thus, one can exploit multiple-pulse filtering techniques based on the differentiating $C_q\sim 0$ or $C_q\gg {\omega }_1$ values (where ${\omega }_1$ is the amplitude of the RF field used in the excitation pulse), such as the TRIP technique developed by Wang et al. (Wang et al., 2021; Zhang et al., 2022). Further, it is often useful to focus on the narrow central transition of the spin 5/2 manifold.(Wu, 2019) Saturation of the first satellite transitions can be achieved by ten pairs of Gaussian pulses of 10 μs duration with the ±300 kHz offset, spaced at 1 μs intervals, referred to as the “RAPT block”, which is an extension of prior scheme by Haase et al.(Haase et al., 1994). These types of filters can be incorporated in the line shapes and relaxation measurements, and an example is shown for the $T_{1\rho }$ pulse sequence in Figure 9. The spin locking field in the range of 20-40 kHz is optimal to lock the central transition.(L. Vugmeyster et al., 2024)

Figure 9.

The pulse sequence for measurements of ¹⁷O NMR CT $T_{1\rho }$ relaxation times: the heat compensation period consists of the spin-locking pulse of duration ${\omega }_{RF}(\max -T)$, where max is the maximum relaxation delay during the data collection and $T$ is the variable relaxation delay, followed by the inter-scan delay $d_1$, the RAPT suppression(Haase et al., 1994) of satellite transitions consisting of loops of off-resonance Gaussian pulses(Yao et al., 2000) applied at the offsets of ±300 kHz; this is followed by the excitation TRIP sequence (Wang et al., 2021), shown here for the case of the 3-pulse TRIP, with the duration of the pulses of either 60° or 30° for the $C_q\sim 0$ or $C_q\gg {\omega }_1$ subspaces of states, respectively. Typical values of ${\omega }_1$ are around 40 to 50 kHz. This is followed by the spin-lock period with the variable delay, ${\omega }_{RF}(T)$, applied at the center of the spectrum (on-resonance) with the spin-locking RF field amplitude of 35 kHz in our case. The FID collection immediately proceeds the spin-lock period. During the heat compensation and relaxation periods, cw proton decoupling is applied in several cases at low temperatures. TPPM proton decoupling(Bennett et al., 1995; Fu, 2009) is applied during the acquisition. Modifications of the pulse sequence can include a) Hahn echo(Hahn, 1950) detection at low temperatures immediately proceeding the spin-locking period.; b) the 7-pulse TRIP variation instead of the 3-pulse TRIP if a higher level of selection is needed at intermediate temperatures. The phase cycle of Vega(Vega, 1992), employed here, which cancels equilibrium population of states and minimizes the dependence of the relaxation rates on the initial conditions.

We will now discuss examples of these types of data for Aβ_1-40 fibrils with the pyro-E3 modification. Specifically, we will discuss the temperature range below 250 K, due to intriguing features of hydration shells’ behavior in this range. We have recently demonstrated that in globular HP36 protein there is a distinct separation of water behavior in the layer in the immediate proximity to the protein surface versus other remote layers. Qualitatively similar features are seen for Aβ fibrils and are most apparent from ¹⁷O CT $T_1$ relaxation build-up curves, obtained via saturation recovery technique: the build-up curves are strongly non-exponential, with relaxation times different by orders of magnitude. For example, at 196 K the fast relaxing component, whose fraction is 20%, is 110 ms, while the slow-relaxing component is 27 s. An accurate sampling of such long components requires long relaxation time periods and can be easily missed if inadequate relaxation time delays are used. On the other hand, short components require sufficient relaxation delay times sampling in the 1-200 ms range as well as employing a short saturation delay time of about 50 μs. $T_{1\rho }$ curves, obtained using the pulse sequence shown in Figure 9, are also bi-exponential. The separation of the time scales is not as drastic as for the case of $T_1$ relaxation but is still rather significant: the fast component is 0.9 ms at 196 K and the slow relaxing component is 27.5 ms. The spin-locking field of 35 kHz was applied to lock the central transition. The RF duty cycle of the probe precludes the use of long relaxation delays beyond 15-50 ms depending on the probe design, thus limiting the extent of sampling.

For quantitative analysis, $T_1$ and $T_{1\rho }$ magnetization build-up/decay curves were fitted to the bi-exponential functions

$$\begin{gathered} M(t)=M_0+(M_{\infty }-M_0)\left(1-p_{fast,T_1}{e}^{-t∕T_1^{fast}}-(1-p_{fast,T_1})e^{-t∕T_1^{slow}}\right) \\ M(t)=M_0\left(p_{fast,T_{1\rho }}{e}^{-t∕T_{1\rho }^{fast}}-(1-p_{fast,T_{1\rho }})e^{-t∕T_{1\rho }^{slow}}\right), \end{gathered}$$ Eq. 2

in which $T_{1\rho }^{fast}$, $T_1^{fast}$ are the fast relaxing components and $T_{1\rho }^{slow}$, $T_1^{slow}$ are the slow relaxing components, $p_{fast,T_1}$ and $p_{fast,T_{1\rho }}$ are the fractions of the components relaxing with the times $T_1^{fast}$ and $T_{1\rho }^{fast}$ respectively, relative to the ones relaxing with the times $T_1^{slow}$ and $T_{1\rho }^{slow}$ respectively.

For both $T_1$ and $T_{1\rho }$ measurements we have employed the TRIP filter discussed above to select only the substates with $C_q\gg {\omega }_1$, as well as 70 kHz cw decoupling during the relaxation period. The selection of large $C_{\mathrm{q}}$ substates of water implies that any unfrozen (supercooled) water contributions are filtered out. Thus, the separation of the dynamics presented in the data of Figures 10 and 11 relate to the hydration layers for which isotropic motions are no longer present. The interpretation of the relaxation data originates from the assumption of different layers giving rise to the slow and fast components, in analogy to the detailed analysis performed for the globular HP36 protein:(Vugmeyster et al., 2025) the tightly bound layer of the protein for the $T_1^{fast}$, the slowly-relaxing bulk layers for the $T_1^{slow}$, and the interaction between the tightly bound layer and its neighboring (remote) layer giving rise to the non-exponentiality of the $T_{1\rho }$ relaxation. The schematic representation of the layers is given in Figure 12. The presence of the exchange between the layers was the most logical model based on the hydration dependence of ¹⁷O and ²H $T_1$ and $T_{1\rho }$ relaxation in HP36 protein. The exchange rate constant between the tightly bound layer remote layers can be extracted from the $T_{1\rho }$ data using the McConnell model.(McConnell, 1958). The fraction $p_{fast,T_{1\rho }}$ is the fraction of the tightly bound layer relative to the remote layers, while $p_{fast,T_1}$ specifies the fraction of the tightly bound and remote layers relative to the bulk. The two-state models for relaxation times approximate a more complex picture of the dynamics in the fibrils. Wang et al.(Wang et al., 2017) have observed different pools of water in the wild-type Aβ fibrils above the bulk freezing point. Our combined fit of relaxation times below the bulk freezing point differentiates at least three different pools. Additionally, a careful examination of the fast-relaxing component reveals substantial non-exponentiality, indicative of heterogeneity of the dynamics within the tightly bound and remote layers, which will be a subject of future investigations.

Figure 10.

¹⁷O CT solid-state NMR data for H₂¹⁷O water in the hydration shells of Aβ_1-40 fibrils with the pyro-E3 modification with water content of 100% w/w, collected at 18.8 T and 196 K. ¹⁷O isotopical enrichment of water was 70%. A) ¹⁷O CT NMR line shape collected using the Hahn echo detection scheme(Hahn, 1950) and using TPPM(Bennett et al., 1995; Fu, 2009) proton decoupling during the acquisition, with the chemical shift referenced to tap water at 280 K. B) An example of non-exponential $T_1$ saturation recovery build-up curve, normalized intensity versus time, in which intensities are obtained via the integration of the entire powder pattern. C) An example of $T_{1\rho }$ normalized magnetization decay curve, obtained at the spin-lock field strength of 35 kHz. The solid lines in B) and C) show the bi-exponential fits of Eq. 2.

Figure 11.

Parameters obtained from the ¹⁷O NMR relaxation curves for water in the hydration shells of Aβ_1-40 fibrils with the pyro-E3 modification. A) Fast and slow relaxing components of the relaxation curves for the ¹⁷O CT $T_1$ and $T_{1\rho }$ experiments, plotted as a function of inverse temperatures, at 18.8 T magnetic field strength. B) Fractions of the fast relaxing components from the bi-exponential fits of the $T_1$ (circles) and $T_{1\rho }$ (squares) relaxation curves, plotted as a function of inverse temperatures. C) The rate constant for the exchange between the protein-bound water layer and remote layers, obtained from the $T_{1\rho }$ data. D) The rate constants for the tethered 2-site tetrahedral reorientations of the tightly bound layer, obtained from the fast-relaxing component of the $T_1$ data, using 9:1 ratio of populations (circles), and the rate constants for the small-angle fluctuations, obtained from the slow component of the $T_1$ data, assuming 15° amplitudes (squares).

Figure 12.

Motional modes used in fitting ¹⁷O CT solid-state NMR relaxation data of hydration shells in pyro-E3 Aβ_1-40 fibrils. A) 2-site tetrahedral reorientations in the tightly bound protein layer, in which one of the hydrogens pivots along the transient hydrogen bond axis due to interactions with the protein surface, with the rate constant $k_{\text{re}}$. B) Small-angle fluctuations and C) exchange between the tightly bound protein layer and remote layers. The layers are schematically shown in three categories: tightly bound, remote, and bulk, around the fibrils.

The $T_1^{fast}$ component can be fitted assuming 2-site tetrahedral reorientations of the water molecule, which are also transiently tethered to the peptide surface and thus only one hydrogen is free to change its position (Figure 12 A). The slow component must originate from small-angle fluctuations (Figure 12 C) when other larger-amplitude modes freeze out in the layers further away from the protein surface. In this case we used 15° amplitude of these fluctuations, but further constraints can originate from additional transverse $T_2$ measurements. $T_2$ relaxation times are expected to be dominated by small-angle fluctuations in the entire temperature regime and would not be useful to provide further constraints on large-amplitude motions in the tightly bound layer. Thus, for water in hydration shells of fibrils the complementarity of several ¹⁷O NMR relaxation measurements leads to a more detailed picture of the dynamics. Future advances can include ¹⁷O CEST experiments as well as performing relaxation measurements under MAS to potentially resolve chemically distinct bound water sites.

Explicit modeling of ¹⁷O relaxation data in general requires an advanced approach, which is based on numerical integration of Liouville – von Neumann equations using the basis of 36 coherences and including the exchange matrix for incoherent part of the Hamiltonian. We have previously described the details of such approach in reference (L. Vugmeyster et al., 2024). The inclusion of motional models is implemented in similarity to the case of deuterium relaxation.

While this review focuses on examples of ¹⁷O studies of Aβ hydration shells, ¹⁷O nuclei are important probes for studies of structure and dynamics of the Aβ aggregates themselves. Studies of hydrogen bonding patterns in Aβ_16-22 and Aβ_11-25 peptides is one of such examples.(Antzutkin et al., 2012) Recent advances of ¹⁷O methods under MAS that permit site-specific resolution as well as ¹⁷O-labeling strategies for amino acids and peptides will enable more studies of such nature as well site-specific studies of bound water dynamics. (Hung et al., 2022; Hung et al., 2023; Keeler et al., 2019)

Figure 5.

²H solid-state NMR pulse sequences, shown for static conditions.(Vugmeyster, 2021) A) Time-domain QCPMG: The full quadrupolar echo acquisition period (${\tau }_a$) is followed by the train of echo units (in square brackets). $d_1$ is the inter-scan delay and ${\tau }_1$ is the pulse ringing delay ${\tau }_{qcpmg}={\tau }_a+2{\tau }_1+{90}^{°}∕2$. Modified from Larsen et al.(Larsen et al., 1997) B) $T_{1\rho }$: the block denoted by “${\omega }_{RF}(\max -T)$” is designed to provide heat compensation; the preparation 90° pulse produces transverse magnetization and is followed by a variable spin-lock delay ${\omega }_{RF}(T)$.(Vugmeyster & Ostrovsky, 2019) Detection is preceded by the quadrupolar echo. C) Q-CEST: The low power RF saturation pulse ${\omega }_{RF}(T,\Omega )$ acting on the longitudinal coherence is followed by the QE detection.(Vugmeyster et al., 2020) For MAS measurements, the QE detection is replaced by a single 90° pulse.