The relayed nuclear Overhauser effect in magnetization transfer and chemical exchange saturation transfer MRI

Abstract

Magnetic resonance (MR) is a powerful technique for noninvasively probing molecular species in vivo but suffers from low signal sensitivity. Saturation transfer (ST) MRI approaches, including chemical exchange saturation transfer (CEST) and conventional magnetization transfer contrast (MTC), allow imaging of low-concentration molecular components with enhanced sensitivity using indirect detection via the abundant water proton pool. Several recent studies have shown the utility of chemical exchange relayed nuclear Overhauser effect (rNOE) contrast originating from non-exchangeable carbon-bound protons in mobile macromolecules in solution. In this review, we describe the mechanisms leading to the occurrence of rNOE based signals in the water saturation spectrum (Z-spectrum), including those from mobile and immobile molecular sources and from molecular binding. While it is becoming clear that MTC is mainly an rNOE based signal, we continue to use the classical MTC nomenclature to separate it from the rNOE signals of mobile macromolecules, which we will refer to as rNOEs. Some emerging applications of the use of rNOEs for probing macromolecular solution components such as proteins and carbohydrates in vivo or studying the binding of small substrates are discussed.

1. Introduction

One of the most powerful aspects of magnetic resonance (MR) is its ability to differentiate molecules based on their chemical and physical environments. The direct detection of signals from nuclear spins (especially protons) in solute molecules is the foundation of most MR spectroscopic methods, but their low concentration in vivo limits such methods to large voxel sizes (mL range for protons) and/or scan times that are excessive from a clinical point of view. It is possible to enhance the sensitivity by several orders of magnitude using indirect detection via the abundant water proton pool, relying on the principles of continuous or rapidly-repeated radiofrequency (RF) based magnetic labeling followed by recurrent magnetization transfer (MT) events that include replenishing the original spin pool. These approaches, pioneered by Balaban and Wolff,^1,2 are being used in the context of MRI to detect the hidden presence of immobile macromolecules in vivo (conventional magnetization transfer contrast, MTC)² and to image low-concentration solute molecules via a wide range of methods encompassed by the chemical exchange saturation transfer (CEST) terminology (see other articles in this issue).^3-9 Analogous to MR spectroscopy, the frequency-specific features of CEST and MTC effects can be visualized by acquiring an “absorption-like” spectrum reflecting the water signal saturation as a function of irradiation (magnetic labeling) frequency, which is defined as a Z-spectrum¹⁰ (Figure 1C).

Figure 1.

¹H NMR spectrum and Z-spectrum for glycogen. (A) Chemical structure and proton assignment of glycogen. (B) One-dimensional ¹H NMR spectrum of glycogen (100 mM, pH 7.4). (C) Z-spectrum for rabbit liver glycogen solution (300 mM glucose unit, pH 7.4, 20 °C.) The bottom row shows the residual signal after subtracting out the fitted direct water saturation signal from the Z-spectrum. Reproduced with permission from Zhou et al., Proc Natl Acad Sci USA 2020; 117; 3144-3149.

In CEST MRI, saturation is transferred using chemical exchange, a principle first demonstrated by Forsen and Hoffman,¹¹ who used saturation transfer to quantitatively extract rates of exchange. It is now well established that the signal enhancement measured in water Z-spectra is not limited to exchange transfer. This can be concluded from signals occurring in the aliphatic proton range when studying mobile macromolecules such as glycosaminoglycans (GAG)¹², proteins¹³, and glycogen¹⁴ (Figure 1). The “signal-enhancement-via-water” principle can be extended to any spin pool that is magnetically coupled to water, as long as a prolonged perturbation of spin magnetization in targeted molecules coincides with a continuous transfer of magnetization.⁴ Non-exchangeable protons, e.g., carbon-bound aliphatic and aromatic protons, can transfer magnetization to nearby dipolar-coupled protons via cross-relaxation, a phenomenon known as the nuclear Overhauser effect (NOE).¹⁵ Depending on the proximity in space of the coupled nuclei (see details below) and speed of rotational motion of the nuclear group, the rates of cross-relaxation can vary from a few times per second in liquid to hundreds of thousands times per second in the solid.

Magnetization transfer between tissue molecules and water can occur via a single direct step (e.g., proton or water exchange, Figure 2A) or involve multiple magnetization transfer pathways (Figures 2B-E). An example of the latter are NOEs originating on aliphatic protons^12,14,16, followed by proton or water exchange, so-called relayed NOEs or rNOEs (Figures 2B-D). Consequently, in vivo Z-spectra contain signals from exchangeable (CEST effects) and non-exchangeable (rNOEs) proton pools. It is now understood that MTC effects are mainly rNOEs, but they may also contain some direct CEST effects from exchangeable protons or water bound in the solid. However, we will keep using the established MTC terminology from the literature. Utilizing a dual-frequency saturation, inhomogeneous MT (ihMT, Figure 2D) is recognized as a new contrast mechanism with improved specificity for aligned structures such as myelinated tissues.¹⁷ Molecular binding can also generate rNOEs to water (Figure 2E), which will be referred as the IMMOBILISE effect.^18,19

Figure 2.

Examples of possible magnetization transfer pathways and signal enhancement in MT MRI. The selective irradiation of mobile or immobile molecular components with a radiofrequency (RF) pulse causes signal decreases in water via mechanisms including chemical exchange (A), relayed NOE (B), MTC (C), inhomogeneous MT (D) and rNOE after binding (E). In (C), the RF irradiation was placed on ─CH, but in principle, RF on ─OH is also a substantial source of MTC effect.

Of these multiple signal sources in the Z-spectrum, the magnetization transfer from non-exchangeable protons to water via rNOEs has recently shown to be useful in specifically detecting macromolecules such as proteins^13,20-23, carbohydrate polymers^12,14, and membrane lipids²⁴. Its successful application is showing early potential for the evaluation of a variety of disorders, including osteoarthritis¹², cancer^13,25, stroke²⁶, renal disease²⁷, Alzheimer’s disease²³, and spinal cord injury²⁸. This review article outlines the mechanisms and underlying theory of rNOE contrast, the different types of rNOE MRI experiments, and potential applications.

2. Magnetization transfer mechanisms

In this section, we describe the two primary components of the rNOE magnetization transfer processes, chemical exchange and cross-relaxation.

2.1. Chemical exchange

Chemical exchange is defined as the exchange of a nuclear spin pool between different magnetic environments, i.e., a terminology based on the chemical shift in NMR spectra caused by differences in magnetic susceptibility that affect the local field around the nucleus. This can include proton exchange between molecules⁴, molecular exchange (bound versus free)²⁹, and even intramolecular structural exchange³⁰, e.g., between enantiomers. Exploiting the physical exchange of protons between molecules, CEST has been used successfully for the enhanced detection (100-1,000 times the solute concentration)^4,31 of a variety of biomolecules in vivo, including proteins³¹, creatine^32,33, D-glucose^34,35, glycosaminoglycans¹², and glycogen³⁶ in a variety of diseases such as tumor^37,38, stroke³¹, Alzheimer’s^23,39, multiple sclerosis^40,41 and osteoarthritis¹². Here, we briefly recall the basic principles of CEST MRI. Readers are referred to existing reviews on CEST principles, techniques and applications ^4-9 as well as several articles in this special issue^42-46 for a more comprehensive overview.

In CEST MRI, exchangeable protons (e.g., ─OH, ─NH, ─NH₂) on solute molecules are magnetically labeled using RF irradiation after which the transfer of this label through proton exchange is detected using the bulk water proton pool (Figure 2A). At chemical equilibrium, the exchange of protons between the solute and water can be described by a two-pool model,

$$H_e\underset{k_{we}}{\overset{k_{ew}}{\rightleftarrows }}{H}_w$$ [M1]

In these two pools, “e” denotes exchangeable protons in the solute and “w” indicates water. Thus k_ew and k_we are the unidirectional exchange rates for these two protons pools. This notation differs slightly from the typical CEST literature, where the index “s” is used for solute. However, the general models for rNOE discussed below require the inclusion of both aliphatic and exchangeable protons in the solute. We therefore now use “e” and “a” to indicate exchangeable and aliphatic protons in the solute, respectively. In addition, capital letters E, W, A are used to indicate magnetization for the three pools. The CEST effect is measured as an accumulating decrease in the water signal upon a RF labeling applied on H_e (with a pulse amplitude of B₁ and an offset corresponding to the H_e resonance frequency). This is due to the fact that, as a consequence of the pool size difference, every labeled solute proton is replaced by a fully magnetized (non-labeled) water proton, after which the process repeats itself. The CEST effect size that can be achieved depends on the experimental labeling parameters (e.g., RF pulse amplitude B₁ and duration). Under the condition of slow exchange on the MR time scale and continuous labeling, we can derive the following analytical solution for the CEST effects from the Bloch-McConnell^47,48 equations:

$$CEST\equiv \frac{(W_{z,0}-W_z)}{W_{z,0}}=\frac{E_{z,0}-E_z}{E_{z,0}}\cdot k_{ew}{T}_{1w}\cdot \frac{E_{z,0}}{W_{z,0}}\approx \alpha \cdot \beta \cdot f$$ [1]

where W_z,0 is the equilibrium z-magnetization before RF labeling (corresponding to M_0w often used in the CEST field⁴⁸) and W_z the z-magnetization during labeling. α is the saturation efficiency of RF on H_e, $\alpha =\frac{E_{z,0}-E_z}{E_{z,0}}\approx \frac{(\gamma B_1{)}^2}{(\gamma B_1{)}^2+(k_{ew}{)}^2}$,⁴ and maximal saturation efficiency (α = 1) can be reached with sufficient RF strength γB₁ ≫ k_ew ; β is the signal enhancement ratio due to magnetization transfer, $\beta =\frac{k_{ew}}{R_{1w}+k_{we}}\approx k_{ew}\cdot T_{1w}$, where R_1w = 1/T_1w is the water longitudinal relaxation rate; f is the equilibrium magnetization fraction of the solute exchangeable proton and water proton pools, $f=\frac{E_{z,0}}{W_{z,0}}=\frac{[H_e]}{[H_w]}=\frac{k_{we}}{k_{ew}}=\frac{n_e[solute]}{2[H_{2}O]}$, in which n_e is the number of exchangeable protons on the solute. Thus, a large signal enhancement ratio of k_ew · T_1w (up to about 10,000 times in theory) can be realized in the CEST effect, and the largest CEST effect that can be obtained is modulated by the solute proton concentration, the exchange rate (highly dependent on pH⁴⁹ and temperature), and T_1w. Equation 1 describes the CEST effect under ideal steady-state conditions free of confounding competing effects. However, in the complex in vivo environment, multiple saturation transfer effects contribute to the water Z-spectrum. In practice therefore, the detection of CEST effects for targeted molecules is often confounded by MTC background, CEST-sensitive molecules with similar chemical shifts, and direct water saturation.⁸ In addition, optimal CEST detection is hard to achieve due to limitations in allowed B₁ strength in humans (thus lower saturation efficiency α) and shorter T_1w in tissue. As a result, CEST effects of bio-molecules reported in vivo are generally detected with only moderate signal enhancement ratios (up to 100-1,000 times).^33,37

2.2. Cross-relaxation

Besides the physical exchange of protons (i.e., chemical exchange), magnetization transfer can occur in the form of cross-relaxation in the presence of dipolar interaction between spins in close proximity. The fundamental physics of dipolar coupling and its relation to molecular motion were well laid out by Bloembergen, Purcell, and Pound (often quoted as BPP) in their seminal work in 1947⁵⁰. Briefly, when two protons (I and S, here we focus on ¹H only) are in close proximity, the thermal (Brownian) motion of proton S causes a local oscillating magnetic field that can induce relaxation of a nearby proton I, the relaxation rate of which is a function of molecular motions. In principle, a quantum mechanical description is needed to address cross-relaxation between coupled spins. Fortunately, the behavior of a two-spin system involving dipolar cross-relaxation was addressed by Solomon⁵¹ who modified Bloch equations to describe,

$$H_I\underset{{\sigma }_{SI}}{\overset{{\sigma }_{IS}}{\rightleftarrows }}{H}_S.$$ [M2]

where σ_SI is the dipolar cross-relaxation rate,

$$\frac{d{I}_z}{dt}=-{\sigma }_{SI}\left(S_z-S_{z,0}\right)-{\rho }_I\left(I_z-I_{z,0}\right)$$ [2]

in which I_z and S_z are the z-magnetizations of the two spins, ρ_I is the longitudinal auto-relaxation rate of spin I. The through-space cross-relaxation between two spins can be detected following the irradiation of one of the spins, e.g., S (S_z → 0 during saturation), and the subsequent signal change of I. If the spin pool magnetization reaches a steady-state ($\frac{d{I}_z}{dt}=0$), Eq. 3 can be derived to determine the enhancement of I, named the Nuclear Overhauser Enhancement or NOE, after Albert Overhauser, who first suggested it:¹⁵

$$NOE=\frac{\left(I_{z,0}-I_z\right)}{I_{z,0}}=\frac{{\sigma }_{SI}}{{\rho }_I}\cdot \frac{S_{z,0}}{I_{z,0}}=\frac{{\sigma }_{SI}}{{\rho }_I}\cdot {\eta }_S\frac{{\gamma }_s}{{\gamma }_I}=\beta \cdot f$$ [3]

β is the transfer rate based enhancement factor, while $f=n_S\frac{{\gamma }_s}{{\gamma }_I}$ describes the ratio of the amount of equilibrium magnetization in the irradiated and receiving pools, in which γ_s and γ_I are the gyromagnetic ratios of the spins and n_S is the number of equivalent S spins. A saturation efficiency can be added to this. A signal enhancement for I can be achieved from interaction with any spin system and is especially large when S is an unpaired electron, which has a much larger gyromagnetic ratio ($\frac{{\gamma }_e}{{\gamma }_H}=660$). This signal enhancement has also been used widely for nuclear hyperpolarization experiments.⁵² It is worth noting that the proton-proton NOE itself cannot achieve a very large signal enhancement (as $\frac{{\gamma }_H}{{\gamma }_H}=1$, $\frac{{\sigma }_{SI}}{{\rho }_I}$ is in range of −1 to 0.5, and n_S generally is not larger than 3-9, e.g., for a methyl group or for a ─C(CH₃)₃ moiety in compounds such as choline, respectively). However, similar to the CEST experiment, enhancement resulting from the NOE can be relayed via transfer processes to other protons while the saturation on the original proton pool is being continuously refreshed, which can build up an effect in a coupled large proton pool. An example of this is the relay of magnetization (or saturation) via proton exchange or water exchange from a molecule to water, where the effect of the magnetization perturbation accumulates, i.e., the exchange-relayed NOE (rNOE).⁴ Notice that with respect to nomenclature, NOE for a single spin pair would mean Nuclear Overhauser Enhancement, but as one often measures the effects of multiple enhancements, the abbreviation NOE is generally given as Nuclear Overhauser Effect.

The similarities in modeling of chemical exchange and cross relaxation have been discussed previously.^53,7 For CEST modeling, the same exchange rate k_ew is manifest in both longitudinal and transverse magnetization exchanges of two pools. Since we use RF saturation, our rNOE modeling describes only the results for the longitudinal components. For such Z-magnetization, cross-relaxation and chemical exchange processes can be described equivalently, namely with a single transfer rate.^53,54 Similar to the chemical exchange rate (k_ew) being important to the observed CEST effects (Eq. 1), the cross-relaxation rate σ_SI is key to the NOE (Eq. 3). It can be expressed as⁵⁴,

$${\sigma }_{SI}=\frac{1}{10}{\left(\frac{{\mu }_0}{4\pi }\hslash {\gamma }_I{\gamma }_S\right)}^2{r}^{-6}\cdot (-J(0)+6J(2\omega ))$$ [4]

where μ₀ = 4π×10⁻⁷ V s A⁻¹ m^−l is the magnetic permeability constant in vacuum and ℏ = 1.0547×10⁻³⁴ J·s is Planck’s constant (h = 6.62607015×10⁻³⁴ J·s) divided by 2π. The constant $\frac{1}{10}{\left(\frac{{\mu }_0}{4\pi }\hslash {\gamma }_I{\gamma }_S\right)}^2=5.7\times {10}^{10}{\mathrm{Å}}^6{\mathrm{s}}^{\text{-}1}$ for a pair of protons (γ_I = γ_S = 26.7519×10⁷ radT⁻¹s⁻¹).¹⁶ As cross-relaxation is induced by the local oscillating field of a neighbor, it is not surprising that the influence of the neighbor drops fast with the internuclear distance r (σ_SI ∝ r⁻⁶). This distance relationship has been used in solution NMR for solving molecular structures. J(ω) is the spectral density function, which is the probability function of finding motions at a certain angular frequency ω,⁵⁰

$$J(\omega )=\frac{{\tau }_c}{1+{{\tau }_c}^2{\omega }^2}$$ [5]

τ_c is the rotational correlation time that the involved protons are experiencing, i.e., due to both molecular motion and intramolecular motion (e.g., rotation of a ─CH₃ group). A rule of thumb is that larger molecules tend to have slower rotational motion (or larger τ_c, Figure 3), but some molecules can have flexible chains or rotating groups (e.g., ─CH₃) experiencing fast “internal motion”,⁵⁵ the correlation time of which need not depend on the overall molecular size.

Figure 3.

The effect of molecular size on MR relaxation rates. (A) NMR correlation time (τ_c) increases with molecular size. (B-D) Calculated proton cross-relaxation rate σ (B), transverse relaxation rate R₂ = 1/T₂ (C), and longitudinal relaxation rate R₁ = 1/T₁ as well as $R_1^{eff}$ (D) as a function of NMR correlation time (τ_c) from Eqs. 4-8.

The efficiency of longitudinal and transverse (T₁, T₂) relaxation^54,56 for individual spin pools without contributions from chemical exchange and cross-relaxation depends on molecular motion:

$$R_1=\frac{1}{T_1}={\rho }_I=\frac{1}{10}{\left(\frac{{\mu }_0}{4\pi }\hslash {\gamma }_I{\gamma }_S\right)}^2{r}^{-6}\cdot (J(0)+3J(\omega )+6J(2\omega ))$$ [6]

$$R_2=\frac{1}{T_2}=\frac{1}{10}{\left(\frac{{\mu }_0}{4\pi }\hslash {\gamma }_I{\gamma }_S\right)}^2{r}^{-6}\cdot (2.5J(0)+4.5J(\omega )+3J(2\omega ))$$ [7]

Based on Eqs. 4-7, we can in principle calculate the relaxation rates (σ_SI, T₁, T₂) for a dipolar coupled proton at any given magnetic field strength (ω) and molecular motion range (τ_c), as shown in Figure 3. Note here that T₁ and T₂ from Eqs. 6-7 are auto-relaxation times without contributions from other relaxation mechanisms (e.g., cross-relaxation, chemical exchange) which can be substantial and should be included when calculating “apparent” relaxation rates. For instance, for a dipolar coupled spin, the effective T₁ relaxation rate ($R_1^{eff}$) also relies on the cross-relaxation term σ_SI (Figure 3D) and is often expressed as,⁵⁷

$$R_1^{eff}={\rho }_I+{\sigma }_{SI}=\frac{1}{10}{\left(\frac{{\mu }_0}{4\pi }\hslash {\gamma }_I{\gamma }_S\right)}^2{r}^{-6}\cdot (3J(\omega )+12J(2\omega ))$$ [8]

Cross-relaxation and chemical exchange are fundamental mechanisms governing spin behavior and thus the magnitude of the rNOE and the appearance of the Z-spectrum are dependent on these rates, as will be discussed in the following section.

3. Exchange relayed NOEs

In this section, we discuss different types of rNOE experiments and the factors that influence effect size in each of these. The non-exchangeable protons in macromolecules such as proteins and semi-solids can couple with bulk water through multi-step mechanisms involving (intra- or inter-molecular) NOEs and proton (or water) exchange.^4,58 While the coupling pathways to water can be complicated and diverse (Figure 2), involving both cross-relaxation and chemical exchange, these multi-step processes are often simplified to a pseudo first-order model $H_a\stackrel{k}{\iff }{H}_{2}O$, where H_a is the labelled aliphatic proton and k can be viewed as the pseudo magnetization transfer rate to water.⁵⁹ This simple two-pool approach has been useful in the quantitative analysis of MTC⁶⁰ and cross-relaxation⁵⁹ data and in relating them to tissue properties. However, a more complete model that incorporates the different transfer mechanisms and differentiates between the NOE and proton exchange steps is needed for proper data understanding.

3.1. NOEs relayed via proton exchange

Chemical exchange relayed NOE can be generalized as a two-step process (Figure 2B-D), in which magnetization of non-exchangeable protons is transferred via a through-space cross-relaxation to a neighboring exchangeable proton and then to water via proton chemical exchange,

$$H_a\underset{{\sigma }_{ea}}{\overset{{\sigma }_{ae}}{\rightleftarrows }}{H}_e\underset{k_{we}}{\overset{k_{ew}}{\rightleftarrows }}{H}_w$$ [M3]

where H_a, H_e represent an aliphatic proton and a neighboring exchangeable proton, σ_ae and σ_ea are the “effective” dipolar cross-relaxation rates. This 3-compartment model has also been used to describe MTC processes, including both water and proton exchange, in solid-like macromolecular systems.^61,62 In a study on the rNOEs in glycogen (glycoNOEs), the above two-step model successfully described the rNOE-based magnetization transfer from molecular aliphatic protons (H_a) to water protons.⁵⁸ A general analytical solution for the rNOE signal can be derived from M3 to be,

$$rNOE\equiv \frac{\left(W_{z,0}-W_z\right)}{W_{z,0}}=\frac{A_{z,0}-A_z}{A_{z,0}}\cdot \frac{-{\sigma }_{ae}}{({\rho }_e+k_{ew})\frac{{\rho }_w+k_{we}}{k_{ew}}-k_{we}}\cdot \frac{A_{z,0}}{W_{z,0}}=\alpha \cdot \beta \cdot f_a$$ [9]

where A_z, W_z are the z-magnetizations for H_a and H_w, respectively. β is the enhancement factor, $\beta =\frac{-{\sigma }_{ae}}{({\rho }_e+k_{ew})\frac{{\rho }_w+k_{we}}{k_{ew}}-k_{we}}$; $\alpha =\frac{A_{z,0}-A_z}{A_{z,0}}$ is the saturation efficiency on H_a. f_a is the fraction of the equilibrium magnetizations of the labeled aliphatic protons and water protons: $f_a=\frac{A_{z,0}}{W_{z,0}}=\frac{n_a[solute]}{2[H_{2}O]}$, the proton concentration fraction of H_a and H_w. In addition, the concentration fraction of relaying exchangeable protons and water protons is $f_e=\frac{E_{z,0}}{W_{z,0}}=\frac{n_e[solute]}{2[H_{2}O]}=\frac{k_{we}}{k_{ew}}$, and $\frac{f_a}{n_a}=\frac{f_e}{n_e}=\frac{[solute]}{2[H_{2}O]}$. The overall rNOE signal depends on magnetization transfer rates for both steps (σ_ae and k_ew) or in case of large rate differences, on the single rate-limiting (i.e., the slowest) step. For instance, when the NOE step is rate-limiting,

$$k_{ew}\gg \mid {\sigma }_{ea}\mid \approx {\rho }_e$$ [10]

then,

$$1+{\rho }_e∕k_{ew}\approx 1$$ [11]

and (with f_e equal to $\frac{k_{we}}{k_{ew}}$),

$$rNOE=\alpha \cdot \frac{-{\sigma }_{ae}\cdot f_a}{{\rho }_w(1+{\rho }_e∕k_{ew})+{\rho }_e\cdot f_e}\approx \alpha \cdot \frac{-{\sigma }_{ae}\cdot f_a}{{\rho }_w+{\rho }_e\cdot f_e}$$ [12]

in which the two-step model is equivalent to the single-step model. A recent study by Jin et al.⁶³ used numerical simulations that include the aliphatic and exchangeable proton pool sizes to describe the rate-limiting condition (Eq. 10) more precisely. In practice, this corresponds to a small multiplier due to the limited number of aliphatic protons sufficiently near to the exchangeable pool to have a measurable cross-relaxation rate. For molecules at low concentration when ρ_w ∙ ρ_e · f_e, we have⁵⁸

$$rNOE\approx \alpha \cdot \left(-{\sigma }_{ae}\cdot T_{1w}\right)\cdot f_a$$ [13]

It is not surprising to see the similarity in the analytical solutions for the rNOE (Eq. 13, under the assumption that NOE is rate-limiting) and CEST (Eq. 1) signals.

The mobility of molecules is the key to understanding rNOE appearances in Z-spectra, especially when cross-relaxation is the rate-limiting step. For small molecules (τ_c<1 ns), cross-relaxation is dominated by the J(2ω) term (double quantum transition) and σ_SI is positive. However, the transfer rate is so small (σ less than +0.01 s⁻¹, Figure 3B) that the rNOE signal from these molecules in Z-spectra is negligibly small. For molecules that are extremely large or have limited mobility (e.g., in semi-solid and solid states), the J(0) term (zero quantum transition) dominates and cross-relaxation is very efficient (σ becomes negative and can be tens of thousands s⁻¹). However, due to extremely short T₂ relaxation times (Figure 3C), their signals are very broad, and consequently signals from semi-solid tissue components (MTC) merge into the background in Z-spectra (Figure 4C). Molecules with τ_c between 10~10⁴ ns (the green region in Figures 3A-B) and cross-relaxation rates on the order of 10~10⁴ s⁻¹ are optimal for generating frequency-specific rNOE signals that can be distinguished in Z-spectra (Figure 4B). This is similar to CEST signals which are distinguishable in Z-spectra when exchange rates are in the slow to intermediate range.

Figure 4.

Simulated rNOE (A, B) and MTC (C) signals in Z-spectra for an aliphatic proton pool (H_a) in molecules with varied rotational motion (in terms of NMR rotational correlation time, τ_c). Z-spectra were simulated using a three-pool rNOE model (M3)⁴². Here the T₁ and T₂ for aliphatic protons (H_a) and exchangeable protons (H_e) were assumed to be the same and calculated using Eqs. 6-7; Cross relaxation rates (σ) between H_a and H_e were calculated using Eq. 4. T_1w and T_2w were assumed to be 2.8 s and 1.8 s, respectively. The proton-proton distance was assumed to be 2 Å. The concentration of exchangeable protons ([H_e]) within the macromolecules (A-C) was 0.1 M, the exchange rate (k_ew) of relaying sites was 1000 s⁻¹. B₁ = 1 μT, saturation duration t_sat = 3 s.

Historically, so-called rNOE and MTC signals have been treated as separate signals in the proton Z-spectrum but from a theoretical point of view, they are similar (Figure 2). The different appearance (line-width) of the signals in Z-spectra (Figure 4) is merely due to a difference in molecular mobility (τ_c) affecting multiple spectral contributions (e.g., dipolar coupling and linewidth due to T₂).^6,64

The molecular mobility may not only affect the relaxation rates, but also the resonant frequency of protons. When molecules are in aligned media (such as crystal and large membrane) and their motions are restricted in certain orientations, residual dipolar coupling will take place and cause line-splitting (as large as several kHz) of proton signal in the NMR spectrum (Figure 2D).⁶⁵ An interesting feature of the strongly coupled protons in the aligned media is that they can be more efficiently saturated using a dual-frequency RF irradiation, compared to single-frequency saturation in routine CEST or MT experiments.⁶⁵ Utilizing the different saturation efficiencies of dual-frequency and single-frequency pulses on aligned molecules, the ihMT approach was recently proposed¹⁷ and demonstrated to successfully target myelin⁶⁶ in vivo. While the mechanism of ihMT experiments has been investigated by several studies,^67,68 it is still worth mentioning that the ihMT processes may be still dominated by the exchange relayed NOEs (Figure 2D).

3.2. NOEs relayed via bound water molecules

As described above, the magnetic label from non-exchangeable protons requires a pathway to water for signal enhancement. This coupling to water can occur via (i) exchangeable protons such as ─OH, ─NH, ─NH₂ (exchange-relayed NOE pathway), or (ii) water exchange (often designated as the “direct NOE pathway” in the MTC literature^69,70). Their respective contribution to the observed coupling between molecular aliphatic protons and water has been under debate for several decades.⁷¹

In principle, in mobile macromolecules, the relayed NOE-based magnetization transfer pathways require an exchangeable proton (H_e) or bound water that is in close vicinity (<3~5 Å) with a labeled aliphatic proton (H_a). The time (or lifetime) for dipolar coupling should be at least on the nanosecond (ns) timescale for efficient magnetization transfer (in terms of cross-relaxation rate, see Eq. 13 and Figure 3). A number of studies^72-75 have indicated that the lifetime of bound water at the molecular hydration interface (surface) is on the picosecond (ps) time scale, i.e., too short for efficient NOE cross-relaxation. Bound water with lifetimes longer than the nanosecond timescale is rarely found to exist in DNA⁷⁶, RNA⁷⁷, and protein interior space⁷⁸ thus suggesting that the “direct NOE” pathway via bound water contributes minimally to the observed signal in Z-spectra of mobile macromolecules and similarly in solid-like substances. While not the topic of this paper, we would like to point out that the lack of pH dependence of signal intensities in Z-spectra is not evidence of a direct water transfer step, as it may merely mean that the exchange step is not rate-determining.^14,49,63

3.3. NOEs relayed after molecular binding

In most cases, small metabolites are tumbling rapidly (ωτ_c ≪ 1) in solution and accordingly the intramolecular proton-proton cross-relaxation (σ → 0) is inefficient (Figure 3B) compared to chemical exchange. Consequently, rNOEs from small molecules are generally not apparent in the water Z-spectrum, but there are exceptions. rNOEs can be increased if the molecular motion is slowed, for instance, by freezing, making the solvent viscous, or through binding to an immobile component, the last of which is relevant to in vivo conditions. Upon binding to immobile receptors (e.g., on membranes), the motion of small molecules is greatly slowed leading to large rNOEs and this can be utilized in MRI for enhanced detection of binding processes. This concept was proposed and validated by Yadav et al., who dubbed it the IMMOBILISE (for “IMaging of MOlecular BInding using Ligand Immobilization and Saturation Exchange”) technique.¹⁸ It was established that even small molecules can have efficient rNOEs with water when their motions are slowed down by transient binding to immobile cross-linked bovine serum albumin (BSA). The principle of the IMMOBILISE approach is shown in Figure 2E. The IMMOBILISE phenomenon is another interesting example of how chemical exchange (in this case molecular binding) and NOE are intertwined.

In a very recent following-up study, Zhou et al.⁷⁹ derived an analytical solution describing the detailed magnetization transfer mechanisms involved in IMMOBILISE MRI and applied the method to quantify the binding constants for several examples of molecular electrostatic interaction. A three-step model was used (Figure 2E), the last two steps of which are similar to the above rNOE model (M3).

$$\mathrm{L}{\mathbf{H}}_{\mathit{a}}\underset{{\mathrm{k}}_{\text{off}}}{\overset{{\mathrm{k}}_{\text{on}}}{\rightleftarrows }}\mathrm{L}{\mathbf{H}}_{\mathit{a}}{\text{RH}}_e\underset{{\sigma }_{ea}}{\overset{{\sigma }_{ae}}{\rightleftarrows }}{\text{LH}}_a\mathrm{R}{\mathbf{H}}_{\mathit{e}}\underset{{\mathrm{k}}_{\text{we}}}{\overset{{\mathrm{k}}_{\text{ew}}}{\rightleftarrows }}{\mathbf{H}}_{\mathit{w}}$$ [M4]

where LH_a and LH_a RH_e represent a ligand aliphatic proton in the free and receptor-bound state; k_on and k_off are the ligand binding on/off rates. Magnetically labeled protons are denoted in boldface: H_a, H_e, H_w. The analytical solution for the rNOE signal from binding was established⁷⁹ and it was shown that the magnitude of the rNOEs in the Z-spectrum is a function of solute concentration and the binding strength:

$$rNOE=\alpha \cdot \frac{1}{\left(\frac{{\rho }_w}{k_{ew}}+\frac{k_{we}}{k_{ew}}+\frac{{\rho }_w}{-{\sigma }_{ae}}+\frac{{\rho }_w}{k_{off}}\right)}\cdot \frac{n_a[L][R]k_{on}}{2[{\mathrm{H}}_2\mathrm{O}]k_{off}}=\alpha \cdot {\beta }^{\prime }\cdot \frac{n_a[R_T]}{2[{\mathrm{H}}_2\mathrm{O}]}\cdot \frac{[L]}{[L]+K_D}$$ [14]

where [L], [R], [R_T] are the concentrations of free ligand, free receptor and total receptor, respectively; K_D = k_off/k_on is the dissociation constant for binding. By measuring rNOE signal as a function of ligand concentration ([L]), the binding affinity (K_D) can be evaluated (Eq. 14). A major strength is that μM to mM levels of ligands can be amplified via the “MRI detectable” water signal, thus allowing potential imaging of micromolar levels of receptors with MRI. While future investigations are needed to further establish the possibility of imaging binding events in vivo, the IMMOBILISE approach in principle provides a path for probing molecular receptors in vivo via MRI.

4. rNOE signal dependence

Concentration fraction (f).

It is apparent that rNOE signals increase with the concentration of the molecules, or to be more precise, the density of “NOE relaying sites” ([H_e]) and the concentration of “neighboring” aliphatic protons ([H_a]) within the macromolecules (Eqs. 9-13). In a complex macromolecule, only aliphatic protons near an NOE relaying site would contribute substantially to the rNOE signals. In some cases, when aliphatic protons (H_a) are abundant, rNOEs can still be limited by the available NOE relaying sites (H_e).

Candidate NOE relaying sites can include: ─OH, ─NH, ─NH₂, ─COOH and ─SH (Figure 5). While very fast exchanging protons (for instance, ─COOH) cannot generate substantial CEST contrast as the high exchange rates result in low labeling efficiency (α → 0 when k_ew>> γB₁, Eq. 1), they can be NOE relaying sites, as suggested for ─COOH in a recent study⁸⁰. The residence time of an exchangeable proton (τ_e) is the inverse of its exchange rate, and is suggested to affect its effective rotational correlation time (τ_eff),^16,81,82

$$\frac{1}{{\tau }_{eff}}\approx \frac{1}{{\tau }_c}+\frac{1}{{\tau }_e}=\frac{1}{{\tau }_c}+k_{ew}$$ [15]

Figure 5.

Illustration of pK_a and k_ew ranges for different exchangeable proton types.

^a Amide proton (─C(=O)NH-), pK_a: ~ 18, Ref ⁸³; k_ew: 10 to 1,200 s⁻¹, Ref ^84-86

^b Hydroxyl proton (─OH), pK_a: 8 to 16, Ref ^87-89; k_ew: 500 to 10,000 s⁻¹, Ref ⁹⁰

^c Imino proton (=NH, secondary amine): pK_a: 8 to 11, Ref ⁹¹; k_ew: 2,000 to 8,000 s⁻¹, Ref ⁹²

^d Thiol proton (─SH): pK_a: 5 to 11, Ref ^93-95; k_ew: 270 to 104,000 s⁻¹, Ref ⁹⁶

^e Amino protons (─NH₂, primary amine): pK_a: 2 to 11, Ref ^91,97-99; k_ew: 500 to 10,000 s⁻¹,Ref ⁹⁰

^f Carboxyl protons (─C(=O)OH): pK_a: 2 to 5, Ref ^99,100; k_ew: 100,000 to 1,000,000 s⁻¹, Ref ¹⁰¹

Therefore, the upper limit of the exchange rates for the labile protons that participate in efficient rNOE transfer (that is, at least 1 ns of τ_eff) is about 10⁹ s⁻¹, a range that covers most exchangeable proton groups (Figure 5). But worth noting is that the proton exchange rate (k_ew) is highly sensitive to pH and is also a function of the acid dissociation constant (pKa) for the relaying sites. Interested readers are referred to previous work by Liepinsh et al. for a detailed understanding of factors determining the proton exchange rate.⁴⁹

pH.

Previously, there was debate as to whether the rNOE signals observed in Z-spectra are sensitive to pH or not^20,102. Studies in proteins²⁰, carbohydrates,⁵⁸ and semi-solids¹⁰³ have shown a pH dependence but other studies failed to detect signal changes when pH was varied^13,20,102. This adds confusion about the origin of the observed signals (“direct” NOEs vs. relayed NOEs). Experiments on liposomes indicate that NOE-based signals in Z-spectra are dominated by exchange-relayed NOE processes. In these experiments, MTC signals were absent in experiments on lipid bilayers (or liposomes) lacking cholesterol. Increasing cholesterol concentration (lipid rotational correlation time and the exchangeable hydroxyl protons in cholesterol) was key to introducing MTC signals to the Z-spectra.^104,105 Since cross-relaxation is not affected by pH, the pH dependence of rNOE-based signals is due to the well-known pH dependence of proton chemical exchange.⁴⁹ It is important to realize, however, that rNOE signal intensities are not always sensitive to pH. Zhou et al.⁵⁸ showed that when k_ew is not the rate-limiting step in M3, as is for instance the case for glycogen and most likely MTC of myelin in vivo, changes in exchange rate resulting from pH changes need not affect the rNOE signal. For rNOEs from molecular binding, pH effects on molecular configuration may affect the binding equilibrium and thus the measured rNOEs after binding (Eq. 14).⁷⁹

Temperature.

The influence of temperature on rNOEs is complex since separate mechanisms in the MT process are affected by temperature differently in addition to changes to the water chemical shift, longitudinal relaxation and structures of macromolecules. An increase in temperature will reduce NOE (or dipolar cross-relaxation) rates (since molecular thermal motion is faster at a higher temperature) in mobile macromolecules and the water longitudinal relaxation rate¹⁰⁶, but higher temperature increases proton exchange rates. When the NOE step is rate-limiting, rNOE size can be insensitive to small temperature changes, e.g., Zhou et al. observed little difference in the glycogen rNOE in H₂O when measured at 20 °C and 37 °C.¹⁴ This temperature insensitivity was attributed to the glycoNOE effect size being a function of −σ_ae · T_1w (Eq. 13), and that temperature fluctuations induce changes of σ_ae and T_1w on a similar relative scale but in opposite directions, thus compensating each other.¹⁴ When the chemical exchange is rate-limiting, the temperature effect on rNOEs would be similar to its effects on CEST signals, that is, signals will increase or decrease depending on how exchange rates vary by temperature and whether exchange rates are in the slow or fast exchange regime.⁴⁹ The apparent MTC rate in collagen was found to decrease initially when lowering temperature, but increased below the freezing point.¹⁰³ For macromolecules such as protein and peptides, temperature changes may also induce structural alterations (e.g., denaturation, renaturation, and aggregation), which in turn affect the proton-proton distances, and thus cross-relaxation rates and overall measured rNOEs.^22,107 For rNOE transfer through molecular binding, consideration of thermal dynamics of binding may be required.⁷⁹ Furthermore, while a 10°C temperature increase will not affect aliphatic proton chemical shift considerably, it will change water chemical shifts by about −0.1 ppm,¹⁰⁸ thus shifting the apparent rNOE positions by +0.1 ppm in the Z-spectrum, which is referenced to water.¹⁴

Experimental settings.

The simplest way of detecting rNOE signals parallels a conventional CEST experiment (i.e., prolonged irradiation of solute protons using a narrow bandwidth saturation pulse and then the readout of the water signal intensity). Most of the technical details that rNOE and CEST experiments have in common have been discussed extensively in several CEST reviews^4,7,8, for instance, correcting for B₁ and B₀ inhomogeneities, and signal quantification approaches. Here, we briefly describe general considerations and guidelines for optimizing saturation and acquisition parameters specifically for in vivo rNOE studies.

As the above equations indicate, adjusting the amplitude of the saturation pulse (B₁, Figure 6) can improve signal visibility and make quantification more straightforward, but this depends on the properties of the molecules studied. Similar to the detection of CEST signals, a sufficiently long (several seconds) RF pulse with high saturation efficiency (i.e., α →1) is required for a large signal size. However, unlike CEST labeling, non-exchangeable protons are irradiated in rNOE experiments. As a consequence, high labeling efficiencies can be achieved with relatively low pulse amplitudes (B₁ < 1.0 μT, see Figure 6). Such low pulse amplitudes are advantageous in terms of specific absorption rate (SAR) and hardware duty-cycle limitations and minimizing conventional magnetization transfer contrast. In addition, the narrow bandwidth of low amplitude pulses improves signal specificity by reducing competing signals (e.g., direct water saturation, other CEST signals) and consequently simplifies data interpretation. In some of the earliest rNOE MRI studies in humans, it was apparent that low amplitude RF pulses (B₁ = 1.0 μT) were favorable for detecting rNOE signals at 7T^13,109. To acquire a 3-dimensional volume, a steady-state approach¹¹⁰ was used to build up a saturation steady-state and this saturation level was maintained until the whole imaging volume was acquired. More specifically, a single 25 ms sinc-Gaussian shaped RF pulse was applied prior to a partial EPI readout. By continuously repeating this acquisition scheme, the saturation level could be maintained for the whole image acquisition. However, it was realized later that such steady-state experiments increase the MTC contribution and this approach highlights white matter due to its myelin content (e.g., see Figure 7B). More recently, Zhou et al.¹⁴ used a UTE based steady-state readout with a 20 ms long Gaussian-shaped RF pulse (B₁ = 0.7 μT) to detect rNOE signals from glycogen whilst a radial readout scheme minimized motion artifacts in the liver. In a separate study on brain tumor patients at 7T, Paech et al.¹¹¹ used a saturation pulse train (five 100 ms long Gaussian-shaped pulses with 100 ms interpulse delay) with an average pulse amplitude of 0.7 μT prior to a 3D image readout. At higher field strengths (9.4T) in murine models,¹⁰² rNOE signals between −2.0 to −5.0 ppm reach a maximum when using a B₁ of around 0.6 μT (4 to 5 s long saturation pulses). At clinical field strengths (3T), low saturation pulse amplitudes with prolonged irradiation (either through long RF pulses or steady-state acquisitions) remain favorable²⁰.

Figure 6.

Simulated rNOE (at −3.5 ppm) and CEST (at +3.5 ppm) signals for small (τ_c = 10 ns) and large (τ_c = 10² ns) proteins and with slow (k_ew = 30 s⁻¹), intermediate (k_ew = 10³ s⁻¹) and fast (k_ew = 10⁴ s⁻¹) exchange rates at 11.7 T and 3 T. The three-pool model (M3) that includes water (H_w), aliphatic proton (H_a), and exchangeable proton (H_e) pools was used for simulating rNOE and CEST signals, with an additional MT pool (H_MT) for simulating MTC background. (A-F) Z-spectra with varied B₁ for different protein sizes and exchange rate (k_ew) at t_sat = 3s, B₀ = 11.7 T. (G) Representative Z-spectra with varied B₁ for large protein and intermediate exchange rate (k_ew) at t_sat = 3s, B₀ = 3 T. (H, I) The dependence of rNOE signals on B₁ at B₀ = 11.7 T and 3 T. For small proteins (τ_c = 10 ns), the transverse relaxation time (T_2a) for H_a was calculated to be 1/22 s, and the longitudinal cross-relaxation rate (σ_ae) was −9 s⁻¹). For large proteins (τ_c = 10² ns), T_2a=1/224 s, σ_ae= −90 s⁻¹. Longitudinal relaxation rate for H_a (ρ_a) equal to −σ_ae, ρ_e = ρ_a, T_2e = T_2a, Ω_a = −3.5 ppm, Ω_e = +3.5 ppm. Concentration of H_a ([H_a]) is 100 mM, [H_e]=[H_a], [H_MTC]= 10 M.

Figure 7.

Examples of CEST and rNOE signals appearing in Z-spectra of rat¹²¹ and human²⁵ brain with tumor (A, B), mouse fed liver¹⁴ (C) and rat brain with focal ischemia²⁶ (D). (A) T₂ weighted image, NOE (−3.5 ppm) map, and the representative Z-spectra for a rat brain bearing 9L gliosarcoma tumor (B₁ = 1.17 μT, t_sat = 3s). Reproduced with permission from Cai et al., NMR Biomed 2015; 28; 1-8. (B) Gadolinium contrast enhancing T₁, NOE (−3.5 ppm) map, and the representative Z-spectra for the glioblastoma patient brain (B₁ = 0.6 μT). Note that the NOE (−3.5ppm) includes residual MTC in white matter, which is therefore highlighted in the image (see text). Reproduced with permission from Zaiss et al., Neuroimage 2015; 112;180-188. (C) T₂ image, glycoNOE (−1 ppm) map, and the representative Z-spectrum for a fed mouse liver (B₁ = 0.7 μT, using an ultra-short echo CEST sequence). Reproduced with permission from Zhou et al., Proc Natl Acad Sci USA 2020; 117; 3144-3149. (D) A representative Z-spectrum for the normal tissue in a rat brain, and rNOE (−1.6 ppm) images at different time points before and after ischemia from a rat brain (B₁ = 1 μT, t_sat = 5s). Reproduced with permission from Zhang et al., Magn Reson Imaging 2016;3;1100-1106.

Relayed NOE signals can be isolated from MTC signals through differences in the transfer rate to water (when compared to other overlapping signal components) or by exploiting the dipole coupling within the solute macromolecules itself. Xu et al.¹¹² exploited the difference in saturation transfer rate for rNOE signals in brain compared to conventional MTC to filter out the latter component^112,113. Intramolecular transfer rate-based editing approaches have also been used to minimize contrast from downfield rNOE signals that overlap with APT signals.^114,115 Other groups have shown that simultaneously irradiating multiple frequency offsets provides an additional degree of freedom to separate coupled spin-systems from other signal components.^116,117 These techniques were originally proposed to remove signals from symmetric (with respect to the water frequency) broad immobile components. Recently, however, Goerke et al. developed a dual-frequency irradiation CEST (dualCEST) MRI that can selectively detect rNOEs from mobile proteins,¹¹⁸ thus providing an opportunity for evaluating the mobile fraction of the proteome in vivo. In line with expectations, the protein rNOE increased with concentration, molecular weight, and slightly with pH. When inducing unfolding, the rNOE is reduced. This technique was then demonstrated useful for examining patients with glioblastoma¹¹⁹. The detection of specific rNOE signal of mobile proteins has the potential for studying related diseases with improved specificity. Another approach that does not require symmetry to remove MTC components is the Time Domain Removal of Irrelevant Magnetization (TRIM) approach¹²⁰ in which the time domain corresponding to the Z-spectrum is used to remove components with short T₂ (MTC components) as well as the large water component.

5. Applications

The ability to detect rNOEs offers a strategy for the enhanced visualization of various molecular components in vivo (Eq. 13), for instance, proteins, carbohydrates, and membrane lipids. A number of studies (see below) have already demonstrated the presence of different rNOEs signals in Z-spectra of several tissues (Figure 7), some of which have shown potential to be used as disease biomarkers.

5.1. Molecular components and disease markers

Proteins.

In vitro studies have shown that proteins contain NOE-based coupling with hydration water⁷² and contribute rNOEs (mobile) and MTC (semi-solids) signals in Z-spectra, with the contribution from hydration water mostly small. Most of the protein side-chain aliphatic protons (─CH₂) are in the range of −2 to −4 ppm (referenced to water), with only a few aromatic (from tryptophan, tyrosine, phenylalanine) or imidazole protons (histidine) at +3 to +4 ppm. The composite backbone amide proton (─NH) signal is visible at around +3.5 ppm, but it is known from high-resolution NMR that amine and amide protons cover the range from 5 to 9 ppm. Consistent with this expected proton chemical shift distribution for protein sidechains and backbone, the Z-spectrum of bovine serum albumin (BSA, MW = 66.5 kD) shows overlapping rNOE signals and CEST signals both up-field and down-field in Z-spectra.²² Interestingly, while the +3.5 ppm peak in the Z-spectrum has generally been assigned solely to CEST effects from protein amide protons (i.e., APT), Sui et al. suggested that some amide protons may also generate rNOEs through nearby faster exchangeable protons and in this way contribute to the +3.5 ppm signal.¹²² From a mechanistic point of view, such amide rNOEs can only be significant if the cross-relaxation rate in the mobile protein (~ 10-50 s⁻¹ depending on molecular size) is faster than the amide proton exchange rate. This may be a way to access the very slow exchanging hydrogen-bonded amide protons in the protein backbone and would require other exchangeable protons to be sufficiently nearby or the protein to be very large to cause such fast cross-relaxation.

The overlapping of signals (rNOE, CEST, and MTC) from different proton groups of multiple macromolecules is a feature of Z-spectra worth noting and it poses a challenge for quantification of the spectral components. Many Z-spectrum analytical methods have been proposed. Of these, the MTR asymmetry method is most widely used for extracting CEST signals in vivo. MT ratio asymmetry (MTR_asym) spectra display the difference between the negative and positive sides of Z-spectrum³⁷, with the goal of removing symmetric contributions such as direct saturation and MTC (often thought to be symmetrical). However, it is now well realized this leads to the mixing of all of the mentioned saturation transfer effects. That this is not always bad is clear from amide proton transfer weighted (APTw) MRI, where Z-spectrum asymmetry analysis has shown great success in the study of brain tumors (see a review and recent consensus paper by Zhou et al.^123,124). However, as commented upon in another review, “The success of this approach is based on a coincidental symbiotic effect of mixing the rNOE, APT and asymmetric MTC contributions”.⁶ Analyzing up-field and down-field signals separately can be achieved by Z-spectral fitting methods such as the Lorentzian difference method (or MTR residual spectrum after removing water direct saturation)^13,125, Multiple-Lorentzian fitting¹⁴, polynomial fitting¹²⁶, AREX or MTR_Rex analysis¹²⁷ as well as exchange rate filtering approaches such as chemical exchange rotation transfer (CERT)¹²⁸ and variable delay multipulse (VDMP) MRI¹²⁹.

Figure 8 shows the processed Z-spectra for native and unfolded BSA at different pH and temperatures, using the so-called relaxation-compensated analysis of the Z-spectrum (AREX).²² These AREX spectra for proteins show that the amine proton pool signal around +2.7 to +3.0 ppm (attributed mainly to amino acids asparagine, glutamine, glutamate, and lysine) is strongly influenced by pH and temperature, confirming the sensitivity of proton exchange to the physiological environment. Protein unfolding caused by the detergent sodium dodecyl sulfate (SDS) reduces rNOE signals, which can be seen to occur both upfield and downfield. The increased protein mobility and additional loss of through-space proton-proton proximity lead to reduced cross-relaxation rates as protein unfolds. The rNOE signals between −3 to −4 ppm were found to be slightly sensitive to pH and temperature in folded, but not unfolded proteins, in line with the rNOE mechanism. Similar results have been observed when BSA is denatured by heat²³ or urea²¹. For instance, Kleimaier et al. studied the rNOEs of hepatocellular carcinoma cells in vitro in a bioreactor and found that they were decreased slightly after a mild heat shock (42 °C) and then recovered within about 100 mins.¹⁰⁷ This observation was interpreted to be linked to protein denaturation, renaturation and aggregation in these cells. It was concluded that protein rNOEs have the potential for evaluating pathological changes in protein expression and proteome structure, such as occur in cancer and neurodegenerative diseases. As is clear from the theory, the rNOEs from proteins are also linearly dependent on concentration²⁰, showing the potential of using rNOEs for the measurement of concentrations of mobile proteins in vivo. Recent dualCEST results¹¹⁸ isolating the protein rNOE signal confirmed its dependency on concentration, molecular weight, protein structure, and, to a lesser extent, pH.

Figure 8.

AREX spectra (B₁ = 0.75 μT, t_sat = 12 s) obtained from BSA solutions (A) at constant temperature and different pH values and (B) at constant pH and different temperatures. Native BSA (top row) corresponds to a concentration of 0 mM of the detergent SDS, unfolded BSA (bottom row) to an SDS concentration of 140 mM. Reprinted with permission from Goerke et al. NMR Biomed 28, 906-913, (2015).

The −3.5 ppm rNOE signal in vivo (see Figure 7), just designated as NOE in the early CEST years,^18,130 is currently being investigated for potential use as a biomarker in several diseases. Jones et al. reported that this signal was reduced in tumor regions in an astrocytoma patient compared to control tissue.¹³ Findings by Zaiss et al. using the AREX method supported these results, indicating that the −3.5 ppm rNOE signal drops significantly in tumor regions for glioblastoma patients (Figure 7B).²⁵ Heo et al. also showed rNOEs were lower in glioma than normal brain, and differed between low and high-grade gliomas.¹⁰⁹ This rNOE at −3.5 ppm has been also demonstrated to differentiate radiation necrosis and tumor progression¹³¹, inspired by earlier APT work by Zhou et al¹³². Chen et al. showed that −3.5 ppm rNOE signal changes could be linked to protein aggregation in a mouse model for Alzheimer’s disease.²³ Jin et al. showed that rNOE at −3.5 ppm was relatively constant during brain ischemia, in agreement with the insensitivity of rNOE to pH change during the initial hours of stroke.¹³³ Blood, which has large concentrations of albumin and hemoglobin also shows large rNOE signals in the aliphatic range.¹³⁴ Despite some insight from these many studies, the origin of the −3.5 ppm signal of the in vivo Z-spectrum remains complex to interpret. Jones et al. linked the −3.5 ppm resonance in vivo to mobile proteins¹³, but it is now understood that their images included substantial residual MTC effects. In line with that, Figure 7B show asymmetric MTC signal in healthy white matter (included in the NOE at −3.5ppm) but not in tumor, and a large part of the contrast change may be due to this difference in MTC asymmetry similar to for instance in APTw MRI at +3.5ppm. Several other factors such as the total water content increase,¹⁰⁹ protein size distribution¹³⁵, lipid composition^118,136 changes may also bias the interpretation. Furthermore, it is worth noting that the apparent −3.5 ppm rNOE signal is not likely from mobile proteins alone, but may include aliphatic signals from other macromolecules. For instance, Goerke et al. showed strong rNOEs at −3.5 ppm in protein-free lipids (liposome form) from purified brain tissues,¹¹⁸ and a recent study on liposomes¹⁰⁵ also shows that membranes can generate rNOEs at this frequency. In agreement with this notion, Shah et al. showed the −3.5 ppm rNOE in blood fell significantly upon lysing red blood cells, which disrupts the cell membrane structure.¹³⁴ Mougin et al. suggested rNOEs at −3.5 ppm in brain were related to myelin distribution,¹³⁷ probably due to the large MTC component discussed above. Small changes in this spectral region were found recently in an animal study of demyelination.^40,41 In addition, fat can also contribute to the apparent rNOEs at −3.5 ppm. Several fat suppression techniques^138-140 have been proposed to improve rNOE quantification in vivo.

Carbohydrates.

Sugar units can be interlinked in a variety of ways to form macromolecular carbohydrates, which serve as an energy reservoir (glycogen in animals and starch in plants) or structural components (such as glycosaminoglycan, chitin, and cellulose). The CEST approach has been extensively applied for the enhanced detection of hydroxyl protons in a variety of glucose-based macromolecular carbohydrates such as glycogen³⁶ (Figure 1), glycosaminoglycan (GAG)¹² and dextran¹⁴¹, which typically resonate around +1 ppm in the Z-spectrum. Carbohydrate rNOEs with water were first shown to appear around −1 ppm and −2.6 ppm in Z-spectra of GAG by Ling et al.,¹² thus indicating the possibility for the enhanced detection of carbohydrates via rNOEs in vivo. Recently, Zhou et al. showed glycogen rNOEs (glycoNOE) at −1 ppm in Z-spectra and used this signal to dynamically map liver glycogen concentration in vivo.¹⁴ (Figure 7C) At first glance, it may appear surprising that the glycogen nanoparticle (10-300 nm in diameter) generates rNOEs with relatively narrow linewidths. As mentioned earlier, such large particle sizes should have very slow tumbling rates and broad resonances similar to conventional MTC signals. Interestingly, the glucose chains in glycogen have fast “internal motions”, with a correlation time on the order of 10 ns,⁵⁷ making its proton resonances relatively narrow and dipolar coupling efficient at the same time. It is noteworthy that the rNOE rates (σ) in glycogen were approximately 40 s⁻¹ (varying with particle size), in contrast to the hydroxyl proton exchange rates which were about several thousand times per second at physiological pH and temperature.^49,58 Since both glycoNOE and glycoCEST signals resonate 1 ppm away from water, the slow NOE rate means the glycoNOE signal is still distinguished at 3T, while hydroxyl proton signals (glycoCEST) coalesce with water.¹⁴ This is expected to be an important advantage of using rNOE for quantifying glycogen when moving to clinical field strengths.

Lipids.

Fatty acid chains generally do not generate rNOEs in water Z-spectra, but can introduce rNOE effects at −3.5 ppm and broad MTC effects when they become membrane components (i.e., phospholipids)²⁴, as shown in purified brain lipids¹¹⁸ and liposomes^104,105. In addition to the rNOEs at −3.5 ppm¹¹⁸ and MTC background¹⁰⁴ from membrane lipids, recent studies on liposomes also showed signals at −1.6 ppm of Z-spectra.¹⁰⁵ In a series of studies, Zu and coworkers identified^26,128, characterized^125,142 this rNOE signal that also appears at −1.6 ppm in the brain in vivo and attributed its origin to membrane lipid choline²⁴. This “rNOE (−1.6)” signal (1-3% in magnitude) has been detected in normal brain tissue and decreased in tumors¹⁴², ischemic stroke lesions (Figure 7D),²⁶ and postmortem brains, and increased with the intake of oxygen.¹²⁵ Therefore, it has the potential to become a biomarker for tumors and stroke. The rNOE (−1.6) intensities were also found to vary in different regions of the animal brain and the apparent position of rNOE (−1.6) shifted to as far as −1.4 ppm after extended periods of anesthesia (with isoflurane).¹²⁵ The observation of rNOE at −1.6 ppm was later reported by Zaiss et al. in healthy human brain tissue and tumors,¹⁴³ and by Shah et al. in human blood¹³⁴.

There is still an ongoing effort to characterize the origin of the rNOE (−1.6) signal. In a recent study, Zu et al. showed membrane lipid phosphocholine units²⁴ can generate an −1.6 ppm rNOE signal in vitro, an observation also supported by Chang et al.¹⁰⁵. These authors suggested that the origin of in vivo NOE (−1.6) is from the membrane Cho phospholipids. In line with this view, the rNOE at −1.6 ppm in red blood cells was found to drop upon lysing, i.e., losing membrane structure.¹³⁴ However, it should be noted that the aliphatic protons of a few compounds such as choline, creatine, and taurine (and metabolites containing those groups) show MR signals at around −1.6 ppm away from water and could potentially contribute to the observed “rNOE (−1.6)” via the IMMOBILISE phenomenon (Figure 2E and Section 3.3). For instance, saturation transfer from solid components to total creatine (tCr = Cr + PCr) aliphatic protons was observed in animal brain and in tumor in vivo^144,145, suggesting a magnetization transfer pathway from creatine-based aliphatic protons (at around −1.6 ppm) to water in vivo. Future investigations are warranted to provide more insights into the origins of rNOE (−1.6) and to explain the observed variations of the signal in normal brain, tumors, ischemia and during anesthesia.

5.2. Molecular Binding

Ligand-receptor binding forms the basis for many biochemical processes such as cellular signaling and metabolism. As discussed above, the rNOEs after ligand binding (or the IMMOBILISE mechanism, Figure 2E) can be used for enhanced detection of ligands bound to immobile receptors. Several studies^18,19 have demonstrated the IMMOBILISE phenomenon in tubes. Figure 9 shows Z-spectra for cross-linked BSA (as a control) and two small ligands N-acetylaspartate (NAA) and lactate bound to immobile cross-linked BSA. Unlike free BSA, which shows both large rNOEs and CEST effects in the Z-spectra (Figure 8), cross-linked BSA is an immobile semi-solid and shows only MTC effects (Figure 9). When mixing cross-linked BSA with small ligands, rNOEs appear up-field in Z-spectra at the frequencies corresponding to the aliphatic protons of those ligands. The signal dependence on ligand concentration can be used for quantifying binding affinity (i.e., dissociation constant, K_D, see Eq. 14 above).

Figure 9.

IMMOBILISE data from 100 mM N-acetylaspartate (NAA) and 100 mM lactate in crosslinked BSA phantoms. Notice the high-resolution IMMOBILISE-based differences agreeing with the spectral appearance for these compounds known from MRS, namely the NAA CH₃ resonance at −2.7 ppm, CH₂ resonances between −2.2 to −2.0 ppm, and the NH resonance at 3.2 ppm (which is temperature-dependent), corresponding to the known MRS frequencies referenced to TSP at 2.0 ppm, 2.5–2.7 ppm, and 7.9 ppm, respectively. For lactate, the CH₃ and CH peaks at −3.4 ppm and −0.6 ppm (MRS: 1.3 and 4.1 ppm) respectively are visible. Reprinted with permission from Yadav et al. Sci Rep 2017; 7; 10138.

Zhou et al. recently used the IMMOBILISE approach to study the electrostatic binding of small ligands to immobile charged receptors.⁷⁹ The detailed description of the IMMOBILISE mechanism (see above) provided several useful insights for its future applications. For instance, approximately 100 μM of ligands and 1 μM of receptors (or binding sites) are required to obtain an IMMOBILISE signal of 1% which the authors set as the in vivo detection threshold. In addition, the ligand binding rate (which increases with the collision rate and the amount of available receptor sites) needs to be in the slow to intermediate (10¹ to 10⁶ s⁻¹) range to allow detection via the IMMOBILISE signal. This is similar to CEST signals which become undetectable for fast exchange; Furthermore, the approach is best suited for binding affinities (K_D) in the weak to moderate (10¹ to 10⁻⁷ M) range, which covers an important category of biologically relevant interactions, including ionic interactions, hydrogen bonds and van der Waal attractions. These insights warrant future studies including exploring in vivo applications.

It should be noted that this “NOE via binding” principle has been utilized in conventional NMR approaches (such as saturation transfer difference, STD¹⁴⁶; WaterLOGSY¹⁴⁷) for the screening of ligand binding to protein receptors. In these methods, however, the selective irradiation of protein signals¹⁴⁶ or water signal¹⁴⁷ is transferred to free ligands, the inverse process. The nomenclature of “transferred NOE” was used there, as intramolecular NOEs occur in the macromolecule before the intermolecular transfer. For IMMOBILISE, this would be incorrect nomenclature therefore. By quantifying the degree of ligand saturation, binding has been characterized for millimolar ligand concentrations (mM level). In principle, when using high-B₁ irradiation outside the liquid proton spectral range, the MTC effect to bound water or bound small molecules¹⁴⁸ is an example of transferred NOEs.

6. Conclusions and Future directions

It is becoming clear that rNOEs are an important and useful contribution to the in vivo Z-spectrum. In addition, a better understanding of transfer mechanisms indicates that both rNOEs and MTC are due to the same exchange relayed NOE coupling mechanism with water, but since dipolar coupling and relaxation rates are highly mobility-dependent, the different appearance of rNOEs and MTC are due to molecular motional differences. Changes in molecular motion, pH, and temperature can influence rNOEs but the extent depends on several factors. Very fast exchanging protons are not suited for obtaining CEST contrast but these protons are favorable for generating signals via the rNOE pathway since they can efficiently transfer magnetization to water. Further, fast exchanging protons do not rate-limit the rNOE process even when environmental factors (e.g., pH) change their exchange rates. Thus, the rNOE process can often be described by a single pH-independent transfer rate. Mobile macromolecules such as proteins, carbohydrates, and membrane lipids may contribute substantially to rNOEs in the Z-spectrum, suggesting opportunities for probing in vivo macromolecules. Importantly, the influence of environmental factors (e.g., pH and temperature) on the global and local structure and motion of these macromolecules will also affect rNOE signals. The exploitation of rNOEs to study binding is a relatively new mechanism that could be potentially utilized for receptor imaging.

Our increased understanding of rNOE pathways shows that this is an important mechanism with lots of potential future applications. The design of CEST contrast agents^3,149,150 to probe physiological disorders is a very active area of research and thus extending these approaches to designing rNOE based contrast agents may greatly expand future applications. The rNOE mechanisms discussed here point a path in the design of molecular probes for generating rNOE contrast. Traditional CEST agents require molecules that have slow exchanging protons (such as amide and guanidinium protons). However, for rNOE studies, it is possible to include macromolecules with fast exchanging protons. Macromolecular polymeric agents with a correlation time of 10-10⁴ ns may generate sufficient rNOE signals when aliphatic-exchangeable proton pairs are available, and this principle can be used to design nanoparticle-size imaging probes. For instance, dextran¹⁵¹ has already been used as a probe for tumor vascular permeability. In addition, rNOEs are being utilized to map glycogen in liver.¹⁴ Measurements of other macromolecules such as proteins²³ in vivo is in principle possible as well. Recent studies utilized rNOEs to detect binding events and show the potential for probing μM to mM levels of ligand receptors using MRI. A deepening understanding of rNOEs in Z-spectra can facilitate the discovery of new contrast agents and provide new opportunities for molecular imaging.

Abbreviations:

RF

radiofrequency

MT

magnetization transfer

MTC

magnetization transfer contrast

NOE

nuclear Overhauser effect/enhancement

rNOE

exchange-relayed/relayed NOE

ihMT

inhomogeneous MT

glycoNOE

rNOEs in glycogen

IMMOBILISE

IMaging of MOlecular BInding using Ligand Immobilization and Saturation Exchange

BSA

bovine serum albumin

SAR

specific absorption rate

MTRasym

MT ratio asymmetry

GAG

glycosaminoglycan

tCr

total creatine

NAA

N-acetylaspartate