Role of chemical exchange on the relayed nuclear Overhauser enhancement signal in saturation transfer MRI

Abstract

Purpose:

The pH sensitivity of chemical exchange-relayed nuclear Overhauser enhancement (rNOE) signal in a saturation transfer experiment is not fully understood and needs further investigation.

Methods:

A three-pool-exchange model was simulated assuming that the magnetization transfer between an NOE pool and water is relayed by a chemical exchange (CE) pool. The saturation transfer signals from bovine serum albumin (BSA) and egg white albumin (EWA) phantoms were measured with different pH or different D₂O/H₂O mixture solutions.

Results:

Simulation results showed that the rNOE signal is independent of the Larmor frequency of the CE pool, indicating any CE pool can effectively relay NOE magnetization. The rNOE signal is sensitive to a change of the CE pool size and/or exchange rate only if the CE becomes a rate-limiting step in the relay process. The rNOE signal from BSA phantoms showed larger pH-dependence at −3.0 ppm than those at −1.9 and −4.0 ppm. However, rNOE signals from aliphatic protons have much weaker pH-dependence than the CEST signal, suggesting that CE is unlikely the rate-limiting step and the rNOE signals in BSA are mainly relayed by fast exchanging protons. The existence of aromatic NOE was confirmed by proton spectroscopy.

Conclusion:

The pH-sensitivity of the rNOE signal is determined by whether the CE process is a rate-limiting step in the relay. The rNOE signal has much weaker pH-sensitivity than the CEST signal in BSA proteins, which can explain the weak pH sensitivity of rNOE in vivo.

Introduction

Chemical exchange saturation transfer (CEST) MRI has emerged as a novel molecular imaging technique because it can probe many important biomolecules such as glucose^1–4, glycogen⁵, creatine^6–9, and mobile proteins^10,11, and has shown great potential in the study of many diseases, including ischemic stroke, tumors, and cartilage degeneration^10–17. In CEST, labile protons from biomolecules of interest are saturated by selective off-resonance irradiation and the saturated magnetization is transferred to the bulk water via chemical exchange resulting in a reduction of longitudinal water magnetization. Such indirect measurement of biomolecules through their interaction with water can often provide a sensitivity enhancement of 1–3 orders of magnitude compared to detecting the biomolecules directly by spectroscopic methods.

Besides CEST signals from labile protons, recent high-field studies have shown that significant Nuclear Overhauser enhancement (NOE) features can also be detected by such a saturation transfer process in glycosaminoglycans¹⁸, glycogen¹⁹, mobile proteins^20,21, as well as in vivo data^20,22. While endogenous CEST signal is usually observed in the downfield frequency range of 0.5 to 4 ppm, NOE signal has been reported in the upfield frequency range for aliphatic protons^18,23–25, and has been suggested in the downfield frequency range for aromatic protons^26,27. The magnitude of the upfield NOE can be much higher than that of the CEST signal and may be useful in certain disease applications^28–30. The downfield aromatic NOE signal, on the other hand, may affect the quantification of some endogenous CEST signals since they overlap in their resonance frequencies.

NOE is a process of dipolar cross-relaxation between two nuclei at a close distance. There are two possible pathways for NOE, namely, direct intermolecular and exchange-relayed dipolar coupling. In exchange-relayed NOE (rNOE), the magnetization is first transferred to an exchangeable proton (such as amide, amine, or hydroxyl) on the macromolecule, which is then passed to water via chemical exchange (CE) (see Fig. 1A). Many previous studies have suggested that relayed NOE should be the dominant pathway for mobile proteins^31,32, and thus, it is generally assumed that relayed NOE applies to in vivo brain CEST studies. A very recent study of glycogen has also suggested that the NOE signal may also be relayed in some carbohydrate macromolecules^19,33.

Fig. 1. Diagram of the relayed NOE process.

(A) In the 3-pool relayed NOE model, the transfer of magnetization between water and an NOE pool with a pool size of f_NOE and a transfer rate of k_NOE (=k_cb) is relayed by a CE pool with a pool size of f_CE and transfer rate of k_CE (=k_ba). (B) Two scenarios are simulated, where the NOE is relayed by amide protons with a slow chemical exchange rate or hydroxyl protons with a fast exchange rate.

The different sources of rNOE versus CEST suggests that they should have some difference in signal properties. However, compared to CEST, signal properties of rNOE have been investigated less and are not yet fully understood. Especially, their relationship with chemical exchange, such as pH sensitivity, is still controversial^20,22. Although a relayed pathway suggests that rNOE signal from mobile proteins should be dependent on the CE process and pH, it is unclear whether the rNOE signal is mostly relayed by the backbone amide or the labile protons from side-chain residues, and whether the pH-sensitivity of rNOE signal would be comparable to those of CEST signals, such as the amide proton transfer effect (APT) in in vivo studies³⁴, or is much weaker^20,35–37.

In this work, we performed simulation studies to examine the signal properties of rNOE, including its dependence on saturation parameters, pool size, and exchange or magnetization transfer rate of the CE and the NOE pools. Phantom studies were performed in bovine serum albumin (BSA) and egg white albumin (EWA) at 9.4 T and 15.2 T to gain insights into the rNOE signals of upfield aliphatic and downfield aromatic protons. Part of our results has been reported in previous ISMRM meetings^26,38.

Methods

To evaluate the signal properties of rNOE, we considered a three-pool exchange model, i.e., the bulk water (pool a), macromolecular labile proton (pool b, defined as CE), and macromolecular aliphatic/aromatic proton (pool c, defined as NOE) pools. We assumed that NOE is relayed by chemical exchange in this study, i.e., magnetization transfer only occurs between NOE and CE pools by spin diffusion due to dipole-dipole coupling and between CE and water pools by chemical exchange (Fig. 1A), and that direct dipole-dipole interaction between NOE and water pools is negligible.

Simulations:

The exchange-relayed NOE signals were simulated with 3-pool Bloch-McConnell Equations described in the Appendix. To evaluate the effect of saturation, relaxation, and exchange parameters on the rNOE signal, typically one specific parameter was varied with all other parameters kept at their default values. The default parameters were: B₀ = 400 MHz (9.4 T), with the Larmor frequencies of the CE and NOE pools δ_CE = 3.5 and δ_NOE = −3.5 ppm^10,20, respectively, and the rate of NOE (k_NOE) = 5 s^{−1 30,39}. In order to yield an rNOE signal on the order of 10% of S₀^28,29, a fractional NOE pool size of f_NOE = 0.03 was assumed. The fractional CE pool size was assumed to be an order of magnitude smaller, i.e., f_CE = 0.003. For simplicity, the magnetization transfer effect of semisolid macromolecules is ignored, and the longitudinal and transverse relaxation rates R₁ and R₂ of protons for all three pools were assumed to be 0.5 s⁻¹ and 1 s⁻¹, respectively. Typically, the Z-spectrum was simulated from 6 to −6 ppm for a saturation power B₁ = 1 μT and saturation pulse duration t_sat = 10 s, with one parameter varied for a few selected values. To quantitatively determine the magnitude of the rNOE or CEST effect, a baseline Z-spectrum with both f_CE = 0 and f_NOE = 0 was calculated. The difference between Z-spectra with both f_CE and f_NOE of non-zero and zero values was obtained.

Endogenous labile protons which are usually detected in CEST experiments have a wide range of exchange rates^10,40, including amide (<100 s⁻¹)^10,40, guanidyl (~1000 s⁻¹)⁴⁰, hydroxyl (1000 to 5000 s⁻¹)^3,40, and amine protons (>4000 s⁻¹)^3,40. To evaluate the dependence of the rNOE signal on the CE rate, two scenarios were used in the simulation of the rNOE signal, as described in Fig. 1B: a slow chemical exchange case represented by amide protons k_ba or k_CE = 30 s⁻¹ and a fast exchange case represented by hydroxyl or amine protons k_CE = 1000 s⁻¹. To determine the dependence of rNOE signal on f_NOE·k_NOE and f_CE·k_CE (Fig. 5B below), f_NOE of 0.002 to 0.05, k_NOE of 0.1 s⁻¹ to 30 s⁻¹, f_CE of 0.0002 to 0.005, and k_CE of 10 s⁻¹ to 3000 s⁻¹ were varied. For simplicity, the exchange rate k_NOE was limited to be ≤30 s⁻¹ so that saturation efficiency with a 1 μT pulse would always be close to 1 and not decrease significantly with an increase in k_NOE.

Fig. 5. The dependence of rNOE signal on CE pool size and exchange rate in logarithms scale.

(A) The rNOE signals as a function of CE rate k_CE on Y-axis and CE pool size f_CE on X-axis in the log₁₀ scale were shown for a representative f_NOE of 0.01 and k_NOE of 5 s⁻¹. The dashed line indicates where f_CE·k_CE = f_NOE·k_NOE = 0.05. When f_CE·k_CE >> 0.05, the rNOE signal is in the red region which is insensitive to a change in either f_CE or k_CE. (B) The rNOE signal as functions of f_NOE·k_NOE and f_CE·k_CE in log₁₀ scale. The line indicates where f_NOE·k_NOE= f_CE·k_CE. In regions close to or below this line, the value of f_NOE·k_NOE is close to or larger than f_CE·k_CE, while the region far above this line has f_NOE·k_NOE << f_CE·k_CE. The magenta and black stars indicate the data points simulated in Fig. 4B and 4D, respectively. The color bar indicates the magnitude of the rNOE signal in percent of S₀ units.

Phantom Experiments:

All experiments were performed on a 9.4 T or a 15.2 T Bruker MRI system with a 38-mm volume coil (Rapid Biomedical or Bruker) for transmission and reception. Magnetic field homogeneity was optimized by localized shimming on a volume of interest. The dependence of the rNOE signal on pH and rNOE pool size was investigated in protein phantoms. Four sets of experiments were performed at room temperature as follows:

1. Saturation power-dependence of CEST vs. rNOE in BSA: 15% BSA was dissolved in phosphate-buffered saline (PBS) and titrated to pH = 5.8, 6.4, 7.0, and 7.6. Z-spectra were measured in a frequency offset range from +7 to −7 ppm with saturation power of 0.75 and 0.12 μT, and a saturation duration of 6 s.

2. pH dependency of CEST vs. rNOE in BSA at 15.2 T: 20% BSA was dissolved in PBS and titrated to 8 different pH values from 5.65 to 8.5. Z-spectra were acquired at a frequency offset range from +7 to −7 ppm with a 6-s and 0.5 μT saturation pulse.

3. CEST vs. rNOE of egg white albumin (EWA) and BSA in varied H₂O/D₂O mixture solution: 20% of EWA or 15% of BSA was dissolved in a mixture of distilled water (H₂O) with percentages of D₂O at 0, 40, 80 and 90%. The addition of D₂O reduces the proton concentration in both bulk water and the exchangeable protons in the proteins, but not the concentration of non-exchangeable aliphatic and aromatic protons. Thus, the NOE pool size increases without changing the CE pool size. In both sets of phantoms, Z-spectra were measured in a frequency offset range from +8 to −8 ppm with a saturation power of 0.25 μT and a saturation duration of 14 s. Because T₁ is strongly affected by the addition of D₂O, the T₁ of these phantoms was measured with an inversion-recovery pulse sequence.

4. Comparison of CEST versus MRS: 15% BSA was dissolved in 99.5% D₂O to enhance the rNOE signal. Z-spectra were measured with 7-s saturation with B₁ = 0.25 μT, and water-suppressed localized ¹H MR spectrum was measured by a short-TE localized stimulated-echo acquisition mode (STEAM) sequence⁴¹. Parameters were TE/TR = 6/6000 ms, NEX = 100, spectral width = 8000 Hz, number of complex data points = 2048, and the voxel size = 1×1×1 mm³.

All experiments except experiment #2 were performed at 9.4 T. CEST images were measured by a single-slice spin-echo echo-planar imaging sequence with continuous-wave RF irradiation. Crushing gradients were applied immediately following the saturation pulse to suppress residual transverse magnetization. Control images were acquired at an offset of 300 ppm for signal normalization. Imaging parameters were a matrix size of 64 × 64, a field of view of 4 cm × 4 cm, and slice thickness of 5 mm. The post-acquisition recovery time, i.e. the time between the acquisition of one saturated image and the saturation pulse of the next image, was 10 s.

Data analysis

For quantitative data analysis, Z-spectra were obtained from regions of interest selected from each phantom with a small B₀ inhomogeneity (with a B₀ shift threshold < 5 Hz). In each phantom, a Z-spectrum with direct water saturation effect (DWS) only was fitted by excluding the data in the offset range of 0.4 to 6 ppm and −0.4 to −6 ppm. Then, the fitted Z-spectrum with DWS only was subtracted from the acquired Z-spectrum to obtain a differential Z-spectrum which removed DWS and contained only the CEST and rNOE signals.

Results:

Simulation of CEST vs. rNOE at various conditions

Since CEST and rNOE signals are both indirectly detected through water, they share many similarities. Indeed, they are both sensitive to water T₁ (Fig. 2A) and are dependent on saturation duration (Fig. 2B). As expected from the 3-pool relayed-exchange model, the rNOE signal is independent of the chemical shift of the CE pool (Fig. 2C): the rNOE signal is still the same even when δ_CE is reduced to 0.1 ppm where the CEST signal is unrecognizable due to severe DWS. Concerning the parameters of the NOE pool, the rNOE signal increases with pool size (Fig. 3A) and NOE rate (Fig. 3B). An increase of the R₂ value of the NOE proton broadens the linewidth of the rNOE signal but has little effect on its magnitude (Fig. 3C). In both Figs. 2 and 3, only one CE rate of 1000 s⁻¹ was assumed.

Fig. 2. Simulation of the effects of 3 parameters on the rNOE signal.

The rNOE signals increase with (A) the T₁ of water and (B) the saturation duration in the same way as the CEST signals. (C) The chemical shift of the CE protons does not affect the rNOE signal.

Fig. 3. Simulation of the effects of 3 parameters of the NOE pool on the rNOE signal.

The rNOE signal increases with pool size (A) and NOE rate (B). (C) An increase of the R₂ of the NOE proton causes a minimal change in the magnitude of the rNOE signal but increases the linewidth.

Fig. 4 evaluates the dependence of the rNOE signal on the CE parameters assuming k_NOE = 5 s⁻¹ and f_NOE = 0.03. When the relay is through a slow CE pool, the rNOE signal increases with CE pool size f_CE (Fig. 4A) and k_CE (Fig. 4B) similarly with the CEST signal. When the relay is through a fast CE pool, the CEST signal still increases with pool size while decreases with an increase of k_CE because the saturation efficiency reduces quickly for faster exchange rates⁴². Nonetheless, the change in rNOE signal is very small in both cases (Fig. 4C, 4D).

Fig. 4. The dependence of rNOE on the CE pool size and exchange rate.

When the relay is through a slow-exchanging proton, both rNOE and CEST signal increase with CE pool size (A) and CE rate (B). When the relay is through a fast-exchanging proton, the rNOE signal is less sensitive to the CE pool size (C) and CE rate (D) than the CEST signal.

The results of Fig. 4 suggest that the rNOE signal is dependent on both f_CE and k_CE. To obtain more insight, the rNOE signal at −3.5 ppm was simulated as a function of f_CE (0.0002 to 0.005) and k_CE (10 to 10^3.5 s⁻¹) with fixed f_NOE = 0.01 and k_NOE = 5 s⁻¹ in Fig. 5A. The axes were shown in logarithmic scale so that a constant f_CE·k_CE appears in a straight line. A dashed line was plotted to show the condition that f_CE·k_CE = 0.05, which equals f_NOE·k_NOE. The same rNOE signals are observed for constant f_CE·k_CE values (parallel to the dashed line), indicating that the effect of a certain change in f_CE is the same as an equal amount of change in k_CE. When f_CE·k_CE is smaller than or comparable to f_NOE·k_NOE (regions with blue to green color), rNOE value is sensitive to a change in either k_CE or f_CE, or more generally, a change in the product f_CE·k_CE. When f_CE·k_CE >> f_NOE·k_NOE (the upper right region with red color), the rNOE value reaches a plateau and is insensitive to a change of k_CE or f_CE. A more general case was shown in Fig. 5B where f_CE·k_CE and f_NOE·k_NOE are both varied, and the black identity line indicates that f_CE·k_CE = f_NOE·k_NOE. The data points simulated in Fig. 4B and 4D were marked as 5 magenta and 4 black stars, respectively. The data points indicated by the magenta stars in the region below the black identity line (f_CE·k_CE < f_NOE·k_NOE) shows large variation in rNOE signals, because the CE process becomes a rate-limiting step. In contrast, the black stars in the region away from the identity line (f_CE·k_CE >> f_NOE·k_NOE) have the same rNOE signals and are insensitive to a change in the pH-sensitive k_CE. Thus, further rNOE simulations were performed for the slow CE condition.

Since rNOE relies on the CE process, it is important to understand the relative magnitude of rNOE versus CEST signals as a function of NOE pool size and chemical exchange rate. For simplicity, we only considered a slow CE case so that the saturation efficiency is close to 1 (and not varied with CE rate). Fig. 6A shows simulated Z-spectra with f_NOE of 0.003 to 0.1 for comparing rNOE and CEST signals. The rNOE signal increases with the NOE pool size, but is smaller than the CEST signal with a smaller CE pool size. Fig. 6B shows CEST and rNOE signals as a function of k_CE for three f_NOE values of 0.3%, 1%, and 3%. The rNOE change by k_CE modulation was less than the CEST signal change, indicating that rNOE has a weaker pH dependence than CEST.

Fig. 6. Comparison of the magnitude and k_CE-sensitivity of CEST and rNOE signals for a slow k_CE = 30 s⁻¹.

(A) the rNOE signal is smaller than the CEST signal, even when f_NOE is much higher than f_CE, and f_NOE·k_NOE is much larger than f_CE·k_CE. (B) Besides the difference in the magnitude, the slope of the rNOE signal versus k_CE is always smaller than that of the CEST signal, suggesting a weaker pH dependence.

CEST vs. rNOE of phantoms with different pH values

The pH dependence of CEST vs. rNOE signals was investigated with phantoms with varied pH. In Z-spectra of pH-dependent BSA acquired with B₁ = 0.75 μT (Fig. 7A), the downfield CEST signals at 2.8 ppm exhibited large pH-dependence due to the amine-water proton exchange from the side-chain lysine residue (k_CE = ~4,000 s⁻¹)⁴³. In contrast, the upfield rNOE signals only slightly differed for four different pH values. The CEST signal is proportional to the saturation efficiency which increases with saturation power^42,44,45. With a much smaller B₁ of 0.12 μT (Fig. 7B), the CEST signals of fast-exchanging protons decreased much more significantly than that of the rNOE, because the saturation efficiency drops much faster for a faster exchange rate. To detect pH-dependence better, DWS was removed from the Z-spectra (Fig. 7C). Three aliphatic NOE peaks can be detected at about −0.8, −2, and from −3 to −4 ppm, all of which are insensitive to pH. Downfield signals contain both the pH-sensitive CEST signal and pH-insensitive NOE of aromatic protons. Since the peaks around 2.8 ppm show very weak pH-dependence, it is likely to have large contribution from aromatic NOE. When the CEST effect is minimized by a small saturation power, the differential Z-spectra of BSA (Fig. 7C) were dominated by the NOE of aromatic and aliphatic protons which have much weaker sensitivity to pH.

Fig. 7. pH-sensitive vs insensitive component of Z-spectra in 15% BSA at 4 pH values.

(A) The amine-water proton exchange at 2.8 ppm is dominant in the Z-spectra of 0.75 μT and is highly sensitive to pH, whereas the upfield rNOE is much less sensitive to pH. (B) At a lower power of 0.12 μT, the CEST signal is minimized due to a very low saturation efficiency, showing pH-insensitive signals at both positive and negative offsets. The magenta dashed lines indicate the fitted Z-spectra with DWS only. (C) The differential Z-spectra for 0.12 μT show very little pH-sensitivity, suggesting a large contribution from both aromatic and aliphatic rNOE.

To further investigate the pH dependency of BSA samples, we studied BSA with wider pH variation at a higher field of 15.2 T for improving spectral resolution. Clear pH-dependence can be seen for downfield and upfield frequencies in the Z-spectra and the differential Z-spectra (Fig. 8A & 8B) acquired with B₁ = 0.5 μT. For quantitative comparison, CEST and rNOE signals at a few selected frequencies (Fig. 8C) were plotted as a function of pH. The CEST signal at 2.8 ppm increases with decreasing pH, as expected for fast exchanging amine protons^25,46. The NOE signals show much weaker pH-dependence than the CEST signal, especially at pH <7.0. Interestingly, the NOE signal at −3 ppm shows much larger pH-dependence than that of −1.9 and −4 ppm. A linear fitted function is rNOE signal (%) = 7.1+0.19×pH for −1.9 ppm, 3.5+1.24×pH for −3ppm, and 8.9+0.43×pH for −4ppm, respectively.

Fig. 8. Comparison of the CEST and rNOE signals of BSA at 15.2 T.

(A) the Z-spectra and (B) the differential saturation transfer signal (i.e., CEST or rNOE) at 8 pH values showed varied peak intensities at different frequency offsets. (C) Although the aliphatic rNOE signals only show weak pH-dependence overall, the signal at −3 ppm has larger pH-dependence than those of −1.9 and −4 ppm.

CEST vs. rNOE of aliphatic and aromatic protons in phantoms with different H₂O/D₂O mixtures

To investigate the impact of the NOE pool size without changing the CE process, water proton concentration in solution was reduced by using H₂O/D₂O mixture. Since the CEST signal is expected to be constant, the change in saturation transfer MRI data is due to the NOE contribution. Fig. 9 shows the saturation transfer experimental results of 20% EWA and 15% BSA in varied H₂O/D₂O mixture. Both Z-spectra indicate that the addition of D₂O enhanced the saturation transfer signal (Fig. 9A and 9B). Because the saturation transfer MR signal is proportional to T₁ which increases with D₂O percentage, this effect should be removed in the analysis of CEST and rNOE signal. In the T₁-corrected differential Z-spectra of both proteins (Fig. 9C and 9D), the upfield rNOE signals increase with D₂O percentage, which can be attributed to a relative increase of f_NOE. Peak magnitude at −3.5ppm is 2.01 and 2.17 times higher in 90% D₂O than that in 0% D₂O for EWA and BSA, respectively, whereas the downfield peak (2 ppm for EWA and 2.2 ppm for BSA) magnitude is 1.36 and 1.48 times higher in 90% D₂O than that in 0% D₂O for EWA and BSA, respectively. The smaller increase of downfield signal with D₂O percentage is likely due to the contribution of both D₂O-insensitive CE and D₂O-sensitive aromatic rNOE signals.

Fig. 9. Comparison of saturation transfer spectra of (A, C) EWA and (B, D) BSA in varied concentration of D₂O.

(A, B) The signal dip in the Z-spectra increases with increasing D₂O percentage. (C, D) The T₁-corrected differential Z-spectra signal increases in both downfield and upfield frequency ranges, with a larger increase upfield.

The existence of the aromatic NOE signal was further confirmed by saturation transfer and MRS studies of BSA in 99.5% D₂O (Fig. 10). Three aliphatic NOE peaks can be seen in the differential Z-spectrum (black arrows, Fig. 10B), which were also confirmed in the proton MR spectrum (Fig. 10C). These aliphatic NOE observations match with Fig. 7C and 8B. At the downfield region, in addition to the residue 2.8 ppm peak of the amine CEST signal, two small peaks appear in the differential Z-spectrum at around 3.75 ppm and 2.2 ppm, which matches well with the frequency range of the aromatic protons in the MR spectrum, and indicates that aromatic NOE signal indeed exists.

Fig. 10. Comparison of saturation transfer and MRS spectrum for BSA in 99.5% of D₂O.

With suppression of the chemical exchange effect by 99.5% D₂O, the signal decay (A) in the CEST Z-spectrum is highly weighted by the rNOE signal. Differential Z spectrum (B) shows peaks with frequencies that match the aromatic and aliphatic protons on the positive (red arrows) and negative frequency (black arrows) offset side in the MRS (C) spectrum, respectively.

Discussions

Our simulation indicates that rNOE signal is closely related to the CE pool but has some unique properties which are distinct from the CEST signal. The rNOE signal is independent of the Larmor frequency of the CE pool, thus, any CE pool can effectively relay NOE magnetization. On the other hand, the rNOE signal has a complicated dependence on the CE pool size and chemical exchange rate. With our simulation parameters, when NOE is relayed by slow-exchanging amide protons, it shows a smaller magnitude and a weaker pH-dependence than the amide-CEST signal. If NOE is relayed by fast chemical exchange protons, it can be almost independent of pH.

Recently, Murase published numerical analyses of the Z-spectra in the presence of multiple exchanging pools which can be applied to exchange-relayed NOE⁴⁷. Zhou et al. has reported a simplified analytical solution for relayed NOE³³ and showed that the pH-sensitivity of the rNOE signal is determined by whether k_CE is much faster than k_NOE. This could lead to a conclusion that the rNOE signal observed in mobile protein would be independent of pH at physiological conditions, because even the slow exchanging amide (30 s⁻¹)¹⁰ is about an order of magnitude faster than the NOE transfer rate (2–3 s⁻¹)^30,39. Our simulation showed that a more general condition for rNOE is the relationship between the product f_CE·k_CE and f_NOE·k_NOE. When f_CE·k_CE >> f_NOE·k_NOE, the capability of the relay is much higher than the magnetization transferred from the NOE pool. A change in f_CE or k_CE will not affect the rNOE signal as long as the condition f_CE·k_CE >> f_NOE·k_NOE is still satisfied. On the other hand, the CE process becomes a rate-limiting step for rNOE when f_CE·k_CE is comparable to or smaller than f_NOE·k_NOE. In this domain, the rNOE signal will be highly dependent on f_CE and k_CE.

The BSA phantom study showed that the rNOE signal has a much smaller pH-dependence than CEST signals, suggesting that the rNOE signal can be separated into two components: The majority of rNOE signals are pH-insensitive and should be relayed by fast-exchanging protons, and the pH-sensitive contribution which is relayed by the slow-exchanging amide proton is small. The high field of 15.2 T allows sufficient spectral separation within the upfield NOE signals and shows that the peak at about −3 ppm has higher pH-dependence than other frequencies. This suggests that compared to −2 ppm and −4 ppm, the rNOE signal at −3 ppm has a higher contribution from the amide-relayed process, which should come from the aliphatic protons closer to the amide groups. Note the above explanation to the pH-dependence of the rNOE signal was based on our simulation and had not been experimentally validated. Besides a change of the exchange rate of the CE pool to the pH-dependent rNOE signal, a change of the protein morphology/folding with pH may also contribute.

The results of the BSA and EWA phantoms also confirmed the previous findings of our group and a few other studies finding that aromatic rNOE signal can be detected in the downfield frequency range^26,27. The overlap of aromatic rNOE with endogenous CEST signals could make the interpretation of CEST contrast in in vivo studies more difficult, thus, it is important to adjust the acquisition or post-processing method to minimize aromatic rNOE signals. For example, a saturation pulse with higher power and shorter duration will be more weighted to the faster exchanging CE pool than the rNOE pool with a slower transfer rate⁴⁸. Alternatively, an aliphatic rNOE based correction may be performed assuming a certain ratio between aromatic and aliphatic NOE signals which does not vary significantly by saturation parameters, tissue types, or pathology³⁰.

APT and rNOE signals can both be detected in the Z-spectrum with relatively small power, thus, they are often measured together and have been postulated to provide complementary information. Recent in vivo studies at high magnetic fields have reported that the magnitude of aliphatic rNOE signal is 8–15% in the white matter^28,29, much larger than the value of ~3% usually observed for APT^10,20,49. Our simulation shows that the rNOE signal, if relayed by the slow exchanging amide pool, should always be smaller than that of the APT CEST signal (e.g., Fig. 6B). This suggests that in addition to the amide group, a large contribution of the rNOE signal should be relayed through faster-exchanging protons such as hydroxyl and amine groups. Thus, the rNOE signal would only have weak pH-sensitivity. Indeed, the change of the aliphatic rNOE signal in ischemic tissue, where the local tissue acidosis can cause a pH drop of more than 0.5 unit^50–52, was reported to be much smaller than that of APT in several animal studies^20,36,37.

Conclusions

Our three-pool simulation shows that the rNOE signal is dependent on the CE pool size and exchange rate and more specifically, the relationship between f_CE·k_CE and f_NOE·k_NOE. The rNOE signal is sensitive to a change of the CE pool size and/or exchange rate only if the CE becomes a rate-limiting step in the relay, and rNOE signal should have a weaker pH-dependence than CEST. Our phantom results strongly suggest that both aliphatic and aromatic NOE signals can be detected in mobile proteins with weak pH-dependence.

Appendix

The spin diffusion between the NOE and CE pools follows the same mathematical model as the chemical exchange between the CE and water pools. Hence, the magnetization of each pool can be described by the Bloch-McConnell Equations which incorporate the magnetization transfer process (i.e., CE and NOE). For a three-pool exchange model, we assume the NOE pool is relayed by the CE pool, and time-dependent magnetization changes are

$$\frac{d{M}_x^a}{dt}=-\left(R_{2a}+k_a\right)M_x^a+k_{ba}{M}_x^b-\left({\delta }_a-\Omega \right)M_y^a$$ [1]

$$\frac{d{M}_x^b}{dt}=k_{ab}{M}_x^a-\left(R_{2b}+k_b\right)M_x^b+k_{cb}{M}_x^c-\left({\delta }_b-\Omega \right)M_y^b$$ [2]

$$\frac{d{M}_x^c}{dt}=k_{bc}{M}_x^b-\left(R_{2c}+k_c\right)M_x^c-\left({\delta }_c-\Omega \right)M_y^c$$ [3]

$$\frac{d{M}_y^a}{dt}=\left({\delta }_a-\Omega \right)M_x^a-\left(R_{2a}+k_a\right)M_y^a+k_{ba}{M}_y^b-{\omega }_1{M}_z^a$$ [4]

$$\frac{d{M}_y^b}{dt}=\left({\delta }_b-\Omega \right)M_x^b+k_{ab}{M}_y^a-\left(R_{2b}+k_b\right)M_y^b+k_{cb}{M}_y^c-{\omega }_1{M}_z^b$$ [5]

$$\frac{d{M}_y^c}{dt}=\left({\delta }_c-\Omega \right)M_x^c+k_{bc}{M}_y^b-\left(R_{2c}+k_c\right)M_y^c-{\omega }_1{M}_z^c$$ [6]

$$\frac{d{M}_z^a}{dt}=R_{1a}{M}_0^a+{\omega }_1{M}_y^a-\left(R_{1a}+k_a\right)M_z^a+k_{ba}{M}_z^b$$ [7]

$$\frac{d{M}_z^b}{dt}=R_{1b}{M}_0^b+{\omega }_1{M}_y^b+k_{ab}{M}_z^a-\left(R_{1b}+k_b\right)M_z^b+k_{cb}{M}_z^c$$ [8]

$$\frac{d{M}_z^c}{dt}=R_{1c}{M}_0^c+{\omega }_1{M}_y^c+k_{bc}{M}_z^b-\left(R_{1c}+k_c\right)M_z^c$$ [9]

where $k_{ab}{M}_0^a=k_{ba}{M}_0^b$

$$k_{bc}{M}_0^b=k_{cb}{M}_0^c$$

$$k_a=k_{ab}$$

$$k_c=k_{cb}$$

$$k_b=k_{ba}+k_{bc}$$

R_1i and R_2i are the longitudinal and transverse relaxation rate of pool i, respectively; δ_i is the Larmor frequency of pool i; Ω is the frequency of the saturation pulse; ω₁ is the Rabi frequency of the saturation pulse (=γB₁ where γ is the gyromagnetic ratio and B₁ is the saturation power); $M_j^i$ is the j-th component of the magnetization of pool i; and $M_0^i$ is the initial magnetization of pool i.