Sensitive, Efficient and Portable Analysis of Molecular Exchange Processes by Hyperpolarized Ultrafast NMR

Abstract Molecular exchange processes are ubiquitous in nature. Here, we introduce a method to analyze exchange processes by using low‐cost, portable, single‐sided NMR instruments. The inherent magnetic field inhomogeneity of the single‐sided instruments is exploited to achieve diffusion contrast of exchange sites and spatial encoding of 2D data. This so‐called ultrafast diffusion exchange spectroscopy method shortens the experiment time by two to four orders of magnitude. Furthermore, because full 2D data are measured in a single scan (in a fraction of a second), the sensitivity of the experiment can be improved by several orders of magnitude using so‐called nuclear spin hyperpolarization methods (in this case, dissolution dynamic nuclear polarization). As the first demonstration of the feasibility of the method in various applications, we show that the method enables quantification of intra‐ and extracellular exchange of water in a yeast cell suspension.

Yeast sample. Fresh baker's yeast, manufactured by Suomen Hiiva, was purchased from a local grocery store Prisma. According to the manufacturer, one gram of yeast includes about 10 9 yeast cells. The cell size is approximately 10 m. The yeast was bought 0-3 days before the experiments and stored in a fridge at around 5C. According to Parkkinen et al., 1 the fraction of dead cells in a similar yeast is only 0-2% if the yeast is stored at 5C less than 16 days. First, 5 g of the yeast was mixed with 1.7 mL of heavy water (D2O) in a vial with inner diameter of 2.5 cm. We note that the added D2O was not isotonic as it did not contain salt. However, the initial amount of (isotonic) water in the yeast sample was higher than the amount of added D2O, and therefore it did not change osmotic pressure drastically. According to literature, yeast cells do not burst in a hypo-osmotic 3 environment. 2,3 Then the vial was placed on the top of the NMR-MOUSE, and 1.5 mL of dDNP hyperpolarized water was introduced into the vial before the UF DEXSY experiment. Dissolution dynamic nuclear polarization. All reagents were purchased from Sigma-Aldrich (Darmstadt, Germany) unless otherwise mentioned. 200 µL aliquets consisting of MilliQ water and glycerol mix (3:2, v:v) and 25 mM 4-hydroxy-2,2,6,6-tetramethylpiperidin-1-oxyl (TEMPOL) 4 were hyperpolarized at 1.35 K, 6.7 T and 187.8 GHz for 1.5 h in a HYPERMAG polarizer (Technical University of Denmark, Copenhagen, Denmark). 5 The frozen sample was dissolved using 13 mL of 100mM sodium ascorbate containing 0.

UF DEXSY simulations Theoretical background for the UF DEXSY data simulations
The excitation-detection profile of NMR-MOUSE was estimated by measuring a 1D spin-echo image of a doped water sample, see Figure 2b. As illustrated in Figure S1, the profile can be approximated by a Gaussian function with mean of 6.3 kHz and standard deviation of 23.4 kHz. Note that the profile shown in Figure S1 is approximative, more precise profile (shown in Figure 2b) measured with imaging parameters identical to the UF DEXSY measurements were used in the analysis explained in the next section.   Signal in the excitation-detection curve can be approximated by the following equation: where B1 is the relative B1 field strength (0  B1  1, 1 corresponds to B1 value of the /2 excitation pulse). The sine term takes into account the position dependent excitation pulse angle, and the B1 term accounts for the detection sensitivity, which is proportional to B1 according to the principle of reciprocity. 6 Eq. 1 does not take into account the effect of selectivity of the hard  refocusing pulse.
The excitation-detection profile was converted to B1 profile using Eq. 1 (see Figure S1). B1 profile was approximated by a Gaussian function with mean of 6.1 kHz and width of 29.3 kHz (see Figures S1 and S2).
If we assume that the flip angle of /2 excitation pulse is exactly 90, when B1 = 1, then the spatially dependent flip angle is If the excitation pulse flip angle is less than 90, then the transverse magnetization after the pulse is less than the original hyperpolarized magnetization M along the z-axis before the pulse, and some longitudinal magnetization remains along the z-axis, as illustrated in Figure S3. Only the transverse magnetization experiences the effect of the gradient pulse and becomes spatially encoded. As there are altogether four /2 pulses in the spatial encoding part of the UF-DEXSY sequence, the encoded magnetization Me stored along the z-axis for the mixing period is proportional to sin 4 (z), while the non-encoded z-magnetization Mne is proportional to cos 4 (z) (see Figure S3).  Ideally the longitudinal magnetization profile after the spatial encoding is where Here,  is the gyromagnetic ratio, G is the gradient strength, tC is the chirp pulse length,  is the chirp pulse bandwidth, and  is the diffusion delay. The ideal magnetization profile for the yeast sample is plotted in Figure S5. In practice, the encoded longitudinal is weighted by the factor of sin 4 (z) (orange line in Figure S4) due to B1 inhomogeneity. Furthermore, there is non-encoded longitudinal magnetization, which is proportional to cos 4 (z) (blue line in Figure S4). Therefore, the total z-magnetization profile after the spatial encoding is t ( ) = sin 4 ( ) e ( ) + cos 4 ( ).
This profile is illustrated in Figure S6. The encoded magnetization dominates at the center, but its maximum value is only about 0.4 due to B1 weighting. The amount of the non-encoded magnetization is significant around |z|  100 m. Due to the non-encoded magnetization, the magnetization profile starts to increase at z < -50 m, i.e., clearly within the encoding region (observed also in the UF DEXSY yeast experiments, see Figure   2). Note that Eq. 5 and Figure S6 do not take into account the effects of artefacts around the edges of the spatial encoding region due to imperfect performance of the chirp pulse; this significantly decreases the amount of encoded magnetization around those regions. This is taken into account in the simulations described in the next section.
Diffusion mixed (Eq. 7) and non-mixed (Eq. 5) total z-magnetization profiles are compared in Figure S8 (mixing time: 100 ms). Due to the diffusion mixing, the slope of the curve in the encoded region is smaller, leading to lower apparent diffusion coefficient, if the diffusion mixing is not taken into account. Figures S9 and S10 show the same curves for mixing times of 10 and 30 ms; the effect of diffusional mixing is much smaller in these curves.  1. The slope in the center of the encoding region decreases with increasing mixing time due to diffusional mixing.

2.
The non-encoded magnetization contributes significantly to the magnetization profiles close to the edges of the encoding region, significantly narrowing the region, in which the spatial encoding is clearly visible.
More precise simulations of the UF DEXSY data, taking also into account of the chirp imperfections around the edges of the spatial encoding region as well as the intra-and extracellular exchange of hyperpolarized water during the mixing time are described in the next section.

UF DEXSY data simulations
The analysis of the UF DEXSY data required simulation of various effects described in the article and previous section. The simulated UF DEXSY data was fitted with the experimental data as illustrated in Figure S11.  Figure S12, which is a sum of a constant factor and two negative gaussian functions. The zero points of the function correspond to /2 chirp pulse angle, while the maximum value in the center corresponds to full  chirp inversion and the maxima close to edges correspond to 0 chirp pulse angle. Hence, we were able to determine the spatially dependent chirp pulse angle, ( ), shown by red line in Figure S12 (1 corresponds to flip angle of ).