Utilizing a Water-Soluble Cryptophane with Fast Xenon Exchange Rates for Picomolar Sensitivity NMR Measurements

Abstract

Hyperpolarized ¹²⁹Xe chemical exchange saturation transfer (¹²⁹Xe Hyper-CEST) NMR is a powerful technique for the ultrasensitive, indirect detection of Xe host molecules (e.g., cryptophane-A). Irradiation at the appropriate Xe-cryptophane resonant radio frequency results in relaxation of the bound hyperpolarized ¹²⁹Xe and rapid accumulation of depolarized ¹²⁹Xe in bulk solution. The cryptophane effectively ‘catalyzes’ this process by providing a unique molecular environment for spin depolarization to occur, while allowing xenon exchange with the bulk solution during the hyperpolarized lifetime (T₁ ≈ 1 min). Following this scheme, a triacetic acid cryptophane-A derivative (TAAC) was indirectly detected at 1.4 picomolar concentration at 320 K in aqueous solution, which is the record for a single-unit xenon host. To investigate this sensitivity enhancement, the xenon binding kinetics of TAAC in water was studied by NMR exchange lifetime measurement. At 297 K, k_on ≈ 1.5 × 10⁶ M⁻¹s⁻¹ and k_off = 45 s⁻¹, which represent the fastest Xe association and dissociation rates measured for a high-affinity, water-soluble xenon host molecule near rt. NMR linewidth measurements provided similar exchange rates at rt, which we assign to solvent-Xe exchange in TAAC. At 320 K, k_off was estimated to be 1.1 × 10³ s⁻¹. In Hyper-CEST NMR experiments, the rate of ¹²⁹Xe depolarization achieved by 14 pM TAAC in the presence of RF pulses was calculated to be 0.17 µM·s⁻¹. On a per cryptophane basis, this equates to 1.2 × 10^{4 129}Xe atoms s⁻¹ (or 4.6 × 10⁴ Xe atoms s⁻¹, all Xe isotopes), which is more than an order of magnitude faster than k_off, the directly measurable Xe-TAAC exchange rate. This compels us to consider multiple Xe exchange processes for cryptophane-mediated bulk ¹²⁹Xe depolarization, which provide at least 10⁷-fold sensitivity enhancements over directly detected hyperpolarized ¹²⁹Xe NMR signals.

INTRODUCTION

Methods for detecting trace analytes play critical roles in chemistry and many applied fields, including biotechnology, biophysics, molecular pathology, metallurgy and homeland security. Nuclear magnetic resonance (NMR) spectroscopy is a versatile technique for probing molecular structure but typically offers limited detection sensitivity, based on the small magnetic moment of commonly employed nuclei (e.g., ¹H, ¹³C, ¹⁵N) and the narrow separation in energy levels between nuclear spin transitions. This leads to small polarization of the nuclear spin reservoir, where the difference in spin populations aligned parallel or anti-parallel to an external magnetic field at thermal equilibrium is typically just 1 in ~10⁵ spins. Thus, significantly enhanced NMR signals can be obtained via hyperpolarization techniques capable of generating a nuclear spin polarization level approaching 100%.^1,2

For applications in biodetection and materials science, we^3–6 and others^7–20 have investigated the noble gas isotope ¹²⁹Xe, which is spin-½ and readily hyperpolarized (HP) via spin-exchange optical pumping.^2,21 However, due to low concentrations of the delivered magnetic species and short spin relaxation lifetimes, the signal intensity is still not ideal for many demanding applications, e.g., clinical MRI.^22,23 When exchanging magnetic species are present, chemical exchange saturation transfer (CEST) can provide another source of signal amplification based on cumulative magnetization transfer through selective saturation.²⁴ For proton MRI, CEST contrast originates from exchange of endogenous or exogenous amide or hydroxyl protons with bulk water protons, or from exchangeable sites on paramagnetic inorganic coordination complexes.^25,26 This gives the possibility of designing extremely sensitive contrast agents that respond to various exchange events, with techniques known as PARACEST²⁷ and LIPOCEST.²⁸ More recently, the analogous technique involving HP ¹²⁹Xe CEST (Hyper-CEST) was developed.⁸ Based on its considerable polarizability, xenon exhibits significant affinity for organic host molecules known as cryptophanes.^{4–6,10,29–32} In one example, Hyper-CEST was applied to virus capsids modified by ~125 cryptophanes, thereby attaining 0.7 pM capsid detection sensitivity.¹⁵

Here we present ultrasensitive Hyper-CEST NMR with a water-soluble triacetic acid cryptophane-A derivative (TAAC, Figure 1).^{5 129}Xe NMR biosensors using similarly derivatized cryptophanes have been shown previously to be useful for detecting a wide variety of analytes.^{3,7,12,33–39} This single-unit cryptophane derivative, TAAC, was indirectly detected at 1.4 picomolar concentration at 320 K in aqueous solution, which is the record for a xenon host. Thermodynamic and kinetic studies of xenon binding were carried out to investigate this sensitivity enhancement, which establish TAAC as a very effective xenon binder/’spin catalyst’ under the Hyper-CEST scheme. Our results suggest multiple Xe exchange processes for cryptophane-mediated HP ¹²⁹Xe NMR signal enhancement.

Figure 1.

Triacetic acid cryptophane-A derivative (TAAC).⁵

EXPERIMENTAL

Materials

TAAC was previously prepared by a thirteen-step synthesis,⁵ and found to be soluble to ~500 µM in aqueous solution (pH 7), owing to its three carboxylates. The identity and purity of TAAC were confirmed by ¹H NMR spectroscopy. TAAC features a xenon association constant (K_A) of 33 000 M⁻¹ at 293 K, making it currently one of the highest-affinity Xe host molecules.^5,6,31

Ultra-filtered water (18 MΩ·cm resistivity) obtained from Mar Cor filtration system, was used to prepare TAAC solutions. TAAC (1.43 mg) was carefully weighed and dissolved in 10 mL water to form a 140 µM solution, which was confirmed by Agilent 8453 UV-vis spectrophotometer (ε₂₈₀ = 12 000 M⁻¹cm⁻¹). For the Hyper-CEST experiments a series of 10-fold dilutions with ultra-filtered water was performed to bring TAAC solution down to picomolar concentrations. Dilutions were made with well calibrated Eppendorf Research pipettes with <1% error. After each dilution, solution was vortexed to homogenize sample. Reagents were used as purchased from Fisher: sodium phosphate dibasic heptahydrate, sodium phosphate monobasic dihydrate. Prior to isothermal titration calorimetry (ITC) measurement, TAAC solution was dialyzed in phosphate buffer (20 mM, pH 7.5) by GE Mini Dialysis Kit (1 kDa cut-off).

In the NMR samples, xenon concentrations were calculated by multiplying the xenon partial pressure with its mole-fraction solubility in water, at a given temperature. For example, during the Hyper-CEST experiment at 320 K, [Xe, all isotopes] is calculated as: xenon partial pressure in gas line × mole fraction solubility (at 320 K, 1 atm) × molarity of water = 0.045 × 4.95 × 10⁻⁵ × 55.5 M = 0.12 mM, following Henry’s Law. The concentration of hyperpolarized ¹²⁹Xe in solution (3.1–4.8 µM) was determined by multiplying [Xe] by the natural isotopic abundance (26.4%) and the hyperpolarization level (10–15%), measured by comparing with thermal Xe sample.⁴⁰

General NMR method

A 500 MHz Bruker BioDRX NMR spectrometer was used for all ¹²⁹Xe NMR measurements. RF pulse frequency for ¹²⁹Xe was 138.12 MHz. Samples were observed using either a 5 mm PABBO NMR probe or a similar 10 mm probe. HP ¹²⁹Xe was generated using a home-built ¹²⁹Xe hyperpolarizer, based on the Nycomed-Amersham (now GE) IGI.Xe.2000 commercial system. A gas mixture of 89% nitrogen, 10% helium, and 1% natural abundance xenon (Concord Gases, NJ) was used for the hyperpolarizer input. ¹²⁹Xe was hyperpolarized to 10–15% after optical pumping of Rb vapor with 795 nm circularly polarized laser, cryogenic separation of Xe, and accumulation and collection in CAV NMR tubes (New Era). For the TAAC spectrum and exchange rate measurements, after introducing HP Xe to sample solution, the sealed NMR tube was shaken vigorously to mix solution with HP ¹²⁹Xe.

Directly recorded ¹²⁹Xe NMR spectra were acquired using 30° hard excitation pulses (7.5 µs on 5 mm probe), or 90° EBurp1 shaped pulses (7.5 ms, 602 Hz excitation bandwidth). Spectra were signal averaged by 10–30 scans. A delay of 0.15 s was given between scans to allow depolarized Xe to leave the cryptophane cavity and fresh HP Xe to enter the cavity. The spectra shown in Figure 2 were exponentially broadened by 4 Hz to give a larger signal/noise ratio. Sample temperature was controlled by VT unit on NMR spectrometer to ± 1 K.

Figure 2.

HP ¹²⁹Xe NMR spectrum of 140 µM TAAC dissolved in ultrafiltered water at 320 K, showing: Xe(aq) peak at 194.3 ppm and Xe@TAAC peak at 65.8 ppm (selectively excited). Lorentzian deconvolved spectrum is shown in red.

At a series of temperatures from 300–325 K, HP ¹²⁹Xe NMR spectra were acquired following the aforementioned protocol and the natural line widths of the Xe@TAAC peaks were fitted (FWHM, Lorentzian) and summarized in Table 1.

Table 1.

Line width of ¹²⁹Xe@TAAC NMR peak at various temperatures, and estimated Xe exchange rates.

Temperature (K)	Line width of Xe@TAAC peak (Hz)*	Estimated kexch (s−1)
300	27.3 ± 1.1	86 ± 3.4
310	157.3 ± 1.1	500 ± 3.4
315	238.3± 3.6	750 ± 11
320	342.2 ± 5.7	1100 ± 18
325	294.2 ± 3.2	920 ± 10

^*Magnetic homogeneity corrected.

Hyper-CEST method

Scheme 1 illustrates the Hyper-CEST experiment involving TAAC. Before starting the pulse sequence each time, a controllable amount of HP Xe was delivered into the 3-mL sample solution, and sealed in the NMR tube for signal stabilization by a homebuilt continuous-flow HP Xe delivery setup (Figure S1). Multiple selective 180-degree radiofrequency (RF) pulses were delivered to the sample at the ¹²⁹Xe@TAAC resonance frequency, while HP Xe and depolarized Xe were dynamically exchanging in and out of TAAC. As a result, depolarized Xe was accumulated in the aqueous sample, and detected by another 90 degree hard excitation pulse. HP Xe in water undergoes depolarization exponentially by the time constant T₁ ≈ 70 s. However, in the Hyper-CEST experiment TAAC served as a “depolarization catalyst”, and could be turned “on” and “off” using a saturation frequency that was either on- or off-resonance with ¹²⁹Xe@TAAC.

Scheme 1.

Saturation transfer processes in ¹²⁹Xe Hyper-CEST NMR with cryptophane.

Utilizing a home-built continuous flow HP Xe delivery setup (Supporting Information, Figure S1), freshly hyperpolarized Xe gas mixture was bubbled through sample solutions at 65 psi. Before starting the pulse program each time, bubbling was stopped by two solenoid valves to maintain magnetic field homogeneity.

The Hyper-CEST experiment was carried out using the pulse program illustrated in Figure 3. DSnob-shaped pulses (parameter sp6) were looped numerous times (L6) to induce xenon polarization transfer. In the low concentration trials, where d12 << sp6 in duration, the radiation became near-continuous. The DSnob pulse power was calibrated to give maximum saturation. With a single DSnob pulse (sp6) irradiated at Xe(aq) frequency, >90% signal was saturated. After the overall polarization was reduced by saturation pulses and chemical exchange, the sample was irradiated with a 90 degree hard pulse to read out the final magnetization state of ¹²⁹Xe in solution. Due to imperfection of frequency selectivity, sp6 contributed significantly to the off-resonance regions of the spectrum after 10 000 repeats. Therefore, for the lowest concentration TAAC Hyper-CEST experiments the Xe(aq) peaks were relaxed faster than the analogous T₁ of HP ¹²⁹Xe in aqueous solution.

Figure 3.

Hyper-CEST pulse sequence diagram, with parameters provided for in-house 10 mm PABBO probe. Different values were chosen considering TAAC concentration, sample temperature, HP Xe flow rate. From a recent saturation transfer optimization,⁵⁴ saturation pulse is DSnob-shaped to enhance power efficiency. Field strength of the shaped pulse was calculated to be 29 µT (cw equivalent).

Isothermal titration calorimetry (ITC)

ITC samples were prepared as described, and xenon binding measurements were performed using a MicroCal VP-ITC titration microcalorimeter (Northampton, MA) at 310 K. Standard protocols and data analyses were used. Control enthalpograms for ITC are presented in the Supporting Information (Figure S2– S4).

Xe@TAAC NMR line widths at different temperatures

The spectra were Lorentzian deconvolved to fit for full width at half maximum (FWHM). Peak widths of the Xe@TAAC peaks were corrected by subtracting the Xe(aq) peak line widths to account for magnet inhomogeneity. The line widths of Xe(aq) peaks range between 8–18 Hz (from 297 K to 320 K), which mainly originates from magnetic field homogeneity. This response of aqueous ¹²⁹Xe to temperature change was negligible compared to ¹²⁹Xe@TAAC peaks (Table 1).

Xenon exchange lifetime measurement

Though 2D EXSY NMR is the standard method for determining exchange rates,⁴¹ selective 1D EXSY NMR^42–44 serves as a better measurement scheme in this case, due to the spectral dominance of the HP ¹²⁹Xe(aq) peak. Using a customized EXSY pulse sequence,⁴³ the Xe@TAAC resonance was selectively excited and acquired twice (separated by designated mixing times), generating two FIDs (initial and recovery). The ratio of signal intensities was calculated to quantify the percentage of Xe@TAAC replenishment, at a manually set mixing time that’s close to the xenon exchange lifetime being fitted. With a series of exchange-replenishment ratios and their corresponding mixing times, Xe exchange lifetime can be fitted, providing a measurement of cryptophane-Xe exchange performance.

RESULTS AND DISCUSSION

Hyperpolarized ¹²⁹Xe NMR spectra of TAAC in aqueous solution

Two peaks arise in the HP ¹²⁹Xe NMR spectrum of 140 µM TAAC aqueous solution (Figure 2): Xe dissolved in water at 320 K (Xe(aq), 194.3 ppm) and Xe bound in TAAC (Xe@TAAC, 65.8 ppm). In HP ¹²⁹Xe detection schemes investigated to date, there is a large excess of Xe (mM) relative to cryptophane (µM),⁴⁵ which results in a Xe(aq) peak that is ~1000 times stronger than Xe@TAAC without selective excitation. Given the almost 130 ppm separation of the two peaks, selective RF pulses focused on Xe@TAAC will have little effect on Xe(aq) under most conditions, which allows selective excitation of the minor “cryptophane-bound” species as well as selective saturation exchange experiments.

Direct detection, even selective excitation (for example, Figure 2), requires micromolar cryptophane, which limits cryptophane biosensor experiments to prevalent biological targets. Some cryptophanes may also be toxic to cells at this concentration.^39,46 Instead of trying to detect directly the ¹²⁹Xe@TAAC peak, the ¹²⁹Xe@TAAC resonance can be indirectly measured more sensitively via magnetization transfer from the much stronger ¹²⁹Xe(aq) NMR signal.

Xenon binding kinetics of TAAC

The thermodynamics of xenon binding is established by the equilibrium shown in eq 1:

$$\text{Xe}+\mathrm{S}@\text{TAAC}\underset{k_{\mathit{\text{off}}}^{\prime }}{\overset{k_{\mathit{\text{on}}}}{\rightleftharpoons }}\text{Xe}@\text{TAAC}+\mathrm{S}$$ (1)

where S@TAAC indicates solvent-bound TAAC. It is experimentally observed⁴⁷ that “empty” cryptophane is preferably bound with solvent, in this case one or multiple water molecules. Because the concentration of solvent is constant, the reverse process in eq 1 can be simplified to be first-order, yielding the rate constant ‘k_off’ (k′_off[S]). This yields eq 2 with the rate constants of xenon binding (k_on) and dissociation (k_off) indicated:

$$k_{\mathit{\text{on}}}[\text{Xe}][\mathrm{S}@\text{TAAC}]=k_{\mathit{\text{off}}}[\text{Xe}@\text{TAAC}]$$ (2)

The maximal Hyper-CEST effect should occur under conditions where all of the cryptophane is encapsulating xenon (to ensure maximal Xe absorption of the RF pulse) while still allowing the most rapid “Xe in”-“Xe out” exchange. The xenon on- and off-rates (k_on, k_off) describe the rates at which HP Xe gains access to the cavity of TAAC and the rate at which depolarized Xe leaves TAAC. This exchange process should occur most rapidly when a HP Xe atom directly displaces depolarized Xe, with no intermediary solvent binding. However, because TAAC experiments are conducted in water, solvent may compete with Xe binding.

Ultrasensitive detection of TAAC

Picomolar TAAC was detected by a series of Hyper-CEST measurements, following the general method developed in the Pines lab.¹⁵ In Figure 4, relative intensity of Xe(aq) signal was plotted against the time of saturation transfer pulse cycles. As in Figure 3, the shaped saturation pulse was configured to resonate at the frequency of Xe@TAAC signal (65.8 ppm). As a control, saturation at a mirror frequency (2 × 194.3 – 65.8 = 322.8 ppm) was established, to perform off-resonance Hyper-CEST. When the saturation pulse was tuned to Xe(aq) frequency, the peak was able to be completely saturated with 2 scans. At 14 pM TAAC concentration and higher, on-resonance Hyper-CEST clearly presented a more sharply decaying Xe depolarization curve, indicating effective saturation transfer. After 10-fold dilution, the difference in depolarization rate was still observable from exponential fits; representative data from three trials are shown. Detection of 1.4 pM TAAC is currently the lowest observed concentration for a single-unit Xe host. Previously, the Pines lab demonstrated detection of 10 nM cryptophane using this technique.⁴⁸ To explain the much greater detection sensitivity obtained in the current experiment, we hypothesized that TAAC must have much more rapid xenon exchange kinetics compared to previously measured cryptophane systems, in addition to its favorably high Xe@TAAC occupancy. To explore the origins of the achieved sensitivity, a series of characterization experiments was performed.

Figure 4.

¹²⁹Xe Hyper-CEST profiles of 14 pM and 1.4 pM TAAC at 320 K plotted as the Xe(aq) peak intensities vs. saturation time. Differences between on- and off-resonance saturation are compared. Exponential fits of data are shown as red and dark curves. Depolarization lifetimes were fitted to be 10 ± 1 s (on) and 38 ± 2 s (off) for 14 pM sample (averaged over two trials); 53 ± 4 s (on) and 65 ± 4 s (off) for 1.4 pM sample (representative of 3 trials), respectively. In each experiment, a series of 2.6 ms DSnob pulses with 20 µs delay was applied. In the Hyper-CEST pulse sequence, the following parameters were used: sp6 = 2.6 ms, d12 = 20 µs, d1 = 1 s, L6 = 8 000 (max, 14 pM) or 10 000 (max, 1.4 pM).

ITC measurement of xenon binding to TAAC

TAAC should be favorable for Hyper-CEST NMR based on its high Xe affinity. Moreover, its strongly positive entropy of Xe binding (ΔS = 5.9 cal·mol⁻¹·K⁻¹ at 293 K) supports high affinity as temperature increases from rt to physiological conditions.⁵ Indeed, ITC measurements performed at 310 K showed the Xe-TAAC association constant to be 33 000 ± 2000 M⁻¹ (Figure 5), the same value determined at 293 K.⁵ During the Hyper-CEST experiment, xenon concentration⁴⁵ is calculated to be 0.12 mM by assuming the hyperpolarized Xe gas mixture, at 1 atm, saturates the sample solution. Therefore, more than 80% of the TAAC molecules were bound to Xe, which is higher than the 45–60% host occupancy in previous Hyper-CEST NMR experiments.^15,20,48

Figure 5.

Enthalpogram of 3.31 mM aqueous xenon solution⁴⁵ titrated into 131 µM TAAC solution (phosphate buffer, 20 mM, pH 7.5) at 310 K.

Xe@TAAC NMR line widths at different temperatures

Spectra were acquired for 140 µM TAAC aqueous solution following the same method as Figure 2, at different temperatures (see Table 1). The spectra were Lorentzian deconvolved to fit for full width at half maximum (FWHM). Peak widths of the Xe@TAAC peaks were corrected by subtracting the Xe(aq) peak line widths to account for magnet inhomogeneity.

Xenon exchange lifetime measurement

Previously, Xe-cryptophane exchange rates in organic solution were measured by 2D ¹²⁹Xe NMR⁴² spectroscopy and approximated by measuring the line width of the Xe@cryptophane NMR resonance.²⁹ Due to the high concentrations of xenon and cryptophane that dissolved in C₂D₂Cl₄,⁴² it was possible to use the small ¹²⁹Xe polarization provided by the NMR magnet. Here, in order to examine the origins of the heightened cryptophane-mediated HP ¹²⁹Xe depolarization achieved with TAAC, we sought to measure the xenon-cryptophane exchange kinetics in aqueous solution by the combination of NMR selective excitation and ¹²⁹Xe hyperpolarization, which was demonstrated previously for a biotin-derivatized xenon biosensor.⁴³

By altering the exchange mixing time, a series of Xe replenishment efficiencies was measured (Figure 6). The xenon exchange lifetime, τ_exch, was determined to be 22 ± 3 ms at 297 K. This τ_exch value is shorter than measured for all previous cryptophanes in water close to rt.^31,32,43,49 Using the measured τ_exch and K_A, xenon dissociation and association rate constants were determined at 297 K: k_off ≈ k_exch = 1/τ_exch = 45 ± 15 s⁻¹ and k_on ≈ 1.5 × 10⁶ M⁻¹s⁻¹. As k_exch is an intermolecular process,²⁹ it likely underestimates the Xe dissocation rate (k_off).⁴³ Despite this difference, the measured rates are more than 2-fold faster than the exchange rates measured for water-soluble cryptophanes with comparable Xe affinity (k_on = 3.8 × 10⁵ M⁻¹s⁻¹; k_off = 13.1 s⁻¹ at 293 K^31,32). Our measured exchange rates with TAAC in water are more typical of cryptophane-A derivatives in organic solvent, where millisecond timescales have been observed.²⁹ A key difference, however, is that in large organic solvents such as C₂D₂Cl₄, the cryptophane should remain empty during the Xe exchange process. In water, solvent binding to TAAC will slow the Xe exchange process.

Figure 6.

Xe-TAAC exchange lifetime measurement by selective EXSY at 297 K. The horizontal axis denotes the mixing time between two consecutive excitations. The vertical axis indicates the ratio of the integrated intensities of Xe@TAAC signals, exchange recovered vs. equilibrium. Data were exponentially fitted to give an exchange lifetime, τ_exch = 22 ± 3 ms. This exchange lifetime is in good agreement with linewidth measurements made at 300 K (Table 1).

It has been established by Pines and co-workers that Hyper-CEST becomes dramatically more sensitive at temperatures slightly above rt,⁴⁸ but the origin of this effect requires further investigation. Using our experimental setup, we were unable to measure the exchange rate (1/τ_exch) exactly at 320 K, where the Hyper-CEST experiment was performed. However, HP ¹²⁹Xe NMR spectra collected at different temperatures (Table 1) provide estimates for k_exch from Xe@TAAC peak line widths: k_exch = 1100 s⁻¹ at 320 K, k_exch = 500 s⁻¹ at 310 K, k_exch = 86 s⁻¹ at 300 K, which is in reasonable agreement with the 1-D EXSY exchange rate measurement at 297 K (k_exch = 45 s⁻¹). For the ~20% water-bound TAAC in solution, the exchange rate should be limited by the dissociation of water en route to Xe binding.

Description of HP Xe depolarization rate

In the overall depolarization “reaction” resulting in thermal equilibration of all xenon nuclear spins in solution, TAAC (together with selective saturation RF pulses) acts as a ‘spin catalyst’. Depolarization curves were fit using first-order kinetics, with the TAAC-mediated HP Xe depolarization rate constant (k_TAAC) and the natural T₁ relaxation rate constant (k₁) both contributing to the observed loss of HP Xe (Supporting Information). By multiplying k_TAAC by the starting HP Xe concentration (3.1 µM), the maximum HP Xe depolarization rate can be expressed as k_TAAC·[HP Xe] = 0.17 µM·s⁻¹. After dividing by TAAC concentration (14 pM), this equates to k_cat = 1.2 × 10⁴ HP Xe-129 atoms depolarized by each TAAC molecule per second. Compared to a virus-capsid-based biosensor which we calculate to have k_cat = 1.3 × 10² s⁻¹,¹⁵ TAAC is observed to have 100-times greater activity on a per-cryptophane basis (Supporting Information).

For TAAC, which is ~80% bound with Xe in solution, the Xe-Xe exchange rate, k_exch(Xe-Xe), should be the critical kinetic parameter for determining Hyper-CEST efficiency. Based on very efficient saturation transfer (> 0.9 in a control experiment), we assume in our analysis of TAAC that k_cat approximates the Xe-Xe exchange rate. Including all Xe isotopes, k_exch(Xe-Xe) should be approximately k_cat/0.26 = 4.6 × 10⁴ s⁻¹. At 320 K this is more than one order of magnitude faster than k_off, the proposed Xe-H₂O exchange rate measured by NMR linewidth. This suggests that there are two different kinetic processes, with only the slower H₂O-Xe exchange process being directly observable by either 1-D EXSY or NMR linewidth measurements. Such millisecond exchange processes are most consistent with previously published Hyper-CEST NMR results,^8,15,20,36 which led to detection of nanomolar cryptophane concentrations.

Some of TAAC’s advantage in a Hyper-CEST detection scheme may arise from differences in cryptophane solubilization; for example, TAAC’s three acetates should promote more open, Xe-accessible conformations of the cryptophane, with high xenon on- and off-rates.⁴⁷ Our previous fluorescence lifetime studies indicated that only 5–10% of TAAC in aqueous solution adopts a more collapsed, non-Xe binding conformation.⁵ In addition, high Xe occupancy and narrower line widths for the HP ¹²⁹Xe-cryptophane complex promote RF saturation leading to efficient HP ¹²⁹Xe depolarization.

Depolarization mechanisms

Multiple processes may contribute to rapid Xe depolarization, beyond the discussed Hyper-CEST Xe-cryptophane-water exchange mechanism (Scheme 1). Weak dipole-dipole interactions between ¹²⁹Xe nuclear spins discount the possibility for through-space depolarization effects. However, there may be significant chemical shift anisotropy of the xenon atom(s) associated with TAAC, which would significantly accelerate relaxation of ¹²⁹Xe nuclei.^50,51 In addition, with induced electron currents in the bound Xe@TAAC complex,⁵² meaningful variations of xenon local magnetic fields can be present, providing another depolarization pathway.⁵³ However, neither effect can explain the >10-fold discrepancy between k_off measured by NMR linewidth (all Xe isotopes) and the faster k_cat Xe depolarization rate determined by Hyper-CEST.

We surmise that the exchange rates that are measurable by either 1-D EXSY or NMR line widths are not measuring the pairwise Xe-Xe exchange rate, but instead a slower process involving the exchange of Xe for intermediary solvent in the ~20% of “empty” (water-bound) TAAC molecules. To consider the potential for a much faster Xe-Xe exchange process, we note the previous observation that Xe exchange rates for cryptophanes in organic solution are accelerated at higher Xe concentrations, indicating an “associative” exchange mechanism.²⁹ Direct Xe-Xe exchange may be critical for avoiding a solvent-bound “kinetic trap”, which we propose should deactivate cryptophane for efficient Hyper-CEST.

Notably, 1.4 pM TAAC detection sensitivity was achieved with natural isotopic abundance Xe (26.4% ¹²⁹Xe) polarized to 10–15%. Thus, most of the TAAC host molecules in solution were occupied with other “silent” Xe isotopes or “thermally polarized” ¹²⁹Xe nuclei not contributing to bulk magnetization. At the initiation of the experiment, TAAC-bound HP ¹²⁹Xe concentration was estimated to be: [TAAC] × TAAC occupancy percentage × ¹²⁹Xe isotopic abundance × hyperpolarization level = 1.4 pM × 80% × 26.4% × 10% = 0.03 pM. Our analysis predicts that at least 10-fold greater detection sensitivity may be achieved for TAAC bound with more highly polarized (50%), isotopically-enriched (86%) ¹²⁹Xe—conditions that should allow more efficient depolarization of ¹²⁹Xe by RF pulses, ‘catalyzed’ by TAAC. In this way, femtomolar detection of TAAC and related xenon-binding molecules should be readily achievable.

CONCLUSIONS

Using ¹²⁹Xe Hyper-CEST NMR spectroscopy, we detected a water-soluble cryptophane TAAC at concentrations as low as 1.4 pM, through enhancement from fast chemical exchange. This is a uniquely sensitive NMR measurement, and, in particular, represents a roughly 100-fold improvement in detection sensitivity over recently published ¹²⁹Xe Hyper-CEST NMR data, on a per cryptophane basis.¹⁵ To investigate the role of TAAC in improving detection sensitivity, Xe binding kinetics of TAAC were characterized for the first time, by combining exchange lifetime with association constant measurements. Favorable thermodynamic and kinetic properties of Xe binding to TAAC were determined.

Kinetic analysis of Hyper-CEST NMR experiments with TAAC revealed a rapid, TAAC-mediated ¹²⁹Xe depolarization mechanism (k_TAAC[HP ¹²⁹Xe] = 1.7 × 10⁻⁷ M·s⁻¹), which corresponds to 1.2 × 10⁴ HP ¹²⁹Xe atoms depolarized per second. Assuming near unity saturation efficiency, this corresponds to greater than one order of magnitude faster Xe exchange than k_off measured by 1-D EXSY and linewidth NMR measurements, which we assign to HP ¹²⁹Xe exchanging with H₂O in the cryptophane cavity. The sub-millisecond kinetic process identified by Hyper-CEST NMR experiments at 320 K is consistent with efficient Xe-Xe exchange. Ongoing theoretical calculations and experiments using different cryptophane moieties are investigating the significance of these two possible Xe exchange pathways. In conclusion, ultrasensitive cryptophane detection supports the further development of xenon host molecules and cryptophane-based biosensors for in vitro and in vivo ¹²⁹Xe magnetic resonance studies.