Magnetic-Field Dependence of LC-Photo-CIDNP in the Presence of Target Molecules Carrying a Quasi-Isolated Spin Pair

Abstract

NMR spectroscopy is well known for its superb resolution, especially at high applied magnetic field. However, the sensitivity of this technique is very low. Liquid-state low-concentration photo-chemically-induced dynamic nuclear polarization (LC-photo-CIDNP) is a promising emerging methodology capable of enhancing NMR sensitivity in solution. LC-photo-CIDNP works well on solvent-exposed Trp and Tyr residues, either in isolation or within proteins. This study explores the magnetic-field dependence of the LC-photo-CIDNP experienced by two tryptophan isotopologs in solution upon in situ LED-mediated optical irradiation. Out of the two uniformly ¹³C,¹⁵N-labeled Trp (Trp-U-¹³C,¹⁵N) and Trp-α-¹³C-β,β,2,4,5,6,7-d₇ species employed here, only the latter bears a quasi-isolated ¹H^α-¹³C^α spin pair. Computer simulations of the predicted polarization due to geminate recombination of both species display a roughly bell-shaped field dependence. However, while Trp-U-¹³C,¹⁵N is predicted to show a maximum at ca. 500 MHz (11.7 T) and a fairly weak field dependence, Trp-α-¹³C-β,β,2,4,5,6,7-d₇ is expected to display a much sharper field dependence accompanied by a dramatic polarization increase at lower field (ca. 200 MHz, 4.7 T). Experimental LC-photo-CIDNP studies on both Trp isotopologs at 1μM concentration, performed at selected fields, are consistent with the theoretical predictions. In summary, this study highlights the prominent field-dependence of LC-photo-CIDNP enhancements ($\mathrm{\epsilon }$) experienced by Trp isotopologs bearing a quasi-isolated spin pair.

1. Introduction

Nuclear magnetic resonance (NMR) spectroscopy is notoriously hampered by low sensitivity, even at the highest currently available applied magnetic fields. While the poor sensitivity of NMR can in principle be overcome by increasing sample concentration, scarce solubility or poor sample availability are often limiting factors. Several approaches have recently been developed to increase the sensitivity of NMR spectroscopy in solution [1]. Among them, chemically [2, 3] and photochemically [4–7] induced dynamic nuclear polarization stand out for their simplicity and fairly straightforward practical implementation.

At low sample concentration (≤ 1μM), the photochemically induced dynamic nuclear polarization (photo-CIDNP) technique is usually referred to as LC-photo-CIDNP [8, 9]. This approach requires photosensitizer dyes with a long triplet-state lifetime [8, 9]. Both photo-CIDNP and LC-photo-CIDNP share the same “radical pair” mechanism in solution, as illustrated in Fig. 1 [5–7, 10]. The process involves the collision of the triplet state (T1) of the photoexcited dye with the molecule of interest (e.g., Trp), followed by rapid electron transfer. The latter process, in turn, leads to the transient oxidation of the molecule of interest and to the generation of a radical pair. The fate of the radical pair leads to a crucial spin sorting process, and lies at the origin of the observed nuclear spin hyperpolarization. Specifically, the radical pair undergoes a nuclear-spin-dependent triplet-singlet transition (T-S mixing in Fig. 1) followed by rapid electron transfer and recombination. In the idealized case of a single nuclear spin on the molecule of interest (within the radical pair) this process enriches the spin state bearing the fastest T-S mixing rate. Conversely, the spin state characterized by slower T-S mixing rate undergoes predominantly radical-pair escape followed by paramagnetic relaxation, which virtually equalizes nuclear-spin populations, and radical quenching. The overall process leads to the observed hyperpolarization. Percent polarization $\left({\mathrm{P}}_{\mathrm{\%}}\right)$ values achievable by photo-CIDNP and LC-photo-CIDNP in solution are typically lower than other NMR sensitivity enhancement techniques, especially in the solid state [11, 12]. On the other hand, the resulting enhancements lead to the facile detection of extremely dilute (μM – nM) aromatic species in solution.

Fig. 1.

Schematic representation of the mechanism of photochemically induced dynamic nuclear polarization (photo-CIDNP) in solution. Dye and Trp denote photosensitizer dye and the tryptophan amino acids, respectively. The symbols S0, S1, T1 refer to ground singlet, first excited singlet and triplet states, respectively. T-S denotes a triplet-singlet transition and $\left[{\mathrm{D}\mathrm{y}\mathrm{e}}^{•-}{\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}\right]$ is the radical pair resulting from the collision between the triplet state of the dye and the tryptophan amino acid. The $\alpha$ and $\beta$ nuclear spin states of Trp are shown as orange and blue circles. Note that the low-concentration analog of photo-CIDNP, known as LC-photo-CIDNP, shares the same mechanism.

LC-photo-CIDNP is usually carried out in oxygen-free environments [13, 14], and it has recently been proven as a valuable tool for the NMR sensitivity enhancement of solvent-exposed tryptophan (Trp) and tyrosine (Tyr) residues, either in isolation or within proteins [15–17].

The replacement of high-power lasers with light-emitting diodes (LEDs) improved accessibility, portability and safety [16]. In combination with the virtual elimination of the recycle delay, LED-mediated LC-photo-CIDNP led to the ultra-rapid detection of 500 nM free Trp and 5 μM SH3 protein via the ¹³C RASPRINT pulse sequence [16]. More recently, it was realized that selective isotope labeling of Trp, including the replacement of aromatic protons and H^β atoms with deuterons and the incorporation of a unique ¹³C at the $\mathrm{\alpha }$ position, leads to even higher enhancements [17]. This strategy enabled data collection on 20 nM Trp, corresponding to ca. 3 ng of sample within only 64 scans [17], in the presence of low-micromolar concentrations of reductive radical quenchers [14].

Despite the above advances, the magnetic field dependence of LC-photo-CIDNP has never been explored, to date. This topic is particularly important because of previous theoretical studies on photo-CIDNP in the presence of flavin mononucleotide and Tyr [4]. These investigations showed that, at low applied magnetic fields, higher photo-CIDNP enhancements are expected [4]. Further, experimental photo-CIDNP field dependence investigations on the LOV-domain flavoprotein in the solid state also showed higher enhancements at low field [18]. Larger enhancements at low field (in the presence of specific isotope substitution of the LOV-domain flavin) were also achieved in the liquid state, under conditions where the solid-state-like triplet mechanism dominates [19]. Additional field-dependent photo-CIDNP studies based on the field-cycling technology at high sample concentration were also carried out [20–25].

In this work, we address the above gap of knowledge by exploring the magnetic field dependence of ¹H-detected ¹³C LC-photo-CIDNP, at low sample concentration in an oxygen-free environment with a high-photoexcited-triplet-state-dye. We focus on the high-field regime and analyze the phenomenon from both the computational and experimental standpoints. In terms of target molecules, we studied the LC-photo-CIDNP field dependence of the uniformly ¹³C and ¹⁵N labeled Trp (Trp-U-¹³C¹⁵N) and Trp-α-¹³C-β,β,2,4,5,6,7-d₇ isotopologs. Our computational predictions show that Trp-α-¹³C-β,β,2,4,5,6,7-d₇ is expected to display a much sharper field dependence and a much larger polarization increase at lower field (ca. 200 MHz, 4.7 T), relative to the other isotopolog. Interestingly, experimental LC-photo-CIDNP studies on Trp-U-¹³C¹⁵N and Trp-α-¹³C-β,β,2,4,5,6,7-d₇ at 1μM concentration, performed on 400, 600 and 750 MHz (9.4, 14.1 and 17.6 T) spectrometers, are qualitatively consistent with the theoretical predictions.

2. Methods

2.1. Materials.

The fluorescein dye (sodium salt), vitamin C (ascorbic acid, VC), oxygen-scavenging enzymes Aspergillus niger glucose oxidase (GO, Enzyme commission classification code EC 1.1.3.4, freeze-dried powder) and bovine liver catalase (CAT, EC 1.11.1.6, freeze-dried powder) were purchased from MilliporeSigma. Uniformly ¹³C,¹⁵N labeled Trp (Trp-U-¹³C,¹⁵N) (Fig. 2a) was purchased from Cambridge Isotopes Laboratories, Inc. The Trp-α-¹³C-β,β,2,4,5,6,7-d₇ isotopolog (IUPAC name: (S)-2-Amino-3-[(2,4,5,6,7-²H₅)-3-indolyl](2-¹³C,3,3-²H₂)propionic acid, Fig. 2a) was prepared and purified as described [17]. Briefly, Trp-α-¹³C-β,β,2,4,5,6,7-d₇ was generated via the Pf TrpB^2B9 and Tm LTA enzymes from formaldehyde-²H₂ (Cambridge Isotope Laboratories, Inc.), glycine(2-¹³C) (Cambridge Isotope Laboratories, Inc.), indole-²H₇ (CDN Isotopes) in the presence of pyridoxal 5’-monophosphate (MilliporeSigma). The preparation and purification of the Pyrococcus furiosus tryptophan synthase $\beta$-subunit 2B9 variant (Pf TrpB^2B9) [26] and Thermotoga maritima L-threonine aldolase (Tm LTA, EC 4.1.2.5) enzymes was carried out as described [27].

Fig. 2.

Description of Trp isotopologs and results of computational predictions. (a) Structure of ¹³C,¹⁵N uniformly labeled Trp (Trp-U-¹³C,¹⁵N) and (S)-2-Amino-3-[(2,4,5,6,7-²H₅)-3-indolyl](2-¹³C,3,3-²H₂)propionic acid (Trp-α-¹³C-β,β,2,4,5,6,7-d₇). (b) Plot illustrating the predicted polarization of LC-photo-CIDNP geminate recombination products at the ¹³C^α position of Trp isotopologs as a function of applied magnetic field (${\mathrm{B}}_0$). Computer simulations were performed using known g-factors [17, 36] and hyperfine coupling constants [17, 36–38] of ${\mathrm{F}\mathrm{l}}^{•-}$ and ${\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}$ (see Supplementary Information for more details).

2.2. Stock solutions.

Stock solutions of Trp-U-¹³C,¹⁵N and Trp-α-¹³C-β,β,2,4,5,6,7-d₇ were prepared upon dissolving the respective solid powders in distilled deionized water. Stock-solution concentrations were measured via a NanoDrop^™ 2000/2000c spectrophotometer (ThermoFisher) using an extinction coefficient of 5,600 M⁻¹ cm⁻¹ at 280 nm. GO (ext. coeff. 267,200 M⁻¹cm⁻¹ at 280 nm) and CAT (ext. coeff. 912,500 M⁻¹cm⁻¹ at 276 nm) for CAT [28] enzyme powders were dissolved in 10 mM potassium phosphate buffer (pH 7.14) and concentrations were assessed by electronic absorption spectroscopy. Enzyme stock solutions were aliquoted, flash-frozen with liquid nitrogen, and stored at −80 °C. Enzyme frozen aliquots were thawed upon incubation in a room-temperature water bath on the same day of the experiment.

2.3. NMR experiments under dark conditions.

The high-concentration dark ¹³C RASPRINT [16] experiments on Trp-U-¹³C,¹⁵N and Trp-α-¹³C-β,β,2,4,5,6,7-d₇ (Fig. 4) were conducted by diluting isotopolog stock solutions in distilled deionized water followed by addition of D₂O to a total 10% v/v. T₁ experiments are described in the supplementary information.

Fig. 4.

LC-photo-CIDNP spectra of Trp isotopologs under dark (LED-off) conditions. Data were collected with the ¹³C RASPRINT pulse sequence (32 scans, 5 s recycle delay) on concentrated samples (concentrations listed in the figure) in H₂O containing 10% D₂O (v/v) on NMR spectrometers operating at (a) 400 (b) 600 and (c) 750 MHz.

2.4. NMR experiments under light conditions.

The light ¹³C RASPRINT [16] experiments involving Trp-U-¹³C,¹⁵N and Trp-α-¹³C-β,β,2,4,5,6,7-d₇ (Fig. 3) were carried out at 1 μM isotopolog concentrations in the presence of 1 μM fluorescein, 2 μM VC, 0.15 μM GO, 0.10 μM CAT, 2.5 mM D-glucose, 10 mM potassium phosphate buffer (pH 7.16), and 10% v/v D₂O. VC (Catalog number: ND-2000, ext. coeff. of 6,956 M⁻¹cm⁻¹ at 250 nm, pH-independent isosbestic point) stock solutions were freshly prepared on each experimental day, and concentrations were measured via a NanoDrop^™ 2000/2000c spectrophotometer (ThermoFisher). A 2.3W power source with emission centered at 266 nm (UHP-mic-LED-450) equipped with a 1.0 mm-diameter and 10 m long polymer optical fiber (POF, Prizmatix, Holon, Israel) were used to induce nuclear hyperpolarization. The LED power at the fiber tip (to be inserted into NMR sample tubes) was 0.21 W. Additional details on the LC-photo-CIDNP experimental setup can be found in the literature [14, 16].

Fig. 3.

LC-photo-CIDNP spectra of Trp isotopologs under light (LED-on) and dark (LED-off) conditions. Data were collected with the ¹³C RASPRINT pulse sequence (32 scans, 50 ms recycle delay) on 1 μM samples in 10 mM potassium phosphate buffer (pH = 7.14) containing 10% D₂O (v/v) on NMR spectrometers operating at (a) 400 (b) 600 and (c) 750 MHz.

2.5. NMR data collection under dark and light conditions.

The ¹³C RASPRINT [16] pulse sequence was employed for experiments under both dark and light conditions. Temperature was calibrated via a 4 % methanol standard in methanol-d₄ at each magnetic field. A 50 ms recycle delay and a 0.2 s optical irradiation time per scan were used under light conditions, while a 5 s recycle delay was used under dark conditions to ensure nearly complete spin-lattice relaxation between scans. This procedure increases experiment duration under dark conditions, yet it ensures that enhancement factors are not artificially inflated due to incomplete longitudinal relaxation under dark conditions.

Experiments at 9.4 T (400 MHz) (Figs. 3a and 4a) were carried out on a Bruker Avance III HD 400 MHz NMR spectrometer equipped with a 5mm BBFO plus Smartprobe, at 24.6°C. Acquisition time (AQ) and total data number of points (TD) were set to 0.2046 s and 2,728, respectively. Data at 14.1 T (600 MHz) were acquired on two separate spectrometers to estimate the error due to individual instruments operating at the same field. Specifically: 600 MHz (I): Bruker Avance III HD 600 MHz equipped with a 5mm Cryoprobe TCI-F {¹⁹F/¹³C/¹⁵N} (Figs. 3b and 4b). 600 MHz (II): Bruker Avance III HD 600 MHz equipped with a 5 mm Cryoprobe QXI {¹H/³¹P/¹³C/¹⁵N} (data shown in Supplementary Information (SI)).

Experiments at 17.6 T (750 MHz) were carried on a Bruker Avance III HD 750 MHz spectrometer equipped with a 5 mm Cryoprobe TXI {¹H/¹³C/¹⁵N} (Figs. 3c and 4c).

The experiments at both 14.1 and 17.6 T had an AQ of 0.2048 s and a TD of 4,096 points.

2.6. NMR data processing and analysis.

Spectra were processed with the MNova (version 14.2.3) software package upon zero-filling to 65,536 complex points. An exponential-decay window function (with line-broadening set to 10 Hz) was applied before Fourier transform. Each spectrum was processed three times with the same zero-filling and window-function parameters but separate manual phase correction. Baseline correction (polynomial function) and integration were performed on these separate data sets to reduce integration errors. The mean value of the integrals for each experiment was used to determine enhancement factors. Under dark conditions, areas were normalized according to eqn 1 below

$${normalizedarea}_{dark}=\frac{{absoulteintergal}_{dark}}{{sampleconc}_{dark}/{sampleconc}_{light}}.$$ (1)

This procedure ensured proper assessment of concentration-independent enhancement factors ($\mathrm{\epsilon }$).

2.7. Computational assessment of polarization of LC-photo-CIDNP geminate-recombination products.

For the two isotopologs studied in this work, computational predictions of the polarization of LC-photo-CIDNP geminate-recombination products were carried out upon determining $P_0$ according to eqn 9. The results are shown in Fig. 2b. Note that the plot of Fig. 2b is conceptually consistent with a previously reported plot illustrating the dependence of ${\mathrm{P}}_0$ on $\mathrm{\Delta }\mathrm{g}$ [17]. Computer simulations followed procedures imparted by a custom-built Python script (Python v. 3.8, Python Software Foundation). All calculations were run either on a MacOS laptop computer or via the UW-Madison Center for High-Throughput Computing (CHTC) [29, 30]. The simulations neglected natural-abundance ¹³C (1%), amino ¹⁴N and ¹⁵N (due to unavailable hyperfine coupling constants) and did not include exchangeable amino protons of both isotopologs. To estimate A values of ²H nuclei in Trp-α-¹³C-β,β,2,4,5,6,7-d₇, we multiplied the A values of all ¹H nuclei at a given position by 0.1535, which is the ratio of the gyromagnetic ratios of ²H and ¹H. All hyperfine coupling constants used in the computation are listed in Supplementary Table S1.

3. Results and Discussion

3.1. Theoretical predictions on the field dependence of LC-photo-CIDNP as a function of isotope composition of the molecule of interest.

In this work, we explored the effect of isolating one target nuclear spin pair (¹H^α-¹³C^α) from other nearby NMR-active spins carrying high gyromagnetic ratios. The isotope configurations corresponding to this scenario are denoted here as quasi-isolated spin pairs. We targeted the computational prediction of the effect of two limiting isotopologs, uniformly ¹³C,¹⁵N-labeled Trp (Trp-U-¹³C,¹⁵N) and Trp-α-¹³C-β,β,2,4,5,6,7-d₇, on the polarization of LC-photo-CIDNP geminate-recombination products as a function of applied magnetic field (${\mathrm{B}}_0$). The covalent structure of the two above isotopologs is shown in Fig. 2a.

We conducted computational predictions to probe the LC-photo-CIDNP polarization of geminate-recombination products of the two above isotopologs at ¹³C^α as a function of ${\mathrm{B}}_0$ based on theoretical considerations by Adrian, Ivanov and others [4, 17, 31, 32], as detailed below. First, we assumed that all Trp molecules undergo electron transfer in solution, upon collision with the photoexcited triplet state of fluorescein$\left({}^{\text{T}1}\text{Fl}\right)$, and form triplet-state Trp fluorescein radical pairs $\left({}^{\mathrm{T}}\left[{\mathrm{F}\mathrm{l}}^{•-}{\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}\right]\right)$. The population difference between any given nuclear-spin configurations 1 and 2, corresponding to the geminate recombination product of a freely diffusing radical pair, can be obtained from the relation below [32]

$$p_1-p_2=p\left(\sqrt{\left|{\omega }_{TS1}\right|{\tau }_d}-\sqrt{\left|{\omega }_{TS2}\right|{\tau }_d}\right)\text{,}$$ (2)

where $p_1$ and $p_2$ denote the populations of nuclear-spin configurations 1 and 2, ${\omega }_{TS1}$ and ${\omega }_{TS2}$ are the triplet-singlet mixing frequencies of configurations 1 and 2, respectively, and $p$ is a normalization factor ensuring that the sum of all possible configurations is equal to 1. The mathematical form of $p$ is further discussed below. In addition, ${\tau }_d$ is the average time during which the $\left[{\mathrm{F}\mathrm{l}}^{•-}{\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}\right]$ radical-pair components remain closely associated, yet at a distance preventing orbital overlap, before long-term dissociation. Values of ${\tau }_d$ were estimated via relation [32].

$${\tau }_d=\frac{{(R_{F{l}^{•-}}+R_{Tr{p}^{•+}})}^2}{D_{F{l}^{•-}}+D_{Tr{p}^{•+}}},$$ (3)

where $R_{F{l}^{•-}}$ and $R_{Tr{p}^{•+}}$, are the van der Waals radii of ${\mathrm{F}\mathrm{l}}^{•-}$ and ${\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}$, which were set to be equal to 4.4 Å and 4.2 Å, respectively [33]. In addition, $D_{F{l}^{•-}}$ (4.2 × 10⁻⁶ cm²s⁻¹) [34] and $D_{{Trp}^{•+}}$ (6.592 × 10⁻⁶ cm²s⁻¹) [35] denote the translational diffusion coefficients of ${\mathrm{F}\mathrm{l}}^{•-}$ and ${\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}$, respectively. Note that the ${\omega }_{TS}$ of a specific nuclear-spin configuration that undergoes T-S mixing (followed by back-electron transfer/recombination) depends on ${\mathrm{B}}_0$, the $\mathrm{g}$-factors of ${\mathrm{F}\mathrm{l}}^{•-}$ and ${\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}$, and the hyperfine coupling constants of ${\mathrm{F}\mathrm{l}}^{•-}$ and ${\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}$ according to relations

$$\mathrm{\Delta }g=g_{F{l}^{•-}}-g_{Tr{p}^{•+}},$$ (4)

$${\omega }_{TS}=\frac{1}{2}\left[\Delta g{\mu }_B{B}_0+{\sum }_{i=0}^a m_{i,F{l}^{•-}}{A}_{i,F{l}^{•-}}-{\sum }_{j=0}^b m_{j,Tr{p}^{•+}}{A}_{j,Tr{p}^{•+}}\right],$$ (5)

where $g_{F{l}^{•-}}$ and $g_{Tr{p}^{•+}}$ are the g-factors values of ${\mathrm{F}\mathrm{l}}^{•-}$ and ${\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}$, which are known from the literature to be 2.003077 [17] and 2.0027 [36] respectively. In addition, $\Delta g$ is the difference between the g-factors of ${\mathrm{F}\mathrm{l}}^{•-}$ and ${\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}$. Further, ${\mu }_B$ is the Bohr magneton, and the summation indexes $i$ and $j$ denote individual nuclei of the ${Fl}^{•-}$ and ${Trp}^{•+}$ radical-pair components, respectively. The letters $a$ and $b$ denote the total numbers of NMR-active nuclear spins of ${\mathrm{F}\mathrm{l}}^{•-}$ and ${\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}$ minus 1. The parameters m and A (see SI) are the magnetic nuclear-spin quantum number and hyperfine coupling constant of each spin $i$ or $j$ [17, 36–38]. We are particularly interested in the ¹³C^α position of Trp, because of its high hyperfine coupling constant and the known relation between its secondary chemical shift [39] or SSP [40] parameter and protein secondary structure. Upon separating the summation term corresponding to the ¹³C^α of ${\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}$ (i.e., the nucleus of interest) in eqn. 5, we get

$${\omega }_{TS,\mathrm{\alpha },\mathrm{\chi }}=\frac{1}{2}\left[\mathrm{\Delta }g{\mu }_B{B}_0+{\sum }_{i=0}^a m_{i,F{l}^{•-}}{A}_{i,F{l}^{•-}}-\frac{1}{2}{A}_0-{\sum }_{j=1}^b m_{j,Tr{p}^{•+}}{A}_{j,Tr{p}^{•+}}\right],$$ (6)

and

$${\omega }_{TS,\mathrm{\beta },\mathrm{\chi }}=\frac{1}{2}\left[\Delta g{\mu }_B{B}_0+{\sum }_{i=0}^a m_{i,F{l}^{•-}}{A}_{i,F{l}^{•-}}+\frac{1}{2}{A}_0-{\sum }_{j=1}^b m_{j,Tr{p}^{•+}}{A}_{j,Tr{p}^{•+}}\right],$$ (7)

where, for simplicity, 0 denotes the ¹³C^α of ${\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}$ and $\mathrm{\chi }$ denotes the nuclear spin configuration of all the other spins except for ¹³C^α. In addition, ${\omega }_{TS,\mathrm{\alpha },\mathrm{\chi }}$ and ${\omega }_{TS,\mathrm{\beta },\mathrm{\chi }}$ are the triplet-singlet mixing frequencies of configurations where 0 is in either the $\mathrm{\alpha }$ or $\mathrm{\beta }$ nuclear spin state but the other nuclear spins are in random configurations. Then, the population difference between configurations $\mathrm{\alpha },\mathrm{\chi }$ and $\mathrm{\beta },\mathrm{\chi }$ can be expressed as

$$p_{\alpha ,\chi }-p_{\beta ,\chi }=p(\sqrt{\left|{\omega }_{TS,\alpha ,\chi }\right|{\tau }_d}-\sqrt{\left|{\omega }_{TS,\beta ,\chi }\right|{\tau }_d}).$$ (8)

Note that the polarization of ¹³C^α of Trp $\left(P_0\right)$ arising from geminate recombination is equal to the sum of all populations with configurations bearing ¹³C^α in its $\mathrm{\alpha }$ spin-state minus the sum of all populations with configurations bearing ¹³C^α is in $\mathrm{\beta }$ spin-state, according to

$$P_0=\sum p_{\alpha ,\chi }-\sum p_{\beta ,\chi }=p\sqrt{{\tau }_d}\left(\sum \sqrt{\left|{\omega }_{TS,\alpha ,\chi }\right|}-\sum \sqrt{\left|{\omega }_{TS,\beta ,\chi }\right|}\right).$$ (9)

This relation is justified by the fact that that ¹³C^α can only assume two nuclear-spin states, either $\mathrm{\alpha }$ or $\mathrm{\beta }$. The numerical value of the normalization factor $p$ should be adjusted to ensure that the sum of the above summations is equal to 1, according to

$$\sum p_{\alpha ,\chi }+\sum p_{\beta ,\chi }=p\sqrt{{\tau }_d}\left(\sum \sqrt{\left|{\omega }_{TS,\alpha ,\chi }\right|}+\sum \sqrt{\left|{\omega }_{TS,\beta ,\chi }\right|}\right)=1.$$ (10)

As a consequence, variations in ${\mathrm{B}}_0$ or specific Trp isotopolog impact the first or the last terms in eqns. 6 and 7, leads to corresponding changes in triplet-singlet mixing frequencies, and population differences between configurations $\mathrm{\alpha },\mathrm{\chi }$ and $\mathrm{\beta },\mathrm{\chi }$. In summary, given the above treatment, it follows that different isotopologs are expected to induce variations in LC-photo-CIDNP hyperpolarization [41].

We carried out memory-intensive computations applying the above formalism to the prediction of the polarization ${(\mathrm{P}}_0)$ of LC-photo-CIDNP geminate recombination products for the ¹H^α,¹³C^α pair of the Trp-U-¹³C,¹⁵N and Trp-α-¹³C-β,β,2,4,5,6,7-d₇ isotopologs in the presence of the fluorescein photosensitizer dye, according to eqn. 9. The results for each of the two isotopologs are shown in Fig. 2b.

Interestingly, the predicted polarization of Trp-α-¹³C-β,β,2,4,5,6,7-d₇ undergoes a dramatic enhancement at low ${\mathrm{B}}_0$. Namely, the expected maximum is at ${\mathrm{P}}_0=0.148$ at 150 MHz (3.5 T). As a comparison, at higher ${\mathrm{B}}_0$, e.g., 750 MHz (17.6 T) the predicted ${\mathrm{P}}_0$ value is $P_0<0.043$, i.e., at least 3.4-fold lower than at the maximum of the field-dependent profile. In contrast, much smaller variations are predicted for the uniformly labeled Trp-U-¹³C,¹⁵N isotopolog (Fig. 2b). For instance, at 150 MHz (3.5 T) the predicted ${\mathrm{P}}_0$ value for Trp-U-¹³C,¹⁵N is more than 7-fold larger than the corresponding value for Trp-α-¹³C-β,β,2,4,5,6,7-d₇. Conversely, at very high field (> ca. 700 MHz or 16.4 T) both isotopologs are expected to exhibit similar behavior.

The above results underscore the importance of LC-photo-CIDNP candidate molecules that carry a quasi-isolated spin pair. The tested Trp isotopolog Trp-α-¹³C-β,β,2,4,5,6,7-d₇, as well as related LC-photo-CIDNP substrates or isotopic substitutions, are expected to display significantly larger LC-photo-CIDNP polarization at low magnetic field. On the other hand, candidate biomolecules that bear lots of nearby NMR-active nuclei with high gyromagnetic ratio in proximity of the site of interest (e.g., the ¹H^α,¹³C^α pair) are more likely to have lots of cancellation effects within the summation elements of eqns 6 and 7, and thereby are more likely to display flatter field-dependence profiles.

In order to place our work in the context of previously published studies, it is interesting to note that somewhat related simulations were carried out by Hore and coworkers in the past [4]. Yet these investigations were performed on flavin mononucleotide (FMN) system that included Tyr, and not Trp, as the molecule of interest [4]. While polarization enhancements at low field were also predicted in this study, the different molecule of interest/dye combination precludes direct comparisons with our work. All other previous field-dependent studies that we are aware of were carried out on the LOV-domain flavoprotein, which carries a built-in photosensitizer and were either done in the solid state [18], or in solution under solid-like conditions [19]. The above features of previous investigations on photo-CIDNP field dependence prevent direct comparisons with our system.

3.2. Experimental determination of LC-photo-CIDNP polarization enhancement factors ($\mathit{\epsilon }$) and percent polarizations $({\mathrm{P}}_{\%)}$ of Trp isotopologs as a function of field strength.

The predictions of Fig. 2b provided an excellent platform for experimental verification, given that the Trp-U-¹³C,¹⁵N and ¹³C^α of Trp-α-¹³C-β,β,2,4,5,6,7-d₇ isotopologs are either commercially available, or amenable to in-house preparation via known procedures [17, 27], respectively. We quantitatively probed the polarization enhancements of both Trp isotopologs by determining resonance areas under dark and light conditions using 400, 600 and 750 MHz NMR spectrometers, corresponding to 9.4, 14.1 and 17.6 T applied fields. The known reverse-INEPT-like ¹³C RASPRINT [16] pulse sequence was employed at both dark and light condition. ¹³C RASPRINT, which has been specifically designed for LC-photo-CIDNP, enables short in situ hyperpolarization (optical irradiation time = 0.2 s). This pulse sequence was optimized for ultrafast data collection (50 ms recycle delay) in aqueous solution. Optically-driven irradiation, generating LC-photo-CIDNP, is followed by ¹³C to ¹H polarization transfer via reverse INEPT, for efficient detection of ¹H^α -¹³C^α pairs [16]. All experiments under light conditions (i.e., LED-on, Fig. 3) were carried out on 1μM Trp-U-¹³C,¹⁵N and 1μM Trp-α-¹³C-β,β,2,4,5,6,7-d₇, and 32 transients were collected in each case. Under dark (LED-off) conditions, no detectable signal was observed for each of the samples at 1μM concentration (Figs. 3a, 3b and 3c). In order to determine enhancements factors (see below) we collected additional data under dark-conditions at much higher concentrations (1.07 mM for Trp-U-¹³C,¹⁵N, 639.3 μM Trp-α-¹³C-β,β,2,4,5,6,7-d₇). Integral values of the ¹H^α resonance were normalized according to eqn. 1. In addition, long (5 s) recycle delays were employed to ensure complete longitudinal relaxation (T1 relaxation) between scans. The LC-photo-CIDNP enhancement factor $\epsilon$, which we defined as

$$\epsilon =\frac{{normalizedarea}_{dark}}{{area}_{light}}.$$ (10)

The experimental enhancement factor $\epsilon$ of Trp-α-¹³C-β,β,2,4,5,6,7-d₇ at 400 MHz was found to be 515.71 ± 30.19. this value decreased dramatically to 213.07 ± 3.67 and 190.5 ± 20.18 upon increasing the spectrometer frequency to 600 and 750 MHz (Figs. 5a and 5b). In contrast, the $\epsilon$ values of Trp-U-¹³C,¹⁵N only varied from 237.75 ± 21.48 to 152.36 ± 4.65 to 242.25 ± 8.27, at spectrometer frequencies of 400, 600 and 750 MHz, respectively, as shown in Figs. 5a and 5b. These results are in exciting qualitative agreement with the computational data of Fig.2, with the Trp-α-¹³C-β,β,2,4,5,6,7-d₇ isotopolog displaying an high enhancement factor $\mathrm{\epsilon }>500$ at 400 MHz.

Fig. 5.

Experimentally determined LC-photo-CIDNP enhancement factors (𝜀) of Trp isotopologs. (a) Bar graph illustrating the polarization enhancement of ¹³C^α (detected via the ¹H^α resonance) of Trp-U-¹³C,¹⁵N and Trp-α-¹³C-β,β,2,4,5,6,7-d₇ for data acquired on spectrometers operating at 400 (24.6°C, n = 6), 600 (24.3°C, n = 3) and 750 (22.7°C, n = 3) MHz. Enhancement factors 𝜀 were determined from the experimental data in Figs 3 and 4 and eqn 10. (b) Table reporting the specific numerical values of the data in panel (a). The letter n denotes the number of experiments. Enhancement factors are reported as avg ± SE.

In addition, we determined thermal-equilibrium percent polarization values at ¹³C^α of Trp $\left(P_{\mathrm{\%},theq}\right)$ to the Boltzmann distribution at each ${\mathrm{B}}_0$ value according to eqn. 11 below. Then, we evaluated the ¹³C^α percent polarization ${(P}_{\mathrm{\%}})$ from $\mathrm{\epsilon }$ and $P_{\mathrm{\%},theq}$ according to eqn 12

$$P_{\mathrm{\%},theq}=tanh(\frac{\hslash \gamma B_0}{2k_{B}T}),$$ (11)

$$P=\epsilon P_{\mathrm{\%},theq},$$ (12)

where $\hslash$ is the Planck constant, ${\mathrm{k}}_{\mathrm{B}}$ is the Boltzmann constant, $\mathrm{\gamma }$ is the gyromagnetic ratio (with: ${\gamma }_{{13}_C}=10.705\mathrm{M}\mathrm{H}\mathrm{z}/\mathrm{T},{\gamma }_{1_H}=42.576\mathrm{M}\mathrm{H}\mathrm{z}/\mathrm{T}$) [42], and $\mathrm{T}$ is the sample temperature. Temperature calibration was carried out with $4\mathrm{\%}$ methanol in methanol-d₄ [43].

The resulting $P_{\mathrm{\%}}$ values of Trp-U-¹³C,¹⁵N and Trp-α-¹³C-β,β,2,4,5,6,7-d₇ are reported in Fig. 6a and 6b. As shown in this figure, the experimentally determined $P_{\mathrm{\%}}$ values for the two Trp isotopologs are significantly different at 400 and 600 MHz but no significant differences were observed at 750 MHz, based on t-tests with significance = 0.05 (${\mathrm{P}}_{400\mathrm{M}\mathrm{H}\mathrm{z}}=3.69\mathrm{e}-5,{\mathrm{P}}_{600\mathrm{M}\mathrm{H}\mathrm{z}}=5.11\mathrm{e}-4$and ${\mathrm{P}}_{750\mathrm{M}\mathrm{H}\mathrm{z}}=0.098$). Despite the fact that our experiment-derived $P_{\mathrm{\%}}$ values are not as striking as the predictions of Fig. 2b, significantly higher values of ${\mathrm{P}}_{\mathrm{\%}}$ were observed for Trp-α-¹³C-β,β,2,4,5,6,7-d₇ relative to Trp-U-¹³C, ¹⁵N consistent with the computational predictions.

Fig. 6.

Experimentally determined LC-photo-CIDNP percent polarization ${(\mathrm{P}}_{\mathrm{\%}})$ of Trp isotopologs. (a) Bar graph illustrating the polarization enhancement of ¹³C^α (detected via the ¹H^α resonance) of Trp-U-¹³C,¹⁵N and Trp-α-¹³C-β,β,2,4,5,6,7-d₇ for data acquired on spectrometers operating at 400 (24.6°C, n = 6), 600 (24.3°C, n = 3) and 750 (22.7°C, n = 3) MHz. ${\mathrm{P}}_{\mathrm{\%}}$ values were determined from the experimental data in Figs 3 and 4 and eqn 12. Thermal polarization values were computationally estimated according to eqn 11. (b) Table reporting the specific numerical values of the data in panel (a). The letter n denotes the number of experiments. Percent polarizations are reported as avg ± SE.

One potential source of error is the fact that all Trp molecules were assumed to lead to the formation of radical pairs, upon collision with ^T1Fl. This treatment omitted taking into account the kinetics of $\left[{\mathrm{F}\mathrm{l}}^{•-}{\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}\right]$ formation. In addition, theoretical ${\mathrm{P}}_{\mathrm{\%}}$ values do not include the influence of all the post-TS-mixing kinetic processes collectively referred to as recombination. F-pair polarization was also neglected, due to the very-low sample concentration. Further, our experimental ${\mathrm{P}}_{\mathrm{\%}}$ values are based on steady-state LC-photo-CIDNP. Therefore, in addition to the above factors, the experiments also include the achievement of steady-state conditions. Theoretical expressions for photo-CIDNP and LC-photo-CIDNP hyperpolarization under steady-state conditions were derived before by Okuno et al. [15, 44]. According to these expressions, steady-state LC-photo-CIDNP is affected by a number of parameters including T₁ relaxation, which takes place during continuous optical irradiation. In order to experimentally probe the role of T₁, we performed ¹³C T₁ measurements on the Trp-U-¹³C,¹⁵N and Trp-α-¹³C-β,β,2,4,5,6,7-d₇ isotopologs at each experimentally relevant field (400, 600 and 750 MHz). The experimental T₁ values are very similar at all fields (Table 1 and SI Fig. S2).

Table 1.

Experimental ¹³C^α T1 values of Trp-U-¹³C,¹⁵N and Trp-α-¹³C-β,β,2,4,5,6,7-d₇ at 400 MHz, 600 MHz and 750 MHz applied fields. T1 values are reported as avg ± SE (n = 2).

T1 measurements
	400 MHz	600 MHz	750 MHz
Trp-U-13C,15N (s)	1.39 ± 0.03	1.35 ± 0.01	1.43 ± 0.03
Trp-α-13C-β,β,2,4,5,6,7-d7 (s)	1.50 ± 0.03	1.48 ± 0.02	1.56 ± 0.02

Therefore, the qualitative comparison of theoretical geminate polarization and experimental steady-state polarization shown in Figs. 2b and 6a is not significantly affected the weak T₁-dependence of steady-state polarization. Finally, it is worth considering that signals attained via LC-photo-CIDNP are not linearly proportional to the number of scans due to some dye and sample degradation upon long-term irradiation. Although we added oxygen-scavenging enzymes GO and CAT and reductive radical quencher VC [14] to our samples, to reduce photodegradative events caused by highly reactive singlet O₂ [13, 45, 46] and degradation products of the ${\mathrm{F}\mathrm{l}}^{•-}$ and ${\mathrm{T}\mathrm{r}\mathrm{p}}^{•+}$ radicals in solution, the observed cumulative signal was only ca. 70% of the signal expected in the absence of photodamage [14].

In all, enhancement factors $\mathrm{\epsilon }$ are in good agreement with the computationally predicted polarization values of Fig.2b, while experimentally determined percent polarizations ${\mathrm{P}}_{\mathrm{\%}}$ are in acceptable agreement only, especially in terms of the important better performance of Trp-α-¹³C-β,β,2,4,5,6,7-d₇ than the Trp-U-¹³C,¹⁵N isotopolog at 400 MHz.

4. Conclusions

This work focuses on the magnetic-field dependence of LC-photo-CIDNP in solution and compares two tryptophan isotopologs: Trp-U-¹³C,¹⁵N and Trp-α-¹³C-β,β,2,4,5,6,7-d₇. The latter isotopolog, which is the only one that displays a quasi-isolated ¹H^α-¹³C^α spin pair, is predicted and observed to display a sharper field dependence, resulting in higher LC-photo-CIDNP enhancements and percent polarizations at lower field relative to the other isotopolog (Trp-U-¹³C,¹⁵N). These results suggest that LC-photo-CIDNP of Trp isotopologs bearing quasi-isolated spin pairs bear competitive advantages at moderate magnetic fields, corresponding to spectrometer frequencies of ca. 150 MHz.

Data Availability

Data Availability The datasets generated during and/or analyzed during the current study are available from the corresponding author upon reasonable request.