J Coupling Constants of <1 Hz Enable 13C Hyperpolarization of Pyruvate via Reversible Exchange of Parahydrogen

Observing pyruvate metabolism in vivo has become a focal point of molecular magnetic resonance imaging. Signal amplification by reversible exchange (SABRE) has recently emerged as a versatile hyperpolarization technique. Tuning of the spin order transfer (SOT) in SABRE is challenging as the small 1H–13C J couplings, in the 13C-pyruvate case, result in SOT being not readily discernible. We demonstrate an experimental method using frequency-selective excitation of parahydrogen-derived polarization SOT sequence (SEPP-SPINEPT); its application led to up to 5700-fold 13C signal gain. In this way, we estimated the lifetime of two Ir–pyruvate SABRE complexes alongside the individual probing of eight small 1H–13C J couplings that connect the hydride protons in these complexes to 1- and 2-13C pyruvate spins, affording values between 0 and 2.69 Hz. Using electronic structure calculations, we define the low-energy structure of the corresponding complexes. Hence, this study demonstrates a novel approach to analyzing the spin topology of short-lived organometallic complexes.

The enhancement factor of the bound substrate was calculated using the signal intensities of the thermal and hyperpolarized pyruvate spectra: is the integral of the same of the same but thermally polarized 13 C signal,  HP and  TP ,  HP and  TP are corresponding receiver gains and the number of scans used to acquire hyperpolarized and thermally polarized signals.
Corresponding polarization was calculated as follows: where  13 is the gyromagnetic ratio of 13 C,  0 is the observation magnetic field,  is the temperature, ℏ is the reduced Planck's constant, and   is Boltzmann's constant.
Temperature dependence of 1 H PASADENA signal for three complexes The SOT in SABRE experiments is challenging due to the interplay of chemical exchange and spin-spin interactions.Therefore, temperature plays an important role in SABRE.After acquiring the 1 H PASADENA spectrum, one can notice three primary iridium complexes (Figure 1).Measuring the signal intensities of 1 H PASADENA, we found that the highest polarization for complex [1] and [2] is reached at 267 K (Figure S1).The sample composition was [Ir] = 5 mM, DMSO = 20 mM, [Pyr].=50 mM in 400 µl of methanol-d4.

Figure S1
. 1 H PASADENA of three primary complexes (Figure 1) as a function of temperature.At 267 K, the PASADENA signal of complex [1] reaches its maximum.

Optimization of the power of the selective pulses
We used selective pulses (SP) with the "Gaus1_180r.1000"shape available in TopSpin with 8, 10, and 12 ms duration.In this section, we describe how we calibrated the power of 10 ms SP pulses.Using the pulse sequence consisting of SP -broad band 90 o pulse -acquisition of free induction decay (FID), we measured the signal as a function of the amplitude of SP (Figure S2).
For an SP with one carrier frequency (SP-1) and a length of 10 ms, 90⁰ is reached at 0.08147 V (0.00013285 W, 38.77 dB) and 180⁰ at a double amplitude of 0.16311 V (0.0005315 W, 32.74 dB).
To excite two hydrogens of [1] (-27.2 ppm and -29.1 ppm) or [2] (-14.97 ppm and -24.08 ppm), we combined two SP with the same shape and different carrier frequencies, e.g., for complex [1] the first at 0 Hz and the second at 761.88 Hz (1.9 ppm to the left or to the right).The resulting SP with two carrier frequencies is called SP-2.

SEPP optimization
SEPP SOT converts the PASADENA two-spin order into the magnetization of one of them.We set out to find the delays τ and τ3 (Figure S3A) of the pulse sequence that provides the highest signal.
We measured the SEPP signal for τ3 of 0, 2.5, 5, and 7.5 ms, the duration of the SPs was Δ= 10 ms, and τ was changing from 0 to 100 ms.In total, 140 experiments were carried out (Figure S3B).The maximum signal was achieved at τ = 10 ms and τ3 = Δ/2 = 5 ms.One can explain that adding τ3 allows the proper rephasing of the spins.Below, we will show that SEPP performance is identical when using different durations of RF pulses (Figure S4).

S-7
Effect of selective pulse length on SEPP Using SEPP, one can transfer the PASADENA spin order into the magnetization of one of the spins.
Here, we analyzed the effect of the pulse length on SEPP performance (Figure S4).We repeated SEPP with three different pulse lengths of 8 ms, 10 ms, and 12 ms in function of τ1 (Figure S4A); no significant difference was found.The maximum for complex [1] at 267 K was reached at  1 ≅ 20 ms ≅ .As one can see, [3] has the fastest R and hence the largest deviation of experimentally optimal  1 from theoretically estimated.On contrast, the [2] has the slowest R and experimentally optimal  1 coincides with the theoretically predicted.
The integrals of the spectral lines were well fitted with a damped sine wave function:  × sin(2 HH  1 ) × exp(−2 1 × ).The results of fit for three complexes are given in Table S1.The signal decay rate  is a superposition of relaxation and dissociation rate.S1.

phINEPT pulse sequence
Application of phINEPT sequence was found to be impractical because the 13 C signal as a function of  1 is modulated by three interactions  HH ,  H a  and  H b  (Figure S5).Therefore, in the main text, we used frequency-selective SOT.

S-9
Estimation of J CH from 1 H PASADENA spectra We compared the 1 H PASADENA spectra for [1] and [2] with either 1-13 C-pyr or 2-13 C-pyr (Figures S6-8).We noticed that full width at half maximum (FWHM) is larger in the spectrum without 13 C decoupling than in the spectrum with 13 C decoupling.This lets us estimate the 1 H-13 C interactions.
First, we measured 1 H PASADENA with 13 C decoupling (Figure S6-8, right-hand side).Then, we fit each spectrum using the sum of two Lorentzian functions: The fit gave us two values of FWHM of both lines.Unfortunately, the two line widths were different due to the radiation-damping effect.
In the second step, we fit the 1 H PASADENA (Figure S6-8, left-hand side) with four Lorentzian functions using the same FWHMs that we evaluated before: ) (Eq S4) Experimental data for 1-13 C-Pyr and 2-13 C-Pyr are plotted in Figures S7-8 and the corresponding estimated  CH are given in Table S2.
The fitting was implemented on MATLAB using nonlinear regression function "nlinfit".The fitting script, together with integrals, are available in Supporting Materials.The reported errors are the results of such fitting.We measured the natural linewidths with 1 H PASADENA{ 13 C} spectrum and then used those values and eq.S3-4, we estimated   interactions.As a result of these small interactions the linewidths in 1 H PASADENA are normally broader than in 1 H PASADENA { 13 C}.The corresponding NMR spectra for complex [1] and [2] are given in Figures S7 and S8.The estimated interactions are given in Table S2.
We employed the SEPP-SPINEPT pulse sequence for each hydride in complexes [1] and [2], and both 1 and 2-13 C pyruvate, and conducted experiments at three temperatures: 256, 261, and 267 K.
Notably, H b (-27.2 ppm) in 2-13 C complex [1] remained unobservable, while H b (-24.09ppm) in 2-13 C complex [2] exhibited a coupling of 2.69 Hz, effectively measured using 1 H PASADENA.For all observable 1 H-13 C interactions, we performed kinetic analysis, fitting the data with the equation A × sin(2πJCHτ2)×exp (-2τ2R), where JCH represents the J coupling between proton and carbon, and R denotes the combined relaxation and exchange parameter.Each hydride possesses its distinct JCH and exchange constant for each temperature.Notably, hydrides within the same complex share the same constant R, similar to the one measured with the SEPP (Table S1).To streamline the analysis, we employed a global fitting approach using MATLAB scripts to fit all parameters simultaneously using 9 or 12 kinetics for each complex (depending on the observable kinetics).Below, we show the fit when we used only 9 kinetics for each complex.Across all nine kinetics, we share nine amplitudes denoted as A1 to A9, three relaxation-exchange parameters  for each temperature, and three unique J coupling interactions.
To help understand the applied global fitting and parameters, see Table S3.Table S9 illustrates which parameters were used and were the same for some kinetics.
The reported errors are the results of such fits using MATLAB nonlinear regression function "nlinfit".The fitting script, together with integrals, are available in Supporting Materials.
Table S3.The sets of parameters used to fit SEPP-SPINEPT kinetics.See that Js are the same for each C-H pair, while Rs are the same for each T.

Estimated temperature of dissociation rate
Measuring J coupling less than 1 Hz is challenging in the presence of fast exchange.One can decrease the temperature to reduce the exchange rate to slow down the exchange rate.Using our SEPP-SPINEPT kinetics at temperatures 256, 261, and 267 K, we estimated the parameter () =   () −  2 ().The typical relaxation rate of IrHH protons is about 1 s, hence if we estimate  2 = 1 s -1 then we can approximate the exchange rates to lower temperatures using Arrhenius's equation: Which is convenient to fit with a linear function as follows: ln( d ) = ln() −  a  (Eq.S6) We also estimated the entropy and enthalpy of activation.By using the Eyring equation in the form Which is convenient to fit with a linear function as follows: ln ( Note that here  is gas constant.(G, H, I, J) exemplary phased spectra at a maximum of polarization with signal enhancement.Kinetics measured using 1-13 C_pyr (black), 2-13 C-pyr (blue).Kinetics measured using 1-13 C-pyr and applying { 1 H} decoupling (red), and 2-13 C-pyr and applying { 1 H} decoupling (green).

Quantum chemical calculations of the complex structures [1-3] and NMR parameters
Molecular structures optimized at the B3LYP-D4/def2-TZVP level of theory are shown in Figure S14.
At the optimized structures, NMR chemical shifts calculated at the GIAO-ZORA-TPSSh/def2-TZVPP level of theory and spin-spin coupling constants calculated at the PBE/pcJ-3 level of theory are given in Table S4.
In the 2D surface scan for complex [1], the H-H and Ir-H2 distances were varied while keeping Ir-H a and Ir-H b distances equal at all times, i.e., two H atoms exhibit symmetrical alignment with respect to the Ir atom.A total of 21 H-H distance values and 18 Ir-H2 distance values were selected to build a grid of 378 points, each of which corresponded to a constrained geometry optimization at the B3LYP-D4/def2-SVP level of theory.Note that in the obtained potential energy surface (PES) (Figure 2B), the energy minimum structure does not exactly coincide with the optimized geometry due to the symmetry restriction on the Ir-H bond lengths and variations in method accuracy.The computed JH-H and JC-H when moving from dihydrogen (RHH = 0.8 Å) to the dihydride complex (RHH = 1.9 Å) on the PES (Figure 2C) were given in Table S5.
Files with the optimised geometries are attached to this manuscript.

Figure S3 .
Figure S3.Optimization of SEPP SOT.SEPP sequence (A), the magnetization of H a (-29.1ppm) of [1] after SEPP as a function of  3 and  (B).The highest polarization achieved was at τ = 10 ms, τ3 = 5 ms, and  = 10 ms.τ was varied in a step of 1 ms between 0 and 20 ms and in a step of 2 ms between 20 and 100 ms.The highest signal was achieved at τ = 10 ms and τ3 = /2 = 5 ms.
As one can see, due to signal decay, optimal  1 differs from predicted

Figure S4 .
Figure S4.The effect of interpulse interval and pulse duration on the SEPP SOT.(A) Scheme of SEPP SOT.(B) 1 H SEPP spectra at some selected  1 values were obtained with 10 ms selective pulses.The red area indicates the integration region.(C) Integrals of polarized by SEPP proton of [1] as a function  1 for three durations of SPs: 8 (black), 10 (red), and 12 ms (blue).No significant difference was found.(D) Integrals of polarized proton of [2] (blue) and [3] (red).All experiments were carried out at 267 K at 9.4 T. The results of fit (C and D) are given in TableS1.

Figure S5 .
Figure S5.The phINEPT spin order transfer.(A) phINEPT sequences.Here only broadband RF pulses are used.(B) The integral of 13 C 1 signal in complex [1] as a function of  1 .The weak 1 H-13 C interactions transfer the polarization from IrHH protons to primary evolution due to 13 C 1 in [1] but the signal is modulated by strong  HH interactions that complicate the analysis.The spin orders after the application of phINEPT are depicted on (A).

Figure S6 .
Figure S6.Stick spectra of 1 H PASADENA spectra without (A) and with 13 C decoupling (B).We measured the natural linewidths with 1 H PASADENA{ 13 C} spectrum and then used those values and eq.S3-4, we estimated   interactions.As a result of these small interactions the linewidths in 1 H PASADENA are normally broader than in 1 H PASADENA { 13 C}.The corresponding NMR spectra for complex [1] and [2] are given in FiguresS7 and S8.The estimated interactions are given in TableS2.

Figure S11 :
Figure S11: Dissociation rate in function of temperature.Dissociation rates of [1] and [2] were plotted using Arrhenius's equation (A) and using Eyring's equation (B).The relaxation rate for hydrogen is estimated to be 1 s -1 .The dissociation rate reaches 1 s -1 for [1] at 249 K and for [2] at 268 K.The estimated energy parameters for complex [1] and [2] are in the table below: