¹³C Isotope Enrichment of the Central Trityl Carbon Decreases Fluid Solution Electron Spin Relaxation Times

Abstract

Electron spin relaxation times for perdeuterated Finland trityl 99% enriched in ¹³C at the central carbon (¹³C₁-dFT) were measured in phosphate buffered saline (pH = 7.2) (PBS) solution at X-band. The anisotropic ¹³C₁ hyperfine (A_x = A_y = 18±2, A_z = 162 ±1 MHz) and g values (2.0033, 2.0032, 2.00275) in a 9:1 trehalose:sucrose glass at 293 K and in 1:1 PBS:glycerol at 160 K were determined by simulation of spectra at X-band and Q-band. In PBS at room temperature the tumbling correlation time, τ_R, is 0.29 ± 0.02 ns. The linewidths are broadened by incomplete motional averaging of the hyperfine anisotropy and T₂ is 0.13 ± 0.02 μs, which is shorter than the T₂ ~ 3.8 μs for natural abundance dFT at low concentration in PBS. T₁ for ¹³C₁-dFT in deoxygenated PBS is 5.9 ± 0.5 μs, which is shorter than for natural abundance dFT in PBS (16 μs) but much longer than in air-saturated solution (0.48 ± 0.04 μs). The tumbling dependence of T₁ in PBS, 3:1 PBS:glycerol (τ_R = 0.80 ± 0.05 ns, T₁ = 9.7 ± 0.7 μs) and 1:1 PBS:glycerol (τ_R = 3.4 ± 0.3 ns, T₁ = 12.0 ± 1.0 μs) was modeled with contributions to the relaxation predominantly from modulation of hyperfine anisotropy and a local mode. The 1/T₁ rate for the 1% ¹²C₁1-dFT in the predominantly ¹³C labeled sample is about a factor of 6 more strongly concentration dependent than for natural abundance ¹²C₁-trityl, which reflects the importance of Heisenberg exchange with molecules with different resonance frequencies and faster relaxation rates. In glassy matrices at 160 K, T₁ and T_m for ¹³C₁-dFT are in good agreement with previously reported values for ¹²C₁-dFT consistent with the expectation that modulation of nuclear hyperfine does not contribute to electron spin relaxation in a rigid lattice.

Graphical Abstract

Introduction

Triphenylmethyl radical, “an instance of trivalent carbon,” was discovered by Gomberg in 1900 [1]. Substituted triarylmethyl radicals were among the concentrated solid and dissolved radicals that Weissman and coworkers measured in early electron paramagnetic resonance (EPR) studies of organic radicals [2]. Water-soluble triarylmethyl radicals (trityls, also called TAMs) have been synthesized with few nuclear spins at all positions where the unpaired electron probability is high, which results in narrow EPR lines and long electron spin relaxation times in fluid solution [3]. These radicals have been shown to be very useful for imaging experiments that monitor local oxygen concentrations in vivo [4–10]. Perdeuterated Finland trityl (dFT) is relatively lipophilic and has been shown to be toxic in mice at high concentrations used in dynamic nuclear polarization (DNP) [8]. Toxicity can be reduced by encapsulation in liposomes [11] or by replacing methyl groups with hydroxyethyls as in OX63 [8]. Pairs of trityl radicals have been attached to proteins or DNA for measurements of interspin distances by double electron-electron resonance [12–16]. Trityl radicals have also been used as polarizing agents for dissolution DNP [17, 18]. Electron spin relaxation times play key roles in each of these applications so it is important to understand how the relaxation mechanisms are impacted by isotope substitution.

In dFT that is enriched with ¹³C at the central carbon ( ¹³C₁-dFT) [19] there is substantial anisotropic coupling to a single I = 1/2 nucleus. The linewidths in the continuous wave (CW) EPR spectra of the isotopically labeled radical correlate with tumbling correlation times, which opens the opportunity to use trityls as probes of molecular motions in addition to oximetry [19]. This isotope substitution permits study of the effect of the ¹³C (I = 1/2) nucleus on electron spin relaxation, testing models that have been developed primarily for ¹⁴N (I = 1) and ¹⁵N (I = 1/2) nitroxides [20–22]. The trityls differ importantly from nitroxides because the g anisotropy for the trityls is much smaller than for nitroxides [23] and therefore the anisotropy that is averaged by molecular tumbling is predominantly nuclear hyperfine anisotropy. The higher molecular weights of the trityls result in longer tumbling correlation times than for nitroxides in the same solvents, which alters the relative contributions from tumbling-dependent relaxation mechanisms. These studies also demonstrate that the T₁ for ¹³C₁-dFT is strongly dependent on oxygen concentration, as needed for oximetry.

The resolved ¹³C hyperfine couplings for isotopomers of trityls in fluid solution are summarized in Table 1. Since the natural abundance of ¹³C is 1.11%, the C_3,3’ positions on the phenyl rings with a degeneracy of 6 have a combined probability of about 6.6%. Including all of the 28 carbons for which there is large enough spin density to give resolved hyperfine splittings there is about 30% probability that a trityl molecule will contain a ¹³C at one of these carbons. A very small fraction of the molecules contains two ¹³C, so most of the remaining 70% contain only ¹²C or have ¹³C hyperfine that is unresolved in the center ¹²C line. Thus, for the natural abundance trityls, the majority of collisions are with isotopomers that have very similar resonance frequencies. The hyperfine splitting from the ¹³C₁ permits study of the impact on spin-spin relaxation from collisions with molecules with significantly different resonance frequencies. The ¹³C₁-dFT sample that was studied was synthesized using the standard protocols developed for the synthesis of dFT starting from the commercially available methyl chloroformate (carbonyl-¹³C) with 99% ¹³C isotopic purity to label the central carbon of the trityl with ¹³C. Thus the ¹³C₁-trityl contains about 1% ¹²C₁-trityl [19], which is designated as the residual signal. For these residual ¹²C₁-trityls most collisions are with ¹³C₁-trityls that have resonance frequencies that are different than for ¹²C₁-trityl because of the hyperfine splitting, which provides a T₂ relaxation pathway.

Table 1.

¹³C Couplings (G) for trityl radicals in fluid solution

carbon	Degeneracy	Bowman [30]	Kuzhelev [48]	Trukhan [49]
C1	1	23.9	23.4	23.7
C2	3	11.3	11.1	11.2
C3,3’	6	9.07	9.0	9.06
C4	6	2.4	2.4	2.37
C5	3	3.4	3.3	3.34
C7	3	1.3	1.3	1.28
C6,6’	6	0.18		0.18

Materials and Methods

Preparation of samples.

¹³C₁-dFT was prepared at West Virginia University as reported in ref. [19] and isolated as the tri-carboxylic acid. Natural abundance dFT was a gift from Prof. Howard Halpern, University of Chicago. Solutions were prepared with concentrations ranging from 0.1 to 1.9 mM in 50 mM sodium phosphate buffer containing 142 mM NaCl (PBS), pH = 7.2, and stored at 4°C. The relatively high buffer concentration was selected to ensure effective buffering over the full range of trityl concentrations studied. The PBS ensures essentially complete deprotonation of the carboxylate groups, which improves solubility relative to the protonated form and avoids the possibility that carboxylate protons might contribute to line broadening or enhanced electron spin relaxation. The 3:1 PBS:glycerol and 1:1 PBS:glycerol mixtures (v:v) were prepared as described previously [24]. A sample immobilized in 9:1 trehalose:sucrose was prepared using the previously reported procedure with a 2000:1 mole ratio of sugar to ¹³C₁-dFT [25].

Samples for fluid solution spectroscopy at ambient temperature (~ 20°C) were contained in Zeus AW19 thin wall Teflon tubing with an internal diameter of about 0.97 mm and 0.05 mm wall thickness. Approximately 20 μL of sample was drawn into the tubing with a pipette. The open end of the tubing was plugged with tube sealant (Fisher brand) that was separated from the liquid by an air bubble. The tubing was folded over and supported in a 4 mm OD quartz tube such that two lengths of sample-containing tubing were in the active volume of the resonator. Nitrogen was purged through the 4 mm tube via an additional thin-wall Teflon tube that extended to the bottom of the EPR tube. O₂ and N₂ exchange through the wall of the tubing [22]. Before acquiring spectra the N₂ purge was continued for at least 30 min, or until the spectral properties became time independent. Samples in trehalose:sucrose glasses at 293 K or in 1:1 buffer:glycerol at 160 K were in 4 mm OD quartz tubes (X-band) or 1.6 mm OD capillaries (Q-band). Buffer:glycerol samples were flash-frozen in liquid nitrogen to ensure glass formation, prior to insertion into a cold resonator (160 K).

EPR spectra

X-band CW spectra were obtained using a Bruker EMX spectrometer with an SHQE cavity. The frequency was measured with an external counter and the magnetic field was calibrated with DPPH using g = 2.0036. A modulation frequency of 100 kHz was used to characterize the ¹³C₁-trityl signals. The linewidth of the signal from the residual ¹²C₁-dFT was so narrow that it was necessary to use 10 kHz modulation frequency to avoid distortion. Modulation amplitudes for the ¹³C lines were less than 20% of the peak-to-peak linewidths. Q-band CW spectra were obtained on a Bruker E580 using an ER5107 dielectric resonator.

X-band relaxation measurements were performed on a Bruker E580 with an ER4118X-MS5 split ring resonator and a nominal 1 kW TWT amplifier. The resonator was overcoupled to Q ~ 180 to reduce the ringdown and deadtime. T_m values were measured by two-pulse electron spin echo with the pulse sequence π/2-τ-π-τ-echo and two-step phase cycling of the first pulse, followed by subtraction of the signals to cancel the FID and resonator ringdown. The value of τ was incremented to record the echo decay. To make the magnetic field less homogenous and thereby decrease the contribution of the free induction decay (FID) to the echo in fluid solution, a plastic-wrapped Allen wrench was positioned on the pole of the magnet, near the resonator. The pulse lengths were varied, with corresponding changes in power attenuation, to check that instantaneous diffusion did not contribute to the echo decays. Since instantaneous diffusion did not make a detectable contribution to the decay, data were acquired with π/2 pulse lengths of 40 ns which corresponds to a B₁ of about 2.2 G. The time constant for spin echo dephasing is designated as T_m [26]. The spin echo dephasing times in fluid solution are close to the experimental deadtime (about 100 ns), which contributes to the uncertainty in the values. The deadtime is due primarily to resonator ringdown after the pulses and reflections from impedance mismatches in the system. For a molecule tumbling relatively rapidly in fluid solution T_m = T₂ so in this paper the spin echo dephasing time constant is designated as T₂ for fluid solution.

T₁ was measured by 3-pulse inversion recovery and by FID-detected inversion recovery. The pulse sequence for inversion recovery was π-T-π/2-τ-π- τ -echo, with 2-step phase cycling of the first pulse, and the value of T was incremented to record the recovery curve. The constant τ value was 140 ns. The initial value of T was 360 ns and the step sizes were to 240 ns for ¹³C₁-dFT or ¹²C₁-dFT, respectively. The pulse sequence for the FID-detected experiment was π-T-π/2-FID with digitization of the FID, stepping of T, and analysis of the amplitude of the FID as a function of T. Without an Allen wrench in the field, the FID detection was preferred. The length of a π/2 pulse in the inversion recovery experiments and FID-detected experiments was 40 ns. T₁ also was measured by long-pulse saturation recovery on a home-built digital saturation recovery spectrometer using a Bruker ER4118X-MS5 resonator [27]. For the saturation recovery experiments the length of the saturating pulse was 20 to 60 μs. Off-resonance data were used to subtract the resonator ring-down and switching artifacts. Values of T₁ obtained by saturation recovery for selected samples were found to be in good agreement with values obtained by inversion recovery, within experimental uncertainty. Inversion recovery inherently provides higher signal-to-noise ratios (S/N) than saturation recovery, so it is the method of choice for T₁ measurements of radicals in the fast motional regime [22], provided T₂ is long enough to detect a spin echo. Comparison of inversion recovery and saturation recovery data is valuable to check for possible contributions to the recovery from spectral diffusion that are decreased in saturation recovery by the use of long low-power saturating pulses (B₁ ~0.5 G). The SR observe B₁ for ¹³C₁-dFT was 1.7 mG, 0.8 mG, and 0.8 mG for samples in PBS, 25% glycerol, and 50% glycerol, respectively. For the sample in air-saturated PBS the observe B₁ was 2.8 mG.

X-band field-swept 2-pulse echo detected spectra of a 0.1 mM 1:1 water: glycerol sample were recorded with 40 ns π/2 pulses and a fixed τ = 200 ns at 160 K. Q-band field-swept 2-pulse echo-detected spectra of 0.1 and 0.03 mM samples in 1:1 PBS:glycerol at 160 K and in trehalose:sucrose at 293 K were recorded with a range of pulse lengths and fixed τ values. The shapes of the echo-detected spectra were dependent on pulse lengths. Longer pulses are more selective and gave somewhat sharper features. However, the longer values of T_m obtained with shorter pulse lengths indicated that there is substantial spectral diffusion, that is more significant near the perpendicular plane. Although spectral diffusion impacts the lineshapes in the echo-detected spectra, it does not change the values of g and A that are obtained from the simulated spectra. The magnetic field at X-band was calibrated with DPPH using g = 2.0036. At Q-band the DPPH signal typically splits into several components, which is not useful for field calibration. A deoxygenated selected single crystal of lithium phthalocyanine that was found to have g = 2.0021 at X-band was used to calibrate the field at Q-band.

Data analysis

First derivative peak-to-peak linewidths in CW spectra were estimated using the cursor in the EMX software and confirmed by simulation with a Lorentzian lineshape. The CW spectra and the first-derivatives of the field-swept echo detected spectra were simulated using the ‘pepper’ function in EasySpin. Values obtained from these simulations were used in the determination of the tumbling correlation times in fluid solution, which were calculated using the ‘garlic’ function in EasySpin. To account for small differences between the observed g_iso and the average of rigid lattice values, all g values were shifted by the same amount in the first step of the simulation process, preserving g anisotropy. Small variations in A_iso were arbitrarily assigned to the much larger value of A_z and the smaller values of A_x and A_y were held constant. The values of A_z, the Gaussian contribution to the linewidths (about 0.05 G), and tumbling correlation time τ_R were varied in the iterative refinements of the simulations. The spin-echo decays in fluid solution and inversion recovery decays at all temperatures were fit with single exponentials or the sum of two exponentials using the Bruker Xepr software. The use of two exponentials did not improve the fit to the data, so results are reported for single exponential fits. The fits to some of the saturation recovery data were better for the sum of two exponentials. However, the signal-to-noise was not high enough to reliably define a second contribution to the relaxation. The spin-echo decays at 160 K were fit with stretched exponentials.

Modeling of T₁

Values of 1/T₁ were calculated as the sum of contributions from modulation of ¹³C hyperfine anisotropy $\frac{1}{T_1^A}$, a local mode $\frac{1}{T_1^{\mathit{\text{local}}}}$, spin rotation $\frac{1}{T_1^{\mathit{\text{SR}}}}$, and modulation of g anisotropy $\frac{1}{T_1^g}$ as described by Eq. (1)– (4). [22, 26, 28, 29]

$$\frac{1}{T_1}=\frac{1}{T_1^A}+\frac{1}{T_1^{\mathit{\text{local}}}}+\frac{1}{T_1^{\mathit{\text{SR}}}}+\frac{1}{T_1^g}$$ (1)

$$\frac{1}{T_1^A}=\frac{2}{9}I(I+1){\sum }_i{\left(A_i-A_{\mathit{\text{iso}}}\right)}^2\frac{{\tau }_R}{1+{\left(\omega {\tau }_R\right)}^2}$$ (2)

where I = 1/2 for ¹³C, A_i is a component of the ¹³C nuclear hyperfine in angular frequency units, A_iso is the average ¹³C hyperfine observed in fluid solution, ω is the angular frequency and τ_R is the tumbling correlation time. This contribution to T₁ is proportional to the square of the anisotropy of the hyperfine interaction, (A_i - A_iso)². Based on the ENDOR data for dFT [30] (A_i - A_iso)² for the isotopomers with a ¹³C at phenyl C₁ or for the ortho carbons are about 0.5% or 2.0%, respectively, of the values for ¹³C₁ and even smaller for other isotopomers. These contributions are too small to have a detectable impact on relaxation times for ¹³C₁-dFT and were not included in the modeling of T₁.

$$\frac{1}{T_1^{\mathit{\text{SR}}}}=\frac{{\sum }_{i=1}^3{\left(g_i-g_e\right)}^2}{9{\tau }_R}$$ (3)

$$\frac{1}{Tq}=\frac{2}{5}{\left(\frac{\omega }{g}\right)}^2\left(\frac{{(\Delta g)}^2}{3}+{(\delta g)}^2\right)\frac{{\tau }_R}{1+{\left(\omega {\tau }_R\right)}^2}$$ (4)

where Δg = g_zz – 0.5(g_xx+g_yy), δg = 0.5(g_xx − g_yy).

The value of $\frac{1}{T_1^{\mathit{\text{local}}}}=6.6\times {10}^4{\text{s}}^{-1}$ at room temperature was determined previously for natural abundance ¹²C₁-dFT and closely-related trityls including OX63 [28] in water solution. The fit to the experimental values of T₁ was improved by increasing $\frac{1}{T_1^{\mathit{\text{local}}}}\text{to}7.6\times {10}^4{\text{s}}^{-1}$ to 7.6×10⁴ s⁻¹. It is plausible that the ionic strength of the PBS buffer could impact this parameter.

Results and Discussion

CW spectra

The fluid solution X-band CW spectrum of ¹³C₁-dFT in PBS (pH 7.2) is shown in Figure 1A. The doublet splitting due to the ¹³C hyperfine coupling of 23.4 G (65.5 MHz) is well resolved. For solutions with concentrations in the range of 0.1 to 0.3 mM the peak-to-peak linewidths for the low-field and high-field hyperfine lines are 0.58 and 0.64 G, respectively. The smaller sharper peak in the center of the spectrum is due to about 1% residual ¹²C₁-dFT, which has a linewidth of 0.037 G when recorded with 10 kHz modulation frequency and modulation amplitude of 0.01 G. The much larger linewidths for the signals from ¹³C₁-dFT than for ¹²C₁-dFT are due to incomplete motional averaging of the anisotropy of the ¹³C hyperfine coupling. In a higher viscosity 3:1 PBS:glycerol solution (Figure 1B) the linewidths for the ¹³C₁-trityl signal are 1.9 and 2.0 G, respectively, which is about a factor of three broader than in PBS. The increased linewidths reflect the tumbling dependence of the incomplete motional averaging. The linewidth for the ¹²C signal was independent of viscosity, which is consistent with prior results [3].

Figure 1.

X-band spectra (black lines) of ¹³C₁-dFT at 20°C (A) 0.2 mM in PBS and (B) 0.2 mM in 3:1 PBS:glycerol. Spectra were simulated (red dashed lines) using the garlic function of the EasySpin toolbox with g = [2.0032 2.0031 2.00265] and A = [17, 17, 162] MHz with τ_R = 0.29 ns, and 0.80 ns for PBS and 3:1 PBS:glycerol, respectively. The sharp signal in the center of the spectrum is from ~1% residual ¹²C₁-dFT in the isotopically enriched sample.

Spectra in Figure 1 were acquired for samples equilibrated with N₂. In samples equilibrated with air at Denver’s reduced atmospheric pressure the linewidths for the ¹³C signal increases by about 0.1 G, which is a small fractional change that is difficult to quantitate. By contrast, a change in the linewidth for the ¹²C signal by 0.1 G is about a factor of three, which is readily measured. Similarly, the linewidths for the ¹³C signals in a 1.0 mM solution are about 0.01 G greater than at 0.1 to 0.3 mM, which is a very small fraction change. For the same concentration change the linewidth for the ¹²C signal increases from 0.037 to 0.046 G, which is readily detectable. Although linewidth changes for ¹²C₁-trityl are a convenient tool for measuring oxygen concentration [31], the weak dependence of the broader ¹³C₁-trityl linewidths on oxygen concentration would be less effective for oximetry.

Hamiltonian parameters

At the cryogenic temperatures that are required to obtain well immobilized spectra in 1:1 buffer:glycerol, T₁ for trityl radicals becomes very long [23], so it is difficult to acquire CW spectra that have lineshapes that are free of passage effects or admixtures of dispersion. Two approaches were taken to address this problem: (i) CW spectra were acquired in 9:1 trehalose:sucrose glass at 293 K (Figure 2), and (ii) field-swept echo-detected spectra were acquired in 1:1 buffer:glycerol at 160 K (Figure S1) The spectra with the narrowest linewidths and therefore the best resolution were the X-band CW spectra in 9:1 trehalose:sucrose (Figure 2A). On the wings of the extrema for both the parallel and perpendicular orientations there are weak sidebands that are assigned to isotopomers that have a second ¹³C, in addition to the ¹³C₁. The sidebands on the parallel lines are highlighted in the insets in Figure 2A. The two small peaks in the center of the spectrum (about 3520 G) are sidebands on the perpendicular turning points. These sidebands are poorly resolved but were simulated with 10% of the radicals having ¹³C hyperfine of about 29 MHz and 10% having ¹³C hyperfine of about 14 MHz. The anisotropy of these couplings are small, but poorly defined because of the low resolution of the sidebands. The larger splitting is assigned to ¹³C_2,3,3’ and the smaller splitting to ¹³C_4,4’,5 on the phenyl rings based on the values summarized in Table 1. Linewidths are greater for the Q-band CW and first derivatives of echo-detected spectra than for the X-band CW spectrum so the contributions from the additional ¹³C sidebands were not resolved in these spectra, although they were included in the simulations. The Q-band spectra were analyzed primarily to define the g anisotropy. At Q-band the CW spectral lineshapes are slightly distorted because a higher than optimal power was needed to maintain the AFC lock. In the Q-band echo-detected spectrum the value of T_m depends on position in the spectrum which is not included in the simulations. There also are contributions to the lineshapes from spectral diffusion that were not included in the simulation. First derivatives of field-swept echo detected spectra at X-band and Q-band for a 1:1 buffer:glycerol sample at 160 K are shown in Figure S1. The major lines in the spectra are very similar to those in trehalose:sucrose. The lines are broader than for the CW spectra and sidebands due to molecules with a second ¹³C are not resolved, so these contributions were not included in the simulations. The extrema for the large A_z are well defined at both X-band and Q-band, which clearly define the values of g_z (2.00275 ± 0.0001) and A_z (162 ± 1 MHz). The relatively narrow linewidths near the perpendicular plane require that anisotropy in the x,y-plane is small. Based on the X-band spectra it was concluded that A_x = A_y = 18 ± 2 MHz. Based on the Q-band spectra it was concluded that g_x = 2.0033 and g_y = 2.0032. The isotropic average of the rigid-lattice g values is 2.0031 ± 0.0001, which differs slightly from the average g value in PBS at room temperature of 2.0028 ± 0.0001. This difference suggests that the molecular conformation in frozen solution is different from that in fluid solution. The average of the anisotropic hyperfine values is 65.3 MHz (23.3 G), which is very similar to the value observed in fluid solution 65.5 MHz (23.4 G). This agreement indicates that the ¹³C hyperfine is not strongly temperature dependent. The g and A values are compared with literature values in Table 2. Even at W-band the g anisotropy in the spectrum of natural abundance ¹²C₁-dFT is not resolved so the reported g values were obtained by simulation of the lineshape. For ¹³C₁-dFT the anisotropy of the ¹³C hyperfine is useful in defining the anisotropy of both the g and A values because the centers of the parallel and perpendicular hyperfine patterns are clearly defined. The variation in reported g values is relatively small, and may be due in part to solvent effects on conformation. The ¹³C hyperfine values observed for ¹³C₁-dFT in 1:1 PBS:glycerol are similar to values reported previously in methanol (Table 2).

Figure 2.

Spectra of ¹³C₁-dFT in 9:1 trehalose:sucrose at 293 K. (A) X-band CW spectrum. The insets show y-axis amplitude multiplied x6.6 to highlight the contributions from isotopomers with a second ¹³C splitting. (B) Q-band CW spectrum. (C) First-derivative of field-swept echo-detected Q-band spectrum. Spectra were simulated with EasySpin using the parameters g = [2.0033 2.0032 2.00275] with A(C₁) = [18.5 18.5 162] MHz 80% weighting; A(C₁) = [18.5 18.5 162] MHz plus A(C2,3,3’) = [29 29 30] MHz 10% weighting; A(C₁) = [18.5 18.5 162] MHz plus A(C4,4’,5) = [14 14 13] MHz 10% weighting (red line). The EasySpin Hstrain parameters for the ¹³C₁ lines were [4.8 4.8 7.3], [ 8.5 8.5 11], and [10 10 11] for X-band CW, Q-band CW, and Q-band echo-detected, respectively. The weak signal from the ~1% ¹²C₁-dFT makes negligible contribution.

Table 2.

g and A values for trityl radicals

radical	Solvent	gx	gy	gz	giso	Ax (MHz)	Ay (MHz)	Az (MHz)	reference
13C1-dFT	9:1 trehalose:sucrose	2.0033	2.0032	2.00275	2.0031 (2.0028)a	18	18	162	This work
dFT	1:1 water:glycerol	2.0030	2.0027	2.0021	2.0026				[23]
dFT	Methanol	2.0029	2.0029	2.0021	2.0026	20	20	159	[30, 49]b
Trityl-CH3	Ethanol	2.00345	2.00338	2.00254	2.00312				[17]
OX63	1:1 water:glycerol	2.0031	2.0027	2.0021	2.0025				[23]
OX63	1:1 water:glycerol	2.0032	2.0032	2.0026	2.0030				[50]

^aValue for fluid PBS solutions.

^bThe paper lists g_‖ - g_⊥ = 0.0008. The values shown in the table assume g_iso = 2.0026 [48].

Tumbling correlation times

The tumbling correlation times, τ_R, for ¹³C₁-dFT were determined by simulating the CW spectra (Figure 1) using the ‘garlic’ function in EasySpin and the g and A values obtained from the simulations shown in Figure 2 (Table 2). At X-band (~ 9.85 GHz) the spread in g values (2.0033 to 2.00275) corresponds to only a difference of ~1.0 G. This very small g anisotropy is why the linewidth for the ¹²C₁-dFT signal is approximately independent of tumbling. This small g anisotropy also means that small uncertainties in the anisotropic g values have little impact on the calculated values of τ_R for ¹³C₁-dFT. The anisotropy that is averaged by the tumbling of ¹³C₁-dFT is predominantly due to the anisotropy in the hyperfine interaction which is A_‖ - A_⊥ ~144 MHz ~ 52 G. Incomplete motional averaging of the anisotropic hyperfine contributes equally to the linewidths of the m_I = ±1/2 lines. This equal contribution to the two hyperfine lines is difficult to distinguish from broadening by oxygen, intermolecular collisions, or over-modulation. Therefore, to get the most accurate values of τ_R it is preferable to work with low-concentration deoxygenated samples and spectra acquired with modulation amplitudes that are small relative to linewidths. Alternatively, these contributions to the linewidths can be included in the EasySpin simulations. The value of τ_R in PBS was calculated as 0.29 ns ± 0.02 ns at 20°C. The uncertainty is based on the standard deviation for multiple measurements and the estimated uncertainties in the nuclear hyperfine values. This value of τ_R is in good agreement with τ_R = 0.29 ns for natural abundance ¹²C₁-trityl-CH₃ in water solution that was determined by analysis of the viscosity dependence of relaxation times at 250 MHz where modulation of electron-proton dipolar interaction dominates T₁ [28]. This contribution to trityl relaxation is negligible at X-band. In 3:1 PBS:glycerol and 1:1 PBS:glycerol solutions τ_r was calculated as 0.80 ± 0.05 ns and 3.4 ± 0.2 ns, respectively.

The linewidths (and therefore tumbling correlation times) in water (data not shown) and PBS are similar. The molar mass of dFT assuming complete deprotonation at pH ~ 7.2 and assuming minimal ion pairing is 1035 g/mole. The impact of the 50 mM PBS on viscosity is small but was considered. The effect of electrolytes on viscosity can be modeled using Eq. [5]. [32]

$$\frac{\eta }{{\eta }_1}=1+A\sqrt{c}+Bc=1+Bc$$ [5]

where η₁ is the viscosity of pure solvent, η is the viscosity of the electrolyte solution, c is the molarity of each ion, A can be calculated based on ionic charge, and B is an empirical parameter. The A√c term is much smaller than the Bc term and often is neglected. Using literature values of B [33, 34] the $\frac{\eta }{{\eta }_1}$ ratio for 50 mM sodium phosphate buffer, containing 142 mM NaCl, was calculated as 1.044, of which about 75% of the effect is from the phosphate ions. This impact of ionic strength on viscosity is less than the uncertainties in τ_R, which also is consistent with the similarity in tumbling correlation times in water and in PBS

The Stokes-Einstein equation, ${\tau }_R=V\eta {/}_{kT}$ where V = molecular volume in m³, η = viscosity in poise, k = Boltzmann’s constant = 1.381×10⁻²³ J/K and T = temperature in Kelvin, can be used to predict tumbling correlation times [35]. For ¹³C₁-dFT in water, the value of τ_R predicted by the Stokes-Einstein model is 0.44 ns, based on T = 293 K, viscosity of water = 1 cP at 20°C and a molecular radius of 7.5 Å. The Stokes-Einstein model predicts τ_R more accurately for solute molecules that are much larger than the solvent than for smaller solutes [36]. For small solutes it has been suggested that the Stokes-Einstein equation should be modified by addition of a slip coefficient c_slip, becoming ${\tau }_R{=}^{c_{\mathit{\text{slip}}}}V\eta {/}_{kT}$ [37, 38], where smaller values of c_slip reflect larger deviations from the model. For ¹³C₁-dFT the ratio of the experimental τ_R (0.29 ns) to the Stokes -Einstein value gives c_slip = 0.66. This value is in good agreement with values obtained for several trityls in water at 250 MHz [28]. The molar mass of 1035 g/mole for dFT is about 6 times larger than for simple nitroxides such as tempol (molar mass = 172 g/mole). The larger molar mass for ¹³C₁-dFT predicts slower tumbling and longer τ_R than for tempol. For small nitroxides in water τ_R is in the range of 9 to 19 ps [22], which is more than a factor of 6 shorter than for ¹³C₁-dFT. Slip coefficients for small nitroxides in water are about 0.1 to 0.2, with the larger values observed for nitroxide with polar substituents [24, 39]. The larger slip coefficient for ¹³C₁-trityl than for small nitroxides is attributed to the larger size of the molecule and the polarity of the three carboxylate groups.

Fluid solution T₂ for ¹³C₁-dFT

Electron spin-spin relaxation times were measured for deoxygenated samples of ¹³C₁-dFT with concentrations between 0.1 and 1.9 mM. In PBS solution T₂ = 0.13 ± 0.02 μs and is independent of concentration, within experimental uncertainty. A typical two-pulse echo decay curve is shown in Figure 3A, along with the fit to a single exponential. Use of the sum of two exponentials did not improve the fit to the data. Differences between values of T₂ for the low-field and high-field hyperfine lines were not statistically significant. This value of T₂ is much shorter than observed for natural abundance ¹²C₁-dFT in PBS (3.8 μs for 0.2 mM solution) because of incomplete motional average of the A anisotropy Figure 1. The corresponding value of ΔB_pp for a Lorentzian line calculated using the expression ΔB_pp(G) = 6.56 x10 ⁻⁸/T₂(s) is 0.50 ± 0.10 G which is in reasonable agreement with the experimental values (Table 3). The experimental linewidths include an additional contribution of about 0.05 G from unresolved nuclear hyperfine coupling. The variation in CW linewidths for ¹³C₁-dFT with concentration is smaller than the estimated uncertainties in T₂. For closely-related trityl OX63 in PBS, the T₂ and CW linewidths have been shown to be dependent on trityl concentration with a slope of 0.165×10⁶ s⁻¹/mM trityl [4]. For OX63 in PBS this concentration dependence could be observed because T₂ at low concentration is 6.3 μs [4]. Contributions to relaxation combine as the sum of reciprocals, so a similar concentration dependence of the much shorter T₂ for ¹³C₁-dFT would not be detectable.

Figure 3.

X-band measurements of electron spin relaxation times at 20°C for ¹³C₁-dFT samples containing ~1% ¹²C₁-dFT. Unless noted the data are for deoxygenated 1.0 mM solutions. A) Two-pulse echo decays for the high-field ¹³C hyperfine line (red) and the ¹²C line (black). Data were acquired with 256 shots per point and averaged for 100 scans. Single exponential fits (dashed black) were calculated with T_m = 0.13 μs for ¹³C and 1.1 μs for ¹²C. B) Three-pulse inversion recoveries for the high-field ¹³C hyperfine line (red) and the ¹²C line (black). Data were acquired with 256 shots per point and averaged for 3 scans for ¹²C and 2 scans for ¹³C. Single exponential fits (black dashed lines) were calculated with T₁ = 6.0 μs for ¹³C and 9.1 μs for ¹²C. C) Long-pulse saturation recovery curves for the high-field ¹³C hyperfine line in PBS (red), 3:1 PBS:glycerol (blue), and 1:1 PBS:glycerol (pink). Data were averaged for 10 scans (30 min). Single exponential fits (black dashed lines) were calculated for T₁ = 5.6 μs in PBS, 9.8 μs in 3:1 PBS: glycerol, and 12.0 μs for 1:1 PBS:glycerol. D) Long-pulse saturation recovery curves for the high-field ¹³C line in air saturated (orange) and deoxygenated (green) solutions. Data were averaged for 10 scans (30 min) for the deoxygenated sample and 5 scans (10 min) for the air saturated sample. Single exponential fits (black dashed lines) were calculated for T₁ = 480 ns and 5.6 μs for the air saturated and deoxygenated samples, respectively. The signal for the deoxygenated sample had not fully recovered to equilibrium in the short time window displayed in the figure, and the fit line is based on a longer time window. The residuals for the fits to the experimental data in this figure are shown in Supplementary Material.

Table 3.

Impact of ¹³C nuclear spin on dFT linewidths and relaxation times (μs) in PBS at X-band at ca. 20°C.

	13C1-dFT in PBSa	12C1-dFT in 13C1-dFT in PBS	12C1-dFT in natural abundance dFT
ΔBpp in PBS, deoxygenated (G)	0.58, 0.64b	0.037 ± 0.002 (0.1 mM) 0.047 ± 0.002 (1 mM)
ΔBpp in PBS, air saturated (G)	0.66, 0.75b	0.14 ±0.01 (1 mM)
T2 (μs), deoxygenated	0.13 ± 0.02	5.6 (0.2 mM, PBS) 2.4 (1 mM, PBS)	11 ± 1 (0.2 mM, water)c 3.8 (0.2 mM, PBS) 0.6 (2 mM PBS)
T1 (μs), deoxygenated	5.9 ± 0.5	11. (0.2 mM, PBS) 3.8 (1 mM, PBS)	17 ±1 (0.2 mM, water)c 16 ±1 (0.2 to 2 mM, PBS)
T1 (μs), air saturated	0.48 ± 0.04

^aFor concentrations between about 0.1 and 1.5 mM.

^bLinewidths for low-field and high-field lines, respectively. Uncertainties are about 0.02 G.

^cValues from ref. [28] in water, 0.2 mM

Fluid solution T₁ for ¹³C₁-dFT

Values of T₁ were measured by 3-pulse inversion recovery or FID-detected inversion recovery for ¹³C₁-dFT concentrations between 0.1 and 1.0 mM in PBS. Differences in values of T₁ obtained by the two methods were not statistically significant. Values of T₁ measured by long-pulse saturation recovery for 0.2 to 1.9 mM samples also were in agreement with the echo and FID-detected experiments. From the three techniques, T₁ in PBS was found to be 5.9 ± 0.5 μs (Figure 3B, 3C). In 3:1 PBS:glycerol, the CW linewidths are about 1.5 to 1.8 G, which corresponds to T₂ of about 40 ns. When T₂ is this short relative to the instrument deadtime it is difficult to detect a spin echo or FID with sufficient signal-to-noise to measure T₁ by pulse methods. For the 3:1 and 1:1 PBS:glycerol samples T₁ was measured by long pulse-saturation recovery for 1.0 mM solutions (Figure 3C). The resulting T₁ values are 9.7 ± 0.7 μs and 12.0 ± 1.0 μs for the 3:1 and 1:1 PBS:glycerol solutions, respectively. The longer T₁ in the more viscous glycerol-containing solutions demonstrates the importance of tumbling-dependent contributions to relaxation. This observation is in contrast to results for ¹²C₁-dFT at X-band where T₁ is independent of viscosity [28].

Equations (1) – (4) were used to model T₁ in PBS, 3:1 PBS:glycerol, and 1:1 PBS:glycerol. These expressions have been developed to model the tumbling dependence of T₁ for nitroxides in fluid solution [20–22]. The uncertainties in the calculated values of T₁ (Table 4) are based on uncertainties in τ_R, which is estimated to be the parameter with the most uncertainty in the calculation. The calculated values of T₁ are within estimated uncertainties of the experimental values. In PBS the magnitude of the contributions decreases in the following order: modulation of hyperfine anisotropy > local mode >> spin rotation > modulation of g anisotropy, which emphasizes the importance of the hyperfine anisotropy. For the slower tumbling in 3:1 and 1:1 PBS:glycerol solutions the contribution from modulation of hyperfine anisotropy is much smaller than in PBS, and it becomes less than the contribution from the local mode.

Table 4.

Contributions to calculated T₁ in deoxygenated solution

	Calculated with ᴦr = 0.29 ± 0.02 ns (PBS)	Calculated with ᴦr = 0.80 ± 0.05 ns (3:1 PBS: glycerol)	Calculated with ᴦr = 3.4 ± 0.3 ns (1:1 PBS: glycerol)
$\frac{1}{T_1^A}\left(s^{-1}\right)$	(8.3±0.5) ×104	(3.0 ± 0.2) ×104	(0.70±0.6) ×104
$\frac{1}{T_1^{\mathit{\text{local}}}}\left(s^{-1}\right)$a	7.6×104	7.6×104	7.6×104
$\frac{1}{T_1^{\mathit{\text{SR}}}}\left(s^{-1}\right)$	(4.6±0.3) ×102	170±10	40±4
$\frac{1}{T_1^g}\left(s^{-1}\right)$	104 ± 7	38±3	9.0±0.8
$\text{Calc}.\frac{1}{T_1}\left(s^{-1}\right)$	(1.59 ± 0.1) ×105	(1.06 ± 0.03) ×105	(0.83 ± 0.02) ×105
Calc T1 (μs)	(6.3 ± 0.4) ×10−6	(9.4 ± 0.3) ×10−6	(12.0 ± 0.2) ×10−6
Exper. T1 (μs)	(5.9 ± 0.5) ×10−6	(9.7 ± 0.7) ×10−6	(12.0 ± 1.0) ×10−6

^aAdjusted to fit the experimental values of T₁.

When the ¹³C₁-dFT sample is air saturated, T₁ decreases to 0.48 μs (Table 3). This very strong dependence of T₁ on oxygen concentration (Figure 3D) is analogous to what has been reported for closely-related trityl OX63, which is the basis for pulsed oximetry at 250 MHz [4, 40]. The strong dependence of T₁ for ¹³C₁-dFT on oxygen concentration means that ¹³C₁-dFT can be used as an oximetric probe analogous to what has been demonstrated for OX63 [4], although shorter T₂ values for ¹³C₁-dFT compared to OX63 will require shorter interpulse spacing when performing inversion recovery oximetry experiments.

Relaxation for ¹³C-dFT at 160 K in 1:1 PBS:glycerol.

Electron spin relaxation times were measured for the same 0.1 mM sample in 1:1 PBS:glycerol for which the echo-detected field-swept spectrum is shown in Figure S2. At 160 K T₁ for the ¹³C₁-dFT lines at X-band and Q-band (140 to 173 μs, depending on position in the line) was similar to the T₁ = 150 μs of the residual ¹²C₁-dFT line. These values also are in good agreement with the previously reported value for natural abundance dFT in 1:1 water:glycerol [28]. The absence of an effect of the ¹³C nuclear hyperfine on T₁ for the immobilized sample of ¹³C₁-dFT is consistent with previous reports that nuclear hyperfine does not contribute to T₁ for organic radicals in a rigid lattice [26, 41]. Values of T_m, obtained by fitting data with a stretched exponential, for both the ¹²C and the ¹³C lines of ¹³C₁-dFT at X-band and Q-band, were 3.0 to 3.5 μs with stretch parameters of 1.5 to 1.7, depending on position in the spectrum. These values also are in good agreement with values for natural abundance dFT reported previously for 1:1 water:glycerol solutions [28].

Relaxation times for the residual 1% ¹²C₁-trityl

For the residual ¹²C₁-dFT signal in the predominantly ¹³C₁-dFT sample T₁ and T₂ are strongly concentration dependent as shown in Figure 4. The plot for 1/T₁ as a function of trityl concentration was fit with 0.18×10⁶ s⁻¹/mM [trityl] + 0.055×10⁶ s⁻¹ , which gives a slope that is about a factor of 5 larger than was observed for OX63 in PBS (0.36×10⁵ s⁻¹/mM [trityl]+0.16×10⁶ s⁻¹) [4]. It has been proposed that the relatively weak concentration dependence of T₁ for OX63 is due to the fact that most of the collisions are with molecules with approximately the same resonance frequencies [42]. In the solution that contains predominantly ¹³C₁-dFT, most of the collisions of residual ¹²C₁-trityl are with ¹³C₁-trityls that have different resonance frequencies and faster relaxation rates which provides an increasingly effective relaxation pathway as concentration is increased. Isotopomers containing a second ¹³C have different resonant frequencies than that of the dominant lines in the spectrum. However the Heisenberg exchange in these low concentration solutions is in the ‘slow exchange’ regime where the impact of a collision on T₂ (or linewidth) is independent of the energy difference between the colliding species [43], so the various isotopomers have similar Heisenberg exchange effects.

Figure 4.

Dependence of 1/T₁ (blue circles) and 1/T₂ (black squares) of the residual 1% ¹²C in ¹³C₁-dFT in 50 mM PBS on the total trityl concentration. The dashed lines are the least squares fit lines: 0.18×10⁶ s⁻¹ /mM [trityl]+0.055×10⁶ s⁻¹ for 1/T₁ and 0.35×10⁶ s⁻¹/mM [trityl]+0.1×10⁵ s⁻¹ for 1/T₂.

Even at low concentration the value of T₂ for the residual ¹²C₁-dFT (5.6 μs) is much shorter than the 11 μs observed previously for 0.2 mM natural abundance ¹²C₁-dFT in water at X-band [28], indicating a greater impact of collisions. In water the three negative charges on the carboxylates may decrease the collision frequencies. Ion pairing of the carboxylates with Na⁺ in the high ionic-strength PBS solutions is expected to be small, based on negligible association of sodium benzoate [44] and limited data from sea water [45]. Ionic strength may decrease collision frequencies of the trityls analogous to what has been observed for nitroxides [46]. Most of the decrease in T₂ is attributed collisions with the faster relaxing ¹³C₁-dFT. The plot of 1/T₂ for residual ¹²C₁-dFT as a function of total trityl concentration was fit with 0.35×10⁶ s⁻¹/mM [trityl]+0.1×10⁵ s⁻¹, which is a slope that is about a factor of 2 larger than for OX63 in PBS (0.165×10⁶ s⁻¹/mM [trityl]+0.16×10⁵ s⁻¹) [4]. Since these data are in the same buffer, interaction with buffer cations is not a factor. About 30% of the greater concentration dependence of T₂ for residual ¹²C₁-dFT (1035 g/mol) than for OX63 (1358 g/mol) is attributed to the smaller molar mass and resulting increase in translational diffusion. Hydrogen bonding to the OH groups of OX63 also may decrease translational diffusion, accounting for some of the difference between ¹²C₁-dFT and OX63 [47]. The remaining contributions to the stronger concentration dependence for residual ¹²C₁-dFT in predominantly ¹³C₁-dFT than for OX63 reflects the fact that most of the collisions are with the faster relaxing ¹³C₁-dFT.

Comparison with relaxation of nitroxides in fluid solution

T₁ for small nitroxides in water at X-band are about 1 μs [22], which raises the question why T₁ is so much shorter for nitroxides than for ¹³C₁-dFT. The typical anisotropic hyperfine couplings for ¹⁵N nitroxides are 21.6, 24.6 and 141 MHz [22]. The anisotropy of these values is similar to that observed for ¹³C₁-dFT so the contributions to 1/T₁ from modulation of the I = 1/2 nuclear hyperfine coupling are expected to be of the same magnitude if τ_R is similar. However, the much shorter τ_R for nitroxides than for trityls in water or PBS solution makes the contributions to T₁ from modulation of hyperfine anisotropy much larger for nitroxides than for trityls. The g anisotropy for typical nitroxides in water (2.0092, 2.0061, 2.0022) is much larger than for trityls [29]. The larger g anisotropy and shorter τ_R makes the contribution from spin rotation larger for nitroxides than for trityls. Thus, the slower tumbling of the trityls is a major factor in the longer values of T₁ for trityls than for low molecular weight nitroxides in solution. By contrast values of T₂ for nitroxides in water are about 0.5 μs [29], which is significantly longer than the 0.13 μs for ¹³C₁-dFT. The slower tumbling of the trityl results in less complete motional averaging of the anisotropic hyperfine interaction than occurs for small nitroxides, leading to broader lines and shorter T₂ for the ¹³C₁-trityl than for nitroxides.

Conclusions

As a result of the longer τ_R and smaller g anisotropy for the trityls than for small nitroxides, values of T₁ for trityls at ambient temperature in PBS solution are longer than for nitroxides. The spin lattice relaxation is dominated by contributions from modulation of A anisotropy and a local mode. Although the ¹³C hyperfine anisotropy for trityls is similar to that for ¹⁵N-nitroxides, T₂ for ¹³C₁-dFT in solution is shorter than for low molecular weight nitroxides because of longer τ_R. The anisotropic ¹³C hyperfine in ¹³C₁-dFT provides a tool for measuring tumbling correlation times. The strong dependence of T₁ for ¹³C₁-dFT on oxygen concentration implies that this one probe can be used to measure both molecular tumbling and oxygen concentration. The much stronger dependence of T₁ on concentration for residual ¹²C₁-dFT in a solution containing predominantly ¹³C₁-dFT than in a solution containing predominantly ¹²C₁-dFT confirms the importance of collisions and Heisenberg exchange with molecules that have different resonance frequencies and faster relaxation.

Research Highlights.

• The T₁ relaxation mechanisms for fluid solution trityls are proven.

• Heisenberg exchange T₂ relaxation in solution is due to ¹³C coupling.

• ¹³C hyperfine coupling does not impact relaxation in the solid state.