Spin-spin Interaction and Relaxation in Two Trityl-Nitroxide Diradicals

Abstract

Trityl-nitroxides show substantial promise as polarizing agents in solid state dynamic nuclear polarization. To optimize performance it is important to understand the impact of spin-spin interactions on relaxation times of the diradicals. CW spectra and electron spin relaxation were measured for two trityl-nitroxides that differ in the substituents on the amide linker and have different strengths of the exchange interaction J. Analysis of the EPR spectra in terms of overlapping AB spin-spin splitting patterns explains the impact of J on various regions of the spectra. Even modest values of J are large relative to the separation between trityl and nitroxide resonances for some nitrogen nuclear spin state. Two conformations for each diradical were observed in CW spectra in fluid solution at X-band and Q-band. For one diradical J = 15 G (83%) and 5 G (17%) at 293 K, and J = 27 G (67%) and 3 G (33%) with interspin distances of 16 Å and 12 Å, respectively, at 80 K. For the second diradical the exchange interaction is stronger: the two conformations in fluid solution at 293 K had J = 113 G (67%) and 59 G (33%) and at 80 K the value of J was 43 G and there were two conformations with interspin distances of 13 and 11.5 Å. The observation of two conformations for each diradical, with different values of J, demonstrates the dependence of their exchange interactions on through-bond orbital interactions. X-band values of spin relaxation rates 1/T₁ and 1/T_m at 80 to 120 K for the trityl-nitroxides are similar to values for nitroxide mono-radicals, and faster than for trityl radicals. These observations show that even for a relatively small value of J, the nitroxide is very effective in enhancing the relaxation of the more slowly relaxing trityl.

Graphical Abstract

1. Introduction

Nitroxides and trityl radicals are invaluable tools for probing many aspects of physiology. For example, the impact of O₂ on the electron spin relaxation of trityl radicals is the basis for quantitative oximetric imaging in vivo [1, 2]. Nitroxides are widely used to probe molecular tumbling [3, 4]. Nitroxides and trityls are used as labels to measure interspin distances via double electron-electron resonance (DEER) [5]. This wide range of applications has stimulated creation of bifunctional probes containing both trityl and nitroxide moieties [6, 7]. An important application of trityl-nitroxides (TN) is as polarizing agents for dynamic nuclear polarization (DNP), which uses microwave saturation of the EPR transitions for organic radicals mixed with the species to be studied by NMR to enhance the NMR signal [8]. The efficiency of DNP experiments depends strongly on the electron spin relaxation of the polarizing agent. Although dinitroxides are very effective as DNP polarizing agents [9], the relatively large g anisotropy of nitroxides decreases effectiveness as DNP polarizing agents as magnetic field is increased. In recent years it has been observed that trityl-nitroxide biradicals [10–14], and the closely-related BDPA-nitroxide biradicals, as well as mixtures of trityl and BDPA, are more effective polarizing agents at high field than dinitroxides [15]. A key characteristic is that a combination of a slowly-relaxing radical and a faster-relaxing radical enhances DNP, especially if one of the radicals has an EPR spectrum that is narrower than that of a nitroxide [16]. The observation that in the trityl-nitroxides the faster-relaxing radical shortens the relaxation time of the slower-relaxing radical, without change in the relaxation time of the faster-relaxing radical, has been commented on [17, 18]. In the present paper we quantify the relaxation properties of two trityl-nitroxide biradicals with different electron-electron exchange couplings, J. The electron spin T₁ and T_m for two TNs with different linkers between a trityl carboxylate group and a piperidinyl nitroxide, NATriPol-1 and GTNMOH, were studied at temperatures between 80 and 120 K. The relaxation times were also obtained and compared for a trityl mono-radical (trityl-CH₃) and for nitroxides H-NATripol-1 and H-GTNMOH in which the trityl moiety had been reduced to the analogous triphenylmethane. The effectiveness of this class of amide-linked TNs as DNP agents has been reported recently [14].

2. Methods and Materials.

2.1. Syntheses

The trityl-nitroxide diradicals and related mono-radicals were prepared at the Tianjin Medical University as outlined in Figure 1 and described in the following paragraphs. The synthesis of NATriPol-1, was reported in [12]. 4-oxo-2,2,6,6-tetramethylpiperidinooxy (1), sodium cyanoborohydride, 2-[2-[[(1,1-Dimethylethyl)dimethylsilyl]oxy]-ethoxy]ethanamine, Boc-N-methylglycine, 1-hydroxybenzotriazole (HOBt), (benzotriazol-1-yloxy) tris(dimethylamino) phosphoniumhexafluoro-phosphate (BOP), N,N-diisopropylethyl-amine (DIPEA) and trifluoroacetic acid (TFA) were purchased and used without further purification. CT-03 (also known as trityl-CH₃ or Finland trityl) and its reduced triphenylmethane form (named as CT-03H) were prepared according to the previously reported methods [19, 20].

Figure 1.

Synthesis of GTNMOH, H-NATriPol-1 and H-GTNMOH.

Compound 2.

Compound 2 was synthesized according to the previously reported method with minor modification [21]. Briefly, to a solution of 4-oxo-2,2,6,6-tetramethylpiperidinooxy (1) (400 mg, 2.35 mmol) and 2-[2-[[(1,1-dimethylethyl)dimethylsilyl]oxy]ethoxy]ethanamine (670 mg, 3.06 mmol) in dry THF (4 mL) was added acetic acid (0.13 mL, 2.35 mmol). The resulting reaction mixture was stirred at ambient temperature for 2 h. Then, sodium cyanoborohydride (747 mg, 3.50 mmol) was added in three portions. After stirring at ambient temperature for 16 h, the reaction mixture was treated with saturated NaHCO₃ solution (10 mL) and extracted with DCM (2 × 10 mL). The combined organic layers were dried over anhydrous sodium sulfate, filtered and concentrated in vacuo. The crude residue was then purified by column chromatography on silica gel using DCM/MeOH (20:1) as an eluent to afford compound 2 (230 mg, 47 %) as a red solid which was used without further characterization.

Compound 3.

To a solution of Boc-N-methylglycine (42.3 mg, 0.23 mmol), HOBt (93.2 mg, 0.69 mmol) and DIPEA (0.13 mL, 2.30 mmol) in DCM (3 mL) was added BOP (203 mg, 0.46 mmol). The resulting solution was stirred at ambient temperature for 30 min. Then, a solution of 2 (100 mg, 0.27 mmol) in DCM (1 mL) was added and the reaction mixture was stirred at ambient temperature for 4 h and quenched with citric acid solution (6%, 10 mL). The organic layer was separated and the aqueous layer was extracted with DCM (2 × 10 mL). The combined organic layers were dried over anhydrous sodium sulfate, filtered and concentrated in vacuo. The crude residue was then separated by column chromatography on silica gel using petroleum ether/ethyl acetate (3:1) as an eluent to afford the precursor of 3. Subsequently, the precursor of 3 in DCM (1 mL) was treated with trifluoroacetic acid (TFA, 1 mL) at ambient temperature for 3 h. After completely removing the solvent and TFA under vacuum, the compound 3 (105 mg, 60%) was obtained as a red oil which was used without further purification. HRMS (ESI, m/z): calcd for C₁₆H₃₂N₃O₄^•+ ([M+H]⁺), 331.2471; found, 331.2462.

H-NATriPol-1.

To a solution of CT-03H (40 mg, 0.04 mmol), HOBt (16 mg, 0.12 mmol) and DIPEA (70 μL, 0.40 mmol) in DMF (3 mL) was added BOP (18 mg, 0.04 mmol). The resulting solution was stirred at ambient temperature for 30 min and then mixed with 4 [12] (23 mg, 0.09 mmol) in DMF (2 mL). After stirring at ambient temperature overnight, the reaction mixture was treated with 1 M HCl (20 mL) and extracted with EtOAc (20 mL). The organic layer was separated, washed with brine (30 mL), dried over anhydrous sodium sulfate, filtered and concentrated in vacuo. The resulting residue was dissolved in phosphate buffer (20 mM, pH 7.4) and purified by column chromatography on reversed-phase C18 using water followed by 0–40% MeOH in H₂O as eluents to give H-NATriPol-1 (26 mg, 53%). H-NATriPol-1, HRMS (ESI, m/z): calcd for C₅₂H₆₂N₃O₇S₁₂^•− ([M-H]⁻), 1223.1163; found, 1223.1071.

GTNMOH and H-GTNMOH.

These two compounds were synthesized using a similar procedure to H-NATriPol-1. GTNMOH (25 mg, 52%) was obtained from 3 (23 mg, 0.09 mmol) and CT-03 (40 mg, 0.04 mmol). H-GTNMOH (24 mg, 47%) was obtained from 3 (23 mg, 0.09 mmol) and CT-03H (40 mg, 0.04 mmol). GTNMOH, HRMS (ESI, m/z): calcd for C₅₆H₆₉N₃O₉S₁₂^••− ([M-H]⁻), 1310.1610; found, 1310.1560. H-GTNMOH, HRMS (ESI, m/z): calcd for C₅₆H₇₀N₃O₉S₁₂^•− ([M-H]⁻), 1311.1688; found, 1311.1526.

2.2. EPR Spectroscopy

Fluid solution samples were in 50 mM sodium phosphate buffer, pH ~ 7.3, containing 142 mM NaCl, which is designated as PBS. Solutions for studies at 80 to 120 K were in 1:1 PBS:glycerol. Most solutions contained a small amount of trityl and/or nitroxide mono-radical that is designated as ‘non-interacting’. For solutions stored at ~ 4°C the concentrations of the mono-radicals increased slowly over a period of several weeks.

X-band CW spectra of fluid solution samples were recorded using a Bruker EMX spectrometer with an SHQE cavity at frequencies between 9.842 and 9.870 GHz. The frequency was measured with an external counter and the magnetic field was calibrated with DPPH, g = 2.0036. Spectra were acquired at ambient temperatures (~293 K) on samples contained in Zeus AW19 thin wall Teflon tubing with an internal diameter of ~0.97 mm and a 0.05 mm wall. 20 μL of sample was drawn into the tubing with a micropipette. The open end was plugged with Critoseal that was separated from the sample by an air bubble. The tubing was folded in half to ensure the sealant was not in the active space of the resonator and to get a high resonator filling factor. The tubing was inserted into a 4 mm OD quartz tube and purged with a flow of N₂ to perform gas exchange with O₂ through the thin wall of the Teflon tubing [22]. Samples were purged for at least 30 minutes or until no further change in linewidths was observed for the non-interacting trityl. Purging with N₂ had no detectable impact on the linewidths for the TN signals. The microwave power was selected to be in the linear response regime for the TN signals and the modulation amplitude was 0.4 G. These parameters caused some broadening of the small signal from non-interacting trityl.

Q-band CW spectra at 293 K were recorded on a Bruker E580 using an ER5107 dielectric resonator. A single crystal of LiPc (lithium phthalocyanine), for which g = 2.0021 had been determined at X-band, was used to calibrate the field at Q-band. Solutions of NATripol-1 and GTNMOH were placed in 1.6 mm OD quartz capillaries. The microwave power was in the linear response regime for the TN signals and the modulation amplitude was 0.4 G.

Pulsed EPR measurements were made using a Bruker E580 with an X-band dielectric resonator in a CF935 flow cryostat cooled by liquid N₂ boiloff gas. The resonator was over-coupled to a Q of 150 to 200. Samples in 1:1 PBS: glycerol in 4 mm OD quartz tubes were flash frozen in liquid nitrogen to ensure glass formation, prior to insertion into the resonator. T_m was measured by two-pulse spin echo, and T₁ was measured by 3-pulse inversion recovery, with π/2 pulse lengths of 80 ns. The output of a 1 kW TWT was attenuated to yield the maximum echo amplitude and adjusted for each experiment.

2.3. Data Analysis

The g and A values for H-NATripol-1 and H-GTNMOH mono-radicals (Table 1) were determined by simulation with EasySpin of spectra in 1:1 PBS: glycerol at 80 K. The tumbling correlation times for the nitroxide moieties in H-NATripol-1 and H-GTNMOH in fluid solution were determined by simulations with EasySpin [23], using the g and A values listed in Table 1. ‘Garlic’ was used for solutions in PBS and ‘chili’ was used for 1:1 PBS: glycerol. Values of A_z were decreased by about 2 MHz to match the average values in fluid solution. Simulations of the fluid solution spectra of the TN were performed using the program CUNO that was written initially for metal-nitroxide interactions [24], and assumes that tumbling is sufficiently rapid that isotropic g and A values can be used. The literature g-value of 2.0026 for trityl-CH₃ [25, 26] and the isotropic g and A values for the nitroxide mono-radicals (Table 1) were held constant and the values of the exchange coupling constant J, populations of conformations, and linewidths were varied to match the spectra. The first-derivatives of field-swept echo detected spectra of the TN at 80 K were simulated using the locally-written program MENO [27] that was initially used to simulate spectra of nitroxide spin-labeled copper(II) complexes. For copper-nitroxides the g and A values for both spins are highly anisotropic so analysis of the spectra for the spin-coupled systems required two angles to define the orientation of the interspin vector relative to the axes of one of the spins and three additional angles to define the orientation of the axes of the second spin to those of the first spin. For trityl radicals the g anisotropy is very small (2.0030, 2.0027, 2.0021 [26]) and there is no resolved nuclear hyperfine so the orientation of the axes of the trityl radical relative to the axes of the nitroxide has negligible impact on the simulated spectra. The nitroxide parameters are close enough to axial, and the lines in the TN spectra are so broad, that the only angle that had major impact on the simulations was the angle between the interspin vector and the nitroxide z axis, which was designated as ε. The anisotropic g and A values for the nitroxide mono-radicals (Table 1) and the g values for the trityl were held constant in the simulations while the values of J, interspin distance r, populations of conformations, values of ε, and linewidths were varied to match the TN spectra. For the spectra of NATripol-1 and GTNMOH there are features in the spectra that are strongly dependent on ε so the estimated uncertainty in ε is about ±5°.

Table 1.

g and A values for immobilized nitroxide at 80 K

Radical	Solvent	gx	gy	gz	Ax (MHz)	Ay (MHz)	Az (MHz)	Ref.
H-NATriPol-1	1:1 PBS: glycerol	2.0092	2.0061	2.0022	17.6	15.4	107	This work
H-GTNMOH	1:1 PBS: glycerol	2.0092	2.0061	2.0022	17.6	15.4	107	This work
Tempamine	CD3OD	2.0090	2.0061	2.0022	20.2	14.6	100.5	[47]
TEMPOL	Trehalose	2.0088	2.0062	2.0020	14.8	26.9	100.2	[22, 32]

This approach is significantly different from prior simulations of TN in which the g and A values were allowed to vary [12, 14]. When the g values were treated as adjustable parameters the best-fit trityl g values for TN were anisotropic [12, 14], which seems unlikely for these weak exchange interactions with J < 20 G. When the nitroxide A values were treated at adjustable parameters the resulting values of A_z were about 24 to 27 G (67 to 76 MHz) [12, 14], which is much smaller than the typical values for nitroxides that are summarized in Table 1, which also seems unlikely for J < 20 G. Given the large number of adjustable parameters in the simulations we decided to fix the g and A at the experimental values for the mono-radicals and adjust only parameters related to the spin-spin interaction.

The two-pulse echo decays were fit with stretched exponentials [28], Eq. 1

$$Y(\tau )=C_0+C_1{e}^{{\left(-2\tau /T_m\right)}^{\beta }}$$ (1)

The inversion recovery data were fit with the sum of two exponentials and also with stretched exponentials [29]. The uncertainty in β is about ±0.05.

3. Results

3.1. EPR spectra of nitroxide mono-radicals in fluid solution at 293 K

The fluid solution spectra of the nitroxide mono-radical analogs of the TN were analyzed to determine the mobility of the nitroxide moiety relative to what would be expected if the linker were rigid. The X-band CW EPR spectra for H-GTNMOH and H-NATripol-1 in 50 mM PBS, pH ~ 7.3 are shown in Figures 2A and 3A. The spectra were simulated with tumbling correlation times, τ_R, of 0.14±0.03 ns and 0.38±0.04 ns, respectively. For trityl-CH₃ (mw = 975) τ_R is 0.27 to 0.29 ns in water [30] or PBS [26, 31]. Since the molar masses of H-GTNMOH (1311.2 g/mol) and H-NATriPol-1 (1223.1 g/mol) are significantly larger than for trityl-CH₃, longer values of τ_R are predicted for the two nitroxides if the linker is sufficiently rigid that nitroxide motion is determined by the motion of the molecule as a whole. The ratio (1.35) of the value of τ_R for H-NATripol-1 (0.38 ns) to that for trityl-CH₃ (0.28 ns) is similar to the ratio of the molar masses (1.25), suggesting that this linker is relatively rigid. The significantly shorter value of τ_R for the nitroxide moiety of H-GTNMOH (0.14 ns) than those for H-NATripol-1 and trityl-CH₃ suggests that this linker permits substantial motion of the nitroxide independent of the molecule as a whole. The different locations of the methyl group on the amide linkages in H-NATripol-1 and H-GTNMOH, appear to restrict nitroxide motion to different extents. In the more viscous 1:1 PBS: glycerol the value of τ_R for H-GTNMOH (Figure 2B) increases to 1.6±0.3 ns. For H-NATripol-1 in 1:1 PBS:glycerol (Figure 3B) the nitroxide tumbling is anisotropic and the components of τ_R around the x, y, and z axes that were used in the simulation shown in Figure 3 were 0.32, 2.0, and 1.0 ns, respectively. For both mono-nitroxides the values of τ_R in 1:1 PBS: glycerol are smaller than the value of τ_R = 3.4±0.3 ns for ¹³C₁-trityl-CD₃ [26], which indicates that in the high viscosity solvent the linker remains relatively flexible. Greater flexibility of the linker may result in a wider range of conformations in the immobilized samples.

Figure 2.

X-band experimental (black) and simulated spectra (red) at 293 K of 0.5 mM H-GTNMOH in PBS (A) and in 1:1 PBS: glycerol (B). Spectra were simulated using EasySpin functions ‘garlic’ and ‘chili’ with the following parameters g = [2.0092 2.0061 2.0022], A (MHz) = [17.6 15.5 109 MHz], and τ_R = 0.14 ns in PBS or 1.6 ns in 1:1 PBS: glycerol.

Figure 3.

X-band experimental (black) and simulated spectra (red) at 293 K of 0.5 mM H-NATriPol-1 in PBS (A) and 1:1 PBS: glycerol (B). Spectra were simulated using EasySpin functions ‘garlic’ and ‘chili’ with the following parameters g = [2.0092 2.0061 2.0022], A (MHz) = [17.6 15.5 109 MHz], and τ_R = 0.38 ns in PBS. In 1:1 PBS: glycerol the anisotropic motion was simulated with τ_R = 0.32, 2.0 and 1.0 ns relative to the x, y, and z axis of the nitroxide.

3.2. EPR spectra of nitroxide mono-radicals immobilized at 80 K

In the analysis of the spectra of the immobilized samples of the TN it was assumed that the nitroxide g and A values are independent of the electron-electron spin-spin interactions. These values were determined by analysis of the spectra of the related nitroxide mono-radicals. The X-band CW (Figure 4A) and field-swept echo-detected spectra (Figure 4B and 4C) for the nitroxide mono-radicals, H-NATriPol-1 and H-GTNMOH, in glassy 1:1 PBS: glycerol are typical for nitroxides [32]. The spectra were simulated with the ‘pepper’ function in EasySpin using the g- and A- values listed in Table 1, which are similar to values for other piperidinyl nitroxides. In each mono-radical sample there was a small amount of TN. The trityl line for the TN is broadened in the echo-detected spectra by the bandwidths of the pulses and the filter used in the routine to calculate the derivative, but that does not impact the g and A values determined by the simulations.

Figure 4.

X-band experimental (black) and simulated rigid lattice spectra (red) of 0.5 mM solutions in 1:1 PBS:glycerol. CW spectrum at 150 K of H-NATriPol-1 (A), first-derivative of field-swept echo-detected spectrum of H-NATriPol-1 at 80 K (B), and first-derivative of field-swept echo-detected spectrum of H-GTNMOH at 80 K (C). The magnetic field axes were shifted to compensate for small differences in the microwave frequencies for data acquisition. Spectra were simulated with EasySpin using ‘pepper’ with the g and A values listed in Table 1.

3.3. Analysis of EPR spectra of trityl-nitroxides in fluid solution as sums of AB splitting patterns.

The Hamiltonian for the trityl-nitroxides diradicals in fluid solution can be written [33] as

$$\widehat{H}=g_1{\beta }_{e}B{\widehat{S}}_1+g_2{\beta }_{e}B{\widehat{S}}_2+h{A}_1{\widehat{S}}_1{\widehat{I}}_1+h{\widehat{S}}_1{\widehat{S}}_1$$ (2)

where g₁ and g₂ are the g values for nitroxide and trityl, A₁ is the nitroxide nitrogen hyperfine coupling in Hz, J is the electron-electron exchange interaction in Hz, β_e is the electron Bohr magneton, and h is Planck’s constant. The first three terms describe the spectra for non-interacting nitroxide and trityl. As reported previously spin-spin interaction between the trityl and nitroxide unpaired electrons causes the signal for each paramagnetic center in fluid solution to split into a doublet [7]. In this report we use the AB splitting formalism that is familiar from NMR spectroscopy of J-coupled nuclei [34] to examine in detail the impact of the spin-spin interaction on specific regions on the TN spectra. The relevant equations are summarized in Table 2. Analysis of electron-electron spin-spin interactions in fluid solution in terms of AB splittings has been applied to metal-nitroxides [35] and dinitroxides [36], but this is the first time it has been used to analyze spectra of trityl-nitroxides. As J increases the unprimed lines move toward the average position and increase in intensity, and the primed lines move away from the center and decrease in intensity. The nitrogen I = 1 splits the nitroxide signal into 3 lines with m_I = −1, 0, and 1, which are designated as N₋₁, N₀, and N₁. Each individual TN molecule contains a nitrogen in one of these nuclear spin states, so there are three superimposed AB patterns corresponding to molecules with the three different nitrogen nuclear spin states. The calculated line positions and intensities at X-band are illustrated in Figure 5 for the 1/3 of the GTMNOH molecules that contain nitrogen m_I = −1 and are in the conformation with J = 15 G. This AB splitting pattern is centered at 3509.3 G (B_avg) and the splitting Δ between this nitroxide line and the trityl line is 22.6 G. The spin-spin interaction produces 4 lines. The subscript “−1” designates the AB pattern that involves the N₋₁ line. The separation between transitions N’₋₁ and N₋₁ equals J, which also is the separation between T₋₁ and T’₋₁. The ratio of the intensity N’₋₁/N₋₁ and of T’₋₁/T₋₁ for this AB pattern is about 3.4 (Figure 5). These lines are also marked in Figure 6 (left panel).

Table 2.

Positions and relative intensities of the four lines in an AB splitting pattern^a

Line	Offset from Bavgb	Relative Intensity
a’	−J/2 − C	1 − sin (2θAB)
a	J/2 − C	1 + sin (22θAB)
b	−J/2 + C	1 + sin (22θAB)
b’	J/2 + C	1 − sin (22θAB)

^aEquations taken from Ref. [34]. B_avg, J, C, Δ are in magnetic field units, which are G in this paper. The designations a’ and a refer to the lines for the spin that is observed at lower field in the absence of interaction. When applied to trityl-nitroxides the designations a’, a, b, and b’ are replaced by N’, N, T, and T’, where N and T refer to nitroxide and trityl, respectively. Δ is the separation between resonance fields for the trityl and nitrogen m_I lines in the absence of spin-spin interaction. C = 0.5*(J² + A²)^1/2 and sin(2θ_AB) = J/2C [34].

^bB_avg is the average of the resonance fields for the two spins in the absence of interaction and is different for TN with each of the three nitrogen m_I values.

Figure 5.

Diagram of AB splitting pattern at X-band for the 1/3 of TN molecules that have nitrogen m_I = −1. The lines that originate from the nitroxide are N’₋₁ and N₋₁ and lines originating from trityl are T₋₁ and T’₋₁. In the absence of spin-spin interaction this nitroxide line is at 3498.0 G and the trityl line is at 3520.6 G (top panel), which corresponds to Δ= 22.6 G and B_avg = 3509.3 G. For J = 15 G (lower panel) the N’₋₁ and N₋₁ lines are at 3488.2 and 3503.2 G, and the T₁ and T’₋₁ lines are at 3515.3 and 3530.3 G. The intensity ratio N’₋₁/ N₋₁ = T’₋₁/ T₋₁ is ~0.3.

Figure 6.

Experimental (black, lower panel) and simulated spectra (red) at 293 K of 0.5 mM GTNMOH in PBS at X-band (9.867 GHz, left) and 0.8 mM GTNMOH at Q-band (33.851 GHz, right). The upper panels show the positions of the nitroxide and trityl lines in the absence of spin-spin interaction. The middle panel, with y axis in arbitrary units, shows the calculated positions of lines for J = 15 G. The simulated spectra are the sum of two contributions with J = 15 and 5 G, with weightings of 83% and 17% respectively. The intensities of the primed transitions are too small to detect at X-band. A small contribution for non-interacting trityl or nitroxide is marked with an * on the X-band and Q-band spectra.

Spectra of GTNMOH in PBS at 293 K and X-band or Q-band and simulations are shown in Figure 6. The top panels show the positions of the nitroxide and trityl lines in the absence of interaction. The middle panels show the positions of the lines for J = 15 G. The simulated spectra are the sum of contributions from two conformations. The values of J are 15±4 (83%) and 5±2 G (17%). The X-band spectrum could be simulated reasonably well with a single J = 15 G, but the resolution of multiple peaks in the Q-band spectra between about 12035 and 12075 G indicated two values of J. The lines shown in Fig. 5 for the AB pattern with nitrogen m_I = −1 at X-band are a subset of the lines for the conformation with J = 15 G that are marked in Fig. 6. At X-band, in the absence of spin-spin interaction the trityl line is about 6 G to high field of the nitroxide m_I = 0 line. Both J = 15 and 5 G are large enough relative to this small Δ = 6 G, that the N₀ and T₀ lines are heavily overlapped near B_avg =3517.7 G. The splitting Δ between the trityl line and the nitrogen m_I = 1 line is about 11 G which is large enough that the T₁ and N₁ lines for J = 15 G are resolved at about 3524 and 3528 G, respectively. The T₋₁ line for J = 15 G is close to the N₀ and T₀ lines and the N₋₁ line is well resolved at 3503 G. At X-band the positions of the lines for J = 5.3 G are close to those for J = 15 G and are not resolved. The intensities of the primed transitions are too weak to observe at X-band, even after extensive signal averaging. At Q-band the trityl line is very close to the nitroxide m_I = 1 line so the T₁ and N₁ lines are superimposed at about B_avg = 12133 G. The Q-band spectra reveal that there is a small amount of non-interacting nitroxide that is marked with * in Figure 6. At Q-band the line at 12040 G is the N’₋₁ line for J = 15 G. The additional line at about 12044 G is assigned as the N’₋₁ line for a second conformation with J = 5.3 G. The weak lines at about 12093 G are the T’₋₁ and T’₀ lines for J = 15 G. At Q-band the values of Δ are substantially larger for the AB patterns involving the nitrogen m_I = −1 and 0 lines than at X-band. Larger values of Δ make the intensities of the primed transitions larger. For example, the relative intensities of the N’₋₁ transition is substantially larger at Q-band than at X-band. The positions of the primed transitions are more strongly dependent on the value of J than for the unprimed transitions so observation of these transitions puts tighter constraints on the value of J than when these transitions are not observed. The sensitivity of the positions of the primed transitions to the value of J also contributes to increased linewidths, which makes detection more difficult.

Spectra of NATriPol-1 in PBS at 293 K and X-band or Q-band and simulations are shown in Figure 7. The top panels show the positions of the nitroxide and trityl lines in the absence of interaction. The middle panels show the positions of the lines for J = 113 G. Although the X-band spectra could be fit fairly well with a single value of J = 113±12 G, the fit to the Q-band spectra was improved by including two conformations with J = 113±12 G (67%) and 59±7 G (33%). The two components are consistent with the X-band spectra. These values of J are large enough relative to the values of Δ for the three AB patterns at both X-band and Q-band that the primed transitions were not observed. At X-band the N₀ and T₀ lines are superimposed and the T₁ and N₁ lines are heavily overlapped. The splitting of the N₋₁ and T₋₁ lines is a useful measure of the value of J, as has been noted previously [12]. At Q-band the N₁ and T₁ lines are heavily overlapped. There is some resolution of the N₀ and T₀ lines and the N₋₁ and T₋₁ lines are well resolved. However, the resolution is decreased by the overlapping contributions from the two conformations.

Figure 7.

Experimental (black, lower panel) and simulated spectra (red) at 293 K of 0.5mM NATriPol-1 in PBS at X-band (9.868 GHz, left) and 0.89 mM NATriPol-1 at Q-band (34.002 GHz, right). The upper panel shows the positions of the nitroxide and trityl lines in the absence of spin-spin interaction. The middle panel, with y axis in arbitrary units, shows the calculated positions of lines for J = 113 G. The simulated spectra are the sum of two contributions with J = 113 and 59 G, with weightings of 67% and 33%, respectively. The intensities of the primed transitions are too small to detect at X-band or Q-band. A small contribution for non-interacting trityl is marked with an * on the X-band spectra. The N₀ and T₀ lines are superimposed at X-band and partially resolved at Q-band.

3.3. Analysis of EPR spectra of trityl-nitroxides in rigid lattice as superpositions of AB splitting patterns

In the rigid lattice the spin Hamiltonian for the trityl-nitroxides includes the terms shown in Eq. (2) plus the dipolar splitting term that can be written as in Eq. (3)

$$D=\frac{3g_1{g}_2{\beta }_e^2}{2r^3}\left(1-3co{s}^2\theta \right)$$ (3)

where β_e is the electron Bohr magneton, r is the interspin distance, and θ is the angle between the interspin vector and the external magnetic field. If r is in Angstroms, D (in Gauss) = 1.39×10⁴ g₂ (1–3cos²θ)/r³.

In frozen solution, analogous to fluid solution, there are AB splitting patterns for the trityl interacting with each of the three nitrogen m_I hyperfine lines. However, unlike fluid solution, both the splitting Δ and the spin interaction are orientation dependent. The spin-spin interaction is the sum of J and the orientation-dependent dipolar interaction. For immobilized TN samples at X-band the trityl signal is about ~4 G to high field of the perpendicular region of the nitroxide signal. Since there is no contribution from nitrogen nuclear hyperfine to the resonance with m_I = 0 and the effect of nitroxide g anisotropy is small at X band, the energy separation Δ is small for m_I = 0 at all orientations with respect to the external magnetic field. Thus for these spins even relatively small values of J are sufficient to cause resonance at the average of the fields for non-interacting spins. For m_I = ±1, Δ varies from relatively small in the nitroxide perpendicular plane where A_⊥ is small, to much larger near the parallel axes where A_|| is larger. Increasing J moves spectral intensity toward the average of the resonance fields for trityl and nitroxide, which for TNs is close to the middle of the nitroxide spectrum. In the limit of J >> A_|| and relatively long interspin distance, the rigid lattice spectrum would be similar to that for nitroxide but with A_|| reduced by a factor of 2. The spin-spin interaction for GTNMOH and NATriPol-1 is much weaker than this limiting case.

The X-band spectrum of GTNMOH in 1:1 PBS: glycerol at 80 K (Figure 8A) is compared with that for H-GTNMOH (Figure 8B) to show the impact of the spin-spin interaction. The spectrum of GTNMOH could be simulated with two conformations J =27±6 (67%) and 3±2 G (33%) with interspin distances of 16±1 and 12±2 Å, respectively. Since two conformations were well resolved in fluid solution it seems plausible that two conformations would persist in the rapidly-frozen immobilized samples. For molecules with m_I = +1 or −1, and orientations in which the magnetic field is along the nitroxide z axis, these values of J are substantially less than the separation Δ ~ 33 G between non-interacting resonance positions. The spin-spin interaction results in splitting of the low-field and high-field regions of the spectra by the sum of J plus the dipolar splitting at this orientation. Both the unprimed and primed transitions of the AB patterns are observed. These regions of the spectrum are strongly dependent on the spin-spin interaction parameters and are very informative in the spectral analysis. For r = 12 and 16 Å, the maximum dipolar splittings along the axis of the interspin vector are 32 and 13 G, respectively. The contribution of the dipolar interaction along the nitroxide z axis are strongly dependent on the angle ε. The widths of the lines are attributed to distributions of values of J and r. The center of the spectrum is complicated by overlap of trityl lines from AB patterns from all orientations of the molecule in the magnetic field as well as the AB patterns from nitroxide perpendicular lines. The sharper feature at about 3455 G has substantial contributions from trityl lines and is strongly dependent on values of J and r.

Figure 8.

Experimental spectra (black) at 80 K in 1:1 PBS: glycerol of 0.5 mM GTNMOH (A) and 0.5 mM H-GTNMOH (B) (as in Figure 4B) at X-band and simulations (red). The * mark denotes the non-interacting trityl in the experimental data. The simulated spectrum of GTNMOH is the sum of contributions from one conformation with J = 27 G, r =16 Å, ε = 140°, and weighting of 67% and a second contribution with J = 3 G, r = 12 Å, ε = 140° and weighting of 33%.

The X-band spectrum of NATriPol-1 in 1:1 PBS: glycerol at 80 K (Figure 9A) is compared with that for H-NATriPol-1 in Figure 9B. The simulated spectrum of NATriPol-1 was obtained with two conformations. The spin-spin interaction parameters are J = 43±4 G for both confirmations with interspin distances of 13±2 (90%) and 11.5±1 Å (10%), respectively. For molecules with m_I = +1 or −1, and orientations in which the magnetic field is along the nitroxide z axis, these values of J are significantly larger than the Δ of about 33 G. For these larger values of J the intensities of the primed transitions are much smaller than for the unprimed transitions so the spin-spin interaction moves much of the intensity toward the average TN positions near the center of the spectrum. The overall width of the signal is sensitive to the values of J and r and the orientation of the interspin vector, ε.

Figure 9.

Experimental spectra (black) at 80 K in 1:1 PBS: glycerol of 0.5 mM NATriPol-1 (A) and 0.5 mM H-NATriPol-1 (B) (as in Figure 4C) at X-band and simulations (red). The * mark denotes the non-interacting trityl in the experimental data. The simulated spectrum for NATriPol-1 is the sum of contributions from one conformation with J = 43 G, r =13 Å, ε = 130°, and weighting of 90% and a second contribution with J = 43 G, r = 11.5 Å, ε = 170° and weighting of 10%.

The echo detected absorption spectra of mono-nitroxide H-GTNMOH and the TN GTNMOH, NATriPol-1 are superimposed in Figure 10B. The absorption spectra highlight the spin density that varies continuously between orientations for which magnetic field is along the parallel or perpendicular axes of the nitroxide. For the nitroxide mono-radicals the spin density in the wings of the spectrum arises from molecules for which the magnetic field is near the z-axis of the nitroxide hyperfine tensor. The spin-spin interaction with the trityl shifts intensity toward the center of the spectrum, which is more evident in the absorption spectrum than in the first derivative. Comparison of the absorption spectra (Fig. 10B) shows that the electron-electron spin-spin interaction is large enough to shift intensity toward the center of the TN spectra and this occurs to a larger extent for NATriPol-1 for which J is larger than for GTNMOH.

Figure 10.

Field dependence of relaxation rates (A) at 80 K in 1:1 PBS: glycerol of 0.5 mM GTNMOH (blue), NATriPol-1 (black), H-GTNMOH (dark green), H-NAtriPol-1 (green) and trityl-CH₃ (red). The rates are the long component of two-component fit to inversion recovery curves, T₁ (plus); stretched exponential fit to inversion recovery curves, T₁ (circle); and stretched exponential fit to echo decay curves, T_m (triangle).

Field-swept echo detected X-band spectra (B) at 80 K in 1:1 PBS: glycerol of 0.5 mM GTNMOH (blue), NATriPol-1 (black), and H-GTNMOH (dark green). The integrated area under the curve for H-GTNMOH is half that for the trityl-nitroxides to account for the factor of two fewer spins.

3.4. Electron Spin Relaxation

Electron spin relaxation rates at 80 K at selected positions in the spectra are shown in Figure 10A. The inversion recovery curves were not single exponentials, so data were analyzed both as the sum of two exponentials and as stretched exponentials [29]. For mono-radicals, the longer component that is obtained by analysis of inversion recovery curves as the sum of two exponentials is typically assigned as T₁ and the shorter component is attributed to spectral diffusion [29]. By contrast, for the strongly overlapping signals in the spectra of the TN the long and short components may be due to transitions with larger and smaller contributions from the trityl. Analyzing the recovery curves for the TN as a distribution using a stretched exponential may be more accurate than focusing on the long component of a two-component fit. The rates obtained from the stretched exponential are consistently faster than the long component of the two-component fit, although the trends as a function of position in the spectrum are similar (Fig. 10 A).

The observed orientation dependence of 1/T₁ for the nitroxide mono-radicals is similar to previous reports [37] with slower relaxation rates for orientations with the magnetic field along the nitroxide z axis (the parallel axis) and faster rates near the perpendicular plane. The 1/T₁ for trityl-CH₃ at this temperature is significantly slower than the slowest value for nitroxide. There is very little intensity in the TN spectra at the magnetic fields that correspond to N_|| for nitroxide mono-radicals (Fig. 10B). 1/T₁ for the TN were therefore measured over a narrower field range than for the nitroxide mono-radicals. Near the center of the spectra (about 3450 G) there is a weak signal from non-interacting trityl. At this position in the spectrum the long component of the two-component fit is dominated by the longer T₁ for trityl. At other positions in the spectrum there is extensive overlap of transitions that have more trityl character and ones with more nitroxide character. The values of 1/T₁ for the TN show little variation across the spectrum and are similar to values for the nitroxide mono-radicals. These observations show that the spin-spin interaction and overlapping transitions result in enhancement of the 1/T₁ relaxation rate for the slower-relaxing trityl and negligible impact on the nitroxide relaxation. The relaxation rates are indistinguishable for the two diradicals with different values of J, which indicates that even relatively small values of J are sufficient to enhance the trityl relaxation rates. The trends in 1/T₁ as a function of position in the spectrum at 90, 100, and 120 K (data not shown) are similar to those shown in Figure 10A at 80 K.

At 80 K 1/T_m for the nitroxide mono-radicals is independent of position in the spectrum and similar to the value for trityl-CH₃ (Fig. 10A). At this temperature the spin echo dephasing is dominated by nuclear spin diffusion from protons in the solvent environment [28]. The 1:1 PBS: glycerol is sufficiently rigid at 80 K that there is little librational motion and the rate of methyl rotation is slow relative to the anisotropy in the hyperfine coupling to the unpaired electron [38]. The 1/T_m for the TN is slightly faster than for the mono-radicals which may be due to some flexibility that modulates the spin-spin interaction. As temperature is increased, 1/T_m values for the nitroxide mono-radicals increase as rotation of the nitroxide gem-dimethyls becomes faster and dominates the echo dephasing [39, 40]. The increase in nitroxide 1/T_m also causes 1/T_m for the TN to increase.

The parameter β in the stretched exponential fits provides insight into the nature of the distribution [41]. Values of β further from 1 indicate wider distributions [29, 42]. Values of β for 1/T₁ and 1/T_m at 80 K are shown in Figure 11. For 1/T₁ of trityl-CH₃ β is ~1 which indicates that the inversion recovery curve is close to a single exponential. This observation is consistent with the fact that the trityl line is very narrow, there is no orientation dependence of 1/T₁ for trityl, and the pulses are sufficiently wide to excite all spins thereby eliminating opportunities for spectral diffusion. By contrast the β values for 1/T₁ for the nitroxide mono-radicals are in the range of 0.4 to 0.5, which indicates wide distributions. Pulse lengths of 80 and 160 ns excite spin bandwidths of about 1 G. Even over these relatively narrow ranges there is substantial orientation dependence of 1/T₁ and there is opportunity for spectral diffusion. The β values for the TN are similar to the values for the nitroxide mono-radicals, reflecting the substantial nitroxide contributions to the transitions. As temperature increases, β increases and becomes closer to 1 as the orientation dependence of T₁ decreases.

Figure 11.

Field dependence of stretched parameter β at 80 K for 1/T₁ (circles) and 1/T_m (triangles) for GTNMOH (blue), H-GTNMOH (dark green), NATriPol-1 (black), H-NATriPol-1 (green), trityl-CH₃ (red), PxCONHPx (magenta), and PxCOenCOPx (orange).

The values of β for 1/T_m at 80 K are all substantially greater than 1 which is characteristic of dephasing by nuclear spin diffusion [43]. Values of ~1.6 for the nitroxide mono-radials are typical of nitroxides at about 80 K [44]. The slightly larger value of β for trityl than for nitroxides is attributed to the longer distance of closest approach for neighboring solvent protons [30]. The slightly smaller values of β for the TNs than for nitroxides may reflect a wider distribution of environments than for the mono-radicals. The values of β for the TN are similar to values for nitroxide diradicals with relatively large J, P_xCONHP_x and P_xCOenCOP_x [45]. As temperature increases (data not shown) the rate of methyl rotation increases which causes a decrease in β for 1/T_m.

4. Discussion

The spin-spin exchange interaction in biradicals should be analyzed as “AB splitting patterns” familiar in NMR, between each pair of transitions, one from one radical and one from the other radical. The overall spectrum is a superposition of many AB patterns. In the case of nitroxide and trityl biradicals, the transitions overlap extensively. In rigid lattice, such as frozen solutions, even at the high concentrations used for DNP, most exchange is through bonds. Consequently, if the linkage between the radicals permits multiple conformations, there will be multiple J couplings, possibly even distributions of J couplings, which makes simulations of the spectra non-unique. The electron exchange inherently exposes the spin on the slowly-relaxing radical to the environment that causes the other radical to relax more rapidly, thus making the relaxation of the slowly-relaxing radical approach that of the faster relaxing radical, and becoming equal to it if the exchange is strong enough, as it is in the cases reported in this paper.

The detailed discussion in the preceding paragraphs of the EPR spectra of TN shows how analysis of the spectra in terms of AB splitting patterns permits understanding of many features. At X-band in fluid solution the trityl signal is close to the nitroxide m_I = 0 line. At Q-band the trityl signal in fluid solution is approximately superimposed on the nitroxide m_I = 1 line. This results in larger values of Δ (Table 2) for m_I = −1 at Q-band than at X-band, which increases the intensities of the N^’₋₁ and improves the accuracy of the determination of the value(s) of J. For both TN, the analysis of the fluid solution spectra at X-band and Q-band revealed the presence of two conformations with different values of J. Analysis of spectra at the two frequencies permits characterization of the two conformations more accurately than could be achieved with data at a single microwave frequency. The two conformations are attributed to the amide linkage because electron-electron spin-spin exchange has been shown to be strongly dependent on the conformation of amide linkages [46]. Diastereomers that result from chirality of the alanine linker could also give rise to two conformations of NATriPol-1.

Previous studies of TN have found that J is strongly dependent on linker [7] and usually decreased with decreasing temperature [12]. For GTNMOH the values of J for the immobilized sample at 80 K (27±6 and 3±2 G) are similar to values observed at 293 K (15±4 and 5±2 G) in fluid solution. For NATriPol-1 the value of J for the immobilized sample at 80 K (43±4 G) is smaller than the average of values at 293 K (113±12 G and 59±7 G). These results suggest that differences between values of J in solution and in rigid lattice depend on details of the linker energetics. For NATriPol-1 in phosphate buffer at ambient temperature the value of J was reported as 61 G [12], which is smaller than the average of the 59 and 113 G observed in PBS. In frozen 60:40 glycerol:water the parameters for NATriPol-1 were J = 17 G and dipolar couplings that correspond to r ~ 17 Å [12]. The differences in parameters may be due to solvent effects on the relatively flexible linkers.

Analysis of the tumbling of the nitroxide mono-radical analogs of the TN in viscous 1:1 buffer:glycerol shows that the mobility of the nitroxide moiety is greater than expected for the diradical as a whole. This mobility may contribute to the temperature dependence of J and to the observation of multiple conformations. Although only two conformations were used in the simulations of spectra for both TN at 80 K, these may be surrogates for more complicated distributions. Exact fit of simulation to experiment should not be expected because contributions to the spectra for isotopomers with ¹³C couplings larger than the widths of the central spin packets of the trityl spectrum were not included. Depending on which of the ¹³C hyperfine couplings are considered, 20% to 30% of the intensity of the trityl spectrum is in these ¹³C sidebands [26]. Each of these ¹³C lines exhibits AB patterns due to coupling to the nitroxide lines, as described for the central lines. Inclusion of these contributions would magnify the number of variables beyond the number of features in the spectra.

The impact of the spin-spin interaction on relaxation rates may be frequency specific. At X-band the resonances for the nitroxide and trityl lines are heavily overlapped which makes Δ for the AB splitting patterns relatively small. Since the trityl g value of 2.0026 is only slightly higher than the nitroxide g_z (2.0022), the trityl signal will overlap with the nitroxide signal for some orientations of the molecule in the magnetic field, independent of resonance frequency. However as the frequency increases the nitroxide signal spreads out so there will be larger values of Δ for an increasing fractions of orientations, which may decrease the impact of the nitroxide on the trityl relaxation rates.

Research Highlights.

• CW spectra of trityl-nitroxides were analyzed as superimposed AB splitting patterns.

• Nitroxide and trityl transitions overlap extensively at X-band.

• The spin-spin exchange interaction is attributed to through-bond exchange.

• X-band values of 1/T₁ for trityl-nitroxides at 80 to 120 K are similar to mono-nitroxides