Effect of Hydrostatic Pressure on the g Tensor and Hyperfine Coupling Constants of the Nitroxide Radical Characterized by Ab Initio Calculations

Abstract

We present a computational study characterizing the effect of hydrostatic pressure on magnetic spin parameters that are used to analyze the electron paramagnetic resonance (EPR) spectra. Site-directed spin labeling (SDSL) in combination with EPR spectroscopy is a powerful tool for investigating the structure and dynamics of biological molecules. In studies using SDSL-based EPR spectroscopy, it is essential to know the spin parameters, such as the g factor and the hyperfine constants, precisely. However, the experimental characterization of these spin parameters under extreme conditions is often challenging. We report quantum chemistry calculations of g tensors and hyperfine coupling tensors (A tensors) for the nitroxide radical spin label in the pressure range of 0–15 GPa. The hydrostatic pressure causes structural changes, which, in turn, result in linear changes of the g and A tensors. The observed linear dependence of the g and A tensors suggests that these quantities can serve as reporters of local pressure in complex environments. The corresponding simulated EPR spectra at 9 and 230 GHz reveal that the changes of the EPR spectrum are more pronounced in the former. Our results indicate that the computational approach can address the challenge of determining magnetic spin parameters under extreme conditions, such as under high hydrostatic pressure.

Hydrostatic pressure plays an important role in biology. Cells experience high hydrostatic pressure in their native environments through a broad range of mechanical stresses, including stretch, compression, and shear stress. Site-directed spin labeling (SDSL) in combination with electron paramagnetic resonance (EPR) spectroscopy has been developed as an efficient tool to elucidate the structure and conformational dynamics of macrobiological molecules in various environments. , In SDSL, a site with an attached spin label is introduced via site-directed mutagenesis. Typical spin labels are small molecules with an unpaired electron and anisotropic g and A values, such as nitroxide radicals, trityl radicals, as well as copper, manganese, and gadolinium complexes. ,− Because the EPR spectrum is sensitive to the anisotropic g and A values, spin labels based on the nitroxide radicals have been used successfully for probing dynamics and conformational changes of target molecules.

SDSL-based EPR spectroscopy has been applied to various biological molecules, including proteins, DNA, and RNA, to probe the local environment, structure, and proximity of individual residues. Recently, the SDSL-based EPR technique has been used to study the stability and heterogeneity of the structural conformation of proteins under high hydrostatic pressure. , In particular, McCoy and Hubbell studied the hydrostatic pressure effects on the conformational exchange of spin-labeled mutants of T4 lysozyme using nitroxide-based SDSL and EPR. From the analysis of the nitroxide EPR spectrum, they observed the pressure dependence of the equilibrium states in structural conformations originating from the rotameric exchange.

The EPR-based structural analysis requires a knowledge of precise values of the g and A tensors for the nitroxide spin label. However, experimental determination of these parameters is quite challenging because it is difficult to distinguish spin properties of the spin label itself from the effects of the biological molecule when the spin label is attached to it, and fast tumbling motions of the spin labels make it difficult to determine them when the study is done with isolated spin labels. Therefore, in practice, the pressure-dependent studies often assume that the g and A tensors of the nitroxide radicals are pressure-independent. ,

Accurate quantum chemistry calculations can assess whether these assumptions are valid. The calculations can also provide these essential spin parameters under extreme conditions, such as high pressure, filling the gap in experimental capabilities. In this contribution, we use high-level computational methods to characterize the effects of pressure on g and A tenors in a nitroxide radical of the 2,2,6,6-tetramethylpiperedine-l-oxyl (TEMPO) molecule. The nitroxide radical is a popular spin label in EPR experiments. Whereas a number of studies have investigated the effects of pressure on various structural and electronic properties (e.g., fluorescence), this is the first computational study reporting the effect of hydrostatic pressure on spin properties.

Several computational approaches have been developed to study molecular structures under pressure, such as methods employing confining potentials − and other means of including pressure in the molecular dynamics and ab initio molecular dynamics simulations. , Here, we use the eXtended Hydrostatic Compression Force Field (X-HCFF) approach combined with density functional theory (DFT), as implemented in the Q-Chem software package. X-HCFF employs mechanical forces applied perpendicular to the tessellated molecular surface in the process of structure optimization to model the effect of the pressure on the molecule. We used X-HCFF to optimize molecular structures under pressures ranging between 0 and 15 GPa. We then use computed structures to calculate g tensors using the coupled-cluster method with single and double excitations (CCSD) combined with the response theory , and A tensors using DFT with several functionals. All calculations were carried out with the Q-Chem software package; additional details are given in the Supporting Information.

The TEMPO radical is a six-membered ring with the NO group, which has an unpaired electron (S = 1/2) residing on an anisotropic orbital and exhibiting hyperfine coupling with the ¹⁴N nuclear spin. Figure shows the molecular structure of TEMPO and the Dyson orbital hosting the unpaired electron.

1.

2,2,6,6-Tetramethylpiperidine-1-oxyl (C₉H₁₈NO, TEMPO) radical. (Left) Skeletal formula of TEMPO. A dot indicates an unpaired electron between the N and O atoms. (Right) Dyson orbital showing the state of the unpaired electron.

Moreover, the electron spin has hyperfine coupling with the ¹⁴N nuclear spin (I = 1) in the nitrogen–oxygen bond. The overall spin Hamiltonian is given by

$$H={\mu }_{\mathrm{B}}\mathrm{S⃗}·ĝ·{\mathrm{B⃗}}_0+\mathrm{I⃗}·Â·\mathrm{S⃗}$$ 1

where S⃗ and I⃗ are electron and nuclear spin operators, respectively, B⃗ ₀ is the external magnetic field, μ_B is the Bohr magneton, ĝ is the g tensor, and  is the hyperfine tensor between the electron and ¹⁴N nuclear spins. According to the Hamiltonian in eq , the energy of the system depends linearly on the values of the ĝ and  tensors. In the discussion below, we report the principal components of the tensors (i.e., g _x , g _y , and g _z ) obtained by diagonalization of the respective computed tensors. We also report isotropic values, i.e., g _iso = (g _x + g _y + g _z )/3 and A _iso = (A _x + A _y + A _z )/3, g-value shifts (i.e., chemical shifts) from the free electron g value, i.e., Δg _x = (g _x – g _e)/g _e, where g _e = 2.00232, as well as the difference from the experimental values, i.e., dg _x = (g _x – g _i ^exp)/g _x ^exp (g _x ^exp = 2.00955, g _y ^exp = 2.00632, and g _z ^exp = 2.00240).

Table shows the experimental values for g and A tensors of TEMPO and compares them with the computed values using the ωB97X-D/6-311+G­(2df,p) optimized structure (no pressure, standard optimization) and using the structure optimized with X-HCFF at a pressure of 0.1 GPa. The g tensors were computed at the CCSD/6-311G­(2df,p) level of theory, and A tensors (coupling between the electron and ¹⁴N nuclear spins) were computed using DFT (with the TPSS0 functional and 6-31++G* basis; the results with other functionals and basis sets are given in the Supporting Information). As one can see, the computed g and A values for X-HCFF/0.1 GPa and standard optimization (no X-HCFF) are identical within the precision used, hence confirming that application of the X-HCFF method does not introduce any artifacts and produces correct structures at the ambient pressure.

1. Experimental Values of g and A Tensors of TEMPO under Ambient Conditions and Computed Theoretical Values.

method	g x	g y	g z	A x (MHz)	A y (MHz)	A z (MHz)
exp.	2.00955	2.00632	2.00240	19.2	19.2	98.1
theo ,	2.01020	2.00643	2.00229	16.6	17.4	85.9
theo ,	2.01020	2.00643	2.00229	16.6	17.4	85.9

^aUsing the ωB97X-D/6-311+G­(2df,p) structure computed with X-HCFF and P = 0.1 GPa.

^bUsing the ωB97X-D/6-311+G­(2df,p) optimized structure (no pressure).

^c g tensors computed with CCSD/6-311G­(2df,p) with core electrons frozen and gauge origin placed in COM. The hyperfine constants were computed with TPSS0/6-31++G*.

Furthermore, we note that the calculated and experimental values agree rather well. The computed g _x , g _y , and g _z values near ambient conditions are 2.01020, 2.00643, and 2.00229, and the corresponding g-value shifts from the free electron g value [Δg _i = (g _i – g _e)/g _e, where i = x, y, and z] are Δg _x = 3938 ppm, Δg _y = 2051 ppm, and Δg _z = −14 ppm. These calculated g shifts are comparable to the results reported in a previous study. The difference from the experimental values at ambient pressure [dg _i = (g _i – g _i ^exp)/g _i ^exp, where i = x, y, and z] are dg _x = 325 ppm, dg _y = 53 ppm, and dg _z = −55 ppm. These small discrepancies between the theoretical and experimental g-tensor values are within the anticipated error bars due to insufficient treatment of correlation and a relatively compact basis set. The computed A values also agree reasonably well with those of the experiment. With TPSS0/6-31++G*, we obtained A _x ^exp = 16.6 MHz, A _y ^exp = 17.4 MHz, and A _z ^exp = 85.9 MHz. The differences from the experimental values [e.g., dA _x = (A _x – A ^exp)/A ^exp] are −13.7, −9.2, and −12.4%. These small differences are in good agreement with the previous computational study at ambient pressure (<11%).

In the Supporting Information, we report additional benchmark results for g and A tenosrs obtained with different basis sets. For A tensors, we also report the results obtained with several other functionals (primarily, from rung 4 and 5 families). CCSD results for g tensors show a modest basis set dependence. In contrast, the DFT results for A tensors depend strongly on the basis and functional, with TPSS0/6-31++G* yielding the best results. The two next best combinations were PBE0/6-31++G* and B97M-rV/6-311+G­(2df,p). We observed that, for many functionals, using larger bases led to larger deviations from the experiment. This sensitivity of the results to the functional provides motivation for developing wave function-based methods and including A tensors in DFT benchmarking and functional development studies; these important tasks are beyond the scope of the present paper. Here, we simply employed the combination of TPSS0 and 6-31++G* for the pressure-dependent study. We tested the trends in pressure dependence using two different methods and observed that, despite the variations in absolute values, the linearity and slope are less sensitive to the method choice.

Next, we investigated the pressure dependence. We first discuss the effect of pressure on the structure, focusing on the NO bond length as the most relevant parameter. The value of the NO bond length from the X-ray crystallography is 1.282 Å. The ωB97X-D/6-311+G­(2df,p) computed value is 1.270 Å (the effect of the basis on the computed structures is discussed in the Supporting Information). Figure shows the N–O distance as a function of the pressure. As one can see, the distance decreases linearly from 1.270 to 1.261 Å as the pressure increases from 0 to 15 GPa. A linear fit to the data yields a slope of −(5.68 ± 0.03) × 10^–4 Å and a perfect R ² value of 1.00.

2.

NO bond distance in ångström as a function of the hydrostatic pressure. The inset shows the same data as a function of the pressure (x axis) in a logarithmic scale. The slope of the pressure dependence was obtained by a linear fit (R ² = 1.00). Method: ωB97X-D/6-311+G­(2df,p).

Using these structures, we computed the g- and A-tensor values of TEMPO. Panels a and b of Figure summarize the results. Both g and A values also change linearly as a function of the pressure; the larger the applied pressure, the smaller the g value and hyperfine coupling anisotropy. The changes in the g tensors are less pronounced than those in the A tensors. By fitting the data with a linear function, we obtained the following slopes for the pressure dependence: −(5.2 ± 0.4) × 10^–6, −(3.36 ± 0.01) × 10^–6, and (0.02 ± 0.05) × 10^–6 GPa^–1 for g _x , g _y , and g _z , respectively. The x and y components decrease by 37 and 26 ppm, respectively, as the pressure increases from 0 to 15 GPa, whereas the z component is nearly constant and fluctuates only by ∼1 ppm. These negative slopes of the pressure dependence correspond to the reduction of the anisotropy as a result of the compression of the NO bond. The results show that the g _x and g _y values are more sensitive to the pressure than the g _z value.

3.

Computed g- and A-tensor values as a function of the pressure. (a) x-, y-, and z-component g values and isotropic g values (g _x , g _y,, g _z , and g _iso) as a function of the pressure, with CCSD/6-311G­(2df,p) using ωB97X-D/6-311+G­(2df,p) structures. (b) A tensors calculated TPSS0/6-31++G* using the ωB97X-D/6-311+G­(2df,p) structures. The differences with respect to the experimental value at ambient pressure are shown on the left. See also Table .

Figure b summarizes the computed pressure dependence on the A-tensor coupling between the electron and ¹⁴N nuclear spins in the TEMPO molecule. Similarly to the g values, we found linear pressure dependence on the A-tensor values. The slopes are −0.095 ± 0.007, −0.091 ± 0.007, and −0.083 ± 0.005 MHz/GPa for A _x , A _y , and A _z , respectively. Therefore, the A-value shifts from 0 to 15 GPa are −7.2, −6.8 and −1.3% for A _x , A _y , and A _z , respectively. Hence, the A _x and A _y values are more sensitive than the A _z value, which is consistent with the pressure dependence of the g tensors.

In order to assess whether these pressure-induced changes in g and A tensors would be visible in the EPR spectra, we simulated 9 GHz (X band) and 230 GHz EPR spectra using the computed g and A values with EasySpin software. We performed the simulations with a rotational correlation time (τ_c) of 2 ns by aiming to study the stability of the spin-label EPR under hydrostatic pressure. The rotational correlation time represents the influence of the molecular motions on the EPR spectrum. In particular, the correlation time of τ_c = 2 ns is typical for the nitroxide radical attached to a protein in an aqueous solution. ,, Figure a shows the EPR spectra at a Larmor frequency of 9 GHz with pressures of 0, 0.5, 1, and 15 GPa. By taking into account the convention of EPR spectroscopy, which utilizes the magnetic field modulation technique, the spectrum was plotted as a derivative of the absorption spectrum. As can be seen, the EPR spectrum spans from 318 to 322 mT, corresponding to the width of 4 mT. The EPR spectra consist of three lines because of the hyperfine coupling of the TEMPO spin. Note that the effects of the anisotropic g factor are very small (see Figure a) because the spectral shifts due to the anisotropic g values are much smaller than the shifts from the hyperfine coupling in the 9 GHz EPR. Furthermore, in the case of the 9 GHz EPR spectrum, the motional averaging effects influence the EPR spectrum because the rotational correlation time of 2 ns is close to the period of Larmor frequency (0.1 ns). Therefore, the motional averaging effects govern the amount of the splitting of three EPR signals; namely, the splitting represented the isotropic hyperfine constant. According to Figure a, the EPR spectra at 0, 0.5, and 1 GPa are indistinguishable; however, the EPR spectrum at 15 GPa is different. In particular, the difference in the peak position at 319 mT between 15 GPa and the others is pronounced. This is due to the ∼3% changes of the A _iso values (see Figure b).

4.

Simulated 9 and 230 GHz EPR spectra for TEMPO under pressures. (a) 9 GHz EPR spectra simulated for the conditions of 0.1, 1, and 15 GPa. (b) 230 GHz EPR spectra simulated for the conditions of 0.1, 1, and 15 GPa. The simulations were performed with EasySpin using the spin parameters shown in Figure . The simulation was performed using the chili function with the line width of 0.1 mT.

Next, Figure b shows the 230 GHz EPR spectra. Similar to the 9 GHz EPR spectra, the plot shows the derivative of the EPR absorption spectrum. As one can see, the shape of the 230 GHz EPR spectrum is different from that at 9 GHz (Figure a). The EPR spectra are much broader by spanning from 8170 to 8220 mT with a corresponding width of 50 mT. The broad EPR signal originates from the anisotropy of the g values. Because the shift of the g value is much pronounced in the high magnetic field used in the 230 GHz EPR (∼8200 mT), the anisotropic g values of the TEMPO spin make the EPR transitions distribute in a wide range of magnetic fields, as shown in Figure b. Moreover, in contrast to the 9 GHz EPR, the period of the Larmor frequency (4.3 ps) is much shorter than the rotational correlation time of 2 ns in the 230 GHz EPR. Therefore, the 230 GHz EPR spectrum is less influenced by the motional averaging effects. Overall, the shape of the EPR spectrum is determined by the anisotropic g values. Thus, the result suggests that the EPR spectral analysis at 230 GHz will be less affected by the pressure effects of the spin label; therefore, the EPR analysis at 230 GHz EPR spectroscopy may be suitable for studying molecular dynamics under hydrostatic pressures without accounting for the changes in magnetic parameters.

In summary, we carried out a computational study of the hydrostatic pressure effects on the g and A tensors of the TEMPO molecule. We observed the linear dependence on the g and A tensors under pressures in the range of 0–15 GPa. The shifts of the g values are in the range from 0 to −37 ppm by increasing the pressure from 0 to 15 GPa, whereas the shifts of the A tensor are in the range from −1 to −7%. We also determined the rates of pressure dependence for x, y, and z components of both g and A tensors. The observed linear dependence on the g and A tensors shows a potential application of the nitroxide radical as a pressure sensor. Furthermore, we examined the effect of the pressure dependence on EPR spectra under a typical condition where the nitroxide radical is used as a spin label. The simulation of EPR spectra with the obtained g and A tensors showed that the pressure-dependent changes in the EPR spectrum are more pronounced in 9 GHz (X band) EPR spectroscopy than those in 230 GHz EPR. This is because the A tensor decreases by a much larger portion than the g tensor when the pressure is increased, and the line width of the 9 GHz EPR is determined by the A values, while the line width of the 230 GHz EPR is determined by the g values. This finding suggests that SDSL-based EPR operated at a high frequency, such as 230 GHz, allows one to circumvent potential spectral changes due to the pressure dependence on the spin label and ensure EPR spectral changes only due to structural changes of target molecules under hydrostatic pressures. Moreover, the present investigation illustrates the utility of the presented computational protocol for determining the pressure dependence of various spin parameters of molecular spins under extreme environments, such as high and low pressures, strong electric fields, and high magnetic fields.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpclett.5c00677.

• Computational details, input parameters used in calculations, calculation of geometry optimization, calculation of g values, calculation of A tensors, calculation of EPR spectra, and compilation of optimized geometries (PDF)

The authors declare the following competing financial interest(s): Anna I. Krylov is the president and part owner of Q-Chem, Inc.