Coupling of ethanolamine ammonia-lyase protein and solvent dynamics characterized by the temperature-dependence of EPR spin probe mobility and dielectric permittivity

Abstract

Electron paramagnetic resonance (EPR) spectroscopy is used to address the remarkable persistence of the native Arrhenius dependence of the 2-aminopropanol substrate radical rearrangement reaction in B₁₂-dependent ethanolamine ammonia-lyase (EAL) from Salmonella typhimurium from physiological to cryogenic (220 K) temperatures. Two-component TEMPOL spin probe mobility in the presence of 10 mM (0.08% v/v) 2-aminopropanol over 200–265 K demonstrates characteristic concentric aqueous-cosolvent mesodomain and protein-associated domain (PAD, hydration layer) solvent phases around EAL in the frozen solution. The mesodomain formed by the relatively small amount of 2-aminopropanol is highly confined, as shown by an elevated temperature for the order–disorder transition (ODT) in the PAD (230–235 K) and large activation energy for TEMPOL rotation. Addition of 2% v/v dimethylsulfoxide expands the mesodomain, partially relieves PAD confinement, and leads to an ODT at 205–210 K. The ODT is also manifested as a deviation of the temperature-dependence of the EPR amplitude of cob(II)alamin and the substrate radical, bound in the enzyme active site, from Curie law behavior. This is attributed to an increase in sample dielectric permittivity above the ODT at the microwave frequency of 9.5 GHz. The relatively high frequency dielectric response indicates an origin in coupled protein surface group–water fluctuations of the Johari–Goldstein β type that span spatial scales of ∼0.1–10 Å on temporal scales of 10⁻¹⁰–10⁻⁷ s. The orthogonal EPR spin probe rotational mobility and solvent dielectric measurements characterize features of EAL protein–solvent dynamical coupling and reveal that excess substrate acts as a fluidizing cryosolvent to enable native enzyme reactivity at cryogenic temperatures.

I. INTRODUCTION

Time-resolved electron paramagnetic resonance (EPR) spectroscopy¹ over the temperature (T) range of 200–250 K allows kinetic resolution of individual steps in the core substrate radical reaction sequence^2–4 in the adenosylcobalamin (coenzyme B₁₂)-dependent ethanolamine ammonia-lyase [EAL; EC 4.3.1.7, cobalamin (vitamin B₁₂)-dependent enzyme superfamily].^5,6 EAL is the first in a sequence of enzymes in the bacterial ethanolamine utilization (Eut) metabolic pathway⁷ that is associated with microbiome homeostasis⁸ and disease conditions in the human gut.^9–11 A rationale for the remarkable persistence of the native substrate radical reactions, which feature continuous Arrhenius relations from ambient T to deep into the cryo-regime, is implied by spin probe EPR experiments: EAL frozen in polycrystalline aqueous solution in the presence of relatively small amounts (≤4.0% v/v) of the added cryosolvent, dimethylsulfoxide (DMSO), is surrounded by a protein-associated domain (PAD, akin to the protein hydration layer) and a concentric, fluid aqueous-cosolvent mesodomain.^12,13 The EAL substrates,¹⁴ either the native aminoethanol² or alternate 2-aminopropanol,³ which are present in excess during cryotrapping to maintain the steady-state, active site substrate radical population, are alkanols, which, like DMSO, are canonical cryosolvents.¹⁵ Here, we address the hypothesis that 2-aminopropanol forms a low-T, fluid PAD-mesodomain system around EAL from Salmonella enterica serovar Typhimurium by characterizing the T-dependent TEMPOL spin probe dynamics and by introducing an orthogonal method that detects the solvent dynamical state through the effects of dielectric permittivity on the EPR sensitivity.

The structural and dynamical features of the PAD and mesodomain that surround EAL in frozen aqueous solution have been characterized through the lens of the rotational correlation times (PAD, slower tumbling, τ_c,s and mesodomain, faster tumbling, τ_c,f) and associated component weights (W_s and W_f) of the EPR spin probe, TEMPOL, by variations of the volume of DMSO added prior to cryotrapping, variation of EAL concentration, and the T-dependence of τ_c and W values.^12,13 The protein hydration layer has a reported thickness equivalent to ∼2 water molecules (∼6 Å).¹⁶ The mean shell thickness of the surrounding mesodomain can be manipulated from 5 to 40 Å by varying the added % DMSO from 0.5% to 4.0% v/v.¹³ At all % DMSO, decreasing T leads to a decrease in TEMPOL tumbling rates in both PAD and mesodomain and eventual abrupt exclusion of TEMPOL from the PAD into the mesodomain over a particular narrow range of T values, owing to PAD ordering, which is specified as the order–disorder transition (ODT).¹³ The divergence of τ_c,f from Arrhenius behavior (enhanced slowing of TEMPOL tumbling in the mesodomain) below the ODT and the increase in the ODT T value with the decrease in added DMSO (decrease in mesodomain shell thickness) suggest that the ODT is triggered by a critical level of confinement from the ice boundary, which is communicated to the PAD through the mesodomain.¹³

EAL turnover of the alternative substrate, 2-aminopropanol, is relatively slow (k_cat = 0.1–0.3 s⁻¹ at physiological T values, relative to ∼30 s⁻¹ for the native aminoethanol), and the K_M value of 10 µM indicates relatively strong binding to the active site.^3,17 Therefore, a relatively low concentration of 10 mM 2-aminopropanol has been used to maintain the substrate radical state during sample mixing and cryotrapping, prior to kinetic decay experiments.³ The 10 mM concentration is equivalent to 0.08% v/v, which is significantly less than the lowest DMSO concentration (0.5% v/v) used previously to study the mesodomain.¹³ Here, we show that 0.08% v/v 2-aminopropanol generates a mesodomain, which displays an elevated ODT T value and activation energy for tumbling, that indicates enhanced confinement, relative to mesodomains formed from DMSO.¹³ An orthogonal approach detects the solvent dynamics directly through the effect of changing solvent dielectric properties on the EPR amplitude of protein-bound paramagnetic states. The results provide a rationale for the low-temperature, native-like reactivity of EAL and characterize the dynamical coupling of EAL with the surrounding solvent.

II. MATERIALS AND METHODS

A. Protein and EPR sample preparation

EAL was produced in Escherichia coli by overexpression of the pBR322 plasmid containing the coding sequence for the enzyme from Salmonella typhimurium.¹⁸ The protein was isolated and purified by ammonium sulfate precipitation as described previously^18,19 with modifications.¹ The EPR samples were prepared as described in previous work.^3,12 The decay reaction mixture contained 20 μM purified EAL (120 μM active sites), 480 μM adenosylcobalamin, 10 mM (S)-2-aminopropanol (Sigma-Aldrich), and 10 mM potassium phosphate buffer (pH 7.5). The TEMPOL spin probe EPR samples were prepared in 10 mM potassium phosphate buffer (pH 7.5) and included 20 μM purified EAL, 10 mM (S)-2-aminopropanol, and 0.2 mM TEMPOL (4-hydroxy-TEMPO, Sigma-Aldrich) spin probe. When present, DMSO (purity, ≥99.9%, EMD Chemical) was added to 2% v/v relative to the sample final volume size of 300 μl. The components were mixed, loaded immediately into 4 mm outer diameter EPR tubes (Wilmad-LabGlass, 707-SQ-250M), and rapidly submerged in liquid nitrogen-chilled iso-pentane at 140 K. All chemicals and reagents used are commercially available and did not require further purification. In subsequent specification of cosolvent concentrations, % is used in place of % v/v, for brevity.

B. Continuous-wave EPR spectroscopy

Continuous-wave (CW) EPR spectra were collected by using a Bruker E500 ElexSys EPR spectrometer equipped with a Bruker ER4122 SHQE X-band cavity resonator. The temperature was controlled by using a Bruker ER4131VT temperature controller and cooling system that consists of nitrogen gas flowing through a coil immersed in liquid nitrogen bath contained in a 4 l Dewar.

1. Temperature-dependence of TEMPOL spin probe EPR spectra

The experimental protocol for TEMPOL spin probe measurements was described in previous work.^12,13 In brief, after calibration, the T was set at the lower or higher limits of the measurement range (200–265 K) and a first EPR spectrum was collected. The next temperature was set (5 K change), and before collecting the spectrum, the system was allowed at least 5 min to equilibrate, and the cavity was retuned. A control sample which was lacking TEMPOL was measured in a similar manner at each T value for baseline correction. The EPR acquisition parameters used are as follows: 9.45 GHz microwave frequency, 0.2 mW microwave power, 0.2 mT magnetic field modulation, 100 kHz modulation frequency, and 4–8 spectra averaged at each T value.

2. Temperature-dependence of EPR signal amplitude

Samples containing the EAL active site-bound paramagnetic species were prepared by using the protocol for time-resolved, full spectrum EPR spectroscopy of the 2-aminopropanol-generated cob(II)alamin–substrate radical pair at cryogenic temperatures.^1,3 The cob(II)alamin-substrate radical pair and uncoupled cob(II)alamin [hereafter, cob(II)alamin is abbreviated as Cbl(II)] represent the residual paramagnetic states following decay to ≤8% of the initial amplitude over >5 × 10⁴ s. The measurement of the T-dependence of the EPR amplitudes was performed for ascending T, and the T-step, equilibration, and spectrum acquisition protocol followed the method used for the TEMPOL spin probe measurements, as described above. A control sample, which lacked the substrate, was measured at each T value for baseline correction. Spectra collected for each sample at 120 K, before and after the T-dependence measurement series, confirmed constant amplitude. The EPR acquisition parameters used for these experiments are as follows: 9.45 GHz microwave frequency, 2.0 mW microwave power, 10 G magnetic field modulation, 100 kHz modulation frequency, 2600–4000 G sweep width, 1024 points, and 4–8 spectra averaged at each T value.

3. Microwave power saturation

The experiments were performed at 200 K and 235 K over a microwave power range of 0.002–205 mW, which correspond to the attenuation settings of 50–0 dB of the Bruker microwave bridge (model ER 049X Super X). The parameters for the spectra acquisition are as follows: 9.45 GHz microwave frequency, 10 G magnetic field modulation, 100 kHz modulation frequency, 2600–4000 G sweep width, and 1024 points. Each spectrum represents the average of 4–16 scans.

C. Simulation of TEMPOL spin probe EPR spectra

The CW-EPR spectra of the TEMPOL spin probe were simulated by using the Chili algorithm in the EasySpin program (http://www.easyspin.org/)²⁰ run on the MATLAB (Mathworks, Inc., Natick, MA) platform. The parameters and the procedure for the simulations are detailed in previous works.^12,13 Briefly, after baseline sample subtraction, the EPR spectral simulations require two components, each described by g tensor (g_x = 2.0130, g_y = 2.0120, g_z = 2.0073) and ¹⁴N hyperfine tensor (A_x = 20.9, A_y = 19.8, A_z = 103 MHz) parameters, with a set of varied parameters: correlation times (τ_c,s and τ_c,f), weights (W_s and W_f), and intrinsic line widths for the slow-motional and fast-motional components, respectively.

D. Power saturation analysis

The EPR signal intensity dependence on the microwave power is assessed in terms of the power for half-saturation. The empirical expression used to fit the experimental data to reveal the effects of power saturation in the weak saturation limit, which is characteristic of the relatively high-T values and metal ion, Co(II)–associated samples addressed here, is^21,22

$$I^{\prime }\left(P\right)=a{\left(1+\frac{P}{P_{1/2}}\right)}^{-\frac{b}{2}},$$ (1)

where P is the incident microwave power, I′(P) is the EPR amplitude divided by the square root of P, P_1/2 is the microwave power at half saturation, and a is a constant. The inhomogeneity parameter, b, can take values from 1 (purely inhomogeneous broadening) to 2 (purely homogeneous broadening).^21,22 The EPR signal of the EAL-bound paramagnets is inhomogeneously broadened,²³ and therefore, the inhomogeneity parameter b was fixed at 1 when fitting the saturation curves for each of the studied species. The parameter P_1/2 was determined by fitting Eq. (1) to the experimental data by using least squares regression analysis implemented in the lsqcurvefit function in MATLAB. Plots of log[I′(P)] as a function of log P are linear with zero slope at low P values, where the system is unsaturated, and transition to a linear dependence with negative slope upon onset and an increase in saturation.

III. RESULTS

A. Temperature-dependence of TEMPOL spin probe rotational mobility in EAL protein-associated domain and mesodomain

The T-dependence of the TEMPOL spin probe EPR spectrum in frozen aqueous solution with EAL and added 10 mM 2-aminopropanol, in the absence and presence of added 2% DMSO, is shown in Fig. 1. The three dominant spectral features arise from the electron–nuclear hyperfine interaction of the unpaired electron spin with the ¹⁴N nuclear spin in TEMPOL.²⁴ At low T, the spectra are characteristic of the rigid-limit powder pattern line shape, which directly shows the anisotropy in the electron g- and dipolar ¹⁴N (nuclear spin, I = 1) hyperfine coupling (A_N,dip) tensors. At the highest T values, rapid tumbling of the spin probe partially averages the anisotropic components, and the line shape collapses around an isotropic g-value with three sharp m_I features separated by the isotropic hyperfine splitting (coupling constant, A_N,iso = 48 MHz). The presence of DMSO shifts the transition from rigid to mobile spectra from ∼230 K (0% DMSO) to ∼210 K (2% DMSO).

FIG. 1.

Temperature dependence of the TEMPOL EPR spectrum in frozen aqueous solution in the presence of EAL and 10 mM 2-aminopropanol (black) and overlaid EPR simulations (red) at different added % v/v DMSO: (a) 0% and (b) 2%. Spectra are normalized to the central peak-to-trough amplitude. Alignment along the magnetic field axis corresponds to the microwave frequency at 200 K.

Simulations of the TEMPOL EPR spectra quantify the probe mobility through rotational correlation time (τ_c) and weight (W) parameters. Two components are required to simulate the spectra, which are described as “slow” (τ_c,s and W_s) and “fast” (τ_c,f and W_f). The slow component has been assigned to TEMPOL in the EAL protein-associated domain (PAD; hydration layer), and the fast component arises from TEMPOL in the surrounding aqueous-cosolvent mesodomain.¹² Simulation overlays are shown in Fig. 1, and the T-dependence of log τ_c and W is presented in Fig. 2 (values are listed in Tables S1 and S2). The dependence of log τ_c on T is segmented into four regions.¹³

FIG. 2.

Temperature dependence of the rotational correlation time [(a) and (b)] and normalized mobility component weights [(c) and (d)] of TEMPOL in the presence of EAL and 10 mM 2-aminopropanol at different added % v/v DMSO: [(a) and (c)] 0% and [(b) and (d)] 2%. The rotational correlation time is presented as the decadic logarithm. Open circles represent the slow component (log τ_c,s, W_s), and solid circles represent the fast component (log τ_c,f, W_f). Upper limit for detection of TEMPOL tumbling by using X-band CW EPR is represented by the horizontal dashed line at log τ_c = −7.0 [(a) and (b)].

In region I, both log τ_c values lie above the tumbling detection criterion (log τ_c > −7.0). In region II, log τ_c,s remains > −7.0, but log τ_c,f moves into the detectable range. In region III, both log τ_c,s and log τ_c,f are in the detectable range and decrease in value, indicating increased mobility with T. The boundary between regions II and III marks a transition in the normalized weights of the two populations, with a shift from the fast tumbling to slow tumbling population with increasing T. The normalized weights remain approximately constant with further increase in T through region III, with a dominant W_s component for 0% DMSO (W_s/W_f = 1.7) and dominant W_f component for 2% DMSO (W_s/W_f = 0.39), in qualitative accord with the larger cryosolvent content of the DMSO system. At the junction of regions III and IV, W_f begins to increase, as the melting of the ice boundary adds to the mesodomain volume. The forms of the T-dependences of log τ_c and W in the EAL, 10 mM 2-aminopropanol systems are comparable, but regions I–IV are shifted to lower T values for 2% DMSO relative to 0% DMSO. In particular, the transition in W values at the region II/III boundary indicates that the ODT occurs over 230–235 K for the 0% DMSO system, while the added 2% DMSO shifts the ODT range to 205–210 K.

B. Temperature-dependence of the EPR amplitude of uncoupled Cbl(II) and substrate radical species in EAL

The T-dependence of the CW-EPR spectra of endogenous paramagnetic species in EAL in long-time decay samples over the range of 190–240 K is presented in Fig. 3. The spectra represent a composite of the Cbl(II)–2-aminopropanol substrate radical pair intermediate and uncoupled Cbl(II).³ The uncoupled Cbl(II) is created by a non-native reaction pathway, which parallels the native decay of the Cbl(II)-substrate radical pair to diamagnetic products.³ The spectra in Fig. 3 are normalized to the amplitude of the Cbl(II) peak feature near g⊥ (290.5 mT) for line shape comparison. As shown by the unnormalized data in Fig. S1, the spectra display the expected trend of decrease in amplitudes with the increase in T due to the declining relative Boltzmann population of the ground spin states.²⁴ Signature features in the spectra were used to obtain the amplitudes of the substrate radical (high field trough) and the uncoupled Cbl(II) (peak near g⊥), as shown in Fig. 3. The T-dependences of the amplitudes display a change in slope at T values that overlap the T range of the spin probe-detected ODT values (Fig. S2), which will be addressed by Curie law analysis in Sec. IV.

FIG. 3.

Temperature dependence of the normalized uncoupled Cbl(II), radical, and Cbl(II)-substrate radical pair spectra in long-time decayed samples of EAL in frozen aqueous solution in the presence of 10 mM 2-aminopropanol and different added % v/v DMSO: (a) 0% and (b) 2%. Spectra are normalized to the peak amplitude of uncoupled Cbl(II) (low-field arrow). Arrows indicate the positions of measurement of the amplitude of uncoupled Cbl(II) (low-field, peak) and substrate radical (high-field, trough).

C. Microwave power-dependence of the EPR amplitude of uncoupled Cbl(II) and substrate radical species in EAL

To determine the regime of microwave power saturation of the EPR signals under the standard measurement conditions, the dependence of the signal amplitudes on P was determined at two T values, corresponding approximately to below and above the ODT. Figure 4 shows a plot of log[I′(P)] as a function of $\log \left(P^{\frac{1}{2}}\right)$ and the corresponding fit to Eq. (1) to obtain the microwave power at half-saturation of the EPR signal (see Figs. S3 and S4 for the unnormalized plot and plot of EPR amplitude vs $P^{\frac{1}{2}}$, respectively). The values of P_1/2 (Table S3) are significantly greater, by factors of 11–170, than the standard value of P = 2.0 mW used to obtain the EPR spectra and amplitudes in Fig. 3. Therefore, the series of T-dependent EPR spectra in Fig. 3 are in the very weak microwave power saturation limit.

FIG. 4.

Power saturation curves for EAL-bound paramagnets in long-time decayed samples of the radical pair in EAL at 200 K (solid) and 235 K (open) in the presence of 10 mM 2-aminopropanol and different added % v/v DMSO: 0% (black) and 2% (blue). (a) Substrate radical. (b) Uncoupled Cbl(II). Lines represent fits to the respective dataset using Eq. (1): 200 K (solid) and 235 K (dashed). Values of log[I′(P)] are normalized to the values at P < 1 mW.

IV. DISCUSSION

A. Solvent structure and dynamics around EAL in frozen aqueous solutions determined by spin probe EPR

In the presence of added 10 mM (0.08%) 2-aminopropanol alone (0% DMSO), the T range of the ODT of 230–235 K approaches the range for the mobility transition of 240–250 K in the EAL hydration layer in the absence of cryosolvent.¹² Mesodomain formation in the 2-aminopropanol system is evidenced by the two-component behavior and characteristic T-dependence of TEMPOL mobility (Fig. 2).¹³ However, the measured W_s value of 0.63 in region III indicates that the volume of the ∼6 Å–thick PAD (3 µl total, per sample¹³) is larger than the mesodomain volume (V_meso). In line with this, a V_meso ≈ 1 µl is estimated by using the dependence of W_s/W_f on V_meso calibrated for maximum freeze-concentrated aqueous DMSO.¹³ The low estimated V_meso value, relative to the significant W_f value of 0.37, suggests that the aqueous 2-aminopropanol phase recruits water (local melting) from the ice boundary to augment the mesodomain. The TEMPOL molecule itself may also create a local “defect” region in the compact mesodomain, which contributes to mobility.²⁵ A relatively confined aqueous-2-aminopropanol mesodomain is consistent with the region III activation energies for TEMPOL motion of 20 and 18 kcal/mol in the PAD and mesodomain, respectively, which are significantly larger than those for the lowest-concentration DMSO system (13 and 9 kcal/mol for 0.5% DMSO; see Fig. S5 and Table S4 for Arrhenius plots and fitting parameters, respectively). Despite the relative confinement of the 2-aminopropanol mesodomain, its demonstrated presence rationalizes the persistence of the native reactivity of the cryotrapped 2-aminopropanol substrate radical in EAL in the frozen aqueous system in the low temperature range of 220–240 K.³

The T range of the ODT for the binary 10 mM (0.08%) 2-aminopropanol 2% DMSO system is 205–210 K, which is the same as for the 2% DMSO-only system.¹³ Thus, DMSO makes a dominant contribution to the PAD and mesodomain properties in the binary system, as expected. The physical origin of the decreased T for the ODT in the PAD in the presence of 2% DMSO, relative to 0.08% 2-aminopropanol alone, is the established decrease in ice boundary confinement, communicated through the increased breadth of the intervening mesodomain.¹³

B. Temperature dependencies of the EPR amplitudes of paramagnetic species in EAL diverge from the Curie law at a temperature that correlates with the PAD order–disorder transition

The amplitude of the EPR signals from the EAL protein-bound paramagnetic species at a particular magnetic field value is addressed by using the Bloch treatment for the steady-state response of a spin sub-system to the microwave magnetic field,²⁶

$${\chi }^{″}=\frac{{\gamma }_e{T}_2{M}_0}{1+{\left({\gamma }_e{H}_0-\omega \right)}^2{T}_2^2+{\gamma }_e^2{H}_1^2{T}_1{T}_2},$$ (2)

where χ″ is the susceptibility corresponding to the rotating frame magnetization component, $M_{y^{\prime }}$, γ_e is the electron magnetogyric ratio, M₀ is the equilibrium magnetization, T₁ and T₂ are the spin-lattice and spin–spin relaxation time constants, respectively, ω is the microwave frequency, and H₀ and H₁ are the resonance and microwave magnetic fields, respectively. At resonance, $\left({\gamma }_e{H}_0-\omega \right)\to 0$. As shown by the microwave power dependence of the EPR amplitude, the experiments performed at the standard P = 2 mW are in the sub-saturation limit, where ${\gamma }_e^2{H}_1^2{T}_1{T}_2\ll 1$ (Fig. 4). Under these conditions, Eq. (2) is reduced to

$${\chi }^{″}\approx {\gamma }_e{T}_2{M}_0.$$ (3)

The Curie law expression for M₀ for a S = 1/2 system is

$$M_0=\frac{\mu N_V{\hslash }^2{\gamma }_e^2{H}_0}{4k_{B}T},$$ (4)

where μ is the magnetic permeability corresponding to the sample system (μ = μ_rμ₀, where μ_r is the relative permeability and μ₀ = 4π × 10⁷ H/m is the permeability of vacuum), N_V is the number of paramagnets in the sample per unit volume, and $\hslash$ is Planck’s constant divided by 2π.²⁷ Equations (3) and (4) lead to the following expression:

$${\chi }^{″}\approx \frac{\mu N_V{\hslash }^2{\gamma }_e^3{T}_2{H}_0}{4k_{B}T}.$$ (5)

The dependence of the EPR amplitudes on inverse T for the paramagnetic species bound in the active site of EAL displays the linear, Curie law T-dependence at low T values, in accord with Eq. (5), and an arcing, concave-down dependence at higher T-values (Fig. 5). These two regions of T-dependence are separated by a transition region. Figure 5 shows the relations for the uncoupled Cbl(II) and substrate radical species for the 0% and 2% DMSO conditions after correction for the different concentrations of residual decay species (N_V) in the linear, Curie law region, in accord with Eq. (5) (see the supplementary material for the method and see Fig. S6 for the overlay plot of all conditions). A rationale for the deviation from Curie law dependence in Fig. 5 is outside of the scope of Eq. (5). An abrupt change in the T-dependence of either μ or T₂ for the paramagnetically dilute samples is not expected,^27,28 and there is no change in linewidth (Fig. 3) that would evidence a significant change in T₂ over the T range. The origin of the high-T divergence from the Curie law is considered in Sec. IV C.

FIG. 5.

Dependence of the EPR amplitude of EAL-bound paramagnets on inverse absolute temperature in the presence of 10 mM 2-aminopropanol and different added % v/v DMSO and overlaid regions of the EPR spin probe-detected order–disorder transition (ODT; inverse 5 K width). (a) Uncoupled Cbl(II), low-field peak amplitude. (b) Substrate radical, high-field trough amplitude. Filled circles—0% DMSO. Open gray circles—2% DMSO. Corresponding temperature values are shown at top.

A comparison of the T values of the TEMPOL spin probe-detected W and log τ_c,f transitions with the T values of the divergence from the Curie law in EPR amplitude vs T dependences shows that they overlap for both 0% and 2% DMSO conditions, as portrayed in Fig. 5. Therefore, the T-dependent transitions in spin probe mobilities and weights, and the EPR amplitude of paramagnetic species bound in EAL, are both consequences of the ODT in the PAD and associated mesodomain confinement.

C. Dielectric permittivity dependence of the EPR amplitude of protein-bound paramagnetic species reveals features of the solvent dynamics around EAL

The deviation from Curie law T-dependence of the EPR amplitude is proposed to arise from a change in the sample dielectric properties, which is detected in the measurement circuit, through a change in the interaction (capacitive and inductive coupling) of the microwave radiation with the sample.^27–29 The EPR signal intensity, S, can be expressed as a function of the quality factor of the microwave resonator, Q, as

$$S=C{\omega }_0\eta P^{1/2}Q,$$ (6)

where the constant C includes the parameters in Eq. (5), ω₀ is the resonant microwave frequency, η is the filling factor, and P is the incident microwave power.²⁸ For microwave rectangular cavity resonators, the loaded Q, Q_L (resonator with quartz Dewar insert and sample under the experimental conditions) can be related to the unloaded Q, Q_u (resonator in isolation) and the imaginary part of the complex electric permittivity (dissipative, or loss, component), ε″, as²⁸

$$\frac{1}{Q_L}=\frac{2}{Q_u}+{\frac{{\pi }^3{r}^4}{a{V}_c}\epsilon }^{″},$$ (7)

where r is the radius of the cylindrical EPR sample (∼0.1 cm for a 0.4 cm outer-diameter quartz sample tube), a is 2.286 cm at X-band, and V_c is the volume of the empty cavity resonator (∼10.0 cm³ for the standard rectangular X-band EPR cavity resonator). Contributions to Q_L from radiation losses from the sample response at resonance, and surface currents at the sample are assumed negligible, relative to the cavity and sample dielectric losses. By incorporating the Q_u value of 7500 for the resonator used here (typical values for cavity resonators of 3000–5000 lead to comparable results) and evaluating the geometric constants in the prefactor of ${\epsilon }^{″}$, an approximate analytical expression for Q_L is

$$Q_L=2.67\times 10^{-4}+1.36\times {10^{-4}\epsilon }^{″}.$$ (8)

The detected value of ε″ represents the heterogeneous composition of the frozen aqueous sample of EAL protein, buffer, aqueous-cryosolvent phase, and ice. At the 9.5 GHz microwave frequency, values³⁰ of ${\epsilon }^{″}$ for pure ice at 190–250 K of 2–4 × 10⁻³ are negligible compared to ${\epsilon }^{″}$ values for the liquid states of DMSO and water (∼20 and 30, respectively, at 293 K²⁸). We use the following simple assumptions to estimate ε″: (1) The value of ε″ for the sample at T values below the ODT is assigned a value characteristic of ice, 2 × 10⁻³. (2) A scaling assumption, based on the relative volumes of ice (2.87 × 10⁻⁴ l, a proportion of 0.96, and assigned ε″ = 2 × 10⁻³) and the PAD mesodomain solvent components (1.30 × 10⁻⁵ l, a proportion of 0.04, for 2% DMSO, and assigned ε″ = 30), is used to approximate an effective ε″ over the sample. Estimated Q_L values of 2500 and 1900 are thus obtained for the mesodomain below and above the ODT, respectively, by using Eq. (8).

The effect of the change in Q_L on the EPR amplitude is assessed from the ratio of the signal intensities, S₂ and S₁, which correspond to the solid and fluid mesodomain, respectively,

$$\frac{S_2}{S_1}=\frac{Q_{\mathrm{L},2}}{Q_{\mathrm{L},1}}.$$ (9)

Equation (9) incorporates the assumptions of constant P (2 mW), constant η (sample does not perturb the microwave electric field in the resonator, as for high dielectric loss, or “lossy,” materials³¹), and negligible change in ω₀ (<0.1%, 190–240 K), which are characteristic of the samples examined here. For the estimated values of Q_L,2 and Q_L,1, Eq. (9) predicts a signal ratio of S₂/S₁ = 0.7. This is in good agreement with the deviation of the data from the Curie law extrapolations above the ODT in Fig. 5, as assessed from the T-dependent ratio of the slopes, which reaches values of ∼0.5 as T approaches 240 K. The curvature in the S₂ dependence above the ODT is consistent with the expected increase in ε″ with the increase in T, owing to increased fluidity in the mesodomain and PAD phases. Overall, the dielectric loss model accounts for the T-dependence of the EPR amplitudes.

A microscopic origin of the change in ε″ is suggested by comparison with the ν and T–dependences of the wide frequency range of dielectric relaxations in protein powder samples at water contents (h ≥ 0.3 g H₂O/g protein), which lead to surface hydration equivalent to ∼1–2 water molecule thickness. At ν ≈ 9.5 GHz and 200–250 K, a class of dielectric relaxation in these systems, distinct from lower frequency, collective α– and local β–like fluctuations, is assigned to the coupling of water with protein surface groups,^32–34 which occurs on length scales of ≤3 Å.^35,36 The relatively high-frequency response and T-dependence of this class are characteristic of the “ν-fluctuation” observed in a wide range of hydrated materials.^37,38 The “ν-fluctuation” is also proposed to arise from coupled water-polar group fluctuations, with characteristics of the Johari–Goldstein β class of local cluster fluctuations.³⁹ These results suggest that the fluctuations responsible for the change in ε″ and T-dependence of the EPR amplitude at 9.5 GHz originate from the coupled solvent–protein, local cluster motions around EAL of the Johari–Goldstein β class. Future work will resolve and quantify individual protein, PAD, and mesodomain contributions to ε″ by systematically varying V_meso and EAL concentration.

V. CONCLUSION

EAL is surrounded by PAD and mesodomain solvent components when frozen in the presence of substrate 2-aminopropanol, which rationalizes the observed adherence of the decay reaction kinetics of the cryotrapped substrate radical to the Arrhenius relation extending from physiological to cryogenic T values.³ The relatively small amount of added 2-aminopropanol (10 mM, 0.08%) leads to the lowest-volume aqueous cosolvent mesodomain yet measured,^12,13 with strong confinement evidenced by a relatively large activation energy to spin probe rotational motion and an elevated ODT in the PAD of 230–235 K. The addition of 2% DMSO dramatically shifts the ODT range to 205–210 K, as predicted by the relief of ice boundary confinement, due to the increased mesodomain volume.¹³ The TEMPOL spin probe mobility component transition, which demarks the ODT in the PAD,^12,13 occurs over a narrow T range that overlaps the locus of deviation from Curie law behavior in the T-dependence of the EPR amplitude of EAL active site-bound uncoupled Cbl(II) and substrate radical for both 0% and 2% DMSO conditions. Thus, the orthogonally detected TEMPOL transitions and Curie law deviation of the EPR amplitude are both manifestations of the ODT in the PAD and associated mesodomain confinement, as depicted in Fig. 6. The Curie law deviation is associated with an increase in the loss component of the sample dielectric permittivity above the ODT, detected at the resonant microwave frequency of 9.5 GHz. This relatively high frequency response, emerging at T values above the ODT, is consistent with an origin in coupled EAL protein surface group–water, local cluster fluctuations of the Johari–Goldstein β class. The dielectric sensitivity and spin probe mobility thus detect dynamics on spatial scales from solvent molecules and their interactions (∼0.1–3 Å) to TEMPOL (∼7 Å; similar to the dimension of protein surface topographical features) and on temporal scales of ∼10⁻¹⁰–10⁻⁷ s. The T- and cosolvent-dependence of this class of fluctuations will be used to probe solvent–protein-reaction dynamical coupling in EAL.

FIG. 6.

Depiction of the fluid phase dynamics around the EAL protein oligomer revealed by the temperature-dependence of the electron spin probe mobility and distribution and EPR amplitude of protein-bound paramagnetic species. Bottom: EAL oligomer surrounded by successive protein-associated domain (PAD; dark gray), mesodomain (light gray), and water ice (blue hatched) phases. Gray-scale signifies the degree of confinement (darker means higher confinement). Transition and top: increased temperature elicits relaxation of mesodomain confinement and triggers the order-to-disorder transition (ODT) in the PAD (both represented as lighter gray shades, top vs bottom) at a particular cosolvent volume-dependent temperature value. The ODT is signaled by a change in TEMPOL (10/EAL oligomer, average) spin probe mobility and distribution from bottom (detectably immobile in PAD—squares and slow-motional in mesodomain—circles) to top [partitioning into PAD; mobile in each phase, slow (orange), fast (red)]. The influence of the change in complex electric permittivity (ε″) on the EPR signal strength is depicted as a decrease in transparency of the system to the electric field component of the microwave radiation.

SUPPLEMENTARY MATERIAL

See the supplementary material for the description of the method for correlation of EPR amplitudes from samples with different EAL-bound paramagnet concentrations; figures showing the temperature dependence of unnormalized EPR spectra, un-normalized microwave power saturation curve, power saturation curve as a function of the square root of microwave power, Arrhenius plot of TEMPOL rotational correlation times, and overlaid dependences of the EPR amplitude of EAL-bound paramagnetic species on inverse temperature; and tables listing simulation parameters for TEMPOL EPR spectra at different temperatures, values of the microwave power at half-saturation of the EPR amplitude for EAL active site-bound paramagnetic species and Arrhenius parameters for TEMPOL tumbling in PAD and mesodomain solvent phases.

AUTHORS’ CONTRIBUTIONS

A.I. purified protein, and A.I. and B.N. prepared EPR samples. A.I. performed EPR spectroscopy. A.I., W.L., and K.W. analyzed and interpreted the results. A.I. and K.W. wrote the manuscript. All authors have given approval to the final version of the manuscript.

DATA AVAILABILITY

The data that support the findings of this study are available within the article and its supplementary material.