NMR of Paramagnetic Compounds

Abstract

Paramagnetic ions and molecules have been exploited quite extensively as extrinsic shift and relaxation probes for investigating the structure and dynamics of biological molecules. The prodigious growth of related research areas is easily discernible as the remarkably widening scope of application in diverse fields in life and material sciences. Sperm whale myoglobin (Mb) is well known as the first protein to have its three-dimensional structure revealed by X-ray crystallographic study and is also known as one of the first paramagnetic proteins studied by NMR. The heme Fe atom in Mb can exhibit a variety of oxidation, ligation, and spin states. In this chapter, Mb is selected as a reference paramagnetic compound to provide an overview of the relationship between the spectral features and the number of unpaired electrons, because the effects of a change in the spin quantum number S, i.e., the number of unpaired electrons, on NMR spectral parameters of a single compound can be readily understood. Field-dependent broadening of signals of proteins with a series of S values is also described.

1 Introduction

The use of paramagnetic ions or molecules as extrinsic shift and relaxation probes for investigating the structures of biological molecules not only in solution, but also in solid states has been exploited much more than originally expected (see Chap. 15) [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45]. In addition, dynamic nuclear polarization (DNP) ascribing to the magnetization transfer occurring from unpaired electrons to nuclei through stochastic modulation of the hyperfine interaction between electron and nuclear spins (see Chap. 4) is gaining increasing attention for a variety of applications, showing its potential in solution and solid-state NMR as well as in MRI [38, 46,47,48,49]. NMR study of paramagnetic compounds originated in solid-state physics in the middle of the 1950s [50, 51], and as is well known, the technique was soon introduced to chemistry and biochemistry. By 1970, the physical principles underlying the technique were well understood and the basic concepts of the technique, together with the theoretical framework for interpreting NMR parameters of paramagnetic compounds, had been well established [1, 2, 10, 52,53,54,55,56,57,58,59,60,61]. The prodigious growth of related research areas is easily witnessed by the remarkably widening scope of application in diverse fields in life and material sciences. A large number of reviews on NMR study of paramagnetic compounds have already appeared, some [10, 19, 62,63,64] comprehensive and others [3,4,5,6,7,8,9, 11,12,13,14,15,16,17,18, 20, 21, 23, 26,27,28,29, 38, 40, 65] more focused. Considering the aim of the present book, this chapter should serve as a reference source for active researchers and as an introduction to this subject for a novice, with particular emphasis on the experimental aspects. In view of the multiple purposes of the chapter, we selected hemoproteins, particularly sperm whale myoglobin [Mb (Fig. 18.1a)], as reference compounds. As is well known, Mb was the first protein to have had its three-dimensional structure revealed by X-ray crystallographic study [66]. Mb is also known as one of the first paramagnetic proteins studied by NMR [67], and paramagnetic hemoproteins such as Mb, cytochrome c, and hemoglobin were extensively investigated by Shulman [68], Wüthrich [69], Ogawa [70], La Mar [71], and Morishima [72] during the late 1960s to the late 1970s. In addition, paramagnetic Mb has been used for one of the landmark NMR measurements, which demonstrated that, in a magnetic field-oriented molecule, a magnetic dipole–dipole interaction does not average to zero [73] and yields a measurable dipolar coupling useful for refinement of structural and dynamic properties of molecules [74].

Fig. 18.1

a Schematic representation of the structure of sperm whale myoglobin (Mb; Protein Data Bank ID 1A6M). The polypeptide chain is illustrated as a ribbon model, and the heme is drawn as a space-filling model. b Structure and numbering system of heme. c Schematic drawing of the heme coordination structure in deoxy Mb [76]. The hydrogen bonding interaction of His93 N _δ H with the Leu89 carbonyl oxygen atom is represented by a broken line

Mb is an oxygen (O₂) storage hemoprotein with a molecular weight of about 17 kDa [75]. The heme cofactor (Fig. 18.1b) is buried inside the protein matrix composed of 153 amino acid residues, and its binding to the protein is stabilized by the coordination bond between the heme iron (Fe) atom and the nitrogen one (N _ε ) of the proximal His (His93) [66, 76,77,78] (Fig. 18.1c), together with hydrophobic interaction of the heme cofactor with the surrounding amino acid residues in the heme pocket and the formation of salt bridges between the heme propionate groups and nearby polar amino acid side chains [76,77,78]. The heme Fe atom in Mb is generally in either the ferrous (Fe²⁺) or ferric (Fe³⁺) state. The numbers of electrons in the 3d orbitals of Fe²⁺ and Fe³⁺ are six and five, respectively (inset of Fig. 18.2). Hence, the total spin quantum number S is the integer and half-integer for Fe²⁺ and Fe³⁺, respectively. Depending upon the degree of spin pairing of electrons in the 3d orbitals, Fe²⁺ can have 4, 2, or 0 unpaired electrons, corresponding to S = 2, 1, or 0, respectively, and Fe³⁺ corresponding to 5, 3, or 1 unpaired electron, S = 5/2, 3/2, or 1/2, respectively. Based on an octahedral ligand field, the energy levels of the five 3d orbitals are split into two groups in such a way that the levels of the $d_{{z^{2} }}$ and $d_{{x^{2} - y^{2} }}$ orbitals are higher than those of the other three orbitals, d _xy , d _yz , and d _xz . The spin state of Mb depends on the chemical nature of the ligand. For heme Fe²⁺, the deoxy form (deoxy Mb) is penta-coordinated with a high-spin configuration, S = 2, and the oxy form (MbO₂) or carbonmonoxy form (MbCO) possesses a low-spin configuration, S = 0. On the other hand, the binding of ligands of relatively weak field strength such as H₂O to heme Fe³⁺ gives high-spin state S = 5/2 [metMb(H₂O)], and low-spin state S = 1/2 is obtained with a strong ligand such as CN⁻ [metMb(CN⁻)]. In addition, the binding of ligands of intermediate field strength such as N₃ ⁻ [metMb(N₃ ⁻)] exhibit a thermal equilibrium between S = 1/2 and S = 5/2 states. Complexes with S = 1 and 3/2 are not so common and have been obtained in some particular systems such as Fe⁴⁺-peroxo species (S = 1) and Fe³⁺ species coupled with O₂ ⁻ (S = 3/2) [79].

Fig. 18.2

400 MHz ¹H NMR spectra of a carbonmonoxy form [Mb(CO)], b met-cyano form [metMb(CN⁻)], c met-azido form [metMb(N₃ ⁻)], d deoxy form (deoxy Mb) of Mb in 90% ¹H₂O/10% ²H₂O, pH 7.4, at 25 °C, and e met-aquo form [metMb(H₂O)] of the protein in 90% ¹H₂O/10% ²H₂O, pH 6.5, at 25 °C. The heme Fe oxidation and ligation states of the proteins are schematically illustrated on the right-hand side of the spectra. The assignments of heme methyl proton signals, i.e., 2-, 7-, 12-, and 18-CH₃, are indicated by the corresponding numbers in the spectra. In (a), four signals are observed at ~3 ppm. In (b), the 7-CH₃ signal at ~5 ppm is buried in the diamagnetic envelope, and in (d), 2- and 18-CH₃ signals are not assigned yet. Assignments of the Val68 C_γH₃ signal of Mb(CO) and the His93 N _δ H proton signal of deoxy Mb are also indicated. In the inset, typical heme Fe oxidation, spin, and ligation states of the protein are illustrated. The intermediate spin complexes, i.e., Fe²⁺ S = 1 and Fe³⁺ S = 3/2 complexes, are obtained in some particular systems [79]

Aside from the importance of Mb in the early history of the NMR study of paramagnetic compounds, the significance of Mb in NMR studies is mainly twofold, as follows. Firstly, as described above, the heme Fe atom in Mb can exhibit a variety of oxidation, ligation, and spin states, and hence, the effects of a change in the S value, i.e., the number of unpaired electrons, on NMR spectral parameters of a single compound, can be readily understood. Secondly, the relationship between the contact shift (δ _c), due to a delocalized unpaired electron, and a pseudo-contact one (δ _pc), due to a through-space dipolar interaction with the unpaired electron spin(s), as to paramagnetic shift (δ _para) is clearly reflected in the spectra of paramagnetic Mbs, and thus, a comprehensive description of the δ _c value can be given in terms of delocalization of unpaired electron density from the paramagnetic center. We intend to portray a range of techniques applied to paramagnetic Mbs, which exhibit widespread utility in life and material sciences.

2 Paramagnetic Effects

The theory behind NMR parameters in paramagnetic systems has been treated thoroughly elsewhere [2, 10, 13, 16]. Only a qualitative description of paramagnetic shifts and relaxation, which will suffice to allow an appreciation of the spectra presented, is given below.

2.1 Paramagnetic Shifts

Analysis of δ _para in terms of the interaction between nuclear and electron spins provides a wealth of information about electronic and molecular structures [2, 8,9,10,11,12,13,14,15,16,17,18,19,20,21]. The observed shift (δ _obs) of a paramagnetic compound is given as in Eq. (18.1), where δ _dia and δ _para are the diamagnetic and paramagnetic contributions, respectively.

$$ \delta_{\text{obs}} = \delta_{\text{dia}} + \delta_{\text{para}} $$

(18.1)

δ _dia is the shift that would have been observed if the molecule contained no unpaired electron, and δ _para is expressed as the sum of δ _c and δ _pc,

$$ \delta_{\text{para}} = \delta_{\text{c}} + \delta_{\text{pc}} $$

(18.2)

δ _c reflects the electronic structure of the molecule, and the metal-centered δ _pc, due to the magnetic dipolar field arising from delocalized unpaired electron(s) at the paramagnetic center, has been used extensively to refine the molecular structure (see Chap. 15 of this book).

In addition to δ _para itself, its temperature dependence also provides valuable information about the molecule. Since both δ _c and δ _pc are proportional to the reciprocal of absolute temperature (T), plots of δ _obs against 1/T, often called Curie plots, exhibit a straight line with the intercept at 1/T → 0, which is equal to δ _dia. However, anomalous Curie plots are occasionally observed, and the thermodynamic nature of the thermal spin equilibrium in metMb(N₃ ⁻) [80] and the thermal equilibrium between ⁵ E, (d _xy )(d _xz )²(d _yz )($d_{{z^{2} }}$)($d_{{x^{2} - y^{2} }}$), and ⁵ B ₂, (d _xy )²(d _xz )(d _yz )($d_{{z^{2} }}$)($d_{{x^{2} - y^{2} }}$), states of high-spin heme Fe²⁺ in deoxy Mb [81], have been quantitatively characterized through analysis of such anomalous temperature-dependent shift changes of the signals.

2.2 Paramagnetic Relaxation

The analysis of nuclear relaxation has provided a wealth of information about the structural and dynamic properties of molecules. In particular, in the case of paramagnetic metalloproteins, the dynamic nature of a molecule is sharply manifested in paramagnetic relaxation observed for paramagnetically shifted NMR signals [2, 10, 13, 14, 16].

The nuclear relaxation rate (R _obs) in a paramagnetic system is expressed as the sum of diamagnetic (R _dia) and paramagnetic (R _para) terms,

$$ R_{\text{obs}} = R_{\text{dia}} + R_{\text{para}} $$

(18.3)

R _dia is the sum of the contributions of the dipole–dipole interaction ($R_{\text{dia}}^{\text{DD}}$), chemical shift anisotropy ($R_{\text{dia}}^{\text{CSA}}$), and others ($R_{\text{dia}}^{\text{other}}$),

$$ R_{\text{dia}} = R_{\text{dia}}^{\text{DD}} + R_{\text{dia}}^{\text{CSA}} + R_{\text{dia}}^{\text{other}} \cdot $$

(18.4)

The contributions of $R_{\text{dia}}^{\text{CSA}}$ to the nuclear spin–lattice (R _1dia) and spin–spin (R _2dia) relaxation rates ($R_{{ 1 {\text{dia}}}}^{\text{CSA}}$ and $R_{{ 2 {\text{dia}}}}^{\text{CSA}}$, respectively) depend on the magnetic field strength and can be written as follows [56],

$$ R_{{ 1 {\text{dia}}}}^{\text{CSA}} = \frac{6}{40}\omega_{I}^{2} \delta_{z}^{2} \left( {1 + \frac{{\eta^{2} }}{3}} \right)J(\omega_{I} ) $$

(18.5)

$$ R_{{ 2 {\text{dia}}}}^{\text{CSA}} = \frac{1}{40}\omega_{I}^{2} \delta_{z}^{2} (3J(\omega_{I} ) + 4J(0)) $$

(18.6)

$$ J(\omega_{I} ) = \frac{{2\tau_{r} }}{{1 + \omega_{I}^{2} \tau_{r}^{2} }}, $$

(18.7)

where $\delta_{z}^{{}}$ is associated with the principal components of the chemical shift tensor, η is the asymmetric parameter of the molecule under consideration, and $J(\omega_{I} )$ represents the spectral density function.

On the other hand, R _para is expressed as the sum of the contributions of metal-centered ($R_{\text{para}}^{\text{MC}}$) and ligand-centered ($R_{\text{para}}^{\text{LC}}$) dipolar terms, the contact hyperfine interaction ($R_{\text{para}}^{\text{C}}$), and Curie spin relaxation ($R_{\text{para}}^{\text{Curie}}$) [2], as illustrated in Fig. 18.3,

Fig. 18.3

Schematic representation of paramagnetic relaxation mechanisms for heme CH₃ protons. Paramagnetic metal-centered relaxation ($R_{\text{para}}^{\text{MC}}$) is due to the dipole–dipole interaction between the nuclear spin and electron spin localized at heme Fe. Paramagnetic ligand-centered relaxation ($R_{\text{para}}^{\text{LC}}$) is due to the dipole–dipole interaction between the nuclear spin and electron spins delocalized from heme Fe into the ligand atoms, and, in the case of the heme CH₃ proton, $R_{\text{para}}^{\text{LC}}$ due to the electron spin delocalized into the p _z orbital of the carbon atom to which CH₃ is covalently attached is predominant. Paramagnetic contact relaxation ($R_{\text{para}}^{\text{C}}$) arises from the contact hyperfine interaction between the nuclear spin and electron spin delocalized into the 1 s orbital of the CH₃ hydrogen atoms. Curie spin relaxation ($R_{\text{para}}^{\text{Curie}}$) arises from the dipole–dipole interaction between the nuclear spin and the time average of the electron magnetic moment (not shown)

$$ R_{\text{para}} = R_{\text{para}}^{\text{MC}} + R_{\text{para}}^{\text{LC}} + R_{\text{para}}^{\text{C}} + R_{\text{para}}^{\text{Curie}} \cdot $$

(18.8)

Using the Solomon–Bloembergen equations [52, 82], together with the expression of $R_{\text{para}}^{\text{Curie}}$ [83, 84] (see Chap. 15 of this book), paramagnetic contributions to the nuclear spin–lattice and spin–spin relaxation rates (R _1para and R _2para, respectively) in a paramagnetic system are expressed by

$$ \begin{aligned} R_{{1{\text{para}}}} & = \frac{2}{15}\left( {\frac{{\mu_{0} }}{4\pi }} \right)^{2} \gamma_{I}^{2} \beta_{e}^{2} \mu_{B}^{2} S(S + 1)\left( {\gamma_{M}^{ - 6} + \varSigma \rho^{2} \gamma_{L}^{ - 6} } \right) \\ & \quad \times \left[ {\frac{{\tau_{c2} }}{{1 + (\omega_{I} - \omega_{S} )^{2} \tau_{c2}^{2} }} + \frac{{3\tau_{c1} }}{{1 + \omega_{I}^{2} \tau_{c1}^{2} }} + \frac{{6\tau_{c2} }}{{1 + (\omega_{I} + \omega_{S} )^{2} \tau_{c2}^{2} }}} \right] \\ & \quad + \frac{2}{3}S(S + 1)\left( {\frac{A}{\hbar }} \right)^{2} \left[ {\frac{{\tau_{e2} }}{{1 + (\omega_{I} + \omega_{S} )^{2} \tau_{e2}^{2} }}} \right] \\ & \quad + \frac{2}{5}\left( {\frac{{\mu_{0} }}{4\pi }} \right)^{2} \frac{{\omega_{I}^{2} \beta_{e}^{4} \mu_{B}^{4} S^{2} (S + 1)^{2} }}{{(3kT)^{2} r_{M}^{6} }}\left( {\frac{{3\tau_{r} }}{{1 + \omega_{I}^{2} \tau_{r}^{2} }}} \right) \\ \end{aligned} $$

(18.9)

$$ \begin{aligned} R_{{2{\text{para}}}} & = \frac{1}{15}\left( {\frac{{\mu_{0} }}{4\pi }} \right)^{2} \gamma_{I}^{2} \beta_{e}^{2} \mu_{B}^{2} S(S + 1)\left( {\gamma_{M}^{ - 6} + \varSigma \rho^{2} \gamma_{L}^{ - 6} } \right) \\ & \quad \times \left[ {4\tau_{c1} + \frac{{3\tau_{c2} }}{{1 + (\omega_{I} - \omega_{S} )^{2} \tau_{c2}^{2} }} + \frac{{3\tau_{c1} }}{{1 + \omega_{I}^{2} \tau_{c1}^{2} }} + \frac{{6\tau_{c2} }}{{1 + \omega_{S}^{2} \tau_{c2}^{2} }} + \frac{{6\tau_{c2} }}{{1 + (\omega_{I} + \omega_{S} )^{2} \tau_{c2}^{2} }}} \right] \\ & \quad + \frac{1}{3}S(S + 1)\left( {\frac{A}{\hbar }} \right)^{2} \left[ {\tau_{e1} + \frac{{\tau_{e2} }}{{1 + (\omega_{I} - \omega_{S} )^{2} \tau_{e2}^{2} }}} \right] \\ & \quad + \frac{1}{5}\left( {\frac{{\mu_{0} }}{4\pi }} \right)^{2} \frac{{\omega_{I}^{2} \beta_{e}^{4} \mu_{B}^{4} S^{2} (S + 1)^{2} }}{{(3kT)^{2} r_{M}^{6} }}\left( {4\tau_{c2} + \frac{{3\tau_{r} }}{{1 + \omega_{I}^{2} \tau_{r}^{2} }}} \right) \\ \end{aligned} $$

(18.10)

$$ \tau_{c1}^{ - 1} = T_{1e}^{ - 1} + \tau {}_{r}^{ - 1} + \tau {}_{\text{ex}}^{ - 1} $$

(18.11)

$$ \tau_{c2}^{ - 1} = T_{2e}^{ - 1} + \tau_{r}^{ - 1} + \tau_{\text{ex}}^{ - 1} $$

(18.12)

$$ \tau_{c1}^{ - 1} = T_{1e}^{ - 1} + \tau_{\text{ex}}^{ - 1} $$

(18.13)

$$ \tau_{c2}^{ - 1} = T_{2e}^{ - 1} + \tau_{ex}^{ - 1} , $$

(18.14)

where, in the present case, $r_{M}$ and $r_{L}$ are the distances between the proton of interest and the Fe atom, and between the proton and the pyrrole carbon atom, respectively, ρ is the unpaired electron density at the pyrrole carbon atoms (Fig. 18.1b), $\left( {\frac{A}{\hbar }} \right)$ is the apparent hyperfine coupling constant, $\omega_{I}$ and $\omega_{S}$ are the Larmor frequencies of the nucleus and electron, respectively, $T_{1e}$ and $T_{2e}$ are the electron longitudinal and transverse relaxation times, respectively, and $\tau_{\text{ex}}$ is the electron exchange time. The other parameters are as usual. In large molecules with highly resolved NMR spectra, $T_{1e} ,T_{2e} \ll \tau_{r}$, and at high magnetic field, $\omega_{I}^{2} T_{1e}^{2} \ll 1$, $1 < \omega_{S}^{2} T_{1e}^{2}$, and $1 < \omega_{S}^{2} T_{2e}^{2}$, Eqs. (18.7) and (18.8) are reduced to the following equations [85, 86]

$$ R_{{1{\text{para}}}} = \frac{2}{15}\left( {\frac{{\mu_{0} }}{4\pi }} \right)^{2} \gamma_{I}^{2} \beta_{e}^{2} \mu_{B}^{2} S(S + 1)\left( {\gamma_{M}^{ - 6} + \varSigma \rho^{2} \gamma_{L}^{ - 6} } \right)T_{1e} $$

(18.15)

$$ \begin{aligned} R_{{2{\text{para}}}} & = \frac{7}{15}\left( {\frac{{\mu_{0} }}{4\pi }} \right)^{2} \gamma_{I}^{2} \beta_{e}^{2} \mu_{B}^{2} S(S + 1)\left( {\gamma_{M}^{ - 6} + \varSigma \rho^{2} \gamma_{L}^{ - 6} } \right)T_{1e} \\ & \quad + \frac{1}{3}S(S + 1)\left( {\frac{A}{\hbar }} \right)^{2} T_{1e} + \frac{4}{5}\left( {\frac{{\mu_{0} }}{4\pi }} \right)^{2} \frac{{\omega_{I}^{2} \beta_{e}^{4} \mu_{B}^{4} S^{2} (S + 1)^{2} }}{{(3kT)^{2} r_{M}^{6} }}\tau_{r} \\ \end{aligned} $$

(18.16)

Equation (18.16) dictates that R _2para depends on the field strength due to the contribution of $R_{\text{para}}^{\text{Curie}}$, the third term on the right-hand side of the equation (see Sect. 18.4.2).

3 ¹H NMR Spectra of Myoglobin with 0, 1, 4, or 5 Unpaired Electrons

In this section, ¹H NMR spectra of Mbs in a variety of oxidation, ligation, and spin states are overviewed to understand the relationship between the number of unpaired electrons and the spectral features. In addition, 400, 600, and 800 MHz ¹H spectra of each form of the protein are compared with each other to observe the field dependence of the spectral parameters.

3.1 Overview

400 MHz ¹H spectra of Mb(CO), metMb(CN⁻), metMb(N₃ ⁻), deoxy Mb, and metMb(H₂O) are shown in Fig. 18.2. Heme methyl (CH₃) proton signals are often used as sensitive probes for the heme electronic structures of hemoproteins [6, 14]. In addition to ready observation of the signals with three-proton intensity, the δ _para values of the hemoprotein provide a measure of the nonequivalence of the four pyrrole environment of the porphyrin ring, i.e., the in-plane asymmetry of the heme electronic structure, because there is a CH₃ group on each pyrrole (Fig. 18.1b), and delocalization of unpaired electron(s) from the heme π-system to the s orbital of the CH₃ protons necessary for the Fermi contact interaction occurs effectively through hyperconjugation [2, 10]. Comparison of the δ _para values of the heme CH₃ proton signals between heme model compounds and hemoproteins in every oxidation/spin state indicated that the spread of the four signals is always much larger in the protein environment [6]. The spread of the four heme CH₃ proton signals in model compound is due to intrinsic in-plane asymmetry of the heme electronic structure, and hence, the increase in the spread of the signals in the protein reflects the asymmetric nature of the heme–protein linkage, which is relevant to regulation of heme Fe reactivity, and hence the protein function [2, 6, 14].

In the presence of a large spread of the four heme CH₃ proton signals, the average shift of the signals is used as a measure of the electronic nature of the heme Fe atom in the protein. The average shift of the signals of diamagnetic Mb(CO) is ~3 ppm [87] (trace 2a), and those of paramagnetic metMb(CN⁻) and metMb(H₂O) are ~14 [88] and ~75 ppm [89, 90], respectively (traces 2B and E, respectively). Thus, the average shift of the paramagnetically shifted heme CH₃ proton signals is roughly proportional to the number of unpaired electrons, i.e., the S value. The average shift of the signals of metMb(N₃ ⁻), i.e., ~23 ppm [91] (trace 2c), is somehow between those of metMb(CN⁻) and metMb(H₂O), because of the intermediate ligand field strength of N₃ ⁻, which renders the energy difference between the Fe³⁺ low-spin (S = 1/2) and high-spin (S = 5/2) states comparable to the thermal energy [91,92,93,94]. Finally, among the physiologically active forms of the protein, deoxy Mb is the least understood in terms of the molecular properties of its heme active site [81, 95,96,97]. Despite extensive efforts, the ground-state electronic structure of the Fe²⁺ high-spin (S = 2) state of deoxy Mb remains to be elucidated [81]. Due to out-of-plane displacement of the Fe atom from the porphyrin plane in the penta-coordinated heme complex in the protein [77] (Fig. 18.1c), the average shift of the four heme CH₃ proton signals of deoxy Mb, i.e., ~15 ppm [96], is rather small, while the signal of the axial His93 N _δ H proton is observed at ~77 ppm [98] (trace 2d).

3.2 Diamagnetic Carbonmonoxy Form [Mb(CO)]

Mb(CO) is often considered as a model of Mb(O₂) that tends to be spontaneously oxidized to metMb(H₂O) through a reaction known as autoxidation. In the absence of a unpaired electron, Mb(CO) is just like an ordinary diamagnetic protein. So the benefit of the higher resolution in the spectrum recorded at higher magnetic field strength can be clearly witnessed in Fig. 18.4. The ring current effect of the porphyrin moiety of heme is considerably greater than that of the phenyl group of such as phenylalanine. As a result, the Val68 C_γH₃ proton signal is resolved at ~−2.5 ppm [99], and signals due to heme 5, 10, 15, and 20-H protons (Fig. 18.1b) are resolved in a downfield-shifted region, i.e., >~9.5 ppm [87]. Hence, the porphyrin π-system of heme itself can be considered as a sort of intrinsic shift reagent. Furthermore, some NH protons involved in intramolecular hydrogen bonding are also resolved below ~9.5 ppm [99, 100].

Fig. 18.4

Portions, 8.8–11.5 ppm, of ¹H NMR spectra of Mb(CO) in 90% ¹H₂O/10% ²H₂O, pH 7.4, at 25 °C, recorded at ¹H frequencies of 400 (a), 600 (b), and 800 MHz (c). Assignments of meso 5-, 10, 15-, and 20-H proton (see Fig. 18.1b) signals are indicated in (c). The signals resolved below ~9.5 ppm are due to NH protons involved in intramolecular hydrogen bonding [99, 100]

3.3 Paramagnetic Deoxy Form (Deoxy Mb) with S = 2

The His93 N _δ H proton signal is resolved at ~77 ppm [98] and the heme CH₃ proton ones in the range of <~20 ppm [96] (trace 2d). The line widths of signals due to the His93 N _δ H and heme CH₃ protons of the protein in a 400 MHz spectrum at 25 °C (trace 2d) are ~450 and ~120 Hz, respectively, and their relaxation times are <~10 ms. Consequently, as far as acquisition of only the paramagnetically shifted signals of the protein is concerned, the repetition time can be set considerably short, provided that the experimental setting is properly optimized. A drawback to such a measurement is that it will distort the spectral features of signals due to protein protons far away from the paramagnetic center because of the long relaxation times. A relatively large number of dummy scans prior to data acquisition will help to reduce the spectral distortion caused by short repetition times.

The unpaired electrons of the heme Fe atom of deoxy Mb are delocalized into the His93 imidazole through the Fe–His σ and π bonds, i.e., σ- and π-delocalization, respectively [2, 10, 101]. The delocalization of the positive spin of an unpaired electron through the σ- and π-delocalization results in a net spin density of the opposite sign, that is, negative, and a positive spin on the His93 N _ε atom, respectively, and the spin on the His93 N _ε atom is further delocalized, through the π system of the imidazole ring, into the N _δ atom, and then finally into the 1s orbital of the His93 N _δ H hydrogen, through σ spin polarization [102]. As a result, the positive spin is delocalized into the 1s orbital of the His93 N _δ H hydrogen through σ-delocalization, whereas the negative spin is delocalized through π-delocalization. Thus, the δ _c value for the His93 N _δ H shift is determined as the difference between the σ- and π-delocalization, and hence, large positive δ _c values indicate that the σ-delocalization dominates over the π-delocalization [101]. The strength of the Fe–His bond is possibly affected by steric and electronic factors. La Mar and de Ropp [103] demonstrated, in a study involving horse radish ferrous peroxidase, that the proximal His N _δ H proton shift is greatly affected by the hydrogen bond between the N _δ H proton and a protein acceptor residue through its effect on the delocalization of the unpaired electron along the N _δ –H bond, and that simultaneous consideration of changes of the stretching frequency of the Fe–His bond [104] and the axial His N _δ H proton shift enables differentiation of the steric and electronic influences on the Fe–His bond [103]. In the case of deoxy Mb, the delocalization of the unpaired electron from the N _δ atom to the 1s orbital of the N _δ H hydrogen decreases with increasing strength of the His93–Leu89 H-bond because the interaction between the N _δ H hydrogen and the unpaired electron density on the His93 imidazole ring is hampered by enhancement of polarization of the charge in the N _δ –H bond. Furthermore, a change in the strength of the His93–Leu89 hydrogen bond (Fig. 18.1c) also influences the Fe–His bond strength in such a manner that the Fe–His bond becomes stronger with increasing His93–Leu89 hydrogen bond strength because of enhancement of the Fe ← His σ donation. Consequently, the strengthening of the Fe–His bond through an increase in the His93–Leu89 H-bond strength results in an increase in the stretching frequency of the Fe–His bond and, inversely, a decrease in the His93 N _δ H shift [103].

In contrast to effective delocalization of unpaired electrons from the heme Fe atom to the His93 imidazole π system through the Fe–His bond, unpaired electron density delocalized from the Fe atom into the porphyrin π system in the penta-coordinated heme complex is considerably smaller than that in a hexa-coordinated one such as metMb(H₂O) (see Sect. 18.3.6) due to the relatively weak electronic interaction between the Fe orbitals and the porphyrin π system in the former complex [102]. As a result, the heme CH₃ proton signals of deoxy Mb exhibit relatively small δ _para values. In addition, the Val68 C_γH₃ proton signal is resolved in upfield-shifted region, i.e., <~−7 ppm [100], in the ¹H spectrum of deoxy Mb, due to magnetic anisotropy of the Fe²⁺ high-spin state [95].

The signals of deoxy Mb increased dramatically with increasing the field strength (Fig. 18.5), and the field-dependent broadening was enhanced for signals of larger paramagnetic molecules [105]. According to the theory proposed by Gueron [83], there will be net polarization of the Fe electron spin magnetic moment that will be oriented along the direction of the external magnetic field. Modulation of this dipolar field due to the spin polarization (known as the “Curie spin”) through rotational diffusion will then introduce an extra field-dependent term into the expression for transverse relaxation (Eq. 18.16). Since the Curie spin contribution is proportional to the square of the magnetic field strength [83, 84], the benefit of higher resolution in a spectrum recorded at higher magnetic field strength is no longer expected for deoxy Mb.

Fig. 18.5

Portions, −15 to 25 ppm, of ¹H NMR spectra of deoxy Mb in 90% ¹H₂O/10% ²H₂O, pH 7.4, at 25 °C, recorded at ¹H frequencies of 400 (a), 600 (b), and 800 MHz (c). Assignments of heme 7- and 12-CH₃ signals are indicated in (c) [96]

3.4 Paramagnetic Met-Cyano Form [MetMb(CN⁻)] with S = ½

Owing to the short spin–lattice relaxation time of electron (T _1e), i.e., ~2 × 10⁻¹² s [4, 20], and the large magnetic anisotropy of hexa-coordinated Fe³⁺ heme complexes with S = 1/2 [106], metMb(CN⁻) exhibits well-resolved and relatively narrow signals useful for characterizing the electronic/molecular structure of its heme active site [14, 106]. The asymmetric nature of the heme–protein linkage can be readily characterized through analysis of the δ _para values of the four heme CH₃ proton signals of metMb(CN⁻). The energy levels for the d _xz and d _yz orbitals are affected by the interaction with axial ligands, and a single unpaired electron resides in either the d _xz or d _yz orbital, whichever possesses the highest energy. Consequently, depending upon the relative energy of the d _xz and d _yz orbitals, π spin delocalization occurs into either pyrroles I, III or II, IV (Fig. 18.6). Since a diatomic cyanide ion is coordinated to the heme Fe atom with its orientation nearly normal as to the heme plane, its coordination does not affect the degree and pattern of the in-plane asymmetry of the heme electronic structure. Consequently, the energy levels for the d _xz and d _yz orbitals are predominantly affected by the orientation of the His93 imidazole ring, relative to the heme, through a repulsive interaction between the p _z orbital of the Fe-bound nitrogen atom of His93 imidazole and the d _xz or d _yz one of the heme Fe atoms (Fig. 18.6a). The Fe–His coordination bond is roughly along the heme normal, and hence, with the orientation of His93 imidazole, as shown in Fig. 18.6a [107], i.e., the projection of the His93 imidazole ring onto the heme plane is along the nitrogen atoms of pyrroles I and II, and the p _z orbital of the Fe-bound nitrogen atom in the yz plane interact repulsively with the d _yz one, raising the energy level of d _yz orbital relative to that of the d _xz one (Fig. 18.6b). Consequently, the unpaired electron spin density delocalized from heme Fe atom into the pyrroles I and III π-system is much greater than that into pyrroles II and IV one, due to the unpaired electron delocalized from the singly occupied d _yz orbital directly to the former pyrroles. In contrast, the energy level of the d _xz orbital is higher than that of the d _yz one with the orientation of the His93 imidazole ring, of which the projection onto the heme plane is along the nitrogen atoms of pyrroles I and III, and the unpaired electron spin density delocalized from the heme Fe atom into the pyrroles II and IV π-system is greater than that into the pyrroles I and III one (Fig. 18.6c). Since the orientation of the His93 imidazole ring in Mb is similar to that illustrated in Fig. 18.6a [76, 77], the δ _c values of the signals due to the heme CH₃ groups at positions 2 and 12 are larger than those at positions 7 and 18.

Fig. 18.6

a Schematic representation of the orientation of the His93 imidazole ring and 2p _z orbital of the His93 N _ε atom, with respect to the heme in Mb [76, 77]. Heme peripheral side chains are eliminated for clarity. Angle ϕ is defined as the angle between the projection of the His93 imidazole plane onto the heme one and the N_II–Fe–N_IV axis. b Splitting of 3d orbital energies of heme Fe³⁺ in metMbCN⁻. With ϕ = ~0°, the energy level of the 3d _yz orbital is higher than that of the 3d _xz one. Hence, electron spin density delocalized from the heme Fe atom into the pyrroles I and III π-system is much greater than that into the pyrroles II and IV one, due to unpaired electron delocalized from the singly occupied d _yz orbital directly to the former pyrroles. Coordination of CN⁻ with its orientation nearly normal to the heme plane does not significantly affect the energy levels of the 3d _yz and 3d _xz orbitals. c Semi-quantitative representation of ϕ dependence of the contact shift (δ _c) of heme 2- and 12-CH₃ (solid line), and 7- and 18-CH₃ (alternate long and short dash line) signals of metMbCN⁻. The δ _c value was estimated with the assumption of fourfold symmetry in the electronic structure of the porphyrin moiety of heme

The large magnetic anisotropy of metMb(CN⁻) induces large δ _pc values for signals arising from protons located close to the heme Fe atom, as can be witnessed by the observation of many resolved signals due to amino acid protons (Fig. 18.7). The combined use of NMR and X-ray studies allows determination of principal components and orientation, with respect to the heme, of the magnetic susceptibility tensor in the protein [106]. Formulation of the δ _pc value is useful for detailed characterization of the local structure. In addition, due to the small Curie spin relaxation expected from the small S value, the signals of metMb(CN⁻) exhibit small field-dependent broadening, i.e., the line widths of heme 12-CH₃ signals recorded at 400, 600, and 800 MHz were 39, 44, and 66 Hz, respectively (Fig. 18.7).

Fig. 18.7

Portions, −13.9 to 32.5 ppm, of ¹H NMR spectra of metMb(CN⁻) in 90% ¹H₂O/10% ²H₂O, pH 7.4, at 25 °C, recorded at ¹H frequencies of 400 (a), 600 (b), and 800 MHz (c). Assignments of heme CH₃ and some amino acid proton signals are indicated in (c)

3.5 Paramagnetic Met-Azido Form [MetMb(N₃ ⁻)] with Mainly S = ½

The met-azido derivatives of hemoproteins in general share the property that they exhibit a thermal equilibrium between low-spin, S = 1/2, and high-spin, S = 5/2, states, due to the intermediate field strength of N₃ ⁻ [92, 93]. Hence, changes in the population of the two spin states in the equilibrium provide a sensitive probe of the effective axial field strength. Among various techniques used to characterize the thermal spin equilibria in proteins, NMR is probably the most sensitive one and provides two separate probes of the average spin magnetization of the heme Fe atom, i.e., the heme CH₃ proton and axial His93 N _δ H proton δ _para values [80, 91]. The thermal spin equilibrium in metMb(N₃ ⁻) is manifested in the curvature or anti-Curie behavior of Curie plots, i.e., the plots of the δ _obs values against the reciprocal of absolute temperature (1/T), of these signals [80, 91]. Fitting of the Curie plots using the van’t Hoff equation provides thermodynamic parameters of the equilibrium [80]. In the case of metMb(N₃ ⁻), the high-spin contents at ambient temperature are ~20%, and the values of ~−13 kJ mol⁻¹ and ~−30 J T ⁻¹ mol⁻¹ have been reported for the enthalpy change (ΔH) and molar entropy (ΔS), respectively [105]. ΔH is simply determined by the difference in thermodynamic energy between the low-spin and high-spin states, and ΔS is determined by the structural and dynamic natures of the heme environment. The appreciable contribution of the high-spin state to the ground-state electron configuration of heme Fe³⁺ in metMb(N₃ ⁻) leads to sizable Curie spin relaxation, which considerably broadens paramagnetically shifted signals with increasing magnetic field strength, e.g., the line width of the heme 12-CH₃ signal at 25 °C was ~140 Hz at 400 MHz, ~160 Hz at 600 MHz, and ~200 Hz at 800 MHz (Fig. 18.8).

Fig. 18.8

Portions, −10 to 40 ppm, of ¹H NMR spectra of metMb(N₃ ⁻) in 90% ¹H₂O/10% ²H₂O, pH 7.4, at 25 °C, recorded at ¹H frequencies of 400 (a), 600 (b), and 800 MHz (c). Assignments of heme CH₃ signals are indicated in (c)

3.6 Paramagnetic Met-Aquo Form [MetMb(H₂O)] with S = 5/2

In the presence of five unpaired electrons in the system, the signals of metMb(H₂O) are observed over the range of ~110 to ~−30 ppm [89, 90]. Although the signals are considerably broad due to its relatively long T _1e, i.e., <~1 × 10⁻¹⁰ s [4, 20], owing to the large chemical shift range, the signals are fairly well separated (Fig. 18.9). In Fe³⁺ high-spin complexes, the relaxation process for the heme proton signals is modulated mainly by T _1e, which is in turn determined by modulation of the zero-field level of the complex [108, 109]. Some Mbs possess penta-coordinated hemes in their Fe³⁺ high-spin complexes because of the absence of Fe-bound H₂O [110]. The heme proton signals of the Mbs with penta-coordinated Fe³⁺ high-spin hemes are narrower than those of the proteins with hexa-coordinated ones, because of the larger zero-field splitting in the former hemes, due to the lower symmetry in the ligand field around the heme Fe, which leads to the reduction of T _1e [110].

Fig. 18.9

Portions, 15–110 ppm, of ¹H NMR spectra of metMb(H₂O) in 90% ¹H₂O/10% ²H₂O, pH 7.0, at 25 °C, recorded at ¹H frequencies of 400 (a), 600 (b), and 800 MHz (c). Assignments of heme side chain proton signals are indicated in (c)

As indicated in trace 2e, signals resolved outside of the so-called diamagnetic envelope, i.e., ~10 to ~0 ppm, are mostly due to heme peripheral side chain protons, and only a few signals due to amino acid protons are resolved. These spectral features indicated that δ _c is large, while δ _pc is relatively small. The δ _pc contribution of metMb(H₂O) is due to magnetic anisotropy caused by zero-field splitting at the heme Fe and is in practice axially symmetric [111]. Since the Curie spin relaxation contribution is significant in high-spin metMb(H₂O), the line widths of paramagnetically shifted signals increased dramatically with increasing magnetic field strength, e.g., the line width of the heme 12-CH₃ signal at 25 °C was ~380 Hz at 400 MHz, ~560 Hz at 600 MHz, and ~950 Hz at 800 MHz (Fig. 18.9).

4 NMR Measurements

4.1 NOEs in Paramagnetic Compounds

Despite the initial prejudice that the presence of unpaired electron(s) in paramagnetic molecules seriously diminishes the magnitude of NOEs through “paramagnetic leakage,” and hence the observation of NOEs in paramagnetic systems is practically unrealistic, nowadays NOE measurements have been extensively applied for signal assignments and structural characterization in various paramagnetic systems [17]. The observation of relatively large NOEs in paramagnetic systems [88, 90, 107, 112, 113] could be rationalized on the basis of the nature of relaxation in the systems. The steady-state NOE in an isolated two-spin is given by Eq. (18.17)

$$ {\text{NOE}}_{i \to j} = \frac{{\sigma_{ij} }}{{\rho_{j} }} $$

(18.17)

where $\sigma_{ij}$ and $\rho_{j}$ are the cross relaxation rate between the interacting protons, i and j, and the intrinsic spin–lattice relaxation rate of spin j, respectively. For paramagnetic system, $\rho_{j} = \rho_{\text{dia}} + \rho_{\text{para}}$ ($\rho_{\text{dia}}$ and $\rho_{\text{para}}$ are the diamagnetic and paramagnetic contributions to $\rho_{j}$, respectively), and for a dominant paramagnetic relaxation ($\rho_{\text{dia}} \ll \rho_{\text{para}}$), the steady-state NOEs are considerably reduced through paramagnetic leakage. Although the magnitude is relatively small, the observation of NOEs has been reported for most accessible oxidation and spin states of proteins.

Since $\sigma_{ij}$ is given by

$$ \sigma_{ij} = \frac{{{\hbar }^{2} \gamma_{H}^{2} }}{{10r^{6} }}\left[ {\frac{{6\tau_{\text{c}} }}{{1 + 4\omega_{H}^{2} \tau_{\text{c}}^{2} }} - \tau_{\text{c}} } \right] $$

(18.18)

where $\gamma_{H}$ is the gyromagnetic ratio of proton, $r$ is the distance between the protons, $\tau_{\text{c}}$ is the correlation time that modulates the dipolar interaction between the two spins, and $\omega_{H}$ is the Larmor frequency of proton. In the case of macromolecules, at high magnetic field and a long $\tau_{\text{c}}$, the molecular motion occurs in the slow motion limit ($\omega _{H}^{2} \tau _{c}^{2} \gg 1$), and Eq. (18.19) is reduced to

$$ \sigma_{ij} = - \frac{{\hbar^{2} \gamma_{H}^{2} \tau_{\text{c}} }}{{10r^{6} }} $$

(18.19)

Thus, the magnitude of the NOEs is simply proportional to $\tau_{\text{c}}$, and hence, as far as $\sigma_{ij}$ is concerned, the observation of NOEs could be more promising for a larger molecule than for a small one. In practice, however, for a diamagnetic system with a large $\tau_{\text{c}}$, the detrimental effects of spin diffusion preclude the collection of any useful data in NOE studies. However, as demonstrated by La Mar and coworkers [90], paramagnetism not only undermines spin diffusion, and hence allows observation of specific NOEs for larger systems, but also improves the magnitude of NOEs with increasing $\tau_{\text{c}}$. Consequently, a large molecular size is likely to be an advantage rather than a disadvantage for observing useful NOEs in a paramagnetic system (Fig. 18.10).

Fig. 18.10

Downfield-shifted portions, 33–108 ppm, of the 500 MHz ¹H NMR spectrum and NOE difference spectra of shark Galeorhinus japonicas metMb in ²H₂O, pH 7.0, at 35 °C. a Reference spectrum and (b–e) NOE difference spectra generated by subtracting the reference spectrum (a) from the spectrum recorded with saturation of the desired signal. Arrows indicate signals that are saturated, and peaks due to the decoupler pulse power spillage are indicated by asterisk. b Saturation of the 18-CH₃ signal exhibiting an NOE to a 17-C_αH one. c Saturation of 17-C_αH signal exhibiting an NOE to 17-${\text{C}}_{{\upalpha^{\prime } }} {\text{H}}$ one. d Saturation of the 12-CH₃ signal exhibiting an NOE to a 13-C_αH one. e Saturation of the 13-C_αH signal exhibiting an NOE to a 13-${\text{C}}_{{\upalpha^{\prime } }} {\text{H}}$ one. The spectra were taken from [91]

The optimization of experimental parameters in 1D and 2D NOE measurements on rapidly relaxing systems, where $\sigma_{ij}$ is much smaller than $\rho_{j}$, has been fully discussed [17, 90]. Considering $\sigma_{ij} \ll \rho_{j}$ in a paramagnetic system, the magnitude of NOEs to be detected is quite small. In the spectrum of a paramagnetic molecule, fast relaxing signals exhibit large δ _para and hence are resolved outside of the diamagnetic envelope. The observation of NOEs between a rapidly relaxing signal and a slowly relaxing one, resonating in the diamagnetic envelope, can be much more effectively performed by conventional 1D NOE difference spectroscopy, provided that the signal-to-noise ratio of spectra is high enough to detect small NOEs. The accumulation of a large number of transients is a simple and easy approach to achieve a satisfactory signal-to-noise ratio. A short acquisition time due to a large spectral width and a relatively low digital resolution generally used for the observation of the spectra of a paramagnetic system, together with rapid repetition owing to fast paramagnetic relaxation, significantly contributes to effective data collection. In general, the detection of a small intensity change becomes more difficult as the signal broadens. Hence, T ₂ is often the determining factor for observing the effect; since T ₂ ≤ T ₁, this is particularly true for signals with short T ₁s.

Practically, there are also other limitations to the NOE method applied to paramagnetic systems. First, when saturating a fast relaxing signal by decoupler irradiation, the necessarily strong decoupler RF field irradiation can induce interfering off-resonance perturbations over a wide region of the spectrum [90]. In such a case, true NOEs may be difficult to distinguish from an off-resonance effect, often called “decoupler power spillage.” Comparison of the relative magnitudes of the effects under conditions of a reduced off-resonance effect and the determination of the actual power profile, as a function of offset, of the decoupler RF field irradiation can usually alleviate the problem. Second, observation of a small intensity difference in a broad signal demands a high dynamic range for the receiver and the digitizer. Selective excitation pulse sequences such as a simple 1–1 jump and return one [114] are helpful for suppressing the diamagnetic signals and allowing the full utilization of the dynamic range.

4.2 Hydrogen Exchange Rates

Biological macromolecules exhibit freedom of various structural changes, which are often relevant to their functions. Consequently, in order to elucidate the functions of the molecules, their static structures described by X-ray crystallographic coordinates must be augmented by their dynamic properties manifested in various spectroscopic data. Among a variety of spectroscopic techniques available for studies of their dynamic nature, NMR is quite unique in terms of not only its sensitivity as to dynamic structures exhibiting a wide range of timescales, but also its ability to provide information from which detailed descriptions of the dynamic structures of molecules in solution can be made.

Upon such dynamic studies involving NMR, it is important to consider the “NMR timescale.” For example, in the case of a molecule with interconvertible conformations, i.e., conformers I and II, which possibly exhibit two distinct NMR signals, whether or not we can observe two separate signals due to conformers I and II depends on the timescale of the interconversion. If the interconversion is sufficiently slow compared with the NMR timescale, signals I and II can be separately observed. On the other hand, if the interconversion is faster than the NMR timescale, a single signal representing the time-averaged conformation of conformers I and II is observed. The NMR timescale of the interconversion between conformers I and II is given by the difference in resonance frequency between signals I and II (Δδ _I/II) and hence depends on magnetic field strength (B ₀) in such a manner that the NMR timescale increases with increasing B ₀ because Δδ _I/II is proportional to B ₀. Taking advantage of the large δ _para, a paramagnetic counterpart possibly exhibits the Δδ _I/II value that is large enough to allow observation of separate signals I and II. Thus, the NMR timescale can be controlled through the paramagnetic effect.

The exchange rates (k _ex) of labile protons provide a wealth of information about the structural and functional features of proteins. For example, the X-ray structures of Mb [76, 77] suggested that the equilibrium structure does not possess channels large enough to permit ligand entry to and exit from the heme cavity. Theoretical calculations [115] have shown that the protein backbone and side chain motions of Mb modulate the energy barrier for O₂ entry. Thus, the dynamics, as well as the structure of a protein, are relevant to its function [116, 117]. One of the most powerful methods for studying protein dynamics is the observation of the exchange behavior of labile protons, which are buried in the protein interior [118,119,120]. The timescale of exchange of labile protons can be considered as a measure of the local dynamic stability [116,117,118,119,120].

k _ex is derived from solvent saturation transfer from the intrinsic spin–lattice relaxation time [T _1(int)] and the saturation factor (F) given by [121]

$$ F = \frac{I}{{I_{0} }} = T_{{1(\text{int} )}}^{ - 1} \times \left( {T_{{1(\text{int} )}}^{ - 1} + \tau_{i}^{ - 1} } \right)^{ - 1} $$

(18.20)

where I and I ₀ are the intensities of a labile proton signal with and without saturation of the ¹H₂O signal, respectively. T _1(int) is the intrinsic spin–lattice relaxation time, with which F is evaluated. τ _i is the lifetime of the labile proton in the protein environment, and hence τ ⁻¹ _i  = k _ex. Consequently, independent measurements of T _1(int) and F allow the determination of k _ex.

If T _1(int) is independently known and remains constant over the pH range used, k _ex is obtained through Eq. (18.20′).

$$ k_{\text{ex}} = \tau_{i}^{ - 1} = T_{{1(\text{int} )}}^{ - 1} \times (1 - F)F^{ - 1} $$

(18.20′)

With the occurrence of exchange, and when T _1(int) cannot be determined directly, k _ex is obtained through Eq. (18.21).

$$ k_{\text{ex}} = T_{{1(\text{int} )}}^{{{\prime }\, - 1}} \times (1 - F) $$

(18.21)

where $T_{{1(\text{int} )}}^{{{\prime } - 1}} = T_{{1(\text{int} )}}^{ - 1} + \tau_{i}^{ - 1}$. In such a case, $T_{{1(\text{int} )}}^{{}}$ can be expressed as

$$ T_{{1(\text{int} )}}^{ - 1} = F \times T_{{1(\text{int} )}}^{{{\prime }\, - 1}} $$

(18.22)

$T_{{1(\text{int} )}}^{{}}$ can be measured as follows. At pH values where $\tau_{i}^{{}}$ of the labile proton is long compared with $T_{{1(\text{int} )}}^{{}}$, i.e., $T_{{1(\text{int} )}}^{{}}$ ≪ $\tau_{i}^{{}}$, a selective saturation recovery experiment with a pulse sequence for solvent suppression is performed. At pH values where $\tau_{i}^{{}}$ ≈ $T_{{1(\text{int} )}}^{{}}$, $T_{{1(\text{int} )}}^{{{\prime } - 1}}$ is obtained by selective inversion recovery with the saturation of the H₂O signal at all times except during acquisition.

In general, k _ex is expressed as [118]

$$ k_{\text{ex}} = k_{A} [{\text{H}}^{\text{ + }} ]^{A} + k_{B} [\text{OH}^{\text{ - }} ]^{B} + k_{W} [\text{H}_{2} {\text{O}}] $$

(18.23)

where k _A , k _B , and k _W are the rate constants for H⁺, OH⁻, and H₂O catalysis, respectively. Exponents A and B are at unity with k _A and k _B close to those observed for a model compound and are less than unity for protons buried in the protein interior and/or involved in hydrogen bonds [118]. When k _A and k _B are comparable in magnitude to each other, the pH value at the minimum k _ex is close to ~7. A change in either k _A or k _B alters the pH value at the minimum k _ex [118].

For example, the His93 N _δ H proton signal of deoxy Mb is observed at ~75 ppm [96] (trace 2D). The His93 N _δ H proton of the protein is hydrogen-bonded to the carbonyl oxygen atom of Leu89, as illustrated in Fig. 18.1c, and exhibits $T_{{1(\text{int} )}}^{{}}$ = ~15 ms and k _ex = ~30 s⁻¹ at pH = 10.6 and 40 °C. Interestingly, the k _ex value of the His93 N _δ H protons of the subunits of the deoxy form of tetrameric human adult hemoglobin, i.e., k _ex = ~10⁻⁴–10⁻⁵ s⁻¹, is several orders of magnitude smaller than that of deoxy Mb [122].

A 400 MHz ¹H NMR spectrum of bovine metMbCN⁻ at 25 °C is shown in Fig. 18.11. In the spectrum, His64 N _ε H and His93 N _δ H proton signals were observed at 23.31 and 20.96 ppm, respectively, and exhibited T _1(int) values of 8.4 and 22 ms, respectively [123]. The F values of the His64 N _ε H and His93 N _δ H protons of the protein at various pH values were measured (Fig. 18.12a), and then, the pH-profiles of the k _ex values of the protons were calculated from the F and T _1(int) values [123] (Fig. 18.12b). The k _ex values of the His64 N _ε H and His93 N _δ H protons exhibited distinctly different pH-profiles. The pH-profile of the k _ex value of the His64 N _ε H proton reflected both acid- and base-catalyzed NH hydrogen exchange, with the minimum k _ex value at pH ~9.5. On the other hand, only the base-catalyzed exchange was manifested in the pH-profile of the k _ex value of His93 N _δ H hydrogen atom. Thus, the k _ex values of the NH protons provide valuable information about the dynamic nature of the heme cavity of the protein.

Fig. 18.11

400 MHz ¹H NMR spectrum of bovine metMb (CN⁻) in 90% ¹H₂O/10% ²H₂O, pH 7.0, at 25 °C. The downfield-shifted portion of the spectrum of the protein in ²H₂O, pH 7.0, at 25 °C is shown in the inset. Assignments of 2-, 12-, and 18-CH₃ signals and His64 N _ε H, His93 N _δ H, and His93 N_amideH ones are shown in the spectrum. The location of these NH protons in the protein is shown in the inset. The spectra were taken from [123]

Fig. 18.12

pH-profiles of a saturation factor (F) and b logarithm of k _ex (s⁻¹) for the His64 N _ε H (filled circle) and His93 N _δ H protons (open circle) in bovine metMbCN⁻ in 90% ¹H₂O/10% ²H₂O at 25 °C [123]. The exchange behavior of histidyl imidazole ring NH hydrogen atoms sharply reflects their local environment. The H⁺ and OH⁻ catalyses involve an attack at different sites of the neutral imidazole side chain, and both acid- and base-catalyzed exchanges were observed for the His64 N _ε H proton. On the other hand, only base-catalyzed exchange was observed for the His93 N _δ H proton because of the coordination of His93 to heme Fe, which precludes acid-catalyzed exchange

5 Concluding Remarks

This chapter has described the fundamentals of ¹H NMR spectra of paramagnetic compounds. Using Mb as a reference compound, the spectral characteristics of paramagnetic compounds possessing a series of S values have been described in order to provide an overview of the effects of changes in the number of unpaired electrons on the spectral features. A few techniques applied to paramagnetic compounds, which provide widespread utility in life and material sciences, have also been described. As described in this chapter, the use of electron spin is opening up new horizons for NMR studies in life and material sciences.