Photo-CIDNP NMR Spectroscopy of Amino Acids and Proteins

Abstract

Photo-chemically induced dynamic nuclear polarization (CIDNP) is a nuclear magnetic resonance (NMR) phenomenon which, among other things, is exploited to extract information on biomolecular structure via probing solvent-accessibilities of tryptophan (Trp), tyrosine (Tyr), and histidine (His) amino acid side chains both in polypeptides and proteins in solution. The effect, normally triggered by a (laser) light-induced photochemical reaction in situ, yields both positive and/or negative signal enhancements in the resulting NMR spectra which reflect the solvent exposure of these residues both in equilibrium and during structural transformations in “real time”. As such, the method can offer – qualitatively and, to a certain extent, quantitatively – residue-specific structural and kinetic information on both the native and, in particular, the non-native states of proteins which, often, is not readily available from more routine NMR techniques. In this review, basic experimental procedures of the photo-CIDNP technique as applied to amino acids and proteins are discussed, recent improvements to the method highlighted, and future perspectives presented. First, the basic principles of the phenomenon based on the theory of the radical pair mechanism (RPM) are outlined. Second, a description of standard photo-CIDNP applications is given and it is shown how the effect can be exploited to extract residue-specific structural information on the conformational space sampled by unfolded or partially folded proteins on their “path” to the natively folded form. Last, recent methodological advances in the field are highlighted, modern applications of photo-CIDNP in the context of biological NMR evaluated, and an outlook into future perspectives of the method is given.

Keywords

Appendix

The radical pair mechanism (RPM) as described in Sect. 2.4 can be recast in terms of the product operator formalism [17, 18]. The triplet T₀ spin-state of the radical pair can be described by the following expression:

$$ \left| {{{\mathrm{ T}}_0}} \right\rangle \left\langle {{{\mathrm{ T}}_0}} \right|=\frac{1}{4}E-{S_{1z }}{S_{2z }}+{{\left\{ {\mathrm{ ZQ}} \right\}}_x}, $$

(1)

where $E$ is the identity operator, ${S_{1z }}{S_{2z }}$ is electron two-spin order, and $\mathrm{ ZQ}$ is electronic zero-quantum coherence:

$$ {{\left\{ {\mathrm{ ZQ}} \right\}}_x}={S_{1x }}{S_{2x }}+{S_{1y }}{S_{2y }}, $$

(2)

$$ {{\left\{ {\mathrm{ ZQ}} \right\}}_y}={S_{1y }}{S_{2x }}+{S_{1x }}{S_{2y }}. $$

(3)

By analogy, the singlet state is described by

$$ \left| \mathrm{ S} \right\rangle \left\langle \mathrm{ S} \right|=\frac{1}{4}E-{S_{1z }}{S_{2z }}-{{\left\{ {\mathrm{ ZQ}} \right\}}_x}. $$

(4)

The initial density operator of the triplet-born radical pair – ignoring the T₊ and T₋ states – can be written in the following form:

$$ \hat{\rho}(0)=\frac{1}{2}\left| {{{\mathrm{ T}}_0}\alpha } \right\rangle \left\langle {{{\mathrm{ T}}_0}\alpha } \right|+\frac{1}{2}\left| {{{\mathrm{ T}}_0}\beta } \right\rangle \left\langle {{{\mathrm{ T}}_0}\beta } \right|=\frac{1}{4}E-{S_{1z }}{S_{2z }}+{{\left\{ {\mathrm{ ZQ}} \right\}}_x}, $$

(5)

where $\alpha$ and $\beta$ correspond to the nuclear spin states of a spin-$\frac{1}{2}$ nucleus coupled to electron 1 with an isotropic hyperfine coupling constant a. This density operator is then allowed to evolve under the electronic Zeeman Hamiltonian ${({\hat{H}}_z}=\left( {{\omega_{s1 }}{S_{1z }}+{\omega_{s2 }}{S_{2z }}} )\right)$ and the electron-nuclear hyperfine Hamiltonian (${{\hat{H}}_h}=\pi a2{S_{1z }}{I_z}$) where $I$ is the nuclear spin:

$$ \begin{array}{lll} {\hat{\rho}(0)} \hfill & {{\mathop---------\xrightarrow{{{(\omega_{s1} }S_{1z }+{\omega_{s2 }}{S_{2z }})t}}}} \hfill & {\displaystyle\frac{1}{4}E-{S_{1z }}{S_{2z }}} \hfill \\\hfill &\hfill & {+{{{\{\mathrm{ ZQ}\}}}_x}\cos ({\omega_{s1 }}-{\omega_{s2 }})t} \hfill \\\hfill &\hfill & {+{{{\{\mathrm{ ZQ}\}}}_y}\sin ({\omega_{s1 }}-{\omega_{s2 }})t,} \hfill \\\end{array} $$

(6)

$$ \begin{array}{lll} {\hat{\rho}(0)} \hfill & {{\mathop---\xrightarrow{{\pi at2{S_{1z }}{I_z}}}}} \hfill & {\displaystyle\frac{1}{4}E-{S_{1z }}{S_{2z }}} \hfill \cr\hfill &\hfill & {+{{{\{\mathrm{ ZQ}\}}}_x}[\cos ({\omega_{s1 }}-{\omega_{s2 }})t\cos (\pi at)]} \hfill \\\hfill &\hfill & {-2{{{\{\mathrm{ ZQ}\}}}_x}{I_z}[\sin ({\omega_{s1 }}-{\omega_{s2 }})t\sin (\pi at)]} \hfill \\\hfill &\hfill & {+{{{\{\mathrm{ ZQ}\}}}_y}[\sin ({\omega_{s1 }}-{\omega_{s2 }})t\cos (\pi at)]} \hfill \\\hfill &\hfill & {+2{{{\{\mathrm{ ZQ}\}}}_y}{I_z}[\cos ({\omega_{s1 }}-{\omega_{s2 }})t\sin (\pi at)],} \hfill \\\end{array} $$

(7)

$$ =\hat{\rho}(t). $$

(8)

The nuclear polarization in the recombination products, which is formed through the singlet channel, is then given by the trace of $\hat{\rho}(0)$ with

$$ \left| \mathrm{ S} \right\rangle \left\langle \mathrm{ S} \right|{I_z}=\left( {\frac{1}{2}\left| {\mathrm{ S}\alpha } \right\rangle \left\langle {\mathrm{ S}\alpha } \right|+\frac{1}{2}\left| {\mathrm{ S}\beta } \right\rangle \left\langle {\mathrm{ S}\beta } \right|} \right){I_z}, $$

(9)

$$ \left| \mathrm{ S} \right\rangle \left\langle \mathrm{ S} \right|{I_z}=\left( {\frac{1}{4}E-{S_{1z }}{S_{2z }}-{{{\left\{ {\mathrm{ ZQ}} \right\}}}_x}} \right){I_z}. $$

(10)

Hence, the expression for the nuclear polarization ${p^r}$ found in the recombination products of the radical reaction after electron back transfer has occurred takes the following form:

$$ {p^r}=\left[ {\hat{\rho}\left| \mathrm{ S} \right\rangle \left\langle \mathrm{ S} \right|{I_z}} \right]=-\frac{1}{4}\sin \left( {{\omega_{s1 }}-{\omega_{s2 }}} \right)t\sin \left( {\pi at} \right). $$

(11)

In addition, the nuclear polarization found in the escape products, which is equal and opposite in phase to the recombination products, is given by the trace of $\hat{\rho}(t)$ with $\left| {{{\mathrm{ T}}_0}} \right\rangle \left\langle {{{\mathrm{ T}}_0}} \right|{I_z}$:

$$ {p^e}=-\frac{1}{4}\sin \left( {{\omega_{s1 }}-{\omega_{s2 }}} \right)t\sin \left( {\pi at} \right). $$

(12)

From (11) and (12) it can easily be shown that no polarization is produced if the g-values of the two radicals are identical or if there is no hyperfine coupling. In these cases and in cases where $\Delta g$ is very small, the CIDNP multiplet effect applies. Moreover, the phase of the polarization as predicted by Kaptein’s sign rule is evident from the signs of $\Delta g$ and the hyperfine coupling constant ${a_i}$ of nucleus $i$ as displayed in the respective equations.