¹³CHD₂–CEST NMR spectroscopy provides an avenue for studies of conformational exchange in high molecular weight proteins

Abstract

An NMR experiment for quantifying slow (millisecond) time-scale exchange processes involving the interconversion between visible ground state and invisible, conformationally excited state conformers is presented. The approach exploits chemical exchange saturation transfer (CEST) and makes use of ¹³CHD₂ methyl group probes that can be readily incorporated into otherwise highly deuterated proteins. The methodology is validated with an application to a G48A Fyn SH3 domain that exchanges between a folded conformation and a sparsely populated and transiently formed unfolded ensemble. Experiments on a number of different protein systems, including a 360 kDa half-proteasome, establish that the sensitivity of this ¹³CHD₂ ¹³C–CEST technique can be upwards of a factor of 5 times higher than for a previously published ¹³CH₃ ¹³C–CEST approach (Bouvignies and Kay in J Biomol NMR 53:303–310, 2012), suggesting that the methodology will be powerful for studies of conformational exchange in high molecular weight proteins.

Appendix: Effects of 2H spin relaxation on 13CHD2–CEST profiles

In a previous set of papers we have discussed the effects of homonuclear scalar couplings on CEST profiles and presented a simple approach for data analysis (Bouvignies et al. 2014; Vallurupalli and Kay 2013). By means of example, consider the case where ¹³CO CEST profiles are obtained from measurements on a uniformly ¹³C labeled protein sample. Each ¹³CO dip is split into a doublet by the approximately 50 Hz ¹³CO–¹³C^α scalar coupling (J_CαCO). Although multiplet components are generally not observed in ¹³CO CEST profiles when weak B₁ fields on the order of 20 Hz or greater are used, the resultant dips are nevertheless broadened by the unresolved couplings and this effect should be taken into account in fits of the profiles to extract accurate exchange parameters. This can be most easily accomplished by solving the Bloch–McConnell equations (McConnell 1958) for two ¹³CO lines, separated by J_CαCO, that correspond to ¹³C^α spins in the up/down positions. Here it is assumed that the longitudinal relaxation of ¹³C^α is slow compared to the rate of exchange between conformers so that the resulting CEST profiles are the simple sum of a pair of profiles, one for ¹³C^α spin up and a second for ¹³C^α spin down. This procedure can be generalized when more than a single homonuclear coupling is present, as described previously (Bouvignies et al. 2014). The situation is more complex for ¹³CHD₂–CEST when ²H decoupling is not used. In this case each ¹³C dip is split into a 1:2:3:2:1 pentet structure from ¹³C–²H scalar coupling interactions. However, the ²H spin flip rate cannot be assumed to be slow compared to the conformational exchange process, so that averaging of the multiplet components can occur simultaneously with chemical exchange, necessitating a more complex treatment. In what follows we assume that ¹H decoupling is employed during the CEST interval, as indicated in the pulse scheme of Fig. 3, and thus neglect the influence of the one bond ¹H–¹³C scalar coupling.

The effects of ²H spin flips on ¹³CHD₂ CEST profiles are best considered by first separating the methyl ¹³C j magnetization $j \in \{ x,y,z\}$ into distinct components according to the spin states of the pair of coupled deuterons. In what follows we consider initially a basis comprised of 6 operators, L1 _j –L6 _j , defined as,

$$ \begin{aligned} L1_{j} & = C_{j} [(1,1)] = 0.25C_{j} (D_{z,1}^{2} + D_{z,1} )(D_{z,2}^{2} + D_{z,2} ) \\ L2_{j} & = C_{j} [(1,0) + (0,1)] = 0.5C_{j} \{ (D_{z,1}^{2} + D_{z,1} )(1 - D_{z,2}^{2} ) + (1 - D_{z,1}^{2} )(D_{z,2}^{2} + D_{z,2} )\} \\ L3_{j} & = C_{j} [(0,0)] = C_{j} \{ (1 - D_{z,1}^{2} )(1 - D_{z,2}^{2} )\} \\ L4_{j} & = C_{j} [(1, - 1) + ( - 1,1)] = 0.25C_{j} \{ (D_{z,1}^{2} + D_{z,1} )(D_{z,2}^{2} - D_{z,2} ) + (D_{z,1}^{2} - D_{z,1} )(D_{z,2}^{2} + D_{z,2} )\} \\ L5_{j} & = C_{j} [( - 1,0) + (0, - 1)] = 0.5C_{j} \{ (D_{z,1}^{2} - D_{z,1} )(1 - D_{z,2}^{2} ) + (1 - D_{z,1}^{2} )(D_{z,2}^{2} - D_{z,2} )\} \\ L6_{j} & = C_{j} [( - 1, - 1)] = 0.25C_{j} (D_{z,1}^{2} - D_{z,1} )(D_{z,2}^{2} - D_{z,2} ). \\ \end{aligned} $$

(7)

In Eq. (7) C _j [(A, B)] denotes the j component of ¹³C magnetization coupled to ²H spin 1 with magnetic quantum number A, A $\in$ (−1, 0, 1) and ²H spin 2 with magnetic quantum number B, and D _z,k is the z-component of magnetization from ²H spin k $\in$ (1, 2). A straightforward, albeit lengthy, calculation shows that the relaxation of L1 _j –L6 _j , considering ²H contributions and adding ¹³C relaxation ($R_{1}^{C}$ or $R_{2}^{C}$) in an ad hoc manner, is given by

$$ \frac{{d\vec{L}_{j} }}{dt} = - \tilde{R}{}_{j}\vec{L}{}_{j} $$

(8)

where

$$ \vec{L}_{j} = \{ L1_{j} ,L2_{j} ,L3_{j} ,L4_{j} ,L5_{j} ,L6_{j} \}^{T} $$

(9)

and

$$ \tilde{R}_{j} = \left( {\begin{array}{*{20}c} { {- 2\kappa_{1}} {-2\kappa_{2}} {-R_{p}^{C} }} & {\kappa_{1} } & 0 & {\kappa_{2} } & 0 & 0 \\ {2\kappa_{1} } & { {-3\kappa_{1}} {-\kappa_{2}} {-R_{p}^{C} }} & {2\kappa_{1} } & {\kappa_{1} } & {\kappa_{2} } & 0 \\ 0 & {\kappa_{1} } & { {-4\kappa_{1}} {-R_{p}^{C}} } & 0 & {\kappa_{1} } & 0 \\ {2\kappa_{2} } & {\kappa_{1} } & 0 & { {-2\kappa_{1}} {-2\kappa_{2}} {-R_{p}^{C}} } & {\kappa_{1} } & {2\kappa_{2} } \\ 0 & {\kappa_{2} } & {2\kappa_{1} } & {\kappa_{1} } & { {-3\kappa_{1}} {-\kappa_{2}} {-R_{p}^{C}} } & {2\kappa_{1} } \\ 0 & 0 & 0 & {\kappa_{2} } & {\kappa_{1} } & { {-2\kappa_{1}} {-2\kappa_{2}} {-R_{p}^{C} } }\\ \end{array} } \right) $$

(10)

where the superscript T in Eq. (9) is the transpose operator,

$$ \begin{aligned} \kappa_{1} & = \frac{6}{5}c^{2} J(\omega_{D} ) \\ \kappa_{2} & = \frac{12}{5}c^{2} J(2\omega_{D} ), \\ \end{aligned} $$

(11)

$\frac{2c}{\pi } \sim 165\;{\text{kHz}}$ is the quadrupolar coupling constant and J(ω _D ) is given by Eq. (2) of the main text. In Eq. (10) the value of p is 1 if j = z (longitudinal relaxation) or 2 if $j \in \{ x,y\}$ (transverse relaxation).

Eq. (8) is written in a basis where $j \in \{ x,y,z\}$. The above equations can be ‘expanded’ by explicitly including terms for each of the x, y and z components so that the 6 × 6 $\tilde{R}$ matrix above ($\tilde{R}_{6}$) becomes an 18 × 18 matrix, $\tilde{R}_{18} = \tilde{I}_{3} \otimes \tilde{R}_{6}$ where $\tilde{I}_{3}$ is a 3 × 3 identity matrix and $\vec{L} = \{ L1_{x} ,L2_{x} ,L3_{x} ,L4_{x} ,L5_{x} ,L6_{x} , \ldots ,L6_{z} \}^{T}$. The effects of chemical shift and ²H–¹³C scalar-coupled evolution couple x and y components of magnetization and are included into matrix $\tilde{R}_{18}$ by noting that

$$ \begin{aligned} \frac{{dC_{x} [(A,B)]}}{dt} & = - (\omega + (A + B)2\pi J_{CD} )C_{y} [(A,B)] \\ \frac{{dC_{y} [(A,B)]}}{dt} & = (\omega + (A + B)2\pi J_{CD} )C_{x} [(A,B)] \\ \end{aligned} $$

(12)

Finally, two-site chemical exchange, $G\mathop{\mathop{\rightleftarrows}\limits_{k_{EG}}}\limits^{k_{GE}}E$, is taken into account (Allard et al. 1998; Helgstrand et al. 2000) by a further expansion of the equations with $\vec{L} = \{ L1_{x}^{G} ,L2_{x}^{G} ,L3_{x}^{G} ,L4_{x}^{G} ,L5_{x}^{G} ,L6_{x}^{G} , \ldots ,L6_{z}^{G} ,L1_{x}^{E} \ldots ,L6_{z}^{E} \}^{T}$

$$ \tilde{R^{\prime}}_{36} = \left( {\begin{array}{*{20}c} {\tilde{R}_{18}^{G} } & {\tilde{0}_{18} } \\ {\tilde{0}_{18} } & {\tilde{R}_{18}^{E} } \\ \end{array} } \right) + \left( {\begin{array}{*{20}c} { - k_{GE} } & {k_{EG} } \\ {k_{GE} } & { - k_{EG} } \\ \end{array} } \right) \otimes \tilde{I}_{18} $$

(13)

where the superscripts G and E denote the ground and excited states and $\tilde{O}_{18}$ is an 18 dimensional null matrix. It is assumed that R ^C₁ values are identical in $\tilde{R}_{18}^{G}$ and $\tilde{R}_{18}^{E}$ but that corresponding spins in ground and excited states have distinct R ^C₂ rates. Software for fitting exchange data is available upon request.