Proton assisted recoupling and protein structure determination

Abstract

We introduce a homonuclear version of third spin assisted recoupling, a second-order mechanism that can be used for polarization transfer between (13)C or (15)N spins in magic angle spinning (MAS) NMR experiments, particularly at high spinning frequencies employed in contemporary high field MAS experiments. The resulting sequence, which we refer to as proton assisted recoupling (PAR), relies on a cross-term between (1)H-(13)C (or (1)H-(15)N) couplings to mediate zero quantum (13)C-(13)C (or (15)N-(15)N recoupling). In particular, using average Hamiltonian theory we derive an effective Hamiltonian for PAR and show that the transfer is mediated by trilinear terms of the form C(1) (+/-)C(2) (-/+)H(Z) for (13)C-(13)C recoupling experiments (or N(1) (+/-)N(2) (-/+)H(Z) for (15)N-(15)N). We use analytical and numerical simulations to explain the structure of the PAR optimization maps and to delineate the PAR matching conditions. We also detail the PAR polarization transfer dependence with respect to the local molecular geometry and explain the observed reduction in dipolar truncation. Finally, we demonstrate the utility of PAR in structural studies of proteins with (13)C-(13)C spectra of uniformly (13)C, (15)N labeled microcrystalline Crh, a 85 amino acid model protein that forms a domain swapped dimer (MW=2 x 10.4 kDa). The spectra, which were acquired at high MAS frequencies (omega(r)2pi>20 kHz) and magnetic fields (750-900 MHz (1)H frequencies) using moderate rf fields, exhibit numerous cross peaks corresponding to long (up to 6-7 A) (13)C-(13)C distances which are particularly useful in protein structure determination. Using results from PAR spectra we calculate the structure of the Crh protein.

Figure 1

(a) PAR pulse sequence for obtaining 2D homonuclear correlation spectra. The PAR mixing consist of continuous wave (cw) irradiation on the ¹H and ¹³C channels that induces a second-order cross term between ¹H–¹³C dipolar couplings [terms 2 and 3 of Eq. 6] in order to transfer polarization from ¹³C₁ to ¹³C₂. (b) The PAR subspace can be seen as a coupled basis between a fictitious ZQ operator involving two ¹³C’s and a ¹H spin. The red arrows indicate PAR recoupling axis and longitudinal tilting field resulting from autocross terms (see Sec. 4).

Figure 2

PAR optimization map simulated using SPINEVOLUTION (Ref. 50). The initial magnetization is on the C₁ spin (C_2,X operator) and is detected after 3 ms PAR mixing on the three spins: (a) C₁ spin, (b) C₂ spin, and (c) H spin (C_1,X, C_2,X, H_X operators, respectively). The spin system is composed of two directly bonded ¹³C’s and one ¹H bonded to the ¹³C₁ spin (see the inset of the figure). The distance between the ¹³C₂ spin and the ¹H is 2.15 Å. The angle between the two CH dipolar vectors is 42° and arises from the usual tetrahedral geometry. Simulations include typical chemical shift tensor values (see SI for details) (Ref. 69). The black dashed lines indicate the locations of the n=0 and ±1 and ±2 HH matching conditions.

Figure 3

PAR optimization maps where the polarization transfer between the ¹³C is monitored as a function of ¹³C and ¹H irradiation strengths (in units of ω_r) and a 1.5 ms mixing period. The spin system is identical to that in Fig. 2. No chemical shift interactions were included in these simulations. The three panels represent (a) analytical simulations of the ¹³C polarization transfer from ¹³C₁ to ¹³C₂ arising from only the TSAR term, (b) ¹³C signal intensity showing the analytical simulation obtained with the TSAR term and the longitudinal autocross-term contributions, and (c) ¹³C signal intensity depicting the numerical simulations performed with SPINEVOLUTION. The two white lines displayed on the contour plots in panels (b) and (c) represent points where χ(1,p_C,p_H)=0 and χ(2,p_C,p_H)=0 (i.e., autocross terms for spatial components m=1 and m=2 are equal to 0), described by equations $p_{\mathrm{H}}=\sqrt{p_{\mathrm{C}}^2-1}$ and $p_{\mathrm{H}}=\sqrt{p_{\mathrm{C}}^2-4}$, respectively.

Figure 4

Simulations of polarization transfer in the PAR experiment for a HC₁C₂ spin system. The chemical shift is not included in the simulations. The PAR ¹³C and ¹H cw rf field strengths correspond to p_C=2.6 and p_H=2.35, respectively [see Fig. 3b]. The panels illustrate simulations that include the following couplings: (a) all dipolar couplings; (b) couplings C₁H and C₂H but not C₁C₂; (c) couplings C₂H and C₁C₂, but not C₁H (note that the polarization remains on C₁); (d) couplings C₁H and C₁C₂ but not C₂H; (e) coupling C₁H but not C₂H or C₁C₂; (f) C₁C₂ but not C₁H and C₂H.

Figure 5

Dependence of PAR polarization transfer on the local geometry of the spin system. (a) The three-spin system geometry used in the simulations: the first ¹³C and the ¹H are fixed in space, whereas the position of the second ¹³C is defined by θ and ϕ, the spherical coordinates with the origin at the ¹H. The distances between the ¹³C’s and the ¹H are constant and equal to 1.1 and 2.6 Å, respectively. The spherical map represents the ¹³C–¹³C polarization transfer efficiency for a PAR mixing time of 4.2 ms using p_C=2.75 and p_H=2.5. Polarization transfer for θ=0 orientation (aligned geometry) as a function of time is presented in panels (b) and (c). The buildup curves labeled (1)–(5) represent analytical simulations performed with the following contributions: (1) both m=1 and m=2 components without autocross terms, (2) both m=1 and m=2 with autocross terms, [(3) and (4)] only m=1 without and with autocross terms, [(5) and (6)] only m=2 without and with autocross terms.

Figure 6

Analytical contour plots of the PAR polarization transfer arising from the m=1 and m=2 components as a function of θ angle for a three spin system described in Fig. 5a with the mixing time and irradiation settings used in Fig. 5 with ϕ=0. (a) m=1 PAR component, (b) m=1 PAR term plus m=1 autocross-term components, (c) m=2 PAR component included, (d) m=2 PAR term and m=2 autocross-term components, (e) m=1 and m=2 PAR components, and (f) m=1 and m=2 PAR plus m=1 and m=2 autocross-term components.

Figure 7

Illustration of dipolar truncation in the CM₅RR and PAR homonuclear recoupling schemes. The spin system 1 is composed of a directly bonded C_αH_α pair and C_remote spins of 4.5 and 3.56 Å distant from the C_α and H_α spins. In the spin system 2, a C_β spin, directly bonded C_α, is also present. (a) The black dashed line depicts the polarization transfer (∼30%) from C_α to C_remote (r_C−C=4.5 Å) using the broadband DQ CM₅RR in the three spin system 1. When a directly bonded C_β spin is added to the spin system (r_C−C=1.5 Å), the polarization transfer to the C_remote (red dash-dot line) is quenched for CM₅RR with most of the polarization being transferred to the directly bonded C_β (blue solid line), thus demonstrating the phenomenon of dipolar truncation. (b) In the PAR simulation the presence of a third strongly coupled spin leads to a partial decrease in polarization transfer to C_remote (red dash-dot line) showing that dipolar truncation is attenuated in the TSAR transfer mechanism. Simulations were performed with SPINEVOLUTION (Ref. 50) ω_r∕2π=20 kHz, ω_0H∕2π=750 MHz ¹H frequency and do not include chemical shifts.

Figure 8

(a) 2D ¹³C–¹³C correlation spectrum of [U–¹³C,¹⁵N]N-f-MLF-OH diluted to 10% in a natural abundance lattice. The spectrum was recorded at ω_0H∕2π=750 MHz and ω_r∕2π=20 kHz with τ_mix=7.5 ms, ω_1C∕2π≈50 kHz, ω_1H∕2π≈47 kHz, and the ¹³C offset at 101 ppm. The circled cross peaks in (a) correspond to ≥4 Å ¹³C–¹³C distances. (b) Numerical simulations of PAR polarization transfer between MC_β and LC_α (highlighted 4.3 Å distance) using rf power levels specified in (a). The spin system includes nearby protons (2xMH_β, MC_α, LH_α, LH) (back solid line) and nearby protons plus MC_α and MC’ (red dash line). The dotted blue line represents simulation on a spin system including nearby protons plus MC_α and MC^′ with the ¹H–¹H couplings removed from the calculation. Simulations include typical chemical shift tensor values (see SI for details) (Ref. 69). The plot illustrates that the contribution of the polarization relayed through MC_α and MC^′ to the polarization transfer between MC_β and LC_α is negligible compared to the direct polarization transfer.

Figure 9

2D ¹³C–¹³C correlation spectra of [U–¹³C,¹⁵N]-Crh protein comparing two advanced recoupling pulse sequences at ω_0H∕2π=750 MHz and ω_r∕2π=20 kHz: (a) Broadband CM₅RR spectrum recorded with τ_m=0.8 ms ω_1C∕2π∼100 kHz and displaying only one-bond dipolar ¹³C–¹³C cross peaks (see the gray monomer of the Crh dimer structure representation in the inset). Note that the spectrum was acquired in ∼15 h without ¹H irradiation during the CMRR mixing time. (b) PAR spectrum corresponding to τ_m=14 ms with ω_1C∕2π∼53 kHz and ω_1H∕2π∼50 kHz cw fields displaying ¹³C–¹³C cross peaks corresponding to medium (4.3 Å) and long (∼5.4 Å) distances (acquired in ∼40 h). Several illustrative examples are shown on the green monomer of the Crh dimer structure representation. A detailed description of the PAR optimization protocol can be found in the SI (Ref. 69).

Figure 10

PAR polarization transfer as a function of the ¹³C–¹³C distance. [(a)–(d)] A sampling of experimental ¹³C–¹³C PAR polarization transfer curves obtained on [U–¹³C,¹⁵N]-Crh protein with ω_r∕2π=20 kHz, ω_0H∕2π=900 MHz and a carrier frequency set to 38.9 ppm: (a) one-bond distance class; (b) 2.5–3.5 Å distance class; (c) 3.5–5 Å distance class; (d) >5 Å distance class. (e) Spin system used in the PAR polarization transfer simulations [(f) and (g)]. Atom coordinates and chemical shift tensors used in the simulations can be found in the SI (Table SI3).

Figure 11

Modification of the long distance polarization transfer in uniformly labeled systems when both first-order ¹³C–¹³C recoupling and second-order TSAR mechanism are simultaneously present. Note the different behavior for the simulations with only ¹³C–¹³C couplings included and the simulations also including ¹H’s. The chosen ¹H irradiations yield substantial TSAR mechanism contribution to overall polarization transfer (except CM₅RR where no ¹H irradiation was used in order to illustrate a case of pure second-order ¹³C–¹³C spin dynamics without TSAR contribution). (a) DQ CM₅RR with 100 kHz ¹³C rf and no ¹H rf. (b) DQ HORROR with 15 kHz ¹³C rf and 80 kHz ¹H rf. (c) ZQ PAR with 56 kHz ¹³C rf and 54 kHz ¹H rf. (d) ZQ SR6₂ (Ref. 6) with 20 kHz ¹³C rf and 82 kHz ¹H rf. (e) ZQ RFDR with 12.5 kHz pulses and 69 kHz ¹H rf. The simulations were performed at [(a), (c), (d), and (e)] ω_r∕2π=20 kHz or (b) ω_r∕2π=30 kHz and ω₀∕2π=700 MHz and include isotropic chemical shift and CSA typical for the aliphatic sites (see SI) (Ref. 69). The spin system is based on the leucine sidechain in the structure of N-f-MLF-OH (Ref. 64). Note that all the pulse sequences except PAR [in (d)] are designed to reintroduce the ¹³C–¹³C dipolar coupling to the first order.

Figure 12

[(a) and (b)] Examples of ¹³C–¹³C correlation spectra of [U–¹³C,¹⁵N]-Crh protein at ω_0H∕2π=900 MHz and ω_r∕2π=20 kHz. Expansion of the aliphatic region for (a) CM₅RR (0.8 ms) and (b) PAR (15 ms). The PAR spectrum contains numerous cross peaks corresponding to medium to long distances that involve methyl groups. As a comparison, the CM₅RR spectrum displays only one-bond cross peaks. A detailed description of the PAR optimization protocol can be found in the SI (Ref. 69). (c) Ensemble of structures of a Crh monomer (residues 12–85) calculated using a unique 2.5–6 Å distance class for all the unambiguous ¹³C–¹³C cross peaks identified using the x-ray structure (Ref. 56) as a homology model. (e) Numerical simulations of the polarization transfer between CH₃ and CH illustrating the influence of the threefold methyl group hopping on the overall polarization transfer. The coordinates for spin system (d) used in the simulations were taken for A20Cα and I47Cδ1 from the x-ray structure (Ref. 56) of the Crh protein. Simulations do not include chemical shift.