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A protocol is presented for correcting the effect of non-specific cross polarization in CHHC solid-state MAS NMR experiments, thus allowing the recovery of the 1H-1H magnetization exchange functions from the mixing-time dependent buildup of experimental CHHC peak intensity. The presented protocol also incorporates a scaling procedure to take into account the effect of multiplicity of a CH2 or CH3 moiety. Experimental CHHC buildup curves are presented for L-Tyrosine.HCl samples where either all or only one in ten molecules are U-13C labeled. Good agreement between experiment and 11-spin SPINEVOLUTION simulation (including only isotropic 1H chemical shifts) is demonstrated for the initial buildup (tmix < 100 μs) of CHHC peak intensity corresponding to an intramolecular close (2.5 Å) H-H proximity. Differences in the initial CHHC buildup are observed between the 1 in 10 dilute and 100 % samples for cases where there is a close intermolecular H-H proximity in addition to a close intramolecular H-H proximity. For the dilute sample, CHHC cross peak intensities tended to significantly lower values for long mixing times (500 μs) as compared to the 100 % sample. This difference is explained as being due to the dependence of the limiting total magnetization on the ratio Nobs/Ntot between the number of protons that are directly attached to a 13C nucleus and hence contribute significantly to the observed 13C CHHC NMR signal, and the total number of 1H spins into the system. 1H-1H magnetization exchange curves extracted from CHHC spectra for the 100 % L-Tyrosine.HCl sample exhibit a clear sensitivity to the root sum squared dipolar coupling, with fast build-up being observed for the shortest intramolecular distances (2.5 Å) and slower, yet observable build-up for the longer intermolecular distances (up to 5 Å).
Solid-state nuclear magnetic resonance increasingly develops as an attractive tool for investigating complex molecular systems with practical relevance in biology, chemistry and materials science. For instance, structural investigations based on identifying protein intra-residue or neighboring residue 13C-13C (13C-15N) connectivities, distances, and angles are now almost routinely available from 13C(15N) solid-state NMR experiments optimized to work on multiply labeled samples [1–12], but constraints useful to elucidate the 3D structure of proteins , or to characterize supramolecular aggregates and crystal packing, are more difficult to obtain. A promising strategy for this purpose is to use the CHHC experiment [14–17], which makes use of the concept that such constraints are easier to extract using 1H-1H magnetization exchange, because protons are closer spaced in regions of interest (folding, or intermolecular contacts), and also more strongly dipolar coupled to each other than low γ nuclei.
1H-1H magnetization exchange can be directly probed in a NOESY-type 1H-1H spin-diffusion two-dimensional correlation experiment . This has been shown for cases of small and moderately sized organic molecules, where sufficient 1H resolution is obtained using fast MAS or homonuclear 1H decoupling [19–24]. In a CHHC experiment (see pulse sequence in Figure 1), 1H-1H magnetization exchange is probed indirectly, taking advantage of the better resolution for the X nucleus. NHHC , NHHN  and PHHP  implementations as well as extensions to 3D C(DQ)C(SQ)HHC and NHHCC experiments  have also been demonstrated. CHHC, NHHC and NHHN experiments are widely applied to biological systems such as microcrystalline proteins [10, 17, 27–32], fibrils [33–37], aggregates [38, 39], chlorophylls [40–43], ion channels [44–46], RNA [47,48] and an anti-cancer agent , where cross peaks observed in spectra recorded with mixing times of typically at least 100 μs are used as distance constraints for structure determination protocols.
The reliability of 1H-1H distance constraints determined from observed cross peaks in CHHC-type experiments has been demonstrated for small model compounds, e.g., amino acids [10, 15, 17, 25, 28, 50, 51] as well as recently the microcrystalline CrH protein , where 1H-1H distances are known from single-crystal diffraction data. Specifically, faster experimental buildup (as a function of the mixing time, tmix) of CHHC peak intensity is observed for shorter 1H-1H distances. Experimental CHHC buildup data has been analysed using a classical spin-diffusion model [15, 16], with the extracted spin diffusion coefficients allowing order-of-magnitude estimates of 1H-1H distances. Reif et al.  and Lange et al.  have shown that a good fit to experimental data is obtained using analytical expressions based on n = 0 rotational resonance  and spectral spin diffusion [53, 54], respectively. These expressions have a squared dependence on the dipolar coupling constant (and hence the internuclear distance) as well as a fitted phenomenological zero-quantum dephasing term, with the latter depending on the MAS frequency . Elena et al. have presented a related treatment of direct 1H-1H magnetization exchange using a multi-spin kinetic rate matrix approach that considers a sum of all relevant magnetization processes between sites i and j in different molecules in the crystal lattice [22, 23].
Advances in computing hardware and density-matrix simulation methodologies [55, 56] mean that the spin dynamics due to 10+ dipolar-coupled nuclei can be simulated. For example, the dephasing in 13C free-induction decays and spin-echo experiments under rotor-synchronised Hahn-echo pulse trains have recently been simulated for 10 coupled spins [57, 58]. In this paper, 1H-1H magnetization exchange is simulated for 11-spin systems corresponding to specific proton-proton proximities in L-tyrosine.HCl, for which experimental CHHC buildup data is presented. Specifically, a protocol is introduced to correct for non-specific cross-polarization (CP) and take into account XHn multiplicity, thus allowing a direct comparison between experimental and simulated data. The effect of inter- and intramolecular 1H-1H proximities on 1H-1H magnetization exchange is investigated using two L-tyrosine.HCl samples where either all or only one in ten molecules are U-13C labeled. For the all U-13C sample, differences in the rate of buildup of CHHC peak intensity are explained by considering the root sum squared dipolar couplings.
U (98 %)-13C labeled L-Tyrosine was obtained from Cambridge Isotope Laboratories (Andover, MA, USA). Conversion to the L-Tyrosine·HCl salt was achieved by dissolving L-tyrosine in 1M HCl, followed by freeze-drying using a vacuum-pump. Two samples were used in this study: U-13C L-Tyrosine·HCl refers to the sample as prepared above. A second sample was prepared by the recrystallization of the U-13C labeled L-Tyrosine with natural abundant L-Tyrosine in 1M HCl, so as to yield a U-13Cdil_10% L-Tyrosine·HCl sample, i.e., one in ten L-Tyrosine·HCl molecules are fully 13C labeled.
Experiments were performed at room temperature on a Bruker AVANCE-400 spectrometer operating at a 13C Larmor frequency of 100 MHz, at an MAS frequency of 10.5 kHz using a Bruker 4 mm double-resonance probe.
In all experiments, CP transfer was optimized for the first Hartmann-Hahn matching condition (ν1C = ν1H − νR), using 1H and 13C rf nutation frequencies of 51 and 40 kHz, respectively. For π/2 1H rf pulses, a π/2 pulse length of 3.8 μs was used. During 13C evolution periods, two-pulse phase-modulated (TPPM) 1H decoupling  was applied at a nutation frequency of 70 kHz (Δϕ = 15° and pulse width of 7.4 μs). A recycle delay of 3 s was used.
The CHHC experiments were performed by using the pulse sequence depicted in Fig. 1, where the unwanted proton polarization left after the first CP contact pulse is removed by phase-cycling the second π/2 pulse on the 1H channel, as introduced in ref. . A contact pulse of 700 μs was used for the first CP, whereas a much shorter contact pulse- (65 μs) was employed for the next two CP steps in order to favorize polarization transfer between bonded 13C-1H in CH and CH2 moieties. A 60 kHz continuous wave decoupling field was also applied on the 13C channel during the mixing time to reduce the negative effect of the 13C-1H dipolar interaction upon the efficiency of 1H-1H polarization transfer. 256 (U-13Cdil_10% sample) and 32 (U-13C sample) transients were coadded for each of 256 t1 increments of 30μs, corresponding to a F1 spectral width of 16.6 kHz which was chosen such as to fit only the six protonated 13C resonances of interest. Sign discrimination in t1 was achieved using the TPPI method. Total acquisition times for each 2D CHHC experiment were 54 hours and 7 hours for the U-13Cdil_10% and U-13C samples, respectively. The signal to noise ratio in the first row of the CHHC experiment for tmix = 0 was better than 75:1 (U-13Cdil_10%) and 120:1 (U-13C samples) for all centreband protonated 13C resonances.
Density-matrix simulations of 1H-1H magnetization exchange during the tmix period of a CHHC experiment were performed using the SPINEVOLUTION program  for 10 kHz MAS and a 1H Larmor frequency of 400 MHz. 11-spin systems based upon the proton coordinates as extracted from the crystal structure of L-Tyrosine·HCl  were considered, using experimental 1H isotropic chemical shift values (see the representative SPINEVOLUTION input files in the Appendix). It was verified that the number of crystallite orientations used was sufficient to ensure convergence. 1H CSAs were neglected – in separate simulations, it was found that small changes to the magnetization exchange curves only started to occur for CSA anisotropies in excess of 40 ppm (for L alanine, the largest calculated 1H CSA has an anisotropy of 17 ppm ). Each simulation directly provides the magnetization-exchange curves that correspond to the transfer from an initially polarized 1H site, to the all chemically distinct proton sites in the system, and took approximately 120 hours on an Opteron Linux workstation.
The transfer of z magnetization between two dipolar coupled 1H nuclei j and k during a mixing time, tmix, under the spin-diffusion operator Û is described here by a polarization transfer function, Fjk (tmix):
In a CHHC experiment, a general 13C-13C SQ-SQ correlation is established between a 13CLHp and a 13CMHq resonance, via 1H-1H magnetization exchange between p 1H nuclei attached to 13CL and q 1H nuclei attached to 13CM. In such a case, it is convenient to define modified polarization transfer functions for the case of unlike and like spins, i.e., corresponding to off-diagonal and diagonal peaks in a 2D CHHC spectrum:
The modified polarization transfer functions correspond to 1H-1H magnetization exchange starting from unit polarization on a given 13CLHp group. For tmix = 0, and .
In this paper, a normalized polarization transfer function is employed according to the definition:
The indirect observation of 1H-1H magnetization exchange in a 2D CHHC experiment benefits from the considerably better 13C as opposed to 1H resolution. However, the two CP steps flanking the 1H-1H magnetization exchange period in the CHHC sequence are usually not fully specific even for the very short CP durations typically used (< 100 μs), i.e., magnetization is not transferred exclusively from a given 13C nucleus to only its directly attached 1H nucleus or nuclei, but rather magnetization “leaks out” onto other 1H nuclei. As a consequence, the intensity of an experimental CHHC cross peak linking a 13CLHp and a 13CMHq resonance, , does not correspond precisely to the 1H-1H polarization transfer functions described above. This section describes a procedure for recovering the 1H-1H polarization transfer functions from the experimental CHHC cross-peak intensities.
The intensity of an experimental CHHC cross peak linking a 13CLHp and a 13CMHq resonance, , corresponds to:
Note that S and I refer to 13C and 1H nuclei, respectively. The coefficient takes into account the variation of initial (i.e., at the start of t1) 13C transverse magnetization for different 13C resonances arising from the first CP step. The xy subscript indicates spin S transverse magnetization present at the end of t1 or the start of t2. The CP propagators in Eq. (5) are considered to include the contact pulse applied to both spin species and the 1H 90° pulse that creates Iz (1H population state) at the start of tmix or converts Iz at the end of tmix into 1H transverse magnetization before the final CP step, i.e., ÛSI (τCP) converts Sxy into Iz, while ÛIS (τCP) converts Iz into Sxy. The CP dynamics can be described in terms of the transferred polarization:
where the coefficient η corresponds to the amount of magnetization transferred to proton(s) directly attached to the initial 13C resonance, while the coefficient ε corresponds to the amount of magnetization transferred to proton(s) attached to a different 13C resonance. Similarly,
It thus follows that
where the term in εLMεML has been neglected.
The intensity of an experimental CHHC diagonal peak for a 13CLHp resonance, , corresponds to:
where the term in εLM2 has been neglected.
For a short tmix, and are both small, while for a short τCP, εLM and εML are also small. For such conditions, Eq. (13) simplifies to
Eq. (12) can, then, be reexpressed as
Rearranging Eq. (16),
Eq. (19) defines how the normalized polarization transfer functions – corresponding to only 1H-1H magnetization exchange, i.e., with no distorting effect from non-specific CP–can be extracted from the experimental CHHC cross peak intensities.
The following describes how the coefficients in Eq. (19) can be experimentally determined. Using the above theoretical model, it can be shown that the ratio βL of the intensity of a specific 13C resonance recorded in a CHHC filtered spectrum (obtained by using the CHHC pulse sequence with t1 and tmix set to zero), , and that acquired after the first CP step, , can be related to the corresponding CP transfer parameter, ηL, and proton multiplicity, through:
It then follows that
By inserting this in eq. (20) the following expression is obtained for the fLM coefficient
which provides the desired dependence only on the experimentally measured parameters βL(M).
For tmix = 0, , and hence Eq. (16) becomes
Within the approximation that ε = εLM = εML ε can be determined:
where ηL and ηM are determined using Eq. (22).
The above calculation is for the case where all carbon nuclei are 13C, i.e., where all molecules are U-13C labelled. For a dilute sample, which corresponds to the case where only a proportion ρ of the molecules are U-13C labeled, it is necessary to correct for the contribution to the diagonal peak intensity of the natural abundance 13C nuclei (denoted here as ξ, with ξ= 0.011 for 13C) in the proportion (1 − ρ) of the molecules at natural abundance. This correction is required since only ξ2 molecules will have two neighboring 13C-labeled atoms, so as to give rise to cross peak intensity , as compared to the ξ molecules that have a single 13C-labeled atom that contributes to the diagonal peak intensity. Considering the diagonal peak intensity, , there is a contribution ξ (1 − ρ) from molecules at natural abundance in addition to the ρ from the U-13C labeled molecules. It is hence necessary to modify Eq. (25)
i.e., for 13C, λ = 0.91 when ρ = 0.1. Eq. (26) does not include a correction to the cross peak intensity which is given by ρ/[ρ + ξ2(1 − ρ)], since this equals 1.00 to two decimal places for 13C when ρ = 0.1.
For a dilute sample, it is also necessary to modify Eq. (19):
Figure 2 compares 13C CP MAS (thin line) and 13C CHHC-filtered (t1 = tmix = 0, τCP = 65 μs for the last two CP steps) spectra (thick line) for (a) U-13C and (b) U-13Cdil_10% L-Tyrosine·HCl. The ηL CP transfer coefficients as determined from a comparison of the signal intensity in the CP MAS and CHHC-filtered experiments (see Eq. (22)) are listed in Table 1.
Fig. 3 presents 2D CHHC (τCP = 65 μs for the last two CP steps) spectra of (a,b) U-13C and (c,d) U-13Cdil_10% L-Tyrosine·HCl recorded with tmix equal to (a,c) 0 and (b,d) 100 μs. Fig. 4 presents rows through the F1 resonances corresponding to the six protonated 13C nuclei, as extracted from the CHHC spectra at zero mixing time. It is evident that non specific CP during the last two CP steps of the CHHC experiment gives rise to noticeable CHHC cross peaks between directly bonded 13C nuclei (i.e., 2 & 4, 3 & 5, and 7 & 8), even for the case of zero mixing time. This is also evident in Fig. 5(a) and (b) which presents the buildup of C7 (βCH2) to C8 (αCH) (open symbols) and C8 to C7 (filled symbols) cross-peak intensity as a function of tmix for (a) U-13C and (b) U-13Cdil_10% L-Tyrosine·HCl. Specifically, the cross-peak intensities are normalized with respect to the intensity of the corresponding diagonal peak for zero mixing time, i.e., such that the C7 to C8 and C8 to C7 cross-peak intensities are divided by the intensity of the C7 and C8 diagonal peak intensity for zero mixing time, respectively. In the case of the U-13Cdil_10% sample, a scaling by the factor λ as defined in Eq. (27) of 0.91 was applied to .
Section 3.2 (see Eqs. (19) & (28)) describes a procedure for recovering the 1H-1H magnetization exchange behavior given by from the experimental CHHC buildup curves. Fig. 5(c) and (d) presents such corrected normalized buildup plots for the C7 to C8 and C8 to C7 cross peaks for (c) U-13C and (d) U-13Cdil_10% L-Tyrosine·HCl. In the evaluation of the εLM coefficients (see Eqs. (25) & (26)), the coefficient was set to zero when , i.e., when a particular cross-peak was less than 1 % of the intensity of the corresponding diagonal peak. The evaluated non-zero εLM coefficients for the different CHHC cross peaks are listed in Table 2. Considering Fig. 5(c) and (d), it is evident that all corrected curves now start at zero. As shown below, this allows for a clear comparison with the 1H-1H magnetization exchange build-up behavior obtained from numerical density matrix simulations. The corrected experimental C7 to C8 and C8 to C7 transfer functions are observed to be the same within (or close to within) the experimental error bars. In the following, experimental values for a CL, CM pair are shown as an average of and .
Corrected normalized buildup plots, i.e., , for U-13C (circles) and U-13Cdil_10% (triangles) L-Tyrosine·HCl are shown in Fig. 6 for the (a) C7-C8 and (b) C2-C4 CHHC cross peaks. The experimental data is compared to a SPINEVOLUTION simulation (solid line) of the 1H-1H magnetization function defined in Eq. (4) for 11-spin systems centered around the H7 (two protons) & H8 and H2 & H4 1H nuclei, as shown in Fig. 6(c) and (d). Inter-proton distances for the 11-spin systems are given in Tables 3 and and44.
Comparing the experimental data in Fig. 6(a) and (b) with the simulated 11-spin 1H-1H magnetization exchange curves, while there is good agreement for short tmix (< 100 μs), it is noticeable that the experimental data for the U-13Cdil_10% sample, in particular, trends to a markedly lower value than that for the simulation at long mixing times. For the diluted sample, the unlabeled molecules located around a fully 13C-labeled molecule can be viewed as a proton bath where a significant amount of the initial polarization is lost, because it cannot be back-transferred to observable 13C NMR signal during the last CP block. This is responsible for the much stronger attenuation of the CHHC cross-peak intensities at large mixing times in the 10%-diluted sample compared to the 100% sample. Quantitatively, the efficiency loss by this mechanism is illustrated in Fig. 7. Specifically, Fig. 7 compares for the U-13C (circles) and U-13Cdil_10% (triangles) L-Tyrosine·HCl samples the evolution with the mixing time of the total observable experimental polarization that originates from an initial unit C7 polarization. This is defined as the sum of the normalized IC7 diagonal peak intensity and the intensities IC7,Cj within its associated cross-peak patterns (corrected by the procedure described above, i.e., ), with j = 2, 3, 4, 5 and 8. Considering that an equal distribution of 1H polarization is obtained at large mixing times, and neglecting spin-lattice relaxation, an asymptotic evolution would be expected towards a saturation level given by the ratio Nobs/Ntot between the number of protons that are directly attached to a 13C nucleus and hence contribute significantly to the observed 13C NMR signal, and the total number of 1H spins into the system. Its value is Nobs/Ntot = 7/12 = 0.58 (NB: there are 7 CH and CH2 protons and 5 NH3 and OH protons in the L-Tyrosine·HCl molecule) and 7/120 = 0.06 in the case of the U-13C and U-13Cdil_10% samples, respectively. As can be seen in Fig. 7, the experimental total polarization trends towards these Nobs/Ntot values.
Considering the experimental data in Fig. 6(a) & (b), differences are apparent for short mixing times (tmix < 100 μs) when comparing the buildup for the U-13C (circles) and U-13Cdil_10% (triangles) samples for (a) the C7 (CH2) & C8 (αCH) and (b) the C2 and C4 (directly bonded aromatic carbons) CHHC cross peaks. Specifically, in Fig. 6(a), the observed buildup rate is faster for the U-13C sample, while in Fig. 6(b), the buildup is the same within the experimental noise for the U-13C and U-13Cdil_10% samples. This is a consequence of additional close intermolecular proximities for the H7,H8 case: the intra-and inter-molecular contributions to the total C7,C8 cross-peak buildup curve are of comparable magnitudes, as they correspond to H7-H8 inter-proton average distances of 2.8 and 3.2 Å, respectively (see Table 3). By comparison, for the H2,H4 case, the nearest intermolecular proximity is 4.5 Å as compared to the intramolecular proximity of 2.5 Å (see Table 4). The 11-spin SPINEVOLUTION simulations (solid line in Fig. 6(a) & (b)) only consider intramolecular 1H-1H magnetization transfer – for H7,H8, see footnote d to Table 3 and the representative SPINEVOLUTION input files in the Appendix. Good agreement between experiment and simulation for short mixing times (< 80 μs) is obtained for the C7,C8 buildup curve for the U-13Cdil_10% sample (triangles in Fig. 6(a)) and for the C2,C4 buildup curves in Fig. 6(b) for both samples, i.e., for those cases where intermolecular proximities do not contribute to the experimentally detected 1H-1H magnetization exchange. The deviations between experiment and simulation at longer mixing times is a consequence of “loss” of magnetization experimentally to 1H nuclei that are not bonded to a visible 13C nucleus as discussed above (see Fig. 7).
Fig. 6 shows examples of 1H magnetization exchange observed for two specific cases, namely an isolated single 1H-1H contact (H2,H4, Fig. 6(b)) and a relatively tight H7-H8 inter-molecular pair in the close neighborhood of a short intra-molecular H7-H8 pair (see Fig. 6(a) for the U-13C sample). This section considers the 1H magnetization exchange behavior for the different cases of 1H-1H contacts found in L-Tyrosine·HCl. Table 5 lists all 1H-1H distances under 5 Å. If we define a “close” 1H-1H contact as a distance under 3.5 Å, the 1H-1H contacts corresponding to the distinct CHHC cross-peaks can be classified either with respect to the number of involved contacts, i.e., single- (H2-H3, H2-H4, H2-H7, H3-H5, H3-H7, H4-H5, H4-H7, H5-H8), double- (H2-H5, H5-H7, H7-H8), and triple contacts (H3-H4), or according to their type, i.e., only intra- (H2-H4, H3-H5, H4-H7, H5-H8), only inter- (H2-H3, H2-H5, H2-H7, H3-H4, H3-H7, H4-H5), and mixed intra- and inter-molecular 1H-1H contacts (H5-H7, H7-H8). Note that for the case of H7 that corresponds to the two CH2 protons, proximities of the same type and from the same other proton to both CH2a and CH2b are only counted once in the above classification – this is consistent with proton multiplicity being explicitly taken into account in the above analysis (see section 3.1).
The simplest case corresponds to single 1H-1H intra-molecular contacts, i.e., C2-C4, C3-C5, C4-C7 and C5-C8. The example of the C2-C4 CHHC buildup curves (Fig. 6(b) has been discussed above: the observed good correspondence between the two experimental curves for the U-13C and U-13Cdil_10% samples on the one hand, and between the experiment and simulation, on the other hand, are illustrative for the conditions that must satisfied by a short 2.5 Å contact (i.e., corresponding to directly bonded CHn moieties) that can be considered as a single contact. It is evident that the added contribution to magnetization exchange dynamics of the closest 1H-1H contacts can be safely neglected if they correspond to inter-proton distances larger than about ~4 Å. The identification of such intramolecular single contacts is useful in that they provide (as discussed below) reference curves for the analysis of other buildup curves that depend on contributions from multiple contacts.
In the following, we consider experimental CHHC data for U-13C L-Tyrosine·HCl, where close intermolecular 1H-1H proximities will affect the observed buildup curves. Specifically, Fig. 8 presents corrected normalized experimental CHHC buildup curves (corresponding to as defined in Eq. (19)) for magnetization starting on (a) C2, (b) C3, (c) C5 and (d) C8. As noted above, the data associated with single 1H-1H intra-molecular contacts, i.e., C2-C4, C3-C5 and C5-C8 constitute single-contact intramolecular reference curves: The C2-C4, C3-C5 and C5-C8 peaks correspond to 1H-1H distances of 2.48 (H2-H4) and 2.47 Å (H3-H5) between neighboring aromatic protons and 2.56 Å (H5-H8) between an aromatic proton and the Cα proton. While all curves are converging to a similar plateau intensity at the longest experimental tmix of 0.5 ms, differences in rate of buildup are clearly evident. Importantly, in agreement with the use of the CHHC experiment to identify structural constraints, it will be shown that the differences in buildup rate are directly related to the root-sum-square coupling, drss, [61–63] for the corresponding 1H-1H proximities (listed in Table 5):
where the dipolar coupling constant, djk, is defined:
The close resemblance between the C2-Cj and C3-Cj patterns in Fig. 8 reveals the presence of relatively similar proton environments around the H2 and H3 protons. In both cases, the upper limit is provided by the corresponding single-contact intramolecular reference curve (C2-C4 and C3-C5), while the lower limit is established by the contact with the H8 proton. The slower buildup of the C2-C8 and C3-C8 curves is consistent with the closest H-H proximity being over 4 Å (H2-H8: intermolecular 4.14 Å, H3-H8: intramolecular 4.75 Å). The remaining CHHC curves in the C2-Cj and C3-Cj patterns are distributed within the two limiting curves. As a common feature, all of them are encoding significant (in some cases multiple) intermolecular contributions, since their fast buildup is inconsistent with the large intramolecular 1H-1H distances (> 4.5 Å). The C2-C3/C3-C2 buildup curve, determined by a single 2.9 Å intermolecular contact, is the only one that can be directly compared with the reference curve in terms of the encoded distances. Nevertheless, the difference between the C2-C7 and C3-C7 buildup curves is consistent with the difference in the corresponding average nearest proton-proton distances of 3.0 and 3.5 Å, respectively and drss = 10.1 and 4.6 kHz, respectively.
It is informative to compare the examples of the C2-C5 and C3-C4 buildup curves that correspond to multiple intermolecular proximities under 3.5 Å (H2-H5 2.76 & 3.19 Å, drss = 6.9 kHz; H3-H4 2.84, 3.20 & 3.24 Å, drss = 7.4 kHz) with the curves corresponding to single H-H proximities, i.e., the two intramolecular C2-C4 and C3-C5 reference curves and the C2-C3/C3-C2 single intermolecular contact, where the closest H-H distances are 2.48 Å (H2-H4), 2.47 Å (H3-H5) and 2.95 Å (H2-H3) and drss = 8.2 kHz (H2-H4), drss = 8.3 kHz (H3-H5) and drss = 5.5 kHz (H2-H3). The closeness of the C3-C4 and C3-C5 buildup curves is consistent with the similar drss values. The effect of multiple 1H-1H proximities leading to a faster buildup is evident when comparing the C2-C5 and C3-C4 curves on the one hand with the C2-C3 curve on the other hand.
A good correspondence between the experimental CHHC data and the corresponding structural parameters was found also for the C5-Cj and C8-Cj patterns in Fig. 8. Notably, C5-Cj is representative for a 1H site tightly coupled to its surrounding protons. Together with the intramolecular reference curves (C5-C3, C5-C8), the other three curves in this pattern also encode short inter-molecular contacts, with 1H-1H distances between 2.8 and 3.1 Å and similar drss values (between 4.9 and 9.7 kHz). At the other extreme, the C8-Cj pattern corresponds to strong couplings of H8 only with intra-molecular protons, whereas all the inter-molecular contacts are larger than 4 Å. This is clearly evidenced by the measured buildup curves.
Fig. 9 compares corrected normalized buildup plots, i.e., , for U-13C (circles) and U-13Cdil_10% (triangles) L-Tyrosine·HCl for the cases where significant intensity (i.e., above the noise level) is observed for the U-13Cdil_10% sample. These cases (C2-C4, C3-C5, C4-C7, C5-C7, C5-C8 and C7-C8) all correspond to closest intramolecular H-H proximities under 3 Å, while for the other cases, the closest intramolecular H-H proximity is over 4 Å. In this context, while Fig. 8 shows CHHC buildup curves for the U-13C sample involving C8 that correspond to closest H-H distances of over 4 Å, for the U-13Cdil_10% sample, it is to be remembered that much CHHC signal intensity is lost to invisible protons attached to 12C nuclei at longer mixing times (see Fig. 7 and section 4.3). Comparing the buildup curves for the U-13C and U-13Cdil_10% samples in the short tmix regime (< 80 μs), it is observed that four of them (C2-C4, C3-C5, C4-C7, and C5-C8) are quite similar in shape, while for the C5-C7 and C7-C8 cases, faster buildup is observed for the U-13C sample. As was discussed in section 4.3 when comparing the CHHC data for C7-C8 and C2-C4 (see Fig. 6), this difference is a consequence of additional close H5-H7 and H7-H8 intermolecular proximities.
CHHC-type experiments are being increasingly applied to indirectly probe 1H-1H magnetization exchange and hence obtain structural constraints, in particular, for large biomolecules. This paper has presented a protocol for correcting the effect of non-specific cross polarization in CHHC experiments, thus allowing the recovery of the 1H-1H magnetization exchange functions from the mixing-time dependent buildup of experimental CHHC peak intensity. The presented protocol also incorporates a scaling procedure to take into account the effect of multiplicity of a CH2 or CH3 moiety. In this way, direct comparison can be made between experimentally determined 1H-1H magnetization exchange functions and numerical density-matrix simulations, without the requirement for any phenomenological factors. For L-Tyrosine.HCl, good agreement between experiment and 11-spin simulation (including only isotropic 1H chemical shifts) is demonstrated for the specific case of initial buildup (tmix < 100 μs) of CHHC peak intensity corresponding to an intramolecular close (2.5 Å) H-H proximity. The derived corrections are not limited to the case of 1H-1H magnetization exchange, i.e., to zero-quantum mixing schemes, but they are also valid to CHHC experiments employing homonuclear 1H-1H recoupling schemes [17,50].
For small and moderately sized organic molecules such as L-Tyrosine.HCl, the experimentally observed buildup of CHHC peak intensity often corresponds to a 1H-1H magnetization exchange behaviour that depends on both intra- and intermolecular proximities. Indeed, it is to be noted that the multi-spin kinetic rate matrix analysis of directly observed 1H-1H magnetization exchange by Elena et al. exploits the dependence on intermolecular 1H-1H proximities to determine the three-dimensional packing of organic molecules in the crystal lattice [22, 23]. In the CHHC experiment, intermolecular effects can be removed by working with dilute samples where a U-13C labeled molecule is recrystallised with an excess of molecules at natural abundance. This approach has been employed in previous studies where distance constraints extracted from CHHC experiments have been used as constraints in the structural determination of the three-dimensional conformation of organic molecules [49–51]. In this paper, experimental CHHC buildup curves were presented for L-Tyrosine.HCl samples where either all or only one in ten molecules are U-13C labeled. For the dilute sample, CHHC cross peak intensities tended to significantly lower values for long mixing times (500 μs) than for the 100 % sample. This difference has been explained here as being due to the dependence of the limiting total magnetization on the ratio Nobs/Ntot between the number of protons that are directly attached to a 13C nucleus and hence contribute significantly to the observed 13C CHHC NMR signal, and the total number of 1H spins into the system.
It has been shown that insight into 1H-1H magnetization exchange under multiple intra- and intermolecular 1H-1H dipolar couplings can be obtained by a consideration of the root sum squared dipolar couplings corresponding to specific CHHC cross peaks. (Note that a sum squared dipolar coupling is also inherent to the multi-spin kinetic rate matrix analysis of directly observed 1H-1H magnetization exchange by Elena et al. [22, 23]) 1H-1H magnetization exchange curves extracted from CHHC spectra for the 100 % L-Tyrosine.HCl sample exhibit a clear sensitivity to the root sum squared dipolar coupling, with fast build-up being observed for the shortest intramolecular distances (2.5 Å) and slower, yet observable build-up for the longer intermolecular distances (up to 5 Å). As is to be expected, differences in the initial CHHC buildup were observed between the 1 in 10 dilute and 100 % samples for cases where there is a close intermolecular H-H proximity in addition to a close intramolecular H-H proximity. The demonstrated usefulness of the CHHC experiment as a valuable and reliable source of quantitative H-H proximity information is consistent with previous studies of other small organic molecules [50, 51] as well the microcrystalline CrH protein , for which 1H-1H distances are known from single-crystal diffraction data.
Of much current interest is the application of CHHC-type experiments, including the recently developed J-CHHC , to large biomolecules, where extracted 1H-1H distances are then used as constraints in structural determination protocols [29, 31, 32, 36, 37, 44, 46, 64]. For large biomolecules, the 1H-1H magnetization exchange as encoded in CHHC-type peaks is less complex than in the case of small and moderately sized molecules since intermolecular 1H-1H proximities do not usually contribute, although NHHC experiments have been used to probe inter monomer contacts for the CrH microcrystalline protein . As noted above, it has been shown here that good agreement between experiment and 11-spin simulation (including only isotropic 1H chemical shifts) was observed for the initial buildup (tmix < 100 μs) of CHHC peak intensity corresponding to a single intramolecular H-H proximity. For large biomolecules, most CHHC-type peaks usually correspond to such single intramolecular H-H proximities, thus suggesting that an analysis of CHHC-type buildup curves (using the protocol presented here to correct for non-specific CP and take into account XHn multiplicity) using multi-spin simulations could be utilised to check and refine H-H distances in as-determined biomolecular structures.
Financial support from the ANCS, EPSRC, and the Royal Society is gratefully acknowledged. Tim Smith and Andrew Marsh (Warwick) are thanked for assistance with sample preparation.
Representative SPINEVOLUTION input files used for the numerical simulation of the Fjk (tmix) polarization transfer functions in Eq. (1).
****** The System ***********************************
spectrometer (MHz) 400
spinning_freq (kHz) 10
nuclei H1 H1 H1 H1 H1 H1 H1 H1 H1 H1 H1
cs_isotropic 3 2.8 4.5 8 8 8 7 7 7 7 3 ppm
exchange_nuclei (4 5 6)
******* Pulse Sequence ******************************
timing (usec) (5) 200
power (kHz) 0
phase (deg) 0
freq_offs (kHz) 0
phase_cycling * *(RCV)
******* Options etc **************************************
rho0 1 1 0 0 0 0 0 0 0 0 0 Iz
observed_spins 1 2 3 4 5 6 7 8 9 10 11 Iz
line_broaden (Hz) *
8.207 −0.698 −0.686 H7a (CH2 - molecule A)
8.554 0.898 −1.274 H7b (CH2 - A)
7.034 0.260 1.303 H8 (CH - A)
5.976 1.412 −1.213 Ha (NH3 - A)
5.169 0.883 0.100 Hb (NH3 - A)
5.951 −0.187 −0.894 Hc (NH3 - A)
10.630 1.831 −0.798 H4 (CHring - A)
9.091 −1.154 1.852 H5 (CHring - A)
9.394 −2.663 −0.444 H2 (CHring inter - C)
9.253 −1.154 −3.245 H5 (CHring inter - B)
7.196 0.260 −3.793 H8 (CH - B)
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