C OMPLEX WITH A F ULL L ENGTH
6.2 Evaluation of Line Widths
Before assessing the suitability of such small rotors for protein samples (where sensitivity is limited), it is useful to evaluate the effects of increasing MAS averaging on proton line widths with a simple small molecule. To accomplish this, 1D experiments were conducted on the natural-abundance dipeptide β-Asp-Ala at spinning frequencies from 15 to 100 kHz at 850 1H Larmor frequency, with no homonuclear decoupling (Figure
6.1). At 15 kHz spinning frequency the proton spectrum is too broad for any features to be easily identified. As expected, more peaks become resolved as ωr is increased, with the
two Asp CH2 proton resonances becoming resolvable at around 65 kHz. At this stage,
these resonances have line widths of 418 ± 5 and 351 ±1 Hz (0.49 ppm and 0.41 ppm, Asp Hβ2 and Hβ3 respectively). As the MAS frequency is increased further, the Ala HN and Asp HN resonances finally become resolved and all other lines continue to narrow. Final proton line widths at 100 kHz are given in Table 1. The narrowest of these is that of Ala Hβ, at 0.25 ppm (211 ± 0.5 Hz). Also of particular note are the widths of the Asp Hβ2 and Hβ3 protons, at 0.34 ppm (292 ± 1 Hz) and 0.32 ppm (274 ± 2 Hz) respectively. These are comparable to the 0.36 ppm and 0.34 ppm corrected line widths that have been achieved using the state of the art eDUMBO-PLUS-1 homonuclear decoupling scheme at a similar field of 800 MHz.298 CH
2 protons are usually the most
difficult to decouple due to their proximity with one another and correspondingly strong
1H-1H couplings, as well as a lack of motional averaging typical of the CH
2 group.
Averaging of the dipolar couplings by this simple “brute force” method does not introduce any undesired artefacts or chemical shift scaling factors.
Contributions to the proton line widths can be grouped into two categories: inhomogeneous broadening, which is primarily due to B0 field and sample
inhomogeneities, and homogeneous broadening, the majority of which originates from the incompletely averaged homonuclear dipolar couplings but which also contains contributions from J-coupling and incoherent relaxation. It is worth remarking that inhomogeneous broadening defines the limiting value for the measurable line width that cannot be eliminated by MAS (or decoupling) without removing chemical shift information altogether. As such it is useful to separate the two broadening components
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in our evaluation. Inhomogeneous contributions to the line widths are strongly sample- dependent; for proteins, effective sample preparation is key to producing samples that exhibit the local order necessary for narrow line widths.
To isolate the homogeneous part, T2’ values for each proton in the dipeptide, i.e.
the transverse dephasing time during a spin-echo experiment, were measured at spinning frequencies from 30 to 100 kHz. Figure 6.2 shows the MAS frequency dependence of the total and spin-echo line widths (equal to 1/(πT2’)) of the protons in β-Asp-Ala. As has
been found in numerous other studies, the line width measurements diminish linearly with decreasing 1/ωr as the dipolar couplings are averaged more effectively.162,227,285,306-309
The rate at which the line width is narrowed with increasing spinning frequency varies between proton sites, and is dependent on the both the local strength of the dipolar coupling and the geometry of the proton network.285 The offset between the two sets of
data for each proton represents the inhomogeneous contribution to the line width, which is refocused in a T2’ experiment. Although this contribution is approximately constant
with varying ωr, the offset is different for the different proton sites, indicating a different
level of inhomogeneous broadening (but usually >125 Hz (>0.15 ppm)). The absolute
Figure 6.1. 1D 1H spectrum of the dipeptide β-L-Asp-L-Ala as a function of MAS
frequency at 850 MHz 1H Larmor frequency. The proton background was suppressed
with a spin echo (24 times the rotor period at each spinning frequency). The sample temperature was not controlled.
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Figure 6.2. Total (crosses) and spin-echo (open circles) line widths for protons in β-Asp-
Ala, as a function of inverse spinning rate at 850 MHz 1H Larmor frequency. Spin echo
line widths were calculated as 1/(πT2’), where T2’ is the magnetisation decay time constant measured in a spin-echo experiment.
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spin-echo line widths should, however, be taken with some degree of care, as systematic errors can arise in cases where a single exponential fits the data T2’ data poorly (we observe such deviations in our data).285 In these cases, the spin-echo line width can in
fact appear larger even than the full line width of the proton resonance. The effects of this can be seen in the data for the largely unresolved Hβ2 and Hβ3 sites, where the spin echo line widths appear much higher than expected but with large associated error bars. For the other, more resolved protons, the lines of best fit for the spin-echo line width data show negative intercept values, as the 1H-1H dipolar couplings will be completely
averaged at a finite spinning frequency (see below).
The spin-echo (homogeneous) line widths at 100 kHz MAS and 850 MHz 1H
Larmor frequency are detailed in Table 6.1. At this spinning frequency and field, for many sites the inhomogeneous contribution is at least as significant a proportion of the overall line width as the homogeneous contribution – in the absence of inhomogeneous broadening, spin-echo line widths at 100 kHz are as narrow as 71 Hz (for Ala Hβ, where the inhomogeneous contribution is twice as large). Because the inhomogeneous contribution constitutes a significant fraction of the observed line width, in going from 65 to 100 kHz MAS (for example), narrowing of the total line width is less than the ratio of the spinning frequencies (1.54), though it is still between a factor of 1.2 and 1.5 for all eight resonances (a reduction of over 120 Hz in some cases). There is clearly still much scope for further reductions in 1H line widths with faster MAS (or new CRAMPS
methods) – extrapolating the full, inhomogeneously-broadened line widths to an infinite spinning frequency yields minimum limiting inhomogeneous line widths of between 84±8 Hz (Asp Hβ) and 170±10 Hz (Ala NH), a theoretical improvement of ~2 times on average. Extrapolation of the homogeneous line width to a value of zero Hz suggests
Table 6.1. Total and homogeneous 1H line widths in β-Asp-Ala, measured at 100 kHz
spinning frequency and 850 MHz 1H Larmor frequency.
Peak OH HN Ala Asp HN Ala Hβ Asp Hβ Hβ2 Asp Hβ3 Asp Ala Hβ Line width (Hz) 229 ± 1 339 ± 5 325 ± 2 ± 0.5 211 259 ± 1 ± 0.5 292 274 ± 2 ± 0.5 269 Line width (ppm) 0.27 0.40 0.38 0.25 0.30 0.34 0.32 0.32 Spin-echo line width (Hz) 78 ± 9 ± 38 146 ± 15 174 ± 10 71 ± 25 138 ± 130 290 ± 120 240 136 ± 6
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that (if the trend continues), for most protons directly bonded to carbons, around 240 kHz may be sufficient to completely average the homonuclear dipolar couplings. For the more mobile Ala Hβ (methyl), Ala HN, Ala OH, Asp HN and Asp OH, it appears that much higher spinning frequencies from around 430 to 1300 kHz will be required.
It is important to also consider the effects of molecular motions upon line narrowing, and the influence of MAS-induced heating upon this. To check that the narrowing observed at 100 kHz resulted primarily from averaging of the anisotropic interactions by MAS rather than by molecular motions, repeat measurements were performed in the presence of sample cooling. At 100 kHz with cooling applied, β-Asp-Ala line widths were different on average by less than 3 Hz (with some resonances wider and some narrower) compared to those in the unregulated experiments, indicating that the increase in temperature associated with spinning faster has, in this case, a negligible effect on the line widths compared to the averaging effect of the physical rotation itself.