## C2 Analysis of Line Shapes

Chemical shifts determined by CP/MAS experiments have been used to characterize the secondary structure of solid polypeptides [16]. In this section, we extend the NMR line shape analysis from Section B.2 to the structural investigation of solid proteins and polypeptides.

Solution NMR lines tend toward Lorentzian shapes in the limit where 7*i = T2. Restricted molecular motion in the solid state gives rise to a statistical ensemble of Lorentzian lines for a given type of nucleus. The resulting broad line has Gaussian nature. Therefore, powdered samples characterized by little intermolecular motion should have Gaussian line shapes. Proteins and other polymers that might be expected to have some degree of molecular motion even in the solid will feature CP/MAS peaks with a fraction of Lorentzian character roughly proportional to the degree of motion.

Nonlinear regression analysis of CP/MAS data onto the appropriate Gaussian, Lorentzian, or mixed Gaussian-Lorentzian model (Section 3.B.2 and Table 3.8) yields the fraction of Lorentzian character of the peaks. An increased amount of Lorentzian character suggested increased local mobility of protein and polypeptide subunits.

Solid adamantane was investigated first as a standard. This small rigid molecule should have pure Gaussian shapes for both of its CP/MAS 13C lines. Indeed the all-Gaussian model gave a better fit than the Gaussian-Lorentzian model in nonlinear regression analysis. Peak areas were within 1% of values computed from the number of carbons in the molecule.

Figure 8.10 shows the CP/MAS 13C spectrum and nonlinear regression results for glutamic acid, and Figure 8.11 shows the results for polyglutamic

Figure 8.10 CP/MAS 13C NMR spectrum of solid glutamic acid. Points are experimental, and outer envelope line represents the best fit by nonlinear regression onto a multiple Gaussian-Lorentzian peak model (Table 3.8). Underlying peaks are the components computed from results of the nonlinear regression analysis. (The authors thank Dr. M. Alaimo for the original data.)

Figure 8.10 CP/MAS 13C NMR spectrum of solid glutamic acid. Points are experimental, and outer envelope line represents the best fit by nonlinear regression onto a multiple Gaussian-Lorentzian peak model (Table 3.8). Underlying peaks are the components computed from results of the nonlinear regression analysis. (The authors thank Dr. M. Alaimo for the original data.)

Figure 8.11 CP/MAS l3C NMR spectrum of powdered polyglutamic acid. Points are experimental, and outer envelope line represents the best fit by nonlinear regression onto a multiple Gaussian-Lorentzian peak model (Table 3.8). Underlying peaks are the components computed from results of the nonlinear regression analysis. (The authors thank Dr. M. Alaimo for the original data.)

Figure 8.11 CP/MAS l3C NMR spectrum of powdered polyglutamic acid. Points are experimental, and outer envelope line represents the best fit by nonlinear regression onto a multiple Gaussian-Lorentzian peak model (Table 3.8). Underlying peaks are the components computed from results of the nonlinear regression analysis. (The authors thank Dr. M. Alaimo for the original data.)

acid. The carbonyl resonances at about 170-175 ppm are approximately 80% Gaussian for both samples when using nonlinear regression onto the Gaussian-Lorentzian model (Table 3.8). One problem that can be seen in fitting the very narrow lines of glutamic acid is that a limited number of data points are available. This is probably responsible for the errors seen at the maxima of the peaks in the glutamic acid spectrum. Polyglutamic acid, with broader peaks, has more data points and shows better agreement between the data and the model at the peak..

The methyl and methylene peaks in the 5-70 ppm regions of the glutamic acid and polyglutamic acid spectra were predominantly Gaussian. Peaks for the polypeptide are significantly broader than for the monomeric glutamic acid. This broadening can be attributed to motion of the backbone secondary structure of polyglutamic acid.

Nonlinear regression analysis of the CP/MAS 13C spectrum of the protein lysozyme (Figure 8.12) revealed different motion characteristics from poly-

Figure 8.12 CP/MAS 13C NMR spectrum of solid lysozyme. Points are experimental, and outer envelope line represents the best fit by nonlinear regression onto a multiple Gaussian-Lorentzian peak model (Table 3.8). Underlying peaks are the components computed from results of the nonlinear regression analysis. (The authors thank Dr. M, Alaimo for the original data.)

Figure 8.12 CP/MAS 13C NMR spectrum of solid lysozyme. Points are experimental, and outer envelope line represents the best fit by nonlinear regression onto a multiple Gaussian-Lorentzian peak model (Table 3.8). Underlying peaks are the components computed from results of the nonlinear regression analysis. (The authors thank Dr. M, Alaimo for the original data.)

glutamic acid. Lysozyme has a carbonyl resonance with 50% Lorentzian character, indicating a rather high degree of motion. The methyl and methylene peaks were largely Gaussian.

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