## B2 Implications from Analysis of a Theoretical Spectrum of Lysozyme

Torii and Tasumi [6-8] calculated the theoretical FT-IR amide I spectrum from the three-dimensional X-ray crystal structure of lysozyme, using a Gaussian envelope of each peptide bond oscillator with a half-width at half-height of 3.0 cm"1. This analysis predicted 16 peaks in the amide I envelope, although 2 of these peaks had very small fractional areas. The force constants used were optimized for D20 and not H20. Therefore, we

Table 7.4 Fractions of Different Structural Features of Lysozyme from the FT-IR Regression Analysis Compared to Results from X-Ray Diffraction

Fractions: Helix Extended Disordered Turns

Source from Fourier deconvoluted spectrum

Amide I 0.320 0.204 0.131 0.311

Amide II 0.278 0.175 0.183 0.364 Source from original spectrum

Amide I 0.266 0.176 0.174 0.384

Amide II 0.323 0.176 0.090 0.411

Average ± SD 0.297 ± 0.029 0.183 ± 0.014 0.145 ± 0.043 0.365 ± 0.042

" As fraction of f3 turns only, does not include all the extended features of the protein. b Difference between 1 and the sum of all other reported fractions.

cannot directly compare the preceding analysis of experimental results for lysozyme with this theoretical spectrum, but we can analyze the published theoretical spectrum [6-8] into its component Gaussian peaks by the procedure in Table 7.1.

Figure 7.5 shows the Fourier deconvoluted theoretical FT-IR spectrum [6] with the best fit of a model consisting of the sum of 14 Gaussian bands. Attempts to use fewer than 14 bands resulted in poorer fits, as shown by the extra sum of squares F test. Addition of more peaks to the regression model caused the areas of the extra bands to approach a zero or negative values. Thus, the analysis by the protocols outlined in Table 7.1 identified all of the major component peaks in this theoretical spectrum.

We can compare these results with an analysis of the experimental spectrum of lysozyme in the amide I region only. The experimental Fourier deconvoluted FT-IR spectrum of lysozyme using an resolution enhancement factor (REF) of 3.8 is shown in Figure 7.6, with the graphical results of a regression analysis. Here, the amide I region is fit to the sum of 14 Gaussian peaks. A small standard deviation of the regression (within 0.1% of maximum A) and a random deviation plot were obtained. No additional bands could be successfully added to the 14 band model. Apparently, the two additional bands are too small to be detected. Good agreement of calculated and experimental data can be seen graphically. None of the

WAVENUMBER, cm'

Figure 7.5 Best fit by nonlinear regression analysis to the theoretical amide I band of lysozyme. One outer envelope line is the theoretical spectrum; the second is the best fit to the model in Table 7.1. (Reprinted with permission from [9], copyright by the American Chemical Society.)

WAVENUMBER, cm'

Figure 7.5 Best fit by nonlinear regression analysis to the theoretical amide I band of lysozyme. One outer envelope line is the theoretical spectrum; the second is the best fit to the model in Table 7.1. (Reprinted with permission from [9], copyright by the American Chemical Society.)

component bands were unacceptably broad, and the fit was similar to that when both amide I and II bands were analyzed (cf. Figures 7.2-7.4). Thus, the 14-peak model gave a successful best fit for both the theoretical and experimental amide I data for lysozyme.

Although the theoretical spectrum contained only an amide I band, the amide II band also appears in spectra obtained in water. We wish to point out a consequence of fitting only the amide I band in the spectrum. Attempts to fit the 14 bands to the experimental amide I envelope of the FD spectrum of lysozyme only, using a resolution enhancement factor of 2.5 ended with bands at the highest and lowest frequencies becoming unacceptably broad (Figure 7.7). This result indicates a problem, because the component bands arise from essentially the same type of vibrational mode in different environments and all band widths should be similar. The calculated and experimental outer envelopes of the amide I band show poorer agreement than in Figure 7.6. However, if the amide II and amide I bands are fit simultaneously (using REF of 2.5 and a model with 29 Gaussian components), inordinately large value bandwidths are not observed (see Figure 7.2) and the fit becomes acceptable. Therefore, it is important to use the amide II band with the amide I when analyzing the FD spectra generated using low REF values of 2-3. Calculations excluding the amide II envelope become very sensitive to the value of REF used, and REF values that are too small may lead to large errors in the estimated secondary structures.

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