## B1 Fits with Two Contributing Components

Proteins that exist as monomers in solution can give a better fit to the model in Table 9.1 for p = 2 that for p = 1. Possible reasons for this result include inhomogeneity or asymmetry in the electron density of the particle.

Because this finding was initially rather unexpected, regression analysis onto the models in Table 9.1 was investigated [4] for ribonuclease as a standard, using scattering data computed from crystallographic coordinates obtained from the Brookhaven Protein Data Bank. Scattered intensities were calculated by means of the Debye equation using the crystallographic coordinates and atomic radii. The resulting scattered intensities are shown as crosses in Figure 9.2. These symbols are somewhat obscured by the

Q LU Cd LU

O CO

1.00

0.75

0.50

1.00

0.75

0.50

Figure 9.2 Scattering data for ribonuclease computed from its crystal structure (+) fit on the model in Table 9.1 with p = 2. Line T is best fit to model in Table 9.1 with p = 2; lines B and A are the individual Gaussian components computed from the regression parameters. (Reprinted from [4] with permission, copyright © 1988 Academic Press.)

Figure 9.2 Scattering data for ribonuclease computed from its crystal structure (+) fit on the model in Table 9.1 with p = 2. Line T is best fit to model in Table 9.1 with p = 2; lines B and A are the individual Gaussian components computed from the regression parameters. (Reprinted from [4] with permission, copyright © 1988 Academic Press.)

regression line.) The fit to the model with p = 1 (not shown) has a relative root mean square error of 0.6% of the maximum and gives a radius of gyration of 14.28 A. By contrast, the p = 2 fit, shown as a solid line, has a relative root mean square error of less than 0.08%, Ra<2 = 14.43 ± 0.04 A and Rai = 0.9 ± 0.2 A. An extra sum of squares F test (see Section 3.C.1) showed that the p = 2 model was the best fit with >99% probability. This demonstrates clearly that a fit to a two-component model can result simply from the electron density characteristic of the protein's molecular structure.

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