The relationship between the fractions of protein secondary structural components as determined from X-ray crystallographic data by the procedures of Kabsch and Sander (KS) and of Levitt and Greer (LG) is analyzed by neural network analysis of these two tabulations of literature data. A linear relationship between the KS and LG reductions of X-ray data to secondary structure descriptors is demonstrated by a regression analysis of the relationships between these sets of structural parameters. Back-propagation neural network analysis was then used to derive equations for determination of the most probable fractions of beta-sheet, bend, turn, and "other" conformations given the fraction of alpha-helix in a globular protein. The deviation of the X-ray values for beta-sheet from that determined with these equations was shown to have a variance that exponentially decreased with increasing fraction of alpha-helix. A second neural network analysis showed that knowledge of both the alpha-helical and beta-sheet fractions in a protein significantly reduces the uncertainty in prediction of the other components of the secondary structure. These analyses provide insight into the nature of the data sets derived from crystal structures. Since these complications of crystal structure data are commonly used as reference information for quantitative evaluation of spectra (for example, FTIR, Raman, and electronic or vibrational circular dichroism) in terms of secondary structure, such internal correlations in the reference sets may have significant effects on the stability of spectroscopic analyses derived from them.

Department of Chemical Physics Faculty of Mathematics and Physics Charles University Prague Czechoslovakia

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