pubmed.ncbi.nlm.nih.gov

Improved amino acid flexibility parameters - PubMed

Improved amino acid flexibility parameters

David K Smith et al. Protein Sci. 2003 May.

Abstract

Protein molecules exhibit varying degrees of flexibility throughout their three-dimensional structures, with some segments showing little mobility while others may be so disordered as to be unresolvable by techniques such as X-ray crystallography. Atomic displacement parameters, or B-factors, from X-ray crystallographic studies give an experimentally determined indication of the degree of mobility in a protein structure. To provide better estimators of amino acid flexibility, we have examined B-factors from a large set of high-resolution crystal structures. Because of the differences among structures, it is necessary to normalize the B-factors. However, many proteins have segments of unusually high mobility, which must be accounted for before normalization can be performed. Accordingly, a median-based method from quality control studies was used to identify outliers. After removal of outliers from, and normalization of, each protein chain, the B-factors were collected for each amino acid in the set. It was found that the distribution of normalized B-factors followed a Gumbel, or extreme value distribution, and the location parameter, or mode, of this distribution was used as an estimator of flexibility for the amino acid. These new parameters have a higher correlation with experimentally determined B-factors than parameters from earlier methods.

PubMed Disclaimer

Figures

Figure 1.
Figure 1.

Raw and normalized B-factors for 1FNA (Dickinson et al. 1994). (A) The experimentally observed B-factors for 1FNA with the Z = 3.0 (upper) and M = 3.5 (lower) cut-off lines indicated. (B) Normalized B-factors after outliers at Z ≥ 3.0 removed (gray circles), and after outliers at M ≥ 3.5 removed (triangles). The lack of variation in the normalized B-factors can be seen if outliers are not removed properly.

Figure 2.
Figure 2.

Plots of the normalized B-factors for each amino acid, counted in bins of 0.2 normalized units, with the Y axis giving the percentage of the B-factors in each bin. The best fit to the Gumbel distribution and the parameters of the fit (λ–location, δ–scale) for each amino acid are shown. Axes scales are the same in all plots.

Figure 3.
Figure 3.

The average autocorrelation function, over lags, or residue separations of 0 to 20, of the B-factors in a chain for the entire dataset. For residue separations of 1 to 7, the coefficients were 0.78, 0.61, 0.46, 0.34, 0.23, 0.15, and 0.09, respectively.

Figure 4.
Figure 4.

The distribution of the B-factors, as observed (black); as modeled by a mixture of three Gaussian functions (green; maximum-likelihood estimates, w = [0.04, 0.27, 0.69]; μ = [5.31, 1.29, −0.45]; σ = [4.19, 0.98, 0.58]); and as modeled by two Gumbel distributions, one with λ = −0.52; δ = 0.93 (red, maximum-likelihood estimate) and another with λ = −0.52; δ = 0.78 (blue, least-squares fit). The observed distribution was smoothed and the area under the curve was normalized to 1.

Figure 5.
Figure 5.

Comparison of the parameters developed here (G) with those of Vihinen et al. (1994; V) and those of Karplus and Schulz (1985; KS). The parameters by each method are shown for two flexible neighbors (red circles), one flexible and one rigid neighbor (green squares), two rigid neighbors (blue triangles), and for the complete data set (magenta diamonds).

Figure 6.
Figure 6.

Means, over the 290 (solid lines) and 196 (dashed lines) protein chain sets, of the correlation coefficients of the flexibility parameters, in sliding windows of lengths 1 to 13, with the experimental B-factors. (Circles) The parameters developed here, (triangles) those of Vihinen et al. (1994), and (squares) those of Karplus and Schulz (1985).

Similar articles

Cited by

References

    1. Altman, R.B., Hughes, C., Zhao, D., and Jardetsky, O. 1994. Compositional characteristics of relatively disordered regions in proteins. Prot. Pept. Lett. 1 120–127.
    1. Altschul, S.F. and Erickson, B.W. 1988. Significance levels for biological sequence comparison using non-linear similarity functions. Bull. Math. Biol. 50 77–92. - PubMed
    1. Altschul, S.F., Gish, W., Miller, W., Myers, E.W., and Lipman, D.J. 1990. Basic local alignment search tool. J. Mol. Biol. 215 403–410. - PubMed
    1. Berman, H.M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T.N., Weissig, H., Shindyalov, I.N., and Bourne, P.E. 2000. The Protein Data Bank. Nucl. Acids Res. 28 235–242. - PMC - PubMed
    1. Box, G.E.P., Jenkins, G.M., and Reinsel, G.C. 1994. Time series analysis. Forecasting and control, 3rd ed. Prentice Hall, Englewood Cliffs, NJ.

Publication types

MeSH terms

Substances

LinkOut - more resources