From complete genomes to measures of substitution rate variability within and between proteins - PubMed (original) (raw)

Comparative Study

. 2000 Jul;10(7):991-1000.

doi: 10.1101/gr.10.7.991.

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Comparative Study

From complete genomes to measures of substitution rate variability within and between proteins

N V Grishin et al. Genome Res. 2000 Jul.

Abstract

Accumulation of complete genome sequences of diverse organisms creates new possibilities for evolutionary inferences from whole-genome comparisons. In the present study, we analyze the distributions of substitution rates among proteins encoded in 19 complete genomes (the interprotein rate distribution). To estimate these rates, it is necessary to employ another fundamental distribution, that of the substitution rates among sites in proteins (the intraprotein distribution). Using two independent approaches, we show that intraprotein substitution rate variability appears to be significantly greater than generally accepted. This yields more realistic estimates of evolutionary distances from amino-acid sequences, which is critical for evolutionary-tree construction. We demonstrate that the interprotein rate distributions inferred from the genome-to-genome comparisons are similar to each other and can be approximated by a single distribution with a long exponential shoulder. This suggests that a generalized version of the molecular clock hypothesis may be valid on genome scale. We also use the scaling parameter of the obtained interprotein rate distribution to construct a rooted whole-genome phylogeny. The topology of the resulting tree is largely compatible with those of global rRNA-based trees and trees produced by other approaches to genome-wide comparison.

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Figures

Figure 1

Figure 1

Interprotein rate variation. An empirical distribution function is shown for the fraction of unchanged sites (a), evolutionary distances (b), and normalized evolutionary distances (c) between likely orthologs for several genome pairs. For genome designations, see Methods. (d) Correlation between the variance of the distribution of normalized evolutionary distances and the mean distance between proteins in genome pairs. (e) Probability density function of interprotein substitution rate. The empirical density function of interprotein substitution rate estimated from distances obtained from genome comparisons (data), from approximation (approx) using formula (3), and from random sampling of the intraprotein rate distribution (random) are shown.

Figure 1

Figure 1

Interprotein rate variation. An empirical distribution function is shown for the fraction of unchanged sites (a), evolutionary distances (b), and normalized evolutionary distances (c) between likely orthologs for several genome pairs. For genome designations, see Methods. (d) Correlation between the variance of the distribution of normalized evolutionary distances and the mean distance between proteins in genome pairs. (e) Probability density function of interprotein substitution rate. The empirical density function of interprotein substitution rate estimated from distances obtained from genome comparisons (data), from approximation (approx) using formula (3), and from random sampling of the intraprotein rate distribution (random) are shown.

Figure 2

Figure 2

Intraprotein rate variation. (a) Dependence of the evolutionary distance d on the fraction of the unchanged sites u estimated from multiple alignments. The curve designated “min” shows the lower bound of the estimated distances. The curve “GAMMA 0.3” shows the d(u) dependency when the gamma distribution with α = 0.3 was used to describe intraprotein rate variation. (b) Estimation of the α parameter of the gamma distribution. The α values were extrapolated to u = 1. The obtained upper estimate for the α parameter is indicated by the red dotted line. (c) Probability density functions used to describe intraprotein rate variation. The figure illustrates two possible shapes of the density function: the L-shaped gamma distribution (GAMMA 0.3) and the bell-shaped log-normal distribution (LOGNORM 1.8). The parameter of the log-normal distribution was obtained by fitting the data from a in the same manner as for the gamma distribution. Dotted lines (LINEXP a;b) show two examples of the combination of linear and exponential densities given by the formula

[Formula: see text]

where A is a normalization constant and c is determined from the requirement of the mean x being equal to 1. The parameter a gives the point where the linear approximation ends; the parameter b determines the intercept.

Figure 3

Figure 3

A phylogenetic tree for complete genomes. The nodes supported by bootstrap values >70% are marked by red dots. The inferred root position is indicated by a black circle. For genome designations, see Methods.

References

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