The evolution of proteins from random amino acid sequences: II. Evidence from the statistical distributions of the lengths of modern protein sequences.

This paper continues an examination of the hypothesis that modern proteins evolved from random heteropeptide sequences. In support of the hypothesis, White and Jacobs (1993, J Mol Evol 36:79-95) have shown that any sequence chosen randomly from a large collection of nonhomologous proteins has a 90% or better chance of having a lengthwise distribution of amino acids that is indistinguishable from the random expectation regardless of amino acid type. The goal of the present study was to investigate the possibility that the random-origin hypothesis could explain the lengths of modern protein sequences without invoking specific mechanisms such as gene duplication or exon splicing. The sets of sequences examined were taken from the 1989 PIR database and consisted of 1,792 "super-family" proteins selected to have little sequence identity, 623 E. coli sequences, and 398 human sequences. The length distributions of the proteins could be described with high significance by either of two closely related probability density functions: The gamma distribution with parameter 2 or the distribution for the sum of two exponential random independent variables. A simple theory for the distributions was developed which assumes that (1) protoprotein sequences had exponentially distributed random independent lengths, (2) the length dependence of protein stability determined which of these protoproteins could fold into compact primitive proteins and thereby attain the potential for biochemical activity, (3) the useful protein sequences were preserved by the primitive genome, and (4) the resulting distribution of sequence lengths is reflected by modern proteins. The theory successfully predicts the two observed distributions which can be distinguished by the functional form of the dependence of protein stability on length. The theory leads to three interesting conclusions. First, it predicts that a tetra-nucleotide was the signal for primitive translation termination. This prediction is entirely consistent with the observations of Brown et al. (1990a,b, Nucleic Acids Res 18:2079-2086 and 18: 6339-6345) which show that tetra-nucleotides (stop codon plus following nucleotide) are the actual signals for termination of translation in both prokaryotes and eukaryotes. Second, the strong dependence of statistical length distributions on sequence-termination signaling codes implies that the evolution of stop codons and translation-termination processes was as important as gene splicing in early evolution. Third, because the theory is based upon a simple no-exon stochastic model, it provides a plausible alternative to a limited universe of exons from which all proteins evolved by gene duplication and exon splicing (Dorit et al. 1990, Science 250:1377-1382).