The covarion model for the evolution of proteins: parameter estimates and comparison with Holmquist, Cantor, and Jukes' stochastic model

Assembling an arsenal, the scorpion way

Background

For survival, scorpions depend on a wide array of short neurotoxic polypeptides. The venoms of scorpions from the most studied group, the Buthida, are a rich source of small, 23–78 amino acid-long peptides, well packed by either three or four disulfide bridges that affect ion channel function in excitable and non-excitable cells.

Results

In this work, by constructing a toxin transcripts data set from the venom gland of the scorpion Buthus occitanus israelis, we were able to follow the evolutionary path leading to mature toxin diversification and suggest a mechanism for leader peptide hyper-conservation. Toxins from each family were more closely related to one another than to toxins from other species, implying that fixation of duplicated genes followed speciation, suggesting early gene conversion events. Upon fixation, the mature toxin-coding domain was subjected to diversifying selection resulting in a significantly higher substitution rate that can be explained solely by diversifying selection. In contrast to the mature peptide, the leader peptide sequence was hyper-conserved and characterized by an atypical sub-neutral synonymous substitution rate. We interpret this as resulting from purifying selection acting on both the peptide and, as reported here for the first time, the DNA sequence, to create a toxin family-specific codon bias.

Conclusion

We thus propose that scorpion toxin genes were shaped by selective forces acting at three levels, namely (1) diversifying the mature toxin, (2) conserving the leader peptide amino acid sequence and intriguingly, (3) conserving the leader DNA sequences.

The estimation of genetic divergence

We have independently repeated the computer simulations on which Nei and Tateno (1978) base their criticism of REH theory and have extended the analysis to include mRNAs as well as proteins. The simulation data confirm the correctness of the REH method. The high average value of the fixation intensity mu 2 found by Nei and Tateno is due to two factors: 1) they reported only the five replications in which mu 2 was high, excluding the forty-five replications containing the more representative data; and 2) the lack of information, inherent to protein sequence data, about fixed mutations at the third nucleotide position within codons, as the values are lower when the estimate is made from the mRNAs that code for the proteins. REH values calculated from protein or nucleic acid data on the basis of the equiprobability of genetic events underestimate, not overestimate, the total fixed mutations. In REH theory the experimental data determine the estimate T2 of the time average number of codons that have been free to fix mutations during a given period of divergence. In the method of Nei and Tateno it is assumed, despite evidence to the contrary, that every amino acid position may fix a mutation. Under the latter assumption, the measure X2 of genetic divergence suggested by Nei and Tateno is not tenable: values of X2 for a alpha hemoglobin divergences are less than the minimum number of fixed substitutions known to have occurred. Within the context of REH theory, a paradox, first posed by Zuckerkandl, with respect to the high rate of covarion turnover and the nature of general function sites in proteins is resolved.

The current status of REH theory

The recent evaluation by Fitch (1980) of REH theory for macromolecular divergence is a severely erroneous and distorted analysis of our work over the past decade. We reply to those distortions here. At present, there is no factual basis for believing Fitch's assessment that corrections which move evolutionary estimates of total mutations fixed closer to the true distance must do so at the expense of an increased variance sufficient to compromise the value of the improvement. By direct calculation the variance in the estimates of total mutations fixed given by REH theory is comparable to that of other models now in the literature for the case in which genetic events are equiprobable. A general argument is given that suggests that, as we consider more and more carefully the selective, functional, and structural constraints on the evolution of genes and proteins, this variance may be expected to decrease toward a lower bound.

The old REH theory remains unsatisfactory and the new REH theory is problematical - a reply to Holmquist and Jukes

In response to criticism of REH theory (Fitch 1980), Holmquist and Jukes (1981) have mostly avoided the criticism or misunderstood it. Since they themselves state in their response that "Amino acid sequence data alone cannot be used to estimate total nucleotide substitutions," they agree with the criticism. Most of their paper treats the newer theory (here designated as the REHN theory) which attempts to use the nucleotide sequences encoding proteins to better estimate total nucleotide substitutions (Holmquist and Pearl 1980). Since I made no criticism of REHN theory, their comments are frequently beside the point of my original criticism of REH theory. Nevertheless, it is shown here that REHN theory is also unsatisfactory in that: One, the varions are now more clearly defined but in such a way as to preclude the same codon from suffering a nucleotide substitution in more than one evolutionary interval. Two, the set of codons that accepts silent substitutions is identical to the set that accepts amino acid changing nucleotide substitutions. Three, the uncertainty in the REH estimate is considerable in that alternative excellent fits to the same observational data may give alternative REH values that differ significantly even before stochastic variation and selective bias are considered. Four, the fit of their model to data is an irrelevancy where there are zero degrees of freedom.

A general method for biological inference: illustrated by the estimation of gene nucleotide transition probabilities

The method of maximum entropy inference developed by Jaynes can be a particularly useful method for obtaining unbiased estimates of biological parameters when the experimental knowledge about a system can be explicitly formulated. Base transition probabilities between genes, though central to evolutionary theory and understanding, present a difficult estimation problem because the ancestral genes are not experimentally accessible. The necessary estimates must therefore be made on the basis of experimental knowledge other than a direct frequency count of base replacements (A leads to C, for example) between contemporary genes. It is shown how maximum entropy inference together with the experimentally observed fact of compositional fidelity in a given gene family can be used to obtain meaningful gene base transition probabilities at each of the three nucleotide positions within codons. Both symmetric and asymmetric transition probabilities are considered. Tables of these probabilities are given for each codon position for the alpha-hemoglobin, beta-hemoglobin, myoglobin, cytochrome c, and the parvalbumin group genes. Tabular values of the average amino acid composition of these five protein families and the average nucleotide composition of their coding genes at varied codon loci are given. It is thus no longer necessary to assume in theories of evolutionary divergence equimolar base ratios A:C:G:U::1:1:1:1 or that each base has an equal chance of mutating to and being fixed as any one of the other three bases.