Richard Holmquist

Evolution of transfer RNA.

Abstract Evolution by gene duplication and subsequent divergence is indicated by similarities common to 43 different transfer RNAs. Pairwise comparisons of these tRNAs reveal additional similarity, greatest for certain pairs of tRNAs for the same amino acid in the same organism, and also occurring in certain pairs of tRNAs for different amino acids in the same organism. Although tRNAs functionally interact with several other molecules, there have been surprisingly few restrictions on the divergence of their primary structures. This divergence has proceeded so far that clear phylogenetic separations are absent in most cases: it it impossible to construct a coherent phylogeny for most of the 43. Selection and stochastic processes have both been active in the evolution of tRNA. Selection has favored moderate change more than expected and has reduced radical change below that expected from stochastic processes alone. Two obvious effects of selection are nine invariant loci, another five that are always purines and five others that are always pyrimidines, in the tRNAs involved in protein synthesis. In addition to these constraints in the primary nucleotide sequence, the method of “identical site equivalents”, introduced here, demonstrates that further constraints exist equivalent to about 12 additional invariant loci. These “invisible” restraints reflect disperse chemical forces maintaining the tertiary structure and reducing evolutionary divergence to an extent quantitatively comparable to that of the nine observable invariant loci. The average divergence (49·4%) for pairs of tRNAs for different amino acids involved in protein synthesis represents an equilibrium between natural selection and stochastic processes. These tRNAs have had time to diverge nearly to the 75% maximum expected from stochastic process alone; this is shown by comparing the two glycine tRNAs involved in peptidoglycan synthesis with tRNAs for different amino acids participating in polypeptide synthesis. The rates of nucleotide replacements in genes coding for the tRNAs and the cytochromes c are about the same: 2 × 10 −10 replacements per nucleotide site per year.

Improved procedures for comparing homologous sequences in molecules of proteins and nucleic acids

Abstract Tables are given which permit, with minimal effort, a rigorous statistical comparison of contemporary homologous DNAs or proteins. The Tables correct without approximation for multiple hits at the same base site, back mutation, multiplyhit codons, the degeneracy of the genetic code, chance identity of two homologous sites, and when the concept of minimum mutation distance is used to analyze the data, for the misclassification of mutagenic events by this concept. The concept of minimum mutation distance is critically examined and found to be deficient as an analytical tool from both experimental and theoretical points of view unless modified to take into account the above phenomena. This modification is described, and the probability distribution of the minimum mutation distance per codon is derived. The above results are presented graphically so that any given experimental situation can be analyzed by inspection, without making lengthy numerical calculations. The results are complete in that they extract the maximum possible information from the experimental data under the conditions for which the procedures are valid.

Theoretical foundations for a quantitative approach to paleogenetics. Part I: DNA.

SummaryBy example, taken from actual experimental data, it is shown that neglecting the phenomena of multiple hits, back mutation, and chance coincidence can lead to errors larger than 100% in the calculated value of the average number of nucleotide base differences to be expected between two homologous polynucleotides. Mathematical formulas are derived to correct quantitatively for these effects, which although they do not change the topology of the phylogenetic trees derived by others, do change materially the quantitative aspects of these phylogenies, such as the length of the legs of the trees. In particular the following problems are solved without approximation:1.Consider a polynucleotide which containsL individual nucleotides. Let exactlyX mutagenic events occur randomly along the length of this polynucleotide. After theX mutagenic events have occurred, in general, a numberx, which is less thanL, nucleotide sites will have been hit; for example, allX mutagenic events might occur at the same nucleotide site. LetN (x) designate the average number of nucleotide sites which have been hit. An explicit formula forN (x) is derived.2.The average numberN′ (x) of nucleotide sites that have been altered will in general be less thanN (x) because of back mutations. An explicit expression forN′ (x) is given.3.An explicit formula for the average number of nucleotide base differencesN (D) between two homologous polynucleotides of the same length is derived, including correction for chance coincidences.

Stochastic versus augmented maximum parsimony method for estimating superimposed mutations in the divergent evolution of protein sequences. Methods tested on cytochrome c amino acid sequences

Abstract Two ways of estimating superimposed fixed mutations in the divergent descent of proteins are examined. One method counts these in terms of a Poisson process operating within selective constraints. The other uses the maximum parsimony method to connect the contemporary sequences through intervening ancestral sequences in an evolutionary tree, and then, from the distribution of fixed mutations in dense regions of this genealogy, estimates how many fixations should be added to sparse regions. An algorithm is described which determines such augmented distances. The two methods yield similar estimates of genetic divergence when tested on a series of cytochrome c amino acid sequences. Within those constraints imposed by Darwinian selection, the dynamic behavior of the evolutionary divergence of proteins is described by the probabilistic pathways of the stochastic model. The parsimony model provides a valid Aufbau-Prinzip for examining which of those pathways occurred along a particular lineage. Concordance of the numerical magnitudes of genetic divergence estimates made by the two methods reveals them as logically consistent complements, not as mutually exclusive antagonists. Both methods indicate that cytochrome c has evolved in a non-uniform manner over geological time and more rapidly than previously estimated.

Evolutionary Clock: Nonconstancy of Rate in Different Species

By using various methods for comparing polypeptide sequences we find that the evolutionary divergence of rattlesnake cytochrome c from cytochromes c of species in other classes has been more rapid than that of cytochrome c of another reptile, the snapping turtle. This suggests that the evolutionary rate of change of cytochromes c is species-dependent as well as time-dependent.

The spatial distribution of fixed mutations within genes coding for proteins

SummaryWe have examined the extensive amino acid sequence data now available for five protein families — the α crystallin A chain, myoglobin, alpha and beta hemoglobin, and the cytochromesc — with the goal of estimating the true spatial distribution of base substitutions within genes that code for proteins. In every case the commonly used Poisson density failed to even approximate the experimental pattern of base substitution. For the 87 species of beta hemoglobin examined, for example, the probability that the observed results were from a Poisson process was the minuscule 10−44. Analogous results were obtained for the other functional families. All the data were reasonably, but not perfectly, described by the negative binomial density. In particular, most of the data were described by one of the very simple limiting forms of this density, the geometric density. The implications of this for evolutionary inference are discussed. It is evident that most estimates of total base substitutions between genes are badly in need of revision.

The evolution of the globin family genes: Concordance of stochastic and augmented maximum parsimony genetic distances for α hemoglobin, β hemoglobin and myoglobin phylogenies☆

Abstract We compare the amino acid sequences of 70 globing, representing the following families: (a) α hemoglobin chains; (b) β hemoglobin chains; (c) myoglobins; (d) two lamprey, a mollusc, and two plant globins. The comparisons show a convergence of maximal and minimal estimates of genetic differences as calculated respectively by the stochastic and maximum parsimony procedures, thus demonstrating for the first time the logical consistency and complementarity of the two procedures. Evolutionary rates are non-constant, varying over a range of 1 to 75 nucleotide replacements per 100 codons per 108 years. These rate differentials are resolved into two components (a) due to change in the number of codon sites free to fix mutations during the period of divergence of the species involved; (b) due to change in fixation intensity at each site. These two components also show non-uniformity along different lineages. Positive Darwinian natural selection can bring about an increase in either component, and negative or stabilizing selection in protein evolution can lead to decreases. Accelerated rates of globin evolution were found in lineages of cold-blooded vertebrates, some marsupials, and early placental mammals, while slower rates were found in warm-blooded vertebrates, especially higher primates. One manifestation of negative selection in the globins is that minimal 3-base type amino acid replacements occur less frequently than would be expected if base replacements had occurred and were accepted at random. The selection against these replacements is not due to atypical behavior with respect to the change in electrical charge involved in the replacements. Interestingly, the globins from the lamprey, sea hare and the legumes are as distant from one another as are α-hemoglobin and β-hemoglobin from myoglobin.

Theoretical foundations for quantitative paleogenetics

REH theory is extended by deriving the theoretical equations that permit one to analyze the nonrandom molecular divergence of homologous genes and proteins. The nonrandomicities considered are amino acid and base composition, the frequencies with which each of the four nucleotides is replaced by one of the other three, unequal usage of degenerate codons, distribution of fixed base replacements at the three nucleotide positions within codons, and distributions of fixed base replacements among codons. The latter two distributions turn out to dominate the accuracy of genetic distance estimates. The negative binomial density is used to allow for the unequal mutability of different codon sites, and the implications of its two limiting forms, the Poisson and geometric distributions, are considered. It is shown that the fixation intensity — the average number of base replacements per variable codon - is expressible as the simple product of two factors, the first describing the asymmetry of the distribution of base replacements over the gene and the second defining the ratio of the average probability that a codon will fix a mutation to the probability that it will not. Tables are given relating these features to experimentally observable quantities inα hemoglobin,β hemoglobin, myoglobin, cytochromec, and the parvalbumin group of proteins and to the structure of their corre-sponding genes or mRNAs. The principal results are (1) more accurate methods of estimating parameters of evolutionary interest from experimental gene and protein sequence data, and (2) the fact that change in gene and protein structure has been a much less efficient process than previously believed in the sense of requiring many more base replacements to effect a given structural change than earlier estimation procedures had indicated. This inefficiency is directly traceable to Darwinian selection for the nonrandom gene or protein structures necessary for biological function. The application of these methods is illustrated by detailed consideration of the rabbitα -andβ hemoglobin mRNAs and the proteins for which they code. It is found that these two genes are separated by about 425 fixed base replacements, which is a factor of two greater than earlier estimates. The replacements are distributed over approximately 114 codon sites that were free to accept base mutations during the divergence of these two genes.

Empirical support for a stochastic model of evolution

SummaryThe stochastic model of molecular evolution was used to makea priori predictions for the total number of one-step nucleotide changes required to account for a given number of amino acid substitutions between two homologous proteins. These predictions are now found to be concordant with empirical data summarized by Dayhoff, Eck and Park (1969). Correction factors are derived for adjusting the “leg lengths” of phylogenetic trees. It is shown that the operations of constructing the phylogenetic tree and applying the correction algorithm are not commutative with respect to obtaining the leg lengths. The effect of this on certain published phylogenies is discussed. It is suggested that, as a first approximation, at any given point in evolutionary time, enthalpic (selective) forces determine the number and position of those codon sites which are free to vary, whereas within these variable sites, entropic (random) processes determine the course of evolution at the molecular level.

The method of parsimony: an experimental test and theoretical analysis of the adequacy of molecular restoration studies☆

Abstract The ability of the principle of parsimony to accurately reconstruct molecular evolutionary pathways from an analysis of amino acid or nucleic acid sequences from extant organisms is tested by direct comparison with a known pathway. Topological errors occur under specified conditions. Importantly, given no errors in the topology, and error-free experimental sequences, the ancestral sequences inferred by the parsimony principle err significantly, the magnitude of the error increasing with the distance of the nodal sequence from the present. These errors are irreducible as an inherent consequence of any evolutionary process in which chance processes operate within the constraints imposed by Darwinian selection. Formulae are derived which predict the errors in the ancestral sequences from a knowledge of only the internodal distances. The parsimony solution is not a reliably good solution. It is necessary to develop a detailed understanding of the interaction between chance processes and natural selection to further advance our understanding of molecular change in proteins and nucleic acids.