The Path from the RNA World

We describe a sequential (step by step) Darwinian model for the evolution of life from the late stages of the RNA world through to the emergence of eukaryotes and prokaryotes. The starting point is our model, derived from current RNA activity, of the RNA world just prior to the advent of genetically-encoded protein synthesis. By focusing on the function of the protoribosome we develop a plausible model for the evolution of a protein-synthesizing ribosome from a high-fidelity RNA polymerase that incorporated triplets of oligonucleotides. With the standard assumption that during the evolution of enzymatic activity, catalysis is transferred from RNA → RNP → protein, the first proteins in the ``breakthrough organism' (the first to have encoded protein synthesis) would be nonspecific chaperone-like proteins rather than catalytic. Moreover, because some RNA molecules that pre-date protein synthesis under this model now occur as introns in some of the very earliest proteins, the model predicts these particular introns are older than the exons surrounding them, the ``introns-first' theory. Many features of the model for the genome organization in the final RNA world ribo-organism are more prevalent in the eukaryotic genome and we suggest that the prokaryotic genome organization (a single, circular genome with one center of replication) was derived from a ``eukaryotic-like' genome organization (a fragmented linear genome with multiple centers of replication). The steps from the proposed ribo-organism RNA genome → eukaryotic-like DNA genome → prokaryotic-like DNA genome are all relatively straightforward, whereas the transition prokaryotic-like genome → eukaryotic-like genome appears impossible under a Darwinian mechanism of evolution, given the assumption of the transition RNA → RNP → protein. A likely molecular mechanism, ``plasmid transfer,' is available for the origin of prokaryotic-type genomes from an eukaryotic-like architecture. Under this model prokaryotes are considered specialized and derived with reduced dependence on ssRNA biochemistry. A functional explanation is that prokaryote ancestors underwent selection for thermophily (high temperature) and/or for rapid reproduction (r selection) at least once in their history. Received: 14 January 1997 / Accepted: 19 May 1997     

The Evolution of Hexamerins and the Phylogeny of Insects

The evolutionary relationships among arthropod hemocyanins and insect hexamerins were investigated. A multiple sequence alignment of 12 hemocyanin and 31 hexamerin subunits was constructed and used for studying sequence conservation and protein phylogeny. Although hexamerins and hemocyanins belong to a highly divergent protein superfamily and only 18 amino acid positions are identical in all the sequences, the core structures of the three protein domains are well conserved. Under the assumption of maximum parsimony, a phylogenetic tree was obtained that matches perfectly the assumed phylogeny of the insect orders. An interesting common clade of the hymenopteran and coleopteran hexamerins was observed. In most insect orders, several paralogous hexamerin subclasses were identified that diversified after the splitting of the major insect orders. The dipteran arylphorin/LSP-1-like hexamerins were subject to closer examination, demonstrating hexamerin gene amplification and gene loss in the brachyceran Diptera. The hexamerin receptors, which belong to the hexamerin/hemocyanin superfamily, diverged early in insect evolution, before the radiation of the winged insects. After the elimination of some rapidly or slowly evolving sequences, a linearized phylogenetic tree of the hexamerins was constructed under the assumption of a molecular clock. The inferred time scale of hexamerin evolution, which dates back to the Carboniferous, agrees with the available paleontological data and reveals some previously unknown divergence times among and within the insect orders. Received: 4 August 1997 / Accepted: 29 October 1997     

Taking Variation of Evolutionary Rates Between Sites into Account in Inferring Phylogenies

As methods of molecular phylogeny have become more explicit and more biologically realistic following the pioneering work of Thomas Jukes, they have had to relax their initial assumption that rates of evolution were equal at all sites. Distance matrix and likelihood methods of inferring phylogenies make this assumption; parsimony, when valid, is less limited by it. Nucleotide sequences, including RNA sequences, can show substantial rate variation; protein sequences show rates that vary much more widely. Assuming a prior distribution of rates such as a gamma distribution or lognormal distribution has deservedly been popular, but for likelihood methods it leads to computational difficulties. These can be resolved using hidden Markov model (HMM) methods which approximate the distribution by one with a modest number of discrete rates. Generalized Laguerre quadrature can be used to improve the selection of rates and their probabilities so as to more nearly approach the desired gamma distribution. A model based on population genetics is presented predicting how the rates of evolution might vary from locus to locus. Challenges for the future include allowing rates at a given site to vary along the tree, as in the ``covarion' model, and allowing them to have correlations that reflect three-dimensional structure, rather than position in the coding sequence. Markov chain Monte Carlo likelihood methods may be the only practical way to carry out computations for these models. Received: 8 February 2001 / Accepted: 20 May 2001     

On the Evolution of Redundancy in Genetic Codes

We simulate a deterministic population genetic model for the coevolution of genetic codes and protein-coding genes. We use very simple assumptions about translation, mutation, and protein fitness to calculate mutation-selection equilibria of codon frequencies and fitness in a large asexual population with a given genetic code. We then compute the fitnesses of altered genetic codes that compete to invade the population by translating its genes with higher fitness. Codes and genes coevolve in a succession of stages, alternating between genetic equilibration and code invasion, from an initial wholly ambiguous coding state to a diversified frozen coding state. Our simulations almost always resulted in partially redundant frozen genetic codes. Also, the range of simulated physicochemical properties among encoded amino acids in frozen codes was always less than maximal. These results did not require the assumption of historical constraints on the number and type of amino acids available to codes nor on the complexity of proteins, stereochemical constraints on the translational apparatus, nor mechanistic constraints on genetic code change. Both the extent and timing of amino-acid diversification in genetic codes were strongly affected by the message mutation rate and strength of missense selection. Our results suggest that various omnipresent phenomena that distribute codons over sites with different selective requirements—such as the persistence of nonsynonymous mutations at equilibrium, the positive selection of the same codon in different types of sites, and translational ambiguity—predispose the evolution of redundancy and of reduced amino acid diversity in genetic codes. Received: 21 December 2000 / Accepted: 12 March 2001     

Exploring Nonnatural Evolutionary Pathways by Saturation Mutagenesis: Rapid Improvement of Protein Function

Random point mutagenesis does not access a large fraction of protein sequence space corresponding to primarily nonconservative amino acid substitutions. The cost of this limitation during directed evolution is unknown. Random point mutagenesis over the entire gene encoding the psychrophilic protease subtilisin S41 identified a pair of residues (Lys211 and Arg212) where mutations provided significant increases in thermostability. These were subjected to saturation mutagenesis to test whether the amino acids not easily accessible by point mutagenesis provide even better ``solutions' to the thermostabilization challenge. A significant fraction of these variants surpassed the stability of the variants with point mutations. DNA sequencing revealed highly hydrophobic residues in the four most stable variants (Pro/Ala, Pro/Val, Leu/Val, and Trp/Ser). These nonconservative replacements, accessible only by multiple (two to three) base substitutions in a single codon, would be extremely rare in a point mutation library. Such replacements are also extremely rare in natural evolution. Saturation mutagenesis may be used advantageously during directed evolution to explore nonnatural evolution pathways and enable rapid improvement in protein traits. Received: 15 March 1999 / Accepted: 28 June 1999     

Conservation of Surfactant Protein A: Evidence for a Single Origin for Vertebrate Pulmonary Surfactant

Surface tension is reduced at the air–liquid interface in the lung by a mixture of lipids and proteins termed pulmonary surfactant. This study is the first to provide evidence for the presence of a surfactant-specific protein (Surfactant Protein A—SP-A) in the gas-holding structures of representatives of all the major vertebrate groups. Western blot analysis demonstrated cross-reactivity between an antihuman SP-A antibody and material lavaged from lungs or swimbladders of members from all vertebrate groups. Immunocytochemistry localized this SP-A–like protein to the air spaces of lungs from the actinopterygiian fish and lungfish. Northern blot analysis indicated that regions of the mouse SP-A cDNA sequence are complementary to lung mRNA from all species examined. The presence of an SP-A–like protein and SP-A mRNA in members of all the major vertebrate groups implies that the surfactant system had a single evolutionary origin in the vertebrates. Moreover, the evolution of the surfactant system must have been a prerequisite for the evolution of airbreathing. The presence of SP-A in the goldfish swimbladder demonstrates a role for the surfactant system in an organ that is no longer used for airbreathing. Received: 5 March 1997 / Accepted: 14 June 1997     

Circular Permutations in the Molecular Evolution of DNA Methyltransferases

Circular permutations of genes during molecular evolution often are regarded as elusive, although a simple model can explain these rearrangements. The model assumes that first a gene duplication of the precursor gene occurs in such a way that both genes become fused in frame, leading to a tandem protein. After generation of a new start codon within the 5′ part of the tandem gene and a stop at an equivalent position in the 3′ part of the gene, a protein is encoded that represents a perfect circular permutation of the precursor gene product. The model is illustrated here by the molecular evolution of adenine-N⁶ DNA methyltransferases. β- and γ-type enzymes of this family can be interconverted by a single circular permutation event. Interestingly, tandem proteins, proposed as evolutionary intermediates during circular permutation, can be directly observed in the case of adenine methyltransferases, because some enzymes belonging to type IIS, like the FokI methyltransferase, are built up by two fused enzymes, both of which are active independently of each other. The mechanism for circular permutation illustrated here is very easy and applicable to every protein. Thus, circular permutation can be regarded as a normal process in molecular evolution and a changed order of conserved amino acid motifs should not be interpreted to argue against divergent evolution. Received: 17 November 1998 / Accepted: 19 February 1999     

A theoretical method for evaluating the relative importance of positive selection and neutral drift from observed base changes

To evaluate the relative importance of positive selection and neutral drift from the nucleotide base changes observed in the homologous alignment of genes, a theoretical equation of base changes is formulated by including both the influence of selection and the base substitutions due to mutations. Under the assumption that the average rate of base substitutions estimated from synonymous changes is the ``true' mutation rate applicable at all positions, this method is applied to the vertebrate globin gene family, and evaluates the departures of base change rates from the ``true' mutation rate at the first and second codon positions as a consequence of preferential selection for the conservation of important function. In addition to the strong effect of selection on the amino acid residues in the internal region mostly common to myoglobin and hemoglobin chains, the distinctive directions of selective parameter values are seen at sites on the globin surface, distinguishing the subunit contact residues of hemoglobins from the polar residues on the surface of myoglobins. Moreover, this effect of selection distinguishing between the myoglobin and hemoglobin chain genes becomes weaker in cold-blooded vertebrates, especially in fish, strongly suggesting the possibility that the clear distinction between these globins is a result of selection out of the changes regarded as neutral ones in an ancestor of vertebrates. Thus, the present method may also serve to investigate the homology of many other proteins from the aspect of molecular evolution, mainly focusing on the evolution of their biological functions. Received: 2 January 1996 / Accepted: 20 February 1997     

The Molecular Evolutionary History of a Winged Bean α-Chymotrypsin Inhibitor and Modeling of Its Mutations Through Structural Analyses

A serine protease inhibitor of the Kunitz-STI (soybean trypsin inhibitor) family, isolated from the legume seeds of winged bean, was found to inhibit chymotrypsin at a 1:2 stoichiometric ratio. When the structure was determined in our laboratory, it was found to form a characteristic β-trefoil fold, which is also seen in other proteins from distant families and sources. The folding organization divides the protein into three approximately equal subdomains related by a pseudo-threefold axis of symmetry passing parallel to the barrel axis of the trefoil. Following the now established idea that the present-day genes originated from ancestral minigenes through evolution, the origin of the proteins having this β-trefoil organization is scrutinized using its subdomain motif as the search probe. The results, based mainly on structural analyses, indicate the independent existence of such a motif, mimicking the unknown ancestral protein(s) that might have been distributed in nature, not only by gene duplication, but also by insertion and permutation in other folds. The understanding led to a hypothesis for the possible origin of the Kunitz-STI family. On the basis of this model of evolution, structurally hypervariable regions were located on the protein where mutations could be designed and a broad range of engineering of the protein's activity could be conceived. Received: 20 January 1999 / Accepted: 6 October 1999     

Sperm Nuclear Basic Proteins (SNBPs) of Agnathans and Chondrichthyans: Variability and Evolution of Sperm Proteins in Fish

We have characterized for the first time SNBPs from the hagfish Eptatratus stouti (Myxini) and the lamprey Lampetra tridentatus (Cephalaspidomorphi) and have found that histones are the major protein components of the sperm of these agnathans. We have also conducted a systematic analysis of SNBPs from different groups of chondrichthyan fishes, including the skate Raja rhina and seven species of sharks. Together with our previous data showing the sporadic nature of SNBP evolution in bony fish (Saperas, N., Ausio, J., Lloris, D. and Chiva, M. [1994] J. Mol. Evol. 39: 282–295), the present study provides a unique insight into the overall evolutionary complexity and variability of the nuclear sperm proteins of fishes. It would appear that despite the discontinuous evolution of these proteins, the macroevolutionary pattern of histone (H type) → protamine-like (PL type) → protamine (P type) has been conserved in fish evolution, as it has in the evolution of other Deuterostomes. Received: 11 June 1996 / Accepted: 6 August 1996     

Episodic Evolution of Protein Hormones in Mammals

Pituitary growth hormone (GH) and prolactin have been shown previously to display a pattern of evolution in which episodes of rapid change are imposed on a low underlying basal rate (near-stasis). This study was designed to explore whether a similar pattern is seen in the evolution of other protein hormones in mammals. Seven protein hormones were examined (with the common α-subunit of the glycoprotein hormones providing an additional polypeptide for analysis)—those for which sequences from at least four eutherian orders are available with a suitable non-eutherian outgroup. Six of these (GH, prolactin, insulin, parathyroid hormone, glycoprotein hormone α-subunit, and luteinizing hormone β-subunit) showed markedly variable evolutionary rates in each case with a pattern of a slow basal rate and bursts of rapid change, the precise positions of the bursts varying from protein to protein. Two protein hormones (follicle-stimulating hormone β-subunit and thyroid-stimulating hormone β-subunit) showed no significant rate variation. Based on the sequences currently available, and pooling data from all eight proteins, the phase of slow basal change occupied about 85% of the sampled evolutionary time, but most evolutionary change (about 62% of the substitutions accepted) occurred during the episodes of rapid change. It is concluded that, in mammals at least, a pattern of prolonged periods of near-stasis with occasional episodes of rapid change provides a better model of evolutionary change for protein hormones than the one of constant evolutionary rates that is commonly favored. The mechanisms underlying this episodic evolution are not yet clear, and it may be that they vary from one group to another; in some cases, positive selection appears to underlie bursts of rapid change. Where gene duplication is associated with a period of accelerated evolution this often occurs at the end rather than the beginning of the episode. To what extent the type of pattern seen for protein hormones can be extended to other proteins remains to be established. Received: 10 October 2000 / Accepted: 18 December 2000     

Episodic Evolution of Protein Hormones: Molecular Evolution of Pituitary Prolactin

Previous studies have shown that pituitary growth hormone displays an episodic pattern of evolution, with a slow underlying evolutionary rate and occasional sustained bursts of rapid change. The present study establishes that pituitary prolactin shows a similar pattern. During much of tetrapod evolution the sequence of prolactin has been strongly conserved, showing a slow basal rate of change (approx 0.27 × 10⁹ substitutions/amino acid site/year). This rate has increased substantially (∼12- to 38-fold) on at least four occasions during eutherian evolution, during the evolution of primates, artiodactyls, rodents, and elephants. That these increases are real and not a consequence of inadvertant comparison of paralogous genes is shown (for at least the first three groups) by the fact that they are confined to mature protein coding sequence and not apparent in sequences coding for signal peptides or when synonymous substitutions are examined. Sequences of teleost prolactins differ markedly from those of tetrapods and lungfish, but during the course of teleost evolution the rate of change of prolactin has been less variable than that of growth hormone. It is concluded that the evolutionary pattern seen for prolactin shows long periods of near-stasis interrupted by occasional bursts of rapid change, resembling the pattern seen for growth hormone in general but not in detail. The most likely basis for these bursts appears to be adaptive evolution though the biological changes involved are relatively small. Received: 31 August 1999 / Accepted: 9 February 2000     

The origin of the genetic code and protein synthesis

A model for a parallel evolution of the genetic code and protein synthesis is presented. The main tenet of this model is that the genetic code, that is, a correspondence between nucleotide and aminoacid coding units, originated from sequence-specific interaction between abiotically synthesized polynucleotides and polypeptides. A sequence-specific binding between oligonucleotides and oligopeptides is supported by experimental findings. Moreover, it is parsimonious enough to be consistent with the relatively simple chemistry of a primordial environment. Proximity between peptides and RNA increased the rate of formation of ester bonds between them. This lead to the accumulation of sequence-specific polypeptide-polynucleotide pairs, that is, of primordial-loaded tRNA. Condensation of short polypeptides into longer products could be catalyzed by a sequence-specific juxtaposition of loaded tRNA over complementary RNA, originating the core of protein synthesis. The accumulation of useful encoded products, for example, catalysts for tRNA loading (primordial aminoacyl-tRNA synthetases) or stabilizers of tRNA-mRNA interactions (primordial ribosomes), permitted the subsequent evolution of protein synthesis and of the genetic code to their mature form. This occurred via a parallel reduction in length of the interacting polynucleotides and polypeptides. Thus, it maintained the correct reading frame of mRNA from the preceding stages of evolution. Received: 27 September 1996 / Accepted: 17 May 1997     

Molecular Evolution in a Multisite Nearly Neutral Mutation Model

A simple nearly neutral mutation model of protein evolution was studied using computer simulation assuming a constant population size. In this model, a gene consists of a finite number of codons and there is no recombination within a gene. Each codon has two replacement and one silent sites. The fitness of a gene was determined multiplicatively by amino acids specified by codons (the independent multicodon model). Nucleotide diversity at replacement sites decreases as selection becomes stronger. A reduction of nucleotide diversity at silent sites also occurs as selection intensifies but the magnitude of the reduction is not a monotone function of the intensity of selection. The dispersion index is close to one. The average value of Tajima's and Fu and Li's statistics are negative and their absolute values increases as selection intensifies. However, their powers of detecting selection under the present model were not high unless the number of sites is large or mutation rate is high. The MK test was shown to detect intermediate selection fairly well. For comparison, the house-of-cards model was also investigated and its behavior was shown to be more sensitive to changes of population size than that of the independent multicodon model. The relevance of the present model for explaining protein evolution was discussed comparing its prediction and recent DNA data. Received: 24 May 1999 / Accepted: 17 August 1999     

Evaluation of Sequence Variation and Selection in the Bindin Locus of the Red Sea Urchin, Strongylocentrotus franciscanus

Recent evidence suggests that gamete recognition proteins may be subjected to directed evolutionary pressure that enhances sequence variability. We evaluated whether diversity enhancing selection is operating on a marine invertebrate fertilization protein by examining the intraspecific DNA sequence variation of a 273-base pair region located at the 5′ end of the sperm bindin locus in 134 adult red sea urchins (Strongylocentrotus franciscanus). Bindin is a sperm recognition protein that mediates species-specific gamete interactions in sea urchins. The region of the bindin locus examined was found to be polymorphic with 14 alleles. Mean pairwise comparison of the 14 alleles indicates moderate sequence diversity (p-distance = 1.06). No evidence of diversity enhancing selection was found. It was not possible to reject the null hypothesis that the sequence variation observed in S. franciscanus bindin is a result of neutral evolution. Statistical evaluation of expected proportions of replacement and silent nucleotide substitutions, observed versus expected proportions of radical replacement substitutions, and conformance to the McDonald and Kreitman test of neutral evolution all indicate that random mutation followed by genetic drift created the polymorphisms observed in bindin. Observed frequencies were also highly similar to results expected for a neutrally evolving locus, suggesting that the polymorphism observed in the 5′ region of S. franciscanus bindin is a result of neutral evolution. Received: 19 June 1998 / Accepted: 2 August 2000     

Origin of the NEFA and Nuc Signal Sequences

The human protein NEFA binds calcium, contains a leucine zipper repeat that does not form a homodimer, and is proposed (along with the homologous Nuc protein) to have a common evolutionary history with an EF-hand ancestor. We have isolated and characterized the N-terminal domain of NEFA that contains a signal sequence inferred from both endoproteinase Asp-N (Asp-N) and tryptic digests. Analysis of this N-terminal sequence shows significant similarity to the conserved multiple domains of the mitochondrial carrier family (MCF) proteins. The leader sequence of Nuc is, however, most similar to the signal sequences of membrane and/or secreted proteins (e.g., mouse insulin-like growth factor receptor). We suggest that the divergent NEFA and Nuc N-terminal sequences may have independent origins and that the common high hydrophobicity governs their targeting to the ER. These results provide insights into signal sequence evolution and the multiple origins of protein targeting. Received: 20 February 1997 / Accepted: 28 July 1997     

Relics from the RNA World

An RNA world is widely accepted as a probable stage in the early evolution of life. Two implications are that proteins have gradually replaced RNA as the main biological catalysts and that RNA has not taken on any major de novo catalytic function after the evolution of protein synthesis, that is, there is an essentially irreversible series of steps RNA → RNP → protein. This transition, as expected from a consideration of catalytic perfection, is essentially complete for reactions when the substrates are small molecules. Based on these principles we derive criteria for identifying RNAs in modern organisms that are relics from the RNA world and then examine the function and phylogenetic distribution of RNA for such remnants of the RNA world. This allows an estimate of the minimum complexity of the last ribo-organism—the stage just preceding the advent of genetically encoded protein synthesis. Despite the constraints placed on its size by a low fidelity of replication (the Eigen limit), we conclude that the genome of this organism reached a considerable level of complexity that included several RNA-processing steps. It would include a large protoribosome with many smaller RNAs involved in its assembly, pre-tRNAs and tRNA processing, an ability for recombination of RNA, some RNA editing, an ability to copy to the end of each RNA strand, and some transport functions. It is harder to recognize specific metabolic reactions that must have existed but synthetic and bio-energetic functions would be necessary. Overall, this requires that such an organism maintained a multiple copy, double-stranded linear RNA genome capable of recombination and splicing. The genome was most likely fragmented, allowing each ``chromosome' to be replicated with minimum error, that is, within the Eigen limit. The model as developed serves as an outgroup to root the tree of life and is an alternative to using sequence data for inferring properties of the earliest cells. Received: 14 January 1997 / Accepted: 19 May 1997     

Structure and Origin of a Novel Dimeric Retroposon B1-dID

Here we describe a new short retroposon family of rodents. Like the primate Alu element consisting of two similar monomers, it is dimeric, but the left and right monomers are different and descend from B1 and ID short retroposons, respectively. Such elements (B1-dID) were found in the genomes of Gliridae, Sciuridae, Castoridae, Caviidae, and Hystricidae. Nucleotide sequences of this retroposon can be assigned to several structural variants. Phylogenetic analysis of B1-dID and related sequences suggests a possible scenario of B1-dID evolution in the context of rodent evolution. Received: 30 August 1999 / Accepted: 20 March 2000     

Protein Tyrosine Kinase cDNAs from Amphioxus, Hagfish, and Lamprey: Isoform Duplications Around the Divergence of Cyclostomes and Gnathostomes

Animals evolved a variety of gene families involved in cell–cell communication and developmental control by gene duplication and domain shuffling. Each family is made up of several subtypes or subfamilies with distinct structures and functions, which diverged by gene duplications and domain shufflings before the divergence of parazoans and eumetazoans. Since the separation from protostomes, vertebrates expanded the multiplicity of members (isoforms) in the same subfamily by further gene duplications in their early evolution before the fish–tetrapod split. To know the dates of isoform duplications more closely, we have conducted isolation and sequencing cDNAs encoding the fibroblast growth factor receptor, Eph, src, and platelet-derived growth factor receptor subtypes belonging to the protein tyrosine kinase family from Branchiostoma belcheri, an amphioxus, Eptatretus burgeri, a hagfish, and Lampetra reissneri, a lamprey. From a phylogenetic tree of each subfamily inferred from a maximum likelihood (ML) method, together with a bootstrap analysis based on the ML method, we have shown that the isoform duplications frequently occurred in the early evolution of vertebrates around or just before the divergence of cyclostomes and gnathostomes by gene duplications and possibly chromosomal duplications. Received: 28 April 1998 / Accepted: 30 June 1999     

Mathematical Elegance with Biochemical Realism: The Covarion Model of Molecular Evolution

There is an apparent paradox in our understanding of molecular evolution. Current biochemically based models predict that evolutionary trees should not be recoverable for divergences beyond a few hundred million years. In practice, however, trees often appear to be recovered from much older times. Mathematical models, such as those assuming that sites evolve at different rates [including a Γ distribution of rates across sites (RAS)] may in theory allow the recovery of some ancient divergences. However, such models require that each site maintain its characteristic rate over the whole evolutionary period. This assumption, however, contradicts the knowledge that tertiary structures diverge with time, invalidating the rate-constancy assumption of purely mathematical models. We report here that a hidden Markov version of the covarion model can meet both biochemical and statistical requirements for the analysis of sequence data. The model was proposed on biochemical grounds and can be implemented with only two additional parameters. The two hidden parts of this model are the proportion of sites free to vary (covarions) and the rate of interchange between fixed sites and these variable sites. Simulation results are consistent with this approach, providing a better framework for understanding anciently diverged sequences than the standard RAS models. However, a Γ distribution of rates may approximate a covarion model and may possibly be justified on these grounds. The accurate reconstruction of older divergences from sequence data is still a major problem, and molecular evolution still requires mathematical models that also have a sound biochemical basis. Received: 13 February 2001 / Accepted: 22 May 2001