Non-random pre-transcriptional evolution in HIV-1. A refutation of the foundational conditions for neutral evolution

The complete base sequence of HIV-1 virus and GP120 ENV gene were analyzed to establish their distance to the expected neutral random sequence. An especial methodology was devised to achieve this aim. Analyses included: a) proportion of dinucleotides (signatures); b) homogeneity in the distribution of dinucleotides and bases (isochores) by dividing both segments in ten and three sub-segments, respectively; c) probability of runs of bases and No-bases according to the Bose-Einstein distribution. The analyses showed a huge deviation from the random distribution expected from neutral evolution and neutral-neighbor influence of nucleotide sites. The most significant result is the tremendous lack of CG dinucleotides (p < 10(-50) ), a selective trait of eukaryote and not of single stranded RNA virus genomes. Results not only refute neutral evolution and neutral neighbor influence, but also strongly indicate that any base at any nucleotide site correlates with all the viral genome or sub-segments. These results suggest that evolution of HIV-1 is pan-selective rather than neutral or nearly neutral.     

Internucleotide correlations and nucleotide periodicity in Drosophila mtDNA: new evidence for panselective evolution

Analysis for the homogeneity of the distribution of the second base of dinucleotides in relation to the first, whose bases are separated by 0, 1, 2,... 21 nucleotide sites, was performed with the VIH-1 genome (cDNA), the Drosophila mtDNA, the Drosophila Torso gene and the human p-globin gene. These four DNA segments showed highly significant heterogeneities of base distributions that cannot be accounted for by neutral or nearly neutral evolution or by the "neighbor influence" of nucleotides on mutation rates. High correlations are found in the bases of dinucleotides separated by 0, 1 and more number of sites. A periodicity of three consecutive significance values (measured by the x29) was found only in Drosophila mtDNA. This periodicity may be due to an unknown structure or organization of mtDNA. This non-random distribution of the two bases of dinucleotides widespread throughout these DNA segments is rather compatible with panselective evolution and generalized internucleotide co-adaptation.     

Misconceptions and false expectations in neutral evolution

Neutral evolution results from random recurrent mutation and genetic drift. A small part of random evolution, that which is related to protein or DNA polymorphisms, is the subject of the Neutral Theory of Evolution. One of the foundations of this theory is the demonstration that the mutation rate (m) is equal to the substitution rate. Since both rates are independent of population size, they are independent of drift, which is dependent upon population size. Neutralists have erroneously equated the substitution rate with the fixation rate, despite the fact that they are antithetical conceptions. The neutralists then applied the random walk stochastic model to justify alleles or bases that were fixated or eliminated. In this model, once the allele or base frequencies reach the monomorphic states (values of 1.0 or 0.0), the absorbing barriers, they can no longer return to the polymorphic state. This operates in a pure mathematical model. If recurrent mutation occurs (as in biotic real systems) fixation and elimination are impossible. A population of bacteria in which m = 10(-8) base mutation (or substitution)/site/generation and the reproduction rate is 1000 cell cycle/year should replace all its genome bases in approximately 100,000 years. The expected situation for all sites is polymorphism for the four bases rather than monomorphism at 1.0 or 0.0 frequencies. If fixation and elimination of a base for more than 500,000 years are impossible, then most of the neutral theory is untenable. A new complete neutral model, which allows for recurrent substitutions, is proposed here based on recurrent mutation or substitution and drift alone. The model fits a binomial or Poisson distribution and not a geometric one, as does neutral theory.     

Is the fixation of observable mutations distributed randomly among the three nucleotide positions of the codon?

Summary The distribution among the three nucleotide positions of the codons of 642 mutations fixed during the descent of 49 sequences of cytochromec was examined. This was compared to the distribution expected if the number of ways of getting a selectively acceptable amino acid alternative from a single nucleotide replacement at each coding position were random,i.e. proportional to the total number of ways of changing the encoded amino acid by a single nucleotide replacement at each coding position. It was found that the observed distribution was significantly different from random, there being 40% more mutations in the first coding position than in the second whereas one would have expected 10% more in the second than in the first. The probability of the result occurring by chance is < 10^–6.The same test was made on the distribution of 347 mutations fixed in the descent of 19 sequences of alpha hemoglobin and 286 mutations fixed in the descent of 16 beta and 4 delta hemoglobins. The result for the alpha hemoglobins was a similar non-randomness but the probability of its occurring by chance rose to 0.005. The result for the beta-delta hemoglobins was in the same direction but was not significant (p = 0.3). The degree of non-randomness among the three genes in the distribution of fixations over the three nucleotide positions of their codons appears to be correlated (negatively) with their rates of evolution, the plasticity required of the molecule to adapt to new environments, and the recency of exploitation of opportunities for change in functional specificity provided by such processes as gene duplication.     

The Coalescent Process in Models with Selection

Statistical properties of the process describing the genealogical history of a random sample of genes are obtained for a class of population genetics models with selection. For models with selection, in contrast to models without selection, the distribution of this process, the coalescent process, depends on the distribution of the frequencies of alleles in the ancestral generations. If the ancestral frequency process can be approximated by a diffusion, then the mean and the variance of the number of segregating sites due to selectively neutral mutations in random samples can be numerically calculated. The calculations are greatly simplified if the frequencies of the alleles are tightly regulated. If the mutation rates between alleles maintained by balancing selection are low, then the number of selectively neutral segregating sites in a random sample of genes is expected to substantially exceed the number predicted under a neutral model.     

The effects of weak selection on neutral diversity at linked sites

The effects of selection on variability at linked sites have an important influence on levels and patterns of within-population variation across the genome. Most theoretical models of these effects have assumed that selection is sufficiently strong that allele frequency changes at the loci concerned are largely deterministic. These models have led to the conclusion that directional selection for selectively favorable mutations, or against recurrent deleterious mutations, reduces nucleotide site diversity at linked neutral sites. Recent work has shown, however, that fixations of weakly selected mutations, accompanied by significant stochastic changes in allele frequencies, can sometimes cause higher diversity at linked sites when compared with the effects of fixations of neutral mutations. This study extends this work by deriving approximate expressions for the mean conditional times to fixation and loss of mutations subject to selection, and analyzing the conditions under which selection increases rather than reduces these times. Simulations are used to examine the relations between diversity at a neutral site and the fixation and loss times of mutations at a linked site that is subject to selection. It is shown that the long-term level of neutral diversity can be increased over the purely neutral value by recurrent fixations and losses of linked, weakly selected dominant or partially dominant favorable mutations, or linked recessive or partially recessive deleterious mutations. The results are used to examine the conditions under which associative overdominance, as opposed to background selection, is likely to operate.     

On the use of nucleic acid sequences to infer early branchings in the tree of life

Simplifying assumptions made in various tree reconstruction methods-- notably rate constancy among nucleotide sites, homogeneity, and stationarity of the substitutional processes--are clearly violated when nucleotide sequences are used to infer distant relationships. Use of tree reconstruction methods based on such oversimplified assumptions can lead to misleading results, as pointed out by previous authors. In this paper, we made use of a (discretized) gamma distribution to account for variable rates of substitution among sites and built models that allowed for unequal base frequencies in different sequences. The models were nonhomogeneous Markov-process models, assuming different patterns of substitution in different parts of the tree. Data of the small-subunit rRNAs from four species were analyzed, where base frequencies were quite different among sequences and rates of substitution were highly variable at sites. Parameters in the models were estimated by maximum likelihood, and models were compared by the likelihood-ratio test. The nonhomogeneous models provided significantly better fit to the data than homogeneous models despite their involvement of many parameters. They also appeared to produce reasonable estimation of the phylogenetic tree; in particular, they seemed able to identify the root of the tree.      

Nearest-neighbor tree species combinations in tropical forest: the role of chance, and some consequences of high diversity

In three permanent inventory plots comprising 12.4 ha of undisturbed forest at La Selva, Costa Rica, all stems ≥10 cm dbh were mapped and identified to species. There were 1628, 1478 and 1954 trees in the plots, representing 168, 166 and 171 species respectively. We determined the species of each nearest-neighbor pair of trees, and asked whether the occurrence of species pairs conforms to a simple random mixing model. If trees are randomly mixed in terms of species, the expected frequency of any nearest neighbor species combination is a function of the relative abundance of the two species. Departures from random mixing could arise from species interactions, differential responses to habitat, or both. The number of possible ij species combinations increases approximately as the square of the number of species. For the 168 species in plot 1, for example, there are 14 196 possible combinations. We compared the expected frequency of each species combination in the three plots (42 736 combinations in all) with observed frequencies. Over 98% of the combinations had observed frequencies of zero and expected frequencies close to zero. A consequence of high diversity is low density of most individual species, and exceedingly low frequencies of the vast majority of species combinations. For each of the 805 combinations with observed frequencies >0, we used simulation to generate a distribution of expected frequencies. We used a t-test to compare the observed frequency with the mean of the simulated distribution for each combination. Only 40 combinations (0.09% of the possible species combinations in the plots) departed from expected frequencies; 39 combinations were more common, and one less common than expected. The overwhelming majority of nearest neighbor species combinations occur at frequencies predictable from their individual abundances.     

Relationship between DNA Polymorphism and Fixation Time

When there is no recombination among nucleotide sites in DNA sequences, DNA polymorphism and fixation of mutants at nucleotide sites are mutually related. Using the method of gene genealogy, the relationship between the DNA polymorphism and the fixation of mutant nucleotide was quantitatively investigated under the assumption that mutants are selectively neutral, that there is no recombination among nucleotide sites, and that the population is a random mating population with N diploid individuals. The results obtained indicate that the expected number of nucleotide differences between two DNA sequences randomly sampled from the population is 42% less when a mutant at a particular nucleotide site reaches fixation than at a random time, and that heterozygosity is also expected to be less when fixation takes place than at a random time, but the amount of reduction depends on the value of 4Nv in this case, where v is the mutation rate per DNA sequence per generation. The formula for obtaining the expected number of nucleotide differences between the two DNA sequences for a given fixation time is also derived, and indicates that, even when it takes a large number of generations for a mutant to reach fixation, this number is 33% less than at a random time. The computer simulation conducted suggests that the expected number of nucleotide differences between the two DNA sequences at the time when an advantageous mutant becomes fixed is essentially the same as that of neutral mutant if the fixation time is the same. The effect of recombination on the amount of DNA polymorphism was also investigated by using computer simulation.     

The effects of multilocus balancing selection on neutral variability

We studied the effect of multilocus balancing selection on neutral nucleotide variability at linked sites by simulating a model where diallelic polymorphisms are maintained at an arbitrary number of selected loci by means of symmetric overdominance. Different combinations of alleles define different genetic backgrounds that subdivide the population and strongly affect variability. Several multilocus fitness regimes with different degrees of epistasis and gametic disequilibrium are allowed. Analytical results based on a multilocus extension of the structured coalescent predict that the expected linked neutral diversity increases exponentially with the number of selected loci and can become extremely large. Our simulation results show that although variability increases with the number of genetic backgrounds that are maintained in the population, it is reduced by random fluctuations in the frequencies of those backgrounds and does not reach high levels even in very large populations. We also show that previous results on balancing selection in single-locus systems do not extend to the multilocus scenario in a straightforward way. Different patterns of linkage disequilibrium and of the frequency spectrum of neutral mutations are expected under different degrees of epistasis. Interestingly, the power to detect balancing selection using deviations from a neutral distribution of allele frequencies seems to be diminished under the fitness regime that leads to the largest increase of variability over the neutral case. This and other results are discussed in the light of data from the Mhc.     

Sequence saturation mutagenesis (SeSaM): a novel method for directed evolution

Sequence saturation mutagenesis (SeSaM) is a conceptually novel and practically simple method that truly randomizes a target sequence at every single nucleotide position. A SeSaM experiment can be accomplished within 2–3 days and comprises four steps: generating a pool of DNA fragments with random length, ‘tailing’ the DNA fragments with universal base using terminal transferase at 3′-termini, elongating DNA fragments in a PCR to the full-length genes using a single-stranded template and replacing the universal bases by standard nucleotides. Random mutations are created at universal sites due to the promiscuous base-pairing property of universal bases. Using enhanced green fluorescence protein as the model system and deoxyinosine as the universal base, we proved by sequencing 100 genes the concept of the SeSaM method and achieved a random distribution of mutations with the mutational bias expected for deoxyinosine.     

Simulation of protein evolution by random fixation of allowed codons

Summary Computer simulation of protein evolution is based on a simple model consisting of random fixation of allowed codons (RFAC). Random replacement of single nucleotides occurs in a DNA sequence. If this results in any of the synonomous codons for allowed amino acids the mutation is fixed, if not, there is no change in the DNA and the cycle is repeated. Multiple fixations at the same nucleotide site, back mutations, degenerate fixations and coincidental identity of amino acids all occur. RFAC simulation begins with a single DNA sequence and follows a phylogeny based on the fossil record. The rate of fixation at the level of DNA is constant. The model upon which RFAC simulation is based is the same as the neutral theory of molecular evolution. The simulation is therefore a test of this theory. The results of simulated and real evolution are compared for fibrinopeptides A in mammals and cytochromes C and hemoglobin and chains in vertebrates. In each case the allowed variation at each site has been set equal to that observed, twice that observed and all protein amino acids. Rates of fixation vary from 2.4 × 10^–10 to 10^–5 accepted nucleotide fixations per codon per year. There is some, although never excellent, agreement between real and simulated evolution, the better fits are obtained in the cases of fibrinopeptides A and cytochromes C. The major source of discrepancy between real evolution and simulation is irregularities in the rates of real evolution. RFAC simulation is compared with the random evolutionary hit (REH) model, augmented maximum parsimony and the accepted point mutations (PAM) approach.     

Sense codon in Escherichia coli are translated in context

The nucleotide frequencies 5' and 3' to the sense codons in highly and weakly expressed genes have been investigated by the chi-squares method. A comparison between the experimental and computer-generated random nucleotide sequences (in which each codon is substituted by a random synonymous one) was made. It was shown that the choice of a particular codon among the synonymous ones in a given position of the gene depends on the three nucleotides 3' and 5' adjacent to the codon in highly expressed genes (the triplet 3' and a single nucleotide 5' to the codons in weakly expressed genes). Concrete patterns for the preferable choice of synonymous codons depending on their contexts are presented. It is suggested that these constraints are related to the efficiency of messenger translation. The constraints on the amino acid sequences of encoded proteins also lead to statistically significant bases in nucleotide frequencies around the sense codons. The biological role of these constraints is discussed.     

Nucleotide sequencing of an apparent proviral copy of env mRNA defines determinants of expression of the mouse mammary tumor virus env gene.

To extend our understanding of the organization and expression of the mouse mammary tumor virus genome, we determined the nucleotide sequence of large regions of a cloned mouse mammary tumor virus strain C3H provirus that appears to be a DNA copy of env mRNA. In conjunction with analysis of several additional clones of integrated and unintegrated mouse mammary tumor virus DNAs, we came to the following conclusions: (i) the mRNA for env is generated by splicing mechanisms that recognize conventional eucaryotic signals at donor and acceptor sites with a leader of at least 289 bases in length; (ii) the first of three possible initiation codons for translation of env follows the splice junction by a single nucleotide and produces a signal peptide of 98 amino acids; (iii) the amino terminal sequence of the major virion glycoprotein gp52env is confirmed by nucleotide sequencing and is encoded by a sequence beginning 584 nucleotides from the 5' end of env mRNA; (iv) the final 17 amino acids at the carboxyl terminus of the primary product of env are encoded within the long terminal repeat by the 51 bases at the 5' end of the U3 domain; and (v) bases 2 through 4 at the 5' end of the long terminal repeat constitute an initiation codon that commences an open reading frame capable of directing the synthesis of a 36-kilodalton protein.     

The Effect of Deleterious Mutations on Neutral Molecular Variation

Selection against deleterious alleles maintained by mutation may cause a reduction in the amount of genetic variability at linked neutral sites. This is because a new neutral variant can only remain in a large population for a long period of time if it is maintained in gametes that are free of deleterious alleles, and hence are not destined for rapid elimination from the population by selection. Approximate formulas are derived for the reduction below classical neutral values resulting from such background selection against deleterious mutations, for the mean times to fixation and loss of new mutations, nucleotide site diversity, and number of segregating sites. These formulas apply to random-mating populations with no genetic recombination, and to populations reproducing exclusively asexually or by self-fertilization. For a given selection regime and mating system, the reduction is an exponential function of the total mutation rate to deleterious mutations for the section of the genome involved. Simulations show that the effect decreases rapidly with increasing recombination frequency or rate of outcrossing. The mean time to loss of new neutral mutations and the total number of segregating neutral sites are less sensitive to background selection than the other statistics, unless the population size is of the order of a hundred thousand or more. The stationary distribution of allele frequencies at the neutral sites is correspondingly skewed in favor of rare alleles, compared with the classical neutral result. Observed reductions in molecular variation in low recombination genomic regions of sufficiently large size, for instance in the centromere-proximal regions of Drosophila autosomes or in highly selfing plant populations, may be partly due to background selection against deleterious mutations.     

Tests of applicability of several substitution models for DNA sequence data

Using linear invariants for various models of nucleotide substitution, we developed test statistics for examining the applicability of a specific model to a given dataset in phylogenetic inference. The models examined are those developed by Jukes and Cantor (1969), Kimura (1980), Tajima and Nei (1984), Hasegawa et al. (1985), Tamura (1992), Tamura and Nei (1993), and a new model called the eight-parameter model. The first six models are special cases of the last model. The test statistics developed are independent of evolutionary time and phylogeny, although the variances of the statistics contain phylogenetic information. Therefore, these statistics can be used before a phylogenetic tree is estimated. Our objective is to find the simplest model that is applicable to a given dataset, keeping in mind that a simple model usually gives an estimate of evolutionary distance (number of nucleotide substitutions per site) with a smaller variance than a complicated model when the simple model is correct. We have also developed a statistical test of the homogeneity of nucleotide frequencies of a sample of several sequences that takes into account possible phylogenetic correlations. This test is used to examine the stationarity in time of the base frequencies in the sample. For Hasegawa et al.'s and the eight-parameter models, analytical formulas for estimating evolutionary distances are presented. Application of the above tests to several sets of real data has shown that the assumption of stationarity of base composition is usually acceptable when the sequences studied are closely related but otherwise it is rejected. Similarly, the simple models of nucleotide substitution are almost always rejected when actual genes are distantly related and/or the total number of nucleotides examined is large.      

Neighbor–neighbor interactions in single-strand polynucleotides: Optical rotatory dispersion studies of the ribonucleotide ApApCp

The neighbor–neighbor interactions in the small ribotrinucleotide ApApCp were investigated with the aid of optical rotatory dispersion measurements. This trinucleotide shows a Cotton effect between 220 and 325 mμ, in the region of its maximum ultraviolet absorption. The specific rotation of the trinucleotide is independent of concentration while the magnitude of the Cotton effect (levorotation) decreases markedly with increasing temperature. Such effects were not observed with the component nucleotides alone, in a simulated hydrolysis mixture, nor with the hydrolyzed trinucleotide. The Cotton effect is attributed to perturbation of the nucleotide base chromophores by neighbor–neighbor intramolecular interaction (stacking), without any hydrogen bonding being involved; this interaction decreases with increasing temperature because of increased internal rotational freedom about the single bonds of the backbone chain with an accompanying disruption of the neighbor–neighbor interaction between the bases. This explanation is supported by a statistical mechanical theory of neighbor-neighbor interactions in polynucleotides, involving the forces between the bases. Application of this technique to further studies of polynucleotides and polypeptides is discussed.