Evolution of human immunodeficiency virus under selection and weak recombination

To predict emergence of drug resistance in patients undergoing antiretroviral therapy, we study accumulation of preexisting beneficial alleles in a haploid population of N genomes. The factors included in the model are selection with the coefficient s and recombination with the small rate per genome r (r < s sqrt of k, where k is the average number of less-fit loci per genome). Mutation events are neglected. To describe evolution at a large number of linked loci, we generalize the analytic method we developed recently for an asexual population. We show that the distribution of genomes over the deleterious allele number moves in time as a "solitary wave" that is quasi-deterministic in the middle (on the average) but has stochastic edges. We arrive at a single-locus expression for the average accumulation rate, in which the effects of linkage, recombination, and random drift are all accounted for by the effective selection coefficient s lnNr/lnNs(2)k/r. At large N, the effective selection coefficient approaches the single-locus value s. Below the critical size N(c) approximately 1/r, a population eventually becomes a clone, recombination cannot produce new sequences, and virus evolution stops. Taking into account finite mutation rate predicts a small, finite rate of evolution at N < N(c). We verify the accuracy of the results analytically and by Monte Carlo simulation. On the basis of our findings, we predict that partial depletion of the HIV population by combined anti-retroviral therapy can suppress emergence of drug-resistant strains.     

Factors affecting the errors in the estimation of evolutionary distances between sequences

Phylogenetic methods that use matrices of pairwise distances between sequences (e.g., neighbor joining) will only give accurate results when the initial estimates of the pairwise distances are accurate. For many different models of sequence evolution, analytical formulae are known that give estimates of the distance between two sequences as a function of the observed numbers of substitutions of various classes. These are often of a form that we call "log transform formulae". Errors in these distance estimates become larger as the time t since divergence of the two sequences increases. For long times, the log transform formulae can sometimes give divergent distance estimates when applied to finite sequences. We show that these errors become significant when t approximately 1/2 |lambda(max)|(-1) logN, where lambda(max) is the eigenvalue of the substitution rate matrix with the largest absolute value and N is the sequence length. Various likelihood-based methods have been proposed to estimate the values of parameters in rate matrices. If rate matrix parameters are known with reasonable accuracy, it is possible to use the maximum likelihood method to estimate evolutionary distances while keeping the rate parameters fixed. We show that errors in distances estimated in this way only become significant when t approximately 1/2 |lambda(1)|(-1) logN, where lambda(1) is the eigenvalue of the substitution rate matrix with the smallest nonzero absolute value. The accuracy of likelihood-based distance estimates is therefore much higher than those based on log transform formulae, particularly in cases where there is a large range of timescales involved in the rate matrix (e.g., when the ratio of transition to transversion rates is large). We discuss several practical ways of estimating the rate matrix parameters before distance calculation and hence of increasing the accuracy of distance estimates.     

Sequence tolerance of the phage lambda PRM promoter: implications for evolution of gene regulatory circuitry

Much of the gene regulatory circuitry of phage lambda centers on a complex region called the O(R) region. This approximately 100-bp region is densely packed with regulatory sites, including two promoters and three repressor-binding sites. The dense packing of this region is likely to impose severe constraints on its ability to change during evolution, raising the question of how the specific arrangement of sites and their exact sequences could evolve to their present form. Here we ask whether the sequence of a cis-acting site can be widely varied while retaining its function; if it can, evolution could proceed by a larger number of paths. To help address this question, we developed a lambda cloning vector that allowed us to clone fragments spanning the O(R) region. By using this vector, we carried out intensive mutagenesis of the P(RM) promoter, which drives expression of CI repressor and is activated by CI itself. We made a pool of fragments in which 8 of the 12 positions in the -35 and -10 regions were randomized and cloned this pool into the vector, making a pool of P(RM) variant phage. About 10% of the P(RM) variants were able to lysogenize, suggesting that the lambda regulatory circuitry is compatible with a wide range of P(RM) sequences. Analysis of several of these phages indicated a range of behaviors in prophage induction. Several isolates had induction properties similar to those of the wild type, and their promoters resembled the wild type in their responses to CI. We term this property of different sequences allowing roughly equivalent function "sequence tolerance " and discuss its role in the evolution of gene regulatory circuitry.     

An Approach to Population and Evolutionary Genetic Theory for Genes in Mitochondria and Chloroplasts, and Some Results

We developed population genetic theory for organelle genes, using an infinite alleles model appropriate for molecular genetic data, and considering the effects of mutation and random drift on the frequencies of selectively neutral alleles. The effects of maternal inheritance and vegetative segregation of organelle genes are dealt with by defining new effective gene numbers, and substituting these for 2N(e) in classical theory of nuclear genes for diploid organisms. We define three different effective gene numbers. The most general is N(lambda), defined as a function of population size, number of organelle genomes per cell, and proportions of genes contributed by male and female gametes to the zygote. In many organisms, vegetative segregation of organelle genomes and intracellular random drift of organelle gene frequencies combine to produce a predominance of homoplasmic cells within individuals in the population. Then, the effective number of organelle genes is N(eo), a simple function of the numbers of males and females and of the maternal and paternal contributions to the zygote. Finally, when the paternal contribution is very small, N( eo) is closely approximated by the number of females, N( f). Then if the sex ratio is 1, the mean time to fixation or loss of new mutations is approximately two times longer for nuclear genes than for organelle genes, and gene diversity is approximately four times greater. The difference between nuclear and organelle genes disappears or is reversed in animals in which males have large harems. The differences between nuclear and organelle gene behavior caused by maternal inheritance and vegetative segregation are generally small and may be overshadowed by differences in mutation rates to neutral alleles. For monoecious organisms, the effective number of organelle genes is approximately equal to the total population size N. We also show that a population can be effectively subdivided for organelle genes at migration rates which result in panmixis for nuclear genes, especially if males migrate more than females.     

Intron positions delineate the evolutionary path of a pervasively appended peptide in five human aminoacyl-tRNA synthetases

Recent progress in genome sequencing has revealed a correspondence between the evolution of multicellularity and the appending of new peptides onto age-old enzyme bodies. Indicative of the pervasive nature of these appended peptides, in some cases the same sequences have been appended to a number of different enzymes. By analyzing the positions of introns within one such roaming peptide, an approximately 50-amino acid motif appended to five human aminoacyl-tRNA synthetases, I have delineated its path in eukaryote evolution. The motif was first acquired as an N-terminal extension by histidyl- and glycyl-tRNA synthetases at a very early stage of eukaryote evolution. Later, but not less than 1200 million years ago, the motif spread from histidyl-tRNA synthetase to the C and N terminals of glutamyl- and prolyl-tRNA synthetase, respectively, and then spread further during the evolution of the Chordate lineage to the N terminal of tryptophanyl-tRNA synthetase. In similar fashion, the motif in glycyl-tRNA synthetase spread to the C terminal of methionyl-tRNA synthetase not later than 1000 million years ago.     

Sequence of C region of L chains from Xenopus laevis Ig

A cDNA expression library, prepared from Xenopus laevis splenocytes, was screened with antibodies to Xenopus Ig. One clone, lambda XIg23, reacted with antibodies to IgY and to IgM; the insert hybridized to approximately 1.3-kb RNA from spleen, the approximate size expected for L chain mRNA. An additional clone, lambda XIg31, was identified by cross-hybridization. The inserts of lambda XIg23 and lambda XIg31 begin in the third framework region of the V region and extend through the C region to the poly(A) tail. Except for a single nucleotide difference, the two C region sequences are identical. The amino acid sequence of the C region was compared with the sequences of a variety of C kappa and C lambda, as well as to C region sequences of L chains from Rana catesbeiana and from two species of shark. The Xenopus C region resembles mouse and human C kappa slightly more than C lambda. The similarity of the Xenopus and Rana C regions to each other is approximately the same as that of either amphibian sequence to mammalian CL. The data are discussed in terms of the evolution of kappa and lambda C regions.     

Common and variable contributions of Fis residues to high-affinity binding at different DNA sequences

Fis is a nucleoid-associated protein that interacts with poorly related DNA sequences with a high degree of specificity. A difference of more than 3 orders of magnitude in apparent Kd values was observed between specific (Kd, approximately 1 to 4 nM) and nonspecific (Kd, approximately 4 microM) DNA binding. To examine the contributions of Fis residues to the high-affinity binding at different DNA sequences, 13 alanine substitutions were generated in or near the Fis helix-turn-helix DNA binding motif, and the resulting proteins were purified. In vitro binding assays at three different Fis sites (fis P II, hin distal, and lambda attR) revealed that R85, T87, R89, K90, and K91 played major roles in high-affinity DNA binding and that R85, T87, and K90 were consistently vital for binding to all three sites. Other residues made variable contributions to binding, depending on the binding site. N84 was required only for binding to the lambda attR Fis site, and the role of R89 was dramatically altered by the lambda attR DNA flanking sequence. The effects of Fis mutations on fis P II or hin distal site binding in vitro generally correlated with their abilities to mediate fis P repression or DNA inversion in vivo, demonstrating that the in vitro DNA-binding effects are relevant in vivo. The results suggest that while Fis is able to recognize a minimal common set of DNA sequence determinants at different binding sites, it is also equipped with a number of residues that contribute to the binding strength, some of which play variable roles.     

The molecular roots of compositional inheritance.

Non-covalent compositional assemblies, made of monomeric mutually catalytic molecules, constitute an alternative to alphabet-based informational biopolymers as a mechanism of primordial inheritance. Such assemblies appear implicitly in many "Metabolism First" origin of life scenarios, and more explicitly in the Graded Autocatalysis Replication Domain (GARD) model [Segréet al. (2000). Proc. Natl Acad. Sci. U.S.A.97, 4112-4117]. In the present work, we provide a detailed analysis of the quantitative molecular roots of such behavior. It is demonstrated that the fidelity of reproduction provided by a newly defined heritability measure eta(*)(s), strongly depends on the values of molecular recognition parameters and on assembly size. We find that if the catalytic rate acceleration coefficients are distributed normally, transfer of compositional information becomes impossible, due to frequent "compositional error catastrophes". In contrast, if the catalytic acceleration rates obey a lognormal distribution, as actually predicted by a statistical formalism for molecular repertoires, high reproduction fidelity is obtained. There is also a clear dependence on assembly size N, whereby maximal eta is seen in a narrow range around N approximately 3.5 N(G)/lambda, where N(G)is the size of the primordial molecular repertoire and lambda is a molecular interaction statistical parameter. Such relationships help define the physicochemical conditions that could underlie the early steps in pre-biotic evolution.     

Genealogical process on a correlated fitness landscape

We study with extensive numerical simulation the genealogical process of 2N haploid genetic sequences. The sequences are under selective pressure, and fitness values are assigned at random, but with a tunable degree of correlation to the fitness values of closely related sequences. The genealogies that we observe can be classified into three different categories, corresponding to different regimes of the mutation rate. At low mutation rates, the sequences remain localized around a small number of central sequences, which leads to trees with short pairwise distances and slow turnover of the most recent common ancestor of the population. At high mutation rates, we observe trees similar (but not identical) to those of neutral evolution. In this regime, the population drifts rapidly, and selection does not influence the distribution of fitness values in the population. The third regime, for intermediate mutation rates, is only found in strongly correlated landscapes. It resembles the one for high mutation rates in that the population drifts rapidly, but nevertheless selection still shapes the distribution of fitness values.     

Morphing molecular specificities between Arm-peptide and NUT-RNA in the antitermination complexes of bacteriophages lambda and P22

Bacteriophage lambda's N-protein includes a 17-amino-acid segment, Arm, rich in arginine and having specific affinity for a 15-nucleotide RNA stem-loop called BOX-B. Parallel but different Arm/BOX-B sequences in lambda's cousin, phage P22, account for some of the type specificity that distinguishes lambda from P22: the N of each works only with its cognate BOX-B in vivo. We find that the specificity of N(lambda) can be shifted gradually to that of N(22) by substituting sets of particular amino acids from Arm(22) into Arm of N(lambda). The determinative amino acids are generally those shown by nuclear magnetic resonance to contact BOX-B RNA; gain or loss of these contact amino acids is reasonably expected to contribute to the affinity of each amino acid sequence. Intermediate sequences may show no function with either BOX-B, or weak function with both BOX-B(lambda) and BOX-B(22), the latter suggesting possible evolutionary paths for specificity shifts.     

Computational analysis of sequence selection mechanisms

Mechanisms leading to gene variations are responsible for the diversity of species and are important components of the theory of evolution. One constraint on gene evolution is that of protein foldability; the three-dimensional shapes of proteins must be thermodynamically stable. We explore the impact of this constraint and calculate properties of foldable sequences using 3660 structures from the Protein Data Bank. We seek a selection function that receives sequences as input, and outputs survival probability based on sequence fitness to structure. We compute the number of sequences that match a particular protein structure with energy lower than the native sequence, the density of the number of sequences, the entropy, and the "selection" temperature. The mechanism of structure selection for sequences longer than 200 amino acids is approximately universal. For shorter sequences, it is not. We speculate on concrete evolutionary mechanisms that show this behavior.     

Genomic organization of low copy number sequences that are associated with deca-satellite DNA in the monkey genome.

A previously described segment of African green monkey DNA (cloned in phage lambda MkA) contains deca-satellite linked to DNA sequences that are estimated to occur once per genome. Sequences homologous to the low copy number sequences in lambda MkA are also associated with species-specific satellite DNAs in the human and mouse genomes. A second clone, lambda Mk8, contains a monkey DNA region that is colinear and homologous to a portion of the low copy number sequences in lambda MkA, but no satellite sequences. The two cloned segments are markedly different starting at a point proximal to the satellite DNA region in lambda MkA. DNA-blotting experiments indicate that lambda Mk8 but not lambda MkA represents the typical genomic organization and that the low copy number segments occur only once per haploid genome. The data suggest that rearrangements such as deletions or inversions occurring in monkey cells account in part for the structure of lambda MkA. Additional rearrangements may have occurred during cloning in E. coli. This unique chromosomal region may be particularly susceptible to recombination.     

Molecular cloning of Snyder-Theilen feline leukemia and sarcoma viruses: comparative studies of feline sarcoma virus with its natural helper virus and with Moloney murine sarcoma virus

Extrachromosomal DNA obtained from mink cells acutely infected with the Snyder-Theilen (ST) strain of feline sarcoma virus (feline leukemia virus) [FeSV(FeLV)] was fractionated electrophoretically, and samples enriched for FeLV and FeSV linear intermediates were digested with EcoRI and cloned in lambda phage. Hybrid phages were isolated containing either FeSV or FeLV DNA "inserts" and were characterized by restriction enzyme analysis, R-looping with purified 26 to 32S viral RNA, and heteroduplex formation. The recombinant phages (designated lambda FeSV and lambda FeLV) contain all of the genetic information represented in FeSV and FeLV RNA genomes but lack one extended terminally redundant sequence of 750 bases which appears once at each end of parental linear DNA intermediates. Restriction enzyme and heteroduplex analyses confirmed that sequences unique to FeSV (src sequences) are located at the center of the FeSV genome and are approximately 1.5 kilobase pairs in length. With respect to the 5'-3' orientation of genes in viral RNA, the order of genes in the FeSV genome is 5'-gag-src-env-c region-3'; only 0.9 kilobase pairs of gag and 0.6 kilobase pairs of env-derived FeLV sequences are represented in ST FeSV. Heteroduplex analyses between lambda FeSV or lambda FeLV DNA and Moloney murine sarcoma virus DNA (strain m1) were performed under conditions of reduced stringency to demonstrate limited regions of base pair homology. Two such regions were identified: the first occurs at the extreme 5' end of the leukemia and both sarcoma viral genomes, whereas the second corresponds to a 5' segment of leukemia virus "env" sequences conserved in both sarcoma viruses. The latter sequences are localized at the 3' end of FeSV src and at the 5' end of murine sarcoma virus src and could possibly correspond to regions of helper virus genomes that are required for retroviral transforming functions.     

B cell development in mice that lack one or both immunoglobulin kappa light chain genes.

We have generated mice that lack the ability to produce immunoglobulin (Ig) kappa light chains by targeted deletion of J kappa and C kappa gene segments and the intervening sequences in mouse embryonic stem cells. In wild type mice, approximately 95% of B cells express kappa light chains and only approximately 5% express lambda light chains. Mice heterozygous for the J kappa C kappa deletion have approximately 2-fold more lambda+ B cells than wild-type littermates. Compared with normal mice, homozygous mutants for the J kappa C kappa deletion have about half the number of B cells in both the newly generated and the peripheral B cell compartments, and all of these B cells express lambda light chains in their Ig. Therefore, homozygous mutant mice appear to produce lambda-expressing cells at nearly 10 times the rate observed in normal mice. These findings demonstrate that kappa gene assembly and/or expression is not a prerequisite for lambda gene assembly and expression. Furthermore, there is no detectable rearrangement of 3' kappa RS sequences in lambda+ B cells of the homozygous mutant mice, thus rearrangements of these sequences, per se, is not required for lambda light chain gene assembly. We discuss these findings in the context of their implications for the control of Ig light chain gene rearrangement and potential applications of the mutant animals.