Markovian approximation to the finite loci coalescent with recombination along multiple sequences

The coalescent with recombination process has initially been formulated backwards in time, but simulation algorithms and inference procedures often apply along sequences. Therefore it is of major interest to approximate the coalescent with recombination process by a Markov chain along sequences. We consider the finite loci case and two or more sequences. We formulate a natural Markovian approximation for the tree building process along the sequences, and derive simple and analytically tractable formulae for the distribution of the tree at the next locus conditioned on the tree at the present locus. We compare our Markov approximation to other sequential Markov chains and discuss various applications.     

TREES SIFTER 1.0: an approximate method to estimate the time to the most recent common ancestor of a sample of DNA sequences

trees sifter 1.0 implements an approximate method to estimate the time to the most recent common ancestor (TMRCA) of a set of DNA sequences, using population evolution modelling. In essence, the program simulates genealogies with a user‐defined model of coalescence of lineages, and then compares each simulated genealogy to the genealogy inferred from the real data, through two summary statistics: (i) the number of mutations on the genealogy (M_n), and (ii) the number of different sequence types (alleles) observed (K_n). The simulated genealogies are then submitted to a rejection algorithm that keeps only those that are the most likely to have generated the observed sequence data. At the end of the process, the accepted genealogies can be used to estimate the posterior probability distribution of the TMRCA.     

The ancestry of a sample of sequences subject to recombination

In this article we discuss the ancestry of sequences sampled from the coalescent with recombination with constant population size 2N. We have studied a number of variables based on simulations of sample histories, and some analytical results are derived. Consider the leftmost nucleotide in the sequences. We show that the number of nucleotides sharing a most recent common ancestor (MRCA) with the leftmost nucleotide is approximately log(1 + 4N Lr)/4Nr when two sequences are compared, where L denotes sequence length in nucleotides, and r the recombination rate between any two neighboring nucleotides per generation. For larger samples, the number of nucleotides sharing MRCA with the leftmost nucleotide decreases and becomes almost independent of 4N Lr. Further, we show that a segment of the sequences sharing a MRCA consists in mean of 3/8Nr nucleotides, when two sequences are compared, and that this decreases toward 1/4Nr nucleotides when the whole population is sampled. A measure of the correlation between the genealogies of two nucleotides on two sequences is introduced. We show analytically that even when the nucleotides are separated by a large genetic distance, but share MRCA, the genealogies will show only little correlation. This is surprising, because the time until the two nucleotides shared MRCA is reciprocal to the genetic distance. Using simulations, the mean time until all positions in the sample have found a MRCA increases logarithmically with increasing sequence length and is considerably lower than a theoretically predicted upper bound. On the basis of simulations, it turns out that important properties of the coalescent with recombinations of the whole population are reflected in the properties of a sample of low size.     

A heuristic method to reconstruct the history of sequences subject to recombination

Summary Sequences subject to recombination and gene conversion defy phylogenetic analysis by traditional methods since their evolutionary history cannot be adequately summarized by a tree. This study investigates ways to describe their evolutionary history and proposes a method giving a partial reconstruction of this history. Multigene families, viruses, and alleles from within populations experience recombinations/gene conversions, so the questions studied here are relevant for a large body of data and the suggested solutions should be very practical. The method employed was implemented in a program, RecPars, written in C and was used to analyze nine retroviruses.     

DNA sequences at immunoglobulin switch region recombination sites.

The immunoglobulin heavy chain switch from synthesis of IgM to IgG, IgA or IgE is mediated by a DNA recombination event. Recombination occurs within switch regions, 2-10 kb segments of DNA that lie upstream of heavy chain constant region genes. A compilation of DNA sequences at more than 150 recombination sites within heavy chain switch regions is presented. Switch recombination does not appear to occur by homologous recombination. An extensive search for a recognition motif failed to find such a sequence, implying that switch recombination is not a site-specific event. A model for switch recombination that involves illegitimate priming of one switch region on another, followed by error-prone DNA synthesis, is proposed.     

Homologous recombination between coinjected DNA sequences peaks in early to mid-S phase.

We have examined the effect of cell cycle position on homologous recombination between plasmid molecules coinjected into synchronized rat fibroblasts. Recombination activity was found to be low in G1 and to rise 10- to 15-fold, peaking in early to mid-S phase.     

The RecE recombination pathway mediates recombination between partially homologous DNA sequences: structural analysis of recombination products

Escherichia coli generalized recombination, utilizing the RecA RecB recombination pathway, requires large stretches (70-200 bp) of complete DNA sequence homology. In contrast, we have found that the RecE pathway can promote recombination between DNA with only short stretches of homology. A plasmid containing 10 partially homologous direct repeats was linearized by digestion with specific restriction enzymes. After transformation, a RecE+ (sbcA) host was able to circularize the plasmid by recombination between partially homologous direct repeat sequences. Recombination occurred in regions of as little as 6 bp of perfect homology. Recombination was enhanced in the regions adjacent to restriction sites used to linearize the plasmid, consistent with a role of double-strand breaks in promoting recombination. A mechanism is proposed in which the 5' exonuclease, ExoVIII, produces 3' single-stranded ends from the linearized plasmid. These pair with other sequences of partial homology. Partial homologies in the sequences flanking the actual join serve to stabilize this recombination intermediate. Recombination is completed by a process of "copy and join." This recombination mechanism requires less homology to stabilize intermediates than the degree of homology needed for mechanisms involving strand invasion. Its role in nature may be to increase genomic diversity, for example, by enhancing recombination between bacteriophages and regions of the bacterial chromosome.     

Reconstructing evolution of sequences subject to recombination using parsimony

The parsimony principle states that a history of a set of sequences that minimizes the amount of evolution is a good approximation to the real evolutionary history of the sequences. This principle is applied to the reconstruction of the evolution of homologous sequences where recombinations or horizontal transfer can occur. First it is demonstrated that the appropriate structure to represent the evolution of sequences with recombinations is a family of trees each describing the evolution of a segment of the sequence. Two trees for neighboring segments will differ by exactly the transfer of a subtree within the whole tree. This leads to a metric between trees based on the smallest number of such operations needed to convert one tree into the other. An algorithm is presented that calculates this metric. This metric is used to formulate a dynamic programming algorithm that finds the most parsimonious history that fits a given set of sequences. The algorithm is potentially very practical, since many groups of sequences defy analysis by methods that ignore recombinations. These methods give ambiguous or contradictory results because the sequence history cannot be described by one phylogeny, but only a family of phylogenies that each describe the history of a segment of the sequences. The generalization of the algorithm to reconstruct gene conversions and the possibility for heuristic versions of the algorithm for larger data sets are discussed.     

A comparison of two popular statistical methods for estimating the time to most recent common ancestor (TMRCA) from a sample of DNA sequences

We have compared two statistical methods of estimating the time to most recent common ancestor (TMRCA) from a sample of DNA sequences, which have been proposed by Templeton (1993) and Bandeltet al. (1995). Monte-Carlo simulations were used for generating DNA sequence data. Different evolutionary scenarios were simulated and the estimation procedures were evaluated. We have found that for both methods (i) the estimates are insensitive to demographic parameters and (ii) the standard deviations of the estimates are too high for these methods to be reliably used in practice.     

Transposon-encoded site-specific recombination: nature of the Tn3 DNA sequences which constitute the recombination site res.

The tnpR gene of transposon Tn3 encodes a site-specific recombination enzyme that acts at res, a DNA region adjacent to tnpR, to convert co-integrate intermediates of interreplicon transposition to the normal transposition end-products. We have used two complementary approaches to study the nature of the Tn3 recombination region, res. Firstly, the DNA-binding sites for tnpR protein were determined in DNase I protection experiments. These identified a 120-bp region between the tnpA and tnpR genes that can be subdivided into three separate protein-binding sites. Genetic dissection experiments indicate that few, if any, other sequences in addition to this 120-bp region are required for res function. Moreover, we have shown that the two directly repeated res regions within a molecule are unequal partners in the recombination reaction: a truncated res region, which is unable to recombine with a second identical res region, can recombine efficiently with an intact res region. This demonstration, along with the observation that tnpR/res recombination acts efficiently on directly repeated res regions within a molecule but inefficiently both on inverted res regions in the same molecule and in the fusion reaction between res regions in different molecules, leads us to propose that one-dimensional diffusion (tracking) of tnpR protein along DNA is used to locate an initial res region, and then to bring a second directly repeated res region into a position that allows recombination between the res regions.     

Engineering of homologous recombination hotspots with AU-rich sequences in brome mosaic virus.

Previously, we observed that crossovers sites of RNA recombinants clustered within or close to AU-rich regions during genetic recombination in brome mosaic bromovirus (BMV) (P. D. Nagy and J. J. Bujarski. J. Virol. 70:415-426, 1996). To test whether AU-rich sequences can facilitate homologous recombination, AU-rich sequences were introduced into parental BMV RNAs (RNA2 and RNA3). These insertions created a homologous RNA2-RNA3 recombination hotspot. Two other AU-rich sequences also supported high-frequency homologous recombination if a common sequence with high or average G/C content was present immediately upstream of the AU-rich element. Homologous RNA recombination did not require any additional sequence motifs or RNA structures and was position nonspecific within the 3' noncoding region. These results suggest that nucleotide content (i.e., the presence of common 5' GC-rich or moderately AU-rich and 3' AU-rich regions) is the important factor that determines the sites of homologous recombination. A mechanism that involves replicase switching during synthesis of positive-sense RNA strands is presented to explain the observed results.     

Estimating the age of the common ancestor of a sample of DNA sequences

We present a simple Monte Carlo method for estimating the age of the most recent common ancestor (MRCA) of a sample of DNA sequences. We show that Templeton's (1993) estimator of the age of the MRCA based on the maximum number of nucleotide differences between two sequences in a sample is inaccurate, and we demonstrate the new method by reanalyzing a sample of DNA sequences from human Y chromosomes and a sample of human Alu sequences.      

Efficiency of homologous DNA recombination varies along the Bacillus subtilis chromosome.

Structures consisting of a genetic marker (erythromycin or kanamycin resistance, thymidylate synthetase) flanked by 3.4-kilobase direct repeats (pBR322 sequences) were inserted in 12 different locations of the Bacillus subtilis chromosome. Recombination between the repeats was followed by the loss of the genetic marker. Recombination frequencies found in different locations varied from 1.2 X 10(-5) to 40 X 10(-5) per cell generation. Such differences were highly significant (P less than 0.001).     

Cre-stimulated recombination at loxP-containing DNA sequences placed into the mammalian genome.

The cre gene of coliphage P1 encodes a 38 kDa protein which efficiently promotes both intra- and intermolecular recombination at specific 34 bp sites called loxP. To demonstrate that the Cre protein can promote DNA recombination at loxP sites resident on a mammalian chromosome, a mouse cell line was constructed containing two directly repeated loxP sites flanking a 2.5 kb yeast DNA fragment and inserted between the SV40 promoter and the neo structural gene to disrupt expression of the neo gene. Expression of the cre gene in this cell line results in excision of the intervening yeast DNA and thus permits sufficient expression of the neo gene to allow cell growth in high concentrations of G418. Southern analysis indicated that Cre-mediated excision occurred at the loxP sites. In the absence of the cre gene such excisive events are quite rare. Cre-mediated recombination should thus be quite useful in effecting a variety of genomic rearrangements in eukaryotic cells.     

Long CTG.CAG repeat sequences markedly stimulate intramolecular recombination

Previous studies have shown that homologous recombination is a powerful mechanism for generation of massive instabilities of the myotonic dystrophy CTG.CAG sequences. However, the frequency of recombination between the CTG.CAG tracts has not been studied. Here we performed a systematic study on the frequency of recombination between these sequences using a genetic assay based on an intramolecular plasmid system in Escherichia coli. The rate of intramolecular recombination between long CTG.CAG tracts oriented as direct repeats was extraordinarily high; recombinants were found with a frequency exceeding 12%. Recombination occurred in both RecA(+) and RecA(-) cells but was approximately 2-11 times higher in the recombination proficient strain. Long CTG.CAG tracts recombined approximately 10 times more efficiently than non-repeating control sequences of similar length. The recombination frequency was 60-fold higher for a pair of (CTG.CAG)(165) tracts compared with a pair of (CTG.CAG)(17) sequences. The CTG.CAG sequences in orientation II (CTG repeats present on a lagging strand template) recombine approximately 2-4 times more efficiently than tracts of identical length in the opposite orientation relative to the origin of replication. This orientation effect implies the involvement of DNA replication in the intramolecular recombination between CTG.CAG sequences. Thus, long CTG.CAG tracts are hot spots for genetic recombination.     

Intrachromosomal recombination between well-separated, homologous sequences in mammalian cells.

In the present study, we investigated intrachromosomal homologous recombination in a murine hybridoma in which the recipient for recombination, the haploid, endogenous chromosomal immunoglobulin mu-gene bearing a mutation in the constant (Cmu) region, was separated from the integrated single copy wild-type donor Cmu region by approximately 1 Mb along the hybridoma chromosome. Homologous recombination between the donor and recipient Cmu region occurred with high frequency, correcting the mutant chromosomal mu-gene in the hybridoma. This enabled recombinant hybridomas to synthesize normal IgM and to be detected as plaque-forming cells (PFC). Characterization of the recombinants revealed that they could be placed into three distinct classes. The generation of the class I recombinants was consistent with a simple unequal sister chromatid exchange (USCE) between the donor and recipient Cmu region, as they contained the three Cmu-bearing fragments expected from this recombination, the original donor Cmu region along with both products of the single reciprocal crossover. However, a simple mechanism of homologous recombination was not sufficient in explaining the more complex Cmu region structures characterizing the class II and class III recombinants. To explain these recombinants, a model is proposed in which unequal pairing between the donor and recipient Cmu regions located on sister chromatids resulted in two crossover events. One crossover resulted in the deletion of sequences from one chromatid forming a DNA circle, which then integrated into the sister chromatid by a second reciprocal crossover.     

Site-specific and illegitimate recombination in the oriV1 region of the F factor. DNA sequences involved in recombination and resolution

We have defined some of the sequences involved in high frequency recA-independent recombination at the oriV1 region of the F factor. Using a mobilization assay, we determined that plasmid pMB080, a pBR322 derivative bearing the PvuII-BamHI (F factor co-ordinates 45.43 to 46.0) fragment from the oriV1 region of F, contained all sequences necessary to undergo efficient site-specific recombination with the F derivative pOX38, which retains the oriV1 region. We constructed a series of pMB080 deletions in vitro using exonucleases S1 and Bal31. Deletions removing a ten base-pair sequence, which forms part of an inverted repeat segment located 62 base-pairs to the left of the NcoI site (45.87) within the cloned fragment, totally eliminated the recA-independent recombination reaction. Other deletions differentially affected both the frequency and stability of cointegrate molecules formed by the site-specific recombination system. The F factor oriV1 region is involved also in low-frequency recombination with several sites on pBR322 and related plasmids. We have determined the precise location of these recombination sites within oriV1 by DNA sequencing. These studies revealed that recombination always took place within an eight base-pair spacer region between the ten base-pair inverted repeats found to be important for oriV1-oriV1 interactions. We propose that the low-efficiency recombination between pBR322 and pOX38 results from the ability of the F site-specific recombination apparatus to weakly recognize and interact with sequences that bear some resemblance to the normal oriV1 recognition elements. Furthermore, we suggest, by analogy with the lambda paradigm, that the nucleotide sequences at the junctions of secondary site recombinants define at least one crossover site used during the normal site-specific recombination process.