Copy Number Distribution Research Articles

Gene Amplification by Unequal Sister Chromatid Exchange: Probabilistic Modeling and Analysis of Drug Resistance Data

Unequal sister chromatid exchange has been proposed as one of several possible mechanisms for gene amplification resulting in tandemly repeated sequences on chromosomes. Two requirements for testing this hypothesis are analytical observations and a mathematical model. Recently observations were reported for the number of tandemly repeated sequences on chromosomes of cells growing in the presence of a toxic drug and the mechanism was proposed to be unequal sister chromatid exchange. We now develop a mathematical model of this process based on the following hypotheses, (i) the extent of slippage between paired sister chromatids is a random variable with geometric distribution, (ii) the number of crossover sites is a random variable with a Poisson distribution, and (iii) cells with less than a threshold number of copies of an essential gene are eliminated when grown in selective conditions. Iterating the model at successive cell divisions results in a Markov chain with a denumerable infinity of states. The resulting distributions of gene copy number per cell at a particular population size are compared to published data on the CAD gene in BHK cells growing in the presence of the drug PALA (Smith et al., 1990, Cell , 63, 1219). The mathematical model can reproduce the observed means and standard deviations of gene copy number per cell and allows construction of confidence region estimates of parameters describing the extent of slippage, density of crossover sites, and strength of selection. An important prediction of the model is that in non-selective conditions the cells with amplified sequences gradually disappear from the population even if they are not at a growth disadvantage, though rare cells with a very large number of amplified sequences might continue to exist. The success of modeling suggests that the proposed mechanism of gene amplification by unequal sister chromatid exchange is consistent with the number of tandemly repeated sequences on chromosomes observed in some circumstances.

Can transposable element copy number distribution parameters be estimated from natural populations of Drosophila melanogaster?

AbstractThe copy frequency distribution of a transposable element family in a Drosophila melanogaster natural population is generally characterised by the values of the Charlesworths' model parameters α and β (Charlesworth & Charlesworth, 1983). The estimation of these parameters is made using the observed distribution of the occupied sites in a population sample. Several results have been interpreted as due either to the influence of stochastic factors or to deterministic factors (transposition, excision, selection…). The accuracy of this method was tested by estimations performed on samples from simulated populations. The results show that with the sample size usually used for natural population studies, the confidence intervals are too large to reasonably deduce either the element copy number distribution or the values of transposition and excision rate and selective coefficients.

Identification of a complete P-element in the genome of Drosophila bifasciata.

A full-size P-element (IbifM3) was isolated from a genomic library of Drosophila bifasciata. The sequence has a length of 2935 bp and is flanked by 8 bp duplications of the target site. The termini are formed by 31 bp inverted repeats. The four exons have intact reading frames and possess the coding capacity for a protein of 753 amino acids and a molecular weight of 86.4 kd. The sections of the D. melanogaster transposase presumed to be functionally important (three leucine zippers and a helix turn helix motif) are conserved in the D. bifasciata P-element. Copy number and genomic distribution resemble the situation in true P-strains of D. melanogaster. Both findings support the idea that IbifM3 represents an active transposon. The sequence comparison between the P-elements of D. bifasciata, D. melanogaster and Scaptomyza pallida reveals relationships not in accordance with the phylogeny of the species. This result suggests a further case of horizontal transmission involving mobile elements in the genus Drosophila.

Replication origin mutations affecting binding of pSC101 plasmid-encoded Rep initiator protein

To investigate the role of binding sites for Rep initiation protein in the replication of pSC101, a series of plasmids was constructed which carried different combinations of mutations in three binding sites within the minimal origin of replication. Mutation of all three sites reduced the affinity of purified Rep protein for the origin by 100-fold, as measured by a competition binding assay. Mutations in individual binding sites prevented binding of Rep protein to the mutant site but not to adjacent wild-type sites. Transformation efficiency, copy number, and stability over 150 generations were measured for each of the mutant plasmids. Unlike other similar plasmids related to pSC101, the Rep binding sites were found not to be equivalent. A mutation in the site RS1, proximal to repeated sequences which serve as DnaB helicase entry sites in oriC, had a severe effect on replication activity. A similar mutation in the distal site RS3 caused a reduction in copy number, but the mutant plasmid was stably maintained despite a broadened distribution of copy number within the population. A mutation in the middle RS2 site had no significant effect on pSC101 replication.

Interphase cytogenetics of a male breast cancer

Direct interphase cytogenetic analysis was performed on nuclei from a male breast tumor using fluorescence in situ hybridization (FISH). DNA probes specific for repetitive pericentromeric regions on chromosomes 1, 7, 9, 11, 15, 17, 18, X, and Y were used to determine chromosome copy numbers in interphase tumor cells. Copy number distributions varied greatly between chromosomes, showing major tumor populations with one (Y), two (X, 9), three (11, 15, 18), and four (1, 7, 17) copies of the pericentromeric targets. The X chromosome was present in two copies in 84.7% of tumor nuclei, with the balance being primarily monosomic. Normal skin fibroblasts cultured from the same patient showed 99% monosomy X. The Y chromosome showed a minor population (12%) with two copies. The DNA index of the tumor was 2.0 as determined by flow cytometry. The proliferative activity of the tumor cells was simultaneously analyzed using detection of in vivo bromodeoxyuridine (BrdU) incorporation. The BrdU labeling index was 13.2%.

A branching-process model for the evolution of transposable elements incorporating selection.

We have formulated a very general mathematical model to analyze the evolution of transposable genetic elements in prokaryotic populations. Transposable genetic elements are DNA sequences able to replicate and insert copies of themselves at new locations in the genome. This work characterizes the equilibrium distribution of copy number under the influence of copy number-dependent selection, transposition and deletion. Our principal results concern the equilibrium distribution of copy number in response to various selective regimes. For particular transposition patterns (e.g., unregulated transposition or copy number-dependent transposition), equilibrium distributions are calculated numerically for a variety of specific selection patterns. Selection is quantified through specification of the expected number of offspring for individuals of each type, which is generally a non-increasing function of copy number, in accord with the usual evolutionary speculations.

The dynamics of gene amplification described as a multitype compartmental model and as a branching process

The present work is aimed at developing the mathematical tools by which the dynamics of gene amplification (GA) can be described in detail. Some discrete compartmental models of GA by disproportionate replication and a general model for other putative GA mechanisms are presented and analyzed. The dynamical distribution of gene copy number in the cell population is calculated with the loss of cells taken either as constant or as copy-number-dependent. Our analysis shows that for a one-copy GA process with constant loss of cells, the relative frequency of single-gene-copy cells ( sensitive cells) converges to zero, with the rate of convergence depending on the amplification probability. In contrast, for a one-copy GA process with copy-number- dependent loss of cells, the relative frequency of single-copy cells is bounded, implying a bounded compartment of many-gene-copy cells. Using branching processes theory we calculate the dynamical distribution of the single-gene-copy compartment as well as its extinction probability. Our models are used for estimating treatment prognosis as affected by drug resistance due to GA, showing significant differences in prognosis resulting from small changes in drug dose.

Evolution of ribosomal RNA gene copy number on the sex chromosomes of Drosophila melanogaster.

A diverse array of cellular and evolutionary forces--including unequal crossing-over, magnification, compensation, and natural selection--is at play modulating the number of copies of ribosomal RNA (rRNA) genes on the X and Y chromosomes of Drosophila. Accurate estimates of naturally occurring distributions of copy numbers on both the X and Y chromosomes are needed in order to explore the evolutionary end result of these forces. Estimates of relative copy numbers of the ribosomal DNA repeat, as well as of the type I and type II inserts, were obtained for a series of 96 X chromosomes and 144 Y chromosomes by using densitometric measurements of slot blots of genomic DNA from adult D. melanogaster bearing appropriate deficiencies that reveal chromosome-specific copy numbers. Estimates of copy number were put on an absolute scale with slot blots having serial dilutions both of the repeat and of genomic DNA from nonpolytene larval brain and imaginal discs. The distributions of rRNA copy number are decidedly skewed, with a long tail toward higher copy numbers. These distributions were fitted by a population genetic model that posits three different types of exchange events--sister-chromatid exchange, intrachromatid exchange, and interchromosomal crossing-over. In addition, the model incorporates natural selection, because experimental evidence shows that there is a minimum number of functional elements necessary for survival. Adequate fits of the model were found, indicating that either natural selection also eliminates chromosomes with high copy number or that the rate of intrachromatid exchange exceeds the rate of interchromosomal exchange.

Analysis of a model for minichromosome segregation in Escherichia coli

The present article contains a theoretical, quantitative analysis of the implications of the Helmstetter-Leonard model (1987, J. molec. Biol. 197, 195-204.) for the segregation of chromosomal DNA in Escherichia coli, on the expected copy-number distribution of minichromosomes in a culture in steady-state exponential growth. According to the model, two determinants are involved in the mechanism of chromosome segregation: a partition system that assures the equal allotment of chromosomes between daughter cells at cell division, and a locus within the minimal oriC region that specifies the attachment site of the chromosomes to the cell envelope at initiation of replication. There are many parameters that must be taken into account in such a study, and since some of them are probabilistic in nature, a strictly analytical approach is not feasible and we had to resort to computer simulation. A wide range of parameter values was tested, in all combinations. The minichromosome copy-number distributions obtained all had a prominent mode equal to the number of oriC binding sites and their main features were determined essentially by that and very little by any of the other parameters of the model. In order to avoid the unrealistic situation in which this one feature completely dominates the results, the original model was modified so that each individual minichromosome is no longer required to replicate during every cell generation, by introducing a limit to the number of unsuccessful attempts to locate a suitable binding site. The copy-number distributions predicted by this version of the model are quantitatively and qualitatively very different and depend on all the components of the model. The simulation results are sufficiently well-behaved to allow consideration as to whether a particular empirical minichromosome copy-number distribution--when such data become available--could in fact be governed by the proposed model; it may even be possible to get a rough estimate for the different parameters involved.

New Foldback transposable element TFB1 found in histone genes of the midge Chironomus thummi

A new Foldback transposable element (TFB1) has been found in the histone H1-H3 intergenic region in the midge Chironomus thummi thummi. TFB1 has long terminal inverted repeats, composed of short, degenerate subrepeats and is flanked by nine or ten base-pair "target site" duplications. TFB1 is present in at least two adjacent histone gene units in Ch. th. thummi, indicating a homogenization of histone gene repeats. The copy number and chromosomal distribution of TFB1 are different in the closely related subspecies Ch. th. thummi and Ch. th. piger. showing that amplification, elimination and transposition of TFB1 have occurred recently during evolution.

Escherichia coli minichromosomes: Random segregation and absence of copy number control

Minichromosomes, i.e. plasmids that can replicate from an integrated oriC, have been puzzling because of their high copy numbers compared to that of the chromosomal oriC, their lack of incompatibility with the chromosome and their high loss frequencies. Using single cell resistance to tetracycline or ampicillin as an indicator of copy number we followed the development of minichromosome distributions in Escherichia coli cells transformed with minichromosomes and then allowed to grow towards the steady state. The final copy number distribution was not reached within 15 to 20 generations. If the minichromosome carried the sop (partitioning) genes from plasmid F, the development of the copy number distribution was further drastically delayed. We conclude that E. coli cells have no function that directly controls minichromosomal copy numbers, hence the absence of incompatibility in the sense of shared copy number control. We suggest that minichromosomes are subject to the same replication control as the chromosome but segregate randomly in the absence of integrated partitioning genes. This, combined with evidence that the lowest copy number classes are normally present despite high average copy numbers, can account for the high loss frequencies.

Propagation of an amplifiable recombinant plasmid in Saccharomyces cerevisiae: flow cytometry studies and segregated modeling

Efficient expression of a foreign protein product by the yeast Saccharomyces cerevisiae requires a stable recombinant vector present at a high number of copies per cell. A conditional centromere yeast plasmid was constructed which can be amplified to high copy number by a process of unequal partitioning at cell division, followed by selection for increased copy number. However, in the absence of selection pressure for plasmid amplification, copy number rapidly drops from 25 plasmids/cell to 6 plasmids/cell in less than 10 generations of growth. Copy number subsequently decreases from 6 plasmids/cell to 2 plasmids/cell over a span of 50 generations. A combination of flow cytometric measurement of copy number distributions and segregated mathematical modeling were applied to test the predictions of a conceptual model of conditional centromere plasmid propagation. Measured distributions of plasmid content displayed a significant subpopulation of cells with a copy number of 4-6, even in a population whose mean copy number was 13.5. This type of copy number distribution was reproduced by a mathematical model which assumes that a maximum of 4-6 centromere plasmids per cell can be stably partitioned at cell division. The model also reproduces the observed biphasic kinetics of plasmid number instability. The agreement between simulation and experimental results provides support for the proposed model and demonstrates the utility of the flow cytometry/segregated modeling approach for the study of multicopy recombinant vector propagation.

Graduated resistance to G418 leads to differential selection of cultured mammalian cells expressing the neo gene

The effects of Geneticin (G418) selection on the growth and survival of cultured mammalian cells expressing the neomycin-resistance gene ( neo) were studied by the analysis of cell clones from two retroviral neo vectorinfected populations. We found a correlation between the neo expression level and growth rates in medium containing varying G418 concentrations. This relationship permits the use of differential selection schemes for the isolation of rare cells with increased expression. Comparison, by clone sampling, of vector-positive populations before and after selection with a G418 concentration in the range usually used for selection, showed different expression level and vector copy number distributions for the population infected with the vector of lower LTR activity, but not for the other. Such biasing effects of G418 selection may be important when selected cells are used for quantitative studies of gene expression.

A mathematical model for plasmid replication and distribution in microbial populations

A mathematical model and a computer program for its implementation have been developed to predict the distribution of plasmid copy numbers in the individual cells of a microbial population. The kinetics of accumulation of plasmid-free cells. the copy number distribution within the population and the mean copy number can all be calculated using the computer program. The model has been shown to accurately predict these parameters for recombinant plasmids in yeast populations.

Stability of pBR322-derived plasmids

The stability of pBR322-derived plasmids was studied during growth of their Escherichia coli host in the absence of antibiotics. Plasmid pBR322, as well as its Δ rom and Δ bla derivatives, were lost from their host within 60 generations, but a number of Δ tet derivatives were quite stable under the same conditions. An evaluation of the data indicated that primary plasmid loss due to random partitioning corresponds to the generation of a plasmid-free cell about every 10 4 divisions (probability P 0; = “intrinsic” instability). Secondary loss of plasmid-carrying cells resulted from a growth advantage of the plasmid-free cells when bacteria die, perhaps due to unrepaired lethal damage in the DNA, under conditions of stationary incubation (= “apparent” instability). This cell death also occurred in the absence of plasmids but was accelerated by the presence of extra plasmid DNA in the cell and further accelerated by a functional tet gene. This was the reason for the differential apparent stabilities of Δ bla and Δ tet plasmids. There was no indication that an accumulation of plasmid multimers contributed to the plasmid instability, as has been suggested in the literature. The value of P 0 = 10 −4 is 14 orders of magnitude greater than expected under the assumption of a random (Poisson) distribution of plasmid copy numbers in a population of cells.

Distribution and abundance of insertion sequences among natural isolates of Escherichia coli.

A reference collection of 71 natural isolates of Escherichia coli (the ECOR collection) has been studied with respect to the distribution and abundance of transposable insertion sequences using DNA hybridization. The data include 1173 occurrences of six unrelated insertion sequences (IS1, IS2, IS3, IS4, IS5 and IS30). The number of insertion elements per strain, and the sizes of DNA restriction fragments containing them, is highly variable and can be used to discriminate even among closely related strains. The occurrence and abundance of pairs of unrelated insertion sequences are apparently statistically independent, but significant correlations result from stratifications in the reference collection. However, there is a highly significant positive association among the insertion sequences considered in the aggregate. Nine branching process models, which differ in assumptions regarding the regulation of transposition and the effect of copy number on fitness, have been evaluated with regard to their fit of the observed distributions. No single model fits all copy number distributions. The best models incorporate no regulation of transposition and a moderate to strong decrease in fitness with increasing copy number for IS1 and IS5, strong regulation of transposition and a negligible to weak decrease in fitness with increasing copy number for IS3, and less than strong regulation of transposition for IS2, IS4 and IS30.

Distribution of transposable elements in prokaryotes

We consider models for the distribution of the number of elements per host genome for families of transposable elements (TEs). The hosts are assumed to be prokaryotes. These models assume (1) a constant rate of infection of uninfected hosts by TEs, (2) replicative transposition within each host, and (3) a reduction of the fitness of a host dependent on the number of TEs it contains. No provision was made for the deletion of individual TEs within a host or for recombination, since both are relatively rare events in prokaryotes. These models mostly assume that the TE performs no fuction for the host, and that the reduction in fitness with increased copy number is due to effects such as the impairment of beneficial genes by transposition or homologous recombination. We also consider a model in which the TEs can convey a selective advantage to the host. The equilibrium distributions of copy number are determined for these models, and are of a variety of classical types. Relevant parameters of the models are estimated using data on the distribution of insertion sequences in natural isolates of Escherichia coli.

Characterization and evolution of a single-copy sequence from the human Y chromosome.

To study the evolution and organization of DNA from the human Y chromosome, we constructed a recombinant library of human Y DNA by using a somatic cell hybrid in which the only cytologically detectable human chromosome is the Y. One recombinant (4B2) contained a 3.3-kilobase EcoRI single-copy fragment which was localized to the proximal portion of the Y long arm. Sequences homologous to this human DNA are present in male gorilla, chimpanzee, and orangutan DNAs but not in female ape DNAs. Under stringent hybridization conditions, the homologous sequence is either a single-copy or a low-order repeat in humans and in the apes. With relaxed hybridization conditions, this human Y probe detected several homologous DNA fragments which are all derived from the Y in that they occur in male DNAs from humans and the apes but not in female DNAs. In contrast, this probe hybridized to highly repeated sequences in both male and female DNAs from old world monkeys. Thus, sequences homologous to this probe underwent a change in copy number and chromosomal distribution during primate evolution.

Characterization and evolution of a single-copy sequence from the human Y chromosome.

To study the evolution and organization of DNA from the human Y chromosome, we constructed a recombinant library of human Y DNA by using a somatic cell hybrid in which the only cytologically detectable human chromosome is the Y. One recombinant (4B2) contained a 3.3-kilobase EcoRI single-copy fragment which was localized to the proximal portion of the Y long arm. Sequences homologous to this human DNA are present in male gorilla, chimpanzee, and orangutan DNAs but not in female ape DNAs. Under stringent hybridization conditions, the homologous sequence is either a single-copy or a low-order repeat in humans and in the apes. With relaxed hybridization conditions, this human Y probe detected several homologous DNA fragments which are all derived from the Y in that they occur in male DNAs from humans and the apes but not in female DNAs. In contrast, this probe hybridized to highly repeated sequences in both male and female DNAs from old world monkeys. Thus, sequences homologous to this probe underwent a change in copy number and chromosomal distribution during primate evolution.

Maintenance of bacterial plasmids: Comparison of theoretical calculations and experiments with plasmid R1 in Escherichia coli

Plasmid R1 was tested for stable maintenance in Escherichia coli K12. Populations carrying a transfer-negative derivative of plasmid R1drd-19 were grown exponentially for 72 generations in LB medium. Out of nearly 5000 cells none had lost the plasmid; hence the rate of loss of the plasmid is less than 3 X 10(-6) per cell and cell generation. Other experiments showed that the loss rate was less than or equal to 10(-7) per cell and cell generation. Plasmid R1 replication is controlled so that, on average, n copies are synthesized per cell and cell generation irrespective of the copy number (as long as it is at least one). A theoretical analysis was performed, based on the assumption that there is a Poissonian spread around n in each class of cells (each class defined by the number of R1 copies at birth). Two models for partitioning were analyzed, Equi-partitioning and Pair Site Partitioning; in the latter, each daughter is guaranteed one plasmid copy, whereas the rest of the copies are assumed to be randomly distributed. The copy number distribution was found to be fairly narrow in both cases, with at least 90% of the population in the range n/2-3n/2 for baby cells and in the range n-3n for cells just before cell division. Plasmid-free cells were estimated to appear at a frequency which for the copy number of R1 (n = 3-4) was 1.5 X 10(-3) - 8 X 10(-5) for equipartitioning and 6 X 10(-3) - 6 X 10(-4) for pair site partitioning, respectively.(ABSTRACT TRUNCATED AT 250 WORDS)