Simultaneous estimation of all the parameters of a stepwise mutation model.

Minisatellite and microsatellite are short tandemly repetitive sequences dispersed in eukaryotic genomes, many of which are highly polymorphic due to copy number variation of the repeats. Because mutation changes copy numbers of the repeat sequences in a generalized stepwise fashion, stepwise mutation models are widely used for studying the dynamics of these loci. We propose a minimum chi-square (MCS) method for simultaneous estimation of all the parameters in a stepwise mutation model and the ancestral allelic type of a sample. The MCS estimator requires knowing the mean number of alleles of a certain size in a sample, which can be estimated using Monte Carlo samples generated by a coalescent algorithm. The method is applied to samples of seven (CA)n repeat loci from eight human populations and one chimpanzee population. The estimated values of parameters suggest that there is a general tendency for microsatellite alleles to expand in size, because (1) each mutation has a slight tendency to cause size increase and (2) the mean size increase is larger than the mean size decrease for a mutation. Our estimates also suggest that most of these CA-repeat loci evolve according to multistep mutation models rather than single-step mutation models. We also introduced several quantities for measuring the quality of the estimation of ancestral allelic type, and it appears that the majority of the estimated ancestral allelic types are reasonably accurate. Implications of our analysis and potential extensions of the method are discussed.SINCE the discovery that a large number of loci with tandemly repeated sequences in human and many eukaryote species are highly polymorphic because of copy number variation of the repeats in different individuals (Jeffreys 1985; Litt and Luty 1989; Weber and May 1989), allele size data from such loci are rapidly becoming the dominant source of genetic markers for genome mapping, forensic testing, and population studies. Loci with repeat sequences longer than 5 bp are generally referred to as minisatellite or variable number tandem repeat loci, and those with repeat sequences between 2 to 5 bp are referred to as microsatellite or short tandem repeat loci (Tautz 1993). Because mutations change the copy number of such loci in a stepwise fashion, rapid accumulation of population samples from minisatellite and microsatellite loci has resurrected the interest of the stepwise mutation model (SMM), which was popular in the 1970s.     

Increased conidiation associated with progression along the sterigmatocystin biosynthetic pathway

The Aspergillus nidulans sterigmatocystin (ST) gene cluster contains both regulatory (aflR) and biosynthetic genes (stc genes) required for ST production. A total of 26 genes are in the cluster, 13 of which have been assigned a known function in the biosynthetic pathway. This complex secondary pathway represents a physiological cost to the fungus. We tested the amount of asexual spore production using a series of isogenic lines of A. nidulans, differing only in a mutation in aflR (resulting in a strain containing no ST intermediates) or a mutation in three stc genes that produced either no ST intermediates (ΔstcJ), an early ST intermediate, norsoloroinic acid (ΔstcE) or a late ST intermediate, versicolorin A (ΔstcU). In two independently replicated experiments we compared the numbers of conidia produced by each of these mutant strains and a wild type ST producer in a neutral (growth media) and a host (corn seed) environment. A stepwise increase in asexual spore production was observed with each progressive step in the ST pathway. Thus, the data suggest that recruitment or loss of these secondary metabolite pathway genes has a selective advantage apart from the physiological activity of the metabolite.     

A mathematical model of breast cancer development, local treatment and recurrence

Cancer development is a stepwise process through which normal somatic cells acquire mutations which enable them to escape their normal function in the tissue and become self-sufficient in survival. The number of mutations depends on the patient's age, genetic susceptibility and on the exposure of the patient to carcinogens throughout their life. It is believed that in every malignancy 4-6 crucial similar mutations have to occur on cancer-related genes. These genes are classified as oncogenes and tumour suppressor genes (TSGs) which gain or lose their function respectively, after they have received one mutative hit or both of their alleles have been knocked out. With the acquisition of each of the necessary mutations the transformed cell gains a selective advantage over normal cells, and the mutation will spread throughout the tissue via clonal expansion. We present a simplified model of this mutation and expansion process, in which we assume that the loss of two TSGs is sufficient to give rise to a cancer. Our mathematical model of the stepwise development of breast cancer verifies the idea that the normal mutation rate in genes is only sufficient to give rise to a tumour within a clinically observable time if a high number of breast stem cells and TSGs exist or genetic instability is involved as a driving force of the mutation pathway. Furthermore, our model shows that if a mutation occurred in stem cells pre-puberty, and formed a field of cells with this mutation through clonal formation of the breast, it is most likely that a tumour will arise from within this area. We then apply different treatment strategies, namely surgery and adjuvant external beam radiotherapy and targeted intraoperative radiotherapy (TARGIT) and use the model to identify different sources of local recurrence and analyse their prevention.     

Neutral two-locus multiple allele models with recombination

General formulae for the homozygosity and variance of linkage disequilibrium are derived for neutral, stationary, two-locus multiple allele models where there is a symmetric type of mutation at each locus. Particular cases examined are K allele models, the infinite alleles model, and the stepwise mutation model. The two-locus infinite allele model is examined at the molecular level and a joint probability generating function is found for the number of heterozygous sites at each locus in two randomly chosen gametes.     

A Mixed Model of Mutation for Electrophoretic Identity of Proteins within and between Populations

A model which is a mixture of the model of infinite alleles and the Ohta-Kimura model of stepwise mutation has been proposed for the study of eletcrophoretic variants in natural populations. Mutations which alter the mobility of a protein are divided into two classes: stepwise mutations and nonstepwise mutations. It is assumed that stepwise mutations follow the Ohta-Kimura model while nonstepwise mutations follow the infinite allele model. It is then shown that even if the proportion of nonstepwise mutations is only 5%, with the other 95% stepwise mutations, the effective number of alleles given by the present model is considerably larger than that given by the Ohta-Kimura model of stepwise mutation. The result has also been applied to study Nei's genetic distance.     

Allele frequencies in multidimensional Wright-Fisher models with a general symmetric mutation structure

The diffusion form of a multiple-allele Wright-Fisher model of allele frequencies of types A₁,…,A_K at a neutral locus where there are general symmetric mutation rates of M_ij (=M_ji) from A_i → A_j is studied. A convenient recurrence relationship for the moments of linear forms in the allele frequencies is found. A formula is derived for the expected homozygosity in the transient and stationary models, which is applied to general stepwise mutation models where mutation over more than one step is possible. The probability that two randomly chosen genes are j steps apart at time t in the stepwise mutation model is found to have a reasonably simple form if conditioning is on the initial allele frequencies arranged in order of magnitude. Of interest is a new geometric charge state model, mutation over several steps roughly corresponding to independent charge changes. The expected homozygosity and expected distance between two randomly chosen genes is tabulated in this model.     

Estimating effective population size or mutation rate with microsatellites

Microsatellites are short tandem repeats that are widely dispersed among eukaryotic genomes. Many of them are highly polymorphic; they have been used widely in genetic studies. Statistical properties of all measures of genetic variation at microsatellites critically depend upon the composite parameter theta = 4Nmicro, where N is the effective population size and micro is mutation rate per locus per generation. Since mutation leads to expansion or contraction of a repeat number in a stepwise fashion, the stepwise mutation model has been widely used to study the dynamics of these loci. We developed an estimator of theta, theta; (F), on the basis of sample homozygosity under the single-step stepwise mutation model. The estimator is unbiased and is much more efficient than the variance-based estimator under the single-step stepwise mutation model. It also has smaller bias and mean square error (MSE) than the variance-based estimator when the mutation follows the multistep generalized stepwise mutation model. Compared with the maximum-likelihood estimator theta; (L) by, theta; (F) has less bias and smaller MSE in general. theta; (L) has a slight advantage when theta is small, but in such a situation the bias in theta; (L) may be more of a concern.     

Stepwise mutation likelihood computation by sequential importance sampling in subdivided population models

An importance sampling algorithm for computing the likelihood of a sample of genes at loci under a stepwise mutation model in a subdivided population is developed. This allows maximum likelihood estimation of migration rates between subpopulations. The time to the most recent common ancestor of the sample can also be computed. The technique is illustrated by an analysis of a data set of Australian red fox populations.     

Mutation Patterns at Dinucleotide Microsatellite Loci in Humans

Microsatellites are a major type of molecular markers in genetics studies. Their mutational dynamics are not clear. We investigated the patterns and characteristics of 97 mutation events unambiguously identified, from 53 multigenerational pedigrees with 630 subjects, at 362 autosomal dinucleotide microsatellite loci. A size-dependent mutation bias (in which long alleles are biased toward contraction, whereas short alleles are biased toward expansion) is observed. There is a statistically significant negative relationship between the magnitude (repeat numbers changed during mutation) and direction (contraction or expansion) of mutations and standardized allele size. Contrasting with earlier findings in humans, most mutation events (63%) in our study are multistep events that involve changes of more than one repeat unit. There was no correlation between mutation rate and recombination rate. Our data indicate that mutational dynamics at microsatellite loci are more complicated than the generalized stepwise mutation models.     

Variance of genetic distance and correlation of heterozygosity between populations under the pressure of stepwise mutation

Using the stepwise mutation model of Ohta and Kimura (1973), formulas are developed for the correlation of heterozygosity and the variance of genetic distance between two finite populations. Studied in detail is the case where the sizes of the two descendant populations are equal to that of the ancestral population and the mutation rate is the same for all loci. Numerical computations are carried out by using the present formulas and those of Li and Nei (1975Genet. Res.25) for the infinite-allele model. The results are as follows: The correlation of heterozygosity decreases with time faster for the stepwise mutation model than for the infinite-allele model. However, the relationships between the correlation of heterozygosity and the normalized genetic identity for the two models are very similar, if the average heterozygosities of the two populations are around 0.20 or less. On the other hand, the variance of genetic distance for the stepwise mutation model may become considerably smaller than that for the infinite-allele model, if the average heterozygosities of the two populations are larger than 0.05. The ratio of the standard deviation to the mean is, however, very large for the stepwise mutation model as well as the infinite-allele model.     

Direct sequencing of PCR products for mutation detection in osteogenesis imperfecta

This work present a short and simple method for mutation detection in type I collagen genes, based on the direct sequencing of single-stranded DNA. The sequencing of type I collagen genes is complicated and difficult because of their large size and highly repetitive and GC-rich coding regions. Although many techniques have been developed for mutation screening in osteogenesis imperfecta (OI), they represent different degrees of sensitivity and are difficult to reproduce and too expensive for application in each laboratory. The method described here is short, easy and especially useful for sequencing of collagen genes in OI cases, in which the region with a suspected structural defect is localized by collagen analysis.     

Limited evidence that cancer susceptibility regions are preferential targets for somatic mutation

BackgroundGenome wide-association studies have successfully identified several hundred independent loci harboring common cancer susceptibility alleles that are distinct from the more than 110 cancer predisposition genes. The latter are generally characterized by disruptive mutations in coding genes that have been established as ‘drivers’ of cancer in large somatic sequencing studies. We set out to determine whether, similarly, common cancer susceptibility loci map to genes that have altered frequencies of mutation.ResultsIn our analysis of the intervals defined by the cancer susceptibility markers, we observed that cancer susceptibility regions have gene mutation frequencies comparable to background mutation frequencies. Restricting analyses to genes that have been determined to be pleiotropic across cancer types, genes affected by expression quantitative trait loci, or functional genes indicates that most cancer susceptibility genes classified into these subgroups do not display mutation frequencies that deviate from those expected. We observed limited evidence that cancer susceptibility regions that harbor common alleles with small estimated effect sizes are preferential targets for altered somatic mutation frequencies.ConclusionsOur findings suggest a complex interplay between germline susceptibility and somatic mutation, underscoring the cumulative effect of common variants on redundant pathways as opposed to driver genes. Complex biological pathways and networks likely link these genetic features of carcinogenesis, particularly as they relate to distinct polygenic models for each cancer type.     

Negative regulatory gene for general control of amino acid biosynthesis in Saccharomyces cerevisiae.

In Saccharomyces cerevisiae, many amino acid biosynthetic pathways are coregulated by a complex general control system: starvation for a single amino acid results in the derepression of amino acid biosynthetic genes in multiple pathways. Derepression of these genes is mediated by positive (GCN) and negative (GCD) regulatory genes. In this paper we describe the isolation and characterization of a previously unreported negative regulatory gene, GCD3. A gcd3 mutation is recessive to wild type, confers resistance to multiple amino acid analogs, and results in overproduction and partially constitutive elevation of mRNA levels for amino acid biosynthetic genes. Furthermore, a gcd3 mutation can overcome the derepression-deficient phenotype of mutations in the positive regulatory GCN1, GCN2, and GCN3 genes. However, the gcd3 mutation cannot overcome the derepression-deficient phenotype of a gcn4 mutation, suggesting that GCD3 acts as a negative regulator of the important GCN4 gene. Northern blot analysis confirmed this conclusion, in that the steady-state levels of GCN4 mRNA are greatly increased in a gcd3 mutant. Thus, the negative regulatory gene GCD3 plays a central role in derepression of amino acid biosynthetic genes.     

Statistical properties of population differentiation estimators under stepwise mutation in a finite island model

Microsatellite loci mutate at an extremely high rate and are generally thought to evolve through a stepwise mutation model. Several differentiation statistics taking into account the particular mutation scheme of the microsatellite have been proposed. The most commonly used is R(ST) which is independent of the mutation rate under a generalized stepwise mutation model. F(ST) and R(ST) are commonly reported in the literature, but often differ widely. Here we compare their statistical performances using individual-based simulations of a finite island model. The simulations were run under different levels of gene flow, mutation rates, population number and sizes. In addition to the per locus statistical properties, we compare two ways of combining R(ST) over loci. Our simulations show that even under a strict stepwise mutation model, no statistic is best overall. All estimators suffer to different extents from large bias and variance. While R(ST) better reflects population differentiation in populations characterized by very low gene-exchange, F(ST) gives better estimates in cases of high levels of gene flow. The number of loci sampled (12, 24, or 96) has only a minor effect on the relative performance of the estimators under study. For all estimators there is a striking effect of the number of samples, with the differentiation estimates showing very odd distributions for two samples.     

Mutations in the helix termination motif of mouse type I IRS keratin genes impair the assembly of keratin intermediate filament

Two classical mouse hair coat mutations, Rex (Re) and Rex wavy coat (Re(wc)), are linked to the type I inner root sheath (IRS) keratin genes of chromosome 11. An N-ethyl-N-nitrosourea-induced mutation, M100573, also maps close to the type I IRS keratin genes. In this study, we demonstrate that Re and M100573 mice bear mutations in the type I IRS gene Krt25; Re(wc) mice bear an additional mutation in the type I IRS gene Krt27. These three mutations are located in the helix termination motif of the 2B alpha-helical rod domain of a type I IRS keratin protein. Immunohistological analysis revealed abnormal foam-like immunoreactivity with an antibody raised to type II IRS keratin K71 in the IRS of Re/+ mice. These results suggest that the helix termination motif is essential for the proper assembly of types I and II IRS keratin protein complexes and the formation of keratin intermediate filaments.     

Many ribosomal protein genes are cancer genes in zebrafish

We have generated several hundred lines of zebrafish (Danio rerio), each heterozygous for a recessive embryonic lethal mutation. Since many tumor suppressor genes are recessive lethals, we screened our colony for lines that display early mortality and/or gross evidence of tumors. We identified 12 lines with elevated cancer incidence. Fish from these lines develop malignant peripheral nerve sheath tumors, and in some cases also other tumor types, with moderate to very high frequencies. Surprisingly, 11 of the 12 lines were each heterozygous for a mutation in a different ribosomal protein (RP) gene, while one line was heterozygous for a mutation in a zebrafish paralog of the human and mouse tumor suppressor gene, neurofibromatosis type 2. Our findings suggest that many RP genes may act as haploinsufficient tumor suppressors in fish. Many RP genes might also be cancer genes in humans, where their role in tumorigenesis could easily have escaped detection up to now.     

Complex mutations in a high proportion of microsatellite loci from the protozoan parasite Plasmodium falciparum

Microsatellite loci are generally assumed to evolve via a stepwise mutational process and a battery of statistical techniques has been developed in recent years based on this or related mutation models. It is therefore important to investigate the appropriateness of these models in a wide variety of taxa. We used two approaches to examine mutation patterns in the malaria parasite Plasmodium falciparum: (i) we examined sequence variation at 12 tri-nucleotide repeat loci; and (ii) we analysed patterns of repeat structure and heterozygosity at 114 loci using data from 12 laboratory parasite lines. The sequencing study revealed complex patterns of mutation in five of the 12 loci studied. Alleles at two loci contain indels of 24 bp and 57 bp in flanking regions, while in the other three loci, blocks of imperfect microsatellites appear to be duplicated or inserted; these loci essentially consist of minisatellite repeats, with each repeat unit containing four to eight microsatellites. The survey of heterozygosity revealed a positive relationship between repeat number and microsatellite variability for both di- and trinucleotides, indicating a higher mutation rate in loci with longer repeat arrays. Comparisons of levels of variation in different repeat types indicate that the mutation rate of dinucleotide-bearing loci is 1.6-2.1 times faster than trinucleotides, consistent with the lower mean number of repeats in trinucleotide-bearing loci. However, despite the evidence that microsatellite arrays themselves are evolving in a manner consistent with stepwise mutation model in P. falciparum, the high frequency of complex mutations precludes the use of analytical tools based on this mutation model for many microsatellite-bearing loci in this protozoan. The results call into question the generality of models based on stepwise mutation for analysing microsatellite data, but also demonstrate the ease with which loci that violate model assumptions can be detected using minimal sequencing effort.     

Evidence for complex mutations at microsatellite loci in Drosophila.

Fifteen lines each of Drosophila melanogaster, D. simulans, and D. sechellia were scored for 19 microsatellite loci. One to four alleles of each locus in each species were sequenced, and microsatellite variability was compared with sequence structure. Only 7 loci had their size variation among species consistent with the occurrence of strictly stepwise mutations in the repeat array, the others showing extensive variability in the flanking region compared to that within the microsatellite itself. Polymorphisms apparently resulting from complex nonstepwise mutations involving the microsatellite were also observed, both within and between species. Maximum number of perfect repeats and variance of repeat count were found to be strongly correlated in microsatellites showing an apparently stepwise mutation pattern. These data indicate that many microsatellite mutation events are more complex than represented even by generalized stepwise mutation models. Care should therefore be taken in inferring population or phylogenetic relationships from microsatellite size data alone. The analysis also indicates, however, that evaluation of sequence structure may allow selection of microsatellites that more closely match the assumptions of stepwise models.