Statistical Alignment with a Sequence Evolution Model Allowing Rate Heterogeneity along the Sequence

We present a stochastic sequence evolution model to obtain alignments and estimate mutation rates between two homologous sequences. The model allows two possible evolutionary behaviors along a DNA sequence in order to determine conserved regions and take its heterogeneity into account. In our model, the sequence is divided into slow and fast evolution regions. The boundaries between these sections are not known. It is our aim to detect them. The evolution model is based on a fragment insertion and deletion process working on fast regions only and on a substitution process working on fast and slow regions with different rates. This model induces a pair hidden Markov structure at the level of alignments, thus making efficient statistical alignment algorithms possible. We propose two complementary estimation methods, namely, a Gibbs sampler for Bayesian estimation and a stochastic version of the EM algorithm for maximum likelihood estimation. Both algorithms involve the sampling of alignments. We propose a partial alignment sampler, which is computationally less expensive than the typical whole alignment sampler. We show the convergence of the two estimation algorithms when used with this partial sampler. Our algorithms provide consistent estimates for the mutation rates and plausible alignments and sequence segmentations on both simulated and real data.     

Differentiation among populations with migration, mutation, and drift: implications for genetic inference

Populations may become differentiated from one another as a result of genetic drift. The amounts and patterns of differentiation at neutral loci are determined by local population sizes, migration rates among populations, and mutation rates. We provide exact analytical expressions for the mean, variance, and covariance of a stochastic model for hierarchically structured populations subject to migration, mutation, and drift. In addition to the expected correlation in allele frequencies among populations in the same geographic region, we demonstrate that there is a substantial correlation in allele frequencies among regions at the top level of the hierarchy. We propose a hierarchical Bayesian model for inference of Wright's F-statistics in a two-level hierarchy in which we estimate the among-region correlation in allele frequencies by substituting replication across loci for replication across time. We illustrate the approach through an analysis of human microsatellite data, and we show that approaches ignoring the among-region correlation in allele frequencies underestimate the amount of genetic differentiation among major geographic population groups by approximately 30%. Finally, we discuss the implications of these results for the use and interpretation of F-statistics in evolutionary studies.     

Effects of recombination rate on human endogenous retrovirus fixation and persistence

Endogenous retroviruses (ERVs) result from germ line infections by exogenous retroviruses. They can proliferate within the genome of their host species until they are either inactivated by mutation or removed by recombinational deletion. ERVs belong to a diverse group of mobile genetic elements collectively termed transposable elements (TEs). Numerous studies have attempted to elucidate the factors determining the genomic distribution and persistence of TEs. Here we show that, within humans, gene density and not recombination rate correlates with fixation of endogenous retroviruses, whereas the local recombination rate determines their persistence in a full-length state. Recombination does not appear to influence fixation either via the ectopic exchange model or by indirect models based on the efficacy of selection. We propose a model linking rates of meiotic recombination to the probability of recombinational deletion to explain the effect of recombination rate on persistence. Chromosomes 19 and Y are exceptions, possessing more elements than other regions, and we suggest this is due to low gene density and elevated rates of human ERV integration in males for chromosome Y and segmental duplication for chromosome 19.     

Environmental heterogeneity enhances clonal interference

Clonal interference (CI) is a phenomenon that may be important in several asexual microbes. It occurs when population sizes are large and mutation rates to new beneficial alleles are of significant magnitude. Here we explore the role of gene flow and spatial heterogeneity in selection strength in the adaptation of asexuals. We consider a subdivided population of individuals that are adapting, through new beneficial mutations, and that migrate between different patches. The fitness effect of each mutation depends on the patch and all mutations considered are assumed to be unconditionally beneficial. We find that spatial variation in selection pressure affects the rate of adaptive evolution and its qualitative effects depend on the level of gene flow. In particular, we find that both low migration and high levels of heterogeneity lead to enhanced CI. In contrast, for high levels of migration the rate of fixation of adaptive mutations is higher when environmental heterogeneity is present. In addition, we observe that the level of fitness variation is higher and simultaneous fixation of multiple mutations tends to occur in the regime of low migration rates and high heterogeneity.     

Identifying gene pathways associated with cancer characteristics via sparse statistical methods

We propose a statistical method for uncovering gene pathways that characterize cancer heterogeneity. To incorporate knowledge of the pathways into the model, we define a set of activities of pathways from microarray gene expression data based on the Sparse Probabilistic Principal Component Analysis (SPPCA). A pathway activity logistic regression model is then formulated for cancer phenotype. To select pathway activities related to binary cancer phenotypes, we use the elastic net for the parameter estimation and derive a model selection criterion for selecting tuning parameters included in the model estimation. Our proposed method can also reverse-engineer gene networks based on the identified multiple pathways that enables us to discover novel gene-gene associations relating with the cancer phenotypes. We illustrate the whole process of the proposed method through the analysis of breast cancer gene expression data.     

A deterministic approach for the estimation of mutation rates in cultured mammalian cells

Unequal growth rates between mutant and wild-type cells in a large population constitute a problem for the estimation of mutation rate. Over a period of cell growth, a selective advantage of one cell type over the other might lead to considerable error in the estimation of mutation rate if equal growth rates are assumed. In this study, we propose a formula and apply it to the estimation of spontaneous mutation rate in a growing population of Chinese hamster V79 cells in which ouabain-resistant mutant cells exhibit a slower growth rate than the wild-type cells. The formula is a generalization of that previously presented by Armitage (1953), and this is the first attempt to apply the deterministic approach for mutation rate estimation to cultured mammalian cells. The value of the estimated rate is compared with that derived from a parallel experiment using the fluctuation test of Luria and Delbrück (1943). The limitations and advantages of taking the deterministic approach to mutation rate estimation in mammalian cell systems are discussed.     

The evolutionary dynamics of endogenous retroviruses

Endogenous retroviruses (ERVs) are vertically transmitted intragenomic elements derived from integrated retroviruses. ERVs can proliferate within the genome of their host until they either acquire inactivating mutations or are lost by recombinational deletion. We present a model that unifies current knowledge of ERV biology into a single evolutionary framework. The model predicts the possible long-term outcomes of retroviral germline infection and can account for the variable patterns of observed ERV genetic diversity. We hope the model will provide a useful framework for understanding ERV evolution, enabling the testing of evolutionary hypotheses and the estimation of parameters governing ERV proliferation.     

Relative efficiency of unequal versus equal cluster sizes in cluster randomized trials using generalized estimating equation models

There is growing interest in conducting cluster randomized trials (CRTs). For simplicity in sample size calculation, the cluster sizes are assumed to be identical across all clusters. However, equal cluster sizes are not guaranteed in practice. Therefore, the relative efficiency (RE) of unequal versus equal cluster sizes has been investigated when testing the treatment effect. One of the most important approaches to analyze a set of correlated data is the generalized estimating equation (GEE) proposed by Liang and Zeger, in which the “working correlation structure” is introduced and the association pattern depends on a vector of association parameters denoted by ρ. In this paper, we utilize GEE models to test the treatment effect in a two‐group comparison for continuous, binary, or count data in CRTs. The variances of the estimator of the treatment effect are derived for the different types of outcome. RE is defined as the ratio of variance of the estimator of the treatment effect for equal to unequal cluster sizes. We discuss a commonly used structure in CRTs—exchangeable, and derive the simpler formula of RE with continuous, binary, and count outcomes. Finally, REs are investigated for several scenarios of cluster size distributions through simulation studies. We propose an adjusted sample size due to efficiency loss. Additionally, we also propose an optimal sample size estimation based on the GEE models under a fixed budget for known and unknown association parameter (ρ) in the working correlation structure within the cluster.     

Experimental estimation of mutation rates in a wheat population with a gene genealogy approach

Microsatellite markers are extensively used to evaluate genetic diversity in natural or experimental evolving populations. Their high degree of polymorphism reflects their high mutation rates. Estimates of the mutation rates are therefore necessary when characterizing diversity in populations. As a complement to the classical experimental designs, we propose to use experimental populations, where the initial state is entirely known and some intermediate states have been thoroughly surveyed, thus providing a short timescale estimation together with a large number of cumulated meioses. In this article, we derived four original gene genealogy-based methods to assess mutation rates with limited bias due to relevant model assumptions incorporating the initial state, the number of new alleles, and the genetic effective population size. We studied the evolution of genetic diversity at 21 microsatellite markers, after 15 generations in an experimental wheat population. Compared to the parents, 23 new alleles were found in generation 15 at 9 of the 21 loci studied. We provide evidence that they arose by mutation. Corresponding estimates of the mutation rates ranged from 0 to 4.97 x 10(-3) per generation (i.e., year). Sequences of several alleles revealed that length polymorphism was only due to variation in the core of the microsatellite. Among different microsatellite characteristics, both the motif repeat number and an independent estimation of the Nei diversity were correlated with the novel diversity. Despite a reduced genetic effective size, global diversity at microsatellite markers increased in this population, suggesting that microsatellite diversity should be used with caution as an indicator in biodiversity conservation issues.     

A note on plating efficiency in fluctuation experiments

In estimating mutation rates using the Luria-Delbrück experimental protocol, it is often assumed that all mutant cells survive the plating procedure to form visible mutant colonies. This assumption of perfect plating efficiency may not hold in certain circumstances, but none of the existing estimation methods that adjust for plating efficiency is strictly based on the likelihood principle. To ameliorate this situation, we propose likelihood based algorithms for computing point and interval estimates of mutation rates.     

Viral RNA mutations are region specific and increased by ribavirin in a full-length hepatitis C virus replication system

High rates of genetic variation ensure the survival of RNA viruses. Although this variation is thought to result from error-prone replication, RNA viruses must also maintain highly conserved genomic segments. A balance between conserved and variable viral elements is especially important in order for viruses to avoid "error catastrophe." Ribavirin has been shown to induce error catastrophe in other RNA viruses. We therefore used a novel hepatitis C virus (HCV) replication system to determine relative mutation frequencies in variable and conserved regions of the HCV genome, and we further evaluated these frequencies in response to ribavirin. We sequenced the 5' untranslated region (5' UTR) and the core, E2 HVR-1, NS5A, and NS5B regions of replicating HCV RNA isolated from cells transfected with a T7 polymerase-driven full-length HCV cDNA plasmid containing a cis-acting hepatitis delta virus ribozyme to control 3' cleavage. We found quasispecies in the E2 HVR-1 and NS5B regions of untreated replicating viral RNAs but not in conserved 5' UTR, core, or NS5A regions, demonstrating that important cis elements regulate mutation rates within specific viral segments. Neither T7-driven replication nor sequencing artifacts produced these nucleotide substitutions in control experiments. Ribavirin broadly increased error generation, especially in otherwise invariant regions, indicating that it acts as an HCV RNA mutagen in vivo. Similar results were obtained in hepatocyte-derived cell lines. These results demonstrate the potential utility of our system for the study of intrinsic factors regulating genetic variation in HCV. Our results further suggest that ribavirin acts clinically by promoting nonviable HCV RNA mutation rates. Finally, the latter result suggests that our replication model may be useful for identifying agents capable of driving replicating virus into error catastrophe.     

Culture of neural cells on polymers coated surfaces for biosensor applications

We focused our study on the olfactory cells growth on biocompatible polymer films electrodeposited on a silicon microsystem. Several substrates such as polyethyleneimine (PEI), polypropyleneimine (PPI), and polypyrrole (PPy), acting as potentially good candidates for cell culture, were tested in order to allow cells to adhere and proliferate. During their growth, the evolution of their morphology was monitored using both confocal microscope and immunohistochemistry, leading to the conclusion of a normal development. An estimation of the adhesion and proliferation rates of rat neuronal cell cultures indicated that PEI and PPI were the best substrates for cultivating olfactory cells.     

Intensive nuclear selection in tryptophan limited cultures of Escherichia coli B/r/l, trp

Summary The paradoxical constancy of the rate of mutation to resistance to bacteriophage T5 was observed long ago by Novick and Szilard. Mutation rates are independent of growth rate in tryptophan limited chemostat cultures, even though both average cell volume and DNA content increase with generation time. To examine nuclear selection in these multinucleate cells, cultures of E. coli B/r/l, trp were exposed briefly to acridine orange/visible light, and cells repackaged to uninucleate forms by shifting growth rates up to 0.5 divisions per hr. The kinetics of accumulation of mutant nuclei indicates that only a single master nucleus replicates in each cell, one of its progeny becomes the master nucleus during the following nuclear generation in the same cell, and both progeny become master nuclei if the cell divides. Autoradiographs showed that master nuclei are located at the ends of cells and that uninucleate cells are produced at each division, except possibly for a small fraction of aberrant divisions. This intensive selection during replication and inheritance of master nuclei provides an explanation for the constancy of cellular mutation rates, which is due to the constancy of the rate of DNA replication in these cultures and the (almost) complete selection for mutant nuclei in mutated cells.Work supported by the U. S. Atomic Energy Commission.     

On the mutation rate of herpes simplex virus type 1

All seven DNA-based microbes for which carefully established mutation rates and mutational spectra were previously available displayed a genomic mutation rate in the neighborhood of 0.003 per chromosome replication. The pathogenic mammalian DNA virus herpes simplex type 1 has an estimated genomic mutation rate compatible with that value.     

Evolution of functionally conserved enhancers can be accelerated in large populations: a population-genetic model

The evolution of cis-regulatory elements (or enhancers) appears to proceed at dramatically different rates in different taxa. Vertebrate enhancers are often very highly conserved in their sequences, and relative positions, across distantly related taxa. In contrast, functionally equivalent enhancers in closely related Drosophila species can differ greatly in their sequences and spatial organization. We present a population-genetic model to explain this difference. The model examines the dynamics of fixation of pairs of individually deleterious, but compensating, mutations. As expected, small populations are predicted to have a high rate of evolution, and the rate decreases with increasing population size. In contrast to previous models, however, this model predicts that the rate of evolution by pairs of compensatory mutations increases dramatically for population sizes above several thousand individuals, to the point of greatly exceeding the neutral rate. Application of this model predicts that species with moderate population sizes will have relatively conserved enhancers, whereas species with larger populations will be expected to evolve their enhancers at much higher rates. We propose that the different degree of conservation seen in vertebrate and Drosophila enhancers may be explained solely by differences in their population sizes and generation times.     

More precisely biased: increasing the number of markers is not a silver bullet in genetic bottleneck testing

In response to our review of the use of genetic bottleneck tests in the conservation literature (Peery et al. 2012, Molecular Ecology, 21 , 3403–3418), Hoban et al. (2013, Molecular Ecology, in press) conducted population genetic simulations to show that the statistical power of genetic bottleneck tests can be increased substantially by sampling large numbers of microsatellite loci, as they suggest is now possible in the age of genomics. While we agree with Hoban and co‐workers in principle, sampling large numbers of microsatellite loci can dramatically increase the probability of committing type 1 errors (i.e. detecting a bottleneck in a stable population) when the mutation model is incorrectly assumed. Using conservative values for mutation model parameters can reduce the probability of committing type 1 errors, but doing so can result in significant losses in statistical power. Moreover, we believe that practical limitations associated with developing large numbers of high‐quality microsatellite loci continue to constrain sample sizes, a belief supported by a literature review of recent studies using next generation sequencing methods to develop microsatellite libraries. conclusion, we maintain that researchers employing genetic bottleneck tests should proceed with caution and carefully assess both statistical power and type 1 error rates associated with their study design.     

Nonparametric inference for local extrema with application to oligonucleotide microarray data in yeast genome

Identifying local extrema of expression profiles is one primary objective in some cDNA microarray experiments. To study the replication dynamics of the yeast genome, for example, local peaks of hybridization intensity profiles correspond to putative replication origins. We propose a nonparametric kernel smoothing (NKS) technique to detect local hybridization intensity extrema across chromosomes. The novelty of our approach is that we base our inference procedures on equilibrium points, namely those locations at which the first derivative of the intensity curve is zero. The proposed smoothing technique provides both point and interval estimation for the location of local extrema. Also, this technique can be used to test for the hypothesis of either one or multiple suspected locations being the true equilibrium points. We illustrate the proposed method on a microarray data set from an experiment designed to study the replication origins in the yeast genome, in that the locations of autonomous replication sequence (ARS) elements are identified through the equilibrium points of the smoothed intensity profile curve. Our method found a few ARS elements that were not detected by the current smoothing methods such as the Fourier convolution smoothing.     

Multi-type Galton-Watson process as a model for proliferating human tumour cell populations derived from stem cells: estimation of stem cell self-renewal probabilities in human ovarian carcinomas

A mathematical model for proliferation of tumour cell populations is developed. The cell population is assumed to be organized in a hierarchy of decreasing proliferative potential and increasing degree of differentiation. Using some elements of the theory of Multi-type Galton-Watson processes, a method is proposed for the estimation of Psr, the probability of self-renewal of tumour stem cells, from the experimental distribution of clonal unit sizes obtained in cell culture studies. Six data sets from patients with advanced adenocarcinoma of the ovary are used to demonstrate the method. Reasonable estimates are obtained, and the theoretical colony size distributions predicted by the model appear to be in good qualitative agreement with the experimental ones, and lend support to a stem cell model of tumour growth. The possible significance of Psr as a prognostic factor is briefly discussed.     

Model-Based Statistical Procedures for the Analysis of in Vitro Mutagenesis Assays

A number of short-term screening assays for potential chemical carcinogens and mutagens involve the measurement of mutation rates in in vitro cell populations. In this paper, statistical procedures are proposed for the analysis of results from these assays. The procedures, which are based on previously developed stochastic models of cell growth and mutation, include hypothesis tests for the comparison of mutation rates in treated and control cultures, and estimation and hypothesis tests for the parameters of a linear mutagenesis dose-response. Computer simulation is used to validate the methods, and they are illustrated by an analysis of data obtained under the mouse lymphoma mutagenesis protocol.     

Approximate Bayesian computation for modular inference problems with many parameters: the example of migration rates

We propose a two‐step procedure for estimating multiple migration rates in an approximate Bayesian computation (ABC) framework, accounting for global nuisance parameters. The approach is not limited to migration, but generally of interest for inference problems with multiple parameters and a modular structure (e.g. independent sets of demes or loci). We condition on a known, but complex demographic model of a spatially subdivided population, motivated by the reintroduction of Alpine ibex (Capra ibex) into Switzerland. In the first step, the global parameters ancestral mutation rate and male mating skew have been estimated for the whole population in Aeschbacher et al. (Genetics 2012; 192 : 1027). In the second step, we estimate in this study the migration rates independently for clusters of demes putatively connected by migration. For large clusters (many migration rates), ABC faces the problem of too many summary statistics. We therefore assess by simulation if estimation per pair of demes is a valid alternative. We find that the trade‐off between reduced dimensionality for the pairwise estimation on the one hand and lower accuracy due to the assumption of pairwise independence on the other depends on the number of migration rates to be inferred: the accuracy of the pairwise approach increases with the number of parameters, relative to the joint estimation approach. To distinguish between low and zero migration, we perform ABC‐type model comparison between a model with migration and one without. Applying the approach to microsatellite data from Alpine ibex, we find no evidence for substantial gene flow via migration, except for one pair of demes in one direction.