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Register a new userInferring clonal evolution of tumors from single nucleotide somatic mutations
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High-throughput sequencing allows the detection and quantification of frequencies of somatic single nucleotide variants (SNV) in heterogeneous tumor cell populations. In some cases, the evolutionary history and population frequency of the subclonal lineages of tumor cells present in the sample can be reconstructed from these SNV frequency measurements. However, automated methods to do this reconstruction are not available and the conditions under which reconstruction is possible have not been described. We describe the conditions under which the evolutionary history can be uniquely reconstructed from SNV frequencies from single or multiple samples from the tumor population and we introduce a new statistical model, PhyloSub, that infers the phylogeny and genotype of the major subclonal lineages represented in the population of cancer cells. It uses a Bayesian nonparametric prior over trees that groups SNVs into major subclonal lineages and automatically estimates the number of lineages and their ancestry. We sample from the joint posterior distribution over trees to identify evolutionary histories and cell population frequencies that have the highest probability of generating the observed SNV frequency data. When multiple phylogenies are consistent with a given set of SNV frequencies, PhyloSub represents the uncertainty in the tumor phylogeny using a partial order plot. Experiments on a simulated dataset and two real datasets comprising tumor samples from acute myeloid leukemia and chronic lymphocytic leukemia patients demonstrate that PhyloSub can infer both linear (or chain) and branching lineages and its inferences are in good agreement with ground truth, where it is available.
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Environmental and genetic mutations can transform the cells in a co-operating healthy tissue into an ecosystem of individualistic tumour cells that compete for space and resources. Various selection forces are responsible for driving the evolution of cells in a tumour towards more malignant and aggressive phenotypes that tend to have a fitness advantage over the older populations. Although the evolutionary nature of cancer has been recognised for more than three decades (ever since the seminal work of Nowell) it has been only recently that tools traditionally used by ecological and evolutionary researchers have been adopted to study the evolution of cancer phenotypes in populations of individuals capable of co-operation and competition. In this chapter we will describe game theory as an important tool to study the emergence of cell phenotypes in a tumour and will critically review some of its applications in cancer research. These applications demonstrate that game theory can be used to understand the dynamics of somatic cancer evolution and suggest new therapies in which this knowledge could be applied to gain some control over the evolution of the tumour.
We consider inference about the history of a sample of DNA sequences, conditional upon the haplotype counts and the number of segregating sites observed at the present time. After deriving some theoretical results in the coalescent setting, we implement rejection sampling and importance sampling schemes to perform the inference. The importance sampling scheme addresses an extension of the Ewens Sampling Formula for a configuration of haplotypes and the number of segregating sites in the sample. The implementations include both constant and variable population size models. The methods are illustrated by two human Y chromosome data sets.
Given a random RNA secondary structure, $S$, we study RNA sequences having fixed ratios of nuclotides that are compatible with $S$. We perform this analysis for RNA secondary structures subject to various base pairing rules and minimum arc- and stack-length restrictions. Our main result reads as follows: in the simplex of the nucleotide ratios there exists a convex region in which, in the limit of long sequences, a random structure a.a.s.~has compatible sequence with these ratios and outside of which a.a.s.~a random structure has no such compatible sequence. We localize this region for RNA secondary structures subject to various base pairing rules and minimum arc- and stack-length restrictions. In particular, for {bf GC}-sequences having a ratio of {bf G} nucleotides smaller than $1/3$, a random RNA secondary structure without any minimum arc- and stack-length restrictions has a.a.s.~no such compatible sequence. For sequences having a ratio of {bf G} nucleotides larger than $1/3$, a random RNA secondary structure has a.a.s. such compatible sequences. We discuss our results in the context of various families of RNA structures.
One of the outstanding challenges in comparative genomics is to interpret the evolutionary importance of regulatory variation between species. Rigorous molecular evolution-based methods to infer evidence for natural selection from expression data are at a premium in the field, and to date, phylogenetic approaches have not been well-suited to address the question in the small sets of taxa profiled in standard surveys of gene expression. We have developed a strategy to infer evolutionary histories from expression profiles by analyzing suites of genes of common function. In a manner conceptually similar to molecular evolution models in which the evolutionary rates of DNA sequence at multiple loci follow a gamma distribution, we modeled expression of the genes of an emph{a priori}-defined pathway with rates drawn from an inverse gamma distribution. We then developed a fitting strategy to infer the parameters of this distribution from expression measurements, and to identify gene groups whose expression patterns were consistent with evolutionary constraint or rapid evolution in particular species. Simulations confirmed the power and accuracy of our inference method. As an experimental testbed for our approach, we generated and analyzed transcriptional profiles of four emph{Saccharomyces} yeasts. The results revealed pathways with signatures of constrained and accelerated regulatory evolution in individual yeasts and across the phylogeny, highlighting the prevalence of pathway-level expression change during the divergence of yeast species. We anticipate that our pathway-based phylogenetic approach will be of broad utility in the search to understand the evolutionary relevance of regulatory change.
It is known (see e.g. Weibull (1995)) that ESS is not robust against multiple mutations. In this article, we introduce robustness against multiple mutations and study some equivalent formulations and consequences.
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