Mathematical Analysis of a Clonal Evolution Model of Tumour Cell Proliferation
József Z. Farkas, Glenn F. Webb
We investigate a partial differential equation model of a cancer cell population, which is structured with respect to age and telomere length of cells. We assume a continuous telomere length structure, which is applicable to the clonal evolution model of cancer cell growth. This model has a non-standard non-local boundary condition. We establish global existence of solutions and study their qualitative behaviour. We study the effect of telomere restoration on cancer cell dynamics. Our results indicate that without telomere restoration, the cell population extinguishes. With telomere restoration, exponential growth occurs in the linear model. We further characterise the specific growth behaviour of the cell population for special cases. We also study the effects of crowding induced mortality on the qualitative behaviour, and the existence and stability of steady states of a nonlinear model incorporating crowding effect. We present examples and extensive numerical simulations, which illustrate the rich dynamic behaviour of the linear and nonlinear models.
Rare recombination events generate sequence diversity among balancer chromosomes in Drosophila melanogaster
Danny E. Miller, Kevin R. Cook, Nazanin Yeganehkazemi, Clarissa B. Smith, Alexandria J. Cockrell, R. Scott Hawley, Casey M. Bergman
Multiply inverted balancer chromosomes that suppress exchange with their homologs are an essential part of the genetic toolkit in Drosophila melanogaster. Despite their widespread use, the organization of balancer chromosomes has not been characterized at the molecular level, and the degree of sequence variation among copies of any given balancer chromosome is unknown. To map inversion breakpoints and study potential sequence diversity in the descendants of a structurally identical balancer chromosome, we sequenced a panel of laboratory stocks containing the most widely used X-chromosome balancer, First Multiple 7 (FM7). We mapped the locations of FM7 breakpoints to precise euchromatic coordinates and identified the flanking sequence of breakpoints in heterochromatic regions. Analysis of SNP variation revealed megabase-scale blocks of sequence divergence among currently used FM7 stocks. We present evidence that this divergence arose by rare double crossover events that replaced a female-sterile allele of the singed gene (sn[X2]) on FM7c with wild type sequence from balanced chromosomes, and propose that many FM7c chromosomes in the Bloomington Drosophila Stock Center have lost sn[X2] by this mechanism. Finally, we characterize the original allele of the Bar gene (B) that is carried on FM7 and validate the hypothesis that the origin and subsequent reversion of the B1 duplication is mediated by unequal exchange. Our results reject a simple non-recombining, clonal mode for the laboratory evolution of balancer chromosomes and have implications for how balancer chromosomes should be used in the design and interpretation of genetic experiments in Drosophila.
Using somatic mutation data to test tumors for clonal relatedness
Irina Ostrovnaya, Venkatraman E. Seshan, Colin B. Begg
A major challenge for cancer pathologists is to determine whether a new tumor in a patient with cancer is a metastasis or an independent occurrence of the disease. In recent years numerous studies have evaluated pairs of tumor specimens to examine the similarity of the somatic characteristics of the tumors and to test for clonal relatedness. As the landscape of mutation testing has evolved, a number of statistical methods for determining clonality have developed, notably for comparing losses of heterozygosity at candidate markers, and for comparing copy number profiles. Increasingly tumors are being evaluated for point mutations in panels of candidate genes using gene sequencing technologies. Comparison of the mutational profiles of pairs of tumors presents unusual methodological challenges: mutations at some loci are much more common than others; knowledge of the marginal mutation probabilities is scanty for most loci at which mutations might occur; the sample space of potential mutational profiles is vast. We examine this problem and propose a test for clonal relatedness of a pair of tumors from a single patient. Using simulations, its properties are shown to be promising. The method is illustrated using several examples from the literature.
A fast method to estimate speciation parameters in a model of isolation with an initial period of gene flow and to test alternative evolutionary scenarios
We consider a model of “isolation with an initial period of migration” (IIM), where an ancestral population instantaneously split into two descendant populations which exchanged migrants symmetrically at a constant rate for a period of time but which are now completely isolated from each other. A method of Maximum Likelihood estimation of the parameters of the model is implemented, for data consisting of the number of nucleotide differences between two DNA sequences at each of a large number of independent loci, using the explicit analytical expressions for the likelihood obtained in Wilkinson-Herbots (2012). The method is demonstrated on a large set of DNA sequence data from two species of Drosophila, as well as on simulated data. The method is extremely fast, returning parameter estimates in less than 1 minute for a data set consisting of the numbers of differences between pairs of sequences from 10,000s of loci, or in a small fraction of a second if all loci are trimmed to the same estimated mutation rate. It is also illustrated how the maximized likelihood can be used to quickly distinguish between competing models describing alternative evolutionary scenarios, either by comparing AIC scores or by means of likelihood ratio tests. The present implementation is for a simple version of the model, but various extensions are possible and are briefly discussed.
Cnidaria: fast, reference-free clustering of raw and assembled genome and transcriptome NGS data
Saulo Alves Aflitos, Edouard Severing, Gabino Sanchez-Perez, Sander Peters, Hans de Jong, Dick de Ridder
Background: Identification of biological specimens is a major requirement for a range of applications. Reference-free methods analyse unprocessed sequencing data without relying on prior knowledge, but generally do not scale to arbitrarily large genomes and arbitrarily large phylogenetic distances. Results: We present Cnidaria, a practical tool for clustering genomic and transcriptomic data with no limitation on genome size or phylogenetic distances. We successfully simultaneously clustered 169 genomic and transcriptomic datasets from 4 kingdoms, achieving 100% identification accuracy at supra-species level and 78% accuracy for species level. Discussion: CNIDARIA allows for fast, resource-efficient comparison and identification of both raw and assembled genome and transcriptome data. This can help answer both fundamental (e.g. in phylogeny, ecological diversity analysis) and practical questions (e.g. sequencing quality control, primer design).
Evolution of genome size in asexual populations
Aditi Gupta, Thomas LaBar, Michael Miyagi, Christoph Adami
Genome sizes have evolved to vary widely, from 250 bases in viroids to 670 billion bases in amoeba. This remarkable variation in genome size is the outcome of complex interactions between various evolutionary factors such as point mutation rate, population size, insertions and deletions, and genome editing mechanisms that may be specific to certain taxonomic lineages. While comparative genomics analyses have uncovered some of the relationships between these diverse evolutionary factors, we still do not understand what drives genome size evolution. Specifically, it is not clear how primordial mutational processes of base substitutions, insertions, and deletions influence genome size evolution in asexual organisms. Here, we use digital evolution to investigate genome size evolution by tracking genome edits and their fitness effects in real time. In agreement with empirical data, we find that mutation rate is inversely correlated with genome size in asexual populations. We show that at low point mutation rate, insertions are significantly more beneficial than deletions, driving genome expansion and acquisition of phenotypic complexity. Conversely, high mutational load experienced at high mutation rates inhibits genome growth, forcing the genomes to compress genetic information. Our analyses suggest that the inverse relationship between mutation rate and genome size is a result of the tradeoff between evolving phenotypic innovation and limiting the mutational load.