Modeling neutral evolution using an in nite-allele Markov branching process

We consider an in nite-allele Markov branching process (IAMBP). Our main focus is the frequency spectrum of this process, i.e., the proportion of alleles having a given number of copies at a speci ed time point. We derive the variance of the frequency spectrum, which is useful for interval estimation and hypothesis testing for process parameters. In addition, for a class of special IAMBP with birth and death o spring distribution, we show that the mean of its limiting frequency spectrum has an explicit form in terms of the hypergeometric function. We also derive an asymptotic expression for convergence rate to the limit. Simulations are used to illustrate the results for the birth and death process

Stochastic hypothesis of transition from inborn neutropenia to AML: interactions of cell population dynamics and population genetics

We present a stochastic model of driver mutations in the transition from severe congenital neutropenia to myelodysplastic syndrome to acute myeloid leukemia (AML). The model has the form of a multitype branching process.We derive equations for the distributions of the times to consecutive driver mutations and set up simulations involving a range of hypotheses regarding acceleration of the mutation rates in successive mutant clones. Our model reproduces the clinical distribution of times at diagnosis of secondary AML. Surprisingly, within the framework of our assumptions, stochasticity of the mutation process is incapable of explaining the spread of times at diagnosis of AML in this case; it is necessary to additionally assume a wide spread of proliferative parameters among disease cases. This finding is unexpected but generally consistent with the wide heterogeneity of characteristics of human cancers

A Countable-Type Branching Process Model for the Tug-of-War Cancer Cell Dynamics

We consider a time-continuous Markov branching process of proliferating cells with a denumerable collection of types. Among-type transitions are inspired by the Tug-of-War process introduced by McFarland et al. (2014) as a mathematical model for competition of advantageous driver mutations and deleterious passenger mutations in cancer cells. We introduce a version of the model in which a driver mutation pushes the type of the cell $L$-units up, while a passenger mutation pulls it $1$-unit down. The distribution of time to divisions depends on the type (fitness) of cell, which is an integer. The extinction probability given any initial cell type is strictly less than $1$, which allows us to investigate the transition between types (type transition) in an infinitely long cell lineage of cells. The analysis leads to the result that under driver dominance, the type transition process escapes to infinity, while under passenger dominance, it leads to a limit distribution. Implications in cancer cell dynamics and population genetics are discussed

Forward-Time Simulations of Human Populations with Complex Diseases

Due to the increasing power of personal computers, as well as the availability of flexible forward-time simulation programs like simuPOP, it is now possible to simulate the evolution of complex human diseases using a forward-time approach. This approach is potentially more powerful than the coalescent approach since it allows simulations of more than one disease susceptibility locus using almost arbitrary genetic and demographic models. However, the application of such simulations has been deterred by the lack of a suitable simulation framework. For example, it is not clear when and how to introduce disease mutants—especially those under purifying selection—to an evolving population, and how to control the disease allele frequencies at the last generation. In this paper, we introduce a forward-time simulation framework that allows us to generate large multi-generation populations with complex diseases caused by unlinked disease susceptibility loci, according to specified demographic and evolutionary properties. Unrelated individuals, small or large pedigrees can be drawn from the resulting population and provide samples for a wide range of study designs and ascertainment methods. We demonstrate our simulation framework using three examples that map genes associated with affection status, a quantitative trait, and the age of onset of a hypothetical cancer, respectively. Nonadditive fitness models, population structure, and gene–gene interactions are simulated. Case-control, sibpair, and large pedigree samples are drawn from the simulated populations and are examined by a variety of gene-mapping methods

Dynamics of Growth and Signaling along Linear and Surface Structures in Very Early Tumors

There exists evidence that in early stages tumors progress along linear, tubular, or irregular surface structures. This seems to be the case for atypical adenomatous hyperplasia (AAH), a precursor of adenocarcinoma of the lung. We previously published a simplified model, which showed that early structures had a potential towards spontaneous invasive growth following a latency phase. The transition was facilitated by diffusion of a growth factor and nonlinear cell cycle regulation in cancer cells. The mechanism is analogous to that in Turing pattern formation, although the patterns are irregular and unstable. We introduce more biologically justifiable signaling, in which only the free growth factor molecules diffuse. Flexible nonlinearities in the model accommodate several growth patterns of cells as well as internal versus external production of the growth factor. We show that the reaction-diffusion setup results in complicated spike-like solutions. We discuss these results in the light of published data on the AAH

Preface to Session 70 " Mathematical models and methods to investigate heterogeneity in cell and cell population biology ": Presentation of Session 70 in ICNAAM 2015, Rhodes

International audienceThis session investigates hot topics related to mathematical representations of cell and cell population dynamics in biology and medicine, in particular, but not only, with applications to cancer. Methods in mathematical modelling and analysis, and in statistical inference using single-cell and cell population data, should contribute to focus this session on heterogeneity in cell populations. Among other methods are proposed: a) Intracellular protein dynamics and gene regulatory networks using ordinary/partial/delay differential equations (ODEs, PDEs, DDEs); b) Representation of cell population dynamics using agent-based models (ABMs) and/or PDEs; c) Hybrid models and multiscale models to integrate single-cell dynamics into cell population behaviour; d) Structured cell population dynamics and asymptotic evolution w.r.t. relevant traits; e) Heterogeneity in cancer cell populations: origin, evolution, phylogeny and methods of reconstruction; f) Drug resistance as an evolutionary phenotype: predicting and overcoming it in therapeutics; g) Theoretical therapeutic optimisation of combined drug treatments in cancer cell populations and in populations of other organisms, such as bacteria

The dependence of expression of NF-κB-dependent genes: statistics and evolutionary conservation of control sequences in the promoter and in the 3′ UTR

Abstract Background The NF-κB family plays a prominent role in the innate immune response, cell cycle activation or cell apoptosis. Upon stimulation by pathogen-associated patterns, such as viral RNA a kinase cascade is activated, which strips the NF-κB of its inhibitor IκBα molecule and allows it to translocate into the nucleus. Once in the nucleus, it activates transcription of approximately 90 genes whose kinetics of expression differ relative to when NF-κB translocates into the nucleus, referred to as Early, Middle and Late genes. It is not obvious what mechanism is responsible for segregation of the genes’ timing of transcriptional response. Results It is likely that the differences in timing are due, in part, to the number and type of transcription factor binding sites (TFBS), required for NF-κB itself as well as for the putative cofactors, in the Early versus Late genes. We therefore applied an evolutionary analysis of conserved TFBS. We also examined whether transcription dynamic was related to the presence of AU-rich elements (ARE) located in 3′UTR of the mRNA because recent studies have shown that the presence of AREs is associated with rapid gene induction. We found that Early genes were significantly enriched in NF-κB binding sites occurring in evolutionarily conserved domains compared to genes in the Late group. We also found that Early genes had significantly greater number of ARE sequences in the 3′UTR of the gene. The similarities observed among the Early genes were seen in comparison with distant species, while the Late genes promoter regions were much more diversified. Based on the promoter structure and ARE content, Middle genes can be divided into two subgroups which show similarities to Early and Late genes respectively. Conclusions Our data suggests that the rapid response of the NF-κB dependent Early genes may be due to both increased gene transcription due to NF-κB loading as well as the contribution of mRNA instability to the transcript profiles. Wider phylogenetic analysis of NF-κB dependent genes provides insight into the degree of cross-species similarity found in the Early genes, opposed to many differences in promoter structure that can be found among the Late genes. These data suggest that activation and expression of the Late genes is much more species-specific than of the Early genes.</p