Tumor architecture and emergence of strong genetic alterations are bottlenecks for clonal evolution in primary prostate cancer.

Prostate cancer (PCA) exhibits high levels of intratumoral heterogeneity. In this study, we developed a mathematical model to study the growth and genetic evolution of PCA. We explored the possible evolutionary patterns and demonstrated that tumor architecture represents a major bottleneck for divergent clonal evolution.

Understanding recessive disease risk in multi-ethnic populations with different degrees of consanguinity.

Population medical genetics aims at translating clinically relevant findings from recent studies of large cohorts into healthcare for individuals. Genetic counseling concerning reproductive risks and options is still mainly based on family history, and consanguinity is viewed to increase the risk for recessive diseases regardless of the demographics. However, in an increasingly multi-ethnic society with diverse approaches to partner selection, healthcare professionals should also sharpen their intuition for the influence of different mating schemes in non-equilibrium dynamics.

The speed of invasion in an advancing population.

We derive rigorous estimates on the speed of invasion of an advantageous trait in a spatially advancing population in the context of a system of one-dimensional F-KPP equations. The model was introduced and studied heuristically and numerically in a paper by Venegas-Ortiz et al. (Genetics 196:497-507, 2014).

From adaptive dynamics to adaptive walks.

We consider an asexually reproducing population on a finite type space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event. On the individual-based level this population can be modelled as a measure-valued Markov process. Multiple variations of this system have been studied in the simultaneous limit of large populations and rare mutations, where the regime is chosen such that mutations are separated.

The recovery of a recessive allele in a Mendelian diploid model.

We study the large population limit of a stochastic individual-based model which describes the time evolution of a diploid hermaphroditic population reproducing according to Mendelian rules. Neukirch and Bovier (J Math Biol 75:145-198, 2017) proved that sexual reproduction allows unfit alleles to survive in individuals with mixed genotype much longer than they would in populations reproducing asexually. In the present paper we prove that this indeed opens the possibility that individuals with a pure genotype can reinvade in the population after the appearance of further mutations.

Survival of a recessive allele in a Mendelian diploid model.

In this paper we analyse the genetic evolution of a diploid hermaphroditic population, which is modelled by a three-type nonlinear birth-and-death process with competition and Mendelian reproduction. In a recent paper, Collet et al. (J Math Biol 67(3):569-607, 2013) have shown that, on the mutation time-scale, the process converges to the Trait-Substitution Sequence of adaptive dynamics, stepping from one homozygotic state to another with higher fitness.

A stochastic model for immunotherapy of cancer.

We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy of malignant tumours. In this context the different actors, T-cells, cytokines or cancer cells, are modelled as single particles (individuals) in the stochastic system.

Optimization of transcription factor binding map accuracy utilizing knockout-mouse models.

Genome-wide assessment of protein-DNA interaction by chromatin immunoprecipitation followed by massive parallel sequencing (ChIP-seq) is a key technology for studying transcription factor (TF) localization and regulation of gene expression. Signal-to-noise-ratio and signal specificity in ChIP-seq studies depend on many variables, including antibody affinity and specificity. Thus far, efforts to improve antibody reagents for ChIP-seq experiments have focused mainly on generating higher quality antibodies.

Stochastic modelling of T-cell activation.

We investigate a specific part of the human immune system, namely the activation of T-cells, using stochastic tools, especially sharp large deviation results. T-cells have to distinguish reliably between foreign and self peptides which are both presented to them by antigen presenting cells. Our work is based on a model studied by Zint et al.

Plasticity of tumour and immune cells: a source of heterogeneity and a cause for therapy resistance?

Immunotherapies, signal transduction inhibitors and chemotherapies can successfully achieve remissions in advanced stage cancer patients, but durable responses are rare. Using malignant melanoma as a paradigm, we propose that therapy-induced injury to tumour tissue and the resultant inflammation can activate protective and regenerative responses that represent a shared resistance mechanism to different treatments. Inflammation-driven phenotypic plasticity alters the antigenic landscape of tumour cells, rewires oncogenic signalling networks, protects against cell death and reprogrammes immune cell functions.

An asymptotic maximum principle for essentially linear evolution models.

Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a low-dimensional maximum principle in the limit N-->infinity (where N, or N(d) with d> or =1, is proportional to the number of types). In order to extend this variational principle to a larger class of models, we consider here a family of reversible matrices of asymptotic dimension N(d) and identify conditions under which the high-dimensional Rayleigh-Ritz variational problem may be reduced to a low-dimensional one that yields the leading eigenvalue up to an error term of order 1/N. For a large class of mutation-selection models, this implies estimates for the mean fitness, as well as a concentration result for the ancestral distribution of types.

Aging in the random energy model.

The random energy model (REM) has become a key reference model for glassy systems. In particular, it is expected to provide a prime example of a system whose dynamics shows aging, a universal phenomenon characterizing the dynamics of complex systems. The analysis of its activated dynamics is based on so-called trap models, introduced by Bouchaud, that are also used to mimic the dynamics of more complex disordered systems.