PhD Position F/M PhD subject - Stochastic modelling and estimation for the distribution of lengthening and abrupt shortening of ALT cells in yeasts

Aix-Marseille University), will provide us with data of telomere length distributions at the population level, for all the telomeres or for a single telomere selected using a specific probe. These are temporal data, obtained from samples regularly collected in cultures. Due to the exponential growth of the population, subpopulations are selected on a daily or bi-daily basis either on Petri dishes with successive transplantations of a single colony, or on liquid experiments with successive dilutions. Most of the data are collected using the Southern blot, but we will also study data obtained with other types of methods, including the TeSLA method, which provides measurements of few telomeres selected in the population.

Then, the PhD student will design a stochastic model of telomere evolution at the level of a single lineage, including mechanisms of abrupt telomere shortening and lengthening. The parameters of this model will be estimated from the data of evolution of the length of single telomeres. We can take our inspiration from the work [1,2] for the modeling part and from [3] for the estimation part.

The third step of the project is to construct a stochastic model of telomere evolution at the level of the population, including the individual mechanisms developed earlier. This will take the form of a branching process, where the progeny of different individuals follow independent processes, structured by the vector of individual telomere lengths. Such infinite-dimensional branching processes will be represented as measure-valued Markov processes following the formalism of [4,5]. In particular, the student will prove that the many-to-one formula holds true for this process, as in [6,7] where the authors study telomere length dynamics, and provide numerical simulations in order to illustrate its main property.

The fourth step of the project will consist in building from the previous model another model for the successive transplantations or dilutions experiments described above, able to account for the collected data of telomere length distribution at the level of the population. This model will include resources dynamics, hence breaking the branching property. The goal is here to estimate the main parameters of the model, namely the rates of abrupt attrition and lengthening of telomeres and their range and the rate of progressive telomere shortening due to the end replication problem, from the data. Due to the complexity of the model, it is particularly difficult to design model-specific methods and we will thus use classical optimisation methods, such as least-square estimates, combined with expert opinion on the biological relevance of the obtained parameters values. One of the biological questions we would like to answer is the following: is the rate of progressive telomere shortening due to the end replication problem the same for ALT yeasts than for normal yeasts (with active telomerase)?

Other questions can also be considered during teh PhD thesis, depending on the progress and the interest of the student, such as modeling questions regarding the proliferative capacity and the competitivity of ALT cells in populations with multiple non-attrition strategies.

Skills

The candidate should have skills in statistics and/or stochastic modeling. R, Python or Matlab programming skills are also required. An affinity or experience with biological applications will be highly appreciated.