Data Availability StatementDatasets are now availabale in figshare, at the following address: https://figshare. biologists to understand cell proliferation mechanisms and to identify potential pathological division processes. 1 Introduction 1.1 Biological background and CFSE Understanding cell proliferation in general, and immune cell dynamics in particular is a great challenge for biologists. Even if tremendous discoveries have been made in the past decades, many mechanisms remain unclear. Our aim here is Puromycin 2HCl to focus our attention at the cell population level and more Puromycin 2HCl specifically to get the best estimates of the few key parameters able to describe proliferation of immune cells stimulated by an antigen. To obtain good parameter estimates for cell population dynamics, it is necessary to get time group of experimental data. A sensible way to get them is by using cell markers. In this ongoing work, we research data acquired with carboxyfluorescein diacetate succinimidyl ester (CFSE). It’s been demonstrated that CFSE brands relaxing and proliferating cells no matter their stage within the department cycle [1, 2]. It binds to intracellular proteins without affecting differentiation or apoptosis during division. Thus experimental data are not biased. Another advantage is usually that this marker is usually believed to be equally distributed between the two daughter cells after their mothers division. Therefore CFSE concentration can be used to count how many divisions a cell has completed. A downside of this method is usually that its fluorescence can only be detected up to seven or eight divisions due to labelling dilution . Despite this problem, CFSE has been one of the most popular marker because of its ability to track cell proliferation quite efficiently. 1.2 Mathematical modelling of cell division Several mathematical models based on CFSE labelling in cell division have been developed. De Boer and Perelson  published a large review of these different models. The simplest one is based on ordinary differential equations (ODE) [5C7]. Although it is simple enough to estimate parameters such as proliferation and death rates , this model may not reflect the real biological process of division. Indeed, as division times are implicitly assumed to be exponentially distributed, a cell that has just divided could divide again instantly, which is unrealistic if one accounts for mitosis and DNA replication . An other approach is the cyton model [8, 9]. In this model, times to division and death for each generation of cells are described using impartial probability functions. This model is usually written as a set of integral equations. A general cyton solver (GCytS) , coded in Matlab, has been developed for parameter estimation. However, CFSE data are generally not rich enough to correctly estimate the nine parameters in the model. Hyrien and Zand proposed a branching Rabbit Polyclonal to PKA alpha/beta CAT (phospho-Thr197) process model in order to describe CFSE data [10, 11]. This model has been improved by Miao . Cells are classified into four subtypes according to the events that occur at the end of a cycle time (death, rest, division or differentiation). This model is a mathematical tool representing cell behaviour and it can predict the average number of cells in different generations as well as the probability to have a certain Puromycin 2HCl number of cells in a given generation. Fitting this model to CFSE data provides satisfactory results. However, this type of model is usually phenomenological, and may fail to explain mechanistic processes. Finally, some models are based on the Smith-Martin model  where the cell cycle is usually divided into two different phases: a resting phase A with a variable length and a phase B,.