J. Bourdon (Coordinator), D. Eveillard, A. Siegel, O. Radulescu, A. Maass, G. Batt
Another difficulty when studying transcriptional networks lies in the experimental technologies. Indeed, event simulations are usually performed at a transcriptional level. But conversely, observations and accurate time-series measurements are performed at a protein level, inducing a population scale viewpoint. The relation between the transcriptional level and the protein level is still badly understood (except for prokaryotes or some signaling pathways in cancer studies). In fact, this is even more complex because the relation between the cell scale and the population scale is not clear (synchronization phenomena between cells, environmental interactions,…). For instance, most of models of system behaviour do have several attractors. Therefore several unsynchronized cells can be captured by different attractors. The main consequence of such a desynchronization is that the population protein behaviour can be addressed by computing the mean protein behaviour of each cell. Such questions have been addressed by using probabilistic Boolean models (Kauffman'01) but conclusions from these studies are rather limited. In our project, we address the question of introducing data at different levels and scales by using Markov chains models for estimating the population behaviour of cells controlled by a regulation system. In order to improve the results of classical probabilistic Boolean models, we introduce a new notion of weighted Markov chains that model in the same time an abstraction of the cell transcriptional dynamics and an estimation of the protein level behaviour in each cell. Finally, studying the statistical properties of such a Markov chain provides meaningful information about the population scale.
The main objective of this task is to include quantitative reasoning and knowledges in purely quantitative models. For that purpose, it is important to notice that almost every experiments that produce quantitative data corresponds to observations on a cell populations. Quantitative observation thus corresponds to mean and/or variance of certain quantities relative to events over a certain distribution of the population. This task is devoted to the theoretical study of probabilistic models based on weighted Markov chains for modeling quantities like protein concentrations. Such models are constructed by introducing probabilities over discrete chronological models. Quantities are then considered as small accumulations induced by discrete events. The main problems here are to