Section: Research Program

Research axis 1: Computational cellular biochemistry

The movement of many biomolecules such as proteins in living cells has been reported as spatially heterogeneous diffusion (position-dependent diffusion coefficient) or even as anomalous diffusion, whereby the mean-squared displacement scales sub-linearly with time, $〈{𝐫}^2〉\sim t^{\alpha }$ with $\alpha <1$. The influences of such deviations from simple Brownian motion on the biochemical reactions that take place in these media are just starting to be explored. Part of our efforts was aimed at improving the modeling of sub-diffusion in an intracellular context by extending the existing models of obstacle-based sub-diffusion to mobile obstacles [37] or proposing age-structured PDEs to model sub-diffusion [38], [43]. We also explored the effects of locally slowed-down diffusion or local sub-diffusion on the dynamics of simple reactions such as the ligand-binding equilibrium or protein aggregation [44], [39], [77], [78], [47].

Gene expression is highly organized in space and diffusing factors often have to reach and bind partners which positions are not well-mixed, but exhibit stationary spatial organization. We have studied how the spatial organization of genes can affect their interaction [64], [65]. Combining modeling and experiments, we have studied the stochasticity of gene expression in single metazoan cells (chicken cells) and provided its quantification via stochasticity measures [89], [33], [48].

Most cellular pathway models and equations assume that the cell / medium is size / volume constant during the whole duration of the process. However there is an important variability in size and volume within tissue, within cell type and of course during the life of a single cell. We have studied the mechanism of lipid storage in adipocytes both at equilibrium and non-equilibrium [80], [79] and confirmed that the main model predictions are indeed present in rats [57], [58].

We will intensify our collaborations with mathematicians and theoretical physicists in order to develop age-structured PDEs as models of subdiffusion and (sub)diffusion-reaction coupling in the perspectives of non-parametric inference for classification of intracellular trajectories or the modeling of subdiffusion-reaction coupling. Regarding experimental data, we are developping collaborations with experts of super-resolution microscopy in order to be able to combine our models with single-molecule trajectory data and spatial localization data at single-molecule resolution in living cells. Moreover, since September 2017, Carole Knibbe shares her research time (co-affiliation) between Beagle and the biomedical research laboratory CarMeN (http://carmen.univ-lyon1.fr). On this occasion, her research has joined Research axis 1. In collaboration with experimental biologists of the CarMeN laboratory (e.g. Marie-Caroline Michalski), she now works on mathematical and computational models of lipolysis kinetics, with the aim of reaching a quantitative understanding of how the spatial supramolecular organization of lipids influences their digestion. A variety of experimental data are available at CarMeN to calibrate the models at the various scales, from in vitro enzymatic data, to cultures of intestinal cells, to animal models, to clinical data in normal and obese patients.