Fitting dynamic models to population data such as the logistic growth equation is a common practice for describing microbial growth, both in natural ecosystems and under research conditions. However, these models are limited to scenarios where population stabilizes at equilibrium, making them unsuitable for systems like batch bioreactors, where populations decline after substrate depletion. In this work, we propose two new population models capable of accurately describing such dynamics while maintaining an interpretable structure in which each parameter has a biological meaning. These models incorporate the growth rate as a function of cumulative biomass, rather than solely the biomass concentration, thereby accounting for memory effects. We establish fundamental properties of these models and demonstrate their applicability and accuracy to describe data from batch bioreactors.
Novel integro-differential models capture growth and decay in batch bioreactors.
Validated with experimental data from microbial and mammalian cell cultures.
Maintenance rates can be estimated using population measurements.
Provide a mechanistic framework linking model parameters to biological processes.
Cell response variability is a starting point in cancer drug resistance that has been difficult to analyze because the tolerant cell states are short lived. Here, we present fate-seq, an approach to isolate single cells in their transient states of drug sensitivity or tolerance before profiling. The drug response is predicted in live cells, which are laser-captured by microdissection before any drug-induced change can alter their states. This framework enables the identification of the cell-state signatures causing differential cell decisions upon treatment.
For complete details on the use and execution of this protocol, please refer to Meyer et al. (2020).
supervised by Madalena Chaves (from INRIA- Biocore team) and Jérémie Roux (from INRIA/IPMC)
Fractional killing caused by cell resistance to anti-cancer drugs is a common phenomenom in cancer fighting. In clonal cell populations, even with obvious genetical proximity, cells responds very differently (in time and magnitude) to death ligands such as TRAIL, a cytotoxic drug that targets only tumoral cells. To understand the causes of cell response heterogeneity, improve TRAIL efficiency and design new therapeutic targets, we model TRAIL-initiated apoptosis, using small deterministic models of protein-protein interactions involved in extrinsic apoptosis. The models obtained are calibrated for each cell of an in vitro experiment involving hundreds of clonal HeLa cells, treated with different TRAIL doses combined with other anti-cancer drugs and observed for several hours. We then study our solutions with dynamical and statisticals tools to find differences between sensible and resistant cells and understand how we can change cell fate and force them to die.
(with Diego Oyarzun from the Biomolecular control group of UoE)
"Resistance to chemotherapy is a central challenge in the fight against cancer. Genetically identical cells from the same tumour often respond differently to treatment, which causes some cells to survive and produce relapse of disease. The ability to predict resistance is a key missing step in precision oncology, and would open new routes for personalized treatments with increased drug efficacy and reduced side-effects. In this project I will build a data-driven approach to predict resistance to chemotherapy from molecular data. My approach will be based on a combination of machine learning and mechanistic modelling applied to single-cell in vitro data from clonal cancer cells. This will ultimately increase the predictive power of our patented method and bring our technology one step closer to the clinic." - quote from my application to the RSE fellowship.
(with Jacky Cresson from LMAP/UPPA)
Fractional calculus is more and more employed in mathematical modeling thanks to its ability to reproduce better natural phenomena dynamics than classical derivatives systems. Nevertheless, the use of fractional derivative is not often fully justified. In my master thesis, we propose a new formalism for fractional calculus and provide several methods to pass from a classical deterministic model to a fractional one, keeping essentials features of the system modeled and reducing the number of equations. We apply our method to a epidemiologic case : the Dengue outbreak in Cape Verde in 2009.
Mathematical modeling
Numerical simulations
Parameter estimation and Identifiability
Bayesian Inference
Bioengineering
AI and Machine learning
Dynamical system analysis in Biology
Cancer
Cell biology
Epidemiology
Fractional calculus