Calibration, Selection and Identifiability Analysis of a Mathematical Model of the in vitro Erythropoiesis in Normal and Perturbed Contexts

Ronan Duchesne, Anissa Guillemin, Fabien Crauste, Olivier Gandrillon
2019 In Silico Biology  
The in vivo erythropoiesis, which is the generation of mature red blood cells in the bone marrow of whole organisms, has been described by a variety of mathematical models in the past decades. However, the in vitro erythropoiesis, which produces red blood cells in cultures, has received much less attention from the modelling community. In this paper, we propose the first mathematical model of in vitro erythropoiesis. We start by formulating different models and select the best one at fitting
more » ... erimental data of in vitro erythropoietic differentiation obtained from chicken erythroid progenitor cells. It is based on a set of linear ODE, describing 3 hypothetical populations of cells at different stages of differentiation. We then compute confidence intervals for all of its parameters estimates, and conclude that our model is fully identifiable. Finally, we use this model to compute the effect of a chemical drug called Rapamycin, which affects all states of differentiation in the culture, and relate these effects to specific parameter variations. We provide the first model for the kinetics of in vitro cellular differentiation which is proven to be identifiable. It will serve as a basis for a model which will better account for the variability which is inherent to the experimental protocol used for the model calibration. Models of haematopoiesis have improved the understanding of both the processes they describe [4] , and the mathematical tools they use. These models comprise non-exhaustively Differential Equations (DE, either ordinary [1, 2, 5] , partial, which can be structured by age, maturity, or a combination of these [6], or even delay differential equations [7]) and agentbased models [8] . They can be fully deterministic [5] or can include a more or less prominent stochastic component [9] [10] [11] . Recent works specifically focusing on erythropoiesis comprise DE-based models [12, 13] and multi-scale descriptions of these phenomena [14] [15] [16] .
doi:10.3233/isb-190471 fatcat:cra4zz7ckndrrnllbc35m2hppq