Practical identifiability in the frame of nonlinear mixed effects models: the example of the in vitro erythropoiesis

Ronan Duchesne,Fabien Crauste,Anissa Guillemin,Olivier Gandrillon

doi:10.1186/s12859-021-04373-4

Abstract

BackgroundNonlinear mixed effects models provide a way to mathematically describe experimental data involving a lot of inter-individual heterogeneity. In order to assess their practical identifiability and estimate confidence intervals for their parameters, most mixed effects modelling programs use the Fisher Information Matrix. However, in complex nonlinear models, this approach can mask practical unidentifiabilities.ResultsHerein we rather propose a multistart approach, and use it to simplify our model by reducing the number of its parameters, in order to make it identifiable. Our model describes several cell populations involved in the in vitro differentiation of chicken erythroid progenitors grown in the same environment. Inter-individual variability observed in cell population counts is explained by variations of the differentiation and proliferation rates between replicates of the experiment. Alternatively, we test a model with varying initial condition.ConclusionsWe conclude by relating experimental variability to precise and identifiable variations between the replicates of the experiment of some model parameters.

Highlights

Nonlinear mixed effects models provide a way to mathematically describe experimental data involving a lot of inter-individual heterogeneity
Cell population differentiation was evaluated by counting differentiated cells in a 30 μL sample of the culture using a counting cell and benzidine (SIGMA) staining which stains haemoglobin in blue
The distribution of estimated likelihood values over the 50 runs of Stochastic Approximation version of the Expectation-Maximization (SAEM) is displayed on Fig. 3A, showing small variations between the estimated log-likelihood values

Summary

Introduction

Nonlinear mixed effects models provide a way to mathematically describe experimental data involving a lot of inter-individual heterogeneity. Inter-individual variability is ubiquitous in biology, from the fluctuations of molecular contents across populations of single cells [1], to the variations of physiologial parameters between whole organisms [2]. This variability has uncountable consequences, for instance at the scale of developmental [3], ecological or evolutionary processes [4, 5]. One often faces significant amounts of variations between replicates of the same biological experiment, which we will refer to as experimental variability This variability can be taken into account by deterministic dynamical models of the biological system, as a random variation around its predicted behaviour [6, 7]. Such models disregard the fact that variability is inherent to the biological nature of the system under study.

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Discussion

Conclusion