Jörg Stelling | Analysis of Cell-to-Cell Variability with Dynamic Non-Linear Mixed Effects Models

Workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks
November 12-14, 2019

Speaker: Jörg Stelling, ETH Zurich

Title: Analysis of Cell-to-Cell Variability with Dynamic Non-Linear Mixed Effects Models

Abstract: A key step for understanding heterogeneity in cell populations is to disentangle sources of cell-to-cell and intra-cellular variability. While single-cell time-lapse data provide potential means for this, the corresponding analysis with dynamic models is a challenging open problem. Most of the existing inference methods address only single-gene expression or neglect correlations between processes that underlie heterogeneous cell behaviors. The talk will focus on a simple, flexible, and scalable method for estimating cell-specific and population-average model parameters to characterize sources and effects of cell-to-cell variability. The framework relies on non-linear mixed effects models (NLMEs) consisting of a dynamic mechanistic ODE model for an individual cell and a statistical model describing the distribution of parameters between cells in a population. NLMEs account for multiple sources of uncertainty such as between-cell variability due to differences in parameters and initial conditions, within-cell variability, and (potentially complex) measurement noise. We demonstrate our framework’s accuracy and performance compared to state-of-the-art methods from pharmacokinetics with a published model and dataset. An application to endocytosis in yeast demonstrates that one can develop dynamic models of realistic size for the analysis of single-cell data. Combined with sensitivity analysis for identifying which biological sub-processes quantitatively and dynamically contribute to cell-to-cell variability, this application shows that shifting the focus from single reactions or parameters to nuanced and time-dependent contributions of sub-processes helps biological interpretation. In perspective, generality and simplicity of the approach can help addressing open problems in analyzing single-cell dynamics such as the principled identification of cell sub-populations based on molecular differences rather than differences in observables or the untangling of contributions of correlated biological processes along cell lineages to observed cellular heterogeneity and effects on population dynamics.