RESEARCH ARTICLE A Nonlinear Mixed Effects Approach for Modeling the Cell-To-Cell Variability of Mig1 Dynamics in Yeast

The last decade has seen a rapid development of experimental techniques that allow data collection from individual cells. These techniques have enabled the discovery and charac-terization of variability within a population of genetically identical cells. Nonlinear mixed ef-fects (NLME) modeling is an established framework for studying variability between individuals in a population, frequently used in pharmacokinetics and pharmacodynamics, but its potential for studies of cell-to-cell variability in molecular cell biology is yet to be ex-ploited. Here we take advantage of this novel application of NLMEmodeling to study cell-to-cell variability in the dynamic behavior of the yeast transcription repressor Mig1. In particu-lar, we investigate a recently discovered phenomenon where Mig1 during a short and tran-sient period exits the nucleus when cells experience a shift from high to intermediate levels of extracellular glucose. A phenomenological model based on ordinary differential equa-tions describing the transient dynamics of nuclear Mig1 is introduced, and according to the NLMEmethodology the parameters of this model are in turn modeled by a multivariate prob-ability distribution. Using time-lapse microscopy data from nearly 200 cells, we estimate thi