Section: New Results

Single Cell Models and Models of Populations: A Mixed Effect Approach

Participants : Grégory Batt, Andres Mauricio Gonzalez Vargas, Pascal Hersen, Artémis Llamosi.

For a long time, experiments and models of gene expression were mainly based on the mean behavior of a population of cells. Although observed early, it is only recently that experimental technique allowed detailed investigation of variability in this process. Since the pioneering work of Elowitz and colleagues, a distinction is drawn between what is called intrinsic and extrinsic variability or noise. Intrinsic noise originates in the randomness of chemical reactions within a cell whether extrinsic noise is the variation in between cells at a given time. Extrinsic variability is associated with population heterogeneity in the concentrations of ribosomes or other molecular players or processes relevant to gene expression (RNAPolII concentration, degradation and dilution rates etc.).

In this work, we propose a modelling framework for gene expression based on a system of ODEs with random parameters following a distribution across the population of cells. In this context, each cell has its own identity which is represented by the value of its parameters. With this model we ask how much of the long term variability can be explained by extrinsic variability alone. We produced long term, time lapse and single-cell data of repeated gene induction in Saccharomyces cerevisiae. One experiment was treated as learning set whereas two were used as test sets. From the learning set, we are able to infer single cell parameters and population distributions which represent accurately in terms of mean and variance the variability in the population. These learned population distributions allowed good predictions on both the learning and test sets.

Our study demonstrates also that the way inference of single cell parameters and distributions is performed is crucial to achieve good performance. Best results being found by joint estimation of the parameters for single cells and for the whole population. With this technique, we noted that very decent fits of the population dynamics can be obtained by estimating only on a very limited number of cells. Concerning the quality of single cell parameters inferred, we validated the presence of an expected significant correlation between the dilution rate and the measured single cell growth rate. This motivates the use of this tool in order to investigate the origins of extrinsic noise, by correlating single cell parameters with measured candidate factors of gene expression variability such as cell density, cell size or age.