Identification from stochastic cell-to-cell variation: a genetic switch case study

Owing to the inherently random and discrete nature of genes, RNAs and proteins within living cells, there can be a wide range of variability both over time in a single cell and from cell to cell in a population of genetically identical cells. Different mechanisms and reaction rates help shape this variability in different ways, and the resulting cell-to-cell variability can be quantitatively measured using techniques such as time-lapse microscopy and fluorescence activated cell sorting (or flow cytometry). It has been shown that these measurements can help to constrain the parameters and mechanisms of stochastic gene regulatory models. In this work, finite state projection approaches are used to explore the possibility of identifying the parameters of a specific stochastic model for the genetic toggle switch consisting of mutually inhibiting proteins: LacI and cI. This article explores the possibility of identifying the model parameters from different types of statistical information, such as mean expression levels, LacI protein distributions and LacI-cI multivariate distributions. It is determined that although the toggle model parameters cannot be uniquely identified from measurements that track just the LacI variability, the parameters could be identified from measurements of the cell-to-cell variability in both regulatory proteins. Based upon the simulated data and the computational investigations of this study, experiments are proposed that could enable this identification.