What can we learn when fitting a simple telegraph model to a complex gene expression model?

Abstract

In experiments, the distributions of mRNA or protein numbers in single cells are often fitted to the random telegraph model which includes synthesis and degradation of mRNA or protein, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by crucial biological mechanisms such as feedback regulation, non-exponential gene inactivation durations, and multiple gene activation pathways. Here we investigate the dynamical properties of four complex gene expression models by fitting their steady-state mRNA or protein number distributions to the simple telegraph model. We show that despite the underlying complex biological mechanisms, the telegraph model with three effective rate parameters can accurately capture the steady-state gene product distributions, as well as the conditional distributions in the active gene state, of the complex models. Some effective rate parameters are reliable and can reflect realistic dynamic behaviors of the complex models, while others may deviate significantly from their real values in the complex models. The effective parameters can be also applied to characterize the capability for a complex model to exhibit multimodality. Using additional information such as single-cell data at multiple time points, we provide an effective method of distinguishing the complex models from the telegraph model. Furthermore, using measurements under varying experimental conditions, we show that fitting the mRNA or protein number distributions to the telegraph model may even reveal the underlying gene regulation mechanisms of the complex models. The effectiveness of these methods is confirmed by analysis of single-cell data for {\it{E. coli}} and mammalian cells.

Transient power-law behaviour following induction distinguishes between competing models of stochastic gene expression

“…It is currently unclear how far away from steady state does one need to be for these methods to perform robustly – if the shape or another property of the steady-state distribution of mRNA counts encapsulates information about the number of inactive states then the latter could be estimated. There is some evidence from comparison of the telegraph and the N -state model with N = 3 that it is not easy to estimate the number of gene states from steady-state count data [38, 39] but a systematic analysis, especially one for larger values of N , remains missing.…”