Using average transcription level to understand the regulation of stochastic gene activation

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

In experiments, the distributions of mRNA or protein numbers in single cells are often fitted to the random telegraph model which includes synthesis and decay 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 relatively 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 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 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 also be 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 E. coli and mammalian cells. All these results are robust with respect to cooperative transcriptional regulation and extrinsic noise. In particular, we find that faster relaxation speed to the steady state results in more precise parameter inference under large extrinsic noise.

A Novel Dynamical Regulation of mRNA Distribution by Cross-Talking Pathways

In this paper, we use a similar approach to the one proposed by Chen and Jiao to calculate the mathematical formulas of the generating function V(z,t) and the mass function Pm(t) of a cross-talking pathways model in large parameter regions. Together with kinetic rates from yeast and mouse genes, our numerical examples reveal novel bimodal mRNA distributions for intermediate times, whereby the mode of distribution Pm(t) displays unimodality with the peak at m=0 for initial and long times, which has not been obtained in previous works. Such regulation of mRNA distribution exactly matches the transcriptional dynamics for the osmosensitive genes in Saccharomyces cerevisiae, which has not been generated by those models with one single pathway or feedback loops. This paper may provide us with a novel observation on transcriptional distribution dynamics regulated by multiple signaling pathways in response to environmental changes and genetic perturbations.

Using average transcription level to understand the regulation of stochastic gene activation

Gene activation is a random process, modelled as a framework of multiple rate-limiting steps listed sequentially, in parallel or in combination. Together with suitably assumed processes of gene inactivation, transcript birth and death, the step numbers and parameters in activation frameworks can be estimated by fitting single-cell transcription data. However, current algorithms require computing master equations that are tightly correlated with prior hypothetical frameworks of gene activation. We found that prior estimation of the framework can be facilitated by the traditional dynamical data of mRNA average level M(t), presenting discriminated dynamical features. Rigorous theory regarding M(t) profiles allows to confidently rule out the frameworks that fail to capture M(t) features and to test potential competent frameworks by fitting M(t) data. We implemented this procedure for a large number of mouse fibroblast genes under tumour necrosis factor induction and determined exactly the 'cross-talking n-state' framework; the cross-talk between the signalling and basal pathways is crucial to trigger the first peak of M(t), while the following damped gentle M(t) oscillation is regulated by the multi-step basal pathway. This framework can be used to fit sophisticated single-cell data and may facilitate a more accurate understanding of stochastic activation of mouse fibroblast genes.