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

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.

Stochastic Transcription with Alterable Synthesis Rates

Background: Gene transcription is a random bursting process that leads to large variability in mRNA numbers in single cells. The main cause is largely attributed to random switching between periods of active and inactive gene transcription. In some experiments, it has been observed that variation in the number of active transcription sites causes the initiation rate to vary during elongation. Results: We established a mathematical model based on the molecular reaction mechanism in single cells and studied a stochastic transcription system consisting of two active states and one inactive state, in which mRNA molecules are produced with two different synthesis rates. Conclusions: By calculation, we obtained the average mRNA expression level, the noise strength, and the skewness of transcripts. We gave a necessary and sufficient condition that causes the average mRNA level to peak at a limited time. The model could help us to distinguish an appropriate mechanism that may be employed by cells to transcribe mRNA molecules. Our simulations were in agreement with some experimental data and showed that the skewness can measure the deviation of the distribution of transcripts from the mean value. Especially for mature mRNAs, their distributions were almost able to be determined by the mean, the noise (or the noise strength), and the skewness.