Solving the time-dependent protein distributions for autoregulated bursty gene expression using spectral decomposition

Wu, Bingjie; Holehouse, James; Grima, Ramon; Jia, Chen

doi:10.1063/5.0188455

Cited by 5 publications

(1 citation statement)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, the existence of two gene activation pathways can also capture the time-course mRNA expression data observed for yeast HSP12 gene under NaCl osmotic stress which exhibit unimodal distributions with a zero peak for small and large times, while exhibit bimodal distributions for intermediate times [59,60]. Such dynamic transitions between different distribution shapes are rarely observed in the telegraph model and other gene expression models [61][62][63].…”

Section: Introductionmentioning

confidence: 95%

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

Jiao,

Li,

Liu

et al. 2024

PLoS Comput Biol

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 95%

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

Jiao,

Li,

Liu

et al. 2024

PLoS Comput Biol

View full text Add to dashboard Cite

show abstract

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

Jiao

Liu

et al. 2023

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Geometry theory of distribution shapes for autoregulatory gene circuits

Sheng,

Lin,

Jiao

et al. 2024

Preprint

Self Cite

View full text Add to dashboard Cite

In this study, we provide a complete mathematical characterization of the phase diagram of distribution shapes in an extension of the two-state telegraph model of stochastic gene expression in the presence of positive or negative autoregulation. Using the techniques of second-order difference equations and nonlinear discrete dynamical systems, we prove that the feedback loop can only produce three shapes of steady-state protein distributions (decaying, bell-shaped, and bimodal), corresponding to three distinct parameter regions in the phase diagram. The boundaries of the three regions are characterized by two continuous curves, which can be constructed geometrically by the contour lines of a series of ratio operators. Based on the geometric structure of the phase diagram, we then provide some simple and verifiable sufficient and/or necessary conditions for the existence of the bimodal parameter region, as well as the conditions for the steady-state distribution to be decaying, bell-shaped, or bimodal. Finally, we also investigate how the phase diagram is affected by the strength of positive or negative feedback.

show abstract

Solving the time-dependent protein distributions for autoregulated bursty gene expression using spectral decomposition

Cited by 5 publications

References 48 publications

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

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

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

Geometry theory of distribution shapes for autoregulatory gene circuits

Contact Info

Product

Resources

About