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Stationary Moments, Distribution Conjugation and Phenotypic Regions in Stochastic Gene Transcription


Pages: --, Volume 16, Issue 5, 2019

doi:

Abstract: Transcription is a pivotal step in gene expression yet a complex biochemical process. It occurs often in a bursty manner, leading to cell-to-cell variability important for the cells surviving in complex environments. Quantitative experiments of such stochastic transcription call for model analysis in a systematic rather than case-by-case fashion. Here we analyze two general yet biologically-reasonable classes of stochastic transcription models: the one considers that promoter structure is general, and the other considers that waiting-time distributions are general. For the former, we show that there are conjugate relationships between models with different transcription exits. This property well reveals the mechanic principle of stochastic transcription in complex cases of transcription factor regulation. For the latter, we establish an integral equation for the mRNA moment-generating function, through which stationary mRNA moments of any orders can be analytically derived. Finally, we analyze parametric regions for robust unimodality and bimodality. The overall analysis not only lays a foundation for quantitative analysis of stochastic transcription but also reveals how the upstream promoter kinetics impact the downstream expression dynamics.


Keywords: stochastic gene transcription; chemical master equation; moment dynamics; bimodality
Mathematics Subject Classification:  

Received: July 2004; Revised: August 2004; Published: November 2004.