Stochasticity in transcriptional, splicing and translational regulations in time and frequency domains

Abstract

Alternative splicing is one of the most important post-transcriptional regulation. Splicing is essential for the expression of most of the human protein coding genes and is associated with several diseases, comprising cancer. It is also strongly used by minor organisms and several viruses. In the past decades, an extensive mathematical literature was developed to model and analyze gene networks under both deterministic and stochastic formalisms. However, such literature is predominantly focused to deal with the modeling of transcriptional and translational regulation, but its extension to comprise post-transcriptional regulation via splicing and its connection with transcriptional and translational regulation is still almost missing in literature. The aim of this work is to theoretically study and complete the knowledge about a general basic open loop and linear modeling scheme of gene expression via alternative splicing and its connection with transcription and translation, under a stochastic dimension. This study showed the pivotal role of the splicing conversion rates capable to both increase or decrease the stochastic noise, as well as their interconnection with the stochastic bursts in gene expression, autocorrelation and noise power spectra. The study also shows when it is important to model the pre-mRNA degradation or, at least, to account for the conversion rate for more than two mRNA isoforms.