Human Papillomavirus Early Promoter Regulatory Core as a Bistable Switch

Frequency response in splicing regulation under mRNA auto-depletion control

Nowadays, there exists a huge literature about stochastic model of transcriptional and translational control in gene networks. However, results related to post-transcriptional regulation via splicing and its connection with transcriptional and translational regulation are almost missing in the current literature and only related to the steady state moments investigation. Nowadays, it is becoming of paramount importance the need for modeling post-transcriptional regulation via splicing especially for DNA viruses or retroviruses. However, there exists only few studies in the literature about splicing regulation and none of them investigate its behavior in the frequency domain that can unveil important features of dynamical stochastic systems that cannot be revealed by the sole steady state moment investigation. The aim of this work is to theoretically investigate a simple gene network subject to splicing regulation with negative feedback control, implemented through mRNA auto-depletion under a frequency domain perspective. This study showed the pivotal role of the burst size, enhancing the noise power spectrum, as well as the splicing conversion rates capable to increase and decrease the noise power spectrum in the pre-mRNA and mRNA, respectively, for high values of conversion rates. Importantly, it shows the capability of the mRNA autodepletion control to modulate the noise as a frequency-dependent amplifying control as a function of the negative feedback strengths.

Frequency analysis of splicing regulation

In the past decades, mathematical modelers developed a huge literature to model and analyze gene networks under both deterministic and stochastic formalisms. Such literature is predominantly focused on modeling transcriptional and translational regulation, while the development of proper mathematical frameworks to model and study post-transcriptional regulation via splicing and its connection with transcriptional and translational regulation are almost missing. Nowadays, it is becoming of paramount importance the need for modeling post-transcriptional regulation via splicing especially for bacteria or viruses. However, current literature is focused on investigating splicing regulation at steady state and none of them have the purpose to investigate gene networks behavior in the frequency domain, thus providing only a partial investigation about the system dynamical response. The aim of this work is to theoretically investigate a simple gene network subjects to splicing regulation with/without negative feedback control under a frequency domain perspective. This study showed the pivotal role of the burst size, as well as splicing conversion rates to modulate the noise and the power spectrum response. It also shows an interesting behavior under the frequency domain induced by the merging effect of burst size, splicing conversion rates and negative feedback strength.

A Human Papillomavirus Early Promoter Minimal Model: Viral Population and Stochasticity

HPV infection starts with the activation of the early promoter (EP) regulatory core and the replication of the viral particles to around 10-100 per cell at the beginning of the infection. For this reason, understanding the deterministic and stochastic role of the population number of viruses inside the cell is of pivotal importance to understand the regulation of the EP and the viral latency.The aim of this study is to extend a recently published minimal model of the EP transcriptional regulation in order to consider the effect of the viral population on gene regulation, to perform the bifurcation analysis and to understand the role of the stochasticity at the beginning of the infection.The bifurcation analysis showed how modeling the viral population number is pivotal to exhibit a bistable behavior, potentially linked to the viral latency. Moreover, the viral population number was identified as an important source of stochasticity, which is of paramount importance to drive the bistable switching mechanism in the first stages of infection.

A Minimal Stochastic Model of Transcriptional and Splicing Regulation

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 results related to post-transcriptional regulation and its connection with transcriptional regulation are poorly investigated. However, it is becoming of paramount importance the need for modeling post-transcriptional regulation via splicing especially for minor organisms or viruses.The aim of this study is to propose a first general basic modeling scheme for modeling gene expression via alternative splicing and investigating the basic deterministic and stochastic features of the pre-mRNA, mRNAs and proteins under different biological conditions.This first study showed the dynamical properties of alternative splicing, the faster kinetics of the pre-mRNA compared to the mRNA and the importance to stochastically model gene networks when considering the post-transcriptional regulation.