Stochastic Modeling of the Co-Regulation between Early and E8 Promoters in Human Papillomavirus

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.

Stochastic modeling of human papillomavirusearly promoter gene regulation

High risk forms of human papillomaviruses (HPVs) promote cancerous lesions and are implicated in almost all cervical cancer. Of particular relevance to cancer progression is regulation of the early promoter that controls gene expression in the initial phases of infection and can eventually lead to pre-cancer progression. Our goal was to develop a stochastic model to investigate the control mechanisms that regulate gene expression from the HPV early promoter. Our model integrates modules that account for transcriptional, post-transcriptional, translational and post-translational regulation of E1 and E2 early genes to form a functioning gene regulatory network. Each module consists of a set of biochemical steps whose stochastic evolution is governed by a chemical Master Equation and can be simulated using the Gillespie algorithm. To investigate the role of noise in gene expression, we compared our stochastic simulations with solutions to ordinary differential equations for the mean behavior of the system that are valid under the conditions of large molecular abundances and quasi-equilibrium for fast reactions. The model produced results consistent with known HPV biology. Our simulation results suggest that stochasticity plays a pivotal role in determining the dynamics of HPV gene expression. In particular, the combination of positive and negative feedback regulation generates stochastic bursts of gene expression. Analysis of the model reveals that regulation at the promoter affects burst amplitude and frequency, whereas splicing is more specialized to regulate burst frequency. Our results also suggest that splicing enhancers are a significant source of stochasticity in pre-mRNA abundance and that the number of viruses infecting the host cell represents a third important source of stochasticity in gene expression.

Human Papillomavirus Early Promoter Regulatory Core as a Bistable Switch

High risk human papillomavirus (HPV) can induce cervical and oropharyngeal cancerous lesions. Different HPV strains, as well as still unknown mechanisms can be associated to a range of biochemical parameters that can importantly affect the HPV gene expression dynamics. For this reason, it is of pivotal importance to investigate how parameters variation can induce interesting behaviors such as viral latency in place of the normal gene replication activity. The aim of this study is to perform bifurcation analysis on a minimal model of the early promoter regulatory core controlled by E2 transcriptional regulation. The bifurcation analysis showed how E2 regulation can induce a bistability on the early promoter gene expression that could explain the interplay between viral latency and gene replication regimen.

Sensitivity Analysis of a Model of Human Papillomavirus Late Promoter Regulation

A mathematical model of Human Papillomavirus late promoter regulation was recently developed, able to predict the main features of HPV gene expression during cellular differentiation under productive infection. A sensitivity analysis is performed to characterize the influence of transcriptional, post-transcriptional and translational regulations on the viral species related to E1, E2, E4 and Li genes. Sensitivity analysis indicates strong influence of parameters related to transcriptional and translational regulation. It also shows a strong influence on the parameters related to post-transcriptional regulation, showing the importance of modeling splicing regulation to well describe the biology of the late promoter.