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.