Oscillatory dynamics of p38 activity with transcriptional and translational time delays

Abstract

Recent experimental evidence reports that oscillations of p38 MAPK (p38) activity would efficiently induce pro-inflammatory gene expression, which might be deleterious to immune systems and may even cause cellular damage and apoptosis. It is widely accepted now that transcriptional and translational delays are ubiquitous in gene expression, which can typically result in oscillatory responses of gene regulations. Consequently, delay-driven sustained oscillations in p38 activity (p38*) could in principle be commonplace. Nevertheless, so far the studies of the impact of such delays on p38* have been lacking both experimentally and theoretically. Here, we use experimental data to develop a delayed mathematical model, with the aim of understanding how such delays affect oscillatory behaviour on p38*. We analyze the stability and oscillation of the model with and without explicit time delays. We show that a sufficiently input stimulation strength is prerequisite for generating p38* oscillations, and that an optimal rate of model parameters is also essential to these oscillations. Moreover, we find that the time delays required for transcription and translation in mitogen-activated protein kinase phosphatase-1 (MKP-1) gene expression can drive p38* to be oscillatory even when the concentration of p38* level is at a stable state. Furthermore, the length of these delays can determine the amplitude and period of the oscillations and can enormously extend the oscillatory ranges of model parameters. These results indicate that time delays in MKP-1 synthesis are required, albeit not sufficient, for p38* oscillations, which may lead to new insights related to p38 oscillations.

Oscillation induced by Hopf bifurcation in the p53–Mdm2 feedback module

“…By introducing the time delay in the model, we investigate the stability and oscillation of the proposed model with and without time delay and find that the time delay occurring in the regulatory process of Mdm2 gene expression is essential for maintaining p53* oscillations. Our results are in excellent agreements with the existing results [20, 23, 24, 27]. Second, we also investigate how different parameters can affect the dynamical behaviour of the system with time delay.…”

“…On the one hand, from a dynamical perspective, the time delay can be used as a bifurcation parameter to study the induced Hopf bifurcation. On the other hand, the time delay is inherent and important for biological systems, especially in gene regulatory network [22, 27, 32]. In this subsection, we will investigate how time delay affects the oscillations in Model 1 through numerical simulations.…”

“…However, a question naturally arises about how to modulate the value of the total time delay in the process. To our knowledge, one effective way is to reduce the number of introns within the gene to shorten the delay based on the fact that the transcription and splicing of intron sequences can increase the time required for the extension and splicing of genes to mature RNA [27, 42, 43]. Takashima et al previously showed that a deletion of all three introns within the Hes7 gene could reduce the delay by 19 min and completely eliminate the oscillatory behaviour [44].…”

Modelling and analysing biological oscillations in quorum sensing networks

“…Specifically, the process from the transcription factor acting on the gene promoter to the appearance of mature mRNA often takes an average of about 10–20 min [37]. At the same time, the synthesis process from mRNA to a mature protein usually takes about 1–3 min [38]. It can be seen that the gene expression process from gene fragment to a mature protein takes about 11–23 min.…”

Contribution of time delays to p53 oscillation in DNA damage response

“…In general, the time delay required for the protein–protein reaction is always omitted because it is much smaller than the time delay required for protein synthesis. Since the transcriptional and translational processes are slow and complex, the time delays in gene expression are inevitable [28]. Typically, there is a delay of about 0.7 h between the initiation of transcription of the Mdm2 gene and the appearance of mature Mdm2 protein.…”