Effects of nonlinear degradation of protein on the oscillatory dynamics in a simple gene regulatory network

Topology and Dynamics of the Zebrafish Segmentation Clock Core Circuit

“…Dimerization-induced changes in stability are known for several bHLH proteins, where complex formation usually results in an increased half-life [41] , [42] . This effect is termed cooperative stability, and theoretical studies have established that this phenomenon can affect the dynamic behavior of genetic networks [43] – [45] . In the context of the segmentation clock, it has been suggested that cooperative stability could increase the region in parameter space where sustained oscillations are possible, rendering the oscillator more robust [46] .…”

Molecular-Memory-Induced Counter-Intuitive Noise Attenuator in Protein Polymerization

“…Furthermore, an inner tradeoff may occur between memory and expression stability, implying that we can control the timescale window to maintain the noise. Nowadays, it is very clear that noise may be detrimental to cells' survival but is also a vital clue to decoding life activity [6,15,24,36,37]. It seems likely that there is a suitable time window for comprehensively understanding the biological function of expression noise.…”

“…The most notable difference is that the nonlinearity becomes more and more apparent, as shown in Figure 6b, implying that burst kinetics always regulate the expression stability in a nonlinear way, and the memory can accelerate this regulation. It should be noted that the superiority of nonlinearity is essential to producing stochastic focus or defocus, and this mechanism has been reported many times [6,9,18,32]. Here, the interruption of memory may alter the progress of this nonlinearity, that is, we can not only reshape the half-power relationship of expression noise, but also mediate expression stability in the time domain.…”

“…Amazingly, by undergoing the series of biochemical reactions verified in the whole genome, including nucleus retention, chromatin state switching, positive or negative feedback, transcriptional bursting, and protein polymerization, the cell can achieve its biological function and maintain stability [3,4]. One must always simplify or omit these intermediate details to construct a Markov or symmetric model that demonstrates the expression process according to the assumption of Markovian, which thus does not reflect the actual situation whereby every biochemical process essentially involves multiple-step reactions [5,6]. Different from the classical Markovian process, the multistep biochemical process may be the source of molecular memory leading to non-Markov kinetic problems or asymmetric stochastic processes [7,8].…”

Local Hopf bifurcation analysis and global existence of periodic solutions in a gene expression model with delays

“…As to the local Hopf bifurcation analysis of Goodwin model with delays, the readers may refer to [11][12][13], which showed that oscillatory expressions of genes can be generated if the delays pass through certain critical values. In addition, based on gene expression model, genetic regulatory networks [14][15][16][17][18][19][20][21][22] have been proposed during the past few years. The dynamical behaviors (mainly including stability and bifurcation) of these models were studied deeply.…”