Modeling and Analysis of Coupled Bio-molecular Circuits
This chapter discusses the dynamical and statistical analysis of some coupled circuits. Simple network motifs are building blocks of complex biological networks, and they can be coupled together to consist of complex networks. The dynamical and statistica
- PDF / 2,528,654 Bytes
- 34 Pages / 439.36 x 666.15 pts Page_size
- 83 Downloads / 193 Views
Modeling and Analysis of Coupled Bio-molecular Circuits
Abstract This chapter discusses the dynamical and statistical analysis of some coupled circuits. Simple network motifs are building blocks of complex biological networks, and they can be coupled together to consist of complex networks. The dynamical and statistical analysis of coupled circuits is a key step to understand the complex life phenomenon. In this chapter, some works on the merged genetic circuits and genetic circuits coupled by the quorum sensing mechanism will be introduced.
4.1 Backgrounds Regulatory molecular networks have numerous pharmacological and medical applications. Simple biological circuits function as basic building blocks of complex biological systems. The investigation on these simple circuits is the first step to understanding the life phenomena at the system level. In Chap. 3, we have introduced some works on the mathematical and dynamical analysis of simple genetic circuits. Simple circuits can be coupled together in real-world systems to play functional roles. In this chapter, on one hand, since genetic oscillators play a fundamental role in biological systems, which are found in many biological processes, such as apoptotic, metabolic, circadian rhythms, cell cycle, and morphogenic pathways, we will first introduce a work on a composite genetic oscillator [1]. On the other hand, we will introduce one of our works on the coupled bistable genetic toggle switch systems [2, 3]. The investigations on the composite or coupled genetic circuits are another important step to understanding the real-world biological systems.
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 J. Lü, P. Wang, Modeling and Analysis of Bio-molecular Networks, https://doi.org/10.1007/978-981-15-9144-0_4
215
216
4 Modeling and Analysis of Coupled Bio-molecular Circuits
4.2 Dynamical Analysis of a Composite Genetic Oscillator 4.2.1 Related Works and Motivations In the literature, several simple synthetic genetic oscillators have been designed [4–14]. Among which, the hyteresis-based relaxation oscillator [14] and the repressilator [6] are two well-known ones. The two simple oscillator networks are shown in Fig. 4.1a, b, respectively. Up to now, the oscillatory mechanisms and the role of oscillations in these regulatory networks have not been fully understood. Actually, oscillations in genetic circuits may be due to different mechanisms. For example, the hyteresis-based relaxation oscillator is susceptible to the Andronov– Hopf bifurcation (AHB), the saddle node on invariant circle (SNIC) bifurcation, or the homoclinic bifurcation (HCB), whereas the repressilator is susceptible to the AHB [1]. In the year 2009, Yang et al. [1] explored two oscillatory mechanisms: the hysteresis-based relaxation oscillator and the repressilator. They combined these mechanisms into one regulatory network, the composite oscillator is shown in Fig. 4.1c. In the mathematical models of the composite oscillator, onl
Data Loading...
