Modeling and Analysis of Simple Genetic Circuits
Complex bio-molecular networks often consist of simple circuits, which are called as network motifs, the thorough investigations on network motifs are the first step to understand the complex biological system. The feed-forward loops, the single gene auto
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Modeling and Analysis of Simple Genetic Circuits
Abstract Complex bio-molecular networks often consist of simple circuits, which are called as network motifs, the thorough investigations on network motifs are the first step to understand the complex biological system. The feed-forward loops, the single gene auto-activated circuit, the single gene auto-repressed circuit, the coupled positive and negative feedback genetic circuits are all typical simple circuits, which have been extensively investigated from the perspective of both mathematical modeling and experiments. In this chapter, we firstly review some mathematical models for simple biological networks. Then, based on mathematical modeling and dynamical analysis, we investigate the relations among the structures, functions, and dynamics of several simple circuits. Finally, we introduce some works on the large-scale exploration of simple bio-molecular networks with specific biological functions.
3.1 Backgrounds Biological networks can be quantitatively investigated through mathematical models [1, 2]. Since GRNs have an important role in every process of life, including cell differentiation, metabolism, the cell cycle, and signal transduction, we mainly consider the mathematical modeling of genetic circuits. By understanding the dynamics of genetic networks, we can shed light on the mechanisms of diseases that occur when these cellular processes are dysregulated. Accurate prediction of the behavior of regulatory networks will also speed up biotechnological projects, as such predictions are quicker and cheaper than lab experiments. Computational methods, both for supporting the development of network models and for the analysis of their functionality, have already been proved to be valuable research tools [3]. Another important application area of related investigations is the synthetic biology. During the last decades, there have been three important experimental studies involving the design of synthetic genetic networks, including (a) a single autorepressive promoter utilized to demonstrate the interplay between negative feedback and internal noise; (b) two repressive promoters used to construct a © 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_3
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3 Modeling and Analysis of Simple Genetic Circuits
genetic toggle switch; (c) three repressive promoters employed to exhibit sustained oscillations. Different sizes of genetic networks can be described by different kinds of models [4]. Single genes can be modeled in molecular detail with stochastic simulations [5] based on the chemical master equation (CME); a differential equation (reaction rate equation: RRE) representation of gene dynamics is more practical when turning to circuits of genes [6]; Approximating gene dynamics by switch-like ON/OFF (Boolean dynamics) behavior allows modeling of mid-sized genetic circuits and still
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