Stability analysis and control of piecewise affine models for genetic regulatory networks with applications in systems and synthetic biology

该项目位于控制工程、系统生物学和合成生物学领域的交叉点。我们研究的主要对象是基因调控网络，它描述了基因与其产物之间的相互作用。需要建立这样的网络的数学模型，在现有的描述它们的不同模型中，分段仿射模型[2]被选择用于本工作，因为它能够结合定性和定量方法的优点。本项目的目标是发展理论和实用工具来分析和控制这些生物系统。这意味着，首先，我们想要了解系统的长期行为、平衡点的存在及其稳定或不稳定的性质，其次，我们的目标是设计能够影响这些行为的外部装置或其他基因调控网络。系统稳定性分析的预定方法是构造和研究李亚普诺夫函数，这是网络的一种能量度量。研究这类函数随时间的演化提供了关于原始系统的信息，但由于系统中的非线性和可能存在的多重均衡，其构造不是平凡的。在生物系统的控制方面，我们将对这一主题进行广泛的文献综述，并将关于遗传调控网络的分段仿射模型稳定性的结果应用于控制问题。合成生物学是这项工作的基础领域之一，它是一个很有前途的领域，而且还在不断发展。许多应用包括癌症治疗中的细胞疗法、糖尿病治疗以及利用生物实体生产药物、燃料和其他材料。此外，这项研究还在系统生物学中找到了应用，研究了已经存在的但没有很好特征的生物系统，以及在控制工程领域中与系统中的非线性和多重平衡的存在相关的有趣挑战。该项目与EPSRC控制工程和合成生物学的研究领域保持一致。生物调控网络定性与定量动态模型的比较研究。《EPJ非线性生物医学物理》，4(1)，5.[2]Casey，R.，De Jong，H.，&Gouzé，J.L.(2006)。遗传调控网络的分段线性模型：均衡及其稳定性。数学生物学学报，52(1)，27-56。

This project sits at the intersection between the areas of Control Engineering, Systems Biology and Synthetic Biology. The main object of our research are genetic regulatory networks, which describe the interaction between genes and their products. A mathematical model of such networks is needed and among the different models available [1] to describe them, the piecewise affine model [2] has been chosen for the present work, due to its capability to merge together the advantages of both qualitative and quantitative approaches.The goal of this project is to develop theoretical and practical instruments for the stability analysis and control of these biological systems. This means that, in first instance, we want to understand the long term behaviour of the system, the existence of equilibria and their stable or unstable nature and secondly we aim to design external devices or other genetic regulatory networks that are able to influence such behaviour.The intended approach for the stability analysis of the system is the construction, and the study, of a Lyapunov function, which is a sort of energy measure for the network. Studying the evolution in time of such function gives information on the original system, but its construction is non-trivial due to the non-linearities and the possible presence of multiple equilibria in the system. An optimization problem needs to be set up in order to find a description of such function, if one exists.In regard to the control of biological systems, an extensive literature review on the topic will be made and ideally the results found regarding the stability of piecewise affine model of genetic regulatory networks will be applied to the control problem.Synthetic biology, which is one of the main area in which the foundation of this work lay, is a promising and ever growing field. Many applications include cell-based therapy in cancer treatment, therapies against diabetes and the production of drugs, fuels and other materials using biological entities. Moreover this research finds application also in Systems biology, studying already existing, but not well characterised, biological systems, and in the field of Control engineering for the interesting challenges related to the non-linearities in the system and the presence of multiple equilibria.The project is aligned with the EPSRC research areas of Control engineering and Synthetic Biology.[1] Saadatpour, A., & Albert, R. (2016). A comparative study of qualitative and quantitative dynamic models of biological regulatory networks. EPJ Nonlinear Biomedical Physics, 4(1), 5. [2] Casey, R., De Jong, H., & Gouzé, J. L. (2006). Piecewise-linear models of genetic regulatory networks: Equilibria and their stability. Journal of Mathematical Biology, 52(1), 27-56.