Abstract:

With the developments of biotechnology and other disciplines such as computational science, synthetic biology has made great progresses in theoretical analysis, functional design, and experimental implementation, which is attracted extensively in the interdisciplinary fields such as computational biology and artificial intelligence. From the perspective of mathematical science, theories of designing various synthetic biological elements with specific functions have been emerging, such as gene switches, gene oscillators, and biological logic gates. From the perspective of technological innovation, great progresses have been made in biosynthesis and functionalization strategies such as genetic engineering and chemical modifications on proteins (enzymes) for self-assembly. The rapid developments of these related aspects have also greatly promoted the development of synthetic biology. This review specifically focuses on theoretical basis and analysis methods behind various synthetic biological networks with specific functions from the perspective of biomolecular network dynamics, including functional biological devices such as switches and oscillators, as well as factors related to mathematics and network theory, including correlations between positive and negative feedback loops and nonlinear dynamics, nonlinear factors and the causes of time delays, stability and bifurcation-related theories, and theoretical basis and analysis methods related to dynamics, such as the robustness and period tunability of periodic oscillators are also addressed, which provides theoretical analysis methods that can be used as reference for further design of more complex or easily synthesized biological devices. Therefore, synthetic biology based on dynamics can start with mathematical modeling and dynamical system theory to construct synthetic gene regulatory networks with specific functions. By applying gene editing technology and adopting reasonable assembly strategies for experimental manipulations, we can verify the theoretical designs. By analyzing gene expression profiles, the feasibility and performance of the theoretical design can be explored. Further analysis of the topology and function of synthetic gene regulatory networks, as well as relationship between dynamics and parameters can help us better understand adjustable design strategies and key factors for redesign.

Key words: dynamics, networks, switches, oscillators, stability, bifurcation

摘要：

随着生物技术与其他各学科如计算科学的发展，合成生物学在功能设计与实验实施方面都取得了长足的进展。合成生物学近年来在计算生物学与人工智能等交叉学科领域引起广泛兴趣。从数学科学的角度，设计各种具有特定功能的合成生物元件的理论不断涌现，如基因开关、基因振子、生物逻辑门等。从生物技术角度，基因工程、蛋白（酶）的化学修饰自组装等生物合成及功能化策略也取得了巨大进步。这些相关方面的长足发展，也大大促进了合成生物学的发展。本文重点从生物分子网络动力学的角度，深入阐述各种具有特定功能的合成生物网络背后的理论基础与分析方法，其中包括生物功能器件如开关与振子，以及数学与网络理论相关的因素，包括正负反馈回路与动力学的相关性、非线性因素与时间延迟产生的原因、稳定性与分支相关理论、周期振子的鲁棒性、周期可调性等动力学相关的理论基础与分析方法，为进一步设计更为复杂或者更易实验合成的生物器件提供可以借鉴的理论分析方法。

关键词: 动力学, 网络, 开关, 振子, 稳定性, 分支