Computational Molecular Biology 2025, Vol.15, No.4, 193-207 http://bioscipublisher.com/index.php/cmb 193 Feature Review Open Access Mathematical Modeling of Synthetic Genetic Circuits Haimei Wang Hainan Institute of Biotechnology, Haikou, 570206, Hainan, China Corresponding author: haimei.wang@hibio.org Computational Molecular Biology, 2025, Vol.15, No.4 doi: 10.5376/cmb.2025.15.0019 Received: 03 Jun., 2025 Accepted: 14 Jul., 2025 Published: 02 Aug., 2025 Copyright © 2025 Wang, This is an open access article published under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.6 Preferred citation for this article: Wang H.M., 2025, Mathematical modeling of synthetic genetic circuits, Computational Molecular Biology, 15(4): 193-207 (doi: 10.5376/cmb.2025.15.0019) Abstract Synthetic genetic circuits are the core research objects in synthetic biology, and the programming of cell behavior is achieved through the combination of engineered gene elements. Mathematical modeling provides crucial support for understanding and designing synthetic genetic circuits, enabling researchers to predict the dynamic behavior of the circuits and guide experimental optimization. This study reviews the categories of synthetic genetic circuits (such as gene switches, oscillators, feedback circuits, etc.) and their biological mechanisms, with a focus on the application of ordinary differential equation (ODE) models, stochastic modeling, and network topology dynamics models in circuit modeling. We expounded on the estimation of model parameters, sensitivity analysis, and the integration methods of experimental data and models, and compared the characteristics of numerical simulation algorithms and commonly used software tools (such as MATLAB, COPASI, BioNetGen, etc.). Through the discussion of the steady-state, oscillation behavior, multiple steady-state and bifurcation analysis of system dynamics, the understanding of the influence of positive and negative feedback mechanisms on system stability is deepened. In addition, we took the classic synthetic gene oscillator Repressilator as a case to conduct modeling and simulation analysis, and compared the model predictions with the experimental data. Finally, the application prospects of synthetic genetic circuits in the fields of bioengineering and medicine were summarized, and the future directions of promoting the design of synthetic circuits with the help of model optimization and artificial intelligence-assisted design were prospected. Research shows that mathematical modeling and computational simulation have become key tools for the study and design of synthetic genetic circuits, providing a theoretical basis and practical guidance for the engineering transformation of complex biological systems. Keywords Synthetic genetic circuit; Mathematical modeling; Ordinary differential equation; Gene oscillator; Feedback regulation 1 Introduction Synthetic biology is all about "assembly" - assembling new life systems with standardized biological components (Vazquez-Vilar et al., 2023) - to put it simply, it is about making cells act according to human designs. In this process, the synthetic genetic circuit is like the "circuit board" of the cell, determining whether it can follow instructions. A typical circuit usually consists of promoters, regulatory proteins and various regulatory elements. When these parts are combined, they can control the switching logic of the target gene. In other words, as long as these components are reasonably selected, cells can perform logical operations like computers, thereby precisely controlling their behavior. Modeling is actually a kind of "rehearsal" in synthetic biology; Toward predictive engineering of gene circuits. It enables people to see in advance the possible manifestations of genetic circuits, avoiding detours and reducing the waste of experimental costs. Because gene regulatory networks are often nonlinear, have feedback, and change over time, it is almost impossible to judge their dynamic behavior with the naked eye. So The mathematical model comes into play. It enables us to conduct "fake experiments" on the computer to infer the consequences of the design and see if the system will be stable or oscillate under different parameters. For instance, if you want to create a gene oscillator, the model can help you figure out how strong the feedback is needed to make it actually vibrate. It can be said that mathematical models provide researchers with a "testing ground" for understanding complex biological processes and are key tools for designing bistable switches, sensors, and even more complex circuits. However, there is a dilemma in this matter: the model is either too simple to grasp the key points or too complex
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