The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the use of theoretical modeling to describe genetic and biochemical circuits becomes more widespread, theoreticians with mathematical and physical backgrounds routinely apply concepts from statistical physics, non-linear dynamics, and network theory to biological systems. This review aims at providing a clear overview of the most important methodologies applied in the field while highlighting current and future challenges. It also includes hands-on tutorials to solve and simulate some of the archetypical biological system models used in the field. Furthermore, we provide concrete examples from the existing literature for theoreticians that wish to explore this fast-developing field. Whenever possible, we highlight the similarities and differences between biochemical and regulatory networks and ‘classical’ systems typically studied in non-equilibrium statistical and quantum mechanics.

中文翻译：

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模拟多稳态基因调控网络的理论和计算工具


过去十年见证了理论和计算模型的激增，用于描述复杂基因调控网络的动态，以及这些相互作用如何产生多稳定和异质细胞群。随着使用理论模型来描述遗传和生化回路变得越来越普遍，具有数学和物理背景的理论家通常将统计物理学、非线性动力学和网络理论的概念应用于生物系统。本综述旨在清晰概述该领域应用的最重要的方法，同时强调当前和未来的挑战。它还包括用于解决和模拟该领域使用的一些典型生物系统模型的实践教程。此外，我们为希望探索这个快速发展领域的理论家提供了现有文献中的具体例子。只要有可能，我们都会强调生化和调控网络与非平衡统计和量子力学中通常研究的“经典”系统之间的异同。