Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel.
Gladstone Institutes, San Francisco, CA, USA.
Nat Commun. 2021 Mar 19;12(1):1788. doi: 10.1038/s41467-021-21700-8.
Biological regulatory systems, such as cell signaling networks, nervous systems and ecological webs, consist of complex dynamical interactions among many components. Network motif models focus on small sub-networks to provide quantitative insight into overall behavior. However, such models often overlook time delays either inherent to biological processes or associated with multi-step interactions. Here we systematically examine explicit-delay versions of the most common network motifs via delay differential equation (DDE) models, both analytically and numerically. We find many broadly applicable results, including parameter reduction versus canonical ordinary differential equation (ODE) models, analytical relations for converting between ODE and DDE models, criteria for when delays may be ignored, a complete phase space for autoregulation, universal behaviors of feedforward loops, a unified Hill-function logic framework, and conditions for oscillations and chaos. We conclude that explicit-delay modeling simplifies the phenomenology of many biological networks and may aid in discovering new functional motifs.
生物调节系统，如细胞信号网络、神经系统和生态网络，由许多成分之间的复杂动态相互作用组成。网络基元模型侧重于小的子网，以提供对整体行为的定量见解。然而，这种模型通常忽略了生物过程固有的或与多步相互作用相关的时间延迟。在这里，我们通过延迟微分方程 (DDE) 模型系统地研究了最常见的网络基元的显式延迟版本，包括分析和数值两种方法。我们发现了许多广泛适用的结果，包括与典型的常微分方程 (ODE) 模型相比的参数减少、在 ODE 和 DDE 模型之间转换的解析关系、何时可以忽略延迟的标准、自调节的完整相空间、前馈回路的通用行为、统一的 Hill 函数逻辑框架，以及振荡和混沌的条件。我们得出结论，显式延迟建模简化了许多生物网络的现象，并可能有助于发现新的功能基元。
