Kim J, Bates D G, Postlethwaite I, Ma L, Iglesias P A
Control and Instrumentation Group, Department of Engineering, University of Leicester, UK.
Syst Biol (Stevenage). 2006 May;153(3):96-104. doi: 10.1049/ip-syb:20050024.
Biological systems that have been experimentally verified to be robust to significant changes in their environments require mathematical models that are themselves robust. In this context, a necessary condition for model robustness is that the model dynamics should not be sensitive to small variations in the model's parameters. Robustness analysis problems of this type have been extensively studied in the field of robust control theory and have been found to be very difficult to solve in general. The authors describe how some tools from robust control theory and nonlinear optimisation can be used to analyse the robustness of a recently proposed model of the molecular network underlying adenosine 3',5'-cyclic monophosphate (cAMP) oscillations observed in fields of chemotactic Dictyostelium cells. The network model, which consists of a system of seven coupled nonlinear differential equations, accurately reproduces the spontaneous oscillations in cAMP observed during the early development of D. discoideum. The analysis by the authors reveals, however, that very small variations in the model parameters can effectively destroy the required oscillatory dynamics. A biological interpretation of the analysis results is that correct functioning of a particular positive feedback loop in the proposed model is crucial to maintaining the required oscillatory dynamics.
经实验验证对其环境中的重大变化具有鲁棒性的生物系统需要其自身具有鲁棒性的数学模型。在这种情况下，模型鲁棒性的一个必要条件是模型动力学不应对模型参数的微小变化敏感。这类鲁棒性分析问题在鲁棒控制理论领域已得到广泛研究，并且发现一般很难解决。作者描述了如何使用鲁棒控制理论和非线性优化中的一些工具来分析最近提出的一个分子网络模型的鲁棒性，该模型是关于在趋化性盘基网柄菌细胞群体中观察到的3',5'-环磷酸腺苷（cAMP）振荡的基础。该网络模型由一个包含七个耦合非线性微分方程的系统组成，能准确再现盘基网柄菌早期发育过程中观察到的cAMP自发振荡。然而，作者的分析表明，模型参数的非常小的变化就能有效地破坏所需的振荡动力学。对分析结果的生物学解释是，所提出模型中特定正反馈回路的正确运作对于维持所需的振荡动力学至关重要。
