Nikolov Svetoslav, Yankulova Elka, Wolkenhauer Olaf, Petrov Valko
Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, Sofia, 1113, Bulgaria.
Nonlinear Dynamics Psychol Life Sci. 2007 Oct;11(4):413-33.
The concepts stability and structural stability (robustness) are used often in systems biology. According to Kitano (2004) robustness is a fundamental property of evolvable complex biological systems. For that reason, the purpose of this review is to clarify: (a) how are strictly formulated concepts, such as stability and robustness of a dynamical system, used in computational systems biology; (b) what is meant by structural stability (robustness) in contemporary biology and how are stability and robustness distinguished from each other; and (c) why is it necessary to investigate whether a cell signal pathway is stable. We formulate the two concepts stability and structural stability (robustness) of a dynamical system with an arbitrary dimensionality, in the way they are known in mathematics and mechanics, and clarify the principal difference between them. We also consider how these two concepts are used in the analysis of a concrete biological system in systems biology. In the last section we formulate when, according to us, in biology (and in systems biology in particular), it should be said that a system (process) is stable, and when it is structurally stable.
稳定性和结构稳定性（鲁棒性）的概念在系统生物学中经常被使用。根据北野宏明（2004年）的观点，鲁棒性是可进化的复杂生物系统的一个基本属性。因此，本综述的目的是阐明：（a）像动态系统的稳定性和鲁棒性这样严格表述的概念在计算系统生物学中是如何使用的；（b）当代生物学中结构稳定性（鲁棒性）是什么意思，以及稳定性和鲁棒性是如何相互区分的；（c）为什么有必要研究细胞信号通路是否稳定。我们按照数学和力学中已知的方式，阐述任意维度动态系统的稳定性和结构稳定性（鲁棒性）这两个概念，并阐明它们之间的主要区别。我们还考虑了这两个概念在系统生物学中对具体生物系统的分析中是如何使用的。在最后一部分，我们阐述了在我们看来，在生物学（特别是系统生物学）中，何时应该说一个系统（过程）是稳定的，以及何时它是结构稳定的。
