Department of Systems and Computer Engineering, University of Naples Federico II, Naples, Italy.
PLoS Comput Biol. 2010 Apr 15;6(4):e1000739. doi: 10.1371/journal.pcbi.1000739.
This paper addresses the problem of providing mathematical conditions that allow one to ensure that biological networks, such as transcriptional systems, can be globally entrained to external periodic inputs. Despite appearing obvious at first, this is by no means a generic property of nonlinear dynamical systems. Through the use of contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all their solutions converge to a fixed limit cycle. General results are proved, and the properties are verified in the specific cases of models of transcriptional systems as well as constructs of interest in synthetic biology. A self-contained exposition of all needed results is given in the paper.
本文解决了为生物网络（如转录系统）提供数学条件以确保其能被外部周期性输入全局同步的问题。尽管这一点乍看起来很明显，但它绝不是非线性动力系统的普遍特性。本文利用动力系统理论中的有力工具——收缩理论，证明了某些受外部周期性信号驱动的系统具有这样的性质：所有解都收敛到一个固定的极限环。文中给出了一般性的结果，并在转录系统模型以及合成生物学中感兴趣的构建体的具体情况下验证了这些性质。文中还给出了所有必要结果的完整论述。
