Shmulevich Ilya, Kauffman Stuart A, Aldana Maximino
Institute for Systems Biology, Seattle, WA 98103, USA.
Proc Natl Acad Sci U S A. 2005 Sep 20;102(38):13439-44. doi: 10.1073/pnas.0506771102. Epub 2005 Sep 9.
Two important theoretical approaches have been developed to generically characterize the relationship between the structure and function of large genetic networks: the continuous approach, based on reaction-kinetics differential equations, and the Boolean approach, based on difference equations and discrete logical rules. These two approaches do not always coincide in their predictions for the same system. Nonetheless, both of them predict that the highly nonlinear dynamics exhibited by genetic regulatory systems can be characterized into two broad regimes, to wit, an ordered regime where the system is robust against perturbations, and a chaotic regime where the system is extremely sensitive to perturbations. It has been a plausible and long-standing hypothesis that genomic regulatory networks of real cells operate in the ordered regime or at the border between order and chaos. This hypothesis is indirectly supported by the robustness and stability observed in the phenotypic traits of living organisms under genetic perturbations. However, there has been no systematic study to determine whether the gene-expression patterns of real cells are compatible with the dynamically ordered regimes predicted by theoretical models. Using the Boolean approach, here we show what we believe to be the first direct evidence that the underlying genetic network of HeLa cells appears to operate either in the ordered regime or at the border between order and chaos but does not appear to be chaotic.
基于反应动力学微分方程的连续方法，以及基于差分方程和离散逻辑规则的布尔方法。对于同一系统，这两种方法的预测并不总是一致。尽管如此，它们都预测遗传调控系统所展现的高度非线性动力学可分为两种宽泛的状态，即系统对扰动具有鲁棒性的有序状态，以及系统对扰动极其敏感的混沌状态。长期以来，一个看似合理的假设是，真实细胞的基因组调控网络在有序状态下运行，或者在有序与混沌的边界运行。在遗传扰动下生物体表型特征中观察到的鲁棒性和稳定性间接支持了这一假设。然而，尚未有系统研究来确定真实细胞的基因表达模式是否与理论模型预测的动态有序状态相符。在此，我们使用布尔方法展示了我们认为是首个直接证据，即HeLa细胞的潜在遗传网络似乎在有序状态下运行，或者在有序与混沌的边界运行，但似乎并非处于混沌状态。
