Bioinformatics Research Centre, Aarhus University, C. F. Møllers Allé 8, 8000 Aarhus, Denmark.
J R Soc Interface. 2012 Jun 7;9(71):1224-32. doi: 10.1098/rsif.2011.0664. Epub 2011 Nov 2.
Multi-stationarity in biological systems is a mechanism of cellular decision-making. In particular, signalling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological inputs. The features that lead to multi-stationarity are of particular interest to determine, as well as the stability, properties of the steady states. In this paper, we determine conditions for the emergence of multi-stationarity in small motifs without feedback that repeatedly occur in signalling pathways. We derive an explicit mathematical relationship ϕ between the concentration of a chemical species at steady state and a conserved quantity of the system such as the total amount of substrate available. We show that ϕ determines the number of steady states and provides a necessary condition for a steady state to be stable-that is, to be biologically attainable. Further, we identify characteristics of the motifs that lead to multi-stationarity, and extend the view that multi-stationarity in signalling pathways arises from multi-site phosphorylation. Our approach relies on mass-action kinetics, and the conclusions are drawn in full generality without resorting to simulations or random generation of parameters. The approach is extensible to other systems.
生物系统中的多稳定性是一种细胞决策机制。特别是，由蛋白质磷酸化调节的信号通路表现出的特征，促进了对不同生物输入的多种反应。导致多稳定性的特征以及稳定状态的稳定性、性质尤其值得关注。在本文中，我们确定了在没有反馈的小图案中出现多稳定性的条件，这些小图案在信号通路中反复出现。我们推导出了一个明确的数学关系 ϕ，它将化学物质在稳定状态下的浓度与系统的守恒量（如可用的底物总量）联系起来。我们表明 ϕ 决定了稳定状态的数量，并为稳定状态提供了一个必要条件，即具有生物可实现性。此外，我们确定了导致多稳定性的图案特征，并扩展了这样一种观点，即信号通路中的多稳定性源于多位点磷酸化。我们的方法依赖于质量作用动力学，并且在不求助于模拟或随机生成参数的情况下，以完全通用的方式得出结论。该方法可扩展到其他系统。
