Computational and Systems Biology, John Innes Centre, Norwich, United Kingdom.
PLoS One. 2009 Aug 13;4(8):e6637. doi: 10.1371/journal.pone.0006637.
Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia), with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling.
豆科植物与固氮细菌（称为根瘤菌）形成有益的共生关系，根瘤菌被容纳在宿主植物根部的独特结构中。豆科植物/根瘤菌共生关系负责全球生物可利用氮的很大一部分。这种共生关系的启动受植物根毛细胞内特征性钙振荡的控制，该信号被根瘤菌激活。最近对钙时间序列数据的分析表明，随机效应在定义振荡的性质方面起着重要作用。然而，使用多种非线性时间序列技术则提出了一种替代解释，即确定性混沌。我们对这种钙振荡反应的性质进行了广泛的非线性时间序列分析。我们通过一系列技术建立了证据，这些技术用于检验确定性、量化线性和非线性分量，并测量系统的局部散度。混沌在自然界中很常见，似乎生物系统可能利用混沌动力学的特性来控制细胞内的过程。具有混沌控制机制的系统在某种意义上更具鲁棒性，因为增强的灵活性允许以更低的能量成本更快速地响应环境变化。以这种方式可以最有效地针对所需的行为，这为生物信号中的非线性机制提供了一些有趣的推测。
