Center for Modeling and Simulation in the Biosciences (BIOMS), University of Heidelberg, Heidelberg, Germany.
PLoS One. 2011 Apr 8;6(4):e18623. doi: 10.1371/journal.pone.0018623.
Lévy walks as a random search strategy have recently attracted a lot of attention, and have been described in many animal species. However, very little is known about one of the most important issues, namely how Lévy walks are generated by biological organisms. We study a model of the chemotaxis signaling pathway of E. coli, and demonstrate that stochastic fluctuations and the specific design of the signaling pathway in concert enable the generation of Lévy walks. We show that Lévy walks result from the superposition of an ensemble of exponential distributions, which occurs due to the shifts in the internal enzyme concentrations following the stochastic fluctuations. With our approach we derive the power-law analytically from a model of the chemotaxis signaling pathway, and obtain a power-law exponent μ ≈ 2.2, which coincides with experimental results. This work provides a means to confirm Lévy walks as natural phenomenon by providing understanding on the process through which they emerge. Furthermore, our results give novel insights into the design aspects of biological systems that are capable of translating additive noise on the microscopic scale into beneficial macroscopic behavior.
莱维漫步作为一种随机搜索策略最近引起了很多关注，并在许多动物物种中得到了描述。然而，关于一个最重要的问题，即生物有机体如何产生莱维漫步，人们知之甚少。我们研究了大肠杆菌趋化信号通路的模型，并证明随机波动和信号通路的特定设计协同作用能够产生莱维漫步。我们表明，莱维漫步是由于随机波动后内部酶浓度的变化导致一系列指数分布的叠加而产生的。通过我们的方法，我们从趋化信号通路模型中推导出了幂律的解析表达式，并得到了幂律指数μ≈2.2，与实验结果一致。这项工作通过提供对它们出现过程的理解，为确认莱维漫步是自然现象提供了一种方法。此外，我们的结果为能够将微观尺度上的加性噪声转化为有益的宏观行为的生物系统的设计方面提供了新的见解。
