Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-8654, Japan.
Department of Integrated Sciences for Life, Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima City, Hiroshima, 739-8526, Japan.
Phys Rev E. 2019 Oct;100(4-1):042403. doi: 10.1103/PhysRevE.100.042403.
Fluctuations in intracellular reactions (intrinsic noise) reduce the information transmitted from an extracellular input to a cellular response. However, recent studies have demonstrated that the decrease in the transmitted information with respect to extracellular input fluctuations (extrinsic noise) is smaller when the intrinsic noise is larger. Therefore, it has been suggested that robustness against extrinsic noise increases with the level of the intrinsic noise. We call this phenomenon intrinsic noise-induced robustness (INIR). As previous studies on this phenomenon have focused on complex biochemical reactions, the relation between INIR and the input-output of a system is unclear. Moreover, the mechanism of INIR remains elusive. In this paper, we address these questions by analyzing simple models. We first analyze a model in which the input-output relation is linear. We show that the robustness against extrinsic noise increases with the intrinsic noise, confirming the INIR phenomenon. Moreover, the robustness against the extrinsic noise is more strongly dependent on the intrinsic noise when the variance of the intrinsic noise is larger than that of the input distribution. Next, we analyze a threshold model in which the output depends on whether the input exceeds the threshold. When the threshold is equal to the mean of the input, INIR is realized, but when the threshold is much larger than the mean, the threshold model exhibits stochastic resonance, and INIR is not always apparent. The robustness against extrinsic noise and the transmitted information can be traded off against one another in the linear model and the threshold model without stochastic resonance, whereas they can be simultaneously increased in the threshold model with stochastic resonance.
细胞内反应的波动（内在噪声）会降低从细胞外输入到细胞反应的信息传输。然而，最近的研究表明，当内在噪声较大时，相对于细胞外输入波动（外在噪声）的传输信息减少幅度较小。因此，有人认为，对外部噪声的鲁棒性随内在噪声水平的增加而增加。我们称这种现象为内在噪声诱导的鲁棒性（INIR）。由于以前对这一现象的研究主要集中在复杂的生化反应上，因此 INIR 与系统的输入输出之间的关系尚不清楚。此外，INIR 的机制仍不清楚。在本文中，我们通过分析简单的模型来解决这些问题。我们首先分析了一个输入-输出关系为线性的模型。我们表明，随着内在噪声的增加，对外部噪声的鲁棒性也随之增加，证实了 INIR 现象的存在。此外，当内在噪声的方差大于输入分布的方差时，对外部噪声的鲁棒性对内在噪声的依赖性更强。接下来，我们分析了一个阈值模型，其中输出取决于输入是否超过阈值。当阈值等于输入的平均值时，实现了 INIR，但当阈值远大于平均值时，阈值模型表现出随机共振，并且 INIR 并不总是明显的。在线性模型和没有随机共振的阈值模型中，外在噪声和传输信息的鲁棒性可以相互权衡，而在具有随机共振的阈值模型中，它们可以同时增加。
