Zheng Likun, Chen Meng, Nie Qing
Department of Mathematics, University of California, Irvine, California 92697, USA ; Center for Complex Biological Systems, University of California, Irvine, California 92697, USA ; Center for Mathematical and Computational Biology, University of California, Irvine, California 92697, USA.
J Math Phys. 2012 Nov;53(11):115616. doi: 10.1063/1.4762825. Epub 2012 Nov 5.
Biological systems are often subject to external noise from signal stimuli and environmental perturbations, as well as noises in the intracellular signal transduction pathway. Can different stochastic fluctuations interact to give rise to new emerging behaviors? How can a system reduce noise effects while still being capable of detecting changes in the input signal? Here, we study analytically and computationally the role of nonlinear feedback systems in controlling external noise with the presence of large internal noise. In addition to noise attenuation, we analyze derivatives of Fano factor to study systems' capability of differentiating signal inputs. We find effects of internal noise and external noise may be separated in one slow positive feedback loop system; in particular, the slow loop can decrease external noise and increase robustness of signaling with respect to fluctuations in rate constants, while maintaining the signal output specific to the input. For two feedback loops, we demonstrate that the influence of external noise mainly depends on how the fast loop responds to fluctuations in the input and the slow loop plays a limited role in determining the signal precision. Furthermore, in a dual loop system of one positive feedback and one negative feedback, a slower positive feedback always leads to better noise attenuation; in contrast, a slower negative feedback may not be more beneficial. Our results reveal interesting stochastic effects for systems containing both extrinsic and intrinsic noises, suggesting novel noise filtering strategies in inherently stochastic systems.
生物系统经常受到来自信号刺激和环境扰动的外部噪声以及细胞内信号转导途径中的噪声影响。不同的随机波动能否相互作用从而产生新的涌现行为？一个系统如何在能够检测输入信号变化的同时降低噪声影响？在此，我们通过分析和计算研究非线性反馈系统在存在大量内部噪声时控制外部噪声的作用。除了噪声衰减，我们还分析了法诺因子的导数以研究系统区分信号输入的能力。我们发现，在一个慢正反馈回路系统中，内部噪声和外部噪声的影响可能会被分离；特别是，慢回路可以降低外部噪声，并提高信号相对于速率常数波动的稳健性，同时保持特定于输入的信号输出。对于两个反馈回路，我们证明外部噪声的影响主要取决于快回路对输入波动的响应方式，而慢回路在确定信号精度方面作用有限。此外，在一个正反馈和一个负反馈的双回路系统中，较慢的正反馈总是导致更好的噪声衰减；相比之下，较慢的负反馈可能并非更有益。我们的结果揭示了包含外在和内在噪声的系统中有趣的随机效应，为固有随机系统提出了新颖的噪声滤波策略。
