Dong Chao-Yi, Yoon Tae-Woong, Bates Declan G, Cho Kwang-Hyun
School of Electrical Engineering, Korea University, Seoul 136-713, Korea.
J Math Biol. 2010 Feb;60(2):285-312. doi: 10.1007/s00285-009-0263-x. Epub 2009 Mar 31.
Feedback circuits are crucial dynamic motifs which occur in many biomolecular regulatory networks. They play a pivotal role in the regulation and control of many important cellular processes such as gene transcription, signal transduction, and metabolism. In this study, we develop a novel computationally efficient method to identify feedback loops embedded in intracellular networks, which uses only time-series experimental data and requires no knowledge of the network structure. In the proposed approach, a non-parametric system identification technique, as well as a spectral factor analysis, is applied to derive a graphical criterion based on non-causal components of the system's impulse response. The appearance of non-causal components in the impulse response sequences arising from stochastic output perturbations is shown to imply the presence of underlying feedback connections within a linear network. In order to extend the approach to nonlinear networks, we linearize the intracellular networks about an equilibrium point, and then choose the magnitude of the output perturbations sufficiently small so that the resulting time-series responses remain close to the chosen equilibrium point. In this way, the impulse response sequences of the linearized system can be used to determine the presence or absence of feedback loops in the corresponding nonlinear network. The proposed method utilizes the time profile data from intracellular perturbation experiments and only requires the perturbability of output nodes. Most importantly, the method does not require any a priori knowledge of the system structure. For these reasons, the proposed approach is very well suited to identifying feedback loops in large-scale biomolecular networks. The effectiveness of the proposed method is illustrated via two examples: a synthetic network model with a negative feedback loop and a nonlinear caspase function model of apoptosis with a positive feedback loop.
反馈回路是许多生物分子调控网络中至关重要的动态基序。它们在许多重要的细胞过程（如基因转录、信号转导和代谢）的调节和控制中起着关键作用。在本研究中，我们开发了一种新颖的计算效率高的方法来识别嵌入细胞内网络的反馈回路，该方法仅使用时间序列实验数据，且不需要网络结构的知识。在所提出的方法中，应用了一种非参数系统识别技术以及谱因子分析，以基于系统脉冲响应的非因果成分推导图形准则。由随机输出扰动产生的脉冲响应序列中出现非因果成分表明线性网络中存在潜在的反馈连接。为了将该方法扩展到非线性网络，我们围绕平衡点对细胞内网络进行线性化，然后选择足够小的输出扰动幅度，以使所得的时间序列响应保持接近所选的平衡点。通过这种方式，线性化系统的脉冲响应序列可用于确定相应非线性网络中反馈回路的存在与否。所提出的方法利用细胞内扰动实验的时间剖面数据，并且仅需要输出节点的可扰动性。最重要的是该方法不需要系统结构的任何先验知识。由于这些原因，所提出的方法非常适合识别大规模生物分子网络中的反馈回路。通过两个例子说明了所提出方法的有效性：一个具有负反馈回路的合成网络模型和一个具有正反馈回路的细胞凋亡非线性半胱天冬酶功能模型。
