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Identification of feedback loops embedded in cellular circuits by investigating non-causal impulse response components

Journal of Mathematical Biology volume 60, Article number: 285 (2010) Cite this article

Abstract

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.

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Authors and Affiliations

  1. School of Electrical Engineering, Korea University, Seoul, 136-713, Korea

    Chao-Yi Dong & Tae-Woong Yoon

  2. School of Information and Engineering, Inner Mongolia University of Technology, 010051, Huhhot, China

    Chao-Yi Dong

  3. Systems Biology Lab, Department of Engineering, University of Leicester, Leicester, LE1 7RH, UK

    Declan G. Bates

  4. Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology (KAIST), 335 Gwahangno, Yuseong-gu, 305-701, Daejeon, Republic of Korea

    Chao-Yi Dong & Kwang-Hyun Cho

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  1. Chao-Yi Dong
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  2. Tae-Woong Yoon
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  3. Declan G. Bates
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  4. Kwang-Hyun Cho
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Correspondence to Tae-Woong Yoon or Kwang-Hyun Cho.

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Dong, CY., Yoon, TW., Bates, D.G. et al. Identification of feedback loops embedded in cellular circuits by investigating non-causal impulse response components. J. Math. Biol. 60, 285 (2010). https://doi.org/10.1007/s00285-009-0263-x

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  • DOI: https://doi.org/10.1007/s00285-009-0263-x

Keywords

  • Biomolecular regulatory networks
  • Feedback loops
  • Nonparametric identification
  • Spectral factor analysis
  • Signaling pathways
  • Systems biology

Mathematics Subject Classification (2000)

  • 92-08
  • 92B05
  • 93B30
  • 93E12
  • 93E10
  • 93E24