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

Chao Yi Dong, Tae Woong Yoon, Declan G. Bates, Kwang Hyun Cho

Research output: Contribution to journalArticle

8 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)285-312
Number of pages28
JournalJournal of Mathematical Biology
Volume60
Issue number2
DOIs
Publication statusPublished - 2010 Sep 1

Fingerprint

Feedback Loop
Impulse Response
Impulse response
Feedback
Networks (circuits)
Nonlinear networks
time series analysis
Equilibrium Point
Output
methodology
Nonparametric Identification
Time series
caspases
Perturbation
Apoptosis
Positive Feedback
Negative Feedback
Signal Transduction
Regulatory Networks
Linear networks

Keywords

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

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Modelling and Simulation

Cite this

Identification of feedback loops embedded in cellular circuits by investigating non-causal impulse response components. / Dong, Chao Yi; Yoon, Tae Woong; Bates, Declan G.; Cho, Kwang Hyun.

In: Journal of Mathematical Biology, Vol. 60, No. 2, 01.09.2010, p. 285-312.

Research output: Contribution to journalArticle

@article{93d398509dc145b7bf717b25efab50d2,
title = "Identification of feedback loops embedded in cellular circuits by investigating non-causal impulse response components",
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.",
keywords = "Biomolecular regulatory networks, Feedback loops, Nonparametric identification, Signaling pathways, Spectral factor analysis, Systems biology",
author = "Dong, {Chao Yi} and Yoon, {Tae Woong} and Bates, {Declan G.} and Cho, {Kwang Hyun}",
year = "2010",
month = "9",
day = "1",
doi = "10.1007/s00285-009-0263-x",
language = "English",
volume = "60",
pages = "285--312",
journal = "Journal of Mathematical Biology",
issn = "0303-6812",
publisher = "Springer Verlag",
number = "2",

}

TY - JOUR

T1 - Identification of feedback loops embedded in cellular circuits by investigating non-causal impulse response components

AU - Dong, Chao Yi

AU - Yoon, Tae Woong

AU - Bates, Declan G.

AU - Cho, Kwang Hyun

PY - 2010/9/1

Y1 - 2010/9/1

N2 - 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.

AB - 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.

KW - Biomolecular regulatory networks

KW - Feedback loops

KW - Nonparametric identification

KW - Signaling pathways

KW - Spectral factor analysis

KW - Systems biology

UR - http://www.scopus.com/inward/record.url?scp=74049150229&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=74049150229&partnerID=8YFLogxK

U2 - 10.1007/s00285-009-0263-x

DO - 10.1007/s00285-009-0263-x

M3 - Article

C2 - 19333603

AN - SCOPUS:74049150229

VL - 60

SP - 285

EP - 312

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 2

ER -