Graphical and analytic criteria for the existence of protein level oscillations in cyclic gene regulatory networks

Yutaka Hori; Tae Hyoung Kim; Shinji Hara

doi:10.1109/CDC.2009.5400718

Graphical and analytic criteria for the existence of protein level oscillations in cyclic gene regulatory networks

Yutaka Hori, Tae Hyoung Kim, Shinji Hara

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

8 Citations (Scopus)

Abstract

This paper investigates the criteria for the existence of protein level oscillations in a class of gene regulatory networks, where a nonlinear differential equation model is considered to analyze its dynamical behavior. There are two steps to derive such criteria: We first employ a Poincaŕe-Bendixson type theorem to restrict the class of solution trajectories, and then carry out a local stability analysis of linearized systems with a generalized frequency variable. Then, our main results, graphical and its equivalent analytic criteria which are easily applicable for the networks consisting of arbitrary number of genes, are derived. Their distinctive features are also verified through numerical simulations.

Original language	English
Title of host publication	Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3521-3526
Number of pages	6
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5400718
Publication status	Published - 2009
Externally published	Yes
Event	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: 2009 Dec 15 → 2009 Dec 18

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Country/Territory	China
City	Shanghai
Period	09/12/15 → 09/12/18

ASJC Scopus subject areas

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2009.5400718

Cite this

Hori, Y., Kim, T. H., & Hara, S. (2009). Graphical and analytic criteria for the existence of protein level oscillations in cyclic gene regulatory networks. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 3521-3526). [5400718] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5400718

Graphical and analytic criteria for the existence of protein level oscillations in cyclic gene regulatory networks. / Hori, Yutaka; Kim, Tae Hyoung; Hara, Shinji.
Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. p. 3521-3526 5400718 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Hori, Y, Kim, TH & Hara, S 2009, Graphical and analytic criteria for the existence of protein level oscillations in cyclic gene regulatory networks. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5400718, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 3521-3526, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 09/12/15. https://doi.org/10.1109/CDC.2009.5400718

Hori Y, Kim TH, Hara S. Graphical and analytic criteria for the existence of protein level oscillations in cyclic gene regulatory networks. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc. 2009. p. 3521-3526. 5400718. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2009.5400718

Hori, Yutaka ; Kim, Tae Hyoung ; Hara, Shinji. / Graphical and analytic criteria for the existence of protein level oscillations in cyclic gene regulatory networks. Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. pp. 3521-3526 (Proceedings of the IEEE Conference on Decision and Control).

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abstract = "This paper investigates the criteria for the existence of protein level oscillations in a class of gene regulatory networks, where a nonlinear differential equation model is considered to analyze its dynamical behavior. There are two steps to derive such criteria: We first employ a Poinca{\'r}e-Bendixson type theorem to restrict the class of solution trajectories, and then carry out a local stability analysis of linearized systems with a generalized frequency variable. Then, our main results, graphical and its equivalent analytic criteria which are easily applicable for the networks consisting of arbitrary number of genes, are derived. Their distinctive features are also verified through numerical simulations.",

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AB - This paper investigates the criteria for the existence of protein level oscillations in a class of gene regulatory networks, where a nonlinear differential equation model is considered to analyze its dynamical behavior. There are two steps to derive such criteria: We first employ a Poincaŕe-Bendixson type theorem to restrict the class of solution trajectories, and then carry out a local stability analysis of linearized systems with a generalized frequency variable. Then, our main results, graphical and its equivalent analytic criteria which are easily applicable for the networks consisting of arbitrary number of genes, are derived. Their distinctive features are also verified through numerical simulations.

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Graphical and analytic criteria for the existence of protein level oscillations in cyclic gene regulatory networks

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