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

研究成果: Conference contribution

8 被引用数 (Scopus)

抄録

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.

本文言語	English
ホスト出版物のタイトル	Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
出版社	Institute of Electrical and Electronics Engineers Inc.
ページ	3521-3526
ページ数	6
ISBN（印刷版）	9781424438716
DOI	https://doi.org/10.1109/CDC.2009.5400718
出版ステータス	Published - 2009
外部発表	はい
イベント	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China 継続期間: 2009 12月 15 → 2009 12月 18

出版物シリーズ

名前	Proceedings of the IEEE Conference on Decision and Control
ISSN（印刷版）	0743-1546
ISSN（電子版）	2576-2370

Other

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

ASJC Scopus subject areas

制御およびシステム工学
モデリングとシミュレーション
制御と最適化

文献へのアクセス

10.1109/CDC.2009.5400718

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引用スタイル

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). Article 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).

研究成果: 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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N2 - 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.

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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BT - Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

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

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