On the existence of oscillatory behavior in gene regulatory networks with cyclic interconnections

Yutaka Hori, Akifumi Takabe, Shinji Hara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

In this paper, we derive an existence condition of periodic oscillations in cyclic gene regulatory networks, of which the dynamical behavior is described by nonlinear differential equations. For this purpose, we first point out that change of the equilibrium point with respect to biochemical parameters is important for comprehensive analysis, and show the properties which the equilibrium point should satisfy. Then, by employing these properties, we derive an analytic condition for the existence of periodic oscillations in cyclic gene regulatory networks where genes have homogeneous dynamics. Compared to preceding studies, our condition has the following distinctive features: (i)it is analytically written only in terms of the system parameters, (ii)it is applicable for cyclic gene regulatory networks consisting of any number of genes. Thus, biological interpretation of the result is easily obtained, and, in fact, it is concluded that cyclic gene regulatory networks with homogeneous gene dynamics tend to have periodic oscillations as the number of genes gets large. Finally, we discuss the case of cyclic gene regulatory networks with heterogeneous gene dynamics.

Original languageEnglish
Title of host publicationICCAS-SICE 2009 - ICROS-SICE International Joint Conference 2009, Proceedings
Pages2525-2530
Number of pages6
Publication statusPublished - 2009
Externally publishedYes
EventICROS-SICE International Joint Conference 2009, ICCAS-SICE 2009 - Fukuoka, Japan
Duration: 2009 Aug 182009 Aug 21

Other

OtherICROS-SICE International Joint Conference 2009, ICCAS-SICE 2009
CountryJapan
CityFukuoka
Period09/8/1809/8/21

Fingerprint

Genes
Differential equations

Keywords

  • Cyclic interconnections
  • Gene regulatory networks
  • Oscillations

ASJC Scopus subject areas

  • Information Systems
  • Control and Systems Engineering
  • Industrial and Manufacturing Engineering

Cite this

Hori, Y., Takabe, A., & Hara, S. (2009). On the existence of oscillatory behavior in gene regulatory networks with cyclic interconnections. In ICCAS-SICE 2009 - ICROS-SICE International Joint Conference 2009, Proceedings (pp. 2525-2530). [5335339]

On the existence of oscillatory behavior in gene regulatory networks with cyclic interconnections. / Hori, Yutaka; Takabe, Akifumi; Hara, Shinji.

ICCAS-SICE 2009 - ICROS-SICE International Joint Conference 2009, Proceedings. 2009. p. 2525-2530 5335339.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hori, Y, Takabe, A & Hara, S 2009, On the existence of oscillatory behavior in gene regulatory networks with cyclic interconnections. in ICCAS-SICE 2009 - ICROS-SICE International Joint Conference 2009, Proceedings., 5335339, pp. 2525-2530, ICROS-SICE International Joint Conference 2009, ICCAS-SICE 2009, Fukuoka, Japan, 09/8/18.
Hori Y, Takabe A, Hara S. On the existence of oscillatory behavior in gene regulatory networks with cyclic interconnections. In ICCAS-SICE 2009 - ICROS-SICE International Joint Conference 2009, Proceedings. 2009. p. 2525-2530. 5335339
Hori, Yutaka ; Takabe, Akifumi ; Hara, Shinji. / On the existence of oscillatory behavior in gene regulatory networks with cyclic interconnections. ICCAS-SICE 2009 - ICROS-SICE International Joint Conference 2009, Proceedings. 2009. pp. 2525-2530
@inproceedings{cf0349140f8b46cabf91224ed7e6d622,
title = "On the existence of oscillatory behavior in gene regulatory networks with cyclic interconnections",
abstract = "In this paper, we derive an existence condition of periodic oscillations in cyclic gene regulatory networks, of which the dynamical behavior is described by nonlinear differential equations. For this purpose, we first point out that change of the equilibrium point with respect to biochemical parameters is important for comprehensive analysis, and show the properties which the equilibrium point should satisfy. Then, by employing these properties, we derive an analytic condition for the existence of periodic oscillations in cyclic gene regulatory networks where genes have homogeneous dynamics. Compared to preceding studies, our condition has the following distinctive features: (i)it is analytically written only in terms of the system parameters, (ii)it is applicable for cyclic gene regulatory networks consisting of any number of genes. Thus, biological interpretation of the result is easily obtained, and, in fact, it is concluded that cyclic gene regulatory networks with homogeneous gene dynamics tend to have periodic oscillations as the number of genes gets large. Finally, we discuss the case of cyclic gene regulatory networks with heterogeneous gene dynamics.",
keywords = "Cyclic interconnections, Gene regulatory networks, Oscillations",
author = "Yutaka Hori and Akifumi Takabe and Shinji Hara",
year = "2009",
language = "English",
isbn = "9784907764333",
pages = "2525--2530",
booktitle = "ICCAS-SICE 2009 - ICROS-SICE International Joint Conference 2009, Proceedings",

}

TY - GEN

T1 - On the existence of oscillatory behavior in gene regulatory networks with cyclic interconnections

AU - Hori, Yutaka

AU - Takabe, Akifumi

AU - Hara, Shinji

PY - 2009

Y1 - 2009

N2 - In this paper, we derive an existence condition of periodic oscillations in cyclic gene regulatory networks, of which the dynamical behavior is described by nonlinear differential equations. For this purpose, we first point out that change of the equilibrium point with respect to biochemical parameters is important for comprehensive analysis, and show the properties which the equilibrium point should satisfy. Then, by employing these properties, we derive an analytic condition for the existence of periodic oscillations in cyclic gene regulatory networks where genes have homogeneous dynamics. Compared to preceding studies, our condition has the following distinctive features: (i)it is analytically written only in terms of the system parameters, (ii)it is applicable for cyclic gene regulatory networks consisting of any number of genes. Thus, biological interpretation of the result is easily obtained, and, in fact, it is concluded that cyclic gene regulatory networks with homogeneous gene dynamics tend to have periodic oscillations as the number of genes gets large. Finally, we discuss the case of cyclic gene regulatory networks with heterogeneous gene dynamics.

AB - In this paper, we derive an existence condition of periodic oscillations in cyclic gene regulatory networks, of which the dynamical behavior is described by nonlinear differential equations. For this purpose, we first point out that change of the equilibrium point with respect to biochemical parameters is important for comprehensive analysis, and show the properties which the equilibrium point should satisfy. Then, by employing these properties, we derive an analytic condition for the existence of periodic oscillations in cyclic gene regulatory networks where genes have homogeneous dynamics. Compared to preceding studies, our condition has the following distinctive features: (i)it is analytically written only in terms of the system parameters, (ii)it is applicable for cyclic gene regulatory networks consisting of any number of genes. Thus, biological interpretation of the result is easily obtained, and, in fact, it is concluded that cyclic gene regulatory networks with homogeneous gene dynamics tend to have periodic oscillations as the number of genes gets large. Finally, we discuss the case of cyclic gene regulatory networks with heterogeneous gene dynamics.

KW - Cyclic interconnections

KW - Gene regulatory networks

KW - Oscillations

UR - http://www.scopus.com/inward/record.url?scp=77950849431&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950849431&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9784907764333

SP - 2525

EP - 2530

BT - ICCAS-SICE 2009 - ICROS-SICE International Joint Conference 2009, Proceedings

ER -