TY - JOUR
T1 - Biochemical oscillations in delayed negative cyclic feedback
T2 - Existence and profiles
AU - Hori, Yutaka
AU - Takada, Masaaki
AU - Hara, Shinji
N1 - Funding Information:
This work was supported in part by the Ministry of Education, Culture, Sports, Science and Technology in Japan through Grant-in-Aid for Exploratory Research No. 19656104 and No. 21656106 , Grant-in-Aid for Scientific Research (A) No. 21246067 , and Grant-in-Aid for JSPS Fellows No. 23-9203 . The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Juergen Hahn under the direction of Editor Frank Allgöwer.
PY - 2013/9
Y1 - 2013/9
N2 - In this paper, we propose a theoretical framework to systematically analyze the existence and the profiles of chemical oscillations in gene regulatory networks with negative cyclic feedback. In particular, we analytically derive the existence conditions and the profiles of oscillations in terms of reaction kinetic parameters and reveal dimensionless quantities that essentially characterize the oscillatory dynamics. These discoveries then allow us to provide general biological insights that are useful for the design of synthetic gene circuits and wet-lab experiments. We point out that time delays due to splicing and transport play an important role for both of the existence and the profiles of oscillations. To this end, we first show that local instability leads to oscillations in cyclic gene regulatory networks, and we derive the existence conditions based on local instability analysis. Then, we analyze the period, phase and amplitude of oscillations using multivariable harmonic balance analysis. These results are demonstrated with two existing biochemical networks, the Pentilator and a self-repression network of a Hes protein.
AB - In this paper, we propose a theoretical framework to systematically analyze the existence and the profiles of chemical oscillations in gene regulatory networks with negative cyclic feedback. In particular, we analytically derive the existence conditions and the profiles of oscillations in terms of reaction kinetic parameters and reveal dimensionless quantities that essentially characterize the oscillatory dynamics. These discoveries then allow us to provide general biological insights that are useful for the design of synthetic gene circuits and wet-lab experiments. We point out that time delays due to splicing and transport play an important role for both of the existence and the profiles of oscillations. To this end, we first show that local instability leads to oscillations in cyclic gene regulatory networks, and we derive the existence conditions based on local instability analysis. Then, we analyze the period, phase and amplitude of oscillations using multivariable harmonic balance analysis. These results are demonstrated with two existing biochemical networks, the Pentilator and a self-repression network of a Hes protein.
KW - Application of nonlinear analysis and design
KW - Cellular, metabolic, cardiovascular, neurosystems
KW - Gene regulatory networks
KW - Large scale complex systems
KW - Systems with time-delays
UR - http://www.scopus.com/inward/record.url?scp=84881476478&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84881476478&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2013.04.020
DO - 10.1016/j.automatica.2013.04.020
M3 - Article
AN - SCOPUS:84881476478
SN - 0005-1098
VL - 49
SP - 2581
EP - 2590
JO - Automatica
JF - Automatica
IS - 9
ER -