Gene Expression Time Delays and Turing Pattern Formation Systems

2006 ◽  
Vol 68 (1) ◽  
pp. 99-130 ◽  
Author(s):  
E. A. Gaffney ◽  
N. A. M. Monk
Keyword(s):  
Gene Expression ◽  
Pattern Formation ◽  
Time Delays ◽  
Turing Pattern ◽  
Formation Systems ◽  
Expression Time

scholarly journals Turing–Hopf bifurcation and spatiotemporal patterns in a Gierer–Meinhardt system with gene expression delay

2021 ◽  
Vol 26 (3) ◽  
pp. 461-481
Author(s):  
Shuangrui Zhao ◽  
Hongbin Wang ◽  
Weihua Jiang
Keyword(s):  
Gene Expression ◽  
Hopf Bifurcation ◽  
Pattern Formation ◽  
Time Delays ◽  
Spatiotemporal Patterns ◽  
Third Order ◽  
Spatially Inhomogeneous ◽  
Math Biol ◽  
Formation Systems ◽  
Expression Time

In this paper, we consider the dynamics of delayed Gierer–Meinhardt system, which is used as a classic example to explain the mechanism of pattern formation. The conditions for the occurrence of Turing, Hopf and Turing–Hopf bifurcation are established by analyzing the characteristic equation. For Turing–Hopf bifurcation, we derive the truncated third-order normal form based on the work of Jiang et al. [11], which is topologically equivalent to the original equation, and theoretically reveal system exhibits abundant spatial, temporal and spatiotemporal patterns, such as semistable spatially inhomogeneous periodic solutions, as well as tristable patterns of a pair of spatially inhomogeneous steady states and a spatially homogeneous periodic solution coexisting. Especially, we theoretically explain the phenomenon that time delay inhibits the formation of heterogeneous steady patterns, found by S. Lee, E. Gaffney and N. Monk [The influence of gene expression time delays on Gierer–Meinhardt pattern formation systems, Bull. Math. Biol., 72(8):2139–2160, 2010.]

Turing Pattern Formation by the CIMA Reaction in a Chemical System Consisting of Quaternary Alkyl Ammonium Cationic Groups

2011 ◽  
Vol 115 (14) ◽  
pp. 3959-3963 ◽  
Author(s):  
Kouichi Asakura ◽  
Ryo Konishi ◽  
Tomomi Nakatani ◽  
Takaya Nakano ◽  
Masazumi Kamata
Keyword(s):  
Pattern Formation ◽  
Chemical System ◽  
Turing Pattern ◽  
Alkyl Ammonium ◽  
Cima Reaction

scholarly journals Comparative approaches to the study of physiology: Drosophila as a physiological tool

2013 ◽  
Vol 304 (3) ◽  
pp. R177-R188 ◽  
Author(s):  
Wendi S. Neckameyer ◽  
Kathryn J. Argue
Keyword(s):  
Gene Expression ◽  
Drosophila Melanogaster ◽  
Pattern Formation ◽  
Signaling Pathways ◽  
Human Disease ◽  
Cognitive Disorders ◽  
Model System ◽  
Critical Questions ◽  
Developmental Signaling ◽  
Shed Light

Numerous studies have detailed the extensive conservation of developmental signaling pathways between the model system, Drosophila melanogaster, and mammalian models, but researchers have also profited from the unique and highly tractable genetic tools available in this system to address critical questions in physiology. In this review, we have described contributions that Drosophila researchers have made to mathematical dynamics of pattern formation, cardiac pathologies, the way in which pain circuits are integrated to elicit responses from sensation, as well as the ways in which gene expression can modulate diverse behaviors and shed light on human cognitive disorders. The broad and diverse array of contributions from Drosophila underscore its translational relevance to modeling human disease.

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