scholarly journals The Influence of Gene Expression Time Delays on Gierer–Meinhardt Pattern Formation Systems

2010 ◽  
Vol 72 (8) ◽  
pp. 2139-2160 ◽  
Author(s):  
S. Seirin Lee ◽  
E. A. Gaffney ◽  
N. A. M. Monk
Keyword(s):  
Gene Expression ◽  
Pattern Formation ◽  
Time Delays ◽  
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.]

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.

The dominant hemimelia mutation uncouples epithelial-mesenchymal interactions and disrupts anterior mesenchyme formation in mouse hindlimbs

Development ◽  
1999 ◽  
Vol 126 (21) ◽  
pp. 4729-4736
Author(s):  
L. Lettice ◽  
J. Hecksher-Sorensen ◽  
R.E. Hill
Keyword(s):  
Gene Expression ◽  
Pattern Formation ◽  
Limb Development ◽  
Limb Bud ◽  
Mouse Mutation ◽  
Number Of Factors ◽  
Limb Outgrowth ◽  
Gene Functions ◽  
Regulatory Loop ◽  
Limb Initiation

Epithelial-mesenchymal interactions are essential for both limb outgrowth and pattern formation in the limb. Molecules capable of communication between these two tissues are known and include the signaling molecules SHH and FGF4, FGF8 and FGF10. Evidence suggests that the pattern and maintenance of expression of these genes are dependent on a number of factors including regulatory loops between genes expressed in the AER and those in the underlying mesenchyme. We show here that the mouse mutation dominant hemimelia (Dh) alters the pattern of gene expression in the AER such that Fgf4, which is normally expressed in a posterior domain, and Fgf8, which is expressed throughout are expressed in anterior patterns. We show that maintenance of Shh expression in the posterior mesenchyme is not dependent on either expression of Fgf4 or normal levels of Fgf8 in the overlying AER. Conversely, AER expression of Fgf4 is not directly dependent on Shh expression. Also the reciprocal regulatory loop proposed for Fgf8 in the AER and Fgf10 in the underlying mesenchyme is also uncoupled by this mutation. Early during the process of limb initiation, Dh is involved in regulating the width of the limb bud, the mutation resulting in selective loss of anterior mesenchyme. The Dh gene functions in the initial stages of limb development and we suggest that these initial roles are linked to mechanisms that pattern gene expression in the AER.

Sign in / Sign up

Export Citation Format

Share Document