scholarly journals A bulk-surface reaction-diffusion system for cell polarization

2020 ◽  
Vol 22 (1) ◽  
pp. 85-117
Author(s):  
Barbara Niethammer ◽  
Matthias Röger ◽  
Juan Velázquez
Author(s):  
Anotida Madzvamuse ◽  
Andy H. W. Chung ◽  
Chandrasekhar Venkataraman

In this article, we formulate new models for coupled systems of bulk-surface reaction–diffusion equations on stationary volumes. The bulk reaction–diffusion equations are coupled to the surface reaction–diffusion equations through linear Robin-type boundary conditions. We then state and prove the necessary conditions for diffusion-driven instability for the coupled system. Owing to the nature of the coupling between bulk and surface dynamics, we are able to decouple the stability analysis of the bulk and surface dynamics. Under a suitable choice of model parameter values, the bulk reaction–diffusion system can induce patterning on the surface independent of whether the surface reaction–diffusion system produces or not, patterning. On the other hand, the surface reaction–diffusion system cannot generate patterns everywhere in the bulk in the absence of patterning from the bulk reaction–diffusion system. For this case, patterns can be induced only in regions close to the surface membrane. Various numerical experiments are presented to support our theoretical findings. Our most revealing numerical result is that, Robin-type boundary conditions seem to introduce a boundary layer coupling the bulk and surface dynamics.


1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Keiichi Kataoka ◽  
Hironori Fujita ◽  
Mutsumi Isa ◽  
Shimpei Gotoh ◽  
Akira Arasaki ◽  
...  

AbstractMorphological variations in human teeth have long been recognized and, in particular, the spatial and temporal distribution of two patterns of dental features in Asia, i.e., Sinodonty and Sundadonty, have contributed to our understanding of the human migration history. However, the molecular mechanisms underlying such dental variations have not yet been completely elucidated. Recent studies have clarified that a nonsynonymous variant in the ectodysplasin A receptor gene (EDAR370V/A; rs3827760) contributes to crown traits related to Sinodonty. In this study, we examined the association between theEDARpolymorphism and tooth root traits by using computed tomography images and identified that the effects of theEDARvariant on the number and shape of roots differed depending on the tooth type. In addition, to better understand tooth root morphogenesis, a computational analysis for patterns of tooth roots was performed, assuming a reaction–diffusion system. The computational study suggested that the complicated effects of theEDARpolymorphism could be explained when it is considered that EDAR modifies the syntheses of multiple related molecules working in the reaction–diffusion dynamics. In this study, we shed light on the molecular mechanisms of tooth root morphogenesis, which are less understood in comparison to those of tooth crown morphogenesis.


2021 ◽  
Vol 31 (3) ◽  
pp. 033118
Author(s):  
Margaret K. McGuire ◽  
Chase A. Fuller ◽  
John F. Lindner ◽  
Niklas Manz

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