scholarly journals Theory of mechano-chemical patterning in biphasic biological tissues

2018 ◽  
Author(s):  
Pierre Recho ◽  
Adrien Hallou ◽  
Edouard Hannezo
Keyword(s):  
Pattern Formation ◽  
Extracellular Fluid ◽  
Reaction Diffusion ◽  
Single Mode ◽  
Biological Tissues ◽  
Tissue Mechanics ◽  
Chemical Patterning ◽  
Biphasic Model ◽  
Cross Diffusion ◽  
Reaction Diffusion Model

The formation of self-organized patterns is key to the morphogenesis of multicellular organisms, although a comprehensive theory of biological pattern formation is still lacking. Here, we propose a biologically realistic and unifying approach to emergent pattern formation. Our biphasic model of multicellular tissues incorporates turnover and transport of morphogens controlling cell differentiation and tissue mechanics in a single framework, where one tissue phase consists of a poroelastic network made of cells and the other is the extracellular fluid permeating between cells. While this model encompasses previous theories approximating tissues to inert monophasic media, such as Turing’s reaction-diffusion model, it overcomes some of their key limitations permitting pattern formation via any two-species biochemical kinetics thanks to mechanically induced cross-diffusion flows. Moreover, we unravel a qualitatively different advection-driven instability which allows for the formation of patterns with a single morphogen and which single mode pattern scales with tissue size. We discuss the potential relevance of these findings for tissue morphogenesis.

scholarly journals Theory of mechanochemical patterning in biphasic biological tissues

2019 ◽  
Vol 116 (12) ◽  
pp. 5344-5349 ◽  
Author(s):  
Pierre Recho ◽  
Adrien Hallou ◽  
Edouard Hannezo
Keyword(s):  
Pattern Formation ◽  
Extracellular Fluid ◽  
Reaction Diffusion ◽  
Biological Tissues ◽  
Tissue Mechanics ◽  
Two Phase ◽  
Cell Network ◽  
Cross Diffusion ◽  
Model Combining ◽  
Reaction Diffusion Model

The formation of self-organized patterns is key to the morphogenesis of multicellular organisms, although a comprehensive theory of biological pattern formation is still lacking. Here, we propose a minimal model combining tissue mechanics with morphogen turnover and transport to explore routes to patterning. Our active description couples morphogen reaction and diffusion, which impact cell differentiation and tissue mechanics, to a two-phase poroelastic rheology, where one tissue phase consists of a poroelastic cell network and the other one of a permeating extracellular fluid, which provides a feedback by actively transporting morphogens. While this model encompasses previous theories approximating tissues to inert monophasic media, such as Turing’s reaction–diffusion model, it overcomes some of their key limitations permitting pattern formation via any two-species biochemical kinetics due to mechanically induced cross-diffusion flows. Moreover, we describe a qualitatively different advection-driven Keller–Segel instability which allows for the formation of patterns with a single morphogen and whose fundamental mode pattern robustly scales with tissue size. We discuss the potential relevance of these findings for tissue morphogenesis.

scholarly journals An in vitro–in silico interface platform for spatiotemporal analysis of pattern formation in collective epithelial cells

2016 ◽  
Vol 8 (8) ◽  
pp. 861-868 ◽  
Author(s):  
M. Hagiwara
Keyword(s):  
Cell Culture ◽  
Pattern Formation ◽  
Epithelial Cells ◽  
In Silico ◽  
Reaction Diffusion ◽  
Spatiotemporal Analysis ◽  
Bronchial Epithelial ◽  
Reaction Diffusion Model ◽  
2D Pattern

The mechanisms of 2D pattern formation in bronchial epithelial cells were dynamically analyzed by controlled cell culture and a reaction-diffusion model.

scholarly journals HIERARCHICAL MODELS FOR SPATIAL PATTERN FORMATION IN BIOLOGY

1995 ◽  
Vol 03 (04) ◽  
pp. 987-997 ◽  
Author(s):  
P. K. MAINI
Keyword(s):  
Pattern Formation ◽  
Spatial Heterogeneity ◽  
Spatial Pattern ◽  
Diffusion Model ◽  
Hierarchical Models ◽  
Reaction Diffusion ◽  
Skeletal Patterning ◽  
Reaction Diffusion Model ◽  
Spatial Pattern Formation ◽  
Set Up

We review some recent work investigating a hierarchy of patterning processes in which a reaction-diffusion model forms the top level. In one such hierarchy, it is assumed that the boundary is differentiated, and it is shown that this can greatly enhance the robustness of the patterns subsequently formed by the reaction-diffusion model. In the second, a spatial heterogeneity in background environment is first set-up by a simple gradient model. The resulting patterns produced by the reaction-diffusion system may be isolated to specific parts of the domain. The application of such hierarchical models to skeletal patterning in the tetrapod limb is considered.

scholarly journals A reaction diffusion model of pattern formation in clustering of adatoms on silicon surfaces

AIP Advances ◽  
2012 ◽  
Vol 2 (4) ◽  
pp. 042101 ◽  
Author(s):  
Trilochan Bagarti ◽  
Anupam Roy ◽  
K. Kundu ◽  
B. N. Dev
Keyword(s):  
Pattern Formation ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Silicon Surfaces ◽  
Reaction Diffusion Model

scholarly journals A contraction-reaction-diffusion model for circular pattern formation in embryogenesis

2021 ◽  
Author(s):  
Tiankai Zhao ◽  
Yubing Sun ◽  
Xin Li ◽  
Mehdi Baghaee ◽  
Yuenan Wang ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Cell Fate ◽  
Diffusion Model ◽  
Early Stage ◽  
Reaction Diffusion ◽  
Diffusion Models ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Reaction Diffusion Model ◽  
Stress Dependent

Reaction-diffusion models have been widely used to elucidate pattern formation in developmental biology. More recently, they have also been applied in modeling cell fate patterning that mimic early-stage human development events utilizing geometrically confined pluripotent stem cells. However, the traditional reaction-diffusion equations could not satisfactorily explain the concentric ring distributions of various cell types, as they do not yield circular patterns even for circular domains. In previous mathematical models that yield ring patterns, certain conditions that lack biophysical understandings had been considered in the reaction-diffusion models. Here we hypothesize that the circular patterns are the results of the coupling of the mechanobiological factors with the traditional reaction-diffusion model. We propose two types of coupling scenarios: tissue tension-dependent diffusion flux and traction stress-dependent activation of signaling molecules. By coupling reaction-diffusion equations with the elasticity equations, we demonstrate computationally that the contraction-reaction-diffusion model can naturally yield the circular patterns.

scholarly journals Spatio-temporal Brusselator Model and Biological Pattern Formation

2021 ◽  
pp. 88-99
Author(s):  
Zakir Hossine ◽  
Oishi Khanam ◽  
Md. Mashih Ibn Yasin Adan ◽  
Md. Kamrujjaman
Keyword(s):  
Pattern Formation ◽  
Diffusion Model ◽  
Initial Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Brusselator Model ◽  
Reaction Diffusion Model ◽  
Biological Pattern Formation ◽  
Spatio Temporal

This paper explores a two-species non-homogeneous reaction-diffusion model for the study of pattern formation with the Brusselator model. We scrutinize the pattern formation with initial conditions and Neumann boundary conditions in a spatially heterogeneous environment. In the whole investigation, we assume the case for random diffusion strategy. The dynamics of model behaviors show that the nature of pattern formation with varying parameters and initial conditions thoroughly. The model also studies in the absence of diffusion terms. The theoretical and numerical observations explain pattern formation using the reaction-diffusion model in both one and two dimensions.

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