Designing modular reaction-diffusion programs for complex pattern formation

TECHNOLOGY ◽  
2014 ◽  
Vol 02 (01) ◽  
pp. 55-66 ◽  
Author(s):  
Dominic Scalise ◽  
Rebecca Schulman
Keyword(s):  
Pattern Formation ◽  
Cell Fate ◽  
Spatial Patterns ◽  
Control Cell ◽  
Reaction Diffusion ◽  
Tissue Growth ◽  
Complex Pattern ◽  
Target Pattern ◽  
Synthetic Dna ◽  
Integrated Programs

Cells use sophisticated, multiscale spatial patterns of chemical instructions to control cell fate and tissue growth. While some types of synthetic pattern formation have been well studied1-6, it remains unclear how to design chemical processes that can reproducibly create similar spatial patterns. Here we describe a scalable approach for the design of processes that generate such patterns, which can be implemented using synthetic DNA reaction-diffusion networks7,8. In our method, black-box modules are connected together into integrated programs for arbitrarily complex pattern formation. These programs can respond to input stimuli, process information, and ultimately produce stable output patterns that differ in size and concentration from their inputs. To build these programs, we break a target pattern into a set of patterning subtasks, design modules to perform these subtasks independently, and combine the modules into networks. We demonstrate in simulation how programs designed with our methodology can generate complex patterns, including a French flag and a stick figure.

Bifurcation Analysis and Spatiotemporal Patterns in a Diffusive Predator–Prey Model

2014 ◽  
Vol 24 (06) ◽  
pp. 1450081 ◽  
Author(s):  
Guangping Hu ◽  
Xiaoling Li ◽  
Shiping Lu ◽  
Yuepeng Wang
Keyword(s):  
Pattern Formation ◽  
Spiral Wave ◽  
Reaction Diffusion ◽  
Spatiotemporal Chaos ◽  
Diffusion System ◽  
Target Pattern ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Impact

In this paper, we consider a species predator–prey model given a reaction–diffusion system. It incorporates the Holling type II functional response and a quadratic intra-predator interaction term. We focus on the qualitative analysis, bifurcation mechanisms and pattern formation. We present the results of numerical experiments in two space dimensions and illustrate the impact of the diffusion on the Turing pattern formation. For this diffusion system, we also observe non-Turing structures such as spiral wave, target pattern and spatiotemporal chaos resulting from the time evolution of these structures.

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 Control of skeletal morphogenesis by the Hippo-YAP/TAZ pathway

Development ◽  
2020 ◽  
Vol 147 (21) ◽  
pp. dev187187
Author(s):  
Hannah K. Vanyai ◽  
Fabrice Prin ◽  
Oriane Guillermin ◽  
Bishara Marzook ◽  
Stefan Boeing ◽  
...  
Keyword(s):  
Cell Fate ◽  
Target Genes ◽  
Control Cell ◽  
Tissue Growth ◽  
Double Knockout ◽  
Cartilage Growth ◽  
Chondrocyte Proliferation ◽  
Specific Expression

ABSTRACTThe Hippo-YAP/TAZ pathway is an important regulator of tissue growth, but can also control cell fate or tissue morphogenesis. Here, we investigate the function of the Hippo pathway during the development of cartilage, which forms the majority of the skeleton. Previously, YAP was proposed to inhibit skeletal size by repressing chondrocyte proliferation and differentiation. We find that, in vitro, Yap/Taz double knockout impairs murine chondrocyte proliferation, whereas constitutively nuclear nls-YAP5SA accelerates proliferation, in line with the canonical role of this pathway in most tissues. However, in vivo, cartilage-specific knockout of Yap/Taz does not prevent chondrocyte proliferation, differentiation or skeletal growth, but rather results in various skeletal deformities including cleft palate. Cartilage-specific expression of nls-YAP5SA or knockout of Lats1/2 do not increase cartilage growth, but instead lead to catastrophic malformations resembling chondrodysplasia or achondrogenesis. Physiological YAP target genes in cartilage include Ctgf, Cyr61 and several matrix remodelling enzymes. Thus, YAP/TAZ activity controls chondrocyte proliferation in vitro, possibly reflecting a regenerative response, but is dispensable for chondrocyte proliferation in vivo, and instead functions to control cartilage morphogenesis via regulation of the extracellular matrix.

SPATIAL PATTERNS INDUCED BY RANDOM SWITCHING

2002 ◽  
Vol 02 (01) ◽  
pp. L21-L29 ◽  
Author(s):  
J. BUCETA ◽  
KATJA LINDENBERG ◽  
J. M. R. PARRONDO
Keyword(s):  
Pattern Formation ◽  
Numerical Simulations ◽  
Spatial Patterns ◽  
Reaction Diffusion ◽  
Homogeneous State ◽  
Ordered Structures ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Random Switching ◽  
Random Alternation

We propose a mechanism whereby a random alternation of two dynamics each leading to a different homogeneous state can lead to complex ordered structures. The proposed general formalism, based on the ideas of so-called paradoxical games, is illustrated via numerical simulations of particular examples. The relevance of the present study to other situations that lead to pattern formation, such as reaction-diffusion systems, is noted.

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