scholarly journals Studies of Turing pattern formation in zebrafish skin

2021 ◽  
Vol 379 (2213) ◽  
Author(s):  
Shigeru Kondo ◽  
Masakatsu Watanabe ◽  
Seita Miyazawa
Keyword(s):  
Pattern Formation ◽  
Diffusion Mechanism ◽  
Model Organism ◽  
Reaction Diffusion ◽  
Cell Interactions ◽  
Pigment Cells ◽  
Turing Pattern ◽  
Reaction Diffusion Model ◽  
Experimental Findings ◽  
Cell Cell

Skin patterns are the first example of the existence of Turing patterns in living organisms. Extensive research on zebrafish, a model organism with stripes on its skin, has revealed the principles of pattern formation at the molecular and cellular levels. Surprisingly, although the networks of cell–cell interactions have been observed to satisfy the ‘short-range activation and long-range inhibition’ prerequisites for Turing pattern formation, numerous individual reactions were not envisioned based on the classical reaction–diffusion model. For example, in real skin, it is not an alteration in concentrations of chemicals, but autonomous migration and proliferation of pigment cells that establish patterns, and cell–cell interactions are mediated via direct contact through cell protrusions. Therefore, the classical reaction–diffusion mechanism cannot be used as it is for modelling skin pattern formation. Various studies are underway to adapt mathematical models to the experimental findings on research into skin patterns, and the purpose of this review is to organize and present them. These novel theoretical methods could be applied to autonomous pattern formation phenomena other than skin patterns. This article is part of the theme issue ‘Recent progress and open frontiers in Turing's theory of morphogenesis’.

scholarly journals Correspondences between parameters in a reaction-diffusion model and connexin functions during zebrafish stripe formation

2021 ◽  
Author(s):  
Akiko Nakamasu
Keyword(s):  
Molecular Mechanisms ◽  
Reaction Diffusion ◽  
The Body ◽  
Pigment Cells ◽  
Turing Pattern ◽  
Reaction Diffusion Model ◽  
Spatial Periodicity ◽  
Pattern Formations ◽  
Mathematical Analyses ◽  
Spotted Pattern

Abstract Different diffusivities among interacting substances actualize the potential instability of a system. When these elicited instabilities manifested as forms of spatial periodicity, they are called Turing patterns. Simulations using general reaction-diffusion (RD) models have demonstrated that pigment patterns on the body trunk of growing fish follow a Turing pattern. Laser ablation experiments performed on zebrafish revealed apparent interactions among pigment cells, which allowed for a three-components RD model to be derived. However, the underlying molecular mechanisms responsible for Turing pattern formation in this system had been remained unknown. A zebrafish mutant with a spotted pattern was found to have a defect in Connexin41.8 (Cx41.8) which, together with Cx39.4, exists in pigment cells and controls pattern formations. Here, molecular-level evidence derived from connexin analyses was linked to the interactions among pigment cells described in previous RD modeling. Channels on pigment cells were generalized as “gates,” and the effects of respective gates were deduced. The model used partial differential equations (PDEs) to enable numerical and mathematical analyses of characteristics observed in the experiments. Furthermore, the improved PDE model included nonlinear reaction terms, enabled the consideration of the behavior of components.

scholarly journals Correspondences between parameters in a reaction-diffusion model and connexin functions during zebrafish stripe formation

2021 ◽  
Author(s):  
Akiko Nakamasu
Keyword(s):  
Molecular Mechanisms ◽  
Reaction Diffusion ◽  
The Body ◽  
Pigment Cells ◽  
Turing Pattern ◽  
Reaction Diffusion Model ◽  
Spatial Periodicity ◽  
Pattern Formations ◽  
Mathematical Analyses ◽  
Spotted Pattern

Abstract Different diffusivities among interacting substances actualize the potential instability of a system. When these elicited instabilities manifested as forms of spatial periodicity, they are called Turing patterns. Simulations using general reaction-diffusion (RD) models have demonstrated that pigment patterns on the body trunk of growing fish follow a Turing pattern. Laser ablation experiments performed on zebrafish revealed apparent interactions among pigment cells, which allowed for a three-components RD model to be derived. However, the underlying molecular mechanisms responsible for Turing pattern formation in this system had been remained unknown. A zebrafish mutant with a spotted pattern was found to have a defect in Connexin41.8 (Cx41.8) which, together with Cx39.4, exists in pigment cells and controls pattern formations. Here, molecular-level evidence derived from connexin analyses was linked to the interactions among pigment cells described in previous RD modeling. Channels on pigment cells were generalized as “gates,” and the effects of respective gates were deduced. The model used partial differential equations (PDEs) to enable numerical and mathematical analyses of characteristics observed in the experiments. Furthermore, the improved PDE model included nonlinear reaction terms, enabled the consideration of the behavior of components.

scholarly journals Influence of survival, promotion, and growth on pattern formation in zebrafish skin

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Christopher Konow ◽  
Ziyao Li ◽  
Samantha Shepherd ◽  
Domenico Bullara ◽  
Irving R. Epstein
Keyword(s):  
Pattern Formation ◽  
Organizational Behavior ◽  
Long Range ◽  
Reaction Diffusion ◽  
Turing Instability ◽  
Survival Model ◽  
Domain Growth ◽  
Pigment Cells ◽  
Diffusion Scheme ◽  
Experimental Findings

AbstractThe coloring of zebrafish skin is often used as a model system to study biological pattern formation. However, the small number and lack of movement of chromatophores defies traditional Turing-type pattern generating mechanisms. Recent models invoke discrete short-range competition and long-range promotion between different pigment cells as an alternative to a reaction-diffusion scheme. In this work, we propose a lattice-based “Survival model,” which is inspired by recent experimental findings on the nature of long-range chromatophore interactions. The Survival model produces stationary patterns with diffuse stripes and undergoes a Turing instability. We also examine the effect that domain growth, ubiquitous in biological systems, has on the patterns in both the Survival model and an earlier “Promotion” model. In both cases, domain growth alone is capable of orienting Turing patterns above a threshold wavelength and can reorient the stripes in ablated cells, though the wavelength for which the patterns orient is much larger for the Survival model. While the Survival model is a simplified representation of the multifaceted interactions between pigment cells, it reveals complex organizational behavior and may help to guide future studies.

Reaction-Diffusion Modeling of Photopolymerization During Femtosecond Projection Two-Photon Lithography

2021 ◽  
Author(s):  
Rushil Pingali ◽  
Sourabh K. Saha
Keyword(s):  
Diffusion Mechanism ◽  
Chemical Properties ◽  
Reaction Diffusion ◽  
Element Model ◽  
Polymerization Process ◽  
Layer By Layer ◽  
Length Scales ◽  
Two Photon ◽  
Reaction Diffusion Model ◽  
Direct Laser

Abstract Two-photon lithography (TPL) is a polymerization-based direct laser writing process that is capable of fabricating arbitrarily complex three-dimensional (3D) structures with submicron features. Traditional TPL techniques have limited scalability due to the slow point-by-point serial writing scheme. The femtosecond projection TPL (FP-TPL) technique increases printing rate by a thousand times by enabling layer-by-layer parallelization. However, parallelization alters the time and the length scales of the underlying polymerization process. It is therefore challenging to apply the models of serial TPL to accurately predict process outcome during FP-TPL. To solve this problem, we have generated a finite element model of the polymerization process on the time and length scales relevant to FP-TPL. The model is based on the reaction-diffusion mechanism that underlies polymerization. We have applied this model to predict the geometry of nanowires printed under a variety of conditions and compared these predictions against empirical data. Our model accurately predicts the nanowire widths. However, accuracy of aspect ratio prediction is hindered by uncertain values of the chemical properties of the photopolymer. Nevertheless, our results demonstrate that the reaction-diffusion model can accurately capture the effect of controllable parameters on FP-TPL process outcome and can therefore be used for process control and optimization.

scholarly journals Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Bernard Girau ◽  
César Torres-Huitzil ◽  
Nikolaos Vlassopoulos ◽  
José Hugo Barrón-Zambrano
Keyword(s):  
Large Scale ◽  
Complex Dynamics ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Fpga Implementation ◽  
Cellular Slime Mold ◽  
Reaction Diffusion Model ◽  
Cellular Slime ◽  
Computational Resources ◽  
Embedded Implementation

We consider here the feasibility of gathering multiple computational resources by means of decentralized and simple local rules. We study such decentralized gathering by means of a stochastic model inspired from biology: the aggregation of theDictyostelium discoideumcellular slime mold. The environment transmits information according to a reaction-diffusion mechanism and the agents move by following excitation fronts. Despite its simplicity this model exhibits interesting properties of self-organization and robustness to obstacles. We first describe the FPGA implementation of the environment alone, to perform large scale and rapid simulations of the complex dynamics of this reaction-diffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations.

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 Fission Yeast Polarization: Modeling Cdc42 Oscillations, Symmetry Breaking, and Zones of Activation and Inhibition

Cells ◽  
2020 ◽  
Vol 9 (8) ◽  
pp. 1769 ◽  
Author(s):  
Bita Khalili ◽  
Hailey D. Lovelace ◽  
David M. Rutkowski ◽  
Danielle Holz ◽  
Dimitrios Vavylonis
Keyword(s):  
Fission Yeast ◽  
Model Organism ◽  
Reaction Diffusion ◽  
Small Gtpases ◽  
Membrane Diffusion ◽  
Gtpase Activating Proteins ◽  
Reaction Diffusion Model ◽  
Membrane Bound ◽  
Negative Feedbacks ◽  
Positive And Negative Feedbacks

Cells polarize for growth, motion, or mating through regulation of membrane-bound small GTPases between active GTP-bound and inactive GDP-bound forms. Activators (GEFs, GTP exchange factors) and inhibitors (GAPs, GTPase activating proteins) provide positive and negative feedbacks. We show that a reaction–diffusion model on a curved surface accounts for key features of polarization of model organism fission yeast. The model implements Cdc42 membrane diffusion using measured values for diffusion coefficients and dissociation rates and assumes a limiting GEF pool (proteins Gef1 and Scd1), as in prior models for budding yeast. The model includes two types of GAPs, one representing tip-localized GAPs, such as Rga3; and one representing side-localized GAPs, such as Rga4 and Rga6, that we assume switch between fast and slow diffusing states. After adjustment of unknown rate constants, the model reproduces active Cdc42 zones at cell tips and the pattern of GEF and GAP localization at cell tips and sides. The model reproduces observed tip-to-tip oscillations with periods of the order of several minutes, as well as asymmetric to symmetric oscillations transitions (corresponding to NETO “new end take off”), assuming the limiting GEF amount increases with cell size.

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