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 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 On the Interplay of Geometrical Shapes and the Analysis of a Dispersal Model for Pattern Formations

2019 ◽  
pp. 1-10
Author(s):  
Zakir Hossine ◽  
Md. Kamrujjaman
Keyword(s):  
Reaction Mechanism ◽  
Finite Difference Method ◽  
Reaction Diffusion ◽  
Diffusion Kinetics ◽  
Dispersal Model ◽  
Reaction Diffusion Model ◽  
Chemical Reaction Mechanism ◽  
Geometrical Shapes ◽  
Pattern Formations ◽  
Selection Of

A reaction-diffusion model is put forward which is capable of generating chemical maps whose concentration contours are similar to the patterns seen on the flanks of zebras, leopards and other mammals. Initially, this type of reaction diffusion kinetics model was introduced by Turing and later Murray applied it to animal coat patterns. Among many chemical reaction mechanism, we consider Schnackenberg reaction mechanism in details and show that the geometry and scale of the domain, the relevant part of the integument, during the time of laying down plays a crucial role in the structural patterns which result. Patterns which exhibit a limited randomness are obtained for a selection of geometries. Finally the system was solved numerically using finite difference method.

HyAlx, an aristaless-related gene, is involved in tentacle formation in hydra

Development ◽  
2000 ◽  
Vol 127 (22) ◽  
pp. 4743-4752 ◽  
Author(s):  
K.M. Smith ◽  
L. Gee ◽  
H.R. Bode
Keyword(s):  
Expression Patterns ◽  
Reaction Diffusion ◽  
The Body ◽  
Related Gene ◽  
Axial Patterning ◽  
Bud Formation ◽  
Isolation And Characterization ◽  
Reaction Diffusion Model ◽  
Head Regeneration

Developmental gradients are known to play important roles in axial patterning in hydra. Current efforts are directed toward elucidating the molecular basis of these gradients. We report the isolation and characterization of HyAlx, an aristaless-related gene in hydra. The expression patterns of the gene in adult hydra, as well as during bud formation, head regeneration and the formation of ectopic head structures along the body column, indicate the gene plays a role in the specification of tissue for tentacle formation. The use of RNAi provides more direct evidence for this conclusion. The different patterns of HyAlx expression during head regeneration and bud formation also provide support for a recent version of a reaction-diffusion model for axial patterning in hydra.

scholarly journals Rethinking calcium profiles around single channels: the exponential and periodic calcium nanodomains

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Sergej L. Mironov
Keyword(s):  
Functional Role ◽  
Reaction Diffusion ◽  
Single Channels ◽  
Calcium Dependent ◽  
Physiological Processes ◽  
Nonlinear Reaction ◽  
Reaction Diffusion Model ◽  
Spatial Periodicity ◽  
Calcium Diffusion ◽  
Theoretical Predictions

AbstractMany fundamental calcium-dependent physiological processes are triggered by high local calcium levels that are established around the sites of calcium entry into the cell (channels). They are dubbed as calcium nanodomains but their exact profiles are still elusive. The concept of calcium nanodomains stems from a linear model of calcium diffusion and is only valid when calcium increases are smaller than the concentration of cytoplasmic buffers. Recent data indicates that much higher calcium levels cause buffer saturation. Therefore, I sought explicit solutions of a nonlinear reaction-diffusion model and found a dichotomous solution. For small fluxes, the steady state calcium profile is quasi-exponential, and when calcium exceeds buffer concentration a spatial periodicity appears. Analytical results are supported by Monte-Carlo simulations. I also imaged 1D- and radial calcium distributions around single α-synuclein channels in cell-free conditions. Measured Ca profiles are consistent with theoretical predictions. I propose that the periodic calcium patterns may well arise under certain conditions and their specific functional role has to be established.

scholarly journals Geometric control of frequency modulation of cAMP oscillations due to Ca2+-bursts in dendritic spines

2019 ◽  
Author(s):  
D. Ohadi ◽  
P. Rangamani
Keyword(s):  
Dendritic Spines ◽  
Molecular Mechanisms ◽  
Neuronal Development ◽  
Temporal Dynamics ◽  
Second Messengers ◽  
Reaction Diffusion ◽  
Long Term Potentiation ◽  
Dynamic Interactions ◽  
Neck Size ◽  
Reaction Diffusion Model

ABSTRACTThe spatiotemporal regulation of cAMP and its dynamic interactions with other second messengers such as calcium are critical features of signaling specificity required for neuronal development and connectivity. cAMP is known to contribute to long-term potentiation and memory formation by controlling the formation and regulation of dendritic spines. Despite the recent advances in biosensing techniques for monitoring spatiotemporal cAMP dynamics, the underlying molecular mechanisms that attribute to the subcellular modulation of cAMP remain unknown. In the present work, we model the spatio-temporal dynamics of calcium-induced cAMP signaling pathway in dendritic spines. Using a 3D reaction-diffusion model, we investigate the effect of different spatial characteristics of cAMP dynamics that may be responsible for subcellular regulation of cAMP concentrations. Our model predicts that the volume-to-surface ratio of the spine, regulated through the spine head size, spine neck size, and the presence of physical barriers (spine apparatus) is an important regulator of cAMP dynamics. Furthermore, localization of the enzymes responsible for the synthesis and degradation of cAMP in different compartments also modulates the oscillatory patterns of cAMP through exponential relationships. Our findings shed light on the significance of complex geometric and localization relationships for cAMP dynamics in dendritic spines.

scholarly journals Application of reaction diffusion model in Turing pattern and numerical simulation

2018 ◽  
Vol 67 (5) ◽  
pp. 050503
Author(s):  
Zhang Rong-Pei ◽  
Wang Zhen ◽  
Wang Yu ◽  
Han Zi-Jian
Keyword(s):  
Numerical Simulation ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Turing Pattern ◽  
Reaction Diffusion Model

scholarly journals Mix & Match: Phenotypic coexistence as a key facilitator of solid tumour invasion

2019 ◽  
Author(s):  
Maximilian A. R. Strobl ◽  
Andrew L. Krause ◽  
Mehdi Damaghi ◽  
Robert Gillies ◽  
Alexander R. A. Anderson ◽  
...  
Keyword(s):  
Alternative Hypothesis ◽  
Cell Movement ◽  
Reaction Diffusion ◽  
Cell Types ◽  
The Body ◽  
Reaction Diffusion Equations ◽  
Species Competition ◽  
Invasion Process ◽  
Malignant Tumours ◽  
Reaction Diffusion Model

AbstractInvasion of healthy tissue is a defining feature of malignant tumours. Traditionally, invasion is thought to be driven by cells that have acquired all the necessary traits to overcome the range of biological and physical defences employed by the body. However, in light of the ever-increasing evidence for geno- and phenotypic intra-tumour heterogeneity an alternative hypothesis presents itself: Could invasion be driven by a collection of cells with distinct traits that together facilitate the invasion process? In this paper, we use a mathematical model to assess the feasibility of this hypothesis in the context of acid-mediated invasion. We assume tumour expansion is obstructed by stroma which inhibits growth, and extra-cellular matrix (ECM) which blocks cancer cell movement. Further, we assume that there are two types of cancer cells: i) a glycolytic phenotype which produces acid that kills stromal cells, and ii) a matrix-degrading phenotype that locally remodels the ECM. We extend the Gatenby-Gawlinski reaction-diffusion model to derive a system of five coupled reaction-diffusion equations to describe the resulting invasion process. We characterise the spatially homogeneous steady states and carry out a simulation study in one spatial dimension to determine how the tumour develops as we vary the strength of competition between the two phenotypes. We find that overall tumour growth is most extensive when both cell types can stably coexist, since this allows the cells to locally mix and benefit most from the combination of traits. In contrast, when inter-species competition exceeds intra-species competition the populations spatially separate and invasion arrests either: i) rapidly (matrix-degraders dominate), or ii) slowly (acid-producers dominate). Overall, our work demonstrates that the spatial and ecological relationship between a heterogeneous population of tumour cells is a key factor in determining their ability to cooperate. Specifically, we predict that tumours in which different phenotypes coexist stably are more invasive than tumours in which phenotypes are spatially separated.

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