Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation

  title={Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation},
  author={Shigeru Kondo and Takashi Miura},
  pages={1616 - 1620}
Turing Model Explained The reaction-diffusion (Turing) model is a theoretical model used to explain self-regulated pattern formation in biology. Although many biologists have heard of this model, a better understanding of the concept would aid its application to many research projects and developmental principles. Kondo and Miura (p. 1616) now review the reaction-diffusion model. Despite the associated mathematics, the basic idea of the Turing model is relatively easy to understand and relates… 


An introduction to reaction-diffusion theory and agent-based modeling, a review of biological pattern formation and the role of reaction-Diffusion systems for morphogenesis, and an implementation of two cellular models, a cellular automaton (CA) and the cellular Potts model, to simulate Turing patterns under varying inhibitor field values and cell-cell adhesion energy coefficients respectively are provided.

Insights from chemical systems into Turing-type morphogenesis

The historical role chemistry has played in the study of the Turing mechanism, the numerous insights chemical systems have yielded into both the dynamics and the morphological behaviour of Turing patterns, and future directions for chemical studies into Turing-type morphogenesis are suggested.

An updated kernel-based Turing model for 1 studying the mechanisms of biological 2 pattern formation 3 4 5

Simulation of the kernel-based Turing model with kernels of various shapes showed that it can generate all standard variations of the stable 2D patterns, as well as some complex patterns that are difficult to generate with conventional mathematical models.

Cooperativity To Increase Turing Pattern Space for Synthetic Biology

This work model a reaction–diffusion system with two morphogens in a monostable regime, inspired by components that were recently described in a synthetic biology study in mammalian cells, and predicts that steep dose–response functions arising from cooperativity are mandatory for Turing patterns.

Transient Turing patterns in a morphogenetic model

This work studies a previously proposed morphogenetic synthetic circuit consisting of two genes controlled by the same regulatory system and finds a parameter region where the persistence time of the transient patterns depends on the distance between the parameters values on which the system is operating and the boundary of Turing patterns.

Testing Turing’s theory of morphogenesis in chemical cells

Significance Turing proposed that intercellular reaction-diffusion of molecules is responsible for morphogenesis. The impact of this paradigm has been profound. We exploit an abiological experimental



How well does Turing's theory of morphogenesis work?

Interactions between zebrafish pigment cells responsible for the generation of Turing patterns

This study identified the interaction network between the pigment cells of zebrafish, and showed that this interaction network possesses the properties necessary to form the Turing pattern.

Applications of a theory of biological pattern formation based on lateral inhibition.

Model calculations are presented for various problems of development on the basis of a theory of primary pattern formation which involves short-range autocatalytic activation and longer-range inhibition (lateral inhibition) and the effects of symmetry can be included into the formalism in a straightforward manner.

Gene Expression Time Delays and Turing Pattern Formation Systems

The effects of incorporating gene expression time delays into a one-dimensional putative reaction diffusion pattern formation mechanism on both stationary domains and domains with spatially uniform exponential growth are investigated.

The Chemical Basis of Morphogenesis

A possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism is discussed, suggesting that certain well-known physical laws are sufficient to account for many of the facts.

Models of biological pattern formation

The aim of the seminar is to demonstrate that it is possible to formulate models in a mathematical precise way that describe essential steps in spite of the appearing complexity of this process.

Pattern formation by local self-activation and lateral inhibition.

  • H. MeinhardtA. Gierer
  • Biology
    BioEssays : news and reviews in molecular, cellular and developmental biology
  • 2000
By computer simulations, the theory accounts for much of the regulatory phenomena observed, including signalling to regenerate removed parts, and the resulting pattern is, to a large extent, independent of the details provided by initial conditions and inducing signals.

Introduction to systems biology.

This chapter introduces analysis of molecular network by use of models, the two approaches to systems biology, and a number of examples of recent successes in systems biology are discussed.

Pattern regulation in the stripe of zebrafish suggests an underlying dynamic and autonomous mechanism

The regenerated patterns and the transition of the stripes during the regeneration process suggest that pattern formation is independent of the prepattern; furthermore, pattern formation occurs by an autonomous mechanism that satisfies the condition of “local self-enhancement and long-range inhibition.