Spatially periodic domain structure in coupled reaction-diffusion equations for segment formation

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    Abstract

    Segment formation is an important process of pattern formation in the developing vertebrate embryo. The mechanism of such pattern formation is considered to be different from that of Turing instability. We propose reaction- diffusion equations generating traveling pulses and coupled reaction-diffusion equations for two genes that generate a domain structure. Next, we construct a synthetic model for segment formation by combining the coupled reaction- diffusion equations. A spatially periodic domain structure is found in the numerical simulation of the model equation. It is shown that the wavelength of the spatially periodic pattern and the proportion of the sizes of the anterior and posterior domains in each segment can be controlled by adjusting some system parameters.

    Original languageEnglish
    Article number024802
    JournalJournal of the Physical Society of Japan
    Volume81
    Issue number2
    DOIs
    Publication statusPublished - Feb 1 2012

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    reaction-diffusion equations
    vertebrates
    embryos
    genes
    proportion
    adjusting
    pulses
    wavelengths
    simulation

    All Science Journal Classification (ASJC) codes

    • Physics and Astronomy(all)

    Cite this

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    title = "Spatially periodic domain structure in coupled reaction-diffusion equations for segment formation",
    abstract = "Segment formation is an important process of pattern formation in the developing vertebrate embryo. The mechanism of such pattern formation is considered to be different from that of Turing instability. We propose reaction- diffusion equations generating traveling pulses and coupled reaction-diffusion equations for two genes that generate a domain structure. Next, we construct a synthetic model for segment formation by combining the coupled reaction- diffusion equations. A spatially periodic domain structure is found in the numerical simulation of the model equation. It is shown that the wavelength of the spatially periodic pattern and the proportion of the sizes of the anterior and posterior domains in each segment can be controlled by adjusting some system parameters.",
    author = "Hidetsugu Sakaguchi",
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    language = "English",
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    N2 - Segment formation is an important process of pattern formation in the developing vertebrate embryo. The mechanism of such pattern formation is considered to be different from that of Turing instability. We propose reaction- diffusion equations generating traveling pulses and coupled reaction-diffusion equations for two genes that generate a domain structure. Next, we construct a synthetic model for segment formation by combining the coupled reaction- diffusion equations. A spatially periodic domain structure is found in the numerical simulation of the model equation. It is shown that the wavelength of the spatially periodic pattern and the proportion of the sizes of the anterior and posterior domains in each segment can be controlled by adjusting some system parameters.

    AB - Segment formation is an important process of pattern formation in the developing vertebrate embryo. The mechanism of such pattern formation is considered to be different from that of Turing instability. We propose reaction- diffusion equations generating traveling pulses and coupled reaction-diffusion equations for two genes that generate a domain structure. Next, we construct a synthetic model for segment formation by combining the coupled reaction- diffusion equations. A spatially periodic domain structure is found in the numerical simulation of the model equation. It is shown that the wavelength of the spatially periodic pattern and the proportion of the sizes of the anterior and posterior domains in each segment can be controlled by adjusting some system parameters.

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