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Spatial-temporal dissipative structures arising in open reactive systems with a negative feedback loop.

A Fernández, O Sinanoğlu

    Bio Systems
    |January 1, 1984
    PubMed
    Summary

    This study presents a systematic method to identify spatial-temporal structures in open reactive systems with negative feedback loops and diffusion. Findings align with experimental observations of non-uniform time periodicity in biological systems.

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    Area of Science:

    • Systems Biology
    • Chemical Kinetics
    • Theoretical Chemistry

    Background:

    • Open reactive systems can exhibit complex spatial-temporal patterns.
    • Negative feedback loops are crucial for pattern formation in biological and chemical systems.
    • Diffusive transport influences the emergence and stability of these patterns.

    Purpose of the Study:

    • To develop a systematic method for predicting spatial-temporal structures in open reactive systems with inhibitory feedback.
    • To analyze the influence of diffusion on pattern formation.
    • To validate the findings using established kinetic models.

    Main Methods:

    • A novel systematic approach was employed to analyze pattern formation.
    • Two established kinetic models (Glass and Higgins) were coupled with diffusion.

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  • Analysis focused on the interplay between reaction kinetics, negative feedback, and transport coefficients.

    • Main Results:

    • The study identified ranges for cooperativity index and Fick transport coefficients that lead to spatial non-uniformity.
    • Time periodicity was observed under specific parameter conditions.
    • The derived parameter ranges are consistent with experimental data from in vitro studies.

    Conclusions:

    • The presented method effectively predicts spatial-temporal pattern formation in complex reaction-diffusion systems.
    • The findings provide a theoretical basis for understanding experimental observations of oscillating reactions.
    • This work contributes to the understanding of self-organization in open chemical and biological systems.