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Pattern regulation in epimorphic fields

V French, P J Bryant, S V Bryant

    Science (New York, N.Y.)
    |September 10, 1976
    PubMed
    Summary
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    This study presents a formal model for pattern regulation in epimorphic fields using polar coordinates. Two simple rules, shortest intercalation and complete circle, explain diverse regenerative behaviors across species.

    Area of Science:

    • Developmental Biology
    • Regenerative Medicine
    • Mathematical Biology

    Background:

    • Epimorphic fields exhibit complex pattern regulation.
    • Understanding the underlying cellular mechanisms is crucial for developmental biology.
    • Positional information guides cell fate and tissue patterning.

    Purpose of the Study:

    • To develop a formal mathematical model for pattern regulation in epimorphic fields.
    • To propose simple cellular rules governing cell behavior within these fields.
    • To provide a unifying framework for experimental embryology results.

    Main Methods:

    • Formal modeling using polar coordinates in two dimensions.
    • Integration of experimental evidence for proposed cellular rules.

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  • Application of the model to diverse biological systems (cockroach legs, Drosophila imaginal disks, amphibian limbs).

    • Main Results:

    • A formal model based on two rules (shortest intercalation and complete circle) successfully explains pattern regulation.
    • The model accounts for a wide range of epimorphic field behaviors.
    • The proposed rules have direct experimental support.

    Conclusions:

    • The proposed model offers a generalizable framework for understanding epimorphic field regulation.
    • The model's predictions can guide future research into cellular mechanisms and applicability to other systems.
    • This work bridges mathematical modeling and experimental embryology.