Expansive growths with uniaxial gradients can explain formation of oblong diversity observed in two-dimensional leaf shapes.

Abstract

Regulation of positional information in fields with different sizes are known as scaling in the area of morphogenesis, and enable integrated and robust developmental processes. Although it is known that interpretation of such scaled patterns leads to formations of relative shapes, the same positional information brings about diversities in morphogenesis. In this research, a boundary of a two-dimensional shape was constructed by propagating points and segments connecting them for a description of a growing form. Cell expansion "with" or "without" cell proliferation were implemented using different simple algorithms, as "additive growth" and "expansive growth", respectively. When the different types of growth algorithm with a biased restriction were calculated, the additive growth maintained a relative shape corresponding to the gradients with different lengths. However, diverse shapes were generated by the gradients in the cases of expansive growth and its combinations even with negate effects by additive growth. As an operative example of this attempt, leaf shapes with smooth margins were calculated using a combination of these growth algorithms. Finally, we concluded that different algorithms brought different responses against the simple positional information, i.e., additive growth always governed by it or expansive growth can escape it. It was predicted theoretically that an expansive growth has a capacity to become a generator of diversity at least in leaf morphogenesis. Summary statementExplanation of different responses against single positional information by different algorithms for two types of growth modes.