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The formation of a tree leaf

Qinglan Xia (2007)

ESAIM: Control, Optimisation and Calculus of Variations

In this article, we build a mathematical model to understand the formation of a tree leaf. Our model is based on the idea that a leaf tends to maximize internal efficiency by developing an efficient transport system for transporting water and nutrients. The meaning of “the efficient transport system” may vary as the type of the tree leave varies. In this article, we will demonstrate that tree leaves have different shapes and venation patterns mainly because they have adopted different efficient...

The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology

H. G. Othmer, K. Painter, D. Umulis, C. Xue (2009)

Mathematical Modelling of Natural Phenomena

We discuss theoretical and experimental approaches to three distinct developmental systems that illustrate how theory can influence experimental work and vice-versa. The chosen systems – Drosophila melanogaster, bacterial pattern formation, and pigmentation patterns – illustrate the fundamental physical processes of signaling, growth and cell division, and cell movement involved in pattern formation and development. These systems exemplify the current state of theoretical and experimental understanding...

The Role of Cell-Cell Adhesion in the Formation of Multicellular Sprouts

A. Szabó, A. Czirók (2010)

Mathematical Modelling of Natural Phenomena

Collective cell motility and its guidance via cell-cell contacts is instrumental in several morphogenetic and pathological processes such as vasculogenesis or tumor growth. Multicellular sprout elongation, one of the simplest cases of collective motility, depends on a continuous supply of cells streaming along the sprout towards its tip. The phenomenon is often explained as leader cells pulling the rest of the sprout forward via cell-cell adhesion. Building on an empirically demonstrated analogy...

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