Intercellular signaling molecules, known as morphogens, act at a long range in developing
tissues to provide spatial information and control properties such as cell fate and tissue …

In 1952, Alan Turing published the reaction-diffusion (RD) mathematical framework, laying
the foundations of morphogenesis as a self-organized process emerging from …

Developing tissues form spatial patterns by establishing concentration gradients of diffusible
signaling proteins called morphogens. The bone morphogenetic protein (BMP) morphogen …

Two influential concepts in tissue patterning are Wolpert's positional information and
Turing's self-organized reaction–diffusion (RD). The latter establishes the patterning of hair …

During development, morphogen gradients encode positional information to pattern
morphological structures during organogenesis. Some gradients, like that of Dpp in the fly …

Pattern formation by bone morphogenetic proteins (BMPs) demonstrates remarkable
plasticity and utility in several contexts, such as early embryonic development, tissue …

Liquid crystal elastomers (LCEs) can undergo large reversible contractions along their
nematic director upon heating or illumination. A spatially patterned director within a flat LCE …

Despite molecular noise and genetic differences between individuals, developmental
outcomes are remarkably constant. Decades of research has focused on the underlying …

The process by which biological systems such as cells, tissues and organisms acquire
shape has been named as morphogenesis and it is central to a plethora of biological …

Morphogen gradients can instruct cells about their position in a patterned tissue. Non-linear
morphogen decay has been suggested to increase gradient precision by reducing the …