Abstract
The combination of laterally activating and inhibiting feedbacks is well known to spontaneously generate spatial organization. It was introduced by Gierer and Meinhardt as an extension of Turing's great insight that two reacting and diffusing chemicals can spontaneously drive spatial morphogenesis per se. In this study, we develop an accessible nonlinear and discrete probabilistic model to study simple generalizations of lateral activation and inhibition. By doing so, we identify a range of modes of morphogenesis beyond the familiar Turing-type modes; notably, beyond stripes, hexagonal nets, pores and labyrinths, we identify labyrinthine highways, Kagome lattices, gyrating labyrinths and multi-colour travelling waves and spirals. The results are discussed within the context of Turing's original motivating interest: the mechanisms which underpin the morphogenesis of living organisms.
Highlights
As a complex multicellular organism grows and develops, each one of its cells follows the same set of genomically encoded instructions, yet different cells beget drastically different fates so bringing about the organism’s complex structure
For lateral activation and inhibition only, the model’s final states of morphogenesis are either striped, hexagonally netted, labyrinthine, spotted or uniform block colour, patterns that are ubiquitous in nature and are well known to be generated by Turing-type models [6]; the additional feedback modules that we introduce generate a surprisingly extended range of static and dynamic patterning modes
A natural extension of the model, which introduces two new lateral feedback modules while retaining rules (i) –(iii), includes in the exponent symmetry breaking nonlinear terms +bSðw À bÞ2Sx associated with the short range, and symmetry preserving nonlinear inhibitory terms +s2Sðw À bÞ3Sx which compete with the short-range activation
Summary
As a complex multicellular organism grows and develops, each one of its cells follows the same set of genomically encoded instructions, yet different cells beget drastically different fates so bringing about the organism’s complex structure. Later Gierer and Meinhardt extended this notion to show how processes other than reaction– diffusion can potentially drive pattern formation: they demonstrated that any process which feeds back on itself over two lateral ranges—one short range that quickens or activates the process, the other long range that competitively slows or inhibits it—can spontaneously generate structural organization [2,3]. This combination of feedbacks has come to be known as short-range activation and long-range inhibition and is widely accepted as the key criteria for Turing-type patterning [3,4,5]. What other types of lateral feedback may be operating to bring about the development of a multicellular organism? What patterns can be generated by recombinations of these feedbacks and what feedbacks are necessary and sufficient to generate a particular pattern?
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
