Speaker
Description
We present a new set of Turing patterns based on the superposition of multiple waves. Turing patterns are well known solutions to a set of reaction-diffusion equations. Such patterns have been studied in the context of embryo development, chemical reactions, nonlinear optics, ecology and random walks, to name a few. The main feature of systems giving rise to Turing patterns is that a stable state of reaction is destabilized when the reactants may diffuse. The system then generates a periodic solution with a dominant wavelength, which establishes the pattern. Additionally, the system provides examples of spontaneous symmetry breaking and self organization behaviour.
Turing originally discovered his results when considering two morphogen species, the chemicals used by cells in an organism to communicate and grow into a pattern during development. The values of the kinetic and diffusion parameters leading to Turing patterns are known as Turing space. The degree and the number of polynomial inequalities defining Turing space, grow rapidly with the number of morphogens. Due to this, Turing patterns for more than two or three morphogens were mostly studied numerically on a case-by-case basis.
Now, we developed a method to construct analytically a linear solution to the reaction-diffusion system for certain regions of Turing space. This linear solution corresponds to a system with a regulatory network of diffusible morphogens. By providing analytical insights into dynamics of the morphogens we are able to show the existence of new types of Turing patterns, and relate these patterns to the structure of the network. These patterns have two dominant wavelengths in the case of four morphogenes. Moreover, we explain how it is possible to have superpositions of n wavelengths for 2n distinct morphogen species. Finally, we discuss possible implications of the obtained class of multimodal Turing patterns for establishing reproducible and precise patterns in biological systems.
