11Pattern formation is fundamental for embryonic development. Although synthetic 12 biologists have created several patterns, a synthetic mammalian reaction-diffusion pattern 13 has yet to be realized. TGF-β family proteins Nodal and Lefty have been proposed to 14 meet the conditions for reaction-diffusion patterning: Nodal is a short-range activator that 15 enhances the expression of Nodal and Lefty whereas Lefty acts as a long-range inhibitor 16 against Nodal. However, the pattern forming possibility of the Nodal-Lefty signaling has 17 never been directly tested, and the underlying mechanisms of differential diffusivity of 18 Nodal and Lefty remain unclear. Here, through a combination of synthetic biology and 19 theoretical modeling, we show that a reconstituted minimal network of the Nodal-Lefty 20 signaling spontaneously gives rise to a pattern in mammalian cell culture. Surprisingly, 21 extracellular Nodal was confined underneath the cells as small clusters, resulting in a 22 narrow distribution range compared with Lefty. We further found that the finger 1 domain 23 of the Nodal protein is responsible for its short-range distribution. By transplanting the 24 finger 1 domain of Nodal into Lefty, we converted the originally long-range distribution 25 of Lefty to a short-range one, successfully preventing the pattern formation. These results 26 indicate that the differences in the localization and domain structures between Nodal and 27 Lefty, combined with the activator-inhibitor topology, are sufficient for reaction-diffusion 28 pattern formation in mammalian cells. 29 30 Main 31One of the goals of synthetic biology is creating a synthetic tissue to understand natural 32 developmental mechanisms 1-3 , to explore the origin of multicellularity 4 and to engineer a 33 programmable tissue for therapeutic purposes 5,6 . The first step towards a synthetic tissue 34 is controlling pattern formation, which enables to place different types of cells properly 35 in a tissue. Several synthetic cellular patterns have been reported previously: Ring patterns were created in genetically engineered bacteria that can sense the concentrations 1 of small molecules 7,8 . In mammalian cells, 2D and 3D patterns were created based on 2 engineered cell sorting mechanisms 9,10 . However, there is another pattern formation 3 mechanism that has not been artificially created in mammalian cells despite its 4 importance: the reaction-diffusion (RD) patterning system.
5The concept of a self-organizing RD system was first proposed by Alan Turing 6 as a chemical system of interacting and diffusible molecules giving rise to various stable 7 patterns, such as spots and stripes [11][12][13][14] . Recent studies have suggested that RD system 8 underlies a number of developmental patterning phenomena, including digit formation in 9 the limb 15,16 , pigmentation on the skin 17 , the formation of hair follicles and feather buds 10 on the skin 18,19 , branching morphogenesis in the lung 20 and rugae formation in the palate 21 .
11In the field of sy...