Synthetic mammalian pattern formation driven by differential diffusivity of Nodal and Lefty

A synthetic mammalian reaction-diffusion pattern has yet to be created, and Nodal-Lefty signaling has been proposed to meet conditions for pattern formation: Nodal is a short-range activator whereas Lefty is a long-range inhibitor. However, this pattern forming possibility has never been directly tested, and the underlying mechanisms of differential diffusivity of Nodal and Lefty remain unclear. Here, through a combination of synthetic and theoretical approaches, we show that a reconstituted Nodal-Lefty network in mammalian cells spontaneously gives rise to a pattern. Surprisingly, extracellular Nodal is confined underneath the cells, resulting in a narrow distribution compared with Lefty. The short-range distribution requires the finger 1 domain of Nodal, and transplantation of the finger 1 domain into Lefty shortens the distribution of Lefty, successfully preventing pattern formation. These results indicate that the differences in localization and domain structures between Nodal and Lefty, combined with the activator-inhibitor topology, are sufficient for reaction-diffusion patterning.

ligands in mammalian cells. An RD pattern requires a minimum of two diffusible 23 molecules, or signaling pathways, and we chose to employ the well-studied Nodal-Lefty 24 signaling pathway, which regulates mesodermal induction, axis formation and left-right 25 patterning [24][25][26] . The Nodal-Lefty pathway has been proposed to meet two conditions for a 26 stable RD pattern 14,27 : Firstly, binding of Nodal to its receptor activates the production of 27 both Nodal and Lefty whereas Lefty inhibits the activity of Nodal 24,28,29 . Secondly, the 28 diffusion of Nodal is reported to be slower than Lefty in zebrafish, chick and mouse 29 embryos 27-31 . In other words, Nodal and Lefty may act as a short-range activator and a 30 long-range inhibitor, respectively, and thus satisfy the requirement for a classic Turing 31 pattern proposed by Gierer and Meinherdt 12,13 . It remains undemonstrated, however, 32 whether the Nodal-Lefty signaling can actually produce an RD pattern, as well as how 33 Nodal and Lefty show different diffusivity. 34 In this study, we have reconstituted a minimal activator-inhibitor circuit of Nodal 35 and Lefty to test if it leads to any pattern formation in mammalian cell culture. We also introduced the (f2)7-Lefty2 construct into the HEK293 cells already engineered with the 1 activator circuit, adding the negative feedback by Lefty (Fig. 1d). The activator-inhibitor 2 circuit initially behaved similarly to the activator circuit: the small domains of reporter-3 positive cells appeared at around 18 hours and became bigger (Fig. 1e). Then the domain 4 growth slowed down at around 30 hours, and a pattern of clear positive domains and 5 negative domains was formed by 36 hours (Fig. 1e,f; Supplementary movie 1). Note that 6 the reporter-positive cells and negative cells are genetically identical since the cell line 7 was cloned. The pattern was reproducible (Fig. 1g), and the average size of positive 8 domains was 196 ± 15 µm ( Fig. 1h; Supplementary fig. 3). The pattern did not change 9 much after 36 hours and kept essentially constant until 60 hours (Fig. 1h,i), even though 10 the entire signal started to decline at 50-60 hours as observed with the activator circuit.

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To assess the periodicity of our synthetic pattern, we calculated the spatial Different distribution ranges of Nodal and Lefty. 24 Why can the synthetic Nodal-Lefty circuit give rise to a pattern? Since a stable RD pattern 25 typically requires a short-range activator and a long-range inhibitor 11-14 , the difference in 26 the diffusion ranges of two diffusible molecules is critical. Although the diffusion of 27 Nodal has been reported to be slower than that of Lefty in zebrafish, chick and mouse 28 embryos 27-31 , our experimental conditions are different from those of the previous studies 29 especially because we culture the cells on a dish as a monolayer with plenty of culture 30 medium. We thus tested whether Nodal and Lefty show different diffusion ranges in our 31 system. To visualize the distribution of Nodal and Lefty, we placed the ligand-producing 32 cells and the receptor cells (i.e., wild-type cells) separately in adjacent areas by using a 33 mold called a culture insert (Fig. 2a). Then the extracellular Nodal and Lefty were 34 exclusively visualized with a split luciferase system called HiBiT (Fig. 2b): The N-35 terminal bigger half of NanoLuc, Large BiT (LgBiT), is added to the medium but does not enter a cell. Thus, the C-terminal smaller half of NanoLuc, the HiBiT tag, binds to 1 LgBiT to reconstitute a functional luciferase only outside the cell (Fig. 2b). Avoiding 2 intracellular signal this way is crucial since the concentrations of Nodal and Lefty are 3 much higher inside the cell, which easily masks their extracellular distributions. Because 4 Nodal and Lefty are cleaved by proteases to become their mature forms 28,34 , we inserted 5 the HiBiT tag into the middle part of the proteins, at the N-terminus of the mature domains 6 ( Fig. 2c,d).

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The luminescence signal of HiBiT-Nodal displayed an extremely narrow 8 distribution (Fig. 2c). The Nodal distribution reached at its equilibrium by four hours after 9 the addition of LgBiT and substrates (Supplementary fig. 5a). To compare the distribution 10 ranges of different proteins, we fitted the normalized distribution to a simple exponential 11 function, exp(-x/λ). The characteristic distance λ is the point where the signal drops to 12 1/e, and λ also represents √D/γ, where D is the effective diffusion coefficient and γ is 13 the degradation rate 35,36 . In the case of HiBiT-Nodal, λ = 28.7 µm (Fig. 2e), suggesting 14 that the effective range of Nodal is only one or two cells since the cell size is 10-20 µm. 15 By contrast, HiBiT-Lefty2 displayed much wider distribution where the signal gradually 16 decreased (Fig. 2d), and λ = 99.8 µm (Fig. 2e), indicating that the effective range of Nodal 17 is 3.5-times narrower than that of Lefty2.

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The molecular sizes of Nodal and Lefty2 are similar (full-length Nodal: 354 aa; 19 full-length Lefty2: 368 aa; mature Nodal: 110 aa; mature Lefty2: 291 aa) and thus unlikely 20 to be the cause of their different diffusion ranges. We hypothesized the existence of a trap 21 mechanism to confine extracellular Nodal in immediate neighboring cells, and focused 22 on Nodal rather than Lefty. Since the full-length Nodal protein comprises the mature 23 domain and prodomain (Fig. 2c), we examined which domain is responsible for the 24 narrow distribution. Whereas the mature domain of Nodal displayed a narrow distribution 25 just like the full-length Nodal (Fig. 2f), the prodomain displayed a wider distribution just 26 like Lefty2 (Fig. 2g,h). The Nodal mature domain further comprises three subdomains 37 : 27 the finger 1 domain, heel domain and finger 2 domain (Fig. 2i). Deleting the finger 1 28 domain from the Nodal mature protein made the distribution wider (Fig. 2j,k), indicating 29 that the finger 1 subdomain of Nodal is responsible for its narrow distribution.

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Extracellular Nodal localizes underneath the cells. 32 We further investigated how the finger 1 domain limits the distribution range of Nodal.

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While a previous study has suggested that binding of Nodal to the Acvr2b receptor slows 34 down the Nodal diffusion in zebrafish 38 , the overexpression or deletion of Acvr2b in our 35 system did not change the Nodal distribution range (Supplementary fig. 5b). Then we checked the localization of extracellular Nodal, noticing that the HiBiT-Nodal signal was 1 in focus at the basal side of cells but out of focus at the lateral or apical side (Fig. 2l). The 2 basal side was judged with the dense structure of cell membrane, and the lateral and apical 3 sides were defined as the points 7.5 µm and 15 µm above the basal side, respectively 4 (Supplementary fig. 6). Consistent with this observation, extracellular Nodal is suggested 5 to localize underneath the cells even in mouse embryos 39 . We also noticed that the HiBiT-6 Nodal near the basal side formed small clusters (Fig. 2l). By contrast, the HiBiT-Lefty2 7 signal was blurry both at the basal and apical sides (Fig. 2m). These results suggest that 8 extracellular Nodal is confined in the space between the cells and the culture dish as  Mathematical models of the pattern forming circuit. 16 To understand the patterning mechanism of our activator-inhibitor circuit in more detail, with Nodal for the co-receptor and receptors 28,40 (Fig. 3a), or Lefty directly binds to and 20 then inhibits Nodal 40 (Fig. 3e). We thus constructed two types of model by using in the right ranges (Fig 3b,f). The patterns resulting from the competitive inhibition model 25 were highly periodic (Fig. 3d), and the patterning parameter range was almost identical 26 with the parameter range that satisfied Turing instability 13 (compare Fig. 3c with 3b), the 27 condition for Turing pattern formation, meaning that these patterns are classic Turing 28 patterns. However, Turing patterns are not the only type of RD system that can perform 29 spatial patterning. The patterns resulting from the competitive inhibition + direct 30 inhibition model were less periodic (Fig. 3h,i), and the Turing instability condition was 31 not satisfied in all the parameter regions tested with this model (Fig. 3g). This non-Turing 32 patterning mechanism is essentially the same as the formation of "solitary localized  Manipulating the diffusion coefficient of Lefty. 19 We further altered another important parameter, the diffusion coefficient of the activator-

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Then we created an activator-inhibitor circuit with F1-Lefty2, instead of wild-30 type Lefty2, and named the new circuit as a "similar range activator-inhibitor circuit" (Fig.   31 4e). F1-Lefty2 inhibited the Nodal signaling although its inhibitor activity was a little 32 weaker than that of wild-type Lefty2 (Fig. 4f). When the (f2)7-F1-Lefty2 construct was 33 added to the activator circuit, the engineered cells did not show a pattern but displayed an 34 almost homogeneous image (Fig. 4g), and the spatial correlation dropped rapidly without that different diffusion ranges of Nodal and Lefty are crucial for the pattern formation 1 through our activator-inhibitor circuit.  underneath the cells may be a common trapping mechanism. 24 Nodal displayed a 3.5-times shorter distribution range than Lefty2 in our 25 measurements. If the degradation rates are similar between Nodal and Lefty2, the 26 effective diffusion coefficient of Nodal should be 12-times smaller than that of Lefty2.

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According to our measurements, the degradation of Lefty2 is actually 2.4-times faster 28 than that of Nodal (Supplementary fig. 8b), suggesting that the effective diffusion 29 coefficient of Nodal is 29-times smaller than that of Lefty2, which is comparable to the 30 value reported in zebrafish 27 . Direct measurements of the diffusion coefficients in our 31 system will be necessary to verify these numbers even though our attempts for FRAP 32 analysis were not successful due to too weak signal of fluorescent fusion Nodal and Lefty.

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In any case, sufficiently large difference in the diffusivity of Nodal and Lefty was proven 34 critical for our pattern formation.
The cells engineered with our activator-inhibitor circuit gave rise to a pattern, 1 which we believe is the first mammalian example of a synthetic RD pattern. Our

Quantification of HiBiT activity
A 30×300 pixels (48×480 μm 2 ) rectangular area was set so that the short side of the independent experiments were averaged and then fitted to the following function:

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In the competitive inhibition model, Lefty was assumed to inhibit Nodal by competing 15 for the co-receptor and receptors. Nodal concentration was more than 2-times higher than the minimum Nodal 8 concentration. Otherwise, the distribution was judged as a "high state" or "low state", 9 depending on if the maximum Nodal concentration was higher than 0.01 or not. where the summation was taken over all pixel points ( , ) and is the mean intensity.

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The radial correlation function ( ) was calculated by averaging the correlation 2 function ( , ) with the constraint = √ 2 + 2 , which is formally given by where ( ) is the Dirac's delta function.