Controlling organoid symmetry breaking uncovers an excitable system underlying human axial elongation

Summary

The human embryo breaks symmetry to form the anterior-posterior axis of the body. As the embryo elongates along this axis, progenitors in the tailbud give rise to tissues that generate spinal cord, skeleton, and musculature. This raises the question of how the embryo achieves axial elongation and patterning. While ethics necessitate in vitro studies, the variability of organoid systems has hindered mechanistic insights. Here we developed a bioengineering and machine learning framework that optimizes organoid symmetry breaking by tuning their spatial coupling. This framework enabled reproducible generation of axially elongating organoids, each possessing a tailbud and neural tube. We discovered that an excitable system composed of WNT/FGF signaling drives elongation by inducing a neuromesodermal progenitor-like signaling center. We discovered that instabilities in the excitable system are suppressed by secreted WNT inhibitors. Absence of these inhibitors led to ectopic tailbuds and branches. Our results identify mechanisms governing stable human axial elongation.

Graphical Abstract

In Brief

A machine learning-driven bioengineering approach generates a robust stem cell model of human axial elongation that uncovers molecular mechanisms underlying self-sustained and stable elongation.

Introduction

During development, the human embryo elongates along its anterior-posterior (A-P) axis ¹. Over the course of elongation, axial progenitor cells specified in the tailbud of the embryo give rise to the posterior neural tube and paraxial mesoderm ^2-6. While the signals involved in A-P axis specification have been studied extensively, the roles and relationships of cell types and signals driving elongation are poorly understood, especially in humans ⁷. Furthermore, the mechanisms that govern stable elongation along a single axis are unknown.

Elucidating the mechanisms underlying human axial elongation requires the use of in vitro stem cell systems. In multiple instances, human and mouse pluripotent stem cell-derived organoids show spontaneous symmetry breaking when exposed to external signals and generate patterned tissues similar to those in developing mammalian embryos ^8-10. However, the inherent variability in such in vitro systems makes it challenging to perform mechanistic studies ^11,12. Overcoming such variability is therefore essential to achieve the goal of understanding human axial elongation.

Here, motivated by principles from physics, we developed an approach that combines bioengineering with machine learning to learn to build hundreds of organoids that reproducibly undergo deterministic A-P symmetry breaking and axial elongation. Using a combination of single-cell and in situ sequencing, live imaging, and perturbations, we characterized elongating organoids and uncovered distinct roles for FGF and WNT signaling during elongation. By determining conditions that sustain organoid elongation without external signals, we discovered that elongation is driven by an excitable system mediated by neuromesodermal progenitor (NMP)-like cells. We further identified a role for secreted inhibitors in maintaining the stability of this excitable system. Finally, we discuss the implications of our findings for modeling related morphogenetic processes and, more broadly, for building robust in vitro models of human development.

Results

Spatial coupling of organoids influences their axial patterning and morphogenesis

In physical systems that undergo symmetry breaking, the underlying degrees of freedom can be coupled to reduce the entropy of the ground state ¹³. Furthermore, the desired ground state can be achieved in such systems by learning the correct couplings ¹⁴. For example, when N spins are not coupled to each other, and each spin can point in one of two directions, the entropy of the ground state is Nlog(2). In contrast, in an Ising ferromagnet, this entropy is log(2), because with ferromagnetic coupling, there are only two ground states: all spins point up or all point down. Inspired by these results, we asked whether we could couple organoids to increase the robustness of symmetry breaking and achieve the desired patterning and morphogenesis accompanying axial elongation in vivo. Specifically, we sought to build organoids that break A-P symmetry, specify a posterior tailbud and anterior neural tube, and elongate along the A-P axis (Fig. 1A). To test whether organoids could be coupled to each other, we cultured human pluripotent stem cells (hPSCs) on coverslips with randomly positioned 150-micron diameter micropatterns of extracellular matrix (see STAR Methods). Upon addition of matrix to the culture medium, hPSCs on each micropattern formed an epithelial cyst enclosing a single lumen, closely approximating the epiblast in vivo ¹⁵ (Fig. 1B). We obtained distinct random arrangements of epithelial cysts on each coverslip, each with a different average density (number of cysts per unit area). To generate organoids, we exposed these cysts to conditions that confer a posterior epiblast identity ^6,16 by activating the canonical WNT pathway using the GSK3ß inhibitor CHIR99021 (CHIR) while inhibiting the BMP and TGFß pathways using the SMAD inhibitors LDN193189 (LDN) and A8301 respectively (Fig. 1C). After four days of differentiation, we stained the differentiated organoids for CDX2, a posterior marker expressed by axial progenitors in the tailbud ^17,18 and SOX1, an anterior marker expressed by cells in the neural tube ¹⁹. Other pairs of markers could be used equivalently to assess A-P patterning, such as TBXT and SOX2, as in a companion manuscript (Yaman et al., 2022). Under fixed differentiation conditions, the proportion of anterior SOX1+ versus posterior CDX2+ fates on a coverslip was positively correlated with average organoid density (r = 0.98) (Fig. 1D, S1A, and S1B).

Fig. 1. Machine learning-driven optimization of organoid arrangements enables reproducible axial elongation.

(A) Left: Micrograph of a human embryo at Carnegie Stage 10 from the Kyoto Collection. Right: Zoomed-in view of posterior neural tube, pseudo-colored to highlight putative neural tube (anterior, blue) and tailbud (posterior, red). Scale bar 1 mm. (B) Top left: Phase contrast image of 150 μm diameter circular PDMS stamp. Top middle: Phase contrast image of micropatterned pluripotent epithelial cyst on day 1. Top right: Cyst stained for tight junction marker ZO1. Bottom: Cyst stained for nuclear markers DAPI, OCT4, and SOX2. Scale bar 50 μm. (C) Organoid differentiation protocol: day −1, hPSCs seeded in mTeSR Plus (MT) with ROCK inhibitor Y-27632 (RI); day 0, media changed to N2B27 with Matrigel, CHIR99021 (CHIR), LDN193189 (LDN), and A8301; day 2, media changed to N2B27 with CHIR and LDN. Matrigel formed a gel that was maintained throughout 4 days of differentiation. (D) Top: Organoids from low density (left), medium density (middle), and high density (right) random arrays on day 4, stained for SOX1 and CDX2. Scale bar 1 mm. Top right: Zoomed-in view of an unpolarized CDX2+ organoid (bottom) and polarized organoid elongated along the SOX1-CDX2 axis (top). μ measures the anterior-posterior (A-P) polarization of CDX2 expression (see STAR Methods). Scale bar 200 μm. (E) Measured polarization (μ_measured) of organoids in (D) plotted on color scale at corresponding micropattern locations in the array. (F) Left: Heat map of organoid density on random arrays evaluated with a Gaussian filter at length scales σ = 200 μm (top) and σ = 1000 μm (bottom). Right: Visualization of gradient of organoid density using a Sobel filter, evaluated at length scales σ = 200 μm (top) and σ = 1000 μm (bottom). For gradient calculations, see Methods S1. Scale bar 1 mm. (G) μ_measured of each organoid (n=2373) from 12 random arrays as a function of selected features, gradient of organoid density at σ = 200 μm (∣∇_ρ200∣) and density at σ = 700 (_ρ700). (H) Predicted polarization (μ_pred) for organoids learned using kernel ridge regression with a radial basis function kernel from data in (G) (see Methods S1), plotted as a function of ∣∇_ρ200∣ and _ρ700. (I) Initial (left) and final (right) timepoint images of simulated annealing on organoid locations using the function learned in (H) with the number of organoids ranging from 2 (top) to 7 (bottom). Scale bar 300 μm. (J), μ_pred as a function of number of organoids, with a maximum for 6 organoids arranged in a hexagon. (K) maximum, mean, and minimum values of μ_pred for hexagonally arranged organoids as a function of inter-hexagon distance. Arrowhead indicates distance selected for experiments (1.6 mm). (L) Image of computationally optimized hexagonal array. Scale bar 1 mm. (M) Organoids on the optimized hexagonal array on day 4, stained for DAPI, SOX1, and CDX2. All organoids that correctly formed a cyst within a hexagonal unit on day 1 possessed polarized CDX2+ and SOX1+ domains and elongated (n=204). Scale bar 1 mm. (N) Confocal images of organoids from hexagonal array on day 4 stained for laminin subunit gamma-1 (laminin), tight junction protein 1 (ZO1), and phospho-histone H3 (pHH3). Organoids display apicobasal polarity with apical mitosis and a basement membrane. The elongating portion of the organoids are not attached to the coverslip, and are surrounded by laminin-rich extracellular matrix, which is present in the media (see STAR Methods). Scale bar 100 μm. (O) Results from a mathematical model of symmetry breaking of hexagonally arranged organoids with a small (left) or large (right) center-to-center spacing. Secreted signal gradient is shown in grayscale. At a close spacing, organoids break symmetry coherently and adopt polarized anterior (blue) and posterior (red) fates. Scale bar represents a length of sqrt(4Dτ) (see STAR Methods). (P) Top: Representative organoids from hexagonal array on consecutive days stained for DAPI, SOX1, and CDX2. Scale bar: 50 μm. Bottom: Violin plot of measured A-P lengths of organoids from a single hexagonal array over time (n=216), with mean (points) and standard deviation (lines), based on Feret diameter (see STAR Methods).

Furthermore, organoids with polarized expression of SOX1 and CDX2 tended to elongate along the SOX1-CDX2 axis, while unpolarized organoids did not elongate (Fig. 1D, right). To quantify the variability in polarization across organoids, we defined polarization μ as the distance between the centroid of CDX2+ cells and the centroid of the organoid (Methods S1). We generally observed significant variations in polarization and axial elongation on individual coverslips. However, in replicate experiments with identical initial arrangements, organoids at the same micropattern positions showed lower variability in polarization and elongation (Fig. S1C and S1D). We concluded that organoids could be coupled and influence each other’s patterning and morphogenesis based on their relative spatial arrangement.

To test whether secreted factors in the extracellular media mediated organoid coupling, we transferred media conditioned by a high-density array to a low-density array (see STAR Methods). Organoids in the low-density array exhibited a shift toward a higher proportion of SOX1+ cells and a lower proportion of CDX2+ cells, suggesting that factors secreted into the culture media are at least partly responsible for mediating organoid coupling by promoting an anterior neural fate at the expense of a posterior axial progenitor fate (Fig. S2A).

Machine learning-driven optimization of organoid arrangements enables reproducible axial elongation

To systematically learn how to spatially arrange organoids to obtain the desired patterning and morphogenesis accompanying axial elongation, we used approaches from machine learning ²⁰ (Methods S1). We first measured the polarization of CDX2 expression ${\mu }_{\text{measured}}^i$ for each organoid i in all 2373 organoids across our random micropattern experiments (Fig. 1E). We then calculated a multi-dimensional feature vector for each organoid, ${\overrightarrow{v}}^i$, with components consisting of the organoid density ρⁱ and the gradient of organoid density ∣∇ρⁱ∣ over a range of length scales from 100 microns to 2000 microns, i.e., ${\overrightarrow{v}}^i=({\rho }_{100}^i,\dots ,{\rho }_{2000}^i,\mid \nabla {\rho }_{100}^i\mid ,\dots ,\mid \nabla {\rho }_{2000}^i\mid )$ (Fig. 1F). We sought to learn the function f of the feature vector that predicted the polarization of each organoid i, i.e., ${\mu }_{\text{pred}}^i=f({\overrightarrow{v}}^i)$, with the minimum least squares error, ${\sum }_i({\mu }_{\text{pred}}^i-{\mu }_{\text{measured}}^i{)}^2$. We used sequential forward selection to determine the most predictive subset of features in $\overrightarrow{v}$, followed by kernel ridge regression with a radial basis function kernel ²¹ and five-fold cross-validation to learn the parameters of f. We determined that two components of ${\overrightarrow{v}}^i$ were most predictive of organoid polarization: the organoid density at 700 microns, ${\rho }_{700}^i$, and the gradient of organoid density at 200 microns, $\mid \nabla {\rho }_{200}^i\mid$ (Fig. 1G). Using the learned function f, we mapped out the predicted polarization of organoids in the space of these two components (Fig. 1H). We then performed simulations to modify the arrangements of organoids until each organoid was predicted to have maximum polarization. To do so, we first performed simulated annealing on small numbers of organoids ranging from 2 to 9 and found that 6 organoids arranged in a hexagon achieved the maximum predicted polarization (Fig. 1I and 1J). To determine the arrangement of these hexagonal units on a coverslip, we calculated μ_pred for each organoid as a function of the distance between these units. We selected the distance such that the predicted polarization was uniformly high across all organoids while fitting as many organoids as possible on a single coverslip (Fig. 1K). The computationally selected arrangement thus consisted of a 6 by 6 array of hexagonal units spaced 1.6 mm apart (Fig. 1L). We conducted our differentiation experiments on coverslips micropatterned with this hexagonal array. After 4 days, every organoid in the array that initially formed a cyst within a hexagonal unit developed a CDX2+ tailbud domain, a SOX1+ neural tube domain, and elongated axially (n=204) (Fig. 1M). Thus, we were able to experimentally tune the coupling between organoids by optimizing their spatial arrangement and inducing them to jointly break A-P symmetry to develop into our desired target pattern.

To understand why hexagonal arrangements of organoids are effective at coherently breaking symmetry, we built a mathematical model of the spatial coupling between organoids via a secreted, diffusive signal that promotes the anterior fate and inhibits the posterior fate under external WNT activation (STAR Methods). The model demonstrated that in hexagonally patterned organoids with a close center-to-center spacing, the signal level was enriched at the interior-facing side of each organoid. Thus, the regions of the organoids facing inwards adopted an anterior fate, while the regions facing outwards adopted posterior fates (Fig. 1O, left). When the organoids in the mathematical model were moved farther apart beyond a critical spacing, the coupling between them through the diffusive signal decreased, and organoids failed to break symmetry robustly (Fig. 1O, right). Consistently in experiments, increasing the spacing between organoids on the hexagon from 200 microns to 400 microns led to a loss of coupling and led to variable polarization of individual organoids (Fig. S2B).

We found that the correctly patterned organoids recapitulated several aspects of the elongating neural tube in vivo. Elongating organoids contained a single lumen enclosed by apical tight junctions (marked by ZO1), a basement membrane (marked by laminin). They exhibited apical mitosis (marked by phospho-histone H3) along the whole A-P axis, consistent with interkinetic nuclear migration (Fig. 1N). The posterior tailbud region marked by CDX2 was composed of a single-layer epithelium (Fig. S2C), consistent with observations in mammalian embryos of the chordoneural hinge and its precursor populations, the node-streak border and caudal lateral epiblast, which collectively house axial progenitors in vivo ^17,22,23. We also observed pseudostratified SOX2+ nuclei as well as junctional N-cadherin and apical F-actin (Fig. S1E). Upon staining organoids for CDX2 and SOX1 at sequential timepoints, we found that CDX2+ axial progenitors were synchronously specified at the prospective posterior pole by day 2 of differentiation and maintained throughout elongation, and a SOX1+ neural tube was specified anteriorly that increased in length over time (Fig. 1P, top; Fig. S1F to S1K). The mean A-P axis length of organoids increased from approximately 150 microns on day 1 to approximately 400 microns on day 4 (Fig. 1P, bottom; Fig. S1H and S1I) and continued to increase through day 7 (see STAR Methods), by which time organoids reached lengths over 1 mm (Fig. 1P, right).

Elongating organoids contain hindbrain, spinal cord, and axial progenitors

To identify the cell types present in elongating organoids, we used single-cell RNA sequencing (scRNA-seq). We performed scRNA-seq on cells pooled from 12 organoids on day 4 of differentiation to obtain high-quality transcriptomes of 7752 cells. Using unsupervised sparse multimodal decomposition (SMD) ²⁴ to infer key genes and cell types simultaneously, we identified a subspace of 26 genes in which we could cluster cells into 4 progenitor cell types, corresponding to spatially distinct regions along the A-P axis. The observed cell types included axial progenitors (marked by CDX2) as well as progenitors of the cervical spinal cord (marked by HOXB4 and CRABP1), posterior hindbrain (marked by NR2F1), and anterior hindbrain (marked by EGR2). We also observed a small cluster of neuronal cells (marked by HES6 and BTG2) (Fig. 2A and 2B). Interestingly, we did not observe any transcriptional signatures of neuromesodermal progenitors (NMPs, marked by TBXT and SOX2), paraxial mesoderm derivatives (marked by TBX6 and MEOX1), or lateral mesoderm derivatives (marked by FOXF1) (Fig. S3C), suggesting that elongation can occur even in the absence of these cell types under external WNT activation. We further demonstrated that the axial progenitors in these organoids are transcriptionally distinct from NMPs and closer to pre-neural tube (PNT) ²⁵ progenitors (Fig. S4), despite both cell types existing in the mammalian tailbud and its precursor tissues in vivo ^6,7 (STAR Methods). This is in concordance with the idea that the embryonic tailbud consists of multiple axial progenitor cell types ^26-28.

Fig. 2. Single-cell sequencing identifies posteriorly polarized WNT and FGF/ERK signaling in axially elongating organoids.

(A) Gene expression heatmap of cells (n=7752) from elongating organoids on day 4 using single cell RNA-sequencing (scRNA-seq). Cells clustered with the Louvain method in a 26-dimensional gene space selected by sparse multimodal decomposition (see Methods) show axial progenitor (CDX2+), spinal cord (HOXB4+ CRABP1+), posterior hindbrain (NR2F1+), anterior hindbrain (EGR2+), and neuronal (HES6+ BTG2+) identities. Expression values are log- and min/max-normalized across cells. (B) UMAP plot of cells from scRNA-seq colored by cell type (bottom) and posterior anterior (P-A) pseudo-spatial coordinate obtained by diffusion mapping (inset). (C) Gene expression heatmap of top 300 differentially expressed genes ordered by computationally inferred cell P-A index. Expression values are log- and min/max-normalized across cells. (D-F) Gene expression profiles as a function of cell P-A index for (E) transcription factors CDX2, MEIS2, HOXB4, HOXB1, (E) non-canonical WNT ligand WNT5A and non-canonical WNT pathway component PRICKLE1, secreted WNT inhibitors SFRP1, SFRP2, (F) FGF ligands FGF8 and FGF17, FGF/ERK pathway targets SPRY1, DUSP6. Each plot displays mean (black) and standard deviation (gray) of log-normalized relative expression values partitioned into 20 bins of equal size. (G) Top: In situ sequencing (STARmap) of selected genes in organoid sample on day 4. Each gene transcript is encoded by a unique 2-color sequence across 2 cycles of sequencing (see legend). Bottom: Using locations of nuclei, transcripts were mapped to individual cells (left). This map was used to assign cell types (right) corresponding to (A). Scale bar: 100 μm. (H) Decoded transcripts in red for selected genes CDX2, MEIS2, WNT5A, SFRP1, overlaid on nuclei (DAPI). Scale bar: 100 μm. (I) Spatial P-A gene expression profiles for selected genes in (D-F) colored by cell type. Each plot displays mean (black) and per-cell (points) log-normalized relative expression values partitioned 10 bins of equal length.

WNT and FGF signals are posteriorly polarized in elongating organoids

Having identified the constituent cell types, we proceeded to investigate the underlying signals that initiate and drive axial elongation. An unbiased search for differentially expressed transcription factors, receptors, and secreted factors across progenitor clusters identified several known WNT and FGF ligands, receptors, and downstream targets (Fig. S3A and S3B). We therefore performed a global single-cell analysis of WNT and FGF pathway genes (Table 1). We also catalogued the corresponding loss of function axial elongation phenotypes in mouse mutants (Table 2). To infer spatial profiles of these signaling pathways in organoids, we built a diffusion map ²⁹ in the Euclidean space of genes identified by SMD to order cells from scRNA-seq along a putative posterior-anterior (P-A) axis (Fig. 2B and 2C; Fig. S3D and S3E). We first validated this pseudo-spatial ordering by verifying the expected P-A localization of axial progenitor, spinal cord, and hindbrain transcription factors such as CDX2, MEIS2, HOXB4, and HOXB1 (Fig. 2D). We then used this pseudo-spatial P-A axis to determine profiles of signaling pathways implicated in axis formation. Out of all WNT ligands, only noncanonical WNT ligands WNT5A and WNT5B were posteriorly polarized (Table 1, Fig. 2E and S3C). We also observed posterior expression of noncanonical WNT component PRICKLE1 and canonical WNT component LEF1 (Fig. S3C). We observed globally high expression of secreted WNT inhibitors SFRP1 and SFRP2, (Fig. 2E), and anterior expression of FRZB (Fig S3C). We did not detect the expression of canonical WNT inhibitors DKK1 or CER1. We observed posteriorly polarized expression of FGF ligands FGF2, FGF8, FGF12, and FGF17, anteriorly polarized expression of FGF3, and posterior expression of FGF/ERK targets SPRY1, SPRY4, DUSP6, and IL17RD (SEF) as well as PEA3-family transcriptional effectors ETV4 and ETV5 (Table 1, Fig. 2F and S3C). To validate these signaling profiles, we performed in situ sequencing on day 4 organoids using STARmap ³⁰ (Fig. 2G). We implemented a revised STARmap protocol and corresponding computational pipeline compatible with 3D tissue sequencing and analysis to spatially map 16 genes selected from scRNA-seq data (STAR Methods). Across three replicates, we observed posteriorly polarized expression of CDX2, WNT5A, PRICKLE1, and FGF8, and global expression of SFRP1 and SFRP2, matching our inferences from scRNA-seq data (Fig. 2H and 2I; Fig. S3F). The results from in situ sequencing validated the cell types and diffusion map trajectories inferred from scRNA-seq (Fig S3G to S3I). Our analyses thus demonstrate that WNT and FGF/ERK signals are localized posteriorly to the tailbud of axially elongating organoids.

Table 1. Global analysis of WNT and FGF pathway genes from scRNA-seq data.

Posterior (P) genes are enriched in axial progenitors relative to spinal cord and hindbrain, while anterior (A) genes are enriched in hindbrain relative to spinal cord and axial progenitors. Global (G) are expressed highly across cells, based on a threshold mean log(expression) value of 1.

WNT ligands	WNT inhibitors	WNT targets/effectors/receptors	FGF ligands	FGF targets/effectors/receptors
WNT1	DKK1	CDX1	FGF1	CDX1
WNT2	DKK2	CDX2 P	FGF2 P	CDX2 P
WNT2B	DKK3	CDX4 P	FGF3 A	CDX4 P
WNT3	DKK4	TBXT	FGF4	TBXT
WNT3A	DKKL1	SOX2	FGF5	NKX1-2 P
WNT4	SFRP1 G	AXIN2	FGF6	SPRY1 P
WNT5A P	SFRP2 G	LGR5	FGF7	SPRY2 G
WNT5B P	FRZB A	LEF1 P	FGF8 P	SPRY4 P
WNT6	SFRP4	TCF7	FGF9	IL17RDP (SEF)
WNT7A	SFRP5	TCF7L1	FGF10	DUSP6 P
WNT7B	WIF1	TCF7L2 G	FGF11	ETV1
WNT8A	SOSTDC1	PRICKLE1 P	FGF12 P	ETV4 P
WNT9A	SOST	PRICKLE2	FGF13	ETV5 P
WNT9B	CER1	VANGL1	FGF15	FGFR1 G
WNT10A	IGFBP4	VANGL2 G	FGF16	FGFR2 G
WNT10B		DVL1	FGF17 P	FGFR3 A
WNT11		DVL2	FGF18	FGFR4
WNT16B		DVL3	FGF19
		ROR2	FGF20
		PTK7 G	FGF21
		LRP5	FGF22
		LRP6	FGF23
		FZD1
		FZD2 G
		FZD3 G
		FZD4
		FZD5
		FZD6
		FZD7 P
		FZD8
		FZD9
		FZD10 P

^PPosterior

^AAnterior

^GGlobal, log(expression) > 1

Table 2. Reported loss-of-function WNT and FGF pathway mouse mutants and axial truncation phenotypes.

WNT ligand and receptor genes, FGF ligand and receptor genes, and WNT and FGF targets. *Loss-of-function, unless specified otherwise (e.g. GOF or gain-of-function)

*LOF mutant	Category	Truncation phenotype	Paper (first author, year)
WNT2B	WNT ligand	No	Van Amerongen, 2006
WNT3	WNT ligand	No anterior-posterior axis	Liu, 1999
WNT3A	WNT ligand	Yes	Takada, 1994; Ikeya, 2001
WNT5A	WNT ligand	Yes	Yamaguchi, 1999; Tai, 2009
WNT5B	WNT ligand	No	Van Amerongen, 2006
WNT3A/WNT8A	WNT ligand	Yes	Cunningham, 2015
WNT5A/WNT11	WNT ligand	Yes	Andre, 2015
FZD7	WNT receptor	No	Van Amerongen, 2006
LRP6	WNT receptor	Yes	Pinson, 2000
FGF2	FGF ligand	No	Zhou, 1998
FGF3	FGF ligand	Yes	Mansour, 1993
FGF8	FGF ligand	Defectivegastrulation	Meyers 1998; Sun 1999
FGF12	FGF ligand	No	Goldfarb, 2007
FGF17	FGF ligand	No	Xu, 2000
HOXB1-Cre; FGF4/FGF8	FGF ligand	Yes	Boulet, 2012
FGFR1	FGF receptor	Defectivegastrulation	Deng, 1994
FGFR1 (chimera)	FGF receptor	Yes	Ciruna, 1997
T-Cre; FGFR1	FGF receptor	Yes	Wahl, 2007
CDX2+/−;CDX1	WNT/FGF target	Yes	Van den Akker, 2002
CDX2	WNT/FGF target	Yes	Chawengsaksophak, 2004
SOX2-Cre; CDX2	WNT/FGF target	Yes	Savory, 2009
CDX2+/−;CDX4	WNT/FGF target	Yes	Young, 2009
CDX2+/−;CDX4;LEF1-GOF	WNT/FGF target	No	Young, 2009
Rosa26-CreER; CDX2	WNT/FGF target	Yes	Van de Ven, 2011
Rosa26-CreER;CDX2/CDX4	WNT/FGF target	Yes	Van de Ven, 2011
Rosa26-CreER; T	WNT/FGF target	Yes	Amin, 2016
Rosa26-CreER; CDX2/T	WNT/FGF target	Yes	Amin, 2016
SOX2-Cre;CDX1/CDX2/CDX4	WNT/FGF target	Yes	Van Rooijen, 2012
T	WNT/FGF target	Yes	Herrmann, 1990
T-Cre; CTNNB1	WNT/FGF target	Yes	Dunty, 2008; Aulehla, 2008
SP5/SP8	WNT/FGF target	Yes	Dunty, 2014

WNT ligands drive axial elongation downstream of canonical WNT activity

Given that WNT signals are polarized in organoids, we next asked whether WNT ligands drive axial elongation downstream of CHIR-mediated canonical WNT activation. We inhibited WNT ligand activity using the Porcupine inhibitor IWP3, which blocks WNT secretion by preventing its palmitoylation ³¹. We found that IWP3-treated organoids failed to elongate, and retained a spherical shape after four days of differentiation (Fig. 3A and 3B; Fig. S5A). However, IWP3-treated organoids retained a significant posterior CDX2+ population, similar in size to control organoids when adjusted for A-P length (Fig. 3C; Fig. S5A and S5B). This suggested that secreted WNT ligands are necessary for elongation in the presence of CHIR, but not for the initial specification of posterior identity. To test whether secreted WNT ligands were required continuously for elongation or acted as an initial trigger, we treated elongating organoids on day 2 with IWP3. We found that organoids were truncated by day 4 despite possessing CDX2+ domains (Fig. 3D to 3F; Fig. S5B), demonstrating that continuous secretion of WNT ligands was necessary for elongation.

Fig. 3. WNT ligands drive elongation downstream of FGF/ERK-dependent CDX2 expression.

(A) Control (left) and IWP3-treated (right) organoids on day 4 stained for SOX1, CDX2, and DAPI. Scale bar: 200 μm. (B) Violin plot of day 4 lengths of control (red) and IWP3-treated organoids (purple) with mean (points) and standard deviation (lines) (Control, n=211; IWP3, n=176; p<0.0001). (C) Bar plot showing percentage of control and IWP3-treated organoids with a CDX2+ domain (see Methods). (Control, n=211; IWP3, n=176). (D) Control (left) and 48h-delayed IWP3-treated (right) organoids on day 4 stained for SOX1, CDX2, and DAPI. Scale bar: 200 μm. (E) Violin plot of relative lengths on day 4 of control (red) and 48h-delayed IWP3-treated (purple) organoids with mean (points) and standard deviation (lines) (Control, n=212; IWP3, n=214; p<0.0001). (F) Bar plot showing percentage of control and 48h-delayed IWP3-treated organoids with a CDX2+ domain (Control, n=212; IWP3, n=214). (G) First row: Initial (day 2) and final (day 4) control (left) and IWP3-treated (right) ZO1-EGFP+ organoids. Second, third row: ZO1-EGFP+ organoids on day 4 without (left) and with (right) IWP3 treatment, stained for CDX2, SOX1, and DAPI. Scale bar: 200 μm. (H) Representative live fluorescence images of tracked ZO1− EGFP+ cells from a control organoid during a 14h time-lapse. Each clone from t=0 is marked with a single color, and cell-cell junctions are traced in green. Scale bar 50 μm. (I) Mean squared relative displacement (MSRD) over time of neighboring cells in control (red) and IWP3-treated (purple) organoids. Error bars indicate standard deviation. (J) Angle histogram of net cell displacements relative to the axis of elongation in control (left, red) and IWP3-treated (right, purple) organoids (Control, n=131; IWP3, n=98). (K) Left: CRISPRi organoids containing an mKate2-expressing guide RNA construct against CDX2 (sgCDX2) on day 4, stained for SOX1 and CDX2. Scale bar: 200 μm. Middle: Violin plot of day 4 lengths of control sgRNA (red) and sgCDX2 (green) CRISPRi organoids with mean (points) and standard deviation (lines) (Control, n=213; sgCDX2, n=214; p<0.0001). Right: Bar plot showing percentage of control (red) and sgCDX2 (green) CRISPRi organoids with a CDX2+ domain (Control, n=213; sgCDX2, n=214). (L) Left: PD0-treated organoids on day 4, stained for SOX1, CDX2, and DAPI. Scale bar: 200 μm. Middle: Violin plot of day 4 lengths of control (red) and PD0-treated (blue) organoids with mean (points) and standard deviation (lines) (Control, n=211; PD0, n=157; p<0.0001). Right: Bar plot showing percentage of control (red) and PD0-treated (blue) organoids with a CDX2+ domain. (Control, n=211; PD0, n=157). (M) Left: 48h-delayed PD0-treated organoids on day 4, stained for SOX1, CDX2, and DAPI. Scale bar: 200 μm. Middle: Violin plot of relative lengths on day 4 of control (red) and 48h-delayed PD0-treated (purple) organoids with mean (points) and standard deviation (lines) (Control, n=212; PD0, n=211; p<0.0001). Right: Bar plot showing percentage of control (left, red) and 48h-delayed PD0-treated (right, blue) organoids with a CDX2+ domain (Control, n=212; PD0, n=211). (N) Signaling model of axial elongation of the neural tube. CHIR-mediated canonical WNT induces FGF/ERK activity, together inducing CDX2 expression. CDX2 promotes expression of secreted WNT ligands, which drive elongation.

To explore the role of WNT ligands in regulating cell behaviors during elongation, we performed live confocal time-lapse imaging of organoids expressing ZO1-EGFP, a fusion reporter of apical tight junctions, with or without delayed IWP3 treatment on day 2 of differentiation. We verified that IWP3 treatment led to truncation of ZO1-EGFP+ organoids even in the presence of a posterior CDX2+ domain (Fig. 3G and S5G). By tracking the displacement of individual cell clones over the course of fourteen hours (Fig. 3H; Movie S1), we found that neighboring clones in control organoids exhibited higher mean squared relative displacements compared to IWP3-treated organoids (Fig. 3I). This suggested that cells experienced increased fluidity ³² in the presence of WNT ligands. We also found that control organoids displayed directed cell movements in the plane of the epithelium along the direction of the elongation axis. In contrast, cell movements in IWP3-treated organoids were undirected with respect to the elongation axis (Fig. 3J and S5H). We additionally performed time-lapse imaging of organoids expressing H2B-mCherry under control conditions to determine whether cell divisions were oriented with respect to the elongation axis. However, there was no correlation between the angle of cell division and elongation direction (Fig. S5I). We concluded that WNT ligands are continuously required to maintain the fluidity of the epithelium to facilitate the rearrangements of neighboring cells in the direction of the elongating axis. Furthermore, the detection of no posterior canonical WNT ligands in single-cell expression data (Fig. 3E) and the observation that the addition of DKK1, a canonical WNT receptor inhibitor, does not affect elongation (Fig. S5E and S5F), suggests that secreted canonical WNT ligands do not play a direct role in elongation. These observations support a potential role for noncanonical WNT ligands in driving elongation.

FGF/ERK-dependent CDX2 expression is required for elongation

We next tested the roles of intrinsic and extrinsic signaling factors implicated upstream of WNT ligand activity in the tailbud. Across vertebrates, WNT ligands are induced by CDX transcription factors ³³. We used CRISPR interference (CRISPRi) to knock down CDX2 expression in a constitutive CRISPRi hPSC line ³⁴ (see STAR Methods). We generated organoids from CRISPRi lines with an integrated CDX2 guide RNA (gRNA) or nonspecific control gRNA. By day 4, organoids with a control gRNA elongated normally. In contrast, organoids with a CDX2 gRNA were truncated and lacked CDX2+ domains (Fig. 3K; Fig. S5J to S5L), suggesting that CDX2 is essential for organoid elongation. Truncation was accompanied by a decrease in proliferation in the tailbud region, based on a reduction in phospho-histone H3 staining, as well as a loss of posterior WNT5A and WNT5B gene expression, based on in situ hybridization chain reaction (Fig. S6A to S6C). To determine if a WNT5A/B knockdown resembles the CDX2 knockdown, we generated CRISPRi organoids with an integrated WNT5A gRNA and transduced them with a virus carrying a WNT5B gRNA, achieving greater than 50% efficiency of genomic integration. Organoids lacking WNT5A alone elongated similarly to wild-type organoids, while organoids lacking both WNT5A and WNT5B were partially but significantly truncated (Fig. S6D to S6F). These results, in conjunction with earlier observations, suggest that noncanonical WNT ligands WNT5A/WNT5B play a role in driving elongation downstream of CDX2.

CDX transcription factors are thought to act downstream of FGF/ERK and canonical WNT signaling in vertebrates ³⁵. To test the role of FGF/ERK, we treated organoids with PD0325901 (PD0), a small molecule inhibitor of ERK1/2 phosphorylation. Following continuous FGF/ERK inhibition, organoids failed to elongate or produce any CDX2+ axial progenitors (Fig. 3L and S5A). This suggested that FGF/ERK was necessary to induce CDX2 expression and subsequent axis elongation. To determine whether FGF/ERK signaling was required throughout the elongation process or only at the outset, we inhibited FGF/ERK on day 2 of differentiation. By day 4, organoids were truncated relative to control organoids and downregulated CDX2 expression, showing FGF/ERK was required not only to induce CDX2 but also to maintain its expression level for elongation to occur (Fig. 3M and S5B). Our results support a model in which canonical WNT activity (driven by CHIR) together with FGF/ERK activity (driven by endogenous FGF ligands) induces and maintains CDX2 expression in the tailbud. In turn, CDX2 drives the secretion of WNT ligands, which are essential for directing elongation by modulating cellular rearrangements (Fig. 3N).

Elongation is sustained by the induction of a neuromesodermal progenitor-like signaling center

In experiments described thus far, we required sustained canonical WNT activation through CHIR to drive elongation. We next asked if organoids had the ability to elongate autonomously even in the absence of this external drive. Axial elongation is thought to be sustained in vivo by NMPs via the production of WNT and FGF ligands ^36-38. Studies in vertebrates have further demonstrated that canonical WNT and FGF/ERK pathways are engaged in a positive feedback loop in a variety of developmental contexts, including the zebrafish and mouse tailbud during somitogenesis ^39-42. We sought to exploit this feedback between WNT and FGF activity to sustain elongation. Thus, we exposed organoids to a transient 24-hour pulse of recombinant FGF2 prior to withdrawing CHIR on day 2 of differentiation. Under control conditions, CHIR withdrawal led to truncated organoids with reduced CDX2 expression (Fig. 4A, middle and 4B; Fig. S6G and S6H), whereas FGF pulse-treated organoids continued to elongate through day 4 of differentiation, showing that a pulse of FGF was sufficient to sustain elongation in the absence of CHIR (Fig. 4A, bottom and 4B; Fig. S6G and S6H, p < 0.0001). To verify the induction of NMPs, we stained FGF pulse-treated organoids for TBXT and SOX2, transcription factors which are known to jointly mark NMPs in vivo ^5,43. Cells in the tailbud of FGF-treated organoids stained positively at the end of the pulse for TBXT and SOX2, with SOX2 at lower levels than in the neural tube, consistent with in vivo expression patterns ⁵. In contrast, control organoids exposed to CHIR alone failed to express TBXT (Fig. 4C to 4E; Fig. S6I and S6J). Furthermore, FGF pulse-treated organoids maintained TBXT+ SOX2+ cells in the CDX2+ tailbud region over the course of elongation, although these cells decreased in number by Day 4 (Fig. S6K). We also found that a CHIR pulse at a concentration higher than in control conditions could generate a similar result (Fig. S6G and S6H) in an FGF/ERK-dependent manner (Fig. S6N). In vertebrates, WNT and FGF ligand production in NMPs is thought to be driven in part by the transcription factor TBXT ^36,38. To test the requirement of TBXT for sustained elongation, we generated CRISPRi organoids with an integrated TBXT guide RNA (Fig. S6L), and exposed them to continuous CHIR or FGF pulse conditions. Compared to CRISPRi organoids containing a control gRNA, organoids with a TBXT gRNA were truncated following the FGF pulse (Fig. S6M). This is consistent with the possibility that TBXT is required for the production of canonical WNT and FGF/ERK signals by NMPs during axial elongation. Accordingly, TBXT+ SOX2+ cells from organoids generated via a CHIR pulse express canonical WNT ligand WNT3A and as well as high levels of FGF ligands FGF8 and FGF17, which activate canonical WNT and FGF/ERK pathways, respectively ⁴⁴. We observed similar signaling profiles in NMPs derived from the posterior mammalian epiblast in vivo ⁴⁵ (STAR Methods). Thus, induction of an NMP-like signaling center enables self-sustained axial elongation of neural tube organoids, likely through the continuous production of posterior signals.

Fig. 4. An excitable system driving axial elongation is triggered by induction of an NMP-like signaling center and is stabilized by secreted inhibitors.

(A) Day 4 control organoids (top), organoids subjected to CHIR withdrawal on day 2 (middle), and organoids treated with an FGF pulse from day 1 to day 2 prior to CHIR withdrawal on day 2 (bottom), stained for CDX2 in red and SOX1 in blue. Scale bar: 200 μm. (B) Violin plot of relative lengths of organoids on day 4 exposed to control (red), CHIR withdrawal (blue), and FGF pulse (red) conditions with mean (points) and standard deviation (lines) (Control, n = 216; CHIR withdrawal, n = 214; FGF pulse, n = 216; p<0.0001, p<0.0001) (C) Phase contrast and fluorescence images of day 2 organoids in control (left) and FGF pulse + CHIR withdrawal (right) conditions, stained for CDX2, SOX2, TBXT, and DAPI. (D) Bar plots showing percentage of day 2 organoids in control (red) and FGF pulse + CHIR withdrawal (magenta) conditions with a CDX2+ domain (left), SOX2+ domain (middle), and TBXT+ domain (right) (Control, n = 199; FGF pulse, n = 184). (E) Zoomed-in fluorescence images of the posterior side of day 2 organoids after a 24-hour FGF pulse, stained for TBXT, SOX2, and DAPI. Co-expression of nuclear TBXT and SOX2 suggest neuromesodermal progenitor (NMP)-like identity. Scale bar: 100 μm. (F) Model of axial elongation as an excitable system. Organoids elongate in media with WNT signal. The rate of elongation is zero when the concentration of CHIR in the media, [CHIR]_media, is zero. An FGF pulse induces an NMP-like signaling center at the posterior end of organoids. In this condition, the rate of elongation is sustained when [CHIR]_media is zero. (G, H) Results from a mathematical model of the excitable system following an ectopic pulse of activator W (green, see colorbar) away from the tailbud where W has high levels (red, see colorbar), in the presence (G) or absence (H) of secreted diffusible inhibitor S (grayscale). The level of activator in response to the ectopic W pulse decays over time with S, but increases and saturates at high levels without S. (I) Control organoids on day 4, stained for DAPI, CDX2, SOX1, and SFRP1. SFRP1 on the organoid was visualized at low contrast (grayscale image). The SFRP1 image was contrast-adjusted (adj.) to visualize SFRP1 bound to the coverslip (color image). Scale bar: 200 μm. (J) Day 4 CRISPRi organoids containing a GFP-expressing guide RNA construct against SFRP2 (sgSFRP2) and treated with WAY3, stained for CDX2, SOX1, and DAPI. Scale bar 200 μm. (K) Bar plots showing number of organoids with single or multiple tails in control (top, red, n = 203), sgSFRP2 (middle, green, n = 206), and WAY3-treated sgSFRP2 (bottom, yellow, n = 179) CRISPRi organoids. (L) Proposed mechanisms underlying axial elongation. Low levels of posteriorly localized FGF/ERK and canonical WNT activity induce CDX2 expression, which in turn induces secretion of WNT ligands, driving axial elongation. High levels of FGF/ERK and canonical WNT activity induce NMP-like cells, which continuously produce FGF/ERK and canonical WNT ligands to maintain CDX2 expression. Local fluctuations in WNT ligand levels (purple) are buffered by global secretion of SFRP1/2, ensuring that elongation occurs only along a single A-P axis.

Secreted WNT inhibitors are required for stable axial elongation

These results suggest that organoids can be excited from a state in which elongation relies on external WNT signals to one in which it can be self-sustained by positive feedback of endogenous FGF and WNT signaling, following an FGF or CHIR pulse (Fig. 4F). Such excitable systems that exhibit positive feedback are known to be susceptible to runaway events ^46,47. A simple mathematical model of the organoid with positive feedback leads to self-sustained activity of an activator (e.g., FGF or WNT) at the tailbud. In the presence of a diffusible inhibitor, the effects of transient ectopic activation away from the tailbud are suppressed. In contrast, when the inhibitor is removed, ectopic activation triggers persistent activity through the positive feedback loop (Fig. 4G and 4H; STAR Methods). Such persistent activity could lead to runaway events such as ectopic axial elongation.

Therefore, we asked whether diffusible WNT or FGF inhibitors might constrain these positive feedback loops to ensure stable elongation along the A-P axis. In our scRNA-seq and STARmap data, we observed globally high expression levels of secreted WNT inhibitors SFRP1 and SFRP2 (Fig. 2E and 2I; Fig. S3B and S3C). To verify that organoids were secreting SFRPs, we stained for SFRP1 protein on day 4. SFRP1 protein was distributed uniformly across the surface of organoids (Fig. 4I, grayscale image). We further adjusted the contrast to visualize SFRP1 protein bound to the coverslip, which showed that SFRP1 was distributed in a gradient along the radial direction away from the center of each hexagon (Fig. 4J, color image, Fig. S7F). This gradient of SFRP1 protein on the coverslip was not an artifact, as it disappeared upon knockdown of SFRP1 (Fig. S7D to S7F). To test whether SFRP1 and SFRP2 suppressed runaway events leading to ectopic sites of elongation, we generated organoids from CRISPRi lines with an integrated SFRP2 gRNA, and treated organoids with WAY316606 (WAY3), a small molecule that inhibits SFRP1 activity by preventing its interaction with WNT ligands ⁴⁸. While knockdown of SFRP2 or inhibition of SFRP1 alone did not produce severe defects (Fig. S7B), simultaneous SFRP1 inhibition and SFRP2 knockdown resulted in ectopic tailbud formation and elongation, characterized by branched structures (Fig. 4K) and an increased average number of tailbuds per organoid (Fig. 4L). Branched structures were not correlated with changes in proliferation rates in the tailbud, suggesting branching may occur due to a defect in the cellular rearrangements underlying elongation (Fig. S7C). We also generated CRISPRi organoids with dually integrated SFRP1 and SFRP2 gRNAs. These organoids exhibited similar defects, and additionally and did not generate an extracellular gradient of SFRP1 (Fig. S7D to S7F). Thus, redundantly acting secreted WNT inhibitors in the form of SFRPs are required to ensure that elongation occurs stably along a single axis.

Discussion

Stochasticity has attracted much attention in biological systems. The large variability exhibited by in vitro organoid models is often attributed to such intrinsic noise. In contrast, it appears that much of the variability observed in vitro is due to variability in spatiotemporal signaling conditions and geometry. Our study shows that this variability can largely be eliminated if the boundary conditions for the underlying dynamical systems can be controlled, in this case, by coupling these systems to each other. Specifically, we built a bioengineering and machine learning framework to learn how to couple organoids to one another and control organoid symmetry breaking in a deterministic manner. Learning to reduce variability in biological systems using a combination of engineering and statistical inference methods has the potential to aid in the discovery of mechanisms underlying the development of complex human tissues.

Our reproducible organoid system enabled us to uncover mechanisms underlying human axial elongation. Our findings show that axial elongation is driven by posteriorly secreted FGF and WNT ligands. The critical constituent cell type secreting these signals in the tailbud is an NMP-like population characterized by SOX2 and TBXT expression that acts as a posterior signaling center in the absence of exogenous signals (Fig. 4L). The NMP-like cells, together with the secreted WNT and FGF signals, form a positive feedback loop to drive autonomous elongation. Despite being bipotent, NMP-like cells give rise only to neural progenitors under the conditions described in this manuscript. This suggests that their ability to act as a signaling center is independent of their potency to generate mesodermal tissue. Accordingly, organoids consist only of a neural tube and tailbud and can elongate axially in the absence of any mesoderm.

Furthermore, as with all excitable systems, including those in biology ^47,49, elongating organoids are prone to runaway events triggered by a positive feedback loop, which is composed of FGF and WNT signals. Removing inhibitors of these signals reveals the instability of the underlying dynamical system, leading to the emergence of ectopic sites of elongation. We propose that secreted inhibitors of the WNT pathway in the form of SFRPs are required for stable elongation along a single anterior-posterior axis (Fig. 4L).

Our model of the elongating neural tube as an excitable system could generalize to other organ primordia in which asymmetric signals are coupled to morphogenesis, especially those in which WNT and FGF signaling have essential roles. These include the limb bud ^41,50 and lung bud ⁵¹, where the polarization of gene expression domains and elongation are essential for proper development. In these instances, too, the identification and knockdown of key inhibitors could uncover instabilities of the underlying dynamical system that drives the outgrowth of these tissues.

Furthermore, the ability of our organoids to robustly generate a posterior population of NMP-like cells opens avenues to studying the coordination of human spinal cord and musculoskeletal development in vitro, as we show in a companion manuscript⁴⁴. While the neural tube can elongate in the absence of paraxial mesoderm, the mesoderm-derived somites serve as an important source of retinoic acid, which mediates downstream patterning of the neural tube by the induction of neural genes such as PAX6. By systematically building up the complexity of tissue-tissue interactions present in the embryo, we may uncover developmental mechanisms that are difficult to dissect in vivo.

Limitations of the Study:

While this manuscript focuses on the mechanisms driving sustained and stable axial elongation, the mechanisms underlying the initial symmetry breaking and the identities of the secreted molecules that couple the organoids remain unknown. Our results, in conjunction with those in a companion manuscript ⁴⁴, show that SFRPs and retinoic acid are not involved in initial symmetry breaking and that SFRPs prevent the formation of ectopic axes during elongation without interfering with initial symmetry breaking. Secreted WNTs also act downstream of initial symmetry breaking to direct axial elongation; however, whether they act through an established non-canonical pathway such as planar cell polarity is unknown. Our discovery of SFRPs as inhibitors of ectopic axis elongation raises the interesting question of how SFRPs and WNTs interact to confine the axis. These questions need to be addressed by measuring and perturbing organoid systems at high spatiotemporal resolution, which has been previously inaccessible in mammalian developmental systems. Furthermore, the mathematical models presented here are for illustration, demonstrating that simple models are sufficient to recapitulate symmetry breaking and runaway events due to positive feedback loops. Lastly, we have used the word “organoid” throughout this paper to describe an organized aggregate of stem cell derivatives that undergo morphogenesis. While a term like “organized stem cell-derived aggregate” is more accurate, we use organoid as it has been routinely used as such in the literature.

STAR METHODS

RESOURCE AVAILABILITY

Lead Contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Sharad Ramanathan (sharad@cgr.harvard.edu).

Materials Availability

Plasmids and cell lines generated in this study will be made available by the lead contact upon request. Materials will be provided upon completion of MTA.

Data and Code Availability

Single-cell RNA-seq data collected for this paper has been deposited at GEO and is publicly available as of the date of publication. Accession numbers are listed in the key resources table. All original code has been deposited on Github and Zenodo and is publicly available as of the date of publication. URLs and DOIs are listed in the key resources table. Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

KEY RESOURCES TABLE

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Antibodies
Rabbit Monoclonal anti-OCT4	Cell Signaling Technology	RRID:AB_2167691
Rat Monoclonal Anti-SOX2	Thermo Fisher Scientific	RRID:AB_11219471
Mouse Monoclonal Anti-ZOI	Thermo Fisher Scientific	RRID:AB_2532187
Goat Polyclonal Anti-SOX1	R and D Systems	RRID:AB_2239879
Goat Polyclonal Anti-TBXT	R and D Systems	RRID:AB_2200235
Goat Polyclonal Anti-TBX6	R and D Systems	RRID:AB_2200834
Rabbit Monoclonal Anti-CDX2	Cell Signaling Technology	RRID:AB_2797879
Mouse Monoclonal Anti-CDX2	R and D Systems	RRID:AB_10556173
Goat Polyclonal Anti-SFRP1	R and D Systems	RRID:AB_2285831
Mouse anti-LAMC1	DSHB	RRID:AB_528343
Rabbit Monoclonal Anti-N-Cadherin	Cell Signaling Technology	RRID:AB_2687616
Rabbit Polyclonal Anti-Phospho-Histone H3 (Ser10)	Cell Signaling Technology	RRID:AB_331535
Bacterial and virus strains
NEB® Stable Competent E. coli (High Efficiency)	New England Biolabs	Cat#C3040H
Chemicals, peptides, and recombinant proteins
mTeSR™ Plus	Stem Cell Technologies	Cat#5825
ReLeSR™	Stem Cell Technologies	Cat#5872
Accutase	Innovative Cell Technologies	Cat#AT104
Matrigel hESC-qualified Matrix, *LDEV-Free	Corning	Cat#354277
Stemolecule™ Y27632	Stemgent	Cat#04-0012-10
CHIR-99021	Selleck Chemicals	Cat#S2924
PD0325901	Selleck Chemicals	Cat#S1036
PD173104	Selleck Chemicals	Cat#S1264
A 83-01	R and D Systems	Cat#2939/10
LDN 193189 dihydrochloride	R and D Systems	Cat#6053/10
IWP-3	Sigma Aldrich	Cat#SML0533
WAY 316606	R and D Systems	Cat#4767/10
Recombinant Human Dkk-1	R and D Systems	Cat#5439-DK-010
N-2 Supplement	Thermo Fisher Scientific	Cat#17502048
B-27™ Supplement (50X), minus vitamin A	Thermo Fisher Scientific	Cat#12587010
Penicillin-Streptomycin	Millipore	Cat#P4458
DMEM/F-12, HEPES, no phenol red	Thermo Fisher Scientific	Cat#11039021
GlutaMAX™ Supplement	Thermo Fisher Scientific	Cat#35050061
MEM Non-Essential Amino Acids Solution (100X)	Thermo Fisher Scientific	Cat#11140050
2-Mercaptoethanol	Thermo Fisher Scientific	Cat#21985023
Bovine Serum Albumin solution	Millipore	Cat#A9576
CloneR™	Stem Cell	Cat#05889
Mycoplasma PCR Detection Kit	Applied Biological Materials	Cat#G238
Alexa Fluor™ 647 Phalloidin	Thermo Fisher Scientific	Cat#A22287
Sylgard™ 184	Ellsworth Adhesives	Cat#4019862
DAPI	Thermo Fisher Scientific	Cat#D1306
DPBS (1X)	Lonza	Cat#BE17-513F
PBS (1X)	Lonza	Cat#BE17-516F
jetPRIME®	Polyplus	Cat#114-07
Lenti-X Concentrator	Clontech	Cat#6311231
Trichloro(1H,1H,2H,2H-perfluorooctyl)silane	Sigma Aldrich	Cat#448931
Cyclohexanone	VWR	Cat#BDH4612
Deposited data
Single cell RNA-seq data	This study	GEO: GSE220472
Single cell RNA-seq data	Diaz-Cuadros, et al.42	GEO: GSE114186
Experimental models: Cell lines
Human: WA01 ESC line (NIH approval number NIHhESC-10-0043)	WiCell	WA01
Human: AICS-0023 iPSC line (WTC11)	AICS	AICS-0023
Human: AICS-0090 iPSC line (WTC11)	AICS	AICS-0090
Human: H2B-mCherry iPSC line	Laboratory of Olivier Pourquié	N/A
Human: Lenti-X™ 293T Cell Line	Takara Bio	Cat#632180
Experimental models: Organisms/strains
E. coli: NEB Stable Competent E. coli	NEB	Cat#C3040H
Recombinant DNA
pgRNA-CKB	Mandegar, et al.31	RRID:Addgene_73501
pLKO5.sgRNA.EFS.GFP	Heckl, et al.68	RRID:Addgene_57822
pMD2.G	Laboratory of Didier Trono	RRID:Addgene_12259
psPAX2	Laboratory of Didier Trono	RRID:Addgene_12260
Software and algorithms
Original code	This paper	https://github.com/iamsmurph/SymBreak https://doi.org/10.5281/zenodo.7457970
ZEN	Zeiss	https://www.zeiss.com/microscopy/en/products/software/zeisszen.html
FIJI/ImageJ	Schindelin, et al.50	https://imagej.net/software/fiji/
Arivis Vision4D	Zeiss	https://www.arivis.com/
llastik	Berg, et al.51	https://www.ilastik.org/index.html
MATLAB	MathWorks	https://www.mathworks.com/products/matlab.html
Scanpy	Wolf, et al.52	https://scanpy.readthedocs.io/en/stable/

EXPERIMENTAL MODELS AND SUBJECT DETAILS

Cell lines

We conducted the majority of our experiments using WA01 human ESCs (H1, WiCell). For timelapse studies, we used WTC-11 human iPSCs (WTC, Allen Institute) with endogenous ZO1 tagged with mEGFP (AICS-0023) as well as hiPSCs with H2B tagged with mCherry (H2B-mCherry) introduced at the AAVS1 locus (provided generously by the Pourquie Lab ⁴⁵). For CRISPRi studies, we used WTC-11 hiPSCs with dCas9-TagBFP-KRAB introduced at the CLYBL locus (AICS-0090). hPSCs were cultured in 6-well tissue culture dishes treated for 1 hour with 1X diluted Matrigel (Corning 354277) and supplied with mTeSR Plus media (Stem Cell Technologies 5825). For routine culture, we passaged by washing with phosphate buffered saline (PBS) followed by ReLeSR (Stem Cell Technologies 5872) treatment for 5 minutes. Every 5 days, cells were passaged in clumps of 10 to 20 cells and seeded in mTeSR Plus. All cell lines used were routinely tested for mycoplasma contamination (Mycoplasma PCR Detection Kit, ABM G238).

For lentiviral production, we used the Lenti-X^™ 293T Cell Line (Takara 632180), a subclone of the HEK 293 cell line. Cells were split 1:10 every 3 days using 0.25% Trypsin-EDTA into a tissue culture treated 10-cm dish (Thermo Fisher 150318) and maintained in 10% fetal bovine serum (FBS) in DMEM/F12 (Thermo Fisher 11039021).

For bacterial transformation, we used NEB Stable Competent E. coli (NEB C3040H). Prior to use, cells were thawed on ice for 10 minutes.

METHOD DETAILS

Soft lithography and microcontact printing

Microcontact printing was performed using polydimethylsiloxane (PDMS) stamps cast on soft lithography masters fabricated in a non-cleanroom setting ⁵². Briefly, round ADEX-50 dry film photoresist films (DJ Microlaminates) were laminated onto round 76.2 mm Si wafers (University Wafers) at 65°C using a SKY laminator. Films were exposed through 8 μm-resolution photomasks (CAD/Art Services), designed on AutoCAD, to 365 nm UV light at an intensity of 25 mW/cm^2 for 13 seconds using a UV lamp (Uvitron), baked at 80°C for 15 minutes, and developed face down in cyclohexanone (VWR BDH4612) on a steel mesh without shaking for 5 minutes, followed by washing with acetone and isopropyl alcohol and drying with compressed air. Afterwards, masters were hard-baked on a hot plate at 200°C for 1 hour and silanized for 1 hour in a vacuum chamber with 50 μl of trichloro(1H,1H,2H,2H-perfluorooctyl) silane (Sigma 448931).

To cast PDMS, the elastomer base and curing agent (Dow Sylgard^™ 184, Ellsworth Adhesives) were mixed at a ratio of 1:9, degassed, poured onto masters and baked at 80°C for 1 hour. Stamps were covered with Scotch tape to prevent dust accumulation and cut using a scalpel. Stamps were brought into the biosafety hood and coated overnight with extracellular matrix consisting of 1X diluted Matrigel, washed with MilliQ water, air dried, and placed onto 22 mm No. 1.5 square borosilicate glass coverslips (VWR 48366-227). Stamps were removed with tweezers just prior to seeding cells.

Organoid differentiation

hPSCs were seeded onto microcontact-printed coverslips containing 150-μm diameter features at 1-2 million cells/mL in pluripotency maintenance media consisting of mTeSR Plus media (MT) supplemented with 10 μM ROCK inhibitor Y-27632 (RI), and washed with fresh MT+RI after 1-2 hours. Once colonies were confluent (day 0), media was switched to differentiation media. Differentiation media consisted of (DMEM/F12 with 1X N2, 1X B27, 1X penicillin/streptomycin, 1% NEAA, 0.5% GlutaMAX, 0.1% ß-mercaptoethanol, and 0.05% bovine serum albumin) supplemented with 0.5 μM A8301, 0.5 μM LDN193189 (LDN), 3 μM CHIR99021 (CHIR), and 6% v/v Matrigel. After 2 days, media was replaced with N2B27 media supplemented with 0.5 μM LDN and 3 μM CHIR. On hexagonal arrays, organoids began to elongate by day 2 and continued to elongate through day 4. We note that the elongating portion of the organoid was surrounded by extracellular matrix throughout these 4 days, rather than being attached to the glass surface, as indicated by movement upon gentle shaking of the culture dish. For long-term culture to day 7, organoids were removed from coverslips and transferred to a 96-well plate. Notably, LDN was not required for the prevention of paraxial mesoderm induction from day 2 onwards (Fig. S2D, right). For conditioned media experiments, media on a random low-density array was replaced on day 1 and day 3 from a random high-density array (Fig. S2A, top). For pulse experiments, media was supplemented on day 1 with an additional 1 μM CHIR99021 or 20 μg/ml recombinant human basic fibroblast growth factor (FGF2) for 24 hours, then washed and replaced with N2B27 media with 0.5 μM LDN. For perturbation experiments, media was supplemented on the days indicated in the text with 1 μM IWP3, 1 μM PD0325901 (PD0), or 20 μM WAY316606 (WAY3).

Immunostaining

Cells were fixed with 4% formaldehyde for 15 minutes at room temperature. Fixed cells were treated with blocking buffer (PBS + 5% normal donkey serum + 0.3% Triton X-100) for 1 h, then overnight at 4°C with primary antibody diluted in staining buffer (PBS + 1% BSA + 0.3% Triton X-100). The following primary antibodies were used at the indicated dilutions: Rabbit anti-OCT4 (1:400, Cell Signaling C30A3); Rat anti-SOX2 (1:400, Thermo Fisher BTJCE), Rabbit anti-N-Cadherin (1:400, Cell Signaling D4R1H), Mouse anti-ZO1-FITC (1:800, Thermo Fisher 1A12), Rabbit anti-CDX2 (1:400, Cell Signaling D11D10), Mouse anti-CDX2 (1:200, R&D MAB3665), Goat anti-SOX1 (1:400, R&D AF3369), Mouse anti-SOX1 (1:200, BD Biosciences N23-844), Mouse anti-LAMC1 (1:50, DSHB 2E8), Rabbit anti-pHH3 (1:400, Cell Signaling 9701), Goat anti-TBXT (1:400, R&D AF2085), Goat anti-TBX6 (1:400, R&D AF4744), Goat anti-SFRP1 (1:200, R&D AF1384), Alexa Fluor^™ 647 Phalloidin (1:20, Thermo Fisher A22287).

After overnight incubation with primary antibody solution on an orbital shaker at 100 rpm, samples were washed three times with PBS, then secondary antibodies diluted in staining buffer were added. We used the following secondary antibodies all at a dilution of 1:1000: donkey anti-rabbit Alexa 568 (Thermo Fisher), donkey anti-goat 488, donkey anti-rat Alexa 488 (Thermo Fisher), and donkey anti-mouse Alexa 647 (Thermo Fisher). We added 300 nM DAPI (Thermo Fisher) to the secondary antibody staining solution to visualize nuclei. After overnight incubation with secondary antibody solution on an orbital shaker at 100 rpm, samples were washed three times with PBS and stored at 4°C for imaging.

Epifluorescence imaging of fixed samples

Fixed samples were imaged on a Zeiss AxioObserver Z1 inverted microscope using Zeiss 10x and 20x plan apo objectives (NA 1.3) using the appropriate filter sets. Images were acquired using an Orca-Flash 4.0 CMOS camera (Hamamatsu). The 43 HE DsRed/46 HE YFP/47 HE CFP/49 DAPI/50 Cy5 filter sets from Zeiss were used. The microscope was controlled using ZEN software.

Confocal imaging of fixed and live samples

Fixed samples were imaged on a Zeiss LSM 980 with Airyscan using a Zeiss 10x (NA 0.45) objective. Detection was performed on DAPI, AlexaFluor 488, AlexaFluor 568 and AlexaFluor 647 channels. A Z-stack with 1-micron intervals was acquired from the lower to upper apical surface of each organoid. After Airyscan processing, a maximum Z intensity projection was performed for visualization purposes.

For live imaging, organoids were maintained in a 37°C incubation chamber at 5% CO₂ and imaged using a Zeiss 20x (NA 0.8) objective every 20 minutes. Detection of ZO1-EGFP was performed on the AlexaFluor 488 channel using the 488 nm laser at 3% intensity, and detection of H2B-mCherry was performed on the AlexaFluor 568 channel using the 561 nm laser at 5% intensity. Focus was maintained using Zeiss Definite Focus to compensate for sample drift. For maximum accuracy, cells in ZO1 and H2B time lapses were tracked manually in FIJI. ZO1 tracks were analyzed with a custom MATLAB script to track net and mean squared relative displacements.

Analysis of live confocal time lapses

Three dimensional images of ZO1 time lapses were compressed to two dimensions + time using a custom MATLAB script. This script applied a threshold to the image based on the ZO1 intensity of each pixel, extracting the pixels with high ZO1 intensity. A plane was fitted to this point cloud and the 2D image was extracted from taking the average of 5 pixels bellow and above the plane. This was done to extract only the bottom apical surface of the organoids, since the top surface also has fluorescence intensity and this could produce noise in a maximum intensity projection. The ZO1 projection was then analyzed using the Manual Tracking plugin on FIJI. The tracks were later exported to MATLAB and for each track we calculated the displacement vectors of the position of the cell center between the initial and final time point that the cell was tracked. We calculated the angle between these vectors and the elongation axis of the organoid defined with respect to the center of the organoid. To calculate the mean squared relative displacement (MSRD) we detected the closest neighbor to each cell at the beginning of that cell’s track and measured the distance between these neighbors across 10 time points. The initial distance was subtracted from the measurements to obtain relative distances. The relative distances were squared and the average squared relative distance for each time point was taken as the MSRD for that time point.

The H2B time lapses were transformed to two dimensional + time images using a simple maximum intensity projection on FIJI. Using the H2B timelapse projection we analyzed the cell division orientation. Cell divisions were identified manually by the characteristic shape and brightness of the condensing chromosomes. We labeled a position in between daughter cells representing the closest position to the mother's nuclei in the previous time point together with the centers of the daughter cells. Vectors were drawn from the mother to the daughters and we calculated the angle of those vectors to the axis of elongation using a custom MATLAB script.

Image segmentation

All epifluorescence images were segmented in FIJI⁵³ or Ilastik⁵⁴ and analyzed in MATLAB or Python (see Methods S1 for details). Confocal images of pHH3 stains were segmented at single cell resolution in Arivis Vision4D using a machine learning pipeline and analyzed in Python.

Single cell RNA sequencing

Organoids were dissociated into a single-cell suspension using the Worthington Papain Dissociation System kit (Worthington Biochemical). Cells were counted on the LUNA-FX7 Automated Cell Counter (Logos Biosystems) using fluorescence detection for viability with an acridine orange/propidium iodide stain (Cat#F23011). The sample was 98.3% viable and had a concentration of ~1000 cells/ul. After counting, the sample was loaded into Chip G per the user guide from 10x Genomics, and no alterations were made at any step of the protocol (Cat#CG000315). GEMs were formed targeting 10,000 cells and reverse transcription completed immediately after. The cDNA was cleaned from the GEM reagents, amplified for a total of 11 cycles and verified via TapeStation (Agilent Technologies). Amplified cDNA was diluted and ran on the 4200 TapeStation instrument using High Sensitivity D5000 tape and reagents (Cat#5067-5592 & 5067-5593). The amplified cDNA was fragmented, end repaired, and A-tailed followed by adaptor ligation, and PCR amplification for a total of 11 cycles with each sample receiving a unique set of dual indices (Cat#1000215). Final libraries were diluted and ran using the High Sensitivity D5000 tape and reagents (Cat#5067-5592 & 5067-5593) on the 4200 TapeStation (Agilent Technologies). Libraries were quantified via Kapa qPCR using the Complete Universal Kit (Cat#07960140001, Roche Sequencing Solutions) and the CFX96 Touch Real-Time PCR Detection System (Bio-Rad Laboratories). Libraries were sequenced on an Illumina NovaSeq instrument using the parameters outlined in the user guide (Read1: 28 bp, i7 index: 10 bp, i5 index: 10 bp, Read2: 90 bp). After sequencing and demultiplexing, the Cell Ranger count pipeline was used to align reads to the GRCh38 human reference genome and produce the associated cell by gene count matrix.

Cells with 5,000 to 50,000 reads were subsampled to a obtain a read count of 5,000 for each cell. Sparse multimodal decomposition (SMD) ²⁴ was performed in Python on the subsampled count matrix. Genes with a Z score from SMD greater than 0 were filtered to remove genes with a log normalized expression mean or standard deviation less than 0.02, genes expressed in more than 90% or less than 10% of cells, and genes associated with the cell cycle, resulting in a list of 26 genes.

To cluster cells in this 26-gene space, we scaled genes to have unit variance and zero mean, then performed Louvain clustering at a resolution of 0.75 using scanpy⁵⁵. We obtained 5 clusters, which were annotated manually based on expressed genes. Diffusion map analysis was performed using the diffusion pseudotime (DPT) method¹⁹ in scanpy. The root cell was selected to be a cell from the axial progenitor cluster with the highest value along the first principal component from principal component analysis. To generate a pseudo-spatial gene expression heatmap, cells were ordered by pseudo-spatial index and their raw gene expression values were smoothed using a Gaussian filter with a kernel size of 300 cells. Genes were then ordered by the center of mass of smoothed gene expression values. To generate pseudo-spatial gene expression plots for individual genes, raw gene expression values were binned into 20 bins of equal size and their mean and standard deviation within each bin was plotted.

To generate a list of transcription factors, receptors, and secreted factors enriched posteriorly and anteriorly, respectively, genes from the corresponding protein classes of the human protein atlas ⁵⁶ were filtered to keep only those genes whose expression in each progenitor cluster was at least 1.5-fold larger than the next most anterior or posterior cluster. To combine mouse and human data, following pre-processing of each dataset, Louvain clustering at a resolution of 0.8 was performed in scanpy in the space of the concatenated list of posterior and anterior transcription factors across all 4 progenitor clusters, after first filtering out genes that were species-specific.

Mapping in vitro and in vivo single cell data

To compare our day 4 organoid data against an in vivo mammalian counterpart, we examined mouse single cell data obtained from the posterior region of two E9.5 mouse embryos ⁴⁵. Mouse and human count matrices were each normalized to 10000 reads per cell, and only genes with greater than 0.02 mean and standard deviation across cells were used for further analysis. Mouse cells were clustered using Leiden clustering (resolution = 0.03) and filtered for clusters that expressed SOX2+ (neural marker) or TBXT+ (NMP marker) but not TBX6 (mesodermal marker). After concatenating mouse dataset with our human dataset, which was pre-processed identically to before, we performed Louvain clustering (resolution = 0.8) in the space of anterior and posterior transcription factors identified across clusters in human data alone in the space of bimodally expressed genes returned by the sparse multimodal decomposition (SMD) algorithm ²⁴. The top differentially expressed genes between mouse and human species based on a Wilcoxon rank-sum test (HES5 and SOX3) were filtered out, and genes known to be differentially expressed between NMPs and non-NMPs were appended (SOX2 and TBXT). Human cells were subsampled to match the number of mouse cells (n=960 cells). Louvain clustering enabled classification of the combined human-mouse population into 5 cell types, including 3 neural tube progenitor cell types and 2 axial progenitor cell types. These corresponded to the 4 progenitor cell types identified from the in vitro human dataset, and NMPs from the in vivo mouse dataset. All NMPs in the combined dataset were derived entirely from mouse, while both mouse and human cells contributed to the other 4 cell types.

We evaluated the mean expression of all transcription factors in each cell type. Axial progenitors in the combined human-mouse dataset were all CDX2+ HOXB9+, and were found to further cluster into two populations, consisting of TBXT+ SOX2-low cells and TBXT− SOX2+ cells. We classified these populations as neuromesodermal progenitors (NMPs) and pre-neural tube (PNT) progenitors, respectively. All NMPs were derived from the mouse dataset alone, while the human dataset lacked NMPs. NMPs expressed several transcription factors in addition to high level of TBXT and a low level of SOX2, including LEF1, ZIC3, ETV4 and ETV5. PNT progenitors were transcriptionally distinct from NMPs, with a lack of TBXT expression and high levels of SOX2, GBX2, and ZIC5. Correlation analysis of human and mouse cell types revealed a high correlation of human progenitor cell types with mouse (r > 0.7), whereas mouse NMPs poorly correlated with all human cell types (r < 0.4). A Wilcoxon rank-sum test across NMP and PNT clusters revealed additional differentially expressed transcription factors between the two axial progenitor populations: ETS2, ARID3B, ARID1A, EVX1, HES7, SALL4, SALL3, and FOXD1 in NMPs and ZIC2, GBX2, GTF3A, HMGA1, ADNP, and SMARCA1 in PNT progenitors (Fig. S7F). As validation of these markers, several genes have been previously observed to mark the tailbud population in mouse embryos, including SALL4 and ETV transcription factors in NMPs ^57,58 and ZIC2 in PNT progenitors ²⁵ and play distinct roles in caudal morphogenesis ^59,60. Other markers, such as ARID3B, have been shown to localize to the tailbud but as of yet have no known roles in this region of the embryo ⁶¹. Unlike axial progenitors, neural tube progenitors were all CDX2− and SOX1+ MEIS2+. Within neural tube progenitors, spinal cord progenitors were enriched for posterior HOX genes including HOXB9 through HOXB3. Posterior hindbrain progenitors expressed higher levels of NR2F1, NR2F2, POU3F2, and PBX3, while anterior hindbrain progenitors expressed higher levels of ID1, MAFB, and anterior HOX gene HOXA2. A Wilcoxon rank-sum test pulled out these same sets of transcription factors between the two hindbrain populations, along with SOX4, HMGA1, and NR6A1 in posterior hindbrain and EGR2, HES5, IRX2, and POU3F1 in anterior hindbrain.

Signaling genes in the FGF and WNT pathways expressed by NMPs and PNT progenitors were characterized based on Table 1. An unbiased analysis revealed differentially expressed genes between the two compartments. Several FGF and WNT ligands, including FGF8, FGF17, WNT5A, and WNT5B, were expressed in both populations, but at higher levels in NMPs than in PNT progenitors. WNT inhibitors SFRP1 and SFRP2 were also present in both cell types, but expressed at higher levels in PNT progenitors relative to NMPs. Canonical WNT ligand WNT3A as well as canonical WNT inhibitors DKK1 and IGFBP4 were specifically expressed in mouse NMPs, while FGF ligand FGF2 was specifically expressed in human PNT progenitors and FGF ligand FGF3 was enriched in both NMPs and in hindbrain, but not PNT progenitors.

In situ sequencing (STARmap)

Glass-bottom 24-well plates (Cellvis, P24-1.5H-N) were treated with oxygen plasma for 5 mins (Anatech Barrel Plasma System, 100W, 40% O2) and followed by methacryloxypropyltrimethoxysilane (Bind-Silane) coating solution (88% ethanol, 10% acetic acid, 1% Bind-Silane, 1% H2O) treatment for 1 hour. The 24-well plates were rinsed with ethanol 3 times and left to dry at room temperature for 3 hours. Micro cover glasses (12 mm) were pretreated with Gel Slick at RT for 15 mins and air-dried before using.

Neural tube organoids were fixed with 1 mL 4% PFA for 30 mins at RT and then washed with PBS 3 times for 10 mins each time. The sample was permeabilized with 1 mL (0.1M glycine, 0.1 U/μL SUPERase·In, 0.5% Triton-X 100 in PBS) for 30 mins and then washed with 1 mL PBST (0.1% Triton-X 100 in PBS) 3 times for 10 mins each. The sample was then incubated in 1X hybridization buffer (2X SSC, 10% formamide, 1% Triton-X 100, 20 mM RVC, 0.2% SDS, 0.1 mg/mL yeast tRNA, and pooled SNAIL probes at 10 nM per oligo) in a 40°C oven with shaking for 48 hours. The sample was washed with 1 mL PBSTV (1% RVC in PBST) at 37°C 3 times for 20 mins each, and then washed with PBST three times for 10 mins each at RT The sample was then incubated in a 1 mL ligation mixture (1:50 T4 DNA ligase, 1:100 BSA, 0.2 U/μL SUPERase-In) at RT overnight and then washed with 1 mL PBST three times for 10 mins each. The sample was incubated in 1 mL RCA mixture (1:50 Phi29 DNA polymerase, 250 μM dNTP, 1:100 BSA, 0.2 U/μL SUPERase-In and 20 μM 5-(3-aminoallyl)-dUTP) at 4°C for 1 hour before incubating at 30°C for 6 hours and then washed with 1 mL PBST 3 times for 10 mins each. The sample was incubated with 20 mM methacrylic acid N-hydroxysuccinimide ester in PBST for 3 hours at RT and washed with PBST 3 times for 10 mins each. The sample was then incubated with monomer buffer (4% acrylamide, 0.2% bis-acrylamide, 2X SSC) overnight at RT The buffer was then aspirated, and 55 μL of polymerization mixture (0.2% ammonium persulfate, 0.2% tetramethylethylenediamine dissolved in monomer buffer) was added to the sample. The Gel Slick coated coverslip was immediately put on the sample, and the polymerization was conducted in an N2 container for 90 mins. The sample was then washed with PBST 3 times for 10 mins each.

Two cycles of sequencing experiments were performed to decode gene identity. Within each cycle, the sample was first treated with a stripping buffer (60% formamide, 0.1% Triton-X-100) at RT 3 times, 15 mins each, followed by PBST wash for 4 times, 10 mins each. Then the sample was incubated with the sequencing mixture (1: 25 T4 DNA ligase, 1: 100 BSA, 10 μM reading probe, and 5 μM fluorescent oligos) at RT for 12 hours. Then the sample was washed by the washing and imaging buffer (2XSSC, 10% formamide, and 0.1% Triton-X-100) 4 times, 10 mins each. DAPI was dissolved in PBST and used for nuclei staining for 2 hours before the first sequencing cycle. Finally, the sample was immersed in the washing and imaging buffer for imaging. Image acquisition was performed with Leica TCS SP8 confocal microscopy with 25X water-immersion objective (NA 0.95).

A data analysis pipeline was built with MATLAB 2019b to decode gene identity and quantify the gene expression level of each cell from the STARmap images. First, sequencing fluorescence images were preprocessed with top-hat filtering by a disk structuring element (radius = 3) to remove the background noise. Second, the contrast of the image for each channel from the second sequencing cycle was adjusted to match the image from the first cycle with histogram matching function imhistmatchn. Third, the composite fluorescence images for the second cycle were registered with the composite fluorescence image from the first cycle using a phase correlation algorithm followed by local distortion registration with function imregdemons. Fourth, the dots of amplicon locations were identified from images in the first cycle by a 3D regional maximum detection algorithm implemented in function imregionalmax. Then the dominant color of every identified dot in each cycle was determined by a 3×3×3 voxel volume surrounding its centroid location. The color sequence for each dot was decoded as a gene barcode and compared with the code-book. Fifth, cell segmentation was performed with ClusterMap ⁶² and CellProfiler ⁶³ then RNA reads were assigned to the segmented cells accordingly, described in detail as follows.

We first used the IdentifyPrimaryObjects function from CellProfiler to segment the DAPI stained nuclei images and then assign each decoded RNA to the segmented nuclei. We next applied ClusterMap to assign RNA out of the nuclei to the corresponding cell. ClusterMap identified cells by incorporating the physical location and gene identity and directly clustering spots of RNAs and DAPI signals. Specifically, to quantify and utilize gene expression information in each spot's local neighborhood, ClusterMap introduced a high-dimensional vector, termed neighborhood gene composition (NGC), which was computed by considering gene expression profiles in a circular window over each RNA spot. The NGC coordinates and physical coordinates of each RNA spot are then computationally integrated into joint physical and NGC (P-NGC) coordinates over each RNA spot. Next, ClusterMap aimed to cluster the RNAs in the P-NGC coordinates for downstream segmentation by density peak clustering (DPC) ⁶⁴. DPC identifies cluster centers with a higher density than the surrounding regions as well as a relatively large distance from points with higher densities. ClusterMap applied DPC to compute two variables: local density ρ and distance δ for each spot in the joint P-NGC space. For each spot, ρ value represents the density of its closely surrounded spots, and δ value represents the minimal distance to spots with higher ρ values. Spots with both high ρ and δ values are highly likely to be cluster centers. ClusterMap then ranked the product of these two variables, γ, in decreasing order to find genuine cluster centers with orders of magnitude higher γ values. After the cluster centers have been selected, the remaining spots are assigned to one of the clusters respectively in descending order of ρ value. Each spot is assigned to the same cluster as its nearest previously assigned neighbor, and each cluster of spots represents an individual cell. Outliers that were falsely assigned among cells can be filtered out using noise detection in DPC. ClusterMap showed identified cells with more precisely outlined cell boundary and illustrated cell morphology and consistent performance among various in situ transcriptomics datasets. The detailed introduction, discussion, and analysis of ClusterMap performance on cell segmentation can be found in our previous report ⁶².

R package Seurat3 was used for the single-cell gene expression analysis. Gene counts of each cell were normalized so that the total count of all genes in each cell equals 100. The normalized count value is then log-transformed with log(x+1). The data normalization was performed with the NormalizeData function in Seurat with a scale factor = 100. Each gene in the cell-by-gene matrix was scaled to unit variance and zero mean with ScaleData function in Seurat followed by dimensionality reduction with principal components analysis (PCA) using RunPCA function in Seurat. Based on the explained variance ratio, the top 10 principal-components were used to construct the k nearest neighbor (kNN) graph for Louvain clustering using FindNeighbors and FindClusters function in Seurat. Uniform Manifold Approximation and Projection (UMAP) was used to visualize the 2D representation of each cell using the RunUMAP function in Seurat. Monocle ^65,66 was used to compute pseudotime along the cell trajectory with UMAP as input with the order_cells function in Monocle3. The CDX2 positive axial progenitor cells were specified as root cells for pseudotime prediction.

Hybridization chain reaction (HCR)

HCR was performed on organoids following a previously published protocol ⁶⁷. Briefly, after fixation with 4% PFA, organoids were washed twice in PBS + 0.1% Tween20 (PBST) and dehydrated in increasing concentrations of methanol in PBST and stored at −20°C. Organoids were rehydrated in decreasing concentrations of methanol in PBST and treated with 25 μg/ml Proteinase K for 4 minutes at room temperature. After two washes in PBST, organoids were refixed in 4% PFA in PBST for 20 minutes at room temperature. After three washes in PBST, organoids were treated with 2 pmol hybridization probe in 0.5 ml probe hybridization buffer, and incubated overnight at 37°C. The following day, organoids were washed three times with probe wash buffer, and twice with 5X SSCT buffer. 6 pmol of amplifier hairpin h1 and h2 were snap-cooled by heating at 95°C for 1.5 minutes and cooling to room temperature for 30 minutes, then added to organoids in 0.1 ml amplification buffer along with DAPI, and incubated overnight at room temperature. The following day, organoids were washed twice in 5X SSCT and twice in PBST before transferring to a glass-bottom well plate for imaging. The following accessions were used to design hybridization probes: SOX2 (NM_003106), WNT5A (NM_003392), WNT5B (NM_032642).

Cloning guide RNA plasmids

pgRNA-CKB ³⁴ and pLKO5.sgRNA.EFS.GFP ⁶⁸ vectors were digested with BsmB1 (NEB R0739) for 1 hr at 37°C and gel purified. Guide RNA (gRNA) sequences were generated using the Broad Institute BPP sgRNA Designer where three gRNAs were designed per target gene. gRNA sequences were ordered as 20 bp single stranded oligos from Integrative DNA Technologies (IDT) containing the BsmBI-v2 (NEB R0739) restriction enzyme sticky end on the 5’ end of the forward oligo and the 3’ end of the reverse oligo. The two oligos per gRNA were duplexed together to generate double stranded DNA for cloning by mixing 25 μL of each 100 μM reconstituted oligo and 2 μL T4 Ligase Buffer (NEB B0202). The reaction was heated to 100°C for 5 min and cooled to room temperature over 20 min. Duplexed gRNAs were diluted 1:10000 in water and 14 μL added to a ligation reaction (NEB M0202). Ligation was allowed to proceed for 1 hr at RT, after which 2 μL was transformed into NEB Stable competent E. coli (NEB C3040H) competent cells by heat shock at 42°C for 30 seconds. Colonies were PCR screened and verified by Sanger Sequencing via Genewiz Plasmids were grown and stored in NEB Stable E. coli. We generated at least 3 gRNA plasmids targeting each of CDX2, WNT5A, WNT5B, SFRP1, and SFRP2. Of these, a single gRNA was ultimately chosen for each gene based on the fluorescence intensity of the generated clones as a proxy for expression level in the cell.

The following guide RNA sequences were used for line generation: mKate2 control (GGAGACGTGACCGTCTCT), GFP control (GGAGACGGACGTCTCC), sgCDX2 (TCTGCAGCCTAGTGGGAAGG), sgWNT5A (CCTGAGTGAATTACCCAGGA), sgWNT5B (GGGGAAGTTTCGGCCCAAGT), sgTBXT (TATTCCACTTGAACTCCCCA), sgSFRP1 (CGGAGGTGCGGCGAGCAGGA), and sgSFRP2 (ACGGCTCATTCTGCTCCCCC). For verification of integration of the gRNAs by Sanger sequence, we used oligos 5’ GAGTTAGGCAGGGATATTCACC 3’ for the pgRNA-CKB vector and 5’ CTGCCCCGGTTAATTTGCA 3’ for the pLKO5.sgRNA.EFS.GFP vector. pgRNA-CKB was a gift from Bruce Conklin (Addgene #73501). pLKO5.sgRNA.EFS.GFP was a gift from Benjamin Ebert (Addgene #57822).

Lentiviral transduction of guide RNAs

One day before viral production, Lenti-X 293 T HEK cells (Takara Bio 632180) were split 1:10 into a tissue culture treated 6-well plate (Stellar Scientific CT229106) in 10% fetal bovine serum (FBS) in DMEM/F12 (Thermo Fisher 11039021) and left to grow overnight at 37°C and 5% CO₂. The next day, plasmids for second generation lentiviral production: envelope expressing plasmid pMD2.G + packaging plasmid psPAX2 + guide RNA plasmid were mixed in 0.197:0.355:0.449 molar ratios, respectively, in 200 μL JetPRIME Buffer + 4 μL JetPRIME Reagent (Polyplus, VWR 114-07). The reaction was incubated for 10 min at room temperature and added dropwise to HEK cells for transfection. 4 hrs post transfection, media was removed from HEK cells using lentiviral BSL2+ safety protocols and replaced with 5% FBS in DMEM/F12. Media containing virus was harvested 24 and 48 hours post-transfection and then concentrated using Lenti-X Concentrator (ClonTech 6311231). First, media was spun at 500g for 15 min and supernatant was transferred to a new conical tube. 2 mL of Lenti-X Concentrator was added and mixed by gently flicking. The mixture was incubated for at least 30 min incubation at 4°C, and spun down at 1500g for 45 min at 4°C to pellet virus. Supernatant was disposed of in bleach and viral pellet was resuspended in 200 μL mTeSR Plus and stored at 4°C for up to 2 weeks. pMD2.G and psPAX2 were gifts from Didier Trono (Addgene #12259, Addgene #12260).

Lentiviral titrations were pre-determined using a serial dilution assay on stem cells. Once a titer was determined, the volume of virus was added dropwise to hPSCs. Cells were treated as lentivirus positive and handled in BSL2+ conditions for at least 3 days post transduction. Media was changed daily with mTeSR Plus and cells were washed 3 times with DPBS (Lonza). After the third day cells were removed from secondary containment and treated as lentivirus negative samples. Cells were sorted by FACS (based on either mKate2 or GFP fluorescence) six days post transduction. To transduce micropatterns directly, harvested virus was added dropwise to micropatterned cells several hours after seeding. To simultaneously knock down SFRP1 and SFRP2, HEK cells were separately transfected by an mKate2-expressing SFRP1 gRNA construct and a GFP-expressing SFRP2 gRNA construct. Harvested viruses were pooled and added to hPSCs, and FACS was performed for mKate2+ GFP+ cells.

Fluorescence-activated cell sorting for cell line generation

Accutase-dissociated cells were sorted using a BD Aria III (BD Biosciences) using a 100 μm nozzle. Cells were gated such that the RFP+ or GFP+ population was taken as the cells with the top 1% fluorescence intensity in FITC or PE channels. One cell was sorted per well of a 96 well plate filled with 100 μL of expansion media, composed of mTeSR Plus supplemented with 10 μM Y-27632 and 1X CloneR (Stem Cell Technologies 5889). Expansion media was replaced every 2 days until cells formed confluent colonies, then passaged into a 6-well plate where they were maintained as normal cell lines. In all cases, cell lines with the brightest mKate2 or GFP fluorescence were selected for mutant analysis. Lines were subsequently screened for a phenotype in our organoid differentiation assay.

Mathematical model of symmetry breaking

Here we provide the reader with a mathematical intuition for why coupling between organoids coordinates their symmetry breaking. As stated in the main text, physical systems with coupled degrees of freedom have a low entropy ground state with broken symmetries. The question is whether we can similarly couple organoids to make their symmetry breaking effectively deterministic. The cells of the organoid are not just passive recipients of signals. In response, they secrete signals of their own. This is the fact that we take advantage of to couple organoids.

To appreciate qualitatively how this might happen, consider a simple model where a symmetry breaking event occurs, leading to appearance of two distinct cell types, anterior and posterior. Cells respond to an activator W by adopting the posterior fate. Additionally, cells secrete a diffusible signal molecule S that opposes the activator by inhibiting the posterior fate and promoting the anterior fate.

Let the signal S have a lifetime τ and a diffusion constant D. Thus the concentration of S, denoted by S for simplicity, obeys the following equation: $\frac{\partial S}{\partial t}=D{\nabla }^{2}S-\frac{S}{\tau }$. The fate adopted by the cells is θ(W − S) where θ(x) is the Heaviside step function, and 1 represents a posterior fate, while 0 represents an anterior fate. Therefore when S > W as measured by a cell, it adopts an anterior fate, while when S < W it adopts a posterior fate. This is equivalent to an infinite Hill coefficient term driving the expression of the anterior and posterior targets.

We can intuitively guess what will happen: molecules of S will diffuse a distance Dτ before they are absorbed or otherwise disintegrate. If any region of neighboring organoid is roughly within this distance, the S secreted by the first organoid will combine with the S secreted by the second organoid. Otherwise the first organoid will have no effect on the second. Therefore, if the organoids are arranged in the right way, it will be possible to get them all to coherently make S in the regions where they are close to each other, robustly inhibiting the posteriorizing effect of the activator W in those regions.

To go beyond these intuitive arguments, we implemented a simple simulation in MATLAB, consisting of a 2D representation of our experiment. We used the built-in partial differential equation solver in order to evolve the concentration of S in time.

Using parameter values D = 0.25 and τ = 1, we simulated 6 organoids arranged hexagonally in a similar fashion to our experimental setup, with an edge-to-edge spacing of 0.5 arbitrary length units. The circular organoids are defined as sources of the signal and thus have a Neumann boundary condition with a constant production rate $\frac{\partial S}{\partial t}=\lambda$, with λ set to 1, while the edges of our system are held at S = 0 for all time t. To initialize the simulation we start with a value of S = 0 everywhere in space. We then evolved the simulation in time steps of δt = 0.1 for 250 steps, by which time the profile of S had reached a steady state.

The model above considered a secreted signal that diffuses. The increased concentration of the signal in the interior is solely due to the proximity of the organoids. If in addition, there is positive feedback (in response to S, the organoids secrete more S), this effect will be further enhanced.

Mathematical model of excitable system

Here we provide a mathematical intuition for how the excitable system underlying axial elongation is prone to instabilities. As stated in the main text, posterior signals such as FGF and WNT are produced in the posterior region of organoids. If these signals are involved in a positive feedback loop, then they have the capacity to trigger runaway signaling events. These runaway events may be prevented by secreted inhibitors of FGF and WNT signaling.

To appreciate how this may happen, we build upon our mathematical model of a generalized diffusible inhibitor. We again assume that the inhibitor is secreted uniformly across the organoid with lifetime τ and diffusion constant D, i.e., $\frac{\partial S}{\partial t}=D{\nabla }^{2}S-\frac{S}{\tau }$. In addition, we assume that activator W activates more W secretion, and enhances W signaling activity. We also assume that W is much less diffusive than its inhibitors, and set its diffusion constant to zero. We assume that S inhibits W by binding to it, making it incapable of binding to the cell surface receptor (as is the case with many secreted inhibitors). Thus the effective level of W at any point in space is W_eff = W − S at that location. We then write the dynamics of activator production at each location $\overrightarrow{r}$ on the surface of the organoid to be $\frac{\partial W}{\partial t}=B\frac{(\frac{W_{\text{eff}}}{W_0}{)}^n}{1+(\frac{W_{\text{eff}}}{W_0}{)}^n}-\frac{W}{\tau }$ where S is the concentration of the inhibitor at that location, τ is set to 1 representing the degradation of the molecule over time, and the second term represents a nonlinear feedback of the activator onto itself. The Hill coefficient n is set to 3. Starting the system with the initial activator concentration throughout the organoid at W(t = 0) = 0.5, we chose parameter values B = 1, S₀ = 0.3, W₀ = 0.2, such that W_max = 1 and $\frac{\partial W}{\partial t}=0\text{at}S=S_0$. We simulated this system of equations using MATLAB as before to generate the results in Figure 4G and 4H. We evolved the values of W with S already in its steady state profile. We used time steps of δt = 0.001 for 10000 steps, by which time the profile of W had reached a steady state, and a clear elongation front was apparent. In addition, we perturbed the steady state with an ectopic pulse of activator (W = 0.5) far away from the tailbud in two conditions. First, levels of S were determined by the steady state concentration of S according to its partial differential equation. Secondly, levels of S were turned to 0 everywhere. This pulse was also allowed to evolve for 10000 steps of δt = 0.001.

QUANTIFICATION AND STATISTICAL ANALYSIS

Gene expression and length quantification along organoid A-P axis

To quantify gene expression along the A-P axis of each organoid, gene expression images were projected onto the organoid midline, computed by skeletonizing the segmented image using the skimage package in Python. For all experiments, a gene expression domain was counted as present in an organoid if it contained a region that exceeded the half-maximal expression of the gene under control conditions (except in the case of TBXT, where it was defined as the half-maximal expression under FGF pulse conditions).

To quantify A-P axis lengths, segmented regions of interest were used to compute either the Feret diameter or major axis corresponding to the ellipse of best fit using the minEnclosingCircle and fitEllipse functions from the cv2 package in Python. The Feret diameter was used for all length quantification unless otherwise specified, but was highly correlated with major axis across timepoints (r=0.99, Fig. S1H). For experiments where time series information was available, the relative A-P length on day 4 was computed by dividing by the length on day 1.

Proliferation index quantification

Tailbud proliferation index was defined as the ratio of pHH3+ cells to DAPI+ cells in either the CDX2+ or SOX1− region of the organoid, depending on the antibody stain used. Due to the difficulty of segmenting cells in the DAPI channel, the DAPI+ area of occupied by the organoid was divided by the average area of a pHH3+ cell across organoids to determine the effective number of cells. This likely produced an underestimate of the number of cells, and therefore an overestimate of the fraction of cells undergoing mitosis, as DAPI+ nuclei were pseudostratified and therefore multi-layered, while pHH3+ nuclei were apical only (Fig. 1N). Thus we dubbed this measure as the tailbud proliferation index, which enables comparisons of relative proliferation rates between organoids.

Supplementary Material

1

Fig. S1. Spatial coupling of organoids influences their axial patterning and morphogenesis, related to Fig. 1. (A) Randomly generated micropattern arrays at low density (first and second column), medium density (third column), and high density (fourth column). Micropatterns have a diameter of 150 μm and a minimum spacing of 50 μm, and fit in an 8000 by 8000 μm region (see Methods S1). (B) Organoids from random arrays in (A) on day 4, stained for SOX1 (blue) and CDX2 (red). n=2373 organoids total. Scale bar 1 mm. (C) Three replicate experiments (left, middle, right) on a low-density random array on day 4, stained for DAPI (top) and SOX1 and CDX2 (bottom). (D) Mean coefficient of variation in measured polarization μ (top) and length based on Feret diameter (bottom) for organoids across and within replicate experiments in (C) (n=105 organoids per experiment). (E) Fluorescence confocal images of organoids from hexagon array on day 4 stained for SOX2, N-cadherin (NCAD), and F-actin (ACTIN). Scale bar 100 μm. (F) Overlay image of organoid contours in a single experiment from day 1 to day 4. Scale bar 1 mm. (G) Organoids on a hexagonal array on consecutive days 1, 2, 3, and 4 stained for DAPI, SOX1, and CDX2. Scale bar 1 mm. (H) Top: Plot of CDX2 expression across organoids on hexagonal array as a function of normalized A-P position on consecutive days (see STAR Methods). Midline represents mean, shaded region denotes standard deviation (n=216). Bottom: Correlation between major axis and Feret diameter for organoids on hexagonal array on consecutive days (r = 0.99). (I) Measured polarization of organoids on hexagonal array on day 1 and day 2. Points indicate organoid centroids. Scale bar = 1 mm. (J) Histogram of measured polarization of organoids on hexagonal array on Day 1 and Day 2 (day 1, n=203; day 2, n=214). (K) Polarized fraction of organoids on day 1 and day 2, where an organoid is polarized if it is above a threshold value, which is varied from 0 to 1 (AUC = 0.999).

2

Fig. S2. Controlled organoid A-P symmetry breaking and morphogenesis, related to Fig. 1. (A) Top: Diagram of conditioned media experiment. On days 1 and 3, media on a random low density array is replaced with media from a matched random high density array (see STAR Methods). Middle: Organoids from control and conditioned low density arrays on day 4, stained for CDX2 (red) and SOX1 (blue). Bottom: Histogram of CDX2+ and SOX1+ fraction of organoids from control and conditioned arrays. Conditioned organoids exhibit a shift toward a lower CDX2+ fraction and higher SOX1+ fraction. (B) Left: Organoids from hexagonal arrays with 200 μm (top), 400 μm (middle), and 800 μm (bottom) intra-hexagon spacings on day 4, stained for CDX2 and SOX1. Scale bar = 1 mm. Middle: Corresponding measured polarization of organoids from hexagonal arrays with different spacings. Bottom right: Polarized fraction of organoids with 200 μm, 400 μm, and 800 μm spacings, where an organoid is polarized if it is above a threshold value, which is varied from 0 to 1 (200 μm vs. 400 μm: AUC=0.71, 400 μm vs. 800 μm: AUC=0.52). (C) Confocal sections of three elongating organoids on day 4, stained for SOX1, CDX2, and ZO1. Scale bar = 100 μm. (D) Organoids from hexagonal arrays on day 4, with or without release from LDN treatment on day 2, stained for DAPI, SOX1, CDX2, and paraxial mesoderm marker TBX6. Lack of TBX6 expression indicates LDN is dispensable from day 2 for preventing mesoderm formation. Scale bar = 1 mm.

3

Fig. S3. Validation of cell types and signaling profiles in elongating organoids, related to Fig. 2. (A) Top: Average gene expression values of posteriorly (left) and anteriorly (right) enriched transcription factors across Louvain-clustered progenitor cell types (AP = axial progenitor, SC = spinal cord, PH = posterior hindbrain, AH = anterior hindbrain. Known targets or effectors of WNT and FGF pathways are highlighted in orange. Bottom: Posteriorly (left) and anteriorly (right) enriched G-protein-coupled-receptors across Louvain-clustered progenitor cell types. Receptors of WNT and FGF pathways are highlighted in orange. Gene expression values are min-max normalized across cell types per gene. (B) Top; Average gene expression of top differentially expressed secreted genes across progenitor clusters, enriched in posterior (left) or anterior (right) cell types. WNT and FGF ligands, inhibitors, and other pathway genes are highlighted in orange (see Table 1 for full list). Gene expression values are min-max normalized across cell types per gene. Gene expression values are min-max normalized across cell types per gene. Bottom: Most abundant secreted genes across cell types. Gene expression values are min-max normalized across cell types and genes. (C) UMAP plot of cells from scRNA-seq colored by log-normalized gene expression. Rows correspond to different classes of genes, including (1) posterior marker genes, (2) anterior marker genes, (3) HOX genes, (4) WNT ligands, (5) WNT inhibitors, (6) WNT pathway genes, (7) FGF ligands and receptors, (8) FGF targets and effectors, (9) mesodermal marker genes. (D) PCA plot of cells from scRNA-seq along first two principal components (PC1 and PC2) in 26-dimensional gene space, colored by cell type. (E) Diffusion map of cells from scRNA-seq (see STAR Methods) plotted along two diffusion components (DC1 and DC2), colored by cell type. (F) Gene expression heatmap of cells (n=359) from organoid sample 1 on day 4 using in situ sequencing (STARmap). Cells clustered in a 16-gene space selected based on diffusion map analysis (see STAR Methods) show axial progenitor (CDX2+ CRABP1−), spinal cord (CDX2+ CRABP1+), posterior hindbrain (CDX2− CRABP1+ EGR2−), and anterior hindbrain (CRABP1+ EGR2+) progenitor identities. Expression values are log− and z-score-normalized across cells. (G) Top: UMAP plot of cells from STARmap applied to organoid sample 1, colored by cell type. Bottom: Fraction of cell types along the elongation axis (x), partitioned into 10 bins of equal length. (H) Top: UMAP plot of cells from STARmap applied to organoid sample 1, colored by pseudo-spatial coordinate inferred from diffusion map analysis (left) and spatial coordinate defined along elongation axis, x (right). Bottom left: Correlation plot of pseudo-spatial coordinate and spatial coordinate x (r = 0.81, p < 2e-16). Bottom right: Plot of cells from STARmap in physical space, where x is the elongating axis and y is the perpendicular axis, colored by pseudo-spatial coordinate. (I) Spatial P-A gene expression profiles for selected genes from STARmap applied to organoid sample 1 (top, n=359 cells), 2 (middle, n=610 cells), 3 (bottom, n=637 cells) colored by cell type. Each plot displays mean (black) and per-cell (points) log-normalized relative expression values partitioned 10 bins of equal length.

4

Fig. S4. Comparison of human and mouse single-cell data, related to Fig. 2. (A) Heatmap of gene expression matrix of combined human and mouse dataset clustered in the space of differentially expressed transcription factor marker genes across cell types in human-only dataset (see STAR Methods). White-to-blue color scale: Normalized mouse gene expression, White-to-red color scale: Normalized human gene expression. Cell types are annotated by marker gene expression. (B) Distribution along 2 UMAP components of human and mouse cells combined (top), human cells only (middle), or mouse cells only (bottom), colored by cell type. (C) Heatmap of Pearson correlation between human and mouse cell types. (D) Top: Plots in (B) colored by species, mouse (black) or human (gray). Bottom: Number of mouse (black) or human (gray) cells of each cell type in combined dataset. NMP = neuromesodermal progenitors, PNT = pre-neural tube, SC = spinal cord, PH = posterior hindbrain, AH = anterior hindbrain. (E) Matrix plot showing mean marker gene expression levels across cell types in combined human and mouse dataset. Gene expression values are normalized across genes to the value per cell type. (F) Left: Top 20 transcription factor genes from NMP (top) and PNT (bottom) clusters based on Wilcoxon rank-sum test across NMP, PNT, and SC cell types. Right: Top 20 transcription factor genes from PH (top) and AH (bottom) clusters based on Wilcoxon rank-sum test across AH, PH, and SC cell types. (G) Matrix plot showing mean FGF ligand (left), WNT ligand (middle) and WNT inhibitor (right) gene expression levels across cell types in combined dataset. Gene expression values are normalized to the maximum value across genes and cell types. (H) UMAP plots showing the distribution of log-normalized gene expression values of most highly expressed FGF and WNT ligands and inhibitors across cells. Plots of human cells display the full non-subsampled dataset (n=8013 cells).

5

Fig. S5. WNT ligands drive elongation downstream of FGF/ERK-dependent CDX2 expression, related to Fig. 3. (A) Control (top), IWP3-treated (middle), and PD0-treated (bottom) organoids on day 4 stained for DAPI (left) and SOX1 and CDX2 (right). Scale bar 1 mm. (B) Plot of CDX2 expression across control (top, n=211), IWP3-treated (middle, n=176), and PD0-treated (bottom, n=157) organoids as a function of normalized A-P position. Midline represents mean, shaded region denotes standard deviation. (C) Control (top), delayed IWP3-treated (middle), and delayed PD0-treated (bottom) organoids on day 4 stained for DAPI (left) and SOX1 and CDX2 (right). Scale bar 1 mm (D) Plot of CDX2 expression across control (top, n=212), delayed IWP3-treated (middle, n=214), and delayed PD0-treated (bottom, n=211) organoids as a function of normalized A-P position. Midline represents mean, shaded region denotes standard deviation. (E) DKK1-treated organoids on day 4 stained for DAPI (left) and SOX1 and CDX2 (right). (F) Control (left), WNT3A-treated (middle), and WNT3A+DKK1-treated (right) hPSC colonies on day 2 stained for SOX2 and TBXT. DKK1 treatment prevents emergence of TBXT+ cells in response to WNT3A. (G) Stereomicroscope images of control (top) and delayed IWP3-treated (bottom) ZO1-EGFP organoids on consecutive days. (H) Net cell displacement vectors for tracked cells in control (top) and delayed IWP3-treated (bottom) organoids for 14 hours starting on day 2. Horizontal black arrow indicates direction of axis elongation. Scale bar 100 μm. (I) Left: Representative live fluorescence images of H2B-mCherry+ cells in control organoids before (left) and after cell (right) division. θ₁ and θ₂ mark cell division angles relative to the axis of elongation (horizontal white arrow). Scale bar: 10 μm. Right: Histogram of cell division angle relative to the axis of elongation in control organoids over 12 hours starting on day 2 (n=121). (J) CRISPRi organoids containing an mKate2-expressing control (top) or CDX2-targeting (bottom, sgCDX2) gRNA constructs on day 4, stained for DAPI (left) and SOX1 and CDX2 (right). Scale bar 1 mm. (K) Fluorescence confocal images of CRISPRi organoids carrying control (top) and CDX2-targeting (bottom) gRNA on day 4, stained for DAPI (left) and SOX1 and CDX2 (right). (L) Plot of CDX2 expression across control sgRNA (top, n=213) and sgCDX2 (bottom, n=214) CRISPRi organoids as a function of normalized A-P position. Midline represents mean, shaded region denotes standard deviation.

6

Fig. S6. A TBXT-dependent excitable system driving elongation is triggered by induction of an NMP-like signaling center, related to Fig. 4. (A) Control (left) and sgCDX2 (right) CRISPRi organoids on day 4 stained for pHH3 (green) and CDX2 (red) or SOX1 (blue), respectively. Scale bar: 200 μm. (B) Tailbud proliferation index (see STAR Methods) in control and sgCDX2 CRISPRi organoids on day 4 (Control, n=6; sgCDX2, n=12; p<0.0001). (C) Hybridization chain reaction (HCR) for control (top) and sgCDX2 (bottom) CRISPRi organoids on day 4 hybridized with probes against WNT5A (left), WNT5B (middle), and SOX2 (right). sgCDX2 organoids express SOX2 but lack WNT5A and WNT5B expression. Scale bar: 200 μm. (D) Brightfield overview image of sgWNT5A CRISPRi organoids on day 4. (E) Left: Brightfield and GFP images of sgWNT5A CRISPRi organoids transduced with sgWNT5B-GFP virus. Scale bar: 100 μm. Right: Zoomed-in view of hexagon of GFP+ sgWNT5A/B organoids, showing greater than 50% transduction efficiency. Scale bar: 200 μm. (F) Violin plot of day 4 lengths of control, sgWNT5A, and sgWNT5B organoids, with mean (points) and standard deviation (lines) (Control, n=214; sgWNT5A, n=208; sgWNT5B, n=202; p=0.01 and p<0.0001) (G) Top: Concentration profiles of CHIR99021 (CHIR) and FGF2 (FGF) in medium for control, CHIR withdrawal, FGF pulse, CHIR pulse conditions. Bottom: Control, CHIR withdrawal, FGF pulse, and CHIR pulse-treated organoids on day 4, stained for DAPI (top) and SOX1 and CDX2 (bottom). (H) Violin plot of relative lengths on day 4 of organoids exposed to control (red), CHIR withdrawal (blue), and FGF pulse (purple) and CHIR pulse (orange) conditions, with mean (points) and standard deviation (lines) (Control, n = 216; CHIR withdrawal, n = 214; FGF pulse, n = 216; CHIR pulse, n = 214; p<0.0001, p<0.0001, p<0.0001). (I) Control (left) and FGF pulse-treated (right) organoids on day 2, stained for DAPI, CDX2, SOX2, and TBXT. Scale bar: 1 mm. (J) Plots of CDX2 (left), SOX2 (middle), TBXT (right) expression across control (red, n=199) and FGF pulse-treated (purple, n=184) organoids as a function of normalized A-P position. Midline represents mean, shaded region denotes standard deviation. (K) Left: Control (left), CHIR withdrawal (middle), and FGF pulse-treated (right) organoids on day 4, stained for DAPI, CDX2, SOX2, and TBXT. Scale bar 1 mm. Right: Zoomed-in views of control (left), CHIR withdrawal (middle), and FGF pulse-treated (right) organoids on day 4 shows retention of TBXT+ cells only in FGF pulse condition. Scale bar: 200 μm. (L) CRISPRi hPSC colonies containing a control gRNA (left, middle) or sgTBXT gRNA construct (right) after 24 hours of exposure to E6 (left) or E6 + CHIR (middle, right) stained for TBXT. Scale bar 200 μm. (M) Violin plot of relative lengths on day 4 of control sgRNA and sgTBXT CRISPRi organoids exposed to CHIR (control, red; sgTBXT, green) and FGF pulse (control, purple; sgTBXT, turquoise) conditions, with mean (points) and standard deviation (lines), (Control, CHIR, n = 216; Control, FGF pulse, n = 216; sgTBXT, CHIR, n = 216; sgTBXT, FGF pulse, n = 206; p=0.57, p<0.001, p<0.0001). (N) Control (top left), CHIR pulse (top right), CHIR pulse + PD0 (bottom left), and CHIR pulse + PD1 (bottom right) treated organoids on day 4, stained for SOX1 and CDX2. Scale bar: 1 mm.

7

Fig. S7. Elongation along a single axis is stabilized by secreted WNT inhibitors, related to Fig. 4. (A) Control organoids on day 4, stained for DAPI, CDX2, SOX1, and SFRP1. SFRP1 image is DAPI-subtracted and contrast adjusted (adj.) to visualize extracellular SFRP1 protein bound to coverslip. Scale bar: 1 mm. (B) Wild type organoids treated with WAY3 (left), CRISPRi organoids containing a GFP-expressing guide RNA construct against SFRP2 (sgSFRP2) (middle), and sgSFRP2 CRISPRi organoids treated with WAY3 (right) on day 4 stained for CDX2, SOX1, and DAPI. Scale bar: 1 mm. (C) Left: WAY3-treated control (top) and sgSFRP2 (bottom) CRISPRi organoids on day 4 stained for DAPI (gray), pHH3 (green) and CDX2 (red). Right: Tailbud proliferation index (see STAR Methods) in WAY-treated control and sgCDX2 CRISPRi organoids wit single and multiple tailbuds on day 4 (Control single-tailbud, n=3; sgSFRP2+WAY3 single-tailbud, n=3; sgSFRP2+WAY3 multiple-tailbud, n=3; p=0.46, p=0.39). Scale bar: 200 μm. (D) WAY3-treated sgSFRP2 CRISPRi organoids (top) and untreated sgSFRP1/2 CRISPRi organoids (bottom) stained for SOX1, CDX2, and SFRP1. SFRP1 image is DAPI-subtracted and contrast-adjusted (adj.). sgSFRP1/2 organoids lack an extracellular SFRP1 gradient, as no protein is bound to the coverslip. Scale bar: 200 μm. (E) Control (top) and sgSFRP1/2 (bottom) CRISPRi organoids on day 4 stained for DAPI, SFRP1, SOX1, and CDX2. Lack of an extracellular SFRP1 gradient is correlated with branching of the CDX2+ tailbud. (F) Left: Quantification of the average extracellular SFRP1 gradient across control (black) and sgSFRP1/2 (green) organoids, arranged in hexagons (n=36). The average region occupied by organoids is shaded in gray. Right: Traces of individual extracellular SFRP1 gradients across control (left) and sgSFRP1/2 (right) organoids, arranged in hexagons (n=36).

9

Movie S1. Time-lapse microscopy of ZO1-EGFP+ organoids, related to Fig. 3. Max intensity projections of control (left) and IWP3-treated (right) organoids imaged on an LSM 980 confocal microscope starting on day 2 of differentiation, with z-stacks acquired every 20 minutes using a 488 nm laser (see STAR Methods). The centroid of each cell was tracked manually in FIJI and is labeled as a colored dot. Time stamps are in hh:mm format. Scale bar: 50 μm.

Highlights.

• Spatially coupled human organoids achieve robust A-P symmetry breaking

• Organoids elongate axially and generate cell types of the posterior neural tube

• Elongation is sustained by WNT/FGF feedback through an NMP-like signaling center

• Elongation is stabilized by secreted inhibitors of WNT signaling