Abstract
Cell patterning in epithelia is critical for the establishment of tissue function during development. The organization of patterns in these tissues is mediated by the interpretation of signals operating across multiple length scales. How epithelial tissues coordinate changes in cell identity across these length scales to orchestrate cellular rearrangements and fate specification remains poorly understood. Here, we use human neural tube organoids as model systems to interrogate epithelial patterning principles that guide domain specification. In silico modeling of the patterning process by cellular automata, validated by in vitro experiments, reveal that the initial positions of floor plate cells, coupled with activator-inhibitor signaling interactions, deterministically dictate the patterning outcome according to a discretized Turing reaction-diffusion mechanism. This model predicts an enhancement of organoid patterning by modulating inhibitor levels. Receptor-ligand interaction analysis of scRNAseq data from multiple organoid domains reveals WNT-pathway ligands as the specific inhibitory agents, thereby allowing for the experimental validation of model predictions. These results demonstrate that neuroepithelia employ reaction-diffusion-based mechanisms during early embryonic human development to organize cellular identities and morphogen sources to achieve patterning. The wider implementation of such in vitro organoid models in combination with in-silico agent-based modeling coupled to receptor-ligand analysis of scRNAseq data opens avenues for a broader understanding of dynamic tissue patterning processes.
Introduction
During embryonic development, complex tissue morphologies emerge from rearrangements of simpler modules. One such module is the single-cell-thick epithelial sheet, which, through precise and timely patterning and morphogenetic events, allows for the specification of cellular identity and tissue growth. To orchestrate the morphology of epithelia in time and space, tissue-wide spatial reference frames are established by biochemical and mechanical signals1, which are interpreted by individual cells to determine fate decisions and ultimately result in short and long range intercellular interactions. The specification of cell fate in the developing neural tube presents a canonical illustration of epithelial pattern formation, where multiple domains are dynamically specified in response the strength, exposure time and cross talk between diffusible signaling factors such as sonic hedgehog (SHH), bone morphogenic protein 4 (BMP4) and retinoic acid (RA). Our understanding of these patterning processes have thus far largely relied on animal models which, while highly reproducible and predictive, nonetheless comprise multiple layers of feedback and redundancy, making it challenging to uncover the underlying regulatory mechanisms.
Due to their capacity for in vivo-like multicellular organization2, organoids have emerged as tractable in vitro platforms to study patterning and morphogenesis in tissues as varied as the optic cup3,4, the intestine5,6, and the cortical plate7, and in gastrulation of the mammalian embryo8. Neural tube organoids (NTOs) derived from pluripotent stem cells (PSCs) are a promising model system to explore epithelial patterning, as they have been shown to recapitulate aspects of dorsoventral (DV)9 and anteroposterior (AP)10 patterning of the neural tube though morphogen stimulation. Given specific morphogen stimulation, NTOs exhibit a floor plate (FP) domain11 corresponding to the organizing region of the ventral neural tube and a source of a SHH gradient which encodes DV domain specification. The establishment of this FP domain is not fully explainable by cytoskeleton-mediated symmetry breaking events11,12 or by the applied signaling factors, as these cultures lack a notochord, which in vivo establishes a reference frame for the initiation of SHH-mediated patterning9,11,13,14. This raises the question as to the nature of FP patterning in vitro, and how this may relate more generally to the establishment of epithelial patterning.
To describe patterning dynamics, positional information (PI)15 as well as reaction-diffusion (RD)16 models have been extensively studied ex vivo, in vitro and in silico. While these two principles have been portrayed as contradictory and mutually exclusive14,17, recent studies have seen the application of combined PI-RD approaches to explain digit patterning18 as well as epithelial NT domain orchestration19. These studies suggests that morphogen source position, in combination with the characteristics of interacting diffusible species, are needed to explain epithelial patterning.
Here, we use a human NTO (hNTO) in vitro platform and a cellular automaton (CA) in silico model to investigate FP patterning dynamics. We establish the model’s fidelity by benchmarking to in vitro experiments and systematically explore the parameter space which is permissive for recapitulating hNTO pattern types and frequencies across various length scales. We also investigate model parameters to predict in vitro routes to enhance patterning in hTNOs, and identify concentration of inhibitor species as a powerful modulator of patterning phenotype. An analysis of receptor-ligand interactions of single cell RNA-sequencing (scRNA-seq) data is used to identify the specific inhibitor species. Finally, we perform perturbation experiments to validate model predictions. The use of simple and tunable CA model in combination with analysis of transcriptomic data reveals insights into mechanisms of human neural tube patterning, and may be extendable to other epithelia.
Human neural tube organoids: an in vitro platform for epithelial patterning
In order to study patterning processes in epithelial tissues, we rely on a highly defined in vitro platform in which single hPSCs are differentiated into pseudostratified epithelial hNTOs within a synthetic polyethylene glycol (PEG) hydrogel matrix supplemented with laminin20 (Fig 1a). In the absence of signaling factors, these organoids remain largely unpatterned and have a forebrain identity. To initiate a FP domain, organoids are treated with RA to caudalize the default forebrain identity11,12 and with smoothened agonist (SAG) to provide a ventralizing signal through the activation of the SHH pathway9. By day 11 of differentiation, hNTOs display various FP expression phenotypes, as identified by the FP marker FOXA2 (Fig 1a). These could be categorized into three groups: those that exhibited a patterned FP, a scattered FP, and those that were devoid of the fate. FOXA2+ hNTOs represented ~60% of all organoids, of which ~34% were patterned (Fig 1b). FP patterning in these organoids was initiated after RA-SAG treatment by the emergence of FOXA2+ cells. These cells were initially scattered within the organoid in a largely disorganized manner, and over time rearranged such that some FOXA2+ domains gradually underwent patterning21 (Supplementary Fig 1). Despite all starting from single cells, organoids were observed to reach different sizes by day 11. No significant difference in organoid size was observed between patterned and scattered organoids (Fig 1c), and average patterning frequency was independent of organoid size (Fig 1d), suggesting that the occurrence of patterning in this system is independent of domain size.
1-D Turing model for patterning human neural tube organoids
To explore mechanisms that could explain FP patterning in hNTOs we sought to develop an in silico model that could best describe in vitro observations. We reasoned that a RD approach16 could be suited to model the transition between an initially scattered expression profile towards a gradually patterned domain based on previous approaches which have used RD to describe patterning in peri-gastrulation tissues22 and retinal organoids23 in vitro.
To tailor the model to our hNTO, we relied on a simple 1-D activator-inhibitor RD system with second-order production rates and first-order decay terms, similar in general form to those previously used in other organoid model systems16,24–26 (Supplementary Fig 2a). Periodic boundary conditions were implemented in order to mimic the epithelial morphology of hNTOs9,20, and parameters of the partial differential equations were chosen based on those previously applied for RD organoid models to describe the production and decay rates of morphogens23 (Supplementary Fig 2a). Cells in the domain could be either FOXA2+, represented as source cells (SCs), or FOXA2-, represented as inactive cells (ICs). To simulate the initially scattered FP expression, a random perturbation was imposed on the activator signal (Φa,m). Once perturbed, the reaction between activator and inhibitor species led to the assignment of each cell in the model as a SC wherever the associated Φa,m was larger than the average overall activator signal Φa,avg, or as an IC where Φa,m was lower than Φa,avg (Supplementary Fig 2b). The calculated expression profiles across the domain at each time step are deterministic in this model, with this RD system converging into a specific pattern for a given set of parameters such as domain size, and activator and inhibitor diffusion coefficients Da and Di.
It is known that domain size plays an important role in RD systems, with patterning typologies being domain size dependent24,25. Indeed we observed that an increase in domain size resulted in larger number of SC poles (Supplementary Fig 2c), indicating that the model led to pattern size-dependence which contradicted in vitro observations. Most importantly, we observed significant phenotype heterogeneity in vitro, with a mix of patterned, scattered and unpatterned organoids within the same culture, whereas this in-silico model rather functioned as an “all-or-nothing” switch, resulting in either fully patterned or fully negative (i.e. unpatterned with no SCs remaining) phenotypes for a given set of physical parameters (Supplementary Fig 2c). Altogether, this suggests that a canonical RD approach cannot fully recapitulate observed in vitro expressions. This led us to investigate modeling approaches that could allow for SC expression profiles similar to those seen in-vitro, including varied patterning phenotypes, heterogeneous phenotypes within an organoid population, and where these findings would be domain-size independent.
Cellular automata model recapitulates in vitro floorplate expression heterogeneity
In our model the only source of stochasticity that can lead to expression heterogeneity is the initial perturbation and location of SCs. We therefore considered the use of a cellular automaton27 (CA) model, which would allow to specify the initial positions of SCs which drive the evolution and dynamics of the system. We implemented an in silico 1-D elementary CA model (Fig 2a), where simulations are run for ten time steps and the identity of each unit cell (SC or IC) in the domain is updated at each time step. Here, SCs are allowed to emit fate-activating and fate-inhibiting signals with concentrations Φa and Φi respectively (Fig 2a). The change in the concentration of these signals after every time step is governed by the equation Φ = Be−λx, where B represents a constant morphogen concentration maintained through replenishment at the source, and decay constant λ represents morphogen diffusion characteristics through the tissue. Together, B and λ govern the interaction range of SCs with their cellular neighborhoods (Fig 2a). Cells in which the net resulting interaction between activator and inhibitor (Σ(Φa,n - Φi,n)) is less than a minimum threshold become (or remain) ICs, whereas those above the threshold become (or remain) SCs. Survivor cells are by default SCs and, when surviving through all ten steps, contribute to the final SC expression, which can then be classified as patterned, scattered or negative (Fig 2a).
We hypothesized that the in vitro expression of individual cells and the ensuing generation of domains could be minimally described in terms of concentration (Ba, Bb), as well as the diffusion characteristics (λa, λb) of activation and inhibition signaling molecules. We therefore combinatorially explored parameters of B and λ for both inhibitor and activator to identify conditions that could lead to patterning of SCs. Out of 1,600 conditions analyzed, only 157 led to SC patterning (Fig 2b). Notably, the highest patterning frequencies (red cluster in Fig 2b) occurred when the activator diffusivity was lower than that of the inhibitor species (in terms of decay constants: λa > λi) (Fig 2c).
To test the CA model in a neural tube-specific context, we chose λa = 0.04, reflecting the observed decay length values for SHH ex vivo28, and found that patterning occurred for k > 1, where k = λa/λi is the decay constant ratio (Supplementary Fig 3). These are conditions within the short range activator and long range inhibitor regime, representing Turing instability scenarios known to favor patterning during morphogenesis16. Therefore the CA approach we develop here can be interpreted as a discretized Turing patterning model, which has as a defining feature the ability to capture specific SC expression patterns given a fixed set of parameters (Supplementary Fig 4).
By mapping the in vitro rate of patterned organoids to model outputs we found the specific ratio between activator and inhibitor decay constants (k ≈ 1.29) which best describes the heterogeneity observed in vitro (patterning events ~34%) (Fig 2d). This indicates that our CA model captures both specific organoid phenotypes, as well as their heterogeneous distribution within a population, suggesting that FP patterning in these epithelial organoids follows a discretized Turing patterning approach, as predicted by our CA model.
As our model relies on previously reported morphogen diffusion values derived from in vivo experiments, we sought to compare the diffusion dynamics of hNTOs to previously reported in vivo observations. We therefore performed fluorescence recovery after photobleaching (FRAP) experiments on day 5 hNTOs, which best describe the microenvironmental state at the onset of patterning (Supplementary Fig 5) and found a diffusion coefficient of DFL = 61.8 μm2.s−1. This result confirmed that hNTOs have similar diffusion dynamics as those reported in vivo (DFL ~ 50 - 100 μm2.s−1) 29,30.
An important characteristic of this model is its ability to demonstrate size-independent patterning, where the frequency of pattering remains relatively constant across different domain sizes (Supplementary Fig 3). This allowed the CA model to predict in vitro FP expressions across various length scales where the average change in patterning frequency given a change in organoid size was negligible (Supplementary Fig 6a). Notably, the model matched FP domain size trends in scattered and patterned hNTOs (Supplementary Fig 6b), suggesting that this modeling approach recapitulates the dynamics leading to each expression type. Moreover, the CA model can not only discriminate between scattered and patterned expressions, but also between patterning subtypes. Here, we accurately recapitulated the relatively rare 2-pole and 3-pole pattern subtypes (Supplementary Fig 7a), with in vitro observations of pole location and frequency quantitatively matching in silico predictions (Supplementary Fig 7b, c).
This model predicts that patterning frequencies can not only be changed by varying molecule diffusion characteristics λ, which are difficult to modulate in vitro, but equally through activator or inhibitor magnitudes (Fig 2e), which can be readily manipulated through pharmacological perturbations. Indeed, by fixing the diffusion characteristics of activator and inhibitor molecules, the model predicted that an increase in patterning frequency is possible through an increase of the inhibitor magnitude Bi (Fig 2f).
Receptor-ligand interaction analysis reveals WNT as putative inhibitor of the RD system
In order to identify the inhibitor species in the hNTO system, we performed receptor-ligand interaction analysis31 on an scRNAseq dataset obtained from dissociated hNTOs at day 5, corresponding to hNTOs after RA-SAG exposure but before FP induction, and at day 11, after FP induction and patterning20. From this dataset, only those cells which could be identified as having dorsal (D), intermediate (I) or ventral (V) fates were retained, and were represented on UMAPs highlighting their states at different time points (Fig 3a) and by D-I-V assignments (Fig 3b). These cells also displayed domain-specific hallmark genes corresponding to expected in vivo expression profiles (Fig 3c). We next focused our analysis on understanding the interactions between cells in the D-V domains, which represent the known morphogen sources in the neural tube, and between cells in the V-V domain, which represent domain self-interaction with the potential to highlight inhibitory molecule candidates.
This analysis revealed 59 and 37 significant interactions for D-V and V-V respectively on day 5, compared to 145 and 32 interactions for D-V and V-V respectively on day 11 (Fig 3d). We further grouped these interactions and categorized them by their major participating ligand or receptor, and highlighted only these interactions that involve known modulators of the FP and ventral domains including antagonists (WNT32,33 and BMP34) and agonists (NOTCH35,36 and FGF37,38) (Fig 3d).
At day 5, we observed FGF, NOTCH, and BMP activity in D-V interactions and FGF and NOTCH in V-V ones (Fig 3d). FGF activity was transient as its fraction declined from day 5 to 11, which is in line with a previous in vivo report of transient FGF signaling being required for FP induction34. The presence of BMP suggested that dorsal cells, although representing only a small population at day 5, already played at this early time point a critical role as sources of BMP required for DV patterning. The top 5 NOTCH activities at day 5 all involved DLK1, a known inhibitor of the NOTCH pathway35. After the induction and patterning of FOXA2 at day 11, DLL3, another inhibitor of NOTCH, was also involved in both interacting pairs. The introduction of WNT signaling in both D-V and in V-V interactions at day 11 represents a significant change in the receptor-ligand makeup compared to day 5. This suggests that WNT signaling and not NOTCH, FGF, or BMP is a marker of a maturing organoid characterized by FP induction and patterning. Furthermore, since FOXA2+ hNTOs are largely devoid of dorsal cells20, it is likely that WNT, and not BMP from dorsal cells, represents the inhibition signaling within single organoids.
WNT signaling promotes floorplate patterning through inhibition
Our CA model predicted that changes to the abundance of inhibitory molecules would affect patterning frequency (Fig 2f). In order to test this prediction experimentally with our newly identified putative inhibitor, we chose to modulate WNT signaling in our cultures using CHIR99021, a small molecule WNT activator (via GSK3β inhibition). We supplemented the growth medium with GSK3βi at different concentrations ranging from 0 to 4 μM (Fig 4a) from day 7, immediately after the induction of the FP, until endpoint day 11 (Fig 4a). Increasing WNT activity resulted in a decrease in the frequency of the scattering phenotype, an increase in the negative (i.e. no FOXA2+ cells) phenotype, and a rise (up to 2uM) then decline in the patterned phenotype (Fig 4a). These in vitro values matched with our CA model, with the increase in GSK3βi concentration from 0 to 4 μM corresponding to an increase in inhibitor magnitude Bi from 1 to 1.14.
We hypothesized that such an increase in patterning events would be accompanied by a larger domain diversity, including the presence of more dorsal domains within the same organoid, which would better recapitulate in vivo conditions. We therefore interrogated the presence of more dorsal identities such as PAX6, and found that increasing GSK3βi concentrations resulted in a gradual decrease of FOXA2+ hNTOs, with a converse increase in PAX6+ organoids (Fig 4b). This is in line with the reported promotion of in vitro dorsal identity in the neural tube by WNT activation34. Furthermore, with increasing GSK3βi concentrations, we found that the fraction of dorsoventral patterning in PAX6+ hNTOs follows a similar trend to in silico patterning (Fig 4c). This underscores the close link between FP patterning and dorsoventral patterning events, and, in the context of organoids, argues for a control mechanism where multiple domains coexist within the same organoid when secondary sources of inhibition or activation are created as a result of domain-domain interactions28,35.
Due to the increase in dorsal fates upon exposure to GSK3βi, and since dorsal fates can be sources of WNT secretion (Fig 4d), we next thought to investigate the effect on expression trends with ICs as surrogates for dorsal cells and as secondary sources of inhibition signals (Supplementary Fig 8a). When comparing the contributions to inhibition signaling from SC (x1) and IC (x2), we found that the best correlation to in vitro data were achieved in conditions where SCs were the sole sources of inhibition (Supplementary Fig 8b,c,d). This in silico result suggests that FP patterning does not require dorsal domains. At first this seemed contradictory to our previous observation (Fig 4c) given the close relation between FP patterning and dorsoventral patterning events with increasing WNT activity. However, we reason that upon WNT activation, FP patterning events are increased through enhanced inhibitor interactions, but that concomitantly, WNT exposure promotes PAX6 expression in FOXA2-regions in the organoid, resulting in dorsoventrally patterned hTNOs. Therefore, our model setup predicted that while FP patterning did not require dorsal domains, dorsal domain patterning depended on patterned FP expressions. Indeed, hNTOs with patterned FPs at a GSK3βi concentration of 0 μM were largely (~66%) devoid of the PAX6 fate (data not shown), further underscoring that FP patterning does not require, neither does it necessarily result in, PAX6 expression within the same organoid. The results, therefore, argue that FP patterning is a self-regulated process as predicted by the model.
Finally, after exploring the upregulation of WNT activity, we tested whether the converse downregulation of WNT activity would have an opposite effect on patterning. The IWP2 small molecule (PROCN inhibitor) was used to decrease WNT activity, resulting in decreased FP patterning frequencies (Supplementary Fig 9a) as predicted by the model (Fig 2e,f). A concentration of 2 μM of IWP2 correlated best with Bi = 0.96, which corresponds to a reduction in inhibitor magnitude (Supplementary Fig 9b).
Altogether in silico and in vitro results suggest that WNT activity plays an important role in shaping FP expression in hNTOs, in accordance with an underlying spatially discretized RD-based model of the system. Importantly, our model predicted that epithelial domains could be rendered largely patterned through an increase of WNT activity, which we verified experimentally. The model suggests that this process occurs by enhancing inhibition signaling. This renders it more difficult for cells to meet the activation threshold which leads to more concise and separated grouping of cells, namely fate polarization or patterns. Increasing WNT activity also allows FOXA2-cells to become PAX6+ which can result in dorsoventral patterning but only at intermediate WNT activities since high levels can eliminate favorable regions, abrogating the FP fate altogether (Fig 5).
Discussion
Cell patterning in epithelia is a key event for proper tissue development during early embryogenesis39,40. To better understand the underlying mechanisms for the establishment of such patterns, in silico models such as PI and RD have been employed15,16,24. In a PI approach, cells recognize their position with respect to a source by interpreting the graded morphogens emanating from that source allowing them to pattern according the signal strength and thus their respective distances to the source. This emphasize the importance of morphogen source position in a PI patterning model. By contrast, an RD approach ignores morphogen positions and relies instead on tissue wide secretion and interaction between morphogen species, which allows initially random expressions to converge to predictable pattern configurations. Here, we use an epithelial organoid model of neural tube patterning to show that FP patterning emerges though a discretized Turing mechanism. Specifically, we use a CA-based approach to show that morphogen source position in the tissue and diffusion characteristics of activators and inhibitors control the organization of cells within the domain space, and are thus likely modulators of FP expression in organoids.
Organoids have often been used as simplified models of patterning and have allowed insight into the underlying biochemical41–44 and mechanical1,20,45,46 factors that control cell fate specification and morphogenesis. We and others have shown that NTOs display patterned FPs9,11,12,20 which emerge, remarkably, despite the lack of the notochord, which in vivo acts as a spatial reference frame for FP patterning28,47,48 through the secretion of SHH morphogens. This suggests that in vitro epithelial patterning follows mechanisms that might differ from those employed in vivo.
Previous work with epithelial organoids suggests that patterning phenomena can be described solely by an RD approach. For example, as in the case of retinal organoids involving Pax6, Fst, and Tgfb223. This simple gene regulatory network was shown to sufficiently explain how organoids spontaneously self-organize to reflect retinal development. Our study demonstrates that such a canonical form of RD could not explain FP pattering in epithelial hNTOs, as key in vitro observations such as patterning heterogeneity and domain size independence could not be recapitulated. Because FP cells are specified by interpreting PI from the notochord SHH source before becoming sources of SHH themselves28,34, we hypothesized that a different modelling framework which considered the initial position of FP cells in the RD model would be necessary to better explain our observations.
Models which combine RD with PI have been shown to predict patterning better than either model separately, notably in the context of digit patterning18. Here, graded Fgf concentrations (PI) control patterning wavelengths stemming from the interactions (RD) between Sox9, Bmp and Wnt across the domain space, allowing for more robust recapitulation of in vivo digit patterning. Furthermore, an in silico PI-RD NT model demonstrates how the introduction of intercellular homeoprotein diffusion in the model better orchestrates domain specification by generating more delineated in vivo-like domain boundaries19.
Our study shows that only when the initial positions of SCs are considered can FP patterns be generated with high fidelity. The developed CA model demonstrated patterning in regimes consistent with a Turing instability mechanism and even exhibited multi-poles patterning as is expected from a RD system. However, only by introducing the activator and inhibitor species at specific SC positions could the reaction between them create highly discretized regions which could persist to maintain a stable pattern. Our results suggest that this discretization adapts the RD system to allow for expression heterogeneity, which ultimately recapitulate in vitro FP observations. This model therefore expands on previous models of epithelial patterning and demonstrates that a CA approach can combine the importance of morphogen source position as well as diffusion characteristics to describe epithelial patterning.
Patterning in epithelial tissues rely on complex and dynamic signaling4,39,49. In the neural tube28,34,43,44,48, WNT32,33, BMP34, NOTCH35,36, FGF37,38 and SHH28 have been recognized as main modulators of patterning which orchestrate domain specification along the dorsoventral as well as anteroposterior axis. Once these morphogens establish a patterning reference frame, inter-domain signaling assist with domain boundary specification. For example, mediated by SHH, NKX2.2 in the p3 domain prevents the progression of the adjacent pMN domain through OLIG2 inhibition in the ventral NT28,38 and in NTOs9. Moreover, intra-domain signaling is required for maintenance of cell identity, similar to the role of SHH in the FP44. Our modelling results argue that intra-domain signaling is required not only for self-maintenance and activation, but also for self-inhibition. Our receptor-ligand interaction analysis suggests that FP patterning is modulated by WNT, a known inhibitor of ventral identities33,34,50. Indeed, FOXA2 abundance variation in response to WNT activity has been previously demonstrated in a microfluidic system10, where moderate levels of WNT were necessary for FP induction but higher ones resulted in loss of FOXA2 and SHH. To investigate whether FP patterning is modulated by inhibition, we performed in silico modeling and validated the outcome though perturbation experiments to show that increasing FP patterning through inhibitory means is possible, but that high inhibition levels cause loss of FP fate in the majority of cultured hNTOs. We further showed that FP patterning is a self-regulated process that does not require the presence of other inhibitory domains since the best correlation to in vitro observations occurs when SCs are the sole sources of inhibition and activation. Interestingly, the expected activator signaling, SHH, was absent in the receptor ligand interaction analysis, which may hint to a different activator in vitro. Therefore, while FP induction occurs through a RA-SAG pulse, later pattern maintenance may rely on pathways other than SHH, such as NOTCH signaling, which has recently been shown to regulate ventral domains in vivo35,36.
Our in silico analysis relies on a simplified 1-D CA model without considering cytoskeleton rearrangement11, growth42, matrix stiffness11, or morphogen exposure time28, which are known to regulate patterning in the NT in vivo and NTOs in vitro. Our model can accommodate more complex activator-inhibitor configurations through the addition of new signaling parameters. These changes could also enable feedback from different cell types and even from neighboring organoids, as well as incorporate signal sequestration, which has been shown to play a role in ventral domain organization42. Given its simplicity, this model nevertheless recapitulates with remarkable fidelity the observed FP patterning phenomena. These findings underscore how the integration of in silico modelling, in vitro experimentation and transcriptomic analysis can be used as a powerful and widely applicable approach to identify the mechanisms and molecular players governing epithelial patterning.
Author Contributions
AA conducted experiments and analysis. AA and SG conducted FRAP experiments. AA, SG, IS and AR interpreted the data and edited the manuscript. AA and AR wrote the manuscript.
Supplementary figures
Materials and Methods
In silico reaction-diffusion (RD) hNTO patterning model
We used an in silico 1-D RD model with one activator and one inhibitor species. The partial differential equations (PDEs) where formulated following previously defined forms23,25.
Where Φa and Φi denote the concentrations of the activator and inhibitor species respectively. The second order generation terms are defined for the activator and inhibitor as Aa(Φa2/Φi) and AiΦa2 respectively. The first order decay terms of the activator and inhibitor are BaΦa and BiΦi. Values for Aa = 0.25, Ai = 1, Ba = 0.1 and Bi = 0.5, are not based on physical parameter values but are chosen to be in the range of previously used values23. The diffusivities of the activator and inhibitors are Da and Di respectively. The diffusivity of the activator molecule was set to that of SHH, a likely activator morphogen28 (Da = 24 μm2/s51,52).
To simulate the RD model we used MATLAB (MATLAB, R2018b, The MathWorks Inc.) where a domain space was divided into 6 μm-wide units, reflecting the width of one cell. The timestep was chosen to be 1 s. For each timestep, the PDEs were solved in a forward implicit manner. The simulation is started by an initial random perturbation to the activator concentration at t = 0 s. The simulation is run for 10000 s, an adequate time for a stable pattern to form which is visually verified as non-changing over time. To evaluate patterning, cellular regions are binarized such that regions where Φa > Φa,avg are evaluated as source cells (SCs) and given a value of 1 and elsewhere as inactive cells (ICs) and given a value of 0.
To assign expression type, we adapted the scheme we used for our in vitro assessment. We first consider a SC domain as occupying a continuous region of SCs along the series, where ICs occupy the space (gaps) between these regions. We then evaluate the SC ratio (SCR = n(SCs) / n(total-cells)). Patterning is assigned when 1) SCR < 0.4, and 2) SCR < 0.5 but with fewer than 5 gaps. This is because upon visual inspection, we observed that for 0.4 < SCR < 0.5, SC distribution is never polarized to one side to be considered as patterned when the number of domain gaps is >5, but becomes polarized for gaps <5. For all other cases scattering is assigned. We enumerated the number of poles in our model by the number of domains detected in each simulation. By varying Di and the length of the domain space, the patterning, scattering or negative expressions and the number of poles for each conditions are used to create the heatmaps (Supplementary Fig 2c).
In silico cellular automaton (CA) hNTO patterning model
We used an in silico 1-D elementary cellular automaton27 model to simulate patterning in hNTOs (MATLAB, R2018b, The MathWorks Inc.). Each cell is represented by a discreate element in a circular series of interacting elements. Cells are allowed two possible identities, 1) SCs, and 2) ICs. Source cells act as sources for 1) activation, Φa, and 2) inhibition, Φi, signals. Each signal (Φ = Be−λx) has a constant profile, where B is the source magnitude, λ is the exponential decay constant that controls signal decay over discreate cell positions x, and where high λ values result in rapid decay compared to lower ones. Cells are able to interact by having their respective signal profiles extend over multiple cells. The model processes 10 steps, where in each step cell interactions take place, creating a new generation of cells with modified states according to 1) activation of ICs, 2) inhibition of SCs, or 3) retention of SC and IC states. Each step advancement creates a new generation as input for the following step until the end step.
To begin the process, at step 1, cells are assigned an IC or SC identity at random, with each having equal chance of becoming either identity. Next The sums of all inhibition signals is subtracted from the sum of activation signals to obtain a net activation profile that extends over the entire cell series. A reassignment of cell states is performed and depends on the net activation value at each cell position, where values higher than a threshold th allows 1) ICs to assume a SC identity, or 2) SCs to retain their state. By contrast, net activation values lower than th 1) inactivates a SC, and 2) maintains the identity of ICs. Once all cell states have been processes, a new generation of cell series is created and passed the a new step which repeats the process. In total 10 steps are executed with the final generation evaluated for patterning using the same algorithm as in the RD model. The percentage of patterned and scattered in silico NTOs are evaluated per run, where a run is composed of 500 in silico NTOs. Three runs are evaluated (total 1,500 in silico NTOs) for each condition to obtain an average value for scattered, patterned and negative expression frequencies.
The in silico NTO sizes were evaluated by first deriving a circumference from the in vitro size bins (Fig 1d) and subsequently divide by the observed widths of nuclei (~6 μm), thereby mapping in vitro hTNO sizes of 50-60, 60-70, 70-80, 80-90, 90-100, 100-110 and > 110 μm to in silico hNTO sizes of ~28, 34, 40, 46, 52, 58 and 64 cell elements respectively.
The parameter space (Fig 2b), was obtained by varying Ba and Bi from 1 to 3 in increments of 0.5, and λa and λi from 0 to 0.1 in increments of 0.01 while using a domain size of 46 cells (average size after in vitro size mapping), producing 1,600 different parameter combinations where 157 cases result in patterning. Each condition comprised of 1,500 in silico NTOs where their outputs are evaluated to obtain average values for patterning, scattering and negative events. A table comprising Ba, Bi, λa, λi, Ba/Bi, k = λa/λi, patterning, scattering and negative frequencies for each condition is passed to the Seurat pipeline for data normalization and scaling53. Graph-based clustering was performed using the FindNeighbors function using the top 5 principle components (PCs) and the FindCluster function (resolution of 0.5) was used to group the cells with similar transcriptional profiles together. For data visualization, the dimensionality reduction technique, Uniform Manifold Approximation and Projection (UMAP), was performed with the RunUMAP function using the top 5 PCs.
Heatmaps (Fig 2d-f) were generated using heatmap.2 function in R. In Fig 2d, the domain size varied from 28 to 64 cells as per the above-mentioned in vitro size mapping. The activator decay constant λa = 0.04 was held constant while k was varied from 1.2 to 1.4 by varying λi while Ba = 2 and Ba/Bi = 2. In Fig 2e, The domain size was held constant at 46 with λa = 0.04 and k = 1.289. The activator and inhibitor magnitudes were centered around 2 and 1 respectively and varied above and below their respective values by 0.05 magnitude points for each increment. The three expression types were then presented separately. In Fig 2f, the domain size varied from 28 to 64 cells as per the above-mentioned in vitro size mapping, with λa = 0.04 and k = 1.289. Activator magnitude was held constant at Ba = 2, while Ba/Bi varied from 1.81 to 2.5 by varying Bi.
The position of each pole in the patterned in silico NTOs was evaluated as the position of its center element. Next the distance between different pole positions was evaluated and converted to an angle (Supplementary Fig 7a).
Culture medium
Essential 8 (E8) - Flex Medium Kit (ThermoFisher Scientific) was supplemented with 1% Penicillin Streptomycin (GIBCO) and used as growth medium for hiPSC culture. Neurobasal medium (GIBCO) and DMEM/F12 (GIBCO) were mixed 1:1 for the neural differentiation medium, which was supplemented with 1% N2 (GIBCO), 2% B-27 (GIBCO), 1 mM sodium pyruvate MEM (GIBCO), 1 mM glutamax (GIBCO), 1 mM non-essential amino acids (GIBCO) and 2% Penicillin Streptomycin (GIBCO).
Human iPSC culture
Human iPSCs were cultured in Matrigel coated 6 well plates to a confluency of 60-70%, before passage every 72 h. Newly passaged colonies were exposed to Y-27632 Rock inhibitor (ROCKi) (Hellobio) at a concentration of 10 μM for the first 24 h.
Human NTO culture in nondegradable PEG hydrogels
Human iPSC derived hNTOs were cultured in nondegrerdable polyethylene glycol (PEG) hydrogels, as previously described20. Briefly, hiPSCs were dissociated into single cells and embedded in a PEG hydrogel premixture. 10 μM droplets of the cell-matrix mixture were added to wells of a 96-well plate and after 20 m of gelation time, neural differentiation medium was added supplemented with 10 μM of ROCKi for the first 3 days. Retinoic acid (Stemcell Technologies) at 0.25 nM and smoothened agonist (Stemcell Technologies) at 1 μM were added to the growth medium for 2 days between days 3 and 5. This was followed by regular medium changes every 2 days until end point day 11.
WNT perturbation experiments
Day 7 hNTOs, representing earliest FOXA2 expression, were treated with GSK3β inhibitor (Tocris, CHIR99021, 4423), an activator of WNT, until endpoint day 11 with concentrations of 1, 2, 3 and 4 μM. For WNT inhibition, IWP2 (Peprotech, 6866167-1MG) was used from day 7 at a concentration of 2 μM until endpoint day 11. Controls were treated with DMSO at dilutions similar to the highest tested concentration of GSK3βi (1:2500).
Immunohistochemistry
Paraformaldehyde (4%) (Sigma-Aldrich) is used to fix hNTOs for 2 hours and then washed by PBS three times. Human NTOs were permeabilized and blocked using .3% Triton X (PanREAC AppliChem) and 0.5% BSA solution (Sigma-Aldrich) for 30 m. FOXA2 primary antibody mouse (Santacruz, sc-374376, 1:200) or rabbit (abcam, ab108422, 1:200) was used to stain for FP expression for 24 h and PAX6 primary antibody (DSHB, PAX6, 1:200) for more dorsal identities. This was followed by 24 h of PBS washes. For an additional 24 h, secondary antibody donkey-anti mouse Alexa Fluor 555/647 (Invitrogen) and donkey-anti rabbit Alexa Fluor 647 were used. Alexa Fluor 647 conjugated phalloidin (Abcam, 1:500) was used for filamentous actin visualization. Hoechst (1:2000) was used to nuclei visualization. Finally, this was followed by another 24 h of PBS washes.
Imaging and image analysis
Images obtained for quantification were obtained using Zeiss Axio Observer Z1 (Carl Zeiss MicroImaging) with a Colibri LED light sources and a 10x air objective. Representative images where obtained using a Leica SP8 DIVE (Leica Microsystems) using confocal or multiphoton modes and a 25x water objective.
Pattern quantification are described elsewhere20. Distinguishing between 1, 2 and 3 poles relied on visual evaluation of each hNTO.
Fluorescein recovery experiment
To in situ observe fluorescein diffusion within hNTOs, we first cultured hNTOs until day 5 following the hNTO protocol (Fig 1a). Day 5 measurements ensured capturing the ECM state at the onset of FP induction and patterning. After the RA-SAG treatment (day 5) we supplied the media with fluorescein to obtain a final concentration of 20 μM. The samples were then incubated for 30 m at 37°C and 5% CO2 to allow fluorescein diffusion throughout the matrix and hNTOs. We employed a confocal microscope (Leica SP8 DIVE, Leica Microsystems) to perform targeted bleaching of fluorescein molecules using 1 s burst of 480 nm laser at full power. A 10x air objective was used and a 60 s observation period of fluorescein recovery immediately followed. The bleach spot was chosen to be off-centered to avoid the acellular lumen, ensuring diffusion observations in cell-filled regions within the hNTOs. The resultant time series were analyzed using the Time Series Analyzer V3 plugin on ImageJ. For each condition, the intensity values were normalized with reference to the maximum value before bleaching. The normalized values were then averaged for each condition, and the resultant values plotted. The Ellenberg diffusion equation29 was used to estimate the diffusion coefficient of fluorescein.
Single Cell RNA sequencing data processing
Data manipulation and subsequent steps were performed using the Seurat53 tool for single cell genomics version 3 in R version 3.4. Single Cell data were obtained from a hNTO data set20 that will become available at GEO. First, we subset the data to retain previously described cells with dorsal (D), intermediate (I) and ventral (V)20 identities summing to 1251 cells of days 5 and 11 of the hNTO differentiation protocol. The criteria for identifying dorsal, intermediate and ventral cells are described elsewhere20. The data was processed to find 2,000 highly variable genes using the FindVariableFeatures function. Cell cycle regression was performed. Data autoscaling was performed and reported using principal component analysis (PCA) using the RunPCA function.
Data Clustering
Graph-based clustering was performed using the FindNeighbors function using the top 5 principle components (PCs) and the FindCluster function (resolution of 0.5) was used to group the cells with similar transcriptional profiles together. For data visualization, the dimensionality reduction technique, Uniform Manifold Approximation and Projection (UMAP), was performed with the RunUMAP function using the top 5 PCs. Cluster annotation focused on identifying D, I and V cells on the UMAPs.
Receptor ligand interaction analysis
To systematically interrogate receptor-ligand interactions between clusters, we took advantage of the Python implementation of CellPhoneDB (v2.1.1)31. A pooled normalized count matrix containing all cells present within the scRNA-seq dataset was used as input to the algorithm. The following parameters were used: counts-data = hgnc_symbol; iterations = 1,000; threshold = 0.10. Only significant interactions (p-value < 0.05) were considered for further analysis. The receptor ligand interaction scores were ranked while highlighting those than involved known modulators of the SHH pathway, namely FGF, NOTCH, WNT, and BMP only in cases where they respectively represent more than 5% of all interactions identified per case. The Circos R package was used for visualization to display a maximum of 5 interactions per group.
Quantification and Statistical Analysis
We used two-way ANOVA statistical tests on grouped data, and an unpaired two-tailed t-test where appropriate with a 95% confidence interval and appropriate corrections (GraphPad Prism 6, Version 6.01, GraphPad Software, Inc.). When determining patterning and scattering significance, the patterned values of the various conditions were used in statistical analysis. Similarly FOXA2+ hNTO values of the various conditions were used when determining the FOXA2+/- hNTOs statistical significance. Pearson correlations were performed to evaluate linear regression where appropriate. Statistical significance was considered for all comparisons with p < 0.05. The cor R function was used to generation the correlation maps. For hierarchical clustering and heatmap generation, we employed the R package heatmap.2.
Data availability
This study did not generate new raw scRNAseq sequencing data. The original processed and metadata files will be made available at GEO.
Acknowledgements
This work was supported by the FWO grant G087018N and FWO postdoctoral fellowship 1217220N, Interreg Biomat-on-Chip grant and Vlaams-Brabant and Flemish Government co-financing, KU Leuven grants C14/17/111 and C32/17/027 and King Baudouin Foundation grant J1810950-207421.
Footnotes
↵* email: adrian.ranga{at}kuleuven.be