Microtissue geometry and cell-generated forces drive patterning of liver progenitor cell differentiation in 3D

Abstract

Three dimensional (3D) microenvironments provide a unique opportunity to investigate the impact of intrinsic mechanical signaling on progenitor cell differentiation. Using a hydrogel-based microwell platform, we produced arrays of 3D, multicellular microtissues in constrained geometries, including toroids and cylinders. These generated distinct mechanical profiles to investigate the impact of geometry and stress on early liver progenitor cell fate using a model liver development system. Image segmentation allowed us to track individual cell fate and characterize distinct patterning of hepatocytic makers to the outer shell of the microtissues, and the exclusion from the inner diameter surface of the toroids. Biliary markers were distributed throughout the interior regions of micropatterned tissues and were increased in toroidal tissues when compared with those in cylindrical tissues. Finite element models of predicted stress distributions, combined with mechanical measurements, demonstrated that intercellular tension correlated with increased hepatocytic fate, while compression correlated with decreased hepatocytic and increased biliary fate. This system, which integrates microfabrication, imaging, mechanical modeling, and quantitative analysis, demonstrates how microtissue geometry can drive patterning of mechanical stresses that regulate cell differentiation trajectories. This approach may serve as a platform for further investigation of signaling mechanisms in the liver and other developmental systems.

Graphical Abstract

A hydrogel-based microwell culture platform was used to produce arrays of multicellular microtissues in constrained geometries. Combined with confocal imaging and mechanical modeling, this was applied to a model liver progenitor cell system to investigate how tissue geometry and the resulting mechanical stress impacted spatial patterning of early liver progenitor cell fate specification.

Introduction

The differentiation and morphogenesis of progenitor cells into functional tissues are orchestrated through a diverse set of biological, chemical, and physical cues from neighboring cells and other elements of microenvironment. Mechanical forces and signaling have been established as crucial factors to cell development and tissue behavior.^[1] Cells generate intrinsic forces, through actomyosin contractility and other mechanisms, and transmit those forces to the extracellular matrix (ECM) through integrin binding, or to neighboring cells through cell-cell adhesion molecules such as cadherins. Individual cells can also experience extrinsic forces, such as shear from fluid flow or compression from external loads. The cytoskeleton resists these intrinsic and extrinsic forces and transmits them to other intracellular components. Through these connections, mechanical forces trigger biochemical pathways, allowing cells to respond through rearrangement of actin, cell-cell or cell matrix adhesions, and even changes in gene expression.^[2] Key mediators of established mechanotransduction pathways include RHO-associated protein kinase 1 (ROCK), Yes-associated protein (YAP)^[3], and WNT^[4]. The nucleus has also been shown to act as a mechanical sensor^[5]. It is mechanically linked to the cytoskeleton via lamin A/C (LMNA), which allows tensile forces to alter accessibility for transcription factors.^[5–6] Nuclear deformation and nuclear envelope unfolding allow the nucleus to respond to compressive forces.^[7]

Much of the work exploring mechanotransduction in stem cells, and the relationship to the microenvironmental characteristics, such as stiffness, geometry, has been constrained to two-dimensional (2D) culture systems. 3D culture better recapitulates in vivo conditions with increased cell-cell interactions and increased freedom for cell motility and reorganization, which are especially important in differentiation and morphogenesis. Compared with those in 2D culture, cells in 3D experience distinct mechanical stresses which influence their biological functions in embryonic development and tumor growth.^[8] As adoption of 3D culture platforms increase, targeted systems that address mechanical loading and signaling have also been developed.^[9] Since even aggregate size, can affect cell behavior^[10], careful engineering is required to investigate cell response to a 3D environment. Microwell-based platforms have emerged that can create large numbers of replicate multicellular structures for use in drug screening, disease modeling, and stem cell culture. ^[11] Platforms utilizing ECM protein or hydrogel encapsulation have been used to demonstrate that the geometry of an embedded 3D tissue can drive morphogenesis and cancer invasion via endogenous stress patterns.^[12] Other systems, utilizing collagen encapsulated tissues supported by mechanically tuned pillars, have shown patterns of ECM protein organization in response to mechanical stress.^[13] Microwell platforms without encapsulating matrices have been suitable for engineering mechanical conditions such that the cell derived forces, caused by physical constraints, were sufficient to alter alignment of ECM proteins.^[14]

Implementation of 3D systems with mechanical constraints to more tissue-specific contexts, such as stem and progenitor cell development has been more limited, particularly with respect to the liver. In the embryo, the hepatic diverticulum is comprised of bipotential progenitor cells (hepatoblasts). These cells will differentiate into either hepatocytes or biliary epithelial cells (cholangiocytes) and eventually develop into the well-described repeating lobular structure of the liver. The process of fate specification and eventual morphogenesis of liver tissue and bile ducts occurs in a spatially and temporally orchestrated process in the region immediately surrounding a portal vein, guided by diverse cues. Hepatocytic fate is primarily associated with signaling through Wnt, HGF, and FGF,^[15] while biliary fate is associated with increased Notch and TGFβ activity.^[16] YAP has also been shown to have a role in Notch and TGFβ signaling, and fate specification in the liver^[17]. Notably, Wnt, Notch, and YAP signaling are linked to mechanosensitivity^{[4, 18]}.

We have previously demonstrated that substrate stiffness and ECM composition influence differentiation^[19], in a model liver progenitor cell line, bipotential mouse embryonic liver (BMEL) cells.^[20] With this same model cell line, we have also characterized the relationship between increased cell-surface traction force with increased biliary differentiation at the periphery of circular, monolayer, multicellular islands.^[21] Here, the traction force distribution was a consequence of the monolayer geometry, demonstrating a relationship between geometry, mechanical loading, and behavior of the liver progenitor cells, an attribute that has been exploited in other 2D stem cell culture systems.^[22] As in other organ systems, 3D culture of liver more closely mimics in vivo conditions, and we have observed that differentiation of BMEL aggregates can also be affected by modifying the 3D environment.^[23] To date, the relationships between geometry, mechanical signaling, and liver progenitor fate specification in 3D has not yet been characterized.

In this work, we implement an ECM-scaffold-free, hydrogel microwell based platform to produce arrays of BMEL cell microtissues. These tissues have constrained 3D geometries with dimensions comparable to those of the liver lobule, which vary the predicted stress distributions. Using a single-cell image-segmentation-based approach, we then characterize the 3D patterns of hepatocytic and biliary marker expression in this model liver progenitor cell line when cultured in cylindrical and toroidal geometries. We also implement a finite element method (FEM) model to predict the stress conditions of different regions of the tissues to investigate how tensile and compressive stresses correlate with early progenitor cell fate. Our findings provide additional evidence that mechanical signaling plays a crucial role in the 3D spatial patterning of progenitor cell fate specification in liver development. These findings highlight the importance of considering tissue geometries and associated stress conditions in 3D cell culture systems used to study stem cell behavior. Further, this developed system of fabrication, imaging, and modeling, could serve as a platform to further investigate mechanobiological relationships in this and other multicellular systems.

Results

Micromolded PEG substrates generate 3D microtissue with defined geometries

We implemented a microwell based approach to generate arrays of bipotential mouse embryonic liver (BMEL) cell 3D tissues with defined geometries. For fabrication, a master wafer was prepared using photolithography and etching. The wafer contained arrays of various geometries where the cross sections of the eventual microwells are etched approximately 200 μm into the wafer (Supplementary Figure 1A). Initial trials using single level PDMS molds required large volumes of high-density cell suspension, limiting the tissues that could be produced. This motivated the incorporation of a loading well similar to the seeding chamber provided by commercially available molds, which are produced via 3D printing rather than soft lithography.^[11b] To achieve a multilevel mold without additional lithography steps or other equipment, we first fabricated a 500 μm PDMS gasket sheet with an array of holes large enough to expose each sub-array of features. We passivated the gasket with a fluoro-silane. The gasket sheet was positioned over the wafer before the addition of PDMS (Figure 1A). After curing, the PDMS was removed from the wafer, and the gasket sheet was peeled from the rest of the PDMS, which was then cut into individual sections. This produced PDMS molds, where each region of molded features was on a raised circular area (Figure 1B, Supplementary Figure S1B).

Figure 1. Micromolding-based process for microwell and tissue fabrication, and image analysis processes.

A) A wafer is prepared via photolithography and DRIE etching and is fit with a passivated PDMS gasket which leaves exposed a circular area around each array of features. PDMS is cured on the wafer, which is then cut to individual PDMS molds. B) A circular gasket is fit around raised region of region of a PDMS mold. C) PEG Prepolymer solution is sandwiched between the mold and an activated coverslip and is polymerized with UV light. D) Representation of a PEG microwell substrate. E) For tissue seeding, the microwell substrates are set into a multi-well plate. A drop of cell suspension is added to the inset region of the substrate and cells fill the microwells. Following centrifugation, excess cells are removed, and cells condense into aggregates. F) Brightfield image of a section of a PEG substrate with an array of microwells with equal cross-sectional area. G) Bright field image of an array of tissues. Scale bars in F and G are 500 μm. H). Top: Brightfield images of cylindrical (left), and toroidal tissues of varied inner diameter (middle and right). Center: 3D renderings of confocal images of nuclei in tissues. Bottom: Nuclei image segmentation overlaid on central confocal image slices of tissues. Scale bars are 200 μm.

For substrate fabrication, we prepared a prepolymer solution consisting of 100 mg mL⁻¹ 4-Arm-PEG-Acrylate (Laysan Bio) and 10 mg mL⁻¹ photoinitiator (Irgacure 2959, BASF). A 1 mm thick PDMS gasket was positioned around the raised area of the PDMS mold (Figure 1B, Supplementary Figure 1C). A droplet of the prepolymer solution was placed over the PDMS mold, and a 12 mm acrylate functionalized coverslip was floated over the droplet. The assembly was exposed to UV light polymerizing the PEG (Figure 1C). The coverslip was removed from the mold, resulting in a PEG microwell substrate with a loading region with ~500 um side walls, and an inset array of microwells approximately 200 μm deep (Figure 1D). This approach enables a wide variety of well geometries with high aspect ratio features, such as cylindrical and toroidal wells of varied inner and outer diameter (Figure 1F). In the shown example, the inner post diameter ranges from 50 to 250 μm and the outer diameter is adjusted such that each well has the same cross-sectional area (equal to that of a 400 μm diameter circle). This approach generates tissues with approximately the same initial number of cells across geometries. When measured optically, well dimensions closely reflected those drawn in CAD for the photomask (Supplementary Figure 1D, E).

For tissue fabrication, the substrates coverslips were placed into 24 well plate wells and sterilized with UV light. A droplet of cell suspension (~10 E6 cells mL⁻¹) was placed in the loading well of each substrate. The plates were centrifuged, thereby driving cells to fill the microwells. Excess cells were removed with media washes (Fig 1E). Because the microwells were non-fouling and non-adhesive, cells were only able to adhere to themselves, and aggregated into dense, 3D tissues constrained by the well geometries. In cylindrical wells, the cells aggregate and condense into cylindrical tissues. In the toroidal wells, the cells aggregate and condense away from the outer walls, but around the central post, resulting in donut shaped tissues (Figure 1 G,H). Confocal images highlight the 3D structure of the microtissues (Figure 1H). After 72 hours in culture, the mean diameter and thickness of the of tissues in 400 μm diameter cylindrical wells were 226 μm 160 μm, respectively. The mean diameter and thickness of condensed tissues in toroidal wells with 150 μm diameter posts were 286 μm and 132 μm, respectively (Supplementary Figure 1G). Subsequent references to toroidal and cylindrical microtissues (toroids and cylinders) describe these two geometries unless otherwise noted. We used image segmentation^[22d] to identify and locate individual nuclei to enable single cell analysis in 3D (Figure 1H). We observed that despite the equal cross-sectional area, the mean final number of cells incorporated into cylinders was higher than that in toroids, at 3498 and 2841 cells respectively (Supplementary Fig S1F).

Hepatocytic and biliary marker patterning in cylindrical microtissues

In this work, we utilized bipotential mouse embryonic liver (BMEL) progenitor cells, which maintain bipotentiality when cultured at low density in growth conditions. These cells express increased markers of hepatocyte function when cultured in a differentiation media at high density and can be induced to express biliary markers in certain conditions.^[19–21] In previous work with BMEL cells, we correlated the expression of the hepatocytic marker, transcription factor HNF4a, with albumin expression, a marker of hepatocyte function. We have also correlated expression of cholangiocytic marker osteopontin (OPN) with the additional biliary markers SOX9 and Ggt1.^[19a] During growth, BMEL cells can transitively express mixed markers. However, consistent with previous studies, in this microwell system we observed a large, correlated increase in HNF4a and albumin expression after 72 hours of culture, as measured by RT-qPCR. Concurrently, there is a gradual fall in OPN expression as the OPN expressed by unspecified cells is reduced even as some cells begin differentiation towards biliary fate, increasing their OPN expression (Supplementary Figure 2). Thus, in this study, we use HNF4a and OPN for markers of the early hepatocytic and cholangiocytic fate specification, which can be observed at 72 hours in these model liver progenitor cells.

To assess the distribution of cells with these markers within tissues, microtissues were fixed and immunostained for OPN and HNF4a after 72 hours of culture. In tissues produced from 400 μm diameter cylindrical wells, cells expressing OPN are sparsely distributed throughout the tissue, while HNF4a expressing cells are almost exclusively found at the outer shell of the tissues (Figure 2A, B, Supplementary Figure 3). To confirm that differences in cell viability were not responsible for these patterns, we performed live/dead assessment using a calcein-AM/ethidium homodimer-1 assay. We do not see significant cell death in the core region or elsewhere in the tissue (Supplementary Figure 4). To quantify patterned behavior across microtissues, we implemented an image segmentation based single cell analysis process to determine cell phenotype and location in a coordinate system normalized by the tissue radius and thickness (Supplementary Figure 5A). We mapped the percentage of HNF4a and OPN+ (%HN4a+ and %OPN+) cells across a normalized radial and Z coordinate (RZ) space from replicate (N = 45) tissues, taking advantage of the rotational symmetry. In this coordinate system, an R and Z equal to 1 corresponds to approximately 113 and 80 μm, respectively. Using this transformation revealed consistent spatial patterning of HNF4a+ cells at the outer surface of the tissues (Figure 2D). OPN+ cells are distributed across the cross section, with some exclusion from the outer region (Figure 2G).

Figure 2. Spatial patterning of HNF4a and OPN expression in cylinder microtissues.

A) XY confocal slice of a representative cylinder microtissue stained for hepatocytic marker HNF4a (red), biliary marker OPN (green), and with DAPI (blue). Scale bar 100 μm B) 3D rendering of confocal image stack, sliced across the approximate center XZ plane. C) Schematic view of the normalized shell coordinate. D) %HNF4a+ cells in RZ space from N=45 tissues. E) %HNF4a+ cells in the Inner, Intermediate, and Outer regions. F) Percentage of HNF4a+ cells versus normalized shell coordinate, mean ± 95% CI shown in gray. G) %OPN+ cells in RZ space. H) %OPN+ cells in the Inner, Intermediate, and Outer regions. I) %OPN+ cells versus normalized shell coordinate, mean ± 95% CI shown in gray. **** p <= 0.0001.

The condensed tissues adopt a final shape with a circular XY cross section, and a more ovular RZ cross section, which can be approximated as a rectangle with semicircular caps (Supplementary Figure 5B, C). Based on this approximation, we calculated a normalized shell coordinate to describe cell position with a single dimension (Figure 2C, Supplementary Figure 5C). Plotting %HNF4a+ cells using this coordinate system further highlights the outer surface patterning of HNF4a+ cells (Figure 2F). Plotting %OPN+ using this coordinate system revealed the decrease in OPN+ cells at the outer surface, and a slight elevation in OPN+ cells just inside of the outer region (Figure 2I). By sorting cells into an inner, intermediate, and outer region based on the shell coordinate (Supplementary Figure 5C) and calculating the percentage cells positive for each marker, we observed a statistically significant difference in %HNF4a+ cells across all regions, with the outer region being the highest, and inner the lowest (Figure 2H). We similarly observed a statistically significant increase in %OPN+ cells in the intermediate region compared to the outer and inner regions.

Hepatocytic and biliary marker patterning in toroid microtissues

Consistent with these results, in toroidal tissues produced with wells with a 150 μm center pillar, OPN+ cells are sparsely distributed across the 3D structure while HNF4a+ cells were primarily found at the outer surface. Notably, the interior surface region contacting the PEG pillar exhibited low levels of HNF4a+ cells (Figure 3A, B, Supplementary Figure 6). Using a live/dead assay, we did not see significant cell death in the core region, pillar contacting surface, or elsewhere in the toroidal condition (Supplementary Figure 4). Plotting %HNF4a+ cells in normalized RZ space from replicate (N = 40) microtissues demonstrates this differentiation patterning is consistent across tissues (Figure 3E). In this coordinate system, R and Z equal to 1 corresponds to approximately 143 and 66 μm, respectively. Plotting %OPN+ cells in normalized RZ space reveals reduced OPN+ cells in the outer shell, but not at the region contacting the pillar (Figure 3I). As the PEG pillar is chemically inert to the cells, this region would be expected to behave as the rest of the outer surface, implicating mechanical interactions in altering the observed differentiation behavior.

Figure 3. Spatial patterning of HNF4a and OPN expression in toroid microtissues.

A) XY confocal slice of a representative toroid microtissue stained for hepatocytic marker HNF4a (red), biliary marker OPN (green), and with DAPI (blue). Scale bar 200 μm B) 3D rendering of confocal image stack, sliced across the approximate central XZ plane. C) Schematic view of the normalized shell coordinate. D) Schematic view of the normalized radial coordinate. E) %HNF4a+ cells in RZ space from N=40 tissues. F) %HNF4a+ cells in the Pillar, Inner, Intermediate, and Outer regions. G) %HNF4a+ cells versus normalized shell coordinate. H) Percentage of HNF4a+ cells versus normalized shell coordinate. Mean ± 95% CI shown in gray. I) %OPN+ cells in RZ space. J) %OPN+ cells in the Pillar, Inner, Intermediate, and Outer regions. K) %OPN+ cells versus normalized shell coordinate. L) Percentage of OPN+ cells versus normalized radial coordinate. Mean ± 95% CI shown in gray. ** p <= 0.01, **** p <= 0.0001.

We similarly used the plane of radial symmetry to define a normalized shell coordinate for the toroidal tissues (Figure 3C, Supplementary Figure 7). Plotting marker expression frequency in this space emphasizes that HNF4a+ cells are mostly found at the outer region, where the %OPN+ cells drops (Figure 3G, K). This coordinate does not indicate proximity to the pillar contacting surface. Thus, we also plotted percentage of cells positive for each marker against normalized radial coordinate (Figure 3D) revealing that the %OPN+ cells increased near the pillar contacting surface, where R is approximately 0.4 (Figure 3L). Using these two coordinates to parse cells into inner, intermediate, outer, and pillar regions (Supplementary Figure S7), we observe that %HNF4a+ cells were present at an increased frequency that was statistically significant compared to each other region, including the pillar (Figure 3F). In contrast, % OPN+ cells were lowest at the outer region. Further, there was a small increase in %OPN+ cells at the pillar surface compared to the inner region (Figure 3J).

In this work, we focused primarily on early progenitor cell fate specification, as indicated by HNF4a or OPN expression. PCR data suggested that the hepatocytic functional marker albumin also rises in these 3D cultures, thus we sought to assess its spatial distribution using immunostaining. Though difficult to distinguish expression at the individual cell level, we observe an increase in albumin stain intensity surrounding regions with HNF4a+ cells in both geometries (Supplementary Figure 8A). When averaged across multiple tissues in normalized RZ space, we see increased albumin stain intensity in the outer shell region, coincident with the previously establish pattern of HNF4a+ cells (Supplementary Figure 8B). Staining tissues for biliary marker cytokeratin 19 (CK19) demonstrates sporadic patches of increased intensity throughout the tissue with some patches of increased intensity at the tissue peripheries without apparent co-patterning with OPN (Supplementary Figure 8C).

Toroid shape and EGF increase early biliary fate specification

Overall, toroidal microtissues show a statistically significant increase in %OPN+ cells per tissue compared to cylindrical tissues (Figure 4A). Treatment with EGF increases the %OPN+ cells in both toroidal and cylindrical microtissues (Figure 4A, C), while causing only a minor decrease in the percentage of HNF4a+ cells (Figure 4B). As with untreated tissues, EGF-treated toroids show an increase in %OPN+ cells compared to EGF-treated cylinders. EGF treatment did not disrupt the spatial pattern of HNF4a+ cells. In both cylinders and toroids, HNF4a+ cells were mostly restricted to the outer surface, and in EGF-treated toroids, HNF4a+ cells were restricted from the pillar contacting surface (Figure 4C).

Figure 4. HNF4a and OPN expression in EGF treated BMEL microtissues.

A) %OPN+ cells per microtissue by shape and treatment. Control is no treatment. B) %HNF4a+ cells per microtissue by shape and treatment. Control is no treatment. C) Confocal slice of a representative EGF treated cylinder (i) and toroid (ii) microtissue stained for HNF4a (red), OPN (green), and with DAPI (blue). Scale bar 100 μm. E) %OPN+ cells in RZ space from N=32 cylinder microtissues. F) %OPN (green) and HNF4a (magenta) positive cells versus normalized shell coordinate in EGF treated cylinder microtissues. G) %OPN (green) and HNF4a (magenta) positive cells versus normalized radial coordinate in EGF treated cylinder microtissues. Mean ± 95% CI shown in gray. H) %OPN+ cells in the Inner, Intermediate, and Outer regions of EGF treated cylinder microtissues. I) %OPN+ cells in RZ space from N=44 toroid microtissues. J) %OPN (green) and HNF4a (magenta) positive cells versus normalized shell coordinate in EGF treated toroid microtissues. K) %OPN (green) and HNF4a (magenta) positive cells versus normalized radial coordinate in EGF treated toroid microtissues. Mean ± 95% CI shown in gray. L) %OPN+ cells in the Pillar, Inner, Intermediate, and Outer regions of EGF treated toroid microtissues. ** p<= 0.01, ***p<=0.001, **** p <= 0.0001.

Along with amplifying overall expression of biliary marker OPN, treatment with EGF amplifies the spatial pattern of OPN expression. Plotting OPN frequency in RZ space reveals that OPN frequency increases in the intermediate area, just inside the outer surface (Figure 4E). Using the normalized shell coordinate highlights that %OPN+ is low at the outer shell, where %HNF4a+ is highest, peaks in the intermediate zone, and decreases moving towards the core (Figure 4F). The pattern also holds true when using the radial coordinate (Figure 4G). This trend is confirmed by comparing %OPN+ in the inner, intermediate, and core regions, as %OPN+ is highest in the intermediate zone (Figure 4H). In toroids, we see that %OPN+ cells similarly increases in the region just inside of the outer shell, as well as near the pillar surface in RZ space (Figure 4I). The increase in %OPN+ cells just inside of the outer shell is highlighted by the shell coordinate plot, where %OPN+ is low near shell coordinate of 1 where %HNF4a+ is highest. %OPN+ peaks near shell coordinate of 0.75 (Figure 4J). Plotting OPN cell frequency versus normalized radial coordinate shows another peak in %OPN+, near the pillar the contacting region where R ≈ 0.4 (Figure 4K). These two peaks are statistically significant ash shown in Figure 4L.

Increased E Cadherin expression colocalized with increased HNF4a+ cells

To further characterize the architecture of the tissues, we stained for actin and E-cadherin (ECAD) along with HNF4a. In cylinders, we observe an outer actin ring, visible in XY cross sections (Figure 5Ai, Supplementary Figure 9Ai). An actin ring similarly forms at the outer periphery in toroids, and at the inner, pillar adjacent surface (Figure 5Ai). ECAD is expressed at low levels throughout, but highest at the outer shell of both cylinder and toroid geometries (Figure 5A iii). In toroid microtissues, ECAD expression does not increase near the pillar contacting region (Figure 5A iv) correlating increased ECAD expression with the regions of increased HNF4a+ cells. Inspection of these regions with higher magnification confirms these patterns and localizes the increased ECAD expression to cell-cell junctions (Supplementary Figure 9A). To assess the consistency and 3D characteristics of this behavior, we averaged actin and ECAD stain intensity across the RZ plane of symmetry of the tissues and averaged this across multiple tissues. From this, we observe that the actin ring extends into an actin shell, further, confirming a co-localized increase in ECAD expression with the region of increased HNF4a+ cells (Figure 5B).

Figure 5. Patterning of actin, E-cadherin, and HNF4a in 3D BMEL microtissues.

A) Confocal image of a representative cylinder (i) and toroid (ii) microtissue stained for HNF4a (red) and actin (yellow), and with DAPI (blue), and a representative cylinder (iii) and toroid (iv) microtissue stained for ECAD (red) and with DAPI (blue). Scale bar 100 μm. B) Averaged actin intensity in RZ symmetry plane averaged from n = 8 (i) cylinder and (ii) toroid tissues in RZ space. Averaged ECAD staining intensity in RZ symmetry plane averaged from n = 8 (iii) cylinder and (iv) toroid microtissues. C) Confocal images of representative (i) 300 μm, (ii) 200 μm, and (iii) 100 μm wide oblong microtissues stained for HNF4a (red) and actin (yellow). Confocal images of representative (iv) 300 μm, (v) 200 μm, and (vi) 100 μm wide oblong microtissues stained for ECAD (red) and with DAPI (blue). Scale bar 100 μm. D) Confocal image of a representative 200 μm wide oblong microtissue stained for HNF4a (red), OPN (green), and with DAPI (blue). Scale bar 100 μm. E) Percentage of HNF4a+ cells in RZ space in the center 25% of the tissue height from N=18 200 μm wide oblong microtissues. F) Descriptive regions of oblong microtissues. G) %HNF4a+ cells in the core, flat, and regions of 200 μm tissues. ***p<=0.001, **** p <= 0.0001.

HNF4a+ cells excluded from flat regions of oblong microtissues

To further explore the relationship between geometry and differentiation, we prepared “oblong” microtissues using wells with a cross section that is rectangular with semicircular caps. Here, the wells were designed with widths of 100, 200, or 300 μm, and lengths producing consistent cross-sectional area as above. All wells have the same depth of approximately 200 μm. After 72 hours of culture, tissues in the 300 μm-wide oblong wells condense into slightly elongated, ovular cylinders. In these geometries, the spatial patterns of actin, ECAD, and HNF4a expression are similar to those observed in cylinder microtissues (Figure 5C i,ii). Microtissues in the 200 and 100 μm-wide oblong wells condense such that they are pressed against the side walls, producing microtissues with flat sides and rounded caps. In these tissues, the cortical actin ring is present around the entire periphery of the microtissue cross section (Figure 5C iii,iv, Supplementary Figure 9A, B). Interestingly, HNF4a+ cells were increased at the round cap regions, and reduced at the flat, wall-contacting sides. Areas of increased ECAD expression also follow a similar pattern (Figure 5C iii–vi, Supplementary Figure 9A, C).

We stained for and quantified %HNF4a+ cells in replicate (N = 18) 200 μm-wide oblong tissues (Figure 5D). Plotting %HNF4a+ cells in normalized XY space for the central 25% of the tissues’ thickness shows that the oblong tissues consistently have higher levels of HNF4a+ cells in the round cap regions in the flat sides, and HNF4a+ cells are infrequently found through the core (Figure 5E). Quantitative analysis by region demonstrates statistical significance of these observations (Figure 5F, G). Interestingly, when viewed in normalized XZ space, we observe that the free top region of the tissues adopts a slightly rounded shape and behaves similarly to the rounded caps. The bottom of the tissues, which remain flat against the surface of the well behaved like the flat sides (Supplementary Figure 10A–D). Based on this finding, we assessed the toroid and cylinder geometries for a similar pattern and found a less pronounced, but statistically significant increase in the level of HNF4a+ cells in the upper versus lower regions of the outer shells (Supplementary Figure 10E–G). Such findings suggest a possible role of curvature in the patterning.

Blebbistatin disrupts HNF4a expression patterning and OPN expression

To investigate the role of actin-myosin contractility on differentiation in 3D, we treated microtissues with blebbistatin immediately after microwell seeding to disrupt actin-myosin contraction during tissue formation. Overall, treatment with blebbistatin reduces OPN+ cells in all geometries, suggesting actomyosin cell contractility is required in biliary fate specification (Figure 6A, B, I, J). In both cylinders and toroids, blebbistatin does not greatly affect overall levels of HNF4a+ cells compared to DMSO-treated tissues (Figure 6I, J), but does appear to disrupt spatial patterning (Figure 6A, B). In the cylinders, there remained increase in %HNF4a+ cells in the shell compared to the core, however this pattern is less pronounced in blebbistatin-treated tissues relative to DMSO-treated tissues (Figure 6C, D). Using the shell coordinate, we observed that the peak level of %HNF4a+ cells is reduced and spreads further into the structure (Figure 6G). Blebbistatin was even more disruptive to the spatial patterning in toroid microtissues (Figure 6E, F), with %HNF4a+ cells being more uniformly distributed across the microtissue volume (Figure 6H). Treatment with ROCK inhibitor Y-27632 did not impact the overall frequency or spatial pattern of biliary or hepatocytic markers in cylinder or toroid microtissues (Supplementary Figure 11) suggesting that generation of the observed patterns is not dependent on ROCK.

Figure 6. Disruption of HNF4a expression patterning with blebbistatin.

Confocal image the central slice of a representative cylinder (A) and toroid (B) blebbistatin-treated microtissue stained for HNF4a (red) OPN (green) and with DAPI (blue). Scale bar 100 μm. C-F) %HNF4a+ heat maps for DMSO and blebbistatin treated cylinder and toroid microtissues. G,H) %HNF4a+ versus shell coordinate for DMSO and blebbistatin-treated cylinder and toroid microtissues. Mean ± 95% CI shown in gray. I,J) Overall %HNF4a and %OPN+ cells per microtissues in DMSO and blebbistatin-treated cylinders and toroids. * p<= 0.05, ** p<= 0.01, **** p <= 0.0001.

Mechanical models suggest differing regions of compression and tension from cell derived forces

To understand the mechanical behavior of the microtissues, we implemented a 3D finite element method (FEM) model, building off previously reported 2D and 3D tissue models (Supplementary Figure 12).^{[22e, 24]} Based on our observed actin and ECAD patterns, we modeled the microtissues as having a contractile shell, similar to that described in the aggregates produced and characterized by Lee.^[25] Based on the increased %OPN+ cells in the region just inside the outer shell, we modeled the intermediate region as stiffer than the core, also as suggested by Lee et. al. (Supplementary Figure 13A). The results of this model suggest that in the cylinders, the outer shell region is primarily under tension, with positive first and second principal stresses, and a near-zero third principal stress. The intermediate and core regions are entirely in compression (Figure 7A, B, Supplementary Figure 13B). The model predicts that the region experiencing the highest magnitude compressive stress (most negative third principal stress) is the intermediate region (Figure 7A, Bii). In the toroid model, the contractile shell region is also primarily under tension, and the intermediate and core regions were entirely in compression, with increased compression at the intermediate region. Differing from the outer shell, the model predicts that the pillar contacting region experiences compression at comparable levels to that in the intermediate zone (Figure 7C, D).

Figure 7. Modeling and measurement of stress in 3D BMEL microtissues.

A) Simulated first and third principal stresses for an RZ slice of a representative cylinder microtissue. B) Simulated principal stresses at the line of Z = 0 from the above RZ slice. C) Simulated first and third principal stresses for an RZ slice of a toroid microtissue. D) Simulated principal stresses at the line of Z = 0 from the above RZ slice. Stress values given in relative, arbitrary units. E) Representative cylinder (i) and toroid (ii) microtissues with an embedded microgel. Scale bar 100 um. Maximum intensity projections of the stressed (iii and iv) and relaxed (v and vi) microgels from the cylinder and toroid geometries shown above. Scale bar 10 um. F) Average compressive stress on microgels in cylinders and toroids plotted versus radial position. G) Brightfield image of an oblong microtissue. H) Simulated first and third principal stresses from the central XY slice of an oblong microtissue. I) Simulated principal stresses at the line of X = 0 (i-ii) and Y = 0 (iii-iv) from the above XY slice.

To validate this model, we imbedded alginate microgels with fluorescent beads into the microtissues to measure forces within the tissue. In these experiments, an image was acquired of the microgel under the stress provided by the tissue. The tissue was lysed with a detergent, and an image is collected of the fully relaxed (stress-free) microgel. The relative displacement of the fluorescent beads was used to measure the total stress on the microgel during tissue culture.^[8c] These microgels were successfully incorporated into both cylinder and toroid microtissues and imaged before and after lysing (Figure 7E). We calculated the relative volume change and average compressive stress in each microgel. All measured microgels in both tissue geometries expanded upon tissue lysing, indicating that the interiors of the tissues are all in compression. The average compressive stress across replicate cylinders and toroids was 695 ± 197 Pa and 590 ± 207 Pa respectively. However, we did not observe a statistically significant difference in average compressive stress between toroids and cylinders or as a function of radial position (Figure 7F). More dense distributions of microgels in toroid and cylinder tissues may be needed to differentiate between stresses present in these geometries.

We next applied the FEM model to our oblong microtissues. Typically, cells of the same type, and in close proximity, self-assemble into spherical shapes, similar to how liquid drops behave.^[26] Their final aggregate shape is dictated by initial geometric constraints as well as characteristics of the cell line.^[27] Our oblong tissues were observed to assemble into shapes where they contact the flat region of the wall, resulting in flat outer surfaces. If the tissue exhibited uniform contraction, the tissue should uniformly shrink away from the walls. Under this model, there would be no stress distribution (Supplementary Figure 13C). Unless the cells are rapidly migrating to achieve a more spherical shape, the continued pressure against the wall should only occur if they are modeled with a contractile shell and passive core. Such a model that omits the walls of the well shows this results in an outward “bowing” at the flat regions of our oblong tissues (Supplementary Figure 13D). When the well walls are included, the contractile regions are primarily in tension. At the round caps, the third principal stress falls to near-zero. However, the wall-contacting regions are experiencing compression at similar levels to those found in the intermediate and core regions (Figure 7H, I).

The results of these models suggest that geometry drives regions of surface compression, which correlates with reduced hepatocytic differentiation and reduced ECAD expression. To explore this relationship further, we fabricated “double pillar” and “dumbbell” shaped microtissues (Figure 8A, D). The FEM model, extrapolated from that of our oblong tissues, predicts that the presence of the pillars should cause the tissues to contract away from the walls, eliminating any compressive surfaces at the periphery, yet maintaining compression against the pillars and in the core (Figure 8B, C). This predicted behavior was confirmed experimentally (Figure 8B). Here we observe that the entire periphery contained increased HNF4a+ cells and increased ECAD expression, including the flat sides, while the compressed regions across the core and pillar contacting regions lack these markers (Figure 8H,J). We also observe the cortical actin ring around the periphery (Figure 8I). The model predicts that the dumbbell microtissues contract such that only the center “bridge region” is compressed against the well wall (Figure 8D), which was similarly confirmed experimentally (Figure 8K). Here, increased HNF4a+ cells and ECAD expression are found around the periphery, except near this flat bridge region (Figure 8L,N). The cortical actin is also found at the periphery, with some decrease at these flat sections (Figure 8M).

Figure 8. Behavior of double pillar and dumbbell microtissues.

A-C) FEM model of double pillar tissue. A) CAD model used for FEM simulation. B) Simulated principal stresses for the center XY slice. C) Simulated principal stresses along the line Y = 0, the yellow line in B (i-ii) and along the line X = 0, the white line in B (iii-iv). D-F) FEM model of dumbbell tissue. A) CAD model used for FEM simulation. B) Simulated principal stresses for the center XY slice. C) Simulated principal stresses along the line Y = 0, the yellow line in E (i-ii) and along the line X = 0, the white line in E (iii-iv). Stresses are given in relative units. G-J) Characterization of double pillar tissues. G) Bright field image. H-I) Central slice of a microtissue stained for HNF4a (red), OPN (green), actin (yellow) and with DAPI (blue). J) Central slice of a microtissue stained for ECAD (red) and with DAPI (blue). G-J) Characterization of dumbbell tissues. K) Bright field image. L-M) Central slice of a microtissue stained for HNF4a (red), OPN (green), actin (yellow) and with DAPI (blue). J) Central slice of a representative microtissue stained for ECAD (red) and with DAPI (blue). Scale bars 200 μm.

Discussion

The novel combination of a molded microwell-based microtissue fabrication platform with the described imaging, analysis, and mechanical modeling pipelines, provides an effective system to characterize spatial patterns of cell fate in 3D. The multilayer two-step PDMS molding process enables creation of a loading well, without additional clean room processes or use of a 3D printer, thereby permitting smaller volumes for cell seeding and for immunostaining. The demonstrated well-defined, high aspect ratio geometries provide a variety of both compressive and tensile stress profiles^[14]. These include cylinder, toroid, oblong, dumbbell, and multi-pillar structures. Of particular note is the toroid geometry with 150 um inner diameter, which is comparable to that of an embryonic mouse portal vein in the developing liver, providing another step in the development of physiologically relevant tissue culture.^[28]

The microwell depth selected was approximately 200 μm, yielding tissues 120 to 190 μm in thickness. By keeping tissue thickness under 200 μm, any individual cell is no more than 100 μm from the outer surface, which has been suggested to be the diffusion limit of oxygen in tissue.^[29] Consequently, microtissues in the size range used here can reduce the possibility of pronounced oxygen gradients and hypoxic core regions, that have been demonstrated to affect larger-diameter spheroid systems ^[30]. While hepatocyte spheroids have been shown to maintain viability in the 200 μm size range^[31], model and measurement systems in the literature suggest that modest oxygen and chemical gradients can still occur.^[32] Such gradients, even if not lethal could also have a role in patterning. However, the live/dead staining images (Supplementary Figure 4) of the liver progenitor microtissues utilized in our studies, suggest that small molecules (like calcein-AM) can achieve near uniform distribution within the microtissues in two hours.

The layer of increased E-cadherin and actin expression at the outer shell of the tissues was consistent with a model of mechanical polarization at the boundary causing an effective tissue surface tension.^[33] According to this model, the outer shell develops a higher degree of contractility from the cortical actin layer that forms. This results in high intercellular tension resolved across cell-cell junctions.^[34] This mechanical polarization is commonly observed in stem and progenitor cell tissues^{[30c, 35]} and has been measured in other 3D aggregates with defined geometries.^[24a] The presence of HN4Fa expressing cells in this contractile region suggests that increased cell-cell tension correlates with hepatocytic differentiation. In this work, we focused on early fate specification indicated by HN4Fa expression, whose nuclear localization aided in tracking individual cell fates. The observed increased albumin stain intensity coincident to regions high in HNF4a+ cells suggests that these cells are beginning hepatocytic differentiation. These patterns are consistent with our previously reported observations in 2D circular islands. In that system, the central region showed the highest hepatocytic differentiation,^[21] which is where the highest cell-cell tension was generated.^[36] Meanwhile, each of the regions lacking in HNF4a+ cells were regions predicted or measured to be experiencing compression due to the cell generated forces. This included the core of all geometries, the region compressed against the center PEG pillar in the toroid tissues, and the flat wall-contacting regions in the oblong tissues. This data suggests that compression decreases the likelihood of early hepatocytic specification. Treatment with blebbistatin to inhibit myosin II affects both intercellular tension in the outer shell, and the resulting compression on the inner regions. This caused reduction of HNF4a+ cells at the outer surface and allowed hepatocytic differentiation to permeate further into the microtissue structure. This supports the hypothesis that intercellular tension facilitates early hepatocytic fate, and conversely, compression inhibits hepatocytic specification. The same effects were not replicated by treatment with Y-27632, which inhibits the phosphorylation of myosin light chain by ROCK. Our previous findings in controlled 2D cultures similarly indicated distinct affects of Y-27632 and blebbistatin treatment on the differentiation of these cells^[21]. As Y-27632 does not directly inhibit myosin, it is possible sufficient intercellular tension is achieved for the pro-hepatocytic effect even with ROCK inhibition. ROCK inhibition can have additional affects, such stabilizing cell junctions including E-cadherin^[37] which here could be aiding in the maintenance of sufficient compression, even if the magnitude is reduced.

The divergent behavior observed in the rounded top region and flatter bottom region observed in the oblong tissues could imply that additional external forces not included in our FEM model, such as gravity or friction, may be providing sufficient downward force to maintain the flatness of the tissue surface and prevent early hepatocytic fate via compression. We also note that lack of curvature corresponds with observed compressive regions. There is a growing body of knowledge suggests that cells and tissues respond to surface curvature in the microenvironment.^[38] The flat compressive regions in our oblong microtissues have zero curvature, while the pillar contacting region has nonzero median curvature yet zero Gaussian curvature.^[24a] There is evidence that cells respond differently to these curvature types.^[39] The double pillar microtissue results suggest that the flat regions are still pushed towards hepatocytic fate in the absence of compression. However, when not constrained against a wall it is possible that sufficient curvature has forms. Additionally, in 2D monolayers, hepatocytic differentiation occurs despite the planar geometry.^[21]

Overall, toroid microtissues had higher levels of cells positive for the biliary marker OPN. This corresponded to increased compression across the core region in the FEM model, when compared to cylinder tissues. In both geometries, we observed increased biliary differentiation in the intermediate region just inside the outer shell. In the toroid tissues, biliary differentiation also increased near the surface contracting against the pillar. These intermediate regions correspond with the regions that exhibit the greatest compressive stress in the FEM model. Consequently, these data demonstrate a positive correlation between biliary fate and regions that would exhibit increased compression. Treatment with blebbistatin greatly reduced OPN expression, correlating reduced compression with reduced biliary fate. Y-27632 did not significantly alter biliary differentiation. However, previous work has shown that Y-27632 can increase biliary differentiation depending on the context.^[19] Thus, inhibition of ROCK may provide opposing signals related to biliary fate. Further, when we stained for a later biliary marker, CK19, we observed it was expressed sporadically throughout the tissue, with a distribution that more closely resembled the spatial profile exhibited by actin at the time point observed. This suggests that full biliary differentiation had not yet occurred at 72 hours, and that there may be interactions or common mechanisms that are influencing cytokeratin and actin expression during the early stages of liver progenitor differentiation within the constrained 3D geometries.

Across all geometries tested, there were significant proportions of cells that, at the 72-hour time point, expressed neither HNF4a nor OPN at observable levels with the immunostaining used. As we have verified their viability, we believe that they maintain their bipotentiality, but display distinct differentiation kinetics. Future assessment using additional markers or culture of disaggregated tissues could enable further insights towards the refinement of the temporal differentiation processes. In our studies, treatment with EGF did increase biliary differentiation in all microtissue geometries, suggesting that these cells maintain their differentiation potential but may require additional factors or treatments to proceed at higher efficiencies. EGF also amplified the spatial patterning aiding in characterizing these patterns. EGF has been previously demonstrated to play a role in both hepatocyte and biliary epithelium formation ^[15a] and has been used in various progenitor and human pluripotent stem cell lines to generate cholangiocytes in vitro.^[40] Studies have reported EGF and EGFR induction of Notch signaling in the context of fate specification and morphogenesis^[41] which is known to be mechanically sensitive.^{[18, 42]} Our results add to growing evidence that EGF plays a role in biliary fate specification possibly in synergy with Notch and stress.^[43] This is one example of mechanisms which can be explored in this system. Modulation of other pathways through drug treatment, siRNA, or genetic editing, would permit exploring their relationships to force and geometry. Reliance on immunostaining can partially limit the refinement of differentiation kinetics. In future efforts, the integration of relevant fluorescent reporters with this platform would enable live cell imaging to track differentiation patterning over time and other dynamic processes.

The patterning observed using the developed system of imaging, mechanical models, and measurements, provide compelling evidence that compression decreases hepatocytic and increases biliary early fate specification in 3D culture. In this system, the tensile shell and compressive regions follow from mechanical polarization at the boundary, something associated with tissue-media boundaries in 3D aggregates. However, mechanical polarization at tissue-tissue boundaries has been observed in vivo, causing local increases in cortical tension and playing a role in cell sorting.^[44] Additionally, compressive forces can be achieved within adhesive matrices in some geometries, and thus may arise in vivo.^[24b] While the mechanisms causing these behaviors remains the subject of follow up work, our observations of this mechanosensitivity are consistent with a growing body of evidence illustrating the importance of biomechanical signaling for cellular fate reported elsewhere in the literature. Studies using embryonic stem cells progenitors found that compressive stress can induce upregulation of SOX9, a transcription factor associated with biliary differentiation.^[45] In bone remodeling and homeostasis, OPN is upregulated in response to compressive loading and is key to transduction of mechanical signals.^[46] Though outside of the hepatic context, these findings support the mechanically sensitive nature of some biliary differentiation pathways. Recent work has demonstrated that cell to substrate traction forces may impose vertical compressive forces on the nucleus resulting in depolymerization of actin and, alteration of chromatin condensation, transcription factor activity, and gene expression.^[47] This provides a possible connection to our observations in 2D and 3D culture, as in 2D, increased biliary and decreased hepatocytic differentiation correlated to regions of high cell to substrate traction force^[21]. Other work has shown that increased cytoskeletal tension represses HNF4A in hepatocytes^[48] and reduced hepatocytic induction of liver stem cells.^[49] Importantly, these systems relied on 2D matrix rigidity to induce cytoskeletal tension, which would result in nuclear compression. Indeed, others have directly implicated nuclear deformation as a biomechanical signal that leads to reduced hepatocyte function in liver cirrhosis.^[7a] Such findings highlight the role of mechanical forces in liver development, regeneration, and disease, and the importance of considering the full 3D nature of how forces are experienced and sensed by cells.

While we successfully demonstrated direct measurement of compressive forces in our tissues using microgels, we were unable to verify the model-predicted differences in the levels of compression between geometries and intratissue regions. This limitation stemmed from an inability to track the relative vertical position of the microgel in the tissue, something that could be corrected using a cell labeling dye to trace tissue boundaries in these experiments. Furthermore, microgels positioned too far from the bottom tissue surface could not be imaged at high enough resolution due to light penetration limitations in the aqueous medium. Despite these challenges, we were able to measure deformation of the elastic round microgels and showed that the cylinder and toroid microtissues exert an average compressive stress of 200 to 1000 Pa, which is on the same order of magnitude as the shear storage modulus of the normal rat liver tissues^[50], suggesting that our microtissues provide significant progress toward mimicking mechanical behavior of in vivo tissues. Future work to optimize implementation of microgels or other emerging techniques to measure cell-generated forces in 3D aggregates^{[8c, 25, 51]} may provide a more precise stress map of theses tissue to validate and refine our mechanical model. It is important to note that a key advantage of our system is in its ability to generate these mechanical forces via microwell geometry, avoiding the use of external devices or treatments, thereby more closely mimicking the in vivo environment.

Conclusion

In this work, we have implemented a microwell-based system to fabricate and analyze the behavior of geometrically defined 3D liver progenitor microtissues. The modularity of the design and ease of implementation allow these methods to be easily adapted to other 3D cell culture applications. The developed system could also be used to generate and analyze standardized 3D tumor models of controlled geometry and characterize or screen for any impact of geometry on drug efficacy. Using an FEM model along with mechanical measurements, we observed in this system that cell-derived forces create regions of varied compressive and tensile stresses, which combined with the tissue geometry correlated to spatial patterns of markers of early hepatocytic and biliary fate specification in liver progenitor cells. This relationship between mechanics and differentiation has not been described in a 3D system, and these findings provide important insight into how geometric features may have a role in orchestrating liver development via mechanical signaling. Understanding these mechanisms could be leveraged in addressing developmental disorders and liver cancers, or in developing approaches to manufacture artificial livers from stem cells.

Materials and Methods

Wafer and PDMS mold fabrication

The master wafer was prepared using soft lithography techniques.^[52] A photomask was drawn in AutoCAD and printed on to transparent plastic (CAD/Art services) which contained arrays of the cross sections of the desired microwell geometries. A thin layer of negative photo resist (KMPR) was spin coated on to a clean 4” silicon wafer, and flood exposed to UV through the photomask. Following development, the exposed features were etched with deep reactive ion etching (STS Pegasus, SPTS Technologies) to a depth of approximately 200 μm.

For PDMS mold fabrication, a gasket sheet of PDMS was first molded between two glass slides using a 500 μm spacer. 6 mm diameter holes (large enough to surround the feature arrays on the wafer) were punched into the sheet. It was then treated with oxygen plasma and incubated with Trichloro(1H,1H,2H,2H-perfluorooctyl)silane vapor under vacuum for at least one hour. The sheet was positioned over the master wafer such that the holes aligned with the feature arrays to be molded. PDMS was poured over the wafer and sheet, fully degassed, and cured at 70° C for at least 3 hours. After curing, the PDMS was removed from the wafer and the gasket sheet was carefully peeled from the rest of the cured PDMS leaving 500 um raised platforms, which create to the loading well, on top of which the feature arrays protrude an additional ~200 um. The two-step PDMS molding technique enables creation of multiple mold levels without requiring additional photolithography or etching steps. Additionally, a PDMS sheet was molded between glass slides using a 1 mm spacer. This sheet was cut into individual gasket pieces, each with a 7 mm hole.

Preparation of micro molded PEG substrates

Polyethylene glycol (PEG) hydrogels substrates were prepared by adapting previous protocols.^{[11a–c, 53]} 12 mm circular coverslips were immersed in 0.1 N NaOH for 1 hour, rinsed with DiH2O and placed on a hot plate at 110°C until dry. The NaOH treated coverslips were activated by immersion in 2% (v/v) 3-(trimethoxysilyl)propyl methacrylate in ethanol and placed on a shaker for 30 min. The activated coverslips were immersed in ethanol on the shaker for 5 min and again dried on a hot plate at 110°C. A 111.11 mg mL⁻¹ 10kDa 4-Arm PEG-acylate (Laysan Bio) prepolymer solution was prepared in 1x PBS. This solution was mixed with Irgacure 2959 (BASF) solution (100 mg mL⁻¹ in methanol) at a volumetric ratio of 9:1 (prepolymer to Irgacure) to achieve a final PEG concentration of 100 mg mL⁻¹. The solution was then degassed under vacuum.

For PEG molding, the 1 mm gasket was positioned around the feature array to be used, leaving approximately 1 mm between the raised platform and the gasket. A 50 μL droplet of prepolymer solution was deposited on the mold. A pipette tip was used to spread the prepolymer solution across the mold and knock bubbles from the mold features. The droplet was covered with an acrylate coverslip, which was lightly pressed against the gasket. The assembly was exposed to UV light using a Spot UV Curing System (OmniCure S1500, Excelitas Technologies) with a 320-390 nm Filter and adjustable collimating adapter, at an intensity of approximately 50 mJ cm⁻² for 30-60 seconds. The coverslip was then carefully removed from the mold and immersed in PBS in a 24 well plate. Prior to use in culture, the substrates were sterilized by immersion in PBS supplemented with 1% (v/v) pen/strep under UVC for 30 minutes.

Cell culture and tissue formation

The experiments utilized BMEL 9A1 cells of passages between 28 and 34. BMEL cells were cultured as previously described.^[20a] For expansion, cells were thawed onto tissue culture plastic flasks coated with collagen I (0.5 mg ml⁻¹) and incubated at 37°C and 5% CO₂. For subculturing, flasks were treated with trypsin-EDTA (0.25% [v/v]) for ≤10 min to detach cells and replated on collagen I coated flasks. Growth media, for expansion, consisted of RPMI 1640 + GlutaMAX (Life Technologies, 61870-127) with fetal bovine serum (10% [v/v], FBS), penicillin/streptomycin (1% [v/v], P/S), human recombinant insulin (10 μg ml⁻¹, Life Technologies, 12585-014), IGF-2 (30 ng ml⁻¹, PeproTech, 100-12), and EGF (50 ng ml⁻¹, PeproTech, AF-100-15).

For tissue formation, cells were collected and resuspended to ~10 E6 cells mL⁻¹ in differentiation media. A 50μL drop of cell suspension was added to the recessed loading well of each substrate. The 24 well plate was then centrifuged to drive cells into the wells. Excessed cells were removed by repeated media rinses. Tissues were cultured in differentiation media at 37°C and 5% CO₂ for 72 hours with a media change after the initial 24 hours. Differentiation media consisted of Advanced RPMI 1640 (Life Technologies, 12633-012) with FBS (2% [v/v]), P/S (0.5% [v/v]), L-glutamine (1% [v/v]), and minimum non-essential amino acids (1% [v/v], Life Technologies, 11140-050).

Growth factor and drug treatments

All growth factors and drugs were prepared and reconstituted according to the instructions of the manufacturers: EGF (PeproTech, AF-100-15) 50 ng ml⁻¹ in PBS with 1% w/v BSA; (−)-blebbistatin (Cayman Chemical, 13013), 1 mg ml⁻¹ in dimethyl sulfoxide (DMSO); Y-27632 (Enzo Life Sciences, 270-333-M005), 5 mg ml⁻¹ in deionized water (DiH₂O). Drugs were added to differentiation media at the following concentrations: (−)-blebbistatin, 25 μm; Y-27632, 15 μm. In experiments with addition of soluble treatments, these were added immediately after the excess cell media rinses. Media and treatments were refreshed after the initial 24 hours.

Immunostaining

Cells were treated with brefeldin A (10 μg ml⁻¹, R&D Systems, 1231/5 in differentiation media) for 2 h prior to fixation by immersion in paraformaldehyde (4% [v/v] in 1× PBS) for 30 min at room temperature. Fixed samples were permeabilized by immersion in Triton X-100 (0.5% [v/v] in 1× PBS) for 1 hour at room temperature. Samples were incubated in blocking buffer (5% [v/v] donkey serum in 1× PBS) for 1 hour at room temperature. Primary antibody solutions were prepared by diluting one or more of the following antibodies in blocking buffer: mouse anti-HNF4a (1/200 from stock, Abcam ab41898), goat anti-OPN (1/60 from stock, R&D Systems, AF808), goat anti-Ecadherin (1/50 from stock, R&D Systems AF748), Actin-stain 488 phalloidin (7/1000 from stock, Cytoskeleton PHDG1-A), goat anti-ALB (1/100 from stock, Bethyl A90-134A), goat anti-CK19 (1/200 from stock, Abcam ab52625). A 50 μL droplet of primary antibody solution was added to the recessed loading well of each substrate. Samples were incubated overnight at room temperature on a shaker. Samples were rinsed via 3 × 15-minute washes in PBS on a shaker. Secondary antibody solutions were prepared by diluting one or more of the following secondary antibodies in blocking buffer: DyLight 550-conjugated donkey anti-mouse IgG (1/50 from stock, Abcam, ab98767) and DyLight 488-conjugated donkey anti-goat IgG (1/50 from stock, Abcam, ab96935). A 50 μL droplet of secondary antibody solution was added to the recessed loading well of each substrate. Samples were incubated overnight at room temperature on a shaker. Samples were rinsed via 2 × 15-minute washes in PBS on a shaker. Samples were incubated in DAPI solution (Invitrogen D1306) for 1 hour, and briefly rinsed in PBS.

A droplet of liquid mountant (ProLong™ Diamond Antifade, Invitrogen) was added to each substrate, and the coverslips were mounted onto standard microscope slides. Mounted samples were cured for at least 24 hours at room temperature. Once cured, samples were sealed with clear nail polish.

3D Tissue Imaging, Segmentation, and analysis

The fluorescently stained samples were imaged using a laser scanning confocal microscope (Leica TCS SP8). 3D image stacks were segmented into individual cells using an adaptation of the MINS (modular interactive nuclear segmentation) MATLAB/C++-based segmentation platform^[22d] on the nuclear image (DAPI) channel. Utilizing the Bio-Formats software tools^[54], the microscope software generated .lif files were directly loaded into the software to sequentially segment all image stacks from each tissue array, and automatically read in metadata such as pixel size.

Semi-automated post processing and analysis was completed using a series of MATLAB scripts. First, an edge detection-based process was used to identify the outer tissue boundary in each image slice to mask out cells and debris not incorporated into the tissue. Due to nature of the microwells, tissues can move and rotate in all three dimensions, thus rotation and alignment is required to compare spatial behavior across replicate tissues. For this, a best fit ellipse was fit to the XZ, YZ, and XY projections of the masked, segmented nuclei data. The orientations of the best fit ellipses were used to rotate the nuclei centroids such that major axes from the XZ and YZ projections were aligned with the horizontal (X) and vertical axis (Y) respectively, the major axis of the XY projection was aligned to the horizontal (X) axis. The nuclei were also translated such that tissue center is at the origin. The major and minor axis of the XY projection were used to normalize the X and Y coordinates, and the height of the tissue was used to normalize the z coordinates. This normalized coordinate system was used in subsequent analysis to enable spatial comparison across replicates independent of slight differences in tissue size after cell aggregation.

For OPN and HNF4a expression analysis, the average intensity of the relevant stains was calculated in each of the segmented nuclei, along with intensity of the surrounding 3D area. The difference between the intensities and the surrounding background were used for analysis to account for intensity difference due to imaging penetration across the thickness of the tissue. A two component gaussian mixture model was applied to these relative intensities within each tissue to sort tissues into positive or negative for each stain.

For phenotype heat map generation, cells from replicate tissues were binned in 2D according to the relevant normalized coordinates, and the percentage of cells within each bin positive for the strain was calculated. For 1D plots, normalized shell and radial coordinates were calculated as described in Supplementary Figure S4. For region-based box plots, regions were separated based on normalized radial and shell coordinates as shown in Supplementary Figure S4.

For e-cadherin, actin, and albumin stain heat map generation, the corresponding images were rotated and centered using the segmented nuclei projection best fit ellipses as described earlier. Images were down sampled by a factor of 4, the XYZ coordinates for each remaining voxel were calculated, and coordinates were normalized using the best fit ellipses. Normalized XY coordinates were converted to a normalized radial coordinate. Voxels were binned into a triangle mesh, and the average intensity in each mesh unit was calculated. This was repeated across multiple tissues using the same mesh to generate an average heat map.

Live/Dead assays

For live/dead assessment, tissues were prepared on glass bottom dishes and treated with 2 μM calcein-AM and 4 μM Ethidium homodimer-1 (Invitrogen L3223) in PBS for 60 minutes at 37°C and imaged over the following hour using a widefield fluorescent microscope (Zeiss Axiovert 200M). To establish appropriate imaging parameters, a dead tissue control was prepared by treating tissues with ice cold 70% ethanol for 15 minutes prior to the live/dead assay.

RNA Isolation, RT-qPCR Analysis

For measurement of liver markers via RT-qPCR, microwell substrates were prepared containing arrays of only cylinder or only toroid wells, and cells were seeded into the wells to form tissues as described above. At the specified time point, the substrate was transferred to a well containing trizol solution (Life Technologies 15596-026), to collect RNA from the tissues within that substrate. For RNA isolation, samples were treated with DNAse (New England Biolabs, M0303S) at 37°C for 30 min and further purified using a RNeasy Mini Kit (Qiagen, 74104) following manufacturer’s instructions. Supermix iScript cDNA synthesis kit (BioRad, 1708841) was utilized to produce cDNA from isolated RNA. This was mixed with SsoAdvanced Universal SYBR Green Supermix (Bio-Rad, 1725264) and primer pairs at a final concentration of 100 nM (primer pair sequences listed in Supplementary Table 1). Thermal cycling and amplification curves measurement was completed using a CFX Connect Real-Time PCR Detection System (Bio-Rad). mRNA expression was calculated relative to Hprt1 and control samples as indicated using Bio-Rad CFX Manager 3.1 software.

Finite element modeling

3D Tissue geometries were drawn in Autodesk inventor with dimensions that approximate measured final tissue dimensions. Separate solid bodies were generated for each material type in the tissue model. These geometries were exported as STEP or IGES files. The finite element mesh generator software Gmsh was used to generate tetrahedral mesh files for each CAD geometry.^[55] The finite element model was produced using the FEBio software suite.^[56] The PreView software was used to import the geometry, set boundary conditions, and specify material properties. Tissues were modeled as a union of bodies with each body being assigned a material.^[24a] The core and intermediate regions were modeled as Neo-Hookean solids. The free outer shell and pillar contacting shell regions were modeled as solid mixtures of a Neo-Hookean material and material with a prescribed isotropic active contraction. Due to the actual stiffness of the tissues being unknown, non-dimensional stiffness and prescribed contraction values were used to analyze the relative stress patterns arising from parameter choices. Intermediate, outer shell, and pillar-contacting shell regions were assigned a Young’s modulus of 1. The core Young’s modulus was set to 0.5. The outer shell and pillar contacting regions’ prescribed stress was set to 5. Because the PEG substrate is much stiffer than the tissue, the microwell boundaries and pillars were either modeled as rigid material with a sliding contact, or a boundary condition preventing displacement normal to the surface. The simulation was run using the FeBio solver as a steady-state static single time point using default settings. Simulation results were visualized in the PostView program, which was also used to export results as a VTK file. Paraview was used to calculate principal stresses, visualize data, and generate figures.^[57]

Microgel force sensor experiments

For microgel force experiments, the microwell substrates were fabricated on a glass bottom 35 mm dish (Cell E&G, GBD00003-200). Alginate microgels with fluorescent particles were fabricated as previously described with 0.5% w/v alginate.^[8c] The droplet suspension was mixed with the cell suspension just before seeding the microwells. Alginate is not stable in RPMI medium. Therefore, in microgel experiments, differentiation media was altered to use Advanced DMEM (Gibco 12491-023) instead of advanced RPMI. Images were acquired using a laser scanning confocal microscope (Leica TCS SP8). Microgels were first located and a low zoom image was collected to be able to mark the XY location of the particle within the tissue. Images of the stressed elastic round microgels were collected, and the tissues were treated with 2.5% Triton X-100 detergent to obtain stress-free conditions. Images of the particles were collected ever 5-10 minutes for approximately 1 hour until the stress-free condition was achieved. ImageJ was used to measure the diameter and centroid location of the tissues and the location of the microgel. 3D confocal images were deconvolved (AutoQuant X3), and the volume was measured using MATLAB scripts. Average compressive stress was calculated based on the Poisson’s ratio of 0.4 and the bulk modulus of 3012 Pa, from interpolation of previous alginate bead stiffness measurements.^[8c]

Statistical analysis

Experiments consisted of three or more biological replicates with multiple tissues per experiment. For percent positive heat map generation, all cells from all replicate tissues in the shown condition were binned in a 50 by 50 RZ space, percent of cells positive for each marker was calculated at each bin location and plotted. For region-based calculations, the percent positive cells in each region for each individual tissue was calculated and plotted. For line plots, the cells in individual tissues were binned in the relevant coordinate space, and a percent positive for the marker was calculated for each bin from each individual tissue. Line plots represent the mean percent positive for each bin position across replicate tissues with the 95% CI ribbons in gray. Line and box blots were generated using the ggplots2 package for R.^[58] For hypothesis testing, Welch’s two-sample t-test was performed using the base t.test function in R. P<0.05 was considered significant. P-values and replicate numbers are indicated in the figure’s captions.