Introduction

Epithelial tissues, comprising an epithelium layer and an underlying connective tissue rich in extracellular matrix (ECM), often exhibit unique curved structures through compressive force-driven epithelial folding. This folding process holds significance for various aspects of epithelial tissue, including development, function, homeostasis, and pathologies1,2,3,4. For instance, intestinal epithelial folding is pivotal in forming intestinal villi5. Abnormal folding or loss of structure relates to disorders like intussusception and celiac disease. Additionally, ECM component degradation, such as collagen and elastin, in the dermis facilitates the folding of skin epithelial tissues. Importantly, epithelial folding orchestrates key transitions in embryonic development like gastrulation and neurulation, underscoring its role in overall success3. Understanding its occurrence and impact on embryonic cells can provide insights into stem cell and tissue morphogenesis regulation in vitro6,7. Thus, exploring epithelial tissue folding is of interest in developmental biology and extends8 to applications in stem cell and tissue engineering9,10,11,12.

Studies on epithelial folding using in vivo animal models, such as Drosophila, mice, and chick embryos, have identified the critical role of compressive force in inducing epithelial folding5,10,13,14,15. However, epithelial folding in in vivo models usually occurs at intervals of several days, making it difficult to examine spatiotemporal changes in folding in real-time. Intriguingly, several natural folding events show dynamic behaviors occurring at short timescales (usually tens of seconds). Therefore, epithelial folding studies based on in vivo models may miss certain phenomena within a short period of the folding event16,17.

Recently, in vitro epithelial folding models offered the potential for observing rapid or real-time epithelial folding. The in vitro models often employ synthetic elastic polymers like polydimethylsiloxane (PDMS) or robust hydrogels such as alginate, polyacrylamide, or hyaluronic acid-methacrylate to recreate biomimetic folding structures in response to external compressive forces6,18,19,20. These models, based on synthetic materials, usually rely on the wrinkling mechanism of a passive system, which can be regulated by adjusting the compressive strain and the stiffness of the materials18,21. Additionally, an innovative approach and system have emerged recently to explore the nature of epithelial folding independently of the substrate17. Previous in vitro models, based on the synthetic materials with a passive system or the active folding of epithelium, not only facilitate the recreation of biomimetic folding structures but also allow for the isolated examination of the influences of either an epithelium or a connective tissue layer on epithelial folding.

However, the interplay between these two components under compression, essential for understanding tissue-scale epithelial folding typically induced by external factors like muscle contraction, gravity, or connective tissue volume changes, remains largely unexplored5,22,23. Moreover, the prior folding investigation was not optimal for considering the distinct biomechanical characteristics of epithelial tissue, specifically poroelasticity which originates from the interstitial fluids within the ECM of the connective tissue layer and plays a vital role in tissue deformation during compression24,25. The limitations identified in the existing models are perceived to be due to an incomplete material composition or the utilization of synthetic materials.

Here, we reconstructed an epithelial tissue folding model based on an in vitro epithelial bilayer composed of an epithelium and an ECM hydrogel mimicking both the composition and configuration of in vivo epithelial tissue. The model allowed us to examine the in situ multifactorial and biomechanical folding events in real-time. Various folding types with distinct structures, such as multiple periodic wrinkles and a single deep fold, were successfully realized in the in vitro epithelial tissue model by applying uniaxial compression. The folding type could also be hierarchically tuned according to the compressive strain. This phenomenon is similar to the wrinkle-to-fold transition, that occurs in a compressed synthetic bilayer material26, but has never been realized in any biological materials. Based on experimental and theoretical approaches with the in vitro epithelial folding model, we suggested the potential integrative contributions of the strain-stiffening epithelium and poroelastic ECM hydrogel to the tissue-scale epithelial folding phenomena.

Results

Epithelial bilayer of epithelium-ECM hydrogel

While many causes and mechanisms inducing epithelial folding have been reported, in vivo tissue-scale epithelial folding is known to be a multifactorial phenomenon resulting from the orchestration of the epithelium and underlying connective tissue layer. Therefore, both the epithelium and connective tissue layers must be considered together to understand epithelial folding, in terms of composition and configuration.

We developed an in vitro epithelial bilayer tissue model composed of an epithelium and an ECM hydrogel layer, which is Caco-2 epithelium and pure collagen hydrogel as example materials, emulating the bilayer structure of in vivo epithelial tissue (Fig. 1a). To apply compressive forces to induce epithelial folding, we placed the epithelial bilayer in a polydimethylsiloxane (PDMS) frame (Fig. 1b). The bilayer was compressed with a motorized compression system allowing elaborate control of both the compressive strain (CS) and compression rate (CR) (Supplementary Fig. 1).

Fig. 1: Schematics of an epithelial bilayer and its folded structures.
figure 1

a Schematic of folding of in vivo epithelial tissues composed of epithelium and connective layer. Human intestinal Caco-2 epithelial cells were used to form an epithelium on a thick type I collagen hydrogel layer, as an example epithelial bilayer. b Schematic of epithelium-ECM hydrogel bilayer and PDMS wall surrounding epithelial bilayer for applying compressive force. c–l Wrinkles and fold on compressed epithelial bilayer, which are indicated with yellow arrows and dashed lines, respectively. Uniaxial compressions of CS = 0.5 and CR = 0.05 mm s-1 and CS = 0.7 and CR = 0.05 mm s-1 were applied on the epithelial bilayers for wrinkles and a fold, respectively. The multiple wrinkles on the epithelial bilayer had similar shape and size having a width of ~76 μm and amplitude of ~88 μm. Fold on bilayer was usually solitary and had a width of ~340 μm and amplitude of ~440 μm: e, f Microscopic top view images. Immunofluorescence images of (g, h) top view, (i, j) cross-section view, and (k, l) magnified top view. Caco-2 epithelium of the epithelial bilayer was labeled with phalloidin (cyan) and DAPI (blue). Scale bars are 100 μm.

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Once the epithelial bilayer is compressed over a certain CS, it folds and shows distinct types of folding with repetitive and regular patterns or a single deep pattern under specific conditions. Although there are several terminologies to describe specific structures of folds (e.g., wrinkles, ridges, creases, and fold)18,21,27, the criteria for the classification of folding types remain obscure and unclear. Herein, we defined (1) multiple folds with repetitive and regular folding patterns as wrinkles and (2) a single deep folding pattern as a fold. Figure 1c–m shows multiple periodic wrinkles and a fold formed on the epithelial bilayer, respectively. Remarkably, the wrinkles and fold generated on the compressed epithelial bilayer appear very similar to those in in vivo epithelial tissues, such as the intestine and skin5,28,29. Despite numerous studies on engineering wrinkles and folds on synthetic elastic materials or hydrogels30,31,32,33, it has been still challenging to create wrinkles or folds with pure biological materials such as cells and ECM. Notably, the epithelial bilayer holds significant biological relevance as it allows for the reconstruction of periodic wrinkles in response to compression only with the biological materials, epithelium, and ECM.

Epithelial wrinkling and subsequent wrinkle-to-fold transition

The unique curved structures formed on the compressed epithelial bilayer, i.e., wrinkles and folds, were found to be mainly determined by CS. Figure 2a, b show the structural change in the epithelial layer from a flat surface to multiple wrinkles, the subsequent folding, respectively, and the corresponding width and amplitude of the wrinkles and folds. We observed the real-time change in the epithelial surface from the original flat surface to the wrinkled surface, where wrinkle patterns emerged on the surface and became denser with increasing CS up to 0.5 (Supplementary Movie 1). Some wrinkle patterns were then gathered and merged in a certain region when the bilayer was compressed at a CS over 0.5. Strikingly, despite stopping the compression motion at CS = 0.7, the wrinkle patterns on the bilayer continued to gather in the region and eventually spontaneously merged into a single huge fold (Supplementary Movie 2). This spontaneous structural change from multiple wrinkles to a single fold of the epithelial bilayer occurred within tens of seconds (Fig. 2c). Figure 2d clearly shows that numerous wrinkle patterns gathered, merged, and eventually formed a large single valley during the transition.

Fig. 2: Folding of the epithelial bilayer under varying compressive strains.
figure 2

a Compressive strain (CS)-dependent structural change of epithelial bilayer at CR = 0.05 mm s-1. b Width and amplitude of folded structures of epithelial bilayer according to CS; In a box-and-whisker plot, the box represents the interquartile range (IQR; middle 50% of values), with the bottom and top indicating the first (25th percentile) and third quartiles (75th percentile), respectively. The line inside the box marks the median (50th percentile). Whiskers extend to the smallest and largest values within 1.5 times the IQR from the quartiles; outliers beyond this range are plotted as individual points. Epithelial bilayer sample n = 5. Statistical analyses were carried out using Student’s t-test. p-values were 1.6 × 10-5 and 1.8 × 10-7 for width and amplitude, respectively. c Schematic illustration of wrinkle-to-fold transition of epithelial bilayer and microscopic time-lapse images showing wrinkle-to-fold transition at CS = 0.7. d Immunofluorescence image showing a moment when wrinkle patterns hierarchically changed to a fold pattern and corresponding magnified image. Caco-2 epithelium of the epithelial bilayer was labeled with phalloidin (cyan) and DAPI (blue). Scale bars are 100 μm in a and 500 μm in d. Source data are provided as a Source Data file.

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We could observe a hierarchical change of wrinkle-to-fold transition in the epithelium from regular and repetitive wrinkles to a single deep fold in response to excessive compression. To our best knowledge, this is the first demonstration and in situ observation of the wrinkling and wrinkle-to-fold transition of biological materials. The results suggest that the epithelium and the underlying connective tissue layer of in vivo epithelial tissue may have undergone such a dramatic structural change that occurred on a short time scale, although these changes have not been observed. Notably, it is noteworthy that the compressive strain (CS) required for the wrinkle-to-fold transition in the epithelial bilayer was significantly higher compared to previous observations in synthetic elastic bilayer systems27. This observation demonstrates the importance of understanding this phenomenon within the context of the unique properties of the epithelium and ECM hydrogel.

Presence and interaction of both epithelium and ECM hydrogel are paramount in wrinkling and folding of epithelial bilayer

Since wrinkle formation and the subsequent wrinkle-to-fold transition of the epithelial bilayer in response to compression have not been realized in the previous in vitro platforms, we attempted to demonstrate whether and how the epithelium and underlying ECM hydrogel are involved in the folding behaviors of the epithelial bilayer.

The isolated epithelium devoid of a substrate is known to adapt to compression in the form of cellular compaction or structural buckling, rather than wrinkle formation. Under a relatively small CS, the epithelial cells of epithelium are compacted in the compression direction while increasing their height to maintain their cytoplasmic volume. In contrast, when the CS exceeds a threshold of ~0.35, which is called the buckling threshold or compression limit17, the epithelium is no longer compacted and begins to buckle and form a single fold. However, as shown in Supplementary Fig. 2, the ECM hydrogel could be compressed at a CS of 0.5 (CR = 0.05 mm s-1) without showing any distinguishable structural changes such as wrinkles or a fold. Notably, the present epithelial bilayer developed multiple periodic wrinkles rather than making a fold when it was compressed at CS = 0.5 without delamination between the epithelium and the ECM hydrogel (Fig. 3a and Supplementary Fig. 3). When we partially formed an epithelium on the top surface of the ECM hydrogel, wrinkle patterns surprisingly developed only in the bilayer region where the epithelium was formed on the ECM hydrogel in response to compression (Supplementary Fig. 4). These results not only clearly suggested that the bilayer of the epithelium and ECM hydrogel tend to form wrinkles and folds in a completely different manner from both the isolated epithelium and ECM hydrogel, but also indicated that the presence and interaction of both the epithelium and ECM hydrogel are necessary for wrinkling in response to compression.

Fig. 3: Involvement of epithelium in epithelial bilayer folding.
figure 3

a Schematic illustrations of structuring of sole epithelium, ECM hydrogel, and epithelial bilayer in response to compression at high CS over 0.4. b Morphological compaction of Caco-2 cells in x-direction according to applied CS and corresponding aspect ratio of Caco-2 cells (defined as L/S, where L and S are long and short axes of cells, respectively) for applied CS; In a box-and-whisker plot, the box represents the interquartile range (middle 50% of values), with the bottom and top indicating the first (25th percentile) and third quartiles (75th percentile), respectively. The line inside the box marks the median (50th percentile). Whiskers extend to the smallest and largest values within 1.5 times the IQR from the quartiles; outliers beyond this range are plotted as individual points. Cells are randomly selected on epithelial bilayer samples of n = 3. Statistical analysis was carried out using one-way analysis of variance (ANOVA) with Tukey’s multiple comparison test. c Cross-sectional views of Caco-2 epithelium of compressed epithelial bilayer and corresponding wrinkle index (defined as Lw, contour length of interface between epithelium and ECM hydrogel, which was normalized by orthographic projection length of epithelium, Lo) at each CS; In the chart, the center line represents the interquartile range (middle 50% of values). The bottom of the range indicates the first quartile (25th percentile), and the top indicates the third quartile (75th percentile). Epithelial bilayer sample n = 3. d, e Schematics and immunofluorescence images of epithelial cells with and without junctional complexes composed of adherens junctions and peripheral actin rings. Immunofluorescence images of compressed Caco-2 cells f with and g without both E-cadherin and peripheral actin rings (CS = 0.5 and CR = 0.05 mm s-1). Caco-2 cells were stained with E-cadherin (red), phalloidin (cyan), and DAPI (blue). Scale bars are 10 μm in b, 100 μm in c, f, and g, and 20 μm in d, e. Source data are provided as a Source Data file.

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Strain-stiffening and collective behavior of epithelium are crucial in wrinkling and folding of epithelial bilayer

As the wrinkling mode of a thin film-thick substrate bilayer is usually determined by the modulus difference between the two layers at a certain CS18, we hypothesized that wrinkling of the epithelial bilayer was induced by the interaction between the different mechanical characteristics of the epithelium and ECM hydrogel during compression. We especially focused on the combined effects of the volume conservation of the epithelium and the high compressibility of the ECM hydrogel on the mechanical instability over the compression limit of the epithelium.

To investigate whether the compression limit of the epithelium was related to the wrinkling of the epithelial bilayer, we examined both morphological changes in individual epithelial cells and structural changes in the epithelium of the bilayer under various CS conditions. When the epithelial bilayer was compressed in the x-direction as indicated in Fig. 1b, most epithelial cells were compacted in the x-direction, and the aspect ratio of the individual cells increased. The aspect ratio of the cells increased until CS = 0.4 and then stopped increasing after the CS exceeded 0.4 (Fig. 3b). Remarkably when the CS exceeded 0.4, the epithelium started to form periodic wrinkles with a drastic increment in the wrinkle index rather than further compaction, as shown in Fig. 3c. At CS = 0.4, the wrinkling behavior of the epithelial bilayer, in which the epithelial cells stopped compacting and the bilayer began to wrinkle, was similar to the buckling behavior of the isolated epithelium over the compression limit of CS = 0.35, as reported in a previous study17. The results unequivocally demonstrate that the epithelial cells of the bilayer respond to compression by adopting a wrinkling mechanism once the compressive strain exceeds 0.4, whereas the underlying ECM hydrogel can be further compressed without structural changes even at CS = 0.5 (Supplementary Fig. 2). It is worth noting the compression-induced stiffening nature of cells. A previous study demonstrated that the cell undergoes significant stiffening when compressed with a CS of approximately 0.4, attributed to the volume conservation of the cell34. This finding aligns with the saturation of the aspect ratio of single epithelial cells within the bilayer at a CS around 0.3–0.4, as depicted in Fig. 3c. In other words, the epithelium is stiffened when it experiences compression, and the point where the stiffness of the epithelium dramatically increases is a critical point of the epithelial bilayer wrinkling.

The experimental results so far suggest that the compressive strain-stiffening of individual epithelial cells plays a crucial role in the wrinkling of the epithelial bilayer. However, to elucidate this phenomenon through the established wrinkling model based on a thin film-thick substrate bilayer, it becomes imperative to validate that an epithelium, composed of epithelial cells, mechanically behaves as a single layer. Should this be confirmed, the epithelium and ECM hydrogel of the epithelial bilayer could be considered as a thin film and a thick substrate, having thicknesses of ~10 μm and ~3000 μm, respectively.

Considering the nature of epithelial cells, they behave as a single film in a collective manner rather than behaving individually. The tight interaction between the epithelial cells allows the epithelium to mechanically behave as a thin film. The transmission of mechanical stress among epithelial cells and their collective behavior are known to be mediated by the cell-cell junctional complex, which is composed of adherens junctions and peripheral actin rings, as depicted in Fig. 3d, e35,36. Interestingly, when the adherens junctions and the peripheral actin rings of epithelial cells were both disrupted in the epithelial bilayer while the viability of the cells was maintained with the treatment of 1,4-dithiothreitol (DTT), the epithelial cells of the compressed bilayer were more likely to behave individually overlapping each other or bursting out, rather than developing wrinkles collectively (Fig. 3f, g and Supplementary Fig. 5).

These results support our hypothesis that the collective behavior of epithelial cells, making an epithelium behave like a single layer, is crucial for wrinkle formation on the epithelial bilayer. The hypothesis was also supported by the result that mesenchymal cells that behave individually on the ECM hydrogel were not forming wrinkles even at CS = 0.5 (Supplementary Fig. 6), which can explain why folding usually occurs in epithelial tissues in vivo. Collectively, the present results indicate that wrinkling of the epithelial bilayer is a result of mechanical instability that arises from the interaction between the thin epithelium and the thick ECM hydrogel layer, similar to the wrinkling of a thin film on a thick substrate in response to compression.

Poroelasticity of ECM hydrogel is substantial in the wrinkling and folding of epithelial bilayer

Not only the CS but also the CR was found to play a significant role in determining surface wrinkling of the present epithelial bilayer. While the epithelial bilayer got wrinkled when it was compressed at a relatively low CR, it frequently buckled out rather than wrinkled when it was compressed with a high CR (Fig. 4a). Notably, wrinkling of the epithelial bilayer is accompanied by sufficient dehydration corresponding to the compressive strain with low CR, while global buckling occurs with limited dehydration with high CR (Supplementary Fig. 7). The result highlights the significant role of dehydration in the time-dependent wrinkling behavior of the epithelial bilayer.

Fig. 4: Involvement of ECM hydrogel in epithelial bilayer folding.
figure 4

a Macroscopic structural difference between compressed epithelial bilayers with low CR = 0.1 mm s-1 and high CR = 1 mm s-1. b Microscopic images of different wrinkle patterns on epithelial bilayers according to different CRs. At smaller CR, periodic wrinkles developed more stably on the epithelial bilayer, resulting in a smaller interspace between adjacent wrinkle patterns, while the width of each wrinkle pattern remained the same. c Measured width and interspace of wrinkle patterns; In the chart, the center square represents the interquartile range (middle 50% of values). The bottom of the range indicates the first quartile (25th percentile), and the top indicates the third quartile (75th percentile). Statistical analyses were carried out using one-way ANOVA with Tukey’s multiple comparison test. (Epithelial bilayer sample n = 3, p -value was 0.010). Scale bars represent 100 μm. d Schematic illustration of compression test of ECM hydrogel. e Stress-CS curves of ECM hydrogel according to different CRs. Stress-strain curves of ECM hydrogel exhibited non-linear behavior of poroelastic materials under compression. There was a small increase in stress until CS ~ 0.4, and then stress exponentially increased with an increase in CS. f ECM hydrogels compressed with different CRs. Scale bar is 2 mm. g Immunofluorescence images of compressed Caco-2 epithelium on 3 mg mL-1 ECM hydrogel (CS = 0.5 and CR = 0.05 mm s-1). h A magnified image indicated with a white dashed line. i Cross-section view. j Immunofluorescence images of compressed Caco-2 epithelium on 5.5 mg mL−1 ECM hydrogel (CS = 0.5 and CR = 0.05 mm s-1). k A magnified image indicated with a white dashed line. l Cross-section view. Caco-2 cells were stained with phalloidin (cyan) and DAPI (blue). Scale bars are 100 μm. Source data are provided as a Source Data file.

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Remarkably, the periodic wrinkle patterns formed on the epithelial bilayer varied depending on the CR (Fig. 4b, c). It was also found that surface wrinkles of the epithelial bilayer could only be stably induced with CR < 0.5 mm s-1. While we acknowledge that both poroelasticity and viscoelasticity can contribute significantly to the time-dependent behavior of the epithelial bilayer and that they likely act in conjunction, our focus in this study was primarily on the role of poroelasticity in the ECM hydrogel, due to the crucial role of dehydration in applying effective compressive strain to the epithelial bilayer. Moreover, as the folding of the isolated epithelium against compression is independent of CR17, we hypothesized that the mechanical characteristics of the ECM hydrogel of the epithelial bilayer play a major role in this CR-dependent behavior.

Interstitial fluid occupies the majority of the in vivo ECM volume. The relationship between structural deformation and fluid permeation inside the porous matrix of ECM, that is, a poroelasticity of ECM, particularly determines the effective stiffness of the fluid-rich ECM, which is a key attribute when considering soft tissue deformation in response to external forces. The ECM hydrogel was prone to buckling instead of squeezing the water out when the dehydration time was insufficient at a high CR (Fig. 4a and Supplementary Fig. 7). This CR-dependent behavior of the ECM hydrogel can be explicated by poroelasticity of the ECM hydrogel. Mechanical compression tests demonstrated that the ECM hydrogel of the epithelial bilayer possesses poroelasticity (Fig. 4d, e). It was revealed that the stress increases with increasing CR, while there were dislocations observed in the stress values at a high CR > 0.5 mm s-1. At the same time, the ECM hydrogel was stably compacted without failure when compressed with a low CR ~0.1 mm s-1. However, when the ECM hydrogel was compressed rapidly with a high CR > 0.5 mm s-1, we could see the fracture failure of the hydrogel along with significant dislocation of stress value in Fig. 4f.

It should be noticed that the criterion for determining the stable formation of wrinkles on the epithelial bilayer without buckling was the same as the fracture failure of the ECM hydrogel, that is, CR ~0.5 mm s-1. These results obviously indicated that the poroelasticity of the ECM hydrogel is strongly related to the CR-dependent behavior of wrinkle formation on the epithelial bilayer.

To demonstrate further the influence of the ECM hydrogel poroelasticity on the wrinkle formation, we prepared another epithelial bilayer composed of the same epithelium and a different ECM hydrogel with a higher collagen concentration compared to the original collagen concentration, which has a denser network of collagen fibrils with smaller pore size, hindering dehydration (Supplementary Fig. 8). Unlike the original epithelial bilayer, the epithelial bilayer with the higher collagen concentration developed a buckle-like macroscopic structure rather than wrinkles at the same CS = 0.5 (Fig. 4g–l). Given that the junctional complex of the epithelium and the ratio of the loss modulus to storage modulus (Tan δ) of the two ECM hydrogels remained similar to each other (Supplementary Figs. 8 and  9), we hypothesized that the viscoelastic property of the epithelial bilayer is not the dominant factor in these CR-dependent wrinkling. That is, it could be considered that the CR-dependent wrinkling of the epithelial bilayer is more likely to originate from the poroelasticity of ECM hydrogel.

Strain-stiffening of epithelium and poroelasticity of ECM hydrogel in wrinkling and folding of epithelial bilayer

Combining the above results supported our hypothesis that the wrinkling and folding of the epithelial bilayer result from the interplay between the unique mechanical characteristics of the epithelial bilayer (both the strain-stiffening and collective behavior of epithelium and the poroelasticity of ECM hydrogel). Our experimental results allowed us to consider the present epithelial bilayer as a strain-stiffening thin film on a poroelastic thick substrate.

To elucidate the wrinkling and the subsequent wrinkle-to-fold transition of the epithelial bilayer, we used a theoretical model for the wrinkling and folding of a thin film on a thick substrate against compression. The model can quantitatively estimate the wrinkled or fold structure by considering in-plane compression and a modulus ratio, defined as β = Ef/Es between the elastic moduli of the thin film (Ef) and thick substrate (Es). Crucially, we incorporated moduli variations for both the strain-stiffening epithelium film and the poroelastic ECM hydrogel substrate. Our theoretical model was limited to conditions of CS and CR under which stable wrinkles are formed.

The moduli variations of the epithelium and the ECM hydrogel were plotted in Fig. 5a. In this plot, the moduli variation of the ECM hydrogel (Es) was determined from mechanical compression test results shown in Fig. 4e. On the other hand, directly measuring the elastic modulus of the epithelium (Ef) poses challenges, and as such, its variation was inferred from previous theoretical models37. Given that the modulus of an intact epithelium typically ranges from ~100 Pa to ~1 kPa17,38, we approximated Ef of the epithelium to be 500 Pa in its pre-compression state. The approximation was experimentally demonstrated with the wrinkling of the epithelial bilayer model composed of the MDCK cell line (Supplementary Fig. 10), known to have stiffness around 500 Pa17. Upon compression, the epithelium becomes stiffer, reaching a plateau at CS ~0.4, where its modulus remains constant due to unaltered epithelial cell morphology. The modulus of the stiffened epithelium (Ef) was deduced from its wrinkling amplitude, which was estimated at ~3.5 kPa (refer to Methods). In contrast, the ECM hydrogel exhibited a modulus Es of less than 100 Pa at CS ~0.3, which increased dramatically when CS > 0.4, reaching a modulus on the order of 1 kPa at CS ~0.7, similar to that of the epithelium.

Fig. 5: Theoretical analysis on mechanical instability of epithelium and ECM hydrogel.
figure 5

a Moduli variations of epithelium and ECM hydrogel of epithelial bilayer according to CS. Compression progressively caused epithelium to stiffen until CS ~ 0.4, and fully compacted epithelium was considered to have uniform Ef as the morphology of epithelial cells remained unchanged at CS > 0.4. The modulus of stiffened epithelium could be indirectly deduced by examining its wrinkled structure. Based on the amplitude of sinusoidal wrinkling in the post-buckling regime of the compressed epithelial bilayer, Ef of compressed, stiffened epithelium was estimated to be ~3.5 kPa (refer to Methods). Es was found to be below 100 Pa at CS < 0.3. However, at CS > 0.4, it increased to in order of 1 kPa. b Phase diagram of surface instabilities according to modulus ratio (β = Ef/Es) between epithelium and ECM hydrogel. Flat film (epithelium in bilayer) is transformed into the wrinkled structure when CS exceeds theoretical criteria as indicated in the red line for given β. When CS increases beyond 0.65, a wrinkled structure could be transformed into a folded structure (or crease).

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With the established moduli variations, we calculated the modulus ratio, β, and incorporated it into the buckling instability model as shown in Fig. 5b. In this model, a flat film is transformed into a wrinkled structure when the CS exceeds a theoretical threshold as indicated in the red line in Fig. 5b for a given β. When the CS increases beyond 0.65, the wrinkled structure could be transformed into either a periodic-double or a folded structure (or crease). The calculated β of the epithelial bilayer varied with CS due to the variations of Ef and Es, and we could observe two different transition points: one transition point from a flat to a wrinkled mode at CS near 0.3–0.4, and the other from a wrinkled to a folded mode at CS near 0.7. Remarkably, the estimated CS values for the wrinkling and the wrinkled-to-fold transition were quite consistent with the experimental results. An intriguing observation pertains to the folding behavior at CS ~0.7, denoted as the second transition point in Fig. 5b, where the moduli of the ECM hydrogel eventually coincide with the moduli of the epithelium as shown in Fig. 5a. Remarkably, when the sole ECM hydrogel layer without the epithelium was compressed, a deep crease (or fold) was formed at CS ~0.7 (Supplementary Fig. 11). At the second transition point, consequently, the entire epithelial bilayer follows the creasing phenomenon exhibited by the ECM hydrogel, that is the wrinkle-to-fold transition of the epithelial bilayer observed in this study.

These findings demonstrate that the wrinkling and folding of the epithelial bilayer can be explained by the theoretical model with the newly introduced moduli variations of both the epithelium and the ECM hydrogel under compression, reflecting the strain-stiffening and collective behavior of the epithelium and the poroelasticity of the ECM hydrogel. Additionally, the proposed phase diagram supports our expectation that strain-stiffening of the epithelium is essentially involved in the wrinkling of the epithelial bilayer (Supplementary Fig. 12).

Discussion

In this study, we replicated various types of folding observed in in vivo epithelial tissues using an in vitro epithelial bilayer that mimicked the composition and configuration of the in vivo epithelial tissue. Specifically, the present in vitro epithelial folding model is of significance because it enabled to reproduction of the periodic wrinkling as well as the hierarchical progression toward deep folding of the epithelium and ECM hydrogel in response to compression. Present experimental and theoretical works offer insight into the in vivo epithelial folding, suggesting the plausible interpretation for the folding phenomena as followings. (1) Epithelial wrinkling and the subsequent wrinkle-to-fold transition can be analyzed by the variations of moduli of the epithelium and the ECM hydrogel of an epithelial bilayer in response to compression. (2) The wrinkling threshold is associated with the compressibility and strain-stiffening nature of the epithelial cells. (3) The collective behavior of epithelial cells enables the epithelium to act as a thin film mediated by tight cell-cell junctional complexes. (4) Finally, the surface buckling instability of the epithelial bilayer is also affected by the compression rate related to the dehydration of poroelastic ECM hydrogel, which corresponds to a connective tissue layer in the in vivo epithelial tissue

As potential extensions of the in vitro epithelial folding model in view of the interplay between the epithelium and the ECM hydrogel, we realized various types of epithelial folding with different epithelial bilayers by changing not only the types of epithelial cells but also the compression conditions. As shown in Supplementary Fig. 13a, two different epithelial bilayers, one composed of intestinal Caco-2 epithelial cells (original bilayer) and lung A549 epithelial cells (another type) on the same ECM hydrogel, were found to develop multiple wrinkles in response to the same compression conditions; however, the detailed morphologies of the wrinkles were different. The result indicated that the formation of wrinkling and folding of the epithelial bilayer is reproducible for various types of epithelial cells, but at the same time, it is a cell-type-specific phenomenon. The stiffness, thickness, and tightness of junctional complexes are anticipated to exert cell-type-specific effects, which in turn results in variation of the epithelial modulus, due to their potential variations across different cell types. In vivo, tissue-specific wrinkling and folding can be realized and investigated using an in vitro epithelial bilayer model by mimicking in vivo tissue with the corresponding cells and connective tissue layer.

By changing the compression conditions, we also observed interesting folding of the epithelial bilayers, as shown in Supplementary Fig. 13b. In-plane folding of the bilayer and triaxial compressive forces on the bilayer results in specific types of epithelial folding. During intestinal development, the intestinal epithelium is exposed to biaxial compressive forces from smooth muscles, thereby resulting in specific zig-zag folding5. We could reconstruct the zig-zag folding of the intestinal epithelium on the in vitro epithelial bilayer by applying biaxial compressive forces to the bilayer (Supplementary Fig. 13c). The morphological zig-zag folding of the in vitro bilayer was similar to that of the in vivo intestinal epithelium. Based on the observations, we expect that the present in vitro epithelial bilayer can be a useful research platform for developmental biology.

The suggested bilayer model can be further expanded in view of mechanobiology. Considering the mechanical compression on the nuclei and the curvature of the substrate affects genomic expression, investigation of cellular response to compression and folded structures on the suggested model will contribute to understanding the mechanobiological nature of cells. For example, the in vivo intestinal morphogenesis during the developmental process is known to be facilitated by epithelial folding, which is driven by the contractility of the smooth muscle layer. The suggested in vitro epithelial bilayer model can be a promising method of intestinal developmental research as it can reliably recapitulate the folding process by introducing specific cell types and ECM components. The epithelial bilayer model offers the advantage of real-time and high-resolution observation, enabling to examine the cellular-level changes during intestinal morphogenesis. The deformation of cytoplasm and nuclei during the folding process can be observed and analyzed by using the model, potentially providing valuable insights into the mechanotransduction involved in the intestinal developmental processes. In particular, we observed distinct deformations in the nuclei of epithelial cells depending on their position within the wrinkle or fold (Supplementary Figs. 14 and 15). Considering the variability in nuclear deformation could potentially lead to region-specific alterations in gene expression levels, we believe that exploring the influence of fold structures, particularly curvature, on the region-specific distribution of intestinal epithelial cell lineages would be intriguing research. Understanding how the fold structure affects the differentiation and spatial organization of these cell lineages could shed light on the complex interplay between mechanical forces and cell fate determination during intestinal development.

Moreover, we expect that this tissue-scale epithelial folding model based on in vitro epithelial bilayer will be widely applied in not only developmental biology and mechanobiology, but also (patho)physiology, tissue mechanics, and tissue engineering. For example, the suggested model also can be exploited in investigating skin pathophysiology. It is well known that skin wrinkles can be induced by dehydration of the dermis under the skin epithelium due to the loss of the collagenous network during the aging process. This mechanism of skin wrinkling may be elaborately reconstructed and investigated by utilizing the correlation between dehydration and wrinkling, which is understood to be strongly associated with the functions of dermal fibroblasts, as demonstrated in the present epithelial bilayer. Furthermore, the wrinkle-to-fold transition of the epithelial bilayer provides clues for understanding the underlying mechanism of deep-fold generation in wrinkled skin.

The concept of the suggested model, which is associated with poroelasticity, can offer valuable strategies for the processing of biological materials, including cells and the ECM. We readily realized a wrinkled ECM bilayer composed of two ECM hydrogel layers with different concentrations (Supplementary Fig. 16), by applying compression. Moreover, the consideration of the poroelastic behavior of hydrogels involved in folding would provide practical insights into engineering artificial epithelial tissues. For instance, this could help create a hydrogel-based skin equivalent with natural wrinkle structures.

It is essential to note that, while we have provided initial suggestions into the importance of biomechanical properties of the epithelium, as well as the poroelasticity of the underlying ECM hydrogel substrate in tissue-scale epithelial folding, the underlying mechanism should be further investigated in more integrative perspective, encompassing biology and mechanics. In particular, as illustrated in Supplementary Fig. 17, the inhibition of actomyosin activity in the epithelium resulted in subtle changes in the folding behaviors of the epithelial bilayer, suggesting potential active involvement of actomyosin activities in epithelial cells. A more comprehensive understanding of epithelial folding could be attained by incorporating the strain-stiffening of the epithelium and the poroelasticity of the ECM, as highlighted in this study, along with further considerations of viscoelasticity, ECM composition, cellular tension, and proliferation. Further investigation is warranted into various biological conditions, including the type and status of cells, composition of the ECM hydrogel, and presence of fibroblasts within the ECM, to elucidate their impact on the wrinkling and folding events of the epithelial bilayer. A post-compression culture system needs to be developed to conduct more comprehensive analyses of the epithelial cells, including investigations into gene- or protein-level changes in response to structural deformation or recovery. Moreover, performing an in-depth analysis of the mechanical aspects, including rigorous measuring of the strain, stiffness, or stress distribution of the epithelium, along with Mullins-like plasticity of ECM hydrogel based on more precise mechanical systems and employing more sophisticated theoretical models39,40, would address our approximation and offer insights for a more comprehensive understanding and the design of phenomena occurring on the epithelial bilayer.

The present study paves the way for investigating the underlying mechanisms of various in vivo epithelial folding mechanisms. Also, the abovementioned future studies will facilitate the application of in vitro epithelial bilayer-based epithelial folding models in developmental biology, physiology, tissue mechanics, tissue engineering, and regenerative medicine.

Methods

Fabrication of epithelium-ECM hydrogel bilayer

Molds for making ECM hydrogel substrates (20 mm × 4 mm × 3 mm in length, width, and height which are parallel in x-, y-, and z-axis in Fig. 1b) were made by curing polydimethylsiloxane (PDMS; Sigma-Aldrich, USA) mixed with curing solution at a 10:1 w/w ratio for 4 h at 80 °C. An ECM hydrogel solution was prepared by mixing rat-tail type I collagen (Corning, USA), 1 M sodium hydroxide (NaOH; Sigma-Aldrich, USA), and 10 × Dulbecco’s modified Eagle’s medium (DMEM; Gibco, USA) with 1: 0.025: 0.1 of volume ratio. Additional 1 × DMEM (Gibco, USA) was mixed with the ECM hydrogel solution to achieve a final collagen concentration of 3 mg mL-1. The prepared ECM hydrogel solution was poured into the PDMS molds and gelated for 1 h in a 5% CO2 incubator at 37 °C. Human intestinal Caco-2 epithelial cells (Korean Cell Line Bank, Republic of Korea) and lung A549 epithelial cells (Korean Cell Line Bank, Republic of Korea) were cultured in DMEM supplemented with 10% (v/v) of fetal bovine serum (Gibco, USA) and 1% (v/v) of amphotericin B (Sigma-Aldrich, USA). The epithelial cells were detached from the culture dishes by treatment with TrypLE (Thermo Fisher Scientific, USA) and seeded on the ECM hydrogel with a cell density of 1 × 106 mL-1 in DMEM. After 3 h of cell attachment, the cell-containing medium was replaced with a fresh medium. Epithelial cells on the ECM hydrogel were cultured for 3 days to form an epithelium. In the case of a mesenchymal bilayer, human adipose-derived stem cells (hASCs; Seoul St. Mary’s Hospital, Republic of Korea, IRB permit NO. KC11TNMS0095) were cultured in DMEM supplemented with 10% (v/v) of fetal bovine serum and 1% (v/v) of amphotericin B. The hASCs were seeded on the ECM hydrogel (3 mg mL-1) with a cell density of 3 × 105 mL-1 in DMEM and cultured for 5 days.

Compression of epithelial bilayer

A PDMS frame in the compression system was fabricated using the same methods as the PDMS mold, and it matched the mold in size. The PDMS frame was placed on a 1 mm-thick glass slide (Marienfled, Germany) and the epithelial bilayer was placed inside the PDMS frame. For the uniaxial compression tests, the epithelial bilayer was compressed using a motorized compressing rod in a precise manner. The compressing rod was designed to have a width of 4 mm and a height of 3 mm; therefore, it could fit inside the PDMS frame, and it was made by cutting polymethyl methacrylate (PMMA; Acryl Choi-ga, Republic of Korea) plates with a laser cutting machine (Machine shop, Republic of Korea). The compression rod was attached to a syringe pump (New Era Pump Systems, USA) to control both the compressive strain and the compression rate. The compression rate of the rod was modulated by the speed of the motor-driven pusher block of the syringe pump. For the various multi-axial compression tests, the epithelial bilayer was manually compressed by pressing the PDMS wall of the frame manually in the desired directions.

Imaging and image analysis

Microscopic morphologies and behaviors of the cells and ECM hydrogel of the epithelial bilayer were examined using a phase-contrast optical microscope (Carl Zeiss, Germany). The video was recorded using the Debut software program (NCH Software, Australia). The ECM hydrogel was fluorescently visualized by mixing fluorescent Rhodamine 123 (Sigma-Aldrich, USA) particles into the ECM hydrogel. Cells on the epithelial bilayer were fluorescently visualized by using a Cell tracker (Vybrant Cell-labeling Solution; Thermo Fisher Scientific, USA) or immunostaining process41. The cells were immunostained as follows: 4% paraformaldehyde solution (Chembio, USA) was used to treat the epithelial cells on the epithelial bilayer for 15 min at room temperature (RT) to fix their status and structure. Fixed epithelial cells were permeabilized with 0.3% (v/v) Triton-X100 (Sigma-Aldrich, USA) for 30 min at RT. Then, the cells were treated with 1% (w/v) bovine serum albumin solution diluted in phosphate-buffered saline (PBS) for 1 h at RT. Epithelial cadherin at the adherens junctions of the epithelial cells was stained by serial treatment with the primary antibody against E-cadherin (ab1416; Abcam, UK) and secondary antibody (ab150077; Abcam, UK) for 6 h at RT in each process. The nuclei and F-actin- forming peripheral actin rings of the epithelial cells were stained with 4’,6-diamidino-2-phenylindole (DAPI, Thermo Fisher Scientific, USA) and Alexa Fluor 680 phalloidin (F-actin, A22286; Invitrogen, USA), respectively, diluted in PBS at 1:100 (v/v) for 1 h at RT42. The immunofluorescence images were obtained using a confocal microscope (Olympus, Japan) and were analyzed using Imaris software (Ver. 10.0.0; Oxford Instruments, UK). Image J software (NIH, USA), Imaris software, and Illustrator software (Adobe, USA) were used to characterize structural features of the epithelial bilayers.

Disrupting adherens junctions and peripheral actin rings of epithelial cells

To disrupt the adherens junction while maintaining the peripheral actin ring of the Caco-2 epithelial cells, TrypLE (Gibco, USA) was applied to the epithelial bilayer for 30 min in a 5% CO2 incubator at 37 °C before compression. The adherens junction and peripheral actin ring of Caco-2 cells were both disrupted by treatment with 10 mM of 1,4-dithiothreitol (DTT; Sigma-Aldrich, USA) for 1 h in a 5% CO2 incubator at 37 °C before compression43. Both TrypLE- and DTT-treated epithelial bilayers were compressed until CS = 0.5 with CR = 0.05 mm s-1.

ECM hydrogel compression test

PMMA molds were fabricated using a laser cutting machine to prepare cylindrical ECM hydrogel samples with a radius of 2 mm and a height of 10 mm. Cylindrical ECM hydrogel samples were prepared using the same fabrication method used for preparing the ECM hydrogel substrate of the epithelial bilayer with a collagen concentration of 3 mg mL-1. The ECM hydrogel samples were placed in our previously developed compression machine with a load cell44. The load cell measured the stress change during the compression of the ECM hydrogel samples.

Fabrication of ECM hydrogel with high collagen concentration

An ECM hydrogel with a high collagen concentration was prepared with a collagen mixture of rat-tail type I collagen at a high concentration of ~9 mg mL-1 (354249; Corning, USA) and rat-tail type I collagen of 3 mg mL-1. The collagen mixture, 1 M NaOH solution, and 10 × DMEM were mixed at a volume ratio of 1: 0.025: 0.1, and an additional 1 × DMEM was added to make a final collagen concentration of 5.5 mg mL-1. To create the ECM–hydrogel bilayer shown in Supplementary Fig. 16, a thick ECM hydrogel substrate of 3 mg mL-1 was prepared in the same method as that of the epithelial bilayer, and 50 µL of collagen hydrogel solution of 9 mg mL-1 was deposited on the prepared thick ECM hydrogel.

Analytical modeling

Generally, the phenomenon of wrinkling in a thin layer (in this case, an epithelium) can be observed when this layer is bonded to a compliant substrate (in this case, an ECM hydrogel), and subjected to in-plane compression. The analytical model for predicting the morphology of wrinkling has been studied through the minimization of strain energy or using scaling laws. As the wrinkle patterns of the epithelial bilayer exhibit periodicity and uniformity along a sufficiently long longitudinal length, we assumed that these patterns can be approximated and analyzed as sinusoidal wrinkles without loss of generality. For the case of sinusoidal wrinkles, the buckled deflection field can be defined as \(w=A\cos \left(2\pi /\lambda x\right)\), where λ is the periodic width, and A is the amplitude. For the substrate with a semi-infinite thickness, the amplitude can be expressed as

$$A={h}_{f}\sqrt{\frac{\varepsilon }{{\varepsilon }_{c}}-1}$$
(1)

where hf is the thickness of the thin layer, ε is the applied compressive strain, and εc is the critical strain. Here, ε does not directly correspond to the CS due to the compaction of the epithelial cells. Until the CS reached ~0.3, the epithelial cells were compacted under in-plane compression conditions. We assumed the compaction behavior of the cells, combined with a relatively low modulus of ECM hydrogel, allows them to adapt to the compression without incurring mechanical instability. Thus, considering the compaction region, we assumed ε as a kind of effective strain by subtracting 0.3 from the applied CS.

The critical strain εc is defined as

$${\varepsilon }_{c}=\frac{1}{4}{\left[\frac{3\left(1-{{v}_{f}}^{2}\right){E}_{s}}{\left(1-{{v}_{s}}^{2}\right){E}_{f}}\right]}^{2/3}$$
(2)

where the elastic modulus and Poisson’s ratio are defined for the film (Ef, vf) and the substrate (Es, vs), respectively. Our primary objective is to predict the theoretical values of Ef, conceptualized as the strain-stiffened elastic modulus of the epithelium using the analytical model. At CS ~0.5 (ε ~0.2), A of the wrinkled morphology was ~45 μm and hf was 25 μm. vf was considered to be 0.5 due to the incompressible behavior of epithelium after CS = 0.3, and the value of vs was determined to be 0.25, which aligns with the generally accepted value for hydrogel. Es was evaluated to be 100 Pa based on the compression test. Therefore, according to Eqs. (1) and (2), we could calculate the modulus of the stiffened epithelium (Ef) and εc as ~3.5 kPa and ~0.4, respectively.

Phase diagram of surface buckling instabilities according to modulus ratio

A thin layer on a thick compliant substrate can show multiple patterns of buckling instability including wrinkling, period-double, folding, and creasing according to a compressive strain42,43. In this study, the in vitro epithelial bilayer exhibited repetitive and regular wrinkles from CS ~0.4 (εwrinkle). As CS increased beyond ~0.7 (εfold), the multiple wrinkling patterns transformed into a single, deep-folded pattern. The transition of surface instability can be understood by considering a phase diagram of surface buckling developed in previous studies, which has been validated through experiments and numerical simulations18,27,45,46. Each instability mode is determined by the modulus ratio, β (=Ef/Es) between the film and substrate, as well as the effective compressive strain, ε. Taking into account the length decrement of the epithelium due to compaction until CS around 0.3, which is a far different behavior or assumption from the incompressible films in previous synthetic systems26, we hypothesized that the effective compressive strain, representing the mismatched strain between the epithelium and ECM hydrogel, would become noticeable at least beyond CS 0.3. Consequently, we reconfigured the previous phase diagram by inserting a compaction regime (an offset of CS 0.3) to align the applied CS and ε as in Fig. 5b. The transition boundary for flat-to-wrinkle was estimated with the calculation of critical strain (Eq. (2)) and the threshold corresponding to β was highlighted with a red dashed line. Non-linear behaviors, such as period double-to-fold or fold-to-crease, following wrinkling at relatively high compressive strains were plotted by referencing experimental and simulation results from previous studies18,27,47. Additionally, the modulus ratio, β between the epithelium and ECM hydrogel, calculated from Fig. 5a, was depicted on the phase diagram as a black dashed line.

Statistics and reproducibility

The structural changes of the epithelial bilayer, as shown by the representative microscopic images in Figs. 1–4 and Supplementary Information, were repeatedly observed across multiple independent experiments. An epithelial bilayer was a unit sample, and observed cells, wrinkles, or folds on the epithelial bilayers were selected randomly if required for analysis. Due to the potential for small defects on samples resulting from handling, which could lead to significantly different phenomena, we excluded the samples with defects from the analysis. The statistical significance was determined by using a Student’s t-test to compare two sets of data, and a one-way analysis of variance (ANOVA) with Tukey’s multiple comparison test for multiple groups.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.