Cell type-specific response to curvature controls tissue growth dynamics in biomaterial pores

Aaron Herrera; Mina Sohrabi Molina; Rebecca Günther; Isabel Orellano; Erik Brauer; Stephanie Diederich; Alicia Serrano; Rose Behncke; Gabriela Korus; Hans Leemhuis; Georg N Duda; Ansgar Petersen

doi:10.1016/j.bioactmat.2026.02.005

. 2026 Feb 18;61:482–497. doi: 10.1016/j.bioactmat.2026.02.005

Cell type-specific response to curvature controls tissue growth dynamics in biomaterial pores

Aaron Herrera ^a,^b,^c, Mina Sohrabi Molina ^a,^b,^c, Rebecca Günther ^a,^b,^c, Isabel Orellano ^a,^b,^c,¹, Erik Brauer ^a,^b,^c, Stephanie Diederich ^a,^b, Alicia Serrano ^b,², Rose Behncke ^a, Gabriela Korus ^a,^b, Hans Leemhuis ^e,³, Georg N Duda ^a,^b,^c,^d, Ansgar Petersen ^a,^b,^c,^d,^⁎

PMCID: PMC12933747 PMID: 41756687

Abstract

In porous biomaterials, pore diameter and surface curvature are critical parameters governing cell migration, multicellular organization, and subsequent tissue formation, ultimately influencing in vivo performance. However, how different cell types respond to curvature and what determines their specific adaptations remain poorly understood. Here, we expose diverse cell types to precisely controlled, physiologically relevant microgeometries, revealing two distinct cellular strategies for adapting to curvature on channel-like surfaces. We examine how cellular stress modulation and the induction of senescence influence curvature responses and identify a universal predictor of curvature adaptation, linked to focal adhesion distribution across cell types and stress states. Consequently, tissue growth dynamics and final tissue architecture vary significantly between cell types. This mechanistic insight enables the prediction of optimal biomaterial pore diameters for specific cell types, offering a valuable framework for designing biomaterials with tailored cell-instructive properties for targeted tissue engineering applications.

Keywords: Curvature, Focal adhesions, Mechanobiology, Cell spanning, 3D organization, Tissue regeneration, Biomaterials

Graphical abstract

Highlights

•
The cellular response to curvature is cell-type dependent, with implications for tissue regeneration and biomaterial design.
•
Focal adhesion distribution is a key parameter controlling how cells respond and adapt to curvature.
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Cell-spanning vs. layer-by-layer growth are alternative mechanisms with consequences for tissue healing speed and structure.
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Cell-instructive biomaterials with tailored curvatures can be engineered to address these distinct healing mechanisms.

1. Introduction

The internal architecture of porous biomaterials critically influences cell behavior, tissue integration, and overall material performance [1,2]. Optimization of pore size and shape has helped to enhance cell infiltration, nutrient diffusion, and vascularization, e.g. in bone graft substitutes and scaffolds designed for tissue regeneration [[3], [4], [5]]. Recent advances in microfabrication and biomimetic engineering now enable precise control over pore geometry and surface curvature at the nano- and microscale, expanding the design possibilities for next-generation biomaterials [[6], [7], [8], [9]]. However, to fully leverage these technological advancements, a deeper understanding of cellular responses to microenvironmental geometry and consequences for tissue growth inside biomaterial pores is essential. It is well accepted that cells feel and respond to the curvature of their environment, both at subcellular scale [10] and at scales much larger than a single cell [3,11]. The curvature of a cell environment influences diverse physiological processes, including apoptosis as a result of geometrical constraints [12], modulation of migration [13,14], alteration of proliferation and differentiation due to curvature-induced cellular stress [[15], [16], [17], [18]], tissue growth [19,20], tissue morphogenesis [21] and wound healing [22,23]. Biophysical models indicate that cellular adaption to curvature is regulated by the remodeling of the actin stress fibers (SFs) [[24], [25], [26]] and the interaction of the cytoskeleton with the cell nucleus acting as a mechanical sensor [27]. On convex surfaces, mesenchymal stromal cells align towards the direction of minimal curvature [11,13,28], potentially to avoid the energetically unfavorable bending of the SFs [24,26]. Furthermore, the additional stress that is transferred from the cytoskeleton to the nucleus restricts migration on and towards convex surfaces [16,27], thus limiting tissue growth on such topologies [20,29]. On concave substrates, SF bending and the associated stress transferred to the nucleus can be avoided by the formation of straight SFs connecting two points of the topology, following the so-called chord model [20,30]. Concave topologies have been also shown to enhance cellular migration on and towards concave topologies [3,16,27,31]. As a result, tissue growth is accentuated on concave substrates [19,20], and correlations between tissue growth and the degree of curvature have been found [32,33]. However, although tissue growth is often modeled as a continuum, following a layer-by-layer tissue apposition process that mimics the characteristics of a liquid wetting a surface [20,32], cells exposed to high curvature seem to behave as discrete elements over the underlying substrate [16,30]. This discrete behavior allows for complex and dynamic organizational patterns beyond simple surface wetting, potentially enabling sprouting or bridging mechanisms [22,34] similar to those observed in morphogenesis [23,35], tumor progression [36], epithelial wound closure [37,38], or angiogenic sprouting [39,40]. According to tensegrity theory, cells establish a pre-stress (tensional integrity) through a balance of intracellular contractile forces and extracellular anchoring points. This theory suggests that different cellular adhesion patterns, by altering this force balance, might result in distinct responses to curvature [41]. Focal adhesions (FAs) are mechanical anchoring points between the biomaterial surface and the cell's mechanical network, especially SFs [42,43] and thus play a pivotal role in cell-material interaction. This linkage is mediated by cell-surface integrins binding to the extracellular matrix (ECM) proteins (e.g., fibronectin, collagen) in a higly specific manner [44]. In particular, mussel-inspired polydopamine (PD) has a strong adsorption onto a wide variety of substrates through covalent bonding or non-covalent strong interfacial interactions [45]. Binding between collagen coating and PD-treated PDMS surfaces can occur via multiple interactions such as hydrogen bonds, cation-π interaction, π-π interaction and covalent bonds between catechol–OH groups of PD and collagen [45]. Lastly, cell adhesion to the collagen coating is primarily driven by α1β1, α2β1 integrins functioning as cellular collagen receptors [46]. While FAs are well recognized for their role in mechanosensation [42,47], their involvement in tissue growth and healing remains poorly understood. Upon implantation, different cell types adhere to the surface of a biomaterial. As a consequence of their distinct morphologies, cell types vary in their capacity to sense and respond to their surroundings [3,41,[48], [49], [50], [51]]. A general understanding of how different cell types with their individual morphological characteristics respond to scaffold pore geometry and related surface curvature is missing. Moreover, the underlying mechanisms remain largely elusive. Unravelling such cell type-specific curvature responses is key for the development of biomaterial environments with tailored geometric features that orchestrate different cell types towards functional tissue regeneration [[52], [53], [54]].

Here, we use in vitro models featuring precisely controlled geometries to investigate details of FA-mediated cellular adhesion to curved surfaces and consequences for tissue formation and wound healing in scaffold pores. To bridge the gap between surface sensing (2D – 2.5D) and volumetric tissue growth in 3D environments, we employed a stepwise approach. We first characterized the response of different cell types to surface curvature using micro-engineered 2.5D substrates (GeoChips) serving as topographic cell culture landscapes. Next, we correlated the distinct cellular response to curvature to the distribution of FAs around the cell in 2D. However, as regeneration involves 3D cell-matrix interaction that are distinct from open surfaces, we subsequently transitioned towards well-defined 3D cylindrical channels. This allowed us to investigate how cell-type-specific curvature sensitivity drives collective self-organization and tissue growth within confined volumetric environments. Finally, we used a biomaterial environment featuring channels with increasing diameter to study the modulation of defect healing by means of curvature. In conclusion, we demonstrated that the cellular sensitivity to curvature is regulated by the cell type-specific FA distribution on the cells and can lead to two distinct tissue growth mechanisms. We reveal a highly dynamic, curvature-controlled process driven by cell spanning, in which pioneer cells bridge the defect and thereby accelerate gap closure. The mechanism of cell spanning is complementary to the previously described layer-by-layer process of tissue formation [20] and is found in stromal cells such as fibroblasts, mesenchymal stromal cells and osteoblasts, but not in surface-lining cells such as endothelial cells. Our findings are fundamental for the development of biomaterial strategies for in situ tissue engineering using pro-regenerative geometries that enable the control of the healing process through the architecture of the biomaterial. Additionally, understanding the cell type-specific curvature response is essential for a better understanding of wound healing processes and might help to unravel the altered cell invasion into tissues leading to the development of pathologies.

2. Results

2.1. Characterizing cell type-specific response to curvature

To investigate the influence of 3D geometry on tissue formation, we first analyzed single cell adaptation to curvature on GeoChips. For this, we chose concave cylindrical surfaces as they provide a spectrum of curvatures depending on cell orientation, ranging between the two principle curvatures of 0 (along the cylinder axis) and the maximum curvature k_max = 1/(D/2) proportional to the inverse cylinder diameter. This allows cells to control their exposure to curvature by rotation and represents the situation found in biomaterials, tissue microenvironments [55,56] and tissue defects [23,[57], [58], [59]]. Following the hypothesis that cells with distinct functions during regeneration exhibit a different response to curvature, five different cell types were pre-screened on 2D flat surfaces to observe their morphology that was hypothesized to be decisive for the interaction with 3D curved surfaces based on our previous work [16]: (1) human dermal fibroblasts (hdFs) as a cell of high relevance for many tissue healing and regeneration scenarios [35,60], (2) human mesenchymal stromal cells (hMSCs) and (3) human osteoblasts (hOBs) present during the onset of bone healing and homeostasis [61,62], (4) pre-osteoblasts (MC3T3-E1s) commonly used to describe processes of tissue growth in the context of bone healing [19,20], and (5) endothelial cells (human umbilical vein endothelial cells, HUVECs) relevant in the process of tissue vascularization and angiogenesis [3,40]. The fibroblast donor used in this study was selected from a set of six pre-screened donors for having a morphology representative of this cell type (Supplementary Fig. S1). hMSCs and hOBs showed a spindle-like morphology comparable to fibroblasts. Pre-osteoblasts and endothelial cells both featured a more round and less spindle-like morphology but were very different in cell size (Fig. 1a).

A surface free of machining artifacts was important to study cellular response to curvature without the influence of surface micro-patterns (Fig. 1b, right, SEM image). Thus GeoChips with high shape fidelity and smooth surfaces were produced by a multi-step molding process utilizing a sacrificial candy mold [63] to remove machining artifacts of the original brass mold. GeoChips with half-cylindrical surfaces featuring diameters between 100 and 1000 μm were produced from PDMS for subsequent cell culture experiments. As a measure of cell orientation, we first analyzed the orientation of the cytoskeletal SFs on cylindrical surfaces compared to flat controls. While a random orientation was observed on flat surfaces (Fig. 1d), even the lowest curvature investigated (Ø = 1000 μm, κ_max = 2 mm⁻¹) imposed a clear preferential orientation on all investigated cell types except endothelial cells. The preferred orientation was detected by the peak of SF distribution either at the highest curvature (hMSCs, α ≈ 90°), or rotated towards lesser curvature (fibroblasts and pre-osteoblasts, α < 90°, osteoblasts, α > 90°) (Fig. 1e). The same principal rotation was found for increasing curvature with decreasing cylinder diameter down to Ø = 400 μm (κ_max = 5 mm⁻¹) while a re-orientation became visible also for hMSCs, transitioning from α < 90° to α > 90° (Fig. 1f). The tendency to align to a specific degree of curvature might indicate a distinct contribution of cell chirality to cell orientation, as observed before on micropatterned surfaces [64] and surfaces with negative Guassian Gaussian curvature [65]. Endothelial cells responded marginally to curvature and only at diameters of Ø = 600 μm or smaller.

As curvature increased on cylinders with Ø = 300 μm, (κ_max = $6 . \overline{6}$ mm⁻¹) the preferred orientation decreased rapidly for all cell types (Fig. 1g). Interestingly, a dramatic increase in migration and differentiation has been observed in this range of curvature in previous studies, indicating an emerging mechano-geometric interference of curvature [11,16,31]. At Ø = 200 μm (κ_max = 10 mm⁻¹), although the overall distribution was the most isotropic compared to all curvatures investigated, peaks were still detected along the direction of greatest curvature (α = 90°) for fibroblasts, hOBs and hMSCs with an additional peak for hMSCs in the direction of low curvature (α ≈ 157.5°) (Fig. 1h).

Remarkably, as the diameter decreased to the range of the cell size and the curvature dramatically increased (Fig. 1i, Ø = 100 μm, κ_max = 20 mm⁻¹), pre-osteoblasts predominantly oriented along the cylinder axis, avoiding the high principal curvature of the cylindrical surface. Endothelial cells followed the same trend but to a lesser degree. Fibroblasts, hMSCs and hOBs also switched their primary orientation from α ≈ 90° to α ≈ 0°, although less dominant compared to pre-osteoblasts. Nevertheless, the proportion of fibroblasts aligned towards the direction of highest curvature (90°) was the largest compared to all other cell types investigated, followed by hMSCs and hOBs.

Taken together, fibroblasts, hMSCs and hOBs showed a fairly consistent response to curvature, while endothelial cells had a distinctly low response at low curvatures (Ø = 800-1000 μm) and pre-osteoblasts showed a disproportionally strong response at high curvature (Ø = 100 μm) (Fig. 1i). To better understand this discrepancy, fibroblasts, pre-osteoblasts and endothelial cells were selected for the subsequent investigations to answer the question why the individual cell types either partially tolerate or mostly avoid an exposure to curvature.

2.2. Differences in cell morphology, focal adhesion distribution and cell force between cell types

While pre-osteoblasts showed the typical curvature-avoidance response reported earlier [13,66], the fairly random orientation of fibroblasts and endothelial cells on half-cylinders with a high principal curvature (Ø = 100 μm) indicated a different response-mechanism to curvature. Analysis of 3D reconstructions from confocal microscopy images of the cell morphology revealed that cells lifted and spanned parts of their bodies of the surface, resulting in a string-like morphology (Fig. 2a, yellow arrows). This behavior was observed most pronounced for fibroblasts, and it was accentuated as curvature increased (Fig. 2b). Spanning was observed in 31.8 ± 11.9 % of fibroblasts at Ø = 100 μm. In contrast, the percentage of pre-osteoblasts and endothelial cells that showed spanning was significantly lower (11.1 ± 8.0 % and 0.7 ± 1.3 % respectively). As curvature decreased, the number of cells spanning also decreased. At Ø = 300 μm, the fraction of spanning fibroblasts was reduced to 5.3 % ± 1.2 %. In comparison to fibroblasts, spanning of pre-osteoblastic and endothelial cells was extremely rare.

Fig. 2 — Incidence of cell spanning on concave-cylindrical surfaces. (a) Lateral view of fibroblasts exposed to cylinders with increasing diameter (decreasing curvature), with spanning cells marked by yellow arrows. (b) Probability of spanning cells in relation to the half-cylinder diameter. (c-e, top to bottom) Representative 3D reconstructed images of fibroblasts, pre-osteoblasts and endothelial cells on concave-cylindrical surfaces with Ø = 100, 200 and 300 μm. Cells were reconstructed in Imaris using the F-actin (magenta, cell surface reconstruction) and nuclei (blue) signal as obtained by confocal microscopy. Half-cylinder contour is indicated by the yellow dashed line. Spanning cells are indicated by yellow arrows in subfigures c-e for clarity. Polar plots on the right depict the percentage of spanning cells and the corresponding angle of cell orientation for fibroblasts (blue), pre-osteoblasts (orange) and endothelial cells (red). The direction 0° - 180° represents the orientation along the cylindrical surface (minimum curvature) and the direction −90° - 90° represents the orientation perpendicular to the cylindrical surface (maximum curvature). (f) Confocal microscopy images of representative cell morphologies for fibroblasts, pre-osteoblasts and endothelial cells depicting F-actin (magenta), nuclei (blue) and focal adhesions via vinculin staining (green). Focal adhesions are indicated by green arrows (example shown on fibroblasts). (g) Cell length quantified as the major axis of an ellipse fitted around the cell. (h) Cell roundness with a value of 1 representing a perfect circle and value of 0 representing a straight line. (i) FSD calculated as the distance between FA clusters (see methods part for detailed description). (j) FA size distribution per cell plotted as the percentage of FAs that fall into the indicated size classes. (k) Representative force vector maps and (l) total cell force quantified via TFM. Statistical significance via Mann-Whitney test (two sided) with Bonferroni correction, ∗p < 0.05. N ≥ 3 GeoChips/cell type for a total of N ≥ 12 half-cylinders/cell type. N ≥ 60 cells/cell type for FA and morphological analysis. 1 donor/cell type. Scale bar 50 μm.

The angle within the half-cylinder at which the cells were observed spanning was matching that of higher curvature (α ≈ 90°) and it was consistent across the different cell types analyzed (Fig. 2c–e). In particular for fibroblasts, the subpopulation that was aligned along the direction of high curvature (Fig. 1i) correlated to the proportion of spanning fibroblasts observed in 3D reconstructions (Fig. 2c). Additional analysis confirmed the initial observation of cell type similarity between fibroblasts, hMSCs and hOBs also in spanning behavior (Supplementary Fig. S2).

Following the tensegrity model [41] and previous reports that relate cell roundness and length to the pattern of cell anchoring to the substrate [67], we further hypothesized that cell morphology and FA distribution play a decisive role in controlling cell adhesion to curved surfaces. Our initial FA analysis on flat 2D substrates revealed clear differences in FA distribution between the three selected cell types (Fig. 2f). FAs of fibroblasts were mostly localized at the distal ends of the cell body, while they showed the highest cell length and the smallest roundness (highest elongation) of the three cell types. In contrast, pre-osteoblasts and endothelial cells showed a rather continuous distribution of FAs around the cell perimeter, a rounder morphology and a reduced cell length compared to fibroblasts. Endothelial cells showed a significantly reduced cell length, but a similar FA distribution and roundness compared to pre-osteoblasts (Fig. 2g and h). Next to these classical cell shape descriptors, we introduced an additional parameter, named the cell's free spanning distance (FSD), to characterize differences of focal adhesions across the cell body more in detail. The FSD is defined as the average of the two largest distances between the clusters of FAs of the cell. FA clusters were defined as sets of FAs that are in close spatial proximity (see materials and methods section for details). The FSD was highest in fibroblasts and lower for pre-osteoblasts and endothelial cells (Fig. 2i). Also concerning FA size distribution, cellular differences between the cell types were found (Fig. 2j), with fibroblasts presenting the highest percentage of small FAs (<0.25 μm²), endothelial cells showing the highest proportion of medium-size FAs (0.25 – 1 μm²), and pre-osteoblasts featuring a comparatively higher number of large FAs (1 – 5 μm² and >5 μm²). Quantification of single cell forces via traction force microscopy (TFM) revealed that pre-osteoblasts exerted the highest total cell force (Fig. 2k and l), in agreement with a high number of large FAs (Fig. 2j). This finding indicates that the tendency of the cell to span on curved substrates is controlled by the distribution of the FAs rather than by the cell's tensional state.

In contrast to the previously observed curvature-dependent cell alignment [3,11,24], the spanning of parts of the cell body away from the surface reported here is considered an alternative and effective mechanism to avoid curvature without changing cell orientation. The decision whether cells choose a spanning configuration over rotation was directly controlled by the degree of curvature on the cylindrical substrates and the individual cell type.

2.3. The free spanning distance (FSD) controls cellular response to concave surfaces

To investigate the dependency between cytoskeletal tension and cell spanning, we systematically modulated cell contractility via small molecules either increasing (CN03, RhoA activator) or reducing cell force (Y27632, ROCK inhibitor), and hindering FA remodeling (PF228, FA-kinase inhibitor) [68]. Cellular senescence associated with patient aging was reported before to alter cell contractility and morphology and was thus included as an additional modulator with high physiologically relevance. DNA crosslinking agent mitomycin C (MMC) was used to induce senescence in fibroblasts [51]. As an alternative way to modulate cell contractility, not based on biochemical modulation (small molecules) but based on cellular mechanosensation [69,70], low-stiffness versions of the GeoChips (E_{PDMS, soft} = 15 ± 3 kPa, mean ± standard deviation) were produced and processed identically to stiff substrates (E_{PDMS, stiff} = 1797 ± 103 kPa, mean ± standard deviation). When evaluating the consequences of the above-described cell force modulations on flat substrates, only minor alterations in cell length were observed (Fig. 3a,b). Only for CN03 treatment, a statistically significant reduction of cell length as a result of the increased cell force was found, while the induction of cellular senescence led to a strong and statistically significant increase in cell length and roundness (Fig. 3b and Supplementary Fig. S3a). Notably, pronounced differences in SF intensity and FA size/number was apparent from histological images (Fig. 3a) in line with the induced modulations of the mechanical stress state. As a direct consequence, a pronounced and statistically significant increase in the FSD with reduced cell force was observed (soft substrates and Y27632), as well as a clear and statistically significant reduction of the FSD with increased cell force (CN03 and PF228) (Fig. 3c). Remarkably, the increase/decrease in FSD was directly reflected by an increase/decrease in the probability of cell spanning across the diverse curvature situation represented by the different cylinder diameters (Fig. 3d and Supplementary Fig. S4). Surprisingly, the relative number of cells that had stress fibers oriented in the direction of high curvature was enhanced with increased cell force (+CN03, +PF228; Ø = 100-200 μm), while their relative number was lower for reduced cell force (+Y27632; Ø = 200 μm) compared to untreated fibroblasts (Supplementary Data S1). These alterations could be a consequence of a shift in the prevalence of apical vs. basal stress fibers related to alterations in cell contractility. Apical and basal stress fibers have previously been shown to play distinct roles in curvature-sensation [13,24].

Fig. 3 — Cell-substrate adhesion characteristics control cell spanning. (a) Representative microscopy images for fibroblasts adhered to a soft substrate, stimulated with CN03 (RhoA activator), Y27632 (ROCK inhibitor), PF228 (Focal adhesion kinase inhibitor), and MMC (DNA crosslinking). (b) Cell length for the distinct modulators and (c) FSD compared to the fibroblasts (dash-dotted reference line indicates the median value). (d) Relationship between probability of spanning cells and cylinder diameter for the selected cell types. (e) Correlation between cell length and probability of cells spanning. (f) Correlation between FSD and probability of cells spanning. In red, allometric fit, given by *y = a x*^b. (g, left) Schematic representation of the boundary conditions (*U, UR* indicating translational and rotational degrees of freedom respectively) and material properties of the FE model representing an individual cell with two adhesion morphologies (C1 = fully adherent, circular morphology, C2 = large FSD, polar morphology) attached to cylindrical surfaces with Ø = 100 and 1000 μm. (g, middle) Resulting cell displacement according to the cell adhesion morphology (C1, C2) on a cylinder with Ø = 100 μm and (g, right) on a cylinder with Ø = 1000 μm in isometric view (top row) and front view (bottom row). Vector plot is combined with deformed shape to better visualize the direction and magnitude of the displacement. Statistical significance via Mann-Whitney test (two sided) with Bonferroni correction, ∗p < 0.05. N ≥ 60 cells/cell type for FA and morphological analysis. N ≥ 3 GeoChips/cell type for a total of N ≥ 12 half-cylinders/condition. 1 donor/cell type. Scale bar 50 μm.

Most importantly, in the above described comparison between cell types, including modulation and induction of cellular senescence, classical morphological parameters like cell length and roundness were not able to describe the probability of cells to span across concave cylindrical surfaces (Fig. 3e and Supplementary Fig. S3b). Only the here introduced FSD, a measure of focal adhesion clustering and distribution, showed a high correlation with the probability of cell spanning (Fig. 3f), highlighting the importance of this parameter in predicting cellular response to curvature.

The high relevance of the FSD for the interaction of cells with curved surfaces was further supported by a finite element (FE) computational model in which single contractile cells were exposed to low and high curvatures. Two distinct cell types (C1 and C2) with similar contractility were modeled, representing a simplification of the experimentally observed morphologies and focal adhesion distributions (Fig. 2g). Both cell types were modeled to adhere to the half-cylindrical experiencing the maximum curvature. With the initiation of cell contraction, the large FSD of cell type C2 (representative for fibroblasts) led to a pronounced detachment from the substrate at high curvatures, while the small FSD of C1 did not allow the cell to lift off the surface (Fig. 3g, middle). In lower curvatures, cell spanning is not promoted regardless of the cell type due to insufficient vertical forces (Fig. 3g, right).

2.4. Cell spanning critically controls tissue growth in channel-like pores

To test whether the observed tendency of single cells to span across curved substrates has consequences for tissue growth in 3D environments, we analyzed the time-dependent cell organization inside cylindrical channels made of polydimethylsiloxane (PDMS) (Fig. 4a). In this approach, the initial single cell behavior merges into collective cell organization within a geometrically uniform environment that is of relevance to study healing of small tissue defects [3,22,32], but also to identify favorable geometric environments for biomaterial design. A channel diameter of 250 μm was chosen as it gave enough space for tissue formation and was in the range where the investigated cell types had demonstrated their distinct curvature responses (Fig. 3d). Cell movement and tissue growth was monitored for 48 h via 3D time-lapse microscopy to extract information about the time-dependency of tissue growth and cell/tissue alignment (Fig. 4b and c). In the following sections, the use of the term “tissue” refers to the collective of cells filling up the channels, while mature tissue will develop at a later stage following the initial patterning of cells investigated here [32].

Initially, all three cell types adhered to the inner channel surface, creating a comparable tubular cell layer (Fig. 4b and d-f, t = 4 h) with a dominant cell alignment along the channel axis (Fig. 4c, t = 4 h). However, already 12 h after seeding, fibroblasts started to span across the channel to connect the opposite sides (Fig. 4d, open arrows), resulting in a strong reduction of the remaining open channel lumen (delimited by the red dashed line). Simultaneously, cell alignment decreased, indicating that the closure process was initiated by cells spanning across the channel perpendicular to the cylinder axis. This observation was in agreement with the cell spanning process observed before on half-cylinder substrates (Fig. 2, Fig. 4b,c, t = 12 h). Channel closure took place already 24 h after cell seeding and was followed by progressive tissue alignment (Fig. 4b–d, t = 48 h).

In contrast to fibroblasts, pre-osteoblasts followed a continuous layer-by-layer tissue apposition as described before [19,20]. Cell spanning was not observed, and tissue growth in the channel was significantly delayed (Fig. 4e). This observation excluded differences in cell proliferation driving gap closure, as additional experiments on TCP showed a significantly higher proliferation of pre-osteoblast (and endothelial) cells compared to fibroblasts (Supplementary Fig. S5). The alignment of pre-osteoblasts decreased with increasing culture time, a trend also observed for endothelial cells but not for fibroblasts (Fig. 4b,c,e, t = 48 h). Lastly, endothelial cells did not show any tissue apposition and the channel remained open throughout the period studied without any significant changes in cell orientation. The non-progressive behavior of endothelial cells is consistent with their function of lining the inner wall of blood vessels to keep the lumen open [71] and reducing their proliferation by contact inhibition [40]. Such a role is significantly different from cells like fibroblasts that aim to repair wounded tissue [60]. Effects of altered proliferation are however expected to play only a minor role in the short time period investigated here.

Together, different strategies of how cells deal with curvature were found to correlate with different mechanisms of tissue growth in channel-like pores. Cells with high spanning capability (fibroblasts) achieved a rapid bridging across the channel. Strikingly, this enabled a significantly faster tissue growth than the layer-by-layer process observed for cells with marginal spanning capability (e.g., pre-osteoblasts, see Fig. 2 and Supplementary Movie S3) that is predominantly described in literature [18,19,32].

2.5. Cell-dependent curvature-response impacts tissue growth into biomaterial pores

In a next step, we investigated how the observed differences in cellular curvature response manifest in environments where both spatial and temporal aspects influence tissue growth. This situation resembles the recruitment of cells into porous biomaterials but also the invasion of cells into small tissue gaps. Soft scaffolds (E = 3.6 ± 0.5 kPa) presenting channels with diameters between 150 μm and 600 μm were fabricated from a collagen-I/III dispersion by incorporation of polymeric filaments with different diameters before freezing/freeze-drying and subsequent filament removal. Scaffolds were placed on top of a cell monolayer to allow cell migration into the channels mimicking cell recruitment from adjacent tissues (Fig. 5a). Due to the micro-porosity of the scaffold (8.92 ± 5.45 μm, mean ± standard deviation, Supplementary Fig. S6) resulting from fast freezing, the cell migration into the bulk material was possible, but hampered compared to migration along the introduced channels (Fig. 5b). The channel diameters were chosen to present a curvature similar to the GeoChip and PDMS channels (Fig. 5b).

Fig. 5 — Channel closure mechanism can be controlled by substrate curvature using scaffolds with well-defined geometries. (a, left) Schematic representation of the in vitro culture setup with collagen scaffold presenting channels of controlled diameter with Ø ≈ 600 μm, Ø ≈ 350 μm and Ø ≈ 150 μm. Monolayer seeding on one side of the biomaterial facilitates migration of cells from one end of the biomaterial. (a, right) SEM image of the microarchitecture (Scale bar 20 μm) and channels within the biomaterial (Scale bars 100 μm). SEM images correspond to the outermost surface of the scaffold. (b) Comparison of template diameter against resulting channel diameter after cross-linking and sterilization of the biomaterial. (c) Representative images of fibroblasts, pre-osteoblasts and endothelial cells within channels of distinct diameters 7 days after seeding. Cell cytoskeleton (F-actin) is depicted in magenta and nuclei in blue. Yellow arrows indicate the direction (arrow angle) and degree of alignment (vector length) for the corresponding region. Scale bar close-up images: 25 μm. (d, left) Degree of channel closure for the investigated channel diameters and cell types. (d, right) Relative degree of tissue alignment for the different channel diameters and cell types. Tissue alignment ranges from 0 (fully isotropic) to 1 (fully anisotropic, dashed line). Tissue across the channel and relative degree of is calculated in the central 50 % of each channel. Data displayed as average with standard deviation. N = 4 scaffolds/cell type. 1 donor/cell type. Scale bars 200 μm (unless otherwise stated).

At day 7 after placing the collagen-scaffold on the cell layer, the tissue growth and the degree of tissue alignment inside the channels were analyzed. Fibroblasts in large-diameter channels formed tissue in a layer-by-layer process and led to the formation of the characteristic meniscus-shaped tissue at the entry of the pore as a result of cell and tissue tension [19,33] (Fig. 5c, left, Ø ≈ 600 μm). The cells forming the tissue were clearly aligned perpendicular to the axis of the channel (Fig. 5c, left, Ø ≈ 600 μm, region 1), resembling the scar-like tissue previously identified as a potential cause for unsuccessful bone defect healing [53]. Deeper inside the channel, cells were visible exclusively on the channel surface, indicating that they were unable to populate the central part of the channel. However, a change in tissue structure was observed at a smaller channel diameter of Ø ≈ 350 μm, where the tissue penetrated deeper into the channel. Here, an additional tissue region could be identified that was less dense and showed no clear cell alignment (Fig. 5c, left, Ø ≈ 350 μm, region 3, and Fig. 5d). Exclusively in the smallest channels (Ø ≈ 150 μm), a third region could be found that was characterized by a population of cells that were almost exclusively spanning across the channel and formed an isotropic cell network with low cell density that extended deep into the channel (Fig. 5c, left, Ø ≈ 150 μm, region 6, Fig. 5d, and Supplementary Fig. S7). This early cell network served as facilitator for the subsequent process of tissue densification and maturation. Due to the low cell density in this phase, the individual cells had the possibility to reorient, enabling a progressive tissue alignment towards the direction of the channel (Fig. 5c, left, region 5, and Fig. 5d). This finding verified that the cell alignment process observed for fibroblasts in PDMS channels applies also when the tissue is growing into channel-like pores rather than forming within such pores (compare degree of alignment for fibroblasts in Fig. 5d, right to tissue alignment in Fig. 4c and d).

In contrast, pre-osteoblasts followed a process of layer-by-layer tissue formation, resulting in the formation of thin layer of cells at the entrance of the channel (Fig. 5c, middle, Ø ≈ 600 μm). Events of cell spanning across the channel were visible exclusively in the channels with the smallest diameter and were found only sporadically (Fig. 5c, middle, Ø ≈ 150 μm), leading to clearly reduced tissue ingrowth into the channel (Fig. 5d, left). Notably, pre-osteoblasts organization in channels of 150 μm diameter was similar to that of fibroblasts in channels of 350 μm diameter, verifying the altered curvature-sensitivity of the two cell types found on GeoChips (Fig. 3d). No preferred tissue orientation was found for pre-osteoblasts (Fig. 5d, right), consistent with the limited tissue alignment in homogeneously seeded PDMS channels (Fig. 4c–e). Finally, endothelial cells were found exclusively on the channel surface and were unable to grow any tissue within the channel (Fig. 5c, right).

As an ultimate confirmation of how relevant the process of cell spanning is for tissue growth in scaffolds in the context of tissue healing and regeneration, macroporous collagen scaffolds with parallel channel-like pores of approximately 100 μm diameter were employed. This scaffold material has proven before to induce bone defects healing solely due to its pore architecture [53]. Here, the monitoring of tissue growth in such scaffolds revealed that fibroblasts with their pronounced cell spanning ability formed tissue most effectively compared to pre-osteoblasts and endothelial cells (Supplementary Data S3), linking the single cell response to curved surfaces to a macroscopic tissue formation process with relevance for tissue regeneration.

3. Discussion

We have shown here fundamental differences in how distinct cell types respond to curvature at diameters between 100 μm and 1000 μm, and demonstrated that these principles are of relevance for understanding and controlling cellular behavior in tissue healing and regeneration. In living tissues, our findings apply in meso-scale defects occurring i.e. after tissue delamination due to mechanical overload or injury [59,72], but most directly, they are of relevance for engineering porous biomaterials to control cellular behavior [73]. As a result of our studies, the tendency of a specific cell type to span across a concave region can be predicted by its FSD. This parameter was introduced here and can easily be extracted from the 2D adhesion pattern on flat substrates. While differences in FA distribution and spanning distance have received little attention in 2D culture, we here demonstrate their fundamental implications for 3D cell organization and tissue growth in scaffold pores. Based on our findings, cells may be classified into types that are capable to close gaps by a fast healing process based on cell spanning in analogy to developmental events [23,35], and cell types that favor a layer-by-layer wound healing associated with a rather slow continuous centripetal tissue apposition [19]. As a point of particular interest, the cell spanning mechanism was also found to be modulated by the elasticity of the substrate and the contractility of the cell, highlighting that cells alter their sensitivity to curvature based on their mechanical environment and their stress state [49]. Such a modulation is particularly relevant during the early stages of wound healing when extremely soft tissue is deposited [58,74] and in soft biomaterials that address this early healing phase. According to our data, soft environments increase the probability of cells to span across concave regions supporting tissue growth (Supplementary Fig. S4). The two proposed mechanisms of wound healing are not exclusive, but can act in a sequential manner. While tissue in pores with large diameter (greater than 100 μm) grows layer-by-layer for all cell types, the resulting reduction of the pore diameter enables at some cell-type specific point the spanning of cells and the initiation of fast pore closure (Supplementary Data S4). Extending this screening of curvature-sensitivity beyond the cell types investigated here, would allow an even broader understanding of geometry-controlled processes during tissue development [55,56] and repair of different tissue types [23,[57], [58], [59]].

Research aiming to understand the role of curvature in cell organization and its consequences for tissue formation is rapidly increasing and has provided relevant new insights over the past decade [18,29,32,75]. The pre-osteoblastic cell line MC3T3-E1 has been used predominantly in such studies [20,32,76]. However, the question of how representative this cell line is for tissue repair processes across tissue gaps of different sizes, taking into consideration the significant differences in morphology and mechanobiology compared to other cell types, has so far not been adequately addressed. In addition, previous studies lack a comprehensive understanding from the perspective of single cell mechanics and how this integrates into more complex tissue organization [2,20,29]. Modelling the processes of tissue apposition as a liquid wetting a surface [20,29,32] seems to be well justified for gap diameters larger than the cell spanning length, but has to be reconsidered for small gap dimensions. Based on the tensegrity theory [41], our results confirm that cellular adhesion via localized FA clusters in small gap diameters induces a distinct response to curvature by facilitating cell spanning. In turn, SFs linked to FAs might alter the nucleus shape, orientation and motility within the cell [77,78], potentially leading to further cellular adaptations with consequences for cell orientation, migration and differentiation [16,27,77]. However, further studies will be required to better understand the related physiological mechanisms. While our study utilized vinculin to quantify adhesion distribution, it is likely that the spanning phenotype is driven by the spatial regulation of the adhesome rather than the presence of a unique protein. Future studies should therefore investigate the role of mechanosensitive events, such as specific proteins in these FA complexes, that could differentiate spanning-capable cells from surface-lining ones. Additional research is also required to understand how and why different cell types express such variable adhesion patterns [47,48,51] and whether this is driven by their distinct roles in tissue repair processes [79].

Our findings suggest that within a cell population, a morphologically distinct subpopulation of cells with a high FSD is specifically capable to span across concave surfaces (Supplementary Data S5). Time-lapse recordings of concave cylindrical channels (Supplementary Movie S1 and S2) and our previous studies on concave spherical surfaces [31] demonstrate that within the same cell population (e.g., fibroblasts or MSCs), spanning cells have a higher migration speed than surface-lining cells. Furthermore, mathematical models have shown that in a mixed population of fast and slow migrating cells, the more motile subpopulation dominates the leading edge of the tissue over time, while the less motile subpopulation is almost absent [80]. This suggests that even though spanning cells accounted for a maximum of 32% of all cells in our experiments (Fig. 2b) they potentially accumulate at the front of tissue formation and repair. This is consistent with the high percentage of spanning cells found at the front of tissue formation in channels of 150 μm diameter (Fig. 5d, region 6). Consequently, their ability to form a first provisional tissue network that subsequently matures and reorganizes suggests that they might act as pioneer cells in microdefect repair. To our knowledge, this is the first time that differences in curvature-response could be linked to the role of distinct cell subpopulations in tissue healing.

In the context of biomaterial design, substrate curvature can be used to harness a cell-type-specific response leading either to a layer-by-layer tissue deposition or to a cell spanning mode that can be utilized to control the resulting tissue micro-structure [32]. Addressing the fast gap closure resulting from the cell spanning mode in biomaterial strategies has already been demonstrated to be advantageous for material-driven bone tissue regeneration [53]. Such biomaterial-guided tissue formation can be achieved by breaking down a large tissue defect into many meso-scale channels with a diameter that enables rapid filling of the channels and ECM deposition through cell spanning. The resulting cell organization (low density fast structural remodeling) can help to prevent the formation of scar-like tissue developing under insufficient architectural guidance [53,81]. First examples for the effectiveness of such biomaterial approaches already exist [53,82,83], but a more rigorous implementation of our findings might be relevant to control the cell type-specific organization in 3D space. It is proposed that future designs incorporate controlled geometrical heterogeneity, linking smaller pores for rapid tissue closure with larger pores to facilitate endothelial cell lining. In this way, feature formation (e.g., vessel lumen vs. tissue gap filling) could be bioengineered in situ in a desired spatial configuration, leading to more advanced and effective tissue regeneration.

4. Conclusions

In conclusion, we demonstrate that the cellular response to curvature is strongly cell-type dependent, bearing consequences for biomaterial design in tissue regeneration. As a key finding, we identified the distribution of FAs as the main parameter controlling how cells conquer curved surfaces while substrate stiffness and cell contractility serve as additional modulators. Cells with a large distance between FA clusters have the ability to span across concave regions and tissue defects of a few 100 μm, whereas cells with homogeneously distributed FAs adapt to curvature by orienting their cytoskeletal stress fibers away from directions of high curvature. This distinct response induces two well-differentiated mechanisms of healing, the cell spanning mechanism which allows structural remodeling of the cell network and features rapid micro-defect healing on the one hand and the layer-by-layer mechanism which is slower and results in a denser tissue on the other hand. Using these new insights, cell-instructive biomaterial strategies can be engineered to provide distinct geometrical elements, e.g. channels of appropriate diameter, for one or multiple cell types of interest, enabling in situ control of the healing mechanism to enhance tissue regeneration.

5. Experimental section

5.1. Cell isolation and culture

Primary human dermal fibroblasts were isolated from skin biopsies obtained from surgical interventions at the Center for Musculoskeletal Surgery, Charité - Universitätsmedizin Berlin. The study was approved by the ethics committee of the Charité – Universitätsmedizin Berlin and all donors gave informed written consent. Fibroblasts were isolated through cellular outgrowth culture. Fibroblasts were cultured in Dulbecco's modified Eagle's medium (41965, 4500 mg/l glucose, Thermo Fisher) supplemented with 10 % v/v fetal bovine serum (S0615, Biochrom AG), 1 % v/v penicillin/streptomycin (A2212, Biochrom AG), and 1 % v/v Non-essential acids (K0293, Biochrom AG). Experiments with fibroblasts were performed at passages 5-8. Primary human mesenchymal stromal cells (hMSCs) and primary human osteoblasts (hOBs) were obtained from the institutional biobank [84] of the Core Unit Cell Tissue Harvesting (Charité – Universitätsmedizin Berlin). Both cell types were derived from the same donor, which undergoes total hip replacement at Charité University Hospital (48 year old female). Written informed consent was given, and ethics approval was obtained from the local ethics committee/institutional review board (IRB) of the Charité University Hospital. The hMSCs were isolated from metaphyseal bone marrow, while the hOBs were isolated from cancellous bone fragments of the femoral head.

Briefly, the hMSCs were isolated by density gradient separation and subsequent adhesion to tissue culture polystyrene as previously described [85]. The hMSC batch used in this study (identifier P819) has been comprehensively described previously [85] and fulfils the accepted minimal MSC criteria, including the characteristic surface marker profile and tri-lineage differentiation potential. The primary osteoblasts were likewise provided by the biobank from the same donor and isolated through cellular outgrowth culture from the bone sample. Routine biobank quality control for osteoblast batches includes assessment of proliferative capacity, alkaline phosphatase (ALP) activity, and matrix mineralization. For the batch used in this study, all three parameters confirmed an osteoblastic phenotype. This data is included in the Supplementary Fig. S12 hMSCs and hOBs were cultured in medium consisting of Dulbecco's modified Eagle's medium (D5546, 1000 mg/l glucose, Sigma) supplemented with 10 % v/v fetal bovine serum (S0615, Biochrom AG), 1% v/v penicillin/streptomycin (A2212, Biochrom AG), and 1 % v/v L-glutamine (35050, Gibco®). Experiments with hMSCs and hOBs were performed at passage 4–5. Murine pre-osteoblasts (MC3T3-E1, CRL-2593TM, ATCC) were cultured in alpha modified minimum essential medium with nucleosides (F 0925, Biochrom AG), supplemented with 10 % v/v FBS, 1 % v/v P/S and 1 % v/v GlutaMAX (35050, Gibco®). Experiments with pre-osteoblasts were performed at passages 19-25. HUVECs (CC-2519, Lonza Group Ltd.) were cultured in endothelial cell growth medium 2 (C-22011, PromoCell®) supplemented with 1 % v/v P/S. Experiments with HUVECs were performed at passages 3-6. All cells were cultured at 37 °C with 5 % CO₂ and 100 % humidity. Medium was refreshed twice per week and cells were expanded before reaching confluency.

5.2. Engineering of the PDMS cultures systems

GeoChips (data shown in Fig. 1, Fig. 2, Fig. 3) were designed in SolidWorks (Dassault Systemes Corp.) and micromachined out of a brass alloy block. Once the brass mold was manufactured, a master GeoChip was created using polydimethylsiloxane (PDMS, Sylgard 184, Dow Corning, MI, USA) in a 1:10 ratio of curing agent to base. For this, PDMS was degassed, poured on the brass mold and polymerized at 70 °C for 2 h. GeoChips for cell culture were then casted from the master sample using a sacrificial candy mold according to a previously described method [63]. Briefly, 10 g of sugar glass were thoroughly mixed with 5 g of light corn syrup. The mixture was heated up for 1 min at 900 W in a microwave. The warm mixture was poured onto the master GeoChip pre-warmed to 120 °C and then transferred to a pressure chamber at 6 bar. Candy mold was kept under pressure for 15 min and acclimatized to room temperature (RT) before removing the master GeoChip. Once the candy mold was prepared, additional PDMS mixture was prepared in a 1:10 (stiff) or 1:45 (soft) ratio and poured in the candy mold. PDMS polymerization was performed in two subsequent steps. First, the PDMS was partially polymerized for 3 h at 50 °C to avoid the glass transition temperature of the candy that would lead to the loss of the architectural features of the surface. Second, the PDMS GeoChip was completely polymerized for 2h at 70 °C. Finally, the candy mold was dissolved in deionized water (diH₂O) at room temperature overnight. The candy mold process resulted in a very smooth surface on the final GeoChips used for cell culture, not showing any machining marks.

Full-cylindrical cell culture substrates (Fig. 4) were produced from a micromachined brass mold that featured arrays of cylinders with the desired dimensions (1.2 mm height and 250 μm diameter) designed in Solidworks. Inserts and ejectors to facilitate the extraction of the PDMS cylindrical channels were produced by 3D printing using polyoxymethylene. A PDMS solution with a 1:10 ratio of curing agent to base was prepared and degassed. The PDMS solution was then poured into the mold and polymerized for 2 h at 70 °C. After cooling down, the PDMS cylindrical channels were extracted from the mold with the help of the ejectors and a lubrication solution made of 1:1 mild soap to diH₂O. PDMS blocks were cut into individual stripes containing 5 to 8 cylindrical channels and further processed for cell culture.

5.3. PDMS surface functionalization

GeoChips and cylindrical channels were sterilized for 30 min in 70 % v/v ethanol and consecutively washed two times with ultrapure water (UPW; L 0040, Biochrom AG). To avoid the regeneration of the hydrophobic PDMS surface and detachment of protein coatings [86], PDMS substrates were incubated overnight with dopamine solution (H8502, Sigma-Aldrich) at a concentration of 0.01 % w/v in 10 mM Tris – HCl buffer (T3253, Sigma-Aldrich) and pH 8.5 at RT. On the following day, the dopamine solution was washed off twice with UPW prior coating application. PDMS substrates were coated using monomeric collagen (L7220, Biochrom AG) at a concentration of 20 μg/ml in UPW and incubating for 2 h at RT under continuous agitation.

5.4. Inhibitors, activators, and induction of cellular senescence

Y27632 (13624, Cell Signaling Technology, Inc.) was supplemented to the medium at a concentration of 10 μM, CN03 (Rho Activator II, Cytoskeleton, Inc.) was used at a concentration of 5 μg/ml, and PF228 (PZ0117, Sigma-Aldrich) was supplemented at a concentration of 100 μM. Senescence was induced by stimulating the cells with DNA crosslinking agent mitomycin C (M4287, Sigma-Aldrich) at a concentration of 1 μg/ml for 24 h, after which the medium was replaced and the cells were cultured for 14 days prior to the experiment.

5.5. Cell culture on GeoChips

Cell suspension was prepared at a density of 50 cells/μl and the DPBS from the GeoChips was removed only immediately before seeding to avoid drying. 1 ml of cell suspension was gently added on top of the GeoChips to obtain a final density of 25000 cells/cm², avoiding any movement of the culture system that could lead to inhomogeneous cell distribution on the geometrical features. GeoChips were further incubated for 24 h prior to fixation with 4 % w/v paraformaldehyde (PFA).

Immunofluorescent staining was performed against actin filaments (Phalloidin-Atto 550, 19083, Sigma-Aldrich, Munich, Germany) and nuclei (DAPI, D3571, Invitrogen). Antibody concentrations and times are detailed in Supplementary Data S6. Imaging within half-cylinders was performed using a Leica SP5 II confocal laser microscope equipped with visible laser lines and a MaiTai HP multiphoton laser (Mai Tai HP®, Spectra Physics) for UV excitation (DAPI). A 25x water immersion objective (numerical aperture = 0.95) was used to record multi-cell images as shown in Fig. 1, Fig. 2. Image stacks were selected to record the complete depth of the half-cylinder at 1024 px x 1024 px obtaining a voxel size of 0.6 μm × 0.6 μm x 2 μm (width x length x depth). Laser power and detector settings were kept constant for the different samples.

5.6. Cell and ECM orientation analysis

Cell and ECM orientation analysis was based on the orientation of the F-actin, fibronectin and collagen-I fibers. Confocal microscopy images were analyzed in Fiji [87] using a custom made macro utilizing OrientationJ [88] (see Supplementary Data S7). In short, the macro obtains the information from the image stack and then sequentially analyses the different channels to obtain cell density, ECM signal (sum of the total signal within a channel to estimate fibrillar collagen deposition based on signal intensity) and ECM orientation. The alignment of structures (cell cytoskeleton or ECM fibers) is shown in normalized cartesian plots where the direction 0 - 180° represents the orientation parallel to the axis of the half-cylinder (GeoChip) or channel walls (PDMS cylindrical channels and scaffolds), and the 90° direction represents the orientation perpendicular to the axis of the half-cylinder or channel walls. Based on the angular increment of 1°, a random distribution would have a constant value of 1/180° = 0.55 % for all angles. Data represents the average of at least 4 GeoChips and 3 scaffolds per cell type and time point, respectively. Analysis of the orientation was performed on the maximum projection images with z-direction perpendicular to the flat parts of the GeoChip surface and perpendicular to the channel axis for PDMS cylindrical channels and scaffolds, respectively. Degree of alignment was defined as the amount of the signal (F-actin for GeoChips, CellTracker™ Green for PDMS channels and F-actin, fibronectin or collagen-I for scaffolds) at the point of highest orientation as determined by a Gaussian fit. Antibody concentrations and incubation times are detailed in Supplementary Data S6. Imaging was performed using a Leica SP5 II confocal laser microscope equipped with visible laser lines and a MaiTai HP multiphoton laser (Mai Tai HP®, Spectra Physics) at 910 nm excitation providing a specific signal for fibrillar collagen type I. A 25x water immersion objective (numerical aperture = 0.95) was used with a voxel size of 0.6 μm × 0.6 μm x 4 μm (width x length x depth).

In addition, due to the curvature of the half-cylinders of the GeoChip, the mismatch between the real angle of a cell on the surface and the measured angle on the projected view could produce an error in the final measurements. Therefore, the relationship between the angle on the half-cylinder surface, projected view and mismatch angle between both was calculated by mean of trigonometric relationships using MATLAB (MathWorks, Inc.). Calculations were taken into account for the final interpretation of the data (Supplementary Data S8). The error was calculated to be highest at angles between 30° and 50° on half-cylindrical surfaces with diameters of 100 and 200 μm. The error decreased with increasing cylinder diameter as their sides were less steep by design (constant maximum depth from surface for all cylinder diameters). However, the projection error does not alter the findings presented in this work that primarily address changes of orientation between angles around 0° (along the channel) and 90° (perpendicular to the channel).

5.7. Cell spanning analysis

Cell spanning from the half-cylinders of the GeoChips was analyzed performing 3D cell contour segmentation using Imaris (Bitplane AG). The number of cells or cell protrusions spanning from the surface and the according angle were analyzed in respect to the total number of cells on the according geometrical feature. The data is shown in in polar plots (Fig. 2) representing the percentage of spanning cells or cell protrusions and the corresponding angle for which this phenomenon took place.

5.8. Focal adhesion distribution analysis and free spanning distance

Chambered coverslips with 8 wells (80826, ibidi GmbH) were coated with monomeric collagen (20 μg/ml in UPW) for 2 h at RT and subsequently washed with PBS before seeding. Cells were brought to suspension and seeded at a density of 15000 cells/cm² to avoid cell-cell contact. Coverslips were incubated for 24 h before fixation with 4 % w/v PFA. Antibody staining was performed against vinculin (V9131, Sigma-Aldrich), complemented by stainings against F-actin (Phalloidin-Atto 633, 68825, Sigma-Aldrich) and nuclei (DAPI, D1306, Thermo Fisher). Antibody concentrations and incubation times are detailed in Supplementary Data S6. Immunofluorescent images were recorded using a 63x water immersion objective (numerical aperture = 1.2) at a resolution of 2048 px x 2048 px [obtaining a voxel size of 0.2 μm × 0.2 μm x 1 μm (width x length x depth)]. A minimum of 60 cells of each type were recorded for the analysis.

FA analysis was performed using a custom-made macro developed for Fiji (see Supplementary Data S9). Briefly, cells were contoured manually and the FAs were binarized based on signal intensity. FAs were counted and sorted according to their size into four different categories: <0.25 μm², 0.25-1 μm², 1-5 μm² and >5 μm². In addition, the distribution of FAs around the cell was calculated detecting the angular position of each FA in a polar coordinate system with the nucleus in its center. The positions of the FAs were grouped in bins of 5° and FA clusters were identified as the bins that surpasses a threshold set to the 30 % of the minimum peak. Finally, free spanning distance was calculated as the average of the two largest Euclidean distances between FA clusters.

5.9. Traction force microscopy

Traction force microscopy was performed as previously described to calculate cell forces [89,90]. In short, coverslips (22 × 40 mm, 01-2240/1, Langenbrinck GmbH) were prepared by successive sonication in sodium dodecyl sulfate (0.1 % w/v), ddH₂O, 70 % v/v and 100 % v/v ethanol for 30 min at 60 °C. Activation of coverslips was performed using 3-Aminopropyltrimethoxysilane (50 % v/v, APTMS, 281778, Sigma-Aldrich) and glutaraldehyde 0.5 % v/v, G5882, Sigma-Aldrich). Polyacrylamide (PAA) gels were casted on activated coverslips using FluoSpheres of 0.1 μm (F8800, Thermo Fischer) embedded in acrylamide (161-0140, Bio-Rad) and bis-acrylamide (161-0142, Bio-Rad). Ammonium persulfate solution (10 % w/v, A3678, Sigma-Aldrich) and tetramethylethylendiamin (TEMED; 161-0800, Bio-Rad) were used for the polymerization of the PAA gels. PAA gels were washed with ddH₂O and coated with 50 μl of collagen solution (20 μg/ml in UPW, L7220, Biochrom AG) combined with UV-light (10 mW/cm² for 150 s) activated sulfosuccinimidyl 6-(4′-azido-2′-nitrophenylamino)hexanoate (Sulfo-SANPAH, 22589; Thermo Fischer). After washing with DPBS, the elastic modulus of the resulting PAA gels was determined by nanoindentation (Piuma, Optics 11, Netherlands) using a 9 μm spherical tip. PAA gels were seeded at a density of 3000 cells/cm². Cells were allowed to adhere for 24 h and stained with CellTracker™ Green (C7025, Thermo Fischer). Cover slips were transferred into a custom-made perfusion chamber mounted on a Leica SP5 equipped with a 63x water immersion objective. Paired images before and after trypsinization were recorded with a spatial resolution of 240 nm × 240 nm x 500 nm (side x width x depth). Strain energy per cell was calculated with Fiji using the Particle Image Velocimetry and Fourier Transform Traction Cytometry plugins based on the cell contour as determined by the CTG signal [91].

5.10. Finite element model of a contractile cell

A three-dimensional FE model of individual cells was developed in Abaqus (Dassault Systemes Corp.). The elastic modulus of the cell was set at 1 kPa, with a Poisson's ratio of 0.49. The substrate is considered infinititely rigid. The morphology of the cells represents a polar and a circular cell (e.g., fibroblasts vs. pre-osteoblasts) initially following the maximum curvature of half-cylinders with Ø = 100 μm and Ø = 1000 μm. The displacement and rotation of the attachment points simulating the focal adhesions was fully restricted (UR = U = 0). The amount of attachment points was kept constant relative to the cell area. In agreement with previous simulation techniques [92], active cell contraction was simulated using a thermal expansion coefficient of 0.001 K^-1 and a negative thermal load of 100 K. At least 55000 C3D4 elements were used for each cell model.

5.11. Live-monitoring of cell organization in 3D using PDMS cylindrical channels

Functionalized PDMS stripes with cylindrical channels were seeded with cells at a density of 7500 cells/μl inside a syringe placed on a roller to facilitate a homogeneous cell attachment. After 1 h incubation at 37 °C, the stripes were washed once in fresh medium, transferred to an optical 24 well plate (82406, ibidi GmbH) and immobilized with sterile custom-made stainless-steel clips (Ø = 0.3 mm, Dentaurum GmbH & Co.KG). The samples were further incubated for 2 h at 37 °C with 5 % CO₂ and 100 % humidity to ensure cell adhesion before further processing. Cells were then incubated in a 1:1000 solution of CellTracker™ Green for 10 min and consequently washed with fresh medium. Optical well plates were transferred to a Leica SP5 confocal microscope equipped with a cell incubation chamber set to 37 °C and 5 % CO₂ for live imaging. Selected spots were recorded every 4 h over 2 days at 512 × 512 pixels obtaining a voxel size of 1.2 μm × 1.2 μm x 4 μm (width x length x depth) and a total depth between 150 and 200 μm. The length of the live-imaging assays was limited to 48 h to avoid the influence of cytotoxic effects on tissue organization due to laser irradiation [93].

5.12. Engineering of 3D collagen channels and seeding

A collagen scaffold was engineered disposing controlled cylindrical channels ranging from 150 μm to 900 μm. To create the template for the channels, surgical sutures with 150 μm, 250 μm and 350 μm diameter (Prolene 8870H, EH7693H, 8833H, Ethicon US, LLC) and cannulas with 400 μm, 600 μm and 900 μm diameter (Sterican® 9180117 and 4657519, Braun Melsungen AG, BD Microlance™ 3, 300700, Becton Dickinson S.A.) were used as templates. Surgical sutures and cannulas were fixed on a 3D printed polymer frame at 500 μm intervals (Supplementary Fig. S8). A cover slide was placed approximately 500 μm away from the fixed suture material and cannulas, and a 1.5 % w/w collagen type I/III dispersion was deposited covering the templates for the channels. The dispersion was subsequently snap-frozen achieving a homogeneous micro-porosity while preserving the geometry of the larger channels. After snap-freezing, samples were cross-linked [94] and sterilized via ethylene-oxide. The scaffold was subsequently cut in slices of 1 mm before seeding. Cells were brought to suspension and plated on the bottom of a well-plate using a rectangular frame to create a squared homogeneous cell layer of 15 mm × 3 mm containing 9000 cells/mm². After 1 h incubation at 37 °C, scaffolds were placed on top of the cell-monolayer after and further incubated for 7 days performing a medium exchange every 3 days. In these experiments, ascorbic acid was not supplemented to the medium to constrain the mechanical contribution of the ECM [95]. After fixation with 4 % w/v PFA, immunofluorescent staining was performed against actin filaments (Phalloidin-Atto 550, 19083, Sigma-Aldrich) and nuclei (DRAQ5, 424101, BioLegend Inc.). Antibody concentrations and incubation times are detailed in Supplementary Data S6. To reduce the light scattering consequence of distinct refractive indices and increase the imaging depth capacity, optical clearing was performed following a modified Benzoic Acid Benzyl Benzoate (BABB, B6630, Fisher Scientific) clearing method [96]. In short, samples were step-wise incubated in increasing concentrations of tert-butanol (107710010, Thermo Fisher) buffered to a pH of 9.5 with trimethylamine (A12646.AK, Fisher Scientific). After dehydration, samples were incubated in BABB solution for 4 h before imaging. Images were recorded with a Zeiss Lightsheet 7 (Carl Zeiss AG) obtaining a maximum voxel size of 0.8 μm × 0.8 μm x 4 μm (width x length x depth). Analysis of the tissue within the channels was performed in the channels with 150, 350 and 600 μm diameter for simplification purposes.

5.13. Cell patterning analysis

Cell and ECM distribution across the cylindrical PDMS channels was calculated using a custom-made macro developed in Fiji (see Supplementary Data S10). Data of signal distribution was normalized to the width of the channel to avoid the influence of variations in the channel size. For the case of the PDMS cylindrical channels, the analysis was performed exclusively based on the CellTracker™ Green signal. Final data is presented as degree of channel closure, quantified as the amount of tissue in the proximity of the substrate (i.e., at a distance of 10 % of the channel diameter from each side of the of channel, in total 20 %) compared to the amount of tissue at the channel center (i.e., a region with a width of 20 % of the channel diameter at the center of the channel). Tissue distribution data used to calculate the ratios can be found in Supplementary Data S2.

5.14. Analysis of cells crossing the 3D collagen channels

Cells crossing the central region of the collagen channels were calculated using a custom-made macro developed in Fiji (see Supplementary Data S11). Images were first binarized and segmented in intervals of 20 μm. Each segment was consequently analyzed identifying the signal corresponding to the cells within the channel until reaching the end of the image stack. Cells detected within the central 50 % of the channel region were quantified as crossing events in the corresponding segment.

5.15. Analysis of tissue orientation and isotropy inside 3D collagen channels

Tissue orientation and isotropy was analyzed in the central 50 % of the channel region using a custom-made macro developed in Fiji (see Supplementary Data S11). 3D reconstructions were created in the two orthogonal planes along the channel. Main orientation and isotropy were analyzed over the projection of the orthogonal views in 20 μm sections. Tissue orientation can obtain values from 0° (parallel to the axis of the channel) to 90° (perpendicular to the axis of the channel). Tissue isotropy can range from 0 (completely anisotropic tissue) to maximum (completely isotropic tissue).

5.16. Scaffold volume analysis

The scaffold volume was measured after sample fixation using a digital scanner (Epson Perfection V200, Epson America, Inc.) at a resolution of 1200 dpi. Top and side view images were obtained to respectively calculate the cross-sectional area and height of each scaffold using Fiji. The scaffold volume was calculated based on these two numbers and used to obtain the scaffold contraction through the different time-points of the experiment and to derive the total cell number inside the scaffolds (calculated volume x local cell density from confocal microscopy images).

5.17. Microtissue growth setup and seeding

A microtissue growth setup [97] was adapted to monitor gap healing in gaps larger than those of the macroporous scaffold (Supplementary Fig. S9a). In short, the setup consists of two clamps with an upper and lower part manufactured of polyether ether ketone and can be fixed by two polycarbonate screws (Skiffy, Essentra AG Germany; # 170020400022). The upper part of the clamp presents small grooves to prevent the slippage of the scaffold under tension. A tool for mounting was used to fix the clamps at a defined distance of 6 mm using two metal pins (Supplementary Fig. S9b). A custom-made spring was fabricated from Ø = 0.3 mm stainless steel wire (Nonium; Dentaurum GmbH & Co.KG) (Supplementary Fig. S9c) with a stiffness of K = 6.57 ± 0.04 N/m. After mounting the spring wire, the microtissue setup was positioned on the glass window of a custom-made incubation chamber allowing free movement without additional mechanical resistance. Incubation chambers were manufactured from stainless steel 316L using a cover-slide (24 × 36 × 0.16 mm; Thermo Fisher Scientific; Menzel # BB024036A1) as a glass window at the bottom to allow in situ microscopy (Supplementary Fig. S9d). Four glass beads were glued into each incubation chamber with Elastosil E43 (Wacker) for a proper positioning of the clamps and wire (Supplementary Fig. S9e). Lids of standard Falcon dishes were used to cover the chambers during culture.

For the analysis of the gap closure in larger gaps, macroporous scaffolds were used. The scaffolds used with the microtissue setup provide a highly orientated pore architecture with a stiffness of E = 0.43 ± 0.04 kPa perpendicular to pore orientation (i.e., axial/lateral direction in experiments) and E = 4.33 ± 0.38 kPa along the pore orientation (i.e., vertical direction). The scaffolds were cut into rectangular shape of 5 × 13 × 1.5 mm (lateral x axial x vertical). Next, a suspension with fibroblasts was prepared at a density of 15000 cells/μl and scaffolds were seeded by dip in method. The scaffolds were further placed into a 12 well plate and incubated at 37 °C for 1 h to allow cell attachment to the scaffold. Subsequently, scaffolds were washed twice in fibroblast medium and mounted into the clamps. A spatula with the same width as the groove of the assembly holder was carefully pushed beneath the clamps. The clamp setup including the respective spring wire was then transferred into the incubation chamber filled with 9 ml of fibroblast culture medium. After two weeks of culture with Dulbecco's modified Eagle's medium, 2 % v/v fetal bovine serum, 1 % v/v penicillin/streptomycin and 1 % v/v Non-essential acids, a gap was created performing a perpendicular cut with a scalpel. The medium was consequently changed, increasing the volume of fetal bovine serum to 10 % v/v and supplementing with 1.36 mM of ascorbic acid to facilitate collagen fibrillogenesis. The evolution of the cells within the gap was monitored every 12 h using bright field microscopy (Axiovert 25, Carl Zeiss AG). Remaining open area was quantified using Fiji by contouring the remaining space limited by the cells. Once the desired state of gap closure was achieved, samples were fixed with 4 % w/v PFA.

Immunofluorescent staining was subsequently performed against actin filaments (Phalloidin-Atto 550, 19083, Sigma-Aldrich, Munich, Germany) and nuclei (DRAQ5, 424101, BioLegend Inc.). Antibody concentrations and incubation times are detailed in Supplementary Data S6. To reduce the scattering consequence of distinct refractive indices and increase the imaging depth capacity, optical clearing was performed following the SeeDB method [98]. In short, samples were step-wise incubated in increasing concentrations of PBS and fructose supplemented with glycerol. Imaging of the gaps was performed using a Leica SP5 II confocal laser microscope equipped with visible laser lines and using a 25x water immersion objective. Image stacks were selected to record the complete area of the gap combining as many tiles as necessary (Individual tile size: 1024 px x 1024 px, voxel size of 0.6 μm × 0.6 μm x 2 μm (width x length x depth)).

5.18. Macroscopic mechanical characterization

The macroscopic stiffness of the PDMS substrates and collagen scaffolds were determined by monoaxial compression testing using a BOSE Test Bench (BOSE ElectroForce® TestBench, TA Instruments) equipped with a 50 g capacity load cell Model 31 Low (Honeywell Corp.) and parallel compression plates. A minimum of 4 samples were cut to a cylindrical shape (Ø = 8 mm, h = 3 mm), immersed in PBS and degassed prior to mechanical characterization. Collagen scaffolds tested in the radial direction were cut in rectangular shape with 10 mm × 10 mm x 7 mm (side x side x height). Each sample was tested three times at a speed of 0.05 mm/s and to maximum strain of ε = 0.1. The elastic modulus was analyzed as the slope of the linear elastic region of the stress over strain curve.

5.19. Statistical analysis

Unless otherwise stated in the figure legend, the presented data are expressed as the mean with standard deviation. Box plots are shown as box with 25 % and 75 % for lower and upper limits. Median value is indicated as horizontal line. Horizontal line outside the box represents outliers. All statistical analyses were performed in OriginPro 2019b (OriginLab Corporation). If not stated otherwise, two-sided Mann–Whitney-U statistical test was used for assessing significance levels with Bonferroni correction for multiple group comparison. A value of p < 0.05 was considered significant. Each experiment was repeated at least three times. The exact number of samples for the experiments are given in the figure captions.

CRediT authorship contribution statement

Aaron Herrera: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Mina Sohrabi Molina: Writing – review & editing, Visualization, Methodology, Investigation, Formal analysis. Rebecca Günther: Writing – review & editing, Resources, Investigation, Formal analysis. Isabel Orellano: Writing – review & editing, Visualization, Resources, Methodology, Investigation, Formal analysis. Erik Brauer: Writing – review & editing, Methodology, Investigation. Stephanie Diederich: Methodology, Investigation. Alicia Serrano: Methodology, Investigation. Rose Behncke: Resources, Methodology, Investigation. Gabriela Korus: Resources, Methodology. Hans Leemhuis: Writing – review & editing, Resources, Methodology. Georg N. Duda: Writing – review & editing, Validation, Supervision, Resources, Funding acquisition. Ansgar Petersen: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization.

Code availability

The custom codes used for data analysis are available from the corresponding author on reasonable request. Custom code necessary for data validation in half-cylindrical geometries is available in the Supplementary Information files.

Ethics approval and consent to participate

Human dermal fibroblasts, human mesenchymal stromal cells and human osteoblasts were used for this study. Ethical approval was obtained from the ethics committee of Charité – Universtätsmedizin Berlin and written informed consent form the donor was given (Human dermal fibroblasts: EA1/359/13- Human mesenchymal stromal cells and human osteoblasts: EA2/099/10).

Declaration of competing interest

Ansgar Petersen is a guest editor of the special issue titled "Bioactive Biomaterials in Germany" in Bioactive Materials and was not involved in the editorial review or the decision to publish this article. All authors declare that there are no competing interests.

Acknowledgements

This work was financially supported by the German Federal Ministry of Education and Research (BMBF) via grants number 13N1215 and 13XP5048D. Additional funding was provided by the German Research Foundation (DFG) - CRC 1444 - 427826188. The authors thank Dr. Simon Reinke, Dorit Jacobi, Dr. Sven Geißler and Dr. Janosch Schoon (Core Unit “Cell Harvesting” of the BIH Centre for Regenerative Therapies) for providing human tissue for the isolation of human mesenchymal stromal cells and human osteoblasts. The authors thank Dr. Katharina Schmidt-Bleek for helpful discussions.

Footnotes

Peer review under the responsibility of editorial board of Bioactive Materials.

^{Appendix A}

Supplementary data to this article can be found online at https://doi.org/10.1016/j.bioactmat.2026.02.005.

Appendix A. Supplementary data

The following is the Supplementary data to this article:

Multimedia component 1

mmc1.docx^{(26.5MB, docx)}

Data availability

The authors declare that the data supporting the findings of this study are available within the paper and its Supplementary Information files. The data and materials generated and/or analyzed during the study are available from the corresponding author on reasonable request.

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PERMALINK

Cell type-specific response to curvature controls tissue growth dynamics in biomaterial pores

Aaron Herrera

Mina Sohrabi Molina

Rebecca Günther

Isabel Orellano

Erik Brauer

Stephanie Diederich

Alicia Serrano

Rose Behncke

Gabriela Korus

Hans Leemhuis

Georg N Duda

Ansgar Petersen

Abstract

Graphical abstract

Highlights

1. Introduction

2. Results

2.1. Characterizing cell type-specific response to curvature

Fig. 1.

2.2. Differences in cell morphology, focal adhesion distribution and cell force between cell types

Fig. 2.

2.3. The free spanning distance (FSD) controls cellular response to concave surfaces

Fig. 3.

2.4. Cell spanning critically controls tissue growth in channel-like pores

Fig. 4.

2.5. Cell-dependent curvature-response impacts tissue growth into biomaterial pores

Fig. 5.

3. Discussion

4. Conclusions

5. Experimental section

5.1. Cell isolation and culture

5.2. Engineering of the PDMS cultures systems

5.3. PDMS surface functionalization

5.4. Inhibitors, activators, and induction of cellular senescence

5.5. Cell culture on GeoChips

5.6. Cell and ECM orientation analysis

5.7. Cell spanning analysis

5.8. Focal adhesion distribution analysis and free spanning distance

5.9. Traction force microscopy

5.10. Finite element model of a contractile cell

5.11. Live-monitoring of cell organization in 3D using PDMS cylindrical channels

5.12. Engineering of 3D collagen channels and seeding

5.13. Cell patterning analysis

5.14. Analysis of cells crossing the 3D collagen channels

5.15. Analysis of tissue orientation and isotropy inside 3D collagen channels

5.16. Scaffold volume analysis

5.17. Microtissue growth setup and seeding

5.18. Macroscopic mechanical characterization

5.19. Statistical analysis

CRediT authorship contribution statement

Code availability

Ethics approval and consent to participate

Declaration of competing interest

Acknowledgements

Footnotes

Appendix A. Supplementary data

Data availability

References

Associated Data

Supplementary Materials

Data Availability Statement

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