Research

Analysis tools for characterizing tissue surfaces of any shape

How are cells aligned on tissue surfaces? Does the alignment depend on local curvature? Where are regions of misalignment? Do these regions correlate spatially with the fluorescence signal of the molecular marker of interest? And how do all these properties change over time?

These are challenging questions that are not easy to answer, as we typically capture two-dimensional images of three-dimensional (3D) tissues. The main difficulty lies in accurately stitching together individual images from a z-stack and reconstructing 3D information, independent of the shape and structure of the multicellular system. We took on this challenge and developed an image analysis pipeline that fully captures tissue properties such as nematic order, topological defects, local curvature, and fluorescence signals from molecular markers across the entire surface of 3D tissues.

Capturing these 3D properties enables us, e.g., to verify theoretical predictions from simulations by investigating the nematic orientation field of surface cells in multicellular aggregates, as well as to link biological mechanisms with physical descriptions in zebrafish heart systems. Our image analysis tools now allow for quantitative analysis of tissue surfaces and help us address the questions outlined above.

➡ Eckert et al., Nat. Commun., 2025
➡ Analysis tools

Nematic and hexatic order in tissues

Cytoskeleton filaments, bacteria, and various cell types often exhibit symmetries such as polar order (symmetry under rotations by 360°) and nematic order (symmetry under rotations by 180°). The latter is one of the most commonly used symmetries in describing tissues. Elongated cells can be modeled as rod-like objects that align collectively, forming so-called liquid crystal phases—specifically nematic phases, which are characterized by long-range orientational order without positional order.

Nematic order, however, requires elongated cells. Are cells really elongated? Not always! In many tissues, such as epithelia, cells are organized in honeycomb-like lattices, where most cells are hexagonal, indicating hexatic order (symmetry under rotations by 60°). This raises an important question: Are tissues better described as nematic or hexatic?

To address this, we combined in vitro experiments with numerical simulations to analyze the symmetry of epithelial tissues. Unexpectedly, we discovered that epithelial tissues support multiple types of liquid crystal orders that co-exist at different length scales: they are predominantly hexatic at small scales—e.g., individual cells or with their neighbors—and predominantly nematic at large scales—e.g., from the perspective of the entire tissue [1]. We also found that the hexanematic crossover—the length scale at which the switch occurs—is not a fixed value. It depends significantly on monolayer density, cell-cell adhesion, and underlying substrate stiffness [2]. We identified this crossover length scale as a robust indicator of changes in mechanics and biochemistry that influence tissue integrity. Therefore, exploring the crossover length scale between hexatic and nematic symmetry provides a deeper understanding of cellular organization during development, homeostasis, and disease.

➡ [1] Armengol-Collado et al., Nat. Phys., 2023
➡ [2] Eckert et al., Nat. Commun., 2023
➡ Analysis tools

From traction forces to detachment forces

One method to measure traction forces of cells is to use elastic micropillar arrays. These consist of µm-sized beams on which cells can adhere at their tips and exert pulling forces through intracellular contraction. This leads to the deflection of the pillars, providing the necessary information to calculate traction forces. The local force resolution of the resulting force field makes this method ideal for quantifying morphology-dependent force distributions within single cells [1] and for investigating changes under external mechanical cues, such as hypergravity [2].

In a doublet configuration, micropillar arrays enable the measurement of forces acting at cell-cell contacts, providing insight into how much of the total traction force is transmitted through these contacts [3]. However, these measured intercellular forces are somewhat equilibrium-like and do not necessarily reflect the maximum force that the contact can withstand. What is the maximum intercellular strength that can hold cells together before the contact raptures?

Building on the elastic micropillar array assay, we designed the Cell-Cell Separation Device (CC-SD) to measure detachment forces between spread cells [3]. The CC-SD consists of pillar arrays connected to blocks to which cells can adhere and connect across the gap between the blocks. By applying a controlled stretch to separate the blocks, the strain at the cell-cell contact increases, eventually causing it to break. The pillars, whose distances remain largely unaffected by the substrate stretch, are used to determine the intercellular adhesion force. Our design allows for a block separation of up to 2.4-fold, which is sufficient to break cell-cell contacts, enabling to study forces resisting tissue rapture.

➡ [1] Eckert et al., Micro, 2021
➡ [2] Eckert et al., Biophys J., 2021
➡ [3] Eckert et al., bioRxiv, 2023