Modelling cell shape in 3D structured environments: A quantitative comparison with experiments

Cell shape plays a fundamental role in many biological processes, including adhesion, migration, division and development, but it is not clear which shape model best predicts three-dimensional cell shape in structured environments. Here, we compare different modelling approaches with experimental data. The shapes of single mesenchymal cells cultured in custom-made 3D scaffolds were compared by a Fourier method with surfaces that minimize area under the given adhesion and volume constraints. For the minimized surface model, we found marked differences to the experimentally observed cell shapes, which necessitated the use of more advanced shape models. We used different variants of the cellular Potts model, which effectively includes both surface and bulk contributions. The simulations revealed that the Hamiltonian with linear area energy outperformed the elastic area constraint in accurately modelling the 3D shapes of cells in structured environments. Explicit modelling the nucleus did not improve the accuracy of the simulated cell shapes. Overall, our work identifies effective methods for accurately modelling cellular shapes in complex environments. Cell shape and forces have emerged as important determinants of cell function and thus their prediction is essential to describe and control the behaviour of cells in complex environments. While there exist well-established models for the two-dimensional shape of cells on flat substrates, it is less clear how cell shape should be modeled in three dimensions. Different from the philosophy of the vertex model often used for epithelial sheets, we find that models based only on cortical tension as a constant geometrical surface tension are not sufficient to describe the shape of single cells in 3D. Therefore, we employ different variants of the cellular Potts model, where either a target area is prescribed by an elastic constraint or the area energy is described with a linear surface tension. By comparing the simulated shapes to experimental images of cells in 3D scaffolds, we can identify parameters that accurately model 3D cell shape.