SPAM - Science, Pizza And Mathematics

Towards Multiscale Modeling of Morphogenesis

Abstract: The interplay between shape, form, and function in cellular systems has fascinated scientists for decades, as understanding this is an important step to model morphogenesis or tissue deformations in general. We contribute to this discussion from two directions. On the one hand, to model tissue deformations it is necessary to model cellular systems on curved and even evolving surfaces. We therefore extend a well-established model, the multiphase field model, first to stationary surfaces beyond the sphere, namely cylinders and tori, and then to evolving surfaces. We focus on this model because it offers a high resolution of the cell shapes. Additionally, we add an extrinsic curvature contribution to the model on stationary surfaces to take the substrate curvature into account. We demonstrate that extrinsic curvature effects can explain the alignment of cell elongation with the principal directions of curvature. Together with specific self-propulsion mechanisms and cell-cell interactions, this effect gets enhanced and can explain observed large-scale, persistent, and circumferential rotation on cylindrical surfaces. On evolving surfaces, we introduce a two-scale model, which uses a multiphase field model on the cell scale and a movement based on a Helfrich energy with cell-dependent bending rigidity on the tissue scale. With this, our model couples the behavior of individual cells with the mechanics at tissue level. On the other hand, we are concerned with reliable shape characterization methods. We find that (irreducible) Minkowski tensors are a robust tool to quantify the p-atic order of cell shapes. We first investigate them in the Euclidean plane, using data from the multiphase field model, the active vertex model, and from experiments. We also discuss the dependency of p-atic orders on key model parameters, namely deformability and activity, and show that different p-atic orders should be studied independently. After that, we generalize the (irreducible) Minkowski tensor to curved surfaces, creating a useful tool to evaluate the cell shape from our multiphase field simulations on curved and evolving surfaces.

Presenter: Lea Happel

TBA