Tyssue: an epithelium simulation library

Abstract

The tyssue Python library seeks to provide a unified interface to implement bio-mechanical models of living tissues. Its main focus is on vertex based epithelium models. tyssue allows to model the mechanical behavior of 2D, apical 3D or full 3D epithelia based on the numerical resolution of the equations of motion for the mesh vertices. Biological processes are modeled through changes in the topological and dynamical properties of the mesh. tyssue is a modular library. Starting with the same tissue geometry, the choice of constraints, energy potential terms and parameters increases the possibility to answer different biological questions and easily explore mechanical hypotheses. Statement of Need Tissue remodeling is a complex process integrating a large number of inputs such as gene expression pattern, cell adherent properties or cell mechanics. It can be difficult to manipulate specific aspects genetically. It can even be hard to simply capture, when the process takes only few minutes. Furthermore, morphogenesis is inherently a mechanical process. To execute complex morphogenetic movements, epithelia are driven by in-plane forces, like constriction of apical cell surface (Heer et al., 2017), and/or out-of-plane forces, such as the apico-basal cable in apoptotic cell (Gracia et al., 2019; Monier et al., 2015) or lateral tension (Sherrard et al., 2010; Sui et al., 2018). Modeling these processes help us to understand how tissues acquire their shape, in complement of the experimental systems, and beyond their limitations. Several vertex models have been developed in the past few years to describe the physics of epithelia (for a review, see Alt et al. (2017)), and common features can be identified. Several kinds of models have already been published. The apical vertex model has been used several times to study topology changes during morphogenetic movement in Drosophila, Hydra and Xenopus (Aegerter-Wilmsen et al., 2012; Aigouy et al., 2010; Farhadifar et al., 2007). Associated with protein dynamics, it has been used to study the effect of protein position on tissue organisation in zebrafish retina (Salbreux et al., 2012). 3D vertex model have been used to study epithelium deformation due to normal development or to cancer development (Eritano et al., 2020; Okuda et al., 2015). Most of the time, models are developed for a specific biological question and are difficult to adapt to other systems, for several reasons. However, there is some exception like Chaste (Cooper et al., 2020), which propose an open source C++ library to model cell populations or how specific events arise at the system level. With the tyssue library, we propose models which are adaptable and scalable with the field of research and the biological question. Topology and mechanics are implemented independently to improve the versatility of models.