A Minimal Spatial Cell Lineage Model Exhibits Tissue Instability, Stratification, and Multi-stability
Wei-Ting Yeh1*, Hsuan-Yi Chen1,2,3
1Physics, National Central University, Taipei, Taiwan
2Physics, Academia Sinica, Taipei, Taiwan
3Physics Division, National Center for Theoretical Sciences, Hsinchu, Taiwan
* presenting author:Wei-Ting Yeh, email:wtyeh1989@gmail.com
Understanding of the development and regulation of biological tissues, especially how active cell events, such as cell division, death (apoptosis), and differentiation affects its dynamics, is an interesting topic in current developmental and cancer biology. To get the deep physical insight of tissue dynamics, we build a minimal model which includes the consideration of spatial resolution and cell lineage dynamics. Although it is hard to get the full solution due to the nonlinear nature of the governing equations, we can still learn lesson in some limiting cases by using analytical approaches. With this model, we obtain a criterion to have stable steady state with tissue stratification and see how different cell lineage and differentiation model could lead to different degree of tissue stratification. Thus, by observing the degree of stratification in vivo, one could deduce the underlying cell differentiation mechanism.

Besides time-independent steady state properties, we also study the dependence of tissue relaxation dynamics on the cell events. It is found that cell turnover inside the tissue in general enhance the relaxation process, however due to stratification, a destabilizing flow created by cell death at apical surface could be enhanced and drive tissue go unstable. The effect of cell lineage and internal conversion of proliferative cells within this context are also discussed. Since the mathematical structure of out minimal model permit the existence of multiple steady states, such instability gives tissue a chance to evolve into another state with different degree of stratification. Since our model is quite simple and general, we think this could be related to certain tissue developmental pattern.

Keywords: cell lineage , cell differentiation, biological tissue dynamics, hydrodynamic instability, cancer invasion