Mathematical modeling of tissue folding and asymmetric tissue flow during epithelial morphogenesis

Recent studies have revealed that intrinsic, individual cell behavior can provide the driving force for deforming a two-dimensional cell sheet to a three-dimensional tissue without the need for external regulatory elements. However, whether intrinsic, individual cell behavior could actually generate the force to induce tissue deformation was unclear, because there was no experimental method with which to verify it in vivo. In such cases, mathematical modeling can be effective for verifying whether a locally generated force can propagate through an entire tissue and induce deformation. Moreover, the mathematical model sometimes provides potential mechanistic insight beyond the information obtained from biological experimental results. Here, we present two examples of modeling tissue morphogenesis driven by cell deformation or cell interaction. In the first example, a mathematical study on tissue-autonomous folding based on a two-dimensional vertex model revealed that active modulations of cell mechanics along the basal-lateral surface, in addition to the apical side, can induce tissue-fold formation. In the second example, by applying a two-dimensional vertex model in an apical plane, a novel mechanism of tissue flow caused by asymmetric cell interactions was discovered, which explained the mechanics behind the collective cellular movement observed during epithelial morphogenesis.