Mathematical Models of Cell-Based Morphogenesis: Passive and Active Remodeling

This book describes the shape formation of living organisms using  mathematical models. Genes are deeply related to the shape of living  organisms, and elucidation of a pathway of shape formation from genes is  one of the fundamental problems in biology. Mathematical cell models  are indispensable tools to elucidate this problem.  

The book  introduces two mathematical cell models, the cell center model and the  vertex model, with their applications. The cell center model is applied  to elucidate the formation of neat cell arrangements in epidermis, cell  patterns consisting of heterogeneous-sized cells, capillary networks,  and the branching patterns of blood vessels. The vertex model is applied  to elucidate the wound healing mechanisms of the epithelium and ordered  pattern formation involving apoptosis. Pattern formation with  differential cell adhesion is also described. The vertex model is then  extended from a two-dimensional (2D) to a three-dimensional (3D) model. A  cell aggregate involving a large cavity is described to explain the  development of the mammalian blastocyst or the formation of an  epithelial vesicle. Epithelial tissues and the polarity formation  process of the epithelium are also explained. The vertex model also  recapitulates active remodeling of tissues and describes the twisting of  tissue that contributes to understanding the cardiac loop formation of  the embryonic tube. The book showcases that mathematical cell models are  indispensable tools to understand the shape formation of living  organisms. Successful contribution of the mathematical cell models means  that the remodeling of collective cells is self-construction. Examining  the successive iterations of self-constructions leads to understanding  the remarkable and mysterious morphogenesis that occurs during the  development of living organisms.  
The intended readers of this book  are not only theoretical or mathematical biologists, but also  experimental and general biologists, including undergraduate and  postgraduate students who are interested in the relationship between  genes and morphogenesis.