Home » » 『Mathematical Models of Cell-Based Morphogenesis』Hisao Honda著・Tatsuzo Nagai著

『Mathematical Models of Cell-Based Morphogenesis』Hisao Honda著・Tatsuzo Nagai著形の科学会 Society for Science on Form, Japan


本多久夫著、長井達三著『Mathematical Models of Cell-Based Morphogenesis: Passive and Active Remodeling』Springer Science+Business Media, Springer。

多細胞生物の形態形成の数理モデル、VoronoiモデルやVertex model関連の長年にわたる研究をまとめました。
“Mathematical Models of Cell-Based Morphogenesis: Passive and Active Remodeling”
by Hisao Honda (Author), Tatsuzo Nagai (Author)
Publisher:Springer; 1st ed. 2022 edition (June 28, 2022)
Hardcover:200 pages (and e-book by Amazon Japan)

Springer Link



Presents the advances in the understanding of pathways from genes to morphogenesis
Demonstrates how to apply mathematical methods such as vertex dynamics to novel biological fields
Examines the relationship between gene signaling and shape determination


Cell Center Model
Applications of the Cell Center Model
Vertex Model
Applications of 2D Cell Models
3D Vertex Model
The World of Epithelial Sheets
Cells Themselves Produce Force for Active Remodeling
Expansion of Shape–Dimension
Mathematical Cell Models and Morphogenesis

About this book

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.


Book Title Mathematical Models of Cell-Based Morphogenesis
Book Subtitle Passive and Active Remodeling
Authors Hisao Honda
Tatsuzo Nagai
Publisher Springer Singapore
発行年月日 2022年06月27日
Number of Pages 192ページ
Hardcover ISBN 978-981-19-2915-1
eBook ISBN 978-981-19-2916-8
Series ISSN 2522-0438
Series E-ISSN 2522-0446
DOI https://doi.org/10.1007/978-981-19-2916-8
Hardcover版価格 17159円(2022年8月1日現在)
eBook版価格 13727円(2022年8月1日現在)
Kindle版価格 17256円(2022年8月1日現在)

最終更新日: 2022年8月4日
2022年08月04日木曜日/2022-08-04T03:01:41+00:00 category :  
Copyright(c) 2022 形の科学会 Society for Science on Form, Japan All Rights Reserved.