Abstract
Geometrical aspects relevant to discussion of deformable epithelial cell sheets are presented. The epithelium is pictured as consisting of cells joined at their lateral surfaces and having cell heights which vary with position over the middle surface, which bisects the cell heights. The Gauss and Mean curvatures are shown to be represented by simple functions of variables Sand h, where Sis an angular deformation of the sheet at each point and his the local cell height. It is argued that the Gauss curvature can often be considered as a simple quadratic function of Sdivided by h 2, while the Mean curvature His defined as S/ h. These two variables are in turn to be considered as monotonic functions of the morphogen(s). A closed set of coupled morphogen and geometry equations are suggested, which, however, represent an open dynamical system in the sense that there is continuous external energy input. A growing, three dimensional entity of continuously changing shape and pattern is thus represented by this growth and form algorithm.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.