TY - JOUR
T1 - The importance of geometry in mathematical models of developing systems
AU - Umulis, David M.
AU - Othmer, Hans G.
PY - 2012/12
Y1 - 2012/12
N2 - Understanding the interaction between the spatial variation of extracellular signals and the interpretation of such signals in embryonic development is difficult without a mathematical model, but the inherent limitations of a model can have a profound impact on its utility. A central issue is the level of abstraction needed, and here we focus on the role of geometry in models and how the choice of the spatial dimension can influence the conclusions reached. A widely studied system in which the proper choice of geometry is critical is embryonic development of Drosophila melanogaster, and we discuss recent work in which 3D embryo-scale modeling is used to identify key modes of transport, analyze gap gene expression, and test BMP-mediated positive feedback mechanisms.
AB - Understanding the interaction between the spatial variation of extracellular signals and the interpretation of such signals in embryonic development is difficult without a mathematical model, but the inherent limitations of a model can have a profound impact on its utility. A central issue is the level of abstraction needed, and here we focus on the role of geometry in models and how the choice of the spatial dimension can influence the conclusions reached. A widely studied system in which the proper choice of geometry is critical is embryonic development of Drosophila melanogaster, and we discuss recent work in which 3D embryo-scale modeling is used to identify key modes of transport, analyze gap gene expression, and test BMP-mediated positive feedback mechanisms.
UR - http://www.scopus.com/inward/record.url?scp=84872653103&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84872653103&partnerID=8YFLogxK
U2 - 10.1016/j.gde.2012.09.007
DO - 10.1016/j.gde.2012.09.007
M3 - Review article
C2 - 23107453
AN - SCOPUS:84872653103
SN - 0959-437X
VL - 22
SP - 547
EP - 552
JO - Current Opinion in Genetics and Development
JF - Current Opinion in Genetics and Development
IS - 6
ER -