Hans G. Othmer, Fellow

Mathematical Modeling of Vertebrate Limb Development

Anew model for limb development that incorporates both outgrowth due to cell growth and division, as well as interactions between morphogens produced in the zone of polarizing activity and the apical epidermal ridge, has been previously developed. The numerically-computed, spatio-temporal distributions of these morphogens demonstrated the importance of interaction between the organizing regions in establishing the morphogenetic terrain on which cells reside and, because growth is explicitly incorporated, it was found that the history of a cell’s exposure to the morphogens depends heavily on where the cell originates in the early limb bud. The mathematical model and the associated computational algorithms were sufficiently flexible that other schemes for the interactions between mophogens, and their effect on the spatio-temporal pattern of growth and gene expression, could easily be tested. Thus an additional result of these researchers’ previous work is a computational tool that can be used to explore the effects of various mutations and experimental interventions on the growth of the limb and the pattern of gene expression.

Recent research revealed details of the biochemical mechanism of differentiation at the molecular level. The team’s future work intends to:

• Modify the existing model to incorporate new molecular information about the mechanism of limb development
• Extend the solution domain to four dimensions (3 spatial + time) to enable a realistic simulation of the limb development process

The aim of this project is to provide a computational tool that can be used to explore the effects of various mutations and experimental interventions on the growth of the limb and the pattern of gene expression.

Research Group

Nelson H. F. Beebe, Department of Mathematics, University of Utah, Salt Lake City, Utah
John Dallon, Department of Mathematics, Brigham Young University, Provo, Utah
Chetan Gadgil, Graduate Student Researcher
Maria E. Gracheva, Research Associate
Nikolaos Mantzaris, Graduate Student Researcher
Sima Setayeshgar, Department of Mathematics, Princeton University, Princeton, New Jersey
Steve Webb, Research Associate