I will discuss a new model for limb development which incorporates outgrowth due to cell growth and division as well as interactions between morphogens produced in specialized signaling regions of the developing limb bud. The numerically-computed spatio-temporal distributions of these morphogens demonstrate the importance of interaction between the organizing regions in establishing the morphogenetic environment of the individual limb bud cells. Because growth is explicitly incorporated, I will show that the history of a cell's exposure to the morphogens depends heavily on where the cell originates in the early limb bud. I will also discuss several theoretically plausible interpretation functions based on the history of a cell's exposure to the morphogens that can qualitatively account form some of the observed patterns of gene expression. The model and associated computational algorithms are sufficiently flexible so that alternative schemes for morphogen interaction and their effect on the spatio-temporal pattern of growth and gene expression can easily be tested.

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1998-1999 Mathematics in Biology