GRADIENT MODEL DESCRIBES THE SPATIAL-TEMPORAL EXPRESSION PATTERN OF HOXA GENES IN THE DEVELOPING VERTEBRATE LIMB

Pattern formation of the developing vertebrate limb is mainly controll ed by the zone of polarizing activity (ZPA) and the apical ectodermal ridge (AER) which may act as sources of diffusing morphogens. These so urces are tightly interconnected and maintained by positive feedback a nd, together with the established role of Wnt7a on the dorsal side of the bud, they constitute a cartesian reference frame for the processes of patterning and growth of the limb bud, As an input to our model we have used the local extent and temporal activity of the AER source as it is reflected by Fgf-4 expression in the ridge. We have assumed tha t this source produces a morphogen which diffuses in the three-dimensi onal limb field and degradates by first-order kinetics. When in a cell the morphogen concentration exceeds a particular threshold value, a g ene is switched on. To every threshold corresponds a specific gene. In the following we introduce an order of increasing concentration thres holds corresponding to the sequence of Hoxa-10, 11, and 13 genes (thre shold collinearity). With this simple rule of correspondence we can re produce both spatial and temporal collinearities of Hoxa gene expressi on. This outcome may be the first direct observable effect of a putati ve morphogen in the developing limb, The expression patterns are essen tially transient, and they are followed by sequential refinements whic h lead to the final limb structures, Furthermore, the continuous flow of the morphogen through the progress zone guarantees the coherent cou rse of patterning and limb growth. Several experiments are proposed fo r additional tests of the validity of the model and the eventual rever sibility of Hoxa gene expression. (C) 1996 Wiley-Liss, Inc.