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 controlled by the zone of polarizing activity (ZPA) and the apical ectodermal ridge (AER) which may act as sources of diffusing morphogens. These sources are tightly interconnected and maintained by positive feedback and, together with the established role of Wnt7 a 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 that this source produces a morphogen which diffuses in the three-dimensional limb field and degradates by first-order kinetics. When in a cell the morphogen concentration exceeds a particular threshold value, a gene is switched on. To every threshold corresponds a specific gene. In the following we introduce an order of increasing concentration thresholds corresponding to the sequence of Hoxa-10, 11, and 13 genes (threshold collinearity). With this simple rule of correspondence we can reproduce both spatial and temporal collinearities of Hoxa gene expression. This outcome may be the first direct observable effect of a putative morphogen in the developing limb. The expression patterns are essentially transient, and they are followed by sequential refinements which lead to the final limb structures. Furthermore, the continuous flow of the morphogen through the progress zone guarantees the coherent course of patterning and limb growth. Several experiments are proposed for additional tests of the validity of the model and the eventual reversibility of Hoxa gene expression.