Autoregulatory feedback loops are requiredThe generation of signals by the exchange of molecules via diffusion works only in small fields. In larger fields the time required to generate patterns by randomly moving molecules would be much too long. Therefore, the signals generated at small scales have to be translated into more permanent states of differentiation that can be maintained upon further growth. The obvious means is a stable concentration- (and thus space-) dependent activation of genes. The choice of a particular pathway under the influence of a morphogenetic signal requires the activation of particular genes and the suppression of alternative genes. This situation has formal similarities with pattern formation in space: spatial patterning requires activation at a particular position and the inhibition in the remaining part. In analogy, the selection of a particular pathway requires the activation of a particular gene and the suppression of the alternative genes. Based on this similarity, I have proposed in 1978 that gene activation requires a direct or indirect feedback of genes on their own activation and their mutual competition such that only one of the alternative genes can remain active in a particular cell. [ PDF ]. Meanwhile many such autoregulatory genes have been found. The genes deformed , hunchback or twist  are examples. As in pattern formation, the feedback has to be non-linear . This condition is satisfied if dimers are involved in the autoregulation.
Unidirectional promotion: activation of several genes by a single gradientFor the position-dependent activation of of several genes by a single gradient genes I have proposed that the cells do not measure a particular morphogen concentration all at ones. Instead, starting from a default gene activity, other genes become activated in a unidirectional manner. Each further step requires a higher morphogen concentration. This process comes to rest if the actual gene activation corresponds to the local morphogen concentration.
The model is based on the following assumptions
An analogyThe situation can be compared with a barrel at the base of a staircase. The barrel may be lifted up by a flood (morphogen signal). After lowering of the flood, the barrel can only remain at a few discrete levels (activation of particular genes). A later, higher flood can lift the barrel up even further; a second lower flood would have no effect.
Pattern regulationA premature removal of the morphogen leads to an arrest in the promotion ( simulation below). Anterior structures remain at a more posterior position while the most posterior structures could be missing. The specification of digits in the chicken wing under the influence of the zone of polarizing activity (ZPA) has this dynamics.
Why antagonists of morphogens could be essentialIn Xenopus there is good evidence that the pattern of the head is set up by a Wnt signal that spreads from the marginal zone [4,5]. Low Wnt concentrations are necessary for the formation of the most anterior structures. Most remarkably, in this region many WNT antagonists are present [6,7], partially supplied under maternal control. If missing, anterior structures (forebrain) will not form. Why is a signal produced that quench the function of other molecules, at least for a substantial period? The model outlined above provides a rational. If a gradient is generated by an pattern-forming system as described above, it may take some times until the concentration opposite to the organizing region has obtained its low steady state level. The same is true if the field is originally so small that the gradient level at the side antipodal to the organizer is too high to determine the most anterior structures. These structures will be missing (blue and magenta gene in the simulation below):
Transplantation upwards or downwards of morphogenetic gradientsThe proposed mode of gene regulation predicts that cells adapt to the new environment after transplantation into a region of higher morphogen concentration. In the simulation below after transplantation of a cell with the 'low ' gene 1 (blue) active into a region of high signal concentration, gene 4 (brown) becomes becomes activated.