1. Gradient-controlled gene activation: cells have to remember to which concentrations they where exposed From “The Algorithmic Beauty of Sea Shells” © Hans Meinhardt and Springer - Company Position Time

2. Permanent switch-like gene activation requires autoregulatory genes Differentiation 6, 117-123 (1976) Pattern formation based on a communication by diffusion can take place only in very small fields; communications over longer distances would take too much time. Therefore, patterns that are formed at small scales should lead permanent changes in the cells, e.g., by a concentration-dependent activation of genes. If a gene product g has a positive feedback on the activation of its own gene, a morphogen m can cause a switch-like activation of a gene in a part of the field. The gene remains active when the signal is no longer available. gene product The signal has an additional activating effect Dimerization for non-linear feedback gene The gene product g The signal m

3. Permanent switch-like gene activation requires autoregulatory genes Differentiation 6, 117-123 (1976) At low concentrations of the gene product g, the negative term is dominating, The concentration of g will decline further. At higher g levels, the autoregulatory term exceeds the decay, and the concentration will increase until the saturation is reached. The morphogen m is assumed to have an activating influence on the g- production. It can bring the system over the threshold such that a permanent switch form low to high g occurs. The gene remains activated even after the morphogen is no longer available. gene product The signal has an additional activating effect Dimerization for non-linear feedback gene The gene product g The signal m

4. The autocatalysis required for gene activation can be realized by a mutual inhibition of two genes A recently discovered example is the formation of the border cells next to the polar cells in Drosophila oocyte development. These border cells (red) are responsible for the departure of the pole cells (green) and their movement towards the proper oocyte. For this function an all-or nothing decision is crucial… Figure kindly supplied by Denise Montell, see Starz-Gaiano et al. (2008). Dev. Cell 14,726-738 If two genes mutually inhibit each other, they may behave as a switching system. One gene becomes activated and the other suppressed. Thus, as in pattern formation, the autoregulation required for a permanent and switch-like gene activation can result of the from an inhibition of an inhibition….

5. 1. Pole cell (green) produce a diffusible signal, UPT (grey) 2. UPT induces a transcription factor, STAT (red); STAT has initially the same distribution as UPT 3. STAT induces APT; APT represses STAT. With this alone, STAT would remain low. However,… 4. …STAT induces at high levels SLBO (black) 5. SLBO and APT inhibit each other and SLOBO inhibits the action of APT on STAT Result: at high STAT levels, the action of APT is suppressed by SLOBO; STAT is high Further away, STAT is very low A step-by-step explanation how the switch-like JAK/STAT activation works:

6. … now the total time course… Green: polar cells; grey: UPT (produced by the polar cells); red: JAK/STAT (activated by UPT); Blue: APT (produced by JAK/STAT and by an JAK-STAT independent base-line production); Black: SLBO (produced by JAK/STAT, stronger production at higher JAK/STAT levels). Due to the mutual inhibition between SLBO and APT, the APT-inhibition of JAK/STAT is suppressed in cells near the polar cells. Due to a longer time constant of APT, the JAK/STAT distribution obtains first a graded distribution before the transition into the ON-OFF distribution occurs. This time course corresponds rather precisely to the observations. Also mutants or patterns after ectopic gene expressions are well described. Note that there is an unusual behavior: cells that are exposed to a low morphogen concentration become de-activated. In contrast, in usual gene activation systems, the cells only become activated if the concentration is above a threshold (see above). (see Starz-Gaiano et al. (2008). Feedback Inhibition of JAK/STAT signaling by apontic is required to limit an invasive cell population. Dev. Cell 14,726-738. A GUIDED TOUR is available in the program sp [GT129b]

7. Switching of the JAK/STAT activation by the antagonistic action of APT and SLBO: the equation used

8. Space-dependent activation of several genes by a morphogen gradient Gene 4 Gene 1 According to the classical view, a graded distribution can activate several genes in a concentration-dependent fashion. The problem: how can a minute concentration difference in adjacent cells be decisive which gene becomes activated? Model: the cells become sequentially promoted. If the concentration is high enough, the next gene will become active; the previously active gene could be suppressed. Like a barrel that is lifted up by a flood: the highest level is decisive on which level the barrel comes to rest. A later higher flood can lift up the barrel further, a second lower flood is without influence. In other words, the cells measure the highest level they were exposed to. J. theor. Biol. 74,307-321, 1978 Models of biological pattern formation, 1982

9. Gene activation: step-wise irreversible promotion A problem that was to be solved: the genes least sensitive for the signal, i.e., genes that require the highest morphogen concentration for activation (gene 4 in the example) must be able to dominate over the genes that are more sensitive. How can an insensitive gene win the competition? Proposed solution: genes that are less sensitive for the morphogen are better in the autoregulation. In the equation above, this requires with c i+1 > c i ; i = gene number. This condition leads, in addition, to the property that each further step requires a higher signal concentration. Although the signal is smoothly graded, there is an all-or-nothing response in the activation of the particular genes. Gene 4 Gene 1 Gene 4 This equation is easy to read: each gene has an autocatalytic feedback on its own activation. All the alternative genes i, i = 1…. n compete with each other (sum-term in the denominator). The morphogen m has an activating influence and may initiate the positive loop if its concentration is sufficient. The mechanism was designed in such a way that activation of each further gene requires a higher concentration of m. J. theor. Biol. 74, 307-321. (1978)

10. Upon a later increase in the morphogen concentration, a corresponding shift in the regions of gene expression occurs…. In contrast, after a lowering of the morphogen concentration, the regions of expression remains unchanged; the „promotion“ is irreversible and the cells cannot fall back. This corresponds to the well-known posterior or distal transformation.

11. Irreversible and unidirectional “promotion” A cell transplanted from a region of low signal concentration into a region of high signal concentration will switch from gene 1 (blue) to gene 4 (brown). Other way round, a cell in which gene 4 is active will not change the gene activity after transplantation into a region of low signal concentration. This unidirectionality corresponds to the posterior or distal transformation. For examples see: Udolf, et al., (1995). Science 269, 1278-1281; Gomez-Skarmeta, et al., (2003) Nature Rev. Neurosci. 4,587-598; Grapin-Botton, et al., (1998) Development 125,1173-1181

12. Problem: if promotion starts too early, anterior structures will be lost… Early in development the cells that should see a low concentration could be too close to the source or the system needs some time until the final low level equilibrated: an too early irreversible promotion would lead to a loss of anterior structures, as shown in the simulation above ….

13. Solution: delay of gene activation by signal antagonists This problem can be solved by a delay of the step-wise promotion. In Xenopus, for instance, the early anterior-posterior determination of the brain is under the control of a WNT-gradient. However, under maternal control, the early embryo is full of WNT antagonists (such as dkk; blue in the simulation). This leads to a delay in the posterior transformation until the maternally supplied antagonist is gone. In this period, regions of low morphogen levels are established and all genes become activated at their correct position.

14. Due to irreversible promotion: a short- ranging signal can organize a larger field Position 43214321 If cell proliferation is essentially restricted to the source region, a short-ranging gradient can control a larger region. Cells leaving the source region due to proliferation enter a region of lower signal strength and attain, therefore, a stable determination. In contrast, in the source region, the promotion can proceed further. Evidence for such a mechanism exists for the determination of the digits in the chicken wing bud [Harfe et al. (2004). Cell 118, 517].

15. Conclusions: The selection of a particular pathway requires the activation of a particular gene and the suppression of the alternative genes. With gene products that have a positive feedback on the activation of their own gene combined with the repression of the alternative genes, the cell has to make an unequivocal choice: only one of the genes that could be activated at a particular stage can become active. Gene activation and pattern formation in space share formal analogies. The long-range inhibition in spatial pattern formation corresponds to the repression of the alternative genes in gene activation. Thus, essential steps in development can be regarded as a sequence of pattern- forming processes in real space coupled with a pattern formation among alternative genes.