Early pattern formation

In figure 3.3a the initial condition, or ``zygote'' of the organism is shown. The state vector and the neighbourhood vector of the zygote are primed with zeros. After two iterations, the housekeeping genes have stabilised. After the first division, the bicoid gene (# 21) will be flipped. In our case it was turned on, so we switch it off. Obviously, after one iteration the bicoid bit is turned back on, because of its Boolean function ALL1. In spite of the network's insensitivity to the bicoid bit, the daughter cells do differentiate after the first division, because the cells ``sense'' each other's neighbourhood vector. Whereas all the bits of the neighbourhood vector were turned off in the zygote stage, the neighbourhood vector of the two cell is now equal to 001001. It is easy to see, that bit 16 will be turned off, because bit 1 of the neighbour vector is turned on. Bit 1 of the state vector is switched off because bit 4 is turned on. In the next iteration, bit 1 will be turned off in the neighbourhood vector, causing bit 16 to flip back on.

After the second division (figure 3.3b) in one of the cells the ``activin'' bit is flipped. The network needs a mechanism to store this signal, because it is only applied during one iteration. This is nicely achieved by a feedback loop on the activin gene. If the activin bit is turned off, it inputs a 0 to itself. The next state will be a 0 again, and so forth. If, however, the activin bit is turned on, it will keep itself turned on.

Interestingly, the state of the activin bit is propagated to a subnet of the bits 4, 23, 7, 11 and 3. To understand the behaviour of this subnet, let us first return to the zygote. In the zygote, all the bits of state vector and the neighbourhood vector were turned off. After the first iteration, bit 4 was switched on. Bit 7 was turned on, because one of its inputs, bit 23 was 0. After the second iteration, bit 23 was turned on, because its input is 1. This caused bit 7 to be turned on. As a result, the bits 11 and 3 were switched off after the following iteration of the network. Now that activin has been switched on, the expression of the subnet is inverted. First, bit 4 is switched off. As a result, the bit 23 is switched off, whereas bit 7 is turned on. Bit 7 finally, switches on the bits 11 and 3.

Now that the activin cell has differentiated, the neighbourhood vector of the surrounding cells changes. In the activin cell, gene 3 is expressed. By these means, in all the surrounding cells gene 17 is suppressed by bit 3 of the neighbourhood vector.

After the third division, the main pattern of the creature has been laid down. In figure 3.3d two changes are apparent. First, some pink cells have dedifferentiated into gray cells. They do not touch the ``activin'' cell any more, so that gene 17 is expressed again. Second, the black ``activin'' cell has divided. It differentiated into the greenish brown cells in about the same way the gray cells appeared after the first division. Now that it is connected to another black cell, bit 3 of the neighbourhood vector is expressed, by which means gene 17 is suppressed.
 

Figure 3.3: The ontogeny of Ontosilica gastrulans segundo (MPEG movie)

 

Figure 3.4: continued.

2000-06-08