5.5.1 De Garis's Convex L

1. Purpose

I am not alone in trying to create a system that emulates the natural process of development. There are numerous scientific papers and books detailing past work done by others in this area. One such book is Evolutionary Design By Computers edited by Peter J. Bentley. This is a collection of papers written about work done to use the power of evolution to create designs. One of the papers written by Dr. Hugo De Garis discusses his work to create a genetic developmental system that can produce desired patterns. I will not go into explicit details here on his work. If you are interested then please see the reference I have provided. However, some minimal explanation is required. His model consists of a chromosome that is used to control the behavior of a cellular automata. The chromosome contains a series of genes, where each gene is composed of a condition field and an action field. The present state of any cell is determined by the state of its neighbors at the end of the last cycle. So on each cycle the present state of the cell is compared to the condition field of each gene and if the condition matches it then the action field is performed. The action field can change the state of the neighboring cells by reproduction. In his early tests he was able to evolve chromosomes that did fairly well at producing concave shapes like squares and triangles. However, attempts to produce shapes with convex curves failed to produce stellar results. He subsequently modified the system in an attempt to improve its ability to produce convex shapes. In his article he attempted to generate an 'L' shape as a basic test. Unfortunately, he still did not produce results that were very impressive. Figure 1 shows his best result of evolving a chromosome to produce this L shape. Figure 2 is another attempt that he made using a concept he termed shaping. Shaping basically means that he tried to evolve a chromosome to do the vertical portion first, then he held that gene constant and tried to evolve the gene to do the horizontal portion. However, this still did not result in very convincing results. His final example produced much better results. He evolved the chromosome without shaping, but moved the initial seed cells further down the neck of the 'L' so they were closer to the bend. His system was better able to cope with this and the results appear much more like an 'L' shape.

Convex 'L' Shape
Figure 1. This is the 'L' Shape results De Garis produced using both operons.

Shaped Convex 'L' Shape
Figure 2. This is the 'L' Shape results De Garis produced using shaping.

Seeded Convex 'L' Shape
Figure 3. This is the 'L' Shape results De Garis produced using more central seeding.

2. The Challenge

When I read about De Garis's attempts I immediately saw how easy it would be to come up with a simple set of genes for my system that would create the 'L' shape he was looking for. These genes were so simple that there was no reason to resort to using evolution, and the basic outlines were done in a few minutes. It then took an hour or two to tweak them to perform exactly as desired and to produce the files needed to visualize everything. The basic gene structure is seen in figure 4, and I outline an explanation of how these genes work below.

Convex 'L' Shape Chromosome
Figure 4. This figure shows the genes involved in producing the convex 'L' shape.

Gene Interaction Steps
  1. This example begins with the cells being initialized with two perpendicular, linear gradients of transcription factors named VZT (Vertical Zone Transcription) and HZT (Horizontal Zone Transcription). This is similar to what would be found in OOGenesis, and in this example it is assumed that the mother would have set up this gradient during the formation of the egg. These TF's have expression functions that are sigmoidal so that they will only up-regulate expression of the G_APOffC gene if the transcription factor is in sufficient quantity. So in other words, this TF will only express this gene if its quantity is over 15,000 for example. By moving this value higher or lower you can move the position of the vertical and horizontal lines of the L shape.
  2. In the portion of cells where the G_APOffC gene is being expressed the protein APOffC (Apoptosis Off Control) is produced. This controller quickly builds up enough quantity in these cells to shut off the G_APR gene. This gene produces the APR (Apoptosis Receptor) protein. This membrane receptor produces a protein that we will discuss in a bit that leads the cell to basically kill itself. So by turning off production of this receptor in the cells in the 'L' portion it prevents these cells from getting that signal and dying.
  3. G_APOffC also turns on the G_APL gene. However, a whole lot more of APOffC has to accumulate in the cells before this takes place. Once it finally does reach the threshold level and turns that gene on it begins to produce the APL (Apoptosis Ligand) protein. This protein is a membrane ligand that mates up with the APR receptor. So all of the cells in the 'L' Shape will now be producing this ligand. However, since all of these cells no longer have the receptor for that ligand, the only cells this will really affect are the ones lining the edge of the 'L' shape.
  4. When the ligand and receptors lining the shape mate up they begin producing the protein APLC (Apoptosis Ligand Control). This gene control builds up in the lining cells to the point where it turns on the G_APL gene. This causes the lining cells to produce the APL ligand protein and will setup a loop where each layer of cells that is not part of the 'L' shape will begin producing ligand and induce the cells next to them to begin producing it also. Soon production of the ligand begins to spread like a wave away from the shape.
  5. In each of these cells APLC also turns on the G_APC gene. This gene produces the APC (Apoptosis Control) protein. This gene control protein builds up and eventually turns off ALL genes in the entire system. This in effect kills these cells because they are no longer producing any proteins. They have been shut off. But again remember that this only occurs in the cells that are not part of the 'L' shape.

3. Results

Convex 'L' Shape Results
Video 1. This video demonstrates the creation of the convex 'L' shape.

Using apoptosis, or programmed cell death, to produce shapes in developing systems is one of natures tried and true methods of building complex shapes. A good example of this is the fingers on our hands. Initially our hands are disk like and the cells between our newly forming fingers commit suicide so that the final shape is a well formed hand. When someone has web's between their fingers this occurs because this process was not completely successful. This same principle is applied here. The 'L' shape itself is initially created using the different levels of gene transcription from the gradient of transcription factors. But what is required is an 'L' shape that actually has different gene states. If we were to simple leave it with the transcription factors then they will slowly fade and we would be left with a square of cells that are identical. We need permanent changes. So the proteins produced by the up-regulation of that gene changes the state of the genes in the shape, and these cells in turn induce changes in the other cells to make them kill themselves and stop all genetic expression. When this example is finished we get a set of cells in the shape of an 'L' that are expressing the G_APL gene and all of the other cells have had all of their genes turned off. If we had wanted to set the system up so that the cells in the 'L' shape had expressed a different gene in addition to G_APL and the other cells not express it then this would have been just as easy.

4. Conclusion

My purpose here was not to disparage Dr. Garis's work. It was to make a comparison between some of the results from someone else in the field with the results of the simulator system that I have put together. I wanted to demonstrate that what other systems find exceedingly difficult can be done almost effortlessly here. Also, the gene interactions found in this system bare a far closer resemblance to what actually happens in nature than that found in the other system. One set of cells begins expressing genes at different rates and this in turn leads those cells to induce neighboring cells into different states. Dr. Garis was attempting to do something similar, but the simulator system that he was using was simply not up to the task of doing this.

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