#### "French flag" spatial pattern, January 2012

Einstein once said: "Things should be made as simple as possible, but not more simple."

Wolpert likes his "French Flag" model (analogy, metaphor) for explaining patterns.

But I think it over-simplifies. (more simple than is possible)

Please tell me what you think...

Wolpert's idea is to imagine a species of very simple [rectangular] worm

```AAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCC
AAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCC
AAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCC
AAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCC
AAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCC
AAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCC
AAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCC
AAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCC
AAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCC
AAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCC
AAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCC
AAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCC
```
This species has only three differentiated cell types "A", "B", "C"

Which are colored red, white and blue. (but that doesn't matter)

```CCCCCCCCCCCCAAAAAAAAAAAAAAAAAAAAAAAA
CBCBCBCBCBCCBBBBBBBBBBBBBBBBBBBBBBBB
CCBCBCBCBCBCAAAAAAAAAAAAAAAAAAAAAAAA
CBCBCBCBCBCCBBBBBBBBBBBBBBBBBBBBBBBB
CCBCBCBCBCBCAAAAAAAAAAAAAAAAAAAAAAAA
CCCCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
```
Approximation of the American flag

```CBBBBBBBBBBBBBBBBBBBBBBB
CCCBBBBBBBBBBBBBBBBBBBBB
CCCCCBBBBBBBBBBBBBBBBBBB
CCCCCCCBBBBBBBBBBBBBBBBB
CCCCCCCCCBBBBBBBBBBBBBBB
CCCCCCCCCAAAAAAAAAAAAAAA
CCCCCCCAAAAAAAAAAAAAAAAA
CCCCCAAAAAAAAAAAAAAAAAAA
CCCAAAAAAAAAAAAAAAAAAAAA
CAAAAAAAAAAAAAAAAAAAAAAA
```
Similar to the Czech flag (which I chose because it has diagonal boundaries between "differentiated cell types"

Imagine a not-quite-so-simple, 3-dimensional, worm; made of five differentiated cell types

1) skin cells
2) nerve cells
3) cartilage cells
4) muscle cells
5) gut cells

Anterior end (with mouth and brain)         Posterior end.

```  SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSkin             SSSSSSSSSSSSSS
SNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNerveSkin          SNNNNNNNNNNNNNNS
SNNNNNNNNNNNervesCCCCCCCCCCCCCCCartilage Skin          SSSCCCCCCCCCSSSS
SNNNNNNNNNNNervesMMMMMMMMMMMMMMMMMMusclesSkin          SSSSMMMMMMMSSSSS
SGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGutSkin          SSSSGGGGGGGGSSSS
food ->      food ->                             SSSSG food GSSSS
SGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGutSkin           SSSGGGGGGGGSSS
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSkin              SSSSSSSSSSSS
```
Longitudinal section of simple worm                                       Cross section of worm

---------------------------

 Wolpert's French flag metaphor is meant to clarify questions about how anatomical patterns develop in the embryo, and how these patterns "regulate" (repair themselves) when an embryo is cut in two by an experimenter. How can one diffusible chemical control the locations where three (or more) differentiated cell types develop. FIRST: Suppose a substance is secreted at one extreme end of the organism (or of an embryo), and diffuses to to other extreme end of the organism (embryo), and is either destroyed or leaks out of the organism. Then a graph of concentration on this diffusing substance will gradually approximate a straight line. SECOND: Next, start out with all the cells of the organism not yet being differentiated. THIRD: Suppose that cells are stimulated to differentiate into the Red cell type where the concentration of the "morphogen" substance is high, specifically, where hits concentration is higher than two thirds maximum. Cells are stimulated to differentiate into the white cell type where the concentration is more than one third maximum, but less than two thirds. And cells are stimulated to differentiate into the blue cell type where the morphogen concentration is less than one third maximum. Notice that this organism is really one dimensional, although pretending to be three dimensional, or at least two dimensional. Try to invent rules for differentiation in the red, white and blue geometric patterns of the American flag! For the Czech flag. For the British Union Jack. If you have two different chemicals, forming gradients in perpendicular directions, rules can be invented for these other flags. For the Czech and British flags, ratios of morphogen concentrations are needed. For the US and British flags, you need lots of cases of synonymous combinations of morphogen concentrations. For example, think how to produce the 13 red and white stripes. If the concentration of the vertical morphogen is between maximum and 12/13 maximum, that causes cells to differentiate into red cells, and also if the concentration is between 11/13 and 10/13 maximum, or if this concentration is between 9/13 maximum and 8/13 maximum. In order to produce the blue area, and the white stars, requires more synonyms (a given cell type differentiating in response to many alternative combinations of morphogen. Between maximum and 12/13 maximum "means" the same as between zero and 1/13 maximum. etc. except where it means blue, etc. If this were how embryos developed, then anatomical patterns would result from the set of rules about which cell type differentiates in response to each possible combination of three morphogen concentrations. Actually, embryonic pattern formation isn't like. Small parts of development maybe somewhat like that. But most are not at all like that.