Biology 466    Unsolved Problems Fall 2010

The Story of Cinderella and the Shoe-Police


Once upon a time, there was a faraway kingdom in which glass slippers were used as identification. Everyone's feet had slightly different shapes, and the Shoe-Police had billions of different machines for making glass slippers. Each one of these slipper making machines had five random control dials, each of which could be set to 10 different settings. These settings controlled the exact shapes of the slippers that would be made by each of the billions of different slipper making machines.

10 times 10 times 10 times 10 times 10 is 100,000 different combinations of settings. These settings were made randomly on each machine, and then the machine was kicked really hard a couple of times to produce some more random differences in the shapes of the glass slippers that would be made by that machine from then on.

At some particular age, when their feet had finished growing, every citizen of the kingdom went down to one of the Shoe-Police headquarters (which were called the Thymus and the Spleen) and tried on glass slippers from as many of the slipper making machines as possible. Every time somebody found a slipper that fit their feet perfectly enough, the police either smashed up and junked whichever machine had made that particular slipper, or either the police locked up that machine in a warehouse (Permanently!!), or possibly the police irreversibly turned off its ability to make any more slippers. Nobody knew for sure which one of these things the Shoe-Police did to the machines. They may have done something else, that nobody has been able to guess. The point was to eliminate any future making of shoes that would fit that particular person, and to do this for every legal person in the kingdom.

For the rest of each person's life, their identity would frequently be checked by the Shoe-Police. This checking consisted of trying on a glass slipper. Each policeman (kind of like that Prince-Charming in the Disney version of that other folk tale) carries around a glass slipper and tries fitting it onto the feet of everybody he meets.

However, the Shoe Police react differently than the Prince. The Prince married Cinderella, because the glass slipper fit her. The Shoe Police would have arrested her, handcuffed her, and put her in jail. The logical reason for this response is that any such person must be some kind of imposter or invader, because otherwise the glass slipper should not fit them. Anybody whose feet exactly fit any of the shapes of glass slippers that are still being manufactured must be an imposter; so they are arrested. Not only are they arrested, but the arrest process stimulates manufacture of lots more glass slippers of the shape that fit them. There is even a manufacture of more machines that make slippers of this exact shape (which turns out to be easy, because these shoe making machines can all duplicate themselves).

Next, let's consider the question whether you would want to say that when the Shoe-Police arrest someone its because they have recognized them as non-self. Don't you think that would be a rather misleading way to think about what has happened? In the real world, a criminal or imposter might be arrested because the real police recognize them, or because there is something wrong with their identification papers or their driver's license, or something. So, for the real police, it would not be misleading to describe them as recognizing an imposter as non-self. But the Shoe-Police don't work that way AT ALL, and neither does the immune system.

In the immune system of vertebrates, including humans, antibody molecules (and also T-cell receptor proteins) are the equivalents of the glass slippers in this story. The equivalents to the shoe making machines are the B and T lymphocytes. The random setting of the controls on these machines is the equivalent to the V(D)J recombination of the genes that code for antibody binding sites (and the equivalent recombination for the T-cell receptor genes). As for the identity of the Shoe-Policemen, they are various different kinds of white blood cells, even including the lymphocytes themselves. I considered having the Shoe-Policemen also be makers of shoes, with each policeman making shoes of a slightly different shape; but that hinders understanding.

The next question is: "What would be the equivalent of an autoimmune disease?". There are several possibilities. One would be that one or more of the discarded ("anti-self") machines escaped from the warehouse, where they were supposed to be locked up forever. A second possibility would be that somebody messed with the control settings on one of the other machines, so that it then made slippers of some slightly different shape, which could fit honest law-abiding citizens of this mythical country. Imagine if there were "wanted posters" in the post office, and somebody took a magic marker and drew on one of the pictures of wanted criminals, so that it looked like you; then the police might arrest you, because your face looks like the one on the wanted poster. Better we should stick to shoes!


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