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I remember learning in microbiology that the human body generates antibodies using a random process so that an enormous variety of antibodies can be produced with a simple genetic code.

Now that I'm trying to learn more about random processes, I find this more interesting than I used to. Has anyone developed a mathematical model for how the genetic code generates these random antibodies? Clearly, we'd like the process to be ergodic, so that as many antibody varieties as possible can be produced. The main reason that I'm interested is because there are so many ways that random and pseudo-random numbers are generated, and it would interesting to see what the body "thinks" is a good random antibody generator.

I did a quick google search, finding links such as this paper, but they seem to assume that antibodies are generated randomly without explaining the mechanism.

So, does anyone know if there is a mathematical model for the process that generates random antibodies?

And, Merry Christmas!

Edit: Steve and Tom have provided a great answer and a great comment about related topics that I think provide a good place to start reading. For now, though, I will leave the question open in case someone can provide a fuller answer in the future. End Edit.

Brian Rushton
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  • I agree with those voting to close that this may not be the most appropriate forum for this question. Can anyone a suggest a better place to ask this? – Brian Rushton Dec 22 '12 at 19:33
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    I'd like to ask fellow MO-ers to keep this question open. I think it's a reasonable, sensible, well-phrased, applied mathematics question. The votes to close so far are for "off topic", but I disagree: to me, good applied questions are bang on topic. (See http://tea.mathoverflow.net/discussion/1483/#Item_13 for recent discussion on how MO seems to be unattractive to applied mathematicians. Closing questions like this doesn't help.) It may be that no one here has the expertise to answer, but that's not a reason to close. – Tom Leinster Dec 22 '12 at 19:50
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    Brian: a related question is how recurrent pathogens such as malaria do their "random" mutations once within the human body. Since these pathogens are way smaller than the human body, and the range from which they're choosing their mutations is (I believe) much narrower than the range of possible human antibodies, this might be a subject on which more is known. One place to start looking might be the work of Mario Recker: http://www.zoo.ox.ac.uk/people/view/recker_m.htm – Tom Leinster Dec 22 '12 at 19:56
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    I have to confess, after I wrote my previous comment, I realized that I accidentally voted to close while checking the previous vote to close. I didn't have enough reputation for this before. Sorry for my mess-up! – Brian Rushton Dec 22 '12 at 20:27
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    Brian, you need 3000 points to vote to close other people's questions, but you can vote to close your own after you reach 250 points. You can also vote to reopen your own questions, which you should obviously do in the unlikely event that this question gets closed. – François G. Dorais Dec 22 '12 at 23:16
  • This question has been posted as a sample question for a proposed mathematical modeling stack exchange site: http://area51.stackexchange.com/proposals/57490/mathematical-modeling?referrer=B5TWQ70QNWlDGxDR-o9vQA2. Users can modify this proposal by asking their own questions and voting for others. – Brian Rushton Jul 09 '13 at 03:12