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The OP is dealing with combinatorial complexity, too. So they might want to look at this figure if they are mutagenizing at the second position of the codon. Again, from Wikipedia (Genetic Code)


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CyberDope was first written at MIT, then again at Kairos, then again by me (privately) in Mathematica. The program gives the best "dopes" for a target set of amino acids. You will need someone who has Mathematica to view this program in ".nb" format and to run it. I would further suggest they upgrade the program into Mathematica ...


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This sort of method is indeed quite useful and frequently used in synthetic biology: I've used a similar approach before to generate 5' insulators for promoters. Calculating the exact theoretical likelihood of what you want, so far as I understand, is a complex combinatoric equation that I wasn't able to get a nice closed form on with a few minutes of work. ...


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