Optimal codon randomization via mathematical programming

- To induce a uniform distribution over the 20 amino acids, 4 conventional oligos are required.
- When spiked oligos are allowed, the number drops to 3.
- Integer Programming can be used to compute the required number for any target distribution.

Codon randomization via degenerate oligonucleotides is a widely used approach for generating protein libraries. We use integer programming methodology to model and solve the problem of computing the minimal mixture of oligonucleotides required to induce an arbitrary target probability over the 20 standard amino acids. We consider both randomization via conventional degenerate oligonucleotides, which incorporate at each position of the randomized codon certain nucleotides in equal probabilities, and randomization via spiked oligonucleotides, which admit arbitrary nucleotide distribution at each of the codon's positions. Existing methods for computing such mixtures rely on various heuristics.