Optimal codon randomization via mathematical programming

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.