MOTIVATION: Synthesizing genes to be expressed in other organisms is an essential tool in biotechnology. While the many-to-one mapping from codons to amino acids makes the genetic code degenerate, codon usage in a particular organism is not random either. This bias in codon use may have a remarkable effect on the level of gene expression. A number of measures have been developed to quantify a given codon sequence's strength to express a gene in a host organism. Codon optimization aims to find a codon sequence that will optimize one or more of these measures. Efficient computational approaches are needed since the possible number of codon sequences grows exponentially as the number of amino acids increases. RESULTS: We develop a unifying modeling approach for codon optimization. With our mathematical formulations based on graph/network representations of amino acid sequences, any combination of measures can be optimized in the same framework by finding a path satisfying additional limitations in an acyclic layered network. We tested our approach on bi-objectives commonly used in the literature, namely, Codon Pair Bias versus Codon Adaptation Index and Relative Codon Pair Bias versus Relative Codon Bias. However, our framework is general enough to handle any number of objectives concurrently with certain restrictions or preferences on the use of specific nucleotide sequences. We implemented our models using Python's Gurobi interface and showed the efficacy of our approach even for the largest proteins available. We also provided experimentation showing that highly expressed genes have objective values close to the optimized values in the bi-objective codon design problem. AVAILABILITY AND IMPLEMENTATION: http://alpersen.bilkent.edu.tr/NetworkCodon.zip. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Synthesizing proteins in heterologous hosts is an important tool in biotechnology. However, the genetic code is degenerate and the codon usage is biased in many organisms. Synonymous codon changes that are customized for each host organism may have a significant effect on the level of protein expression. This effect can be measured by using metrics, such as codon adaptation index, codon pair bias, relative codon bias and relative codon pair bias. Codon optimization is designing codons that improve one or more of these objectives. Currently available algorithms and software solutions either rely on heuristics without providing optimality guarantees or are very rigid in modeling different objective functions and restrictions. RESULTS: We develop an effective mixed integer linear programing (MILP) formulation, which considers multiple objectives. Our numerical study shows that this formulation can be effectively used to generate (Pareto) optimal codon designs even for very long amino acid sequences using a standard commercial solver. We also show that one can obtain designs in the efficient frontier in reasonable solution times and incorporate other complex objectives, such as mRNA secondary structures in codon design using MILP formulations. AVAILABILITY AND IMPLEMENTATION: http://alpersen.bilkent.edu.tr/codonoptimization/CodonOptimization.zip.