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Designing Autocorrelated Genes

The redundancy in the genetic code enables a protein to be encoded by many different sequences. Recent studies show that the degree of tRNA autocorrelation in a coding sequence has important effects on translation speed. The tRNA pairing index (TPI) has been used widely to study the phenomenon of autocorrelation in sequences. However TPI only counts successive transitions of tRNA usage, without regard to how far apart they occur in the sequence. In this paper, we propose a new type of autocorrelation measure, DICA (Distance Incorporated Codon Autocorrelation), which weighs positional distance between codons as well as the number of transitions. We demonstrate that our DICA correlates better to the expression level of a particular gene than TPI. Finally, we devise exact and heuristic algorithms to find near optimally autocorrelated and anti-autocorrelated genes for the purposes of synthetic gene design.