In-phase implies large likelihood for independent codon model: distinguishing coding from non-coding sequences

It is proven that under the independent codon model, the likelihood of a DNA coding sequence read according to the correct frame is asymptotically larger than that read with an incorrect frame. Based on this proposition, a single set of probabilities of the codon usage is enough for discriminating the six frames of coding sequences under the independent codon model. The direct coding sequence of Escherichia coli genome is taken as an example to examine the codon independency by using the mutual information and χ2 analysis. The contrast between the coding frame and the two offset frames is evident. A self-learning approach for generating training set is proposed to estimate probability parameters.