Compositional Differences

A more informative method to determine coding regions, takes advantage of the frequencies in which the various codons occur in coding regions. For example, the amino acids Leucine, Alanine and Tryptophan are coded by 6,4 and 1 different codons respectively. In a translation of a uniformly random DNA sequence, these amino acids should occur in the ratio 6:4:1, but in a protein they occur in a different ratio - 6.9:6.5:1. Therefore coding DNA is not random. Another example of the non-uniformness of coding DNA is the fact that A or T occurs in the 3^rd position of a codon 90% of the time, while G or C occur only 10% of the time (these statistics are different for different species). Assume that $a_1,b_1,c_1,a_2,b_2,c_2,\ldots ,a_{n+1},b_{n+1}$ is a coding sequence of bases with an unknown reading frame. Let f_abc denote the frequency with which the codon abc appear in a coding region. Under the assumption that successive codons are chosen independently at random according to the frequencies f_abc, the probability of observing the sequence of n codons appearing in the reading frame starting with a₁b₁c₁ is

$$p_1=f_{a_1b_1c_1}\times f_{a_2b_2c_2}\times\ldots\times f_{a_nb_nc_n}$$

Similarly, the probability of observing the n codons in the second and third coding frames are :

$$\begin{eqnarray*}p_2&=&f_{b_1c_1a_2}\times f_{b_2c_2a_3}\times\ldots\times f_{b... ...}\times f_{c_2a_3a_3}\times \ldots\times f_{c_na_{n+1}b_{n+1}} \end{eqnarray*}$$

The probability P_i which is the probability of the ith reading frame being the translated one (assuming the region is coding) can be calculated as follows:

$$P_i=\frac{p_i}{p_1+p_2+p_3}$$

  

Figure 7.6: Application of codon frequency method to bases 1 to 10,000 of the liverwort Marchantia chloroplast genome. The horizontal scale marks every 100th base, and the bars above indicate the extent of known protein coding segments. The three boxes above contain plots of the probability that each of the three reading frames is coding for a protein. The short vertical lines that bisect the mid-height of each box mark the positions of the stop codons in the corresponding reading frames. The vertical scale within each box is of log(P/1-P), so that, for example, 4 points up the scale from the mid-height corresponds to 99.99% probability of the current region being coding.

The above computation can be used in a search algorithm as follows: Slide a window of size n along the sequence, and compute P_i for each start position of the window. The Codon Preference program, which is part of the GCG library, implements this method. Figure 7.6 shows the plot of log(P/1-P), which is the log likelihood, for the three reading frames. It shows that the value of log(P/1-P) is usually above 4 ( $P>99.99\%$ ) in regions where the DNA sequence codes for a protein in that reading frame. This method depends on the accuracy of the codon frequency statistics of already found genes. The algorithm will also have difficulty in detecting horizontal gene transfer and other causes of heterogeneity.

  

Figure: Periodicity of T: for each gap size n, the number of occurrences of the pattern T$\ldots$T, with n bases between the two T's, was counted. Plotted is the present difference of that number from the number of such pair expected if the bases occurred at random. Since the T's occur preferentially at the second codon position, in coding regions, the present difference at n=2,5,8,... is noticeably large.

Various other methods have also been tried. One variation of the codon frequency method is to use 6-tuple frequencies, which are more informative than 3-tuple (codon) frequencies. Another approach (which is illustrated in figure 7.7) considers the periodicity of certain bases in protein coding regions, whose statistical behaviour distinguishes them from non coding regions.