Strong short-range correlations and dichotomic codon classes in coding DNA sequences

The study of correlation structures in DNA sequences is of great interest because it allows us to obtain structural and functional information about underlying genetic mechanisms. In this paper we present a study of the correlation structure of protein coding sequences of DNA based on a recently developed mathematical representation of the genetic code. A fundamental consequence of such representation is that codons can be assigned a parity class (odd-even). Such parity can be obtained by means of a nonlinear algorithm acting on the chemical character of the codon bases. In the same setting the Rumer’s class can be naturally described and a new dichotomic class, the hidden class, can be defined. Moreover, we show that the set of DNA’s base transformations associated to the three dichotomic classes can be put in a compact group-theoretic framework. We use the dichotomic classes as a coding scheme for DNA sequences and study the mutual dependence between such classes. The same analysis is carried out also on the chemical dichotomies of DNA bases. In both cases, the statistical analysis is performed by using an entropy-based dependence metric possessing many desirable properties. We obtain meaningful tests for mutual dependence by using suitable resampling techniques. We find strong short-range correlations between certain combinations of dichotomic codon classes. These results support our previous hypothesis that codon classes might play an active role in the organization of genetic information.

Figure 1

Algorithmic representation of the codon dichotomic classes: (a) parity class, (b) Rumer’s class; 1…4 indicate the degeneracy.

Figure 2

Scheme of the position dependent coding for the K-Am class in the third codon position and the S-W class in the first codon position.

Figure 3

(Color online) Scheme of the position dependent coding for the parity and the hidden classes, both of them out of frame 1, i.e., the first base is discarded. The coding involves a window of two consecutive bases in cyan (gray).

Figure 4

(Color online) $S_{\rho }\left(k\right)$ computed on K-Am (3rd bases) and S-W (1st bases) (left), and on R-Y (3rd bases) and S-W (1st bases) (right). Dashed lines: confidence bands at levels 95% (green/light gray) and 99% (blue/dark gray).

Figure 5

Algorithmic representation of the coding of the hidden class; ${\mathrm{H}}_1$ and ${\mathrm{H}}_2$ denote the two categories of the class.

Figure 6

(Color online) $S_{\rho }\left(k\right)$ computed on the three dichotomic classes (all of them with frame shift 1): parity vs Rumer’s (left), parity vs hidden (center) see also Fig. 3, Rumer’s vs hidden (right). Dashed lines: confidence bands at levels 95% (green/light gray) and 99% (blue/dark gray).