# Dichotomic classes, short range correlations and entropy optimization in coding sequences

### Simone Giannerini

University of Bologna, Department of Statistical Sciences, Italy

In this talk we introduce and study dichotomic classes, quantities
that arise naturally from a mathematical model of the genetic code.
Dichotomic classes can be defined as nonlinear functions of the
information contained in a dinucleotide, that is, a group of two
adjacent bases. Interestingly, such classes, that represent precise
biochemical interactions, emerge naturally from the mathematical
model. Moreover, dichotomic classes possess precise symmetry
properties and can be put in a group theoretic framework.

We use the dichotomic classes as a coding scheme for DNA sequences
and study the mutual dependence between such classes. We obtain
meaningful tests for dependence by using an entropy based measure
possessing many desirable properties together with suitable
resampling techniques. We find universal strong short-range
correlations between certain combinations of dichotomic classes.
These correlations point to the existence of a local structure that
might be related to the mechanisms of error correction and entropy
optimization in the management of genetic information.