Sum rules for free energy and frequency distribution of DNA dinucleotides

The large discrepancy between the values of the free energy for DNA dinucleotides (or dimers) measured by different teams has raised a debate, yet unsettled. Here the free energy is fitted by a three parameter empiric formula derived in the framework of the crystal basis model of genetic code. Approximate sum rules are derived and compared satisfactorily with the data. On the basis of theoretical and phenomenological arguments, a relation between the correlation functions of dimer distribution and the free energy is assumed. From consistency conditions, sum rules are derived. A check of these conditions with different samples of experimental data is performed, allowing us to argue on the self-consistency and the reliability of the different sets of experimental data.