Irreducible representation for nucleotide sequence physical properties and self-consistency of nearest-neighbor dimer sets.

A compact representation of usual DNA/RNA four-nucleotide sets based on molecular affinity classes is proposed. In a geometrical correspondence to this formulation, it follows that intrinsic tetrahedral symmetry correlates nucleotide properties. This representation also leads to a proper decomposition frame for any sequence-dependent physical expectation. Thermodynamic and other physical properties of nucleotide sequences are most often stated within the scope of nearest-neighbor models and decomposed in terms of dimer properties. The inverse problem of obtaining dimer set properties is, however, well known to be ill-posed due to sequence composition closure relations. Analysis of the dimer set composition and structure within the novel tetrahedral formulation provides important self-consistency relations, solving the ill posed nature of the original formulation. As an applied example, we analyze DNA oligomer duplex free energy data available on the literature. It is shown that imposition of stringent self-consistency relations does not decrease fit quality to the experimental data set. On the other hand, an improved dimer set with physically consistent free energies is obtained. Meaningful corrections to previous determinations are found when the self-consistent set is applied to calculate free energies for sequences with composition order bias.