# 32  Watson-Crick-Franklin Helices

## 32.1 Free Energy Change at 37 °C

Folding free energy changes for Watson-Crick-Franklin helices are predicted using the equation:

ΔG°37 Watson-Crick-Franklin = ΔG°37 intermolecular initiation + ΔG°37 AU end penalty (per AU end) + ΔG°37 symmetry (self-complementary duplexes) + Σ[ΔG°37 stacking]

where intermolecular initiation is applied for bimolecular structure formation, the AU end penalty is applied once per each AU pair at the end of a helix, the symmetry correction is applied to self-complementary duplexes, and the stacking term is a sum of sequence-dependent parameters over all base pair stacks. For helices of P uninterrupted basepairs, there are P-1 stacks of pairs.

## 32.2 Examples

### Self complementary duplex

ΔG°37 = ΔG°37 intermolecular initiation + ΔG°37 symmetry + ΔG°37(MU followed by GC) + ΔG°37(GC followed by CG) + ΔG°37(CG followed by GC) + ΔG°37(GC followed by CG) + ΔG°37(CG followed by UM)

ΔG°37 = 4.1 kcal/mol + 0.43 kcal/mol - 1.6 kcal/mol - 3.4 kcal/mol - 2.4 kcal - 3.4 kcal/mol - 1.6 kcal/mol

ΔG°37 = -7.87 kcal/mol

Note that, for example, the parameters for (MU followed by GC) are the same as (CG followed by UM) because the correct directionality of the strands is preserved.

### Non-self complementary duplex

ΔG°37 = ΔG°37 intermolecular initiation + ΔG°37(GC followed by CG) + ΔG°37(CG followed by MU) + ΔG°37(MU followed by CG) + ΔG°37(CG followed by GC)

ΔG°37 = 4.1 kcal/mol - 3.4 kcal/mol - 1.3 kcal/mol - 1.9 kcal/mol - 2.4 kcal/mol

ΔG°37 = -4.9 kcal/mol

## 32.3 Parameter Tables

The table of parameters is available as plain text for free energy change.