21  Watson-Crick-Franklin Helices

21.1 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 symmetry} (self-complementary duplexes) + Σ[ΔG°₃₇ stacking]

where intermolecular initiation is applied for bimolecular structure formation, 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.

21.2 Enthalpy Change

Enthalpy changes for Watson-Crick-Franklin helices are predicted using the equation:

ΔH°_{Watson-Crick-Franklin} = ΔH°_{intermolecular initiation} + ΔH°_{AT end penalty} (per AT end) + Σ[ΔH°_stacking]

where terms are the same as those above for free energy changes except that the AT end penalty is applied once per each AT pair at the end of a helix. Note that the symmetry correction for self-complementary duplexes is absent because that stability cost is an entropic cost.

21.3 Examples

Self complementary duplex

ΔG°₃₇ = ΔG°_{37 intermolecular initiation} + ΔG°_{37 symmetry} + ΔG°₃₇(AT 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 TA)

ΔG°₃₇ = 1.0 kcal/mol + 0.43 kcal/mol – 1.3 kcal/mol – 2.2 kcal/mol – 2.2 kcal/mol – 2.2 kcal/mol – 1.3 kcal/mol

ΔG°₃₇ = -19.47 kcal/mol

ΔH° = ΔH°_{intermolecular initiation} + 2×ΔH°AT _{end penalty} + ΔH°(AT followed by GC) + ΔH°(GC followed by CG) + ΔH°(CG followed by GC) + ΔH°(GC followed by CG) + ΔH°(CG followed by TA)

ΔH° = -7.2 kcal/mol + 2×3.2 kcal/mol – 5.8 kcal/mol – 7.9 kcal/mol – 9.8 kcal/mol – 7.9 kcal/mol – 5.8 kcal/mol

ΔH°= -51.7 kcal/mol

Note that, for example, the parameters for (AT followed by GC) are the same as (CG followed by TA) 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 AT) + ΔG°₃₇(AT followed by CG) + ΔG°₃₇(CG followed by GC)

ΔG°₃₇ = 1.0 kcal/mol – 2.2 kcal/mol – 1.5 kcal/mol – 1.4 kcal/mol – 2.2 kcal/mol

ΔG°₃₇ = -6.3 kcal/mol

ΔH° = ΔH°_{intermolecular initiation} + ΔH°(GC followed by CG) + ΔH°(CG followed by AT) + ΔH°(AT followed by CG) + ΔH°(CG followed by GC)

ΔH° = -7.2 kcal/mol - 7.9 kcal/mol – 9.9 kcal/mol – 5.8 kcal/mol – 9.8 kcal/mol

ΔH°= –40.6 kcal/mol

Note Free energy and enthalpy change associated with AT end is zero and 3.2 kcal/mol respectively.

21.4 Parameter Tables

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