2.4.4.1 Thermodynamics of Secondary Structure Elements. The free energy of an RNA conform-
ation has to take into account the contributions of interactions between bases, sugars, phosphates, ions and
solvent. The most reliable parameters are those derived experimentally from the Tmprofiles (Section 2.5.1)
of double-helical regions of RNA and data for each of the 10 nearest-neighbour sequences are given in
Table 2.7. They are accurate enough to predict the expected thermodynamic behaviour of any RNA duplex
to within about 10% of its experimental value.^63
Other structural features are less easy to predict. It is clear that stacking interactions are more important
than base-pairings so that an odd purine nucleotide ‘dangling’ at the 3-end of a stem can contribute some
–4 kJ mol^1 to the stability of the adjacent duplex. The energies for mispairs or loops are rather less accur-
ate, but always destabilising and change with the size of the loop (Table 2.8). Energies of these irregular
secondary structures also depend on base composition, for example a single base bulge for uridine costs
about8 kJ mol^1 and for guanosine about14 kJ mol^1.
By use of such data, the prediction of secondary structure is a conceptually simple task that can be han-
dled by a modest computer while the more advanced programmes search sub-optimal structures as well as
that of lowest free energy.
Interactions between separate regions of secondary structure are defined as tertiary interactions. One
example is that of pseudoknots, which involve base-pairing between one strand of an internal loop and a
distant single-strand region (Section 7.6.3, Figure 7.41). Pseudoknots can also involve base-pairing
between components of two separate hairpin loops and examples with 3–8 bp have been described as a
DNA and RNA Structure 63
Table 2.7 Thermodynamic parameters for RNA helix initiation and propagation in 1 M NaCl
Propagation H S G Propagation H S G
sequence (kJ mol^1 ) (J K^1 mol^1 ) (kJ mol^1 ) sequence (KJ mol^1 ) (J K^1 mol^1 ) (kJ mol^1 )
↑
AU
↑AU
AU↓ 27.7 77.3 3.8 GC↓ 55.8
149 9.6↑
UA
↑UA
AU↓ 23.9 65.1 3.8 GC↓ 42.8
110 8.8↑
AU
↑GC
UA↓ 34.1 94.9 4. 6CG↓ 33.6 81.5 8.4↑
AU
↑CG
CG↓ 44.1
117 7. 6GC↓ 59.6
147 14.7↑
UA
↑GC
CG↓ 31.9 80.6 7.1 CG↓ 51.2
125 12.4
Initiation (0) 45.4 14.6
Symmetry 0 5.9 1.7 Symmetry 0 0 0
correction (self- correction
complementary) (non-self-
complementary)
Arrows point in a 5-3direction to designate the stacking of adjacent base pairs.
The enthalpy change for helix initiation is assumed to be zero.
Table 2.8 Free energy increments for loops (kJ mol^1 in 1 M NaCl, 37°C)
Loop size Internal loop Bulge loop Hairpin loop
1— 14 —
2 4 22 —
3 5.4 25 31
4 7.1 28 25
5 8.8 31 18.5
6 10.5 34.5 18