Nucleic acid structure

DNA

B-form DNA

• pitch: 340 nm/turn
• minor groove angle: 137.5078°
• Twist angle of 34.7°
• frequency: 10.4 bases/turn
• The roll and tilt angles vary by a few degrees depending on the basepairs. The dinucleotide AA (or TT) causes significant variations in the roll and tilt angles

RNA

The extra 2'-OH usually prevents formation of the B-form helix found in DNA.

A-form RNA

• 11 bases/turn
• The basepair stacks are tilted and displaced with respect to the axis of the helix

Pseudoknots

RNA is normally assumed by folding algorithms to fold without pseudoknots. A non-pseudoknotted structure in parenthesis format would close all parenthesis in order, i.e. [()]. A pseudoknot has the form [(]). In a pseudoknot, the knotted region the "()" pairing cannot exceed 9 or 10 basepairs. This constraint is because of the helical structure of RNA which forms 10 or 11 basepairs per turn. With a full turn, the two strands of the pseudoknot would form a true knot which is physically and biologically unrealistic.

Thermodynamics

$\Delta G^0 = -RT log K = \Delta H^0 - T\cdot\Delta S^0$ where $K=\frac{\rm [duplex]}{\rm [single-strand]^2}$

At the melting temperature, Tm, 2[duplex] = [single − strand] and from conservation of total RNA, 2[duplex] + [single − strand] = [RNA]total. From this, we can derive that:

$T_m = \frac{\Delta H^0}{\Delta S^0 + R\cdot log[{\rm RNA}]_{total}}$

You can experimentally find the melting curve and extract the values of ΔH0 and ΔS0 from which you can get ΔG0. The Freier-Turner rules shows the incremental ΔG0 of stacking another basepair to the end of another pair. The top row shows the 5' basepair, the left column shows the 3' basepair, and the values are in kcal/mol. For example, a GC basepair followed by a CG basepair has -3.4 kcal/mol. This data was calculated for the folding of RNA at 37°C.

 GU UG AU UA CG GC GU -0.5 -0.6 -0.5 -0.7 -1.5 -1.3 UG -0.5 -0.5 -0.7 -0.5 -1.5 -0.9 AU -0.5 -0.7 -0.9 -1.1 -1.8 -2.3 UA -0.7 -0.5 -0.9 -0.9 -1.7 -2.1 CG -1.9 -1.3 -2.1 -2.3 -2.9 -3.4 GC -1.5 -1.5 -1.7 -1.8 -2.0 -2.9

To calculate the total energy of a RNA duplex, simply sum the contribution of each pair plus a nucleation term for the first pair, which has been experimentally determined to be 3.4 kcal/mol. It's positive because of entropic loss due to association of two strands.

Loops can be analyzed similarly. The Freier and Turner values for loops are:

 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 25 30 Length Bulges 3.3 5.2 6.0 6.7 7.4 8.2 9.1 10.0 10.5 11.0 11.8 12.5 13.0 13.6 14.0 15.0 15.8 Terminal loops ∞ ∞ 7.4 5.9 4.4 4.3 4.1 4.1 4.2 4.3 4.9 5.6 6.1 6.7 7.1 8.1 8.9 Internal loops -- 0.8 1.3 1.7 2.1 2.5 2.6 2.8 3.1 3.6 4.4 5.1 5.6 6.2 6.6 7.6 8.4

Some 4 base terminal loops (tetraloops) are more stable than would be predicted. These include the sequences GNRA, UNCG, and CUYG.