Nucleic acid structure

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  • Pitch of helix is distance along helix axis for one complete helix turn
    • The pitch equls the number of nucleotides in one turn multipled by the unit height
  • The unit twist is 360 divided by the number of nucleotides in one turn and is the rotation between neighboring nucleotides
  • Different double helical structures can be seen called A, A', B, α-B', β-B', C, C', C'', D, E, and Z
    • The letters denote structural differences, the α and β are associated with packing differences, and primers indicate small variations
  • the various double helices are represented with two numbers [math]N_m[/math] (from crystallography nomenclature)
    • N is the number of nucleotides to reach the exact same point along the helix axis
    • m is the number of helical turns to reach the exact same point along the helix axis


DNA can form a wide range of double helical structures. Random sequences are found in the A, B, and C forms. Repetitive sequences can form D, E, and Z forms.

B-form DNA

  • radius: 100 nm
  • 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


The extra 2'-OH usually prevents formation of the B-form helix found in DNA. Double-helical RNA is usually of the A or A' form:

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


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.


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

At the melting temperature, [math]T_m[/math], [math]2[{\rm duplex}] = [{\rm single-strand}][/math] and from conservation of total RNA, [math]2[{\rm duplex}] + [{\rm single-strand}] = [{\rm RNA}]_{total}[/math]. From this, we can derive that:

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

You can experimentally find the melting curve and extract the values of [math]\Delta H^0[/math] and [math]\Delta S^0[/math] from which you can get [math]\Delta G^0[/math]. The Freier-Turner rules shows the incremental [math]\Delta G^0[/math] 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 -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:

Length 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 25 30
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.

Triple helices

Purines have a second face (the Hoogsteen face) that can hydrogen bond with a pyrimidine (A with U and G with C). In Hoogsteen pariing, the two strands are parallel. In reverse Hoogsteen pairing, the two strands are antiparallel. When one strand of a Watson-Crick paired helix contains a homopurine region, it can make Hoogsteen or reverse Hoogsteen pairing with a third homopyrimidine strand inserted into the major groove of the duplex to form a triple helix.

Tetraloop-receptor interactions

Tetraloops of the GNRA family can interact with specific helical structures. Different loops interact with different receptors.