Nucleic acid structure

General

• 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 symmetries of the various double helices are represented with two numbers [math]\displaystyle{ 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
• the axial rise is the distance along helical axis between nucleotides
• 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 axial rise
• The unit twist is 360 divided by the number of nucleotides in one turn and is the rotation between neighboring nucleotides

Structure	Pitch (Å)	Helical symmetry	Axial rise (Å)	Twist (°)	Minor groove width (Å)	Major groove width (Å)	Minor groove depth (Å)	Major groove depth (Å)
A	28.2	[math]\displaystyle{ 11_1 }[/math]	2.56	32.7	11.0	2.7	2.8	13.5
B	33.8	[math]\displaystyle{ 10_1 }[/math]	3.38	36.0	5.7	11.7	7.5	8.5
C	31.0	[math]\displaystyle{ 9.33_1 }[/math]	3.32	38.6	4.8	10.5	7.9	7.5
B'	32.9	[math]\displaystyle{ 10_1 }[/math]	3.29	36
C'	29.5	[math]\displaystyle{ 9_1 }[/math]	3.28	40
C	29.1	[math]\displaystyle{ 9_1 }[/math]	3.23	40
D	24.3	[math]\displaystyle{ 8_1 }[/math]	3.04	45	1.3	8.9	6.7	5.8
E	24.35	[math]\displaystyle{ 7.5_1 }[/math]	3.25	48
S	43.4	[math]\displaystyle{ 6_5 }[/math]	3.63	30.0
Z	45	[math]\displaystyle{ 6_5 }[/math]	3.7

DNA

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

• 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. 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

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

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

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

[math]\displaystyle{ 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]\displaystyle{ \Delta H^0 }[/math] and [math]\displaystyle{ \Delta S^0 }[/math] from which you can get [math]\displaystyle{ \Delta G^0 }[/math]. The Freier-Turner rules shows the incremental [math]\displaystyle{ \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	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:

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.