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
  • If all bases were coplanar and the pairs perpendicular to the helix axis, the rise should equal the van der Waals distance of 3.4 Å
• The pitch is the distance along the 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
• The base-pair tilt is when the base pair plane is not exactly perpendicular to the helical axis.
  • 0° is the plane perpendicular to the helical axis
  • tilt is defined relative to looking at the base pair plane from the 1'-C/N linkage side. Tilting this plane clockwise is positive tilt and negative tilt is counterclockwise
  • There is a linear relationship between the tilt of an individual base with the axial rise per nucleotide
• Sugar puckering is the deviation from planarity for the 5 atoms of the sugar ring. The 5 atoms are never seen to be planar. It can be in an envelope form where 4 atoms are in a plane and the fifth is out by 0.5Å or in a twist form where two adjacent atoms are out of the plane made by the other three atoms. Atoms on the same side as the 5'-C are called endo and those on the opposite side are called exo.
• Dislocation is the displacement of base-pairs from the helix axis

Except for the left-handed S/Z helices, the structures are broadly classified into A and B families. The essential distinction between A and B type helices is in the sugar puckering. In A helices, 3'-endo sugar puckering is seen and in B-type helices, 2'-endo (or 3'-exo) is seen. This leads to differences in distance between phosphates from 5.9Å in A-type to 7.0Å in B-type helices. Base-pair tilt is positive in A-type (10-20°) and negative in B-type helices (-16.4 - -5.9°).

In A-type double helices, the axial rise can vary from 2.59 to 3.29 Å but has small variation in rotation from 30.0° to 32.7°. In B-type helices, the axial rise only changes from 3.03 to 3.37 Å but the rotation varies from 36° to 45°

In B-DNA, the disolcation is about -0.2-1.8Å into the minor groove. In A-DNA, the helix axis is pushed into the major groove with the dislocation about 4.4-4.9Å

DNA

DNA can form a wide range of double helical structures. Random sequences are found in the A, B, and C forms. Designed repetitive sequences can form D, E, and Z forms. Native DNA adopts the B-form with 10 base-pairs per turn in its crystalline state. But in solution, the molecule underwinds, yielding 10.3-10.6 base pairs per turn.

Some parameters for B-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

Typical parameters for DNA helices:

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	-30.0

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. At low ionic strength, the A-RNA double helix dominates, but with > 20% salt, A'-RNA is formed. Both are right-handed antiparallel helices. Some key parameters and differences are:

Type	Pitch (Å)	Bases/turn	Axial rise (Å)	Base-pair tilt
A-type	30	11	2.73-2.81	16-19°
A'-type	36	12	3.0	10°

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	1