# Nucleic acid structure

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## 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 Nm (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 28.2 111 2.56 32.7 11.0 2.7 2.8 13.5
B 33.8 101 3.38 36.0 5.7 11.7 7.5 8.5
C 31.0 9.331 3.32 38.6 4.8 10.5 7.9 7.5
B' 32.9 101 3.29 36
C' 29.5 91 3.28 40
C 29.1 91 3.23 40
D 24.3 81 3.04 45 1.3 8.9 6.7 5.8
E 24.35 7.51 3.25 48
S 43.4 65 3.63 -30.0
Z 45 65 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

$\Delta G^0 = -RT log K = \Delta H^0 - T\cdot\Delta S^0$ 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 1