Nucleic acid structure

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DNA

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

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \Delta G^0 = -RT log K = \Delta H^0 - T\cdot\Delta S^0} where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle K=\frac{\rm [duplex]}{\rm [single-strand]^2}}

At the melting temperature, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle T_m} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 2[{\rm duplex}] = [{\rm single-strand}]} and from conservation of total RNA, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 2[{\rm duplex}] + [{\rm single-strand}] = [{\rm RNA}]_{total}} . From this, we can derive that:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \Delta H^0} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \Delta S^0} from which you can get Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \Delta G^0} . The Freier-Turner rules shows the incremental Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \Delta G^0} 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