RNA Secondary RNA Secondary Structure PredictionStructure Prediction

16s rRNA

RNA Secondary Structure

Hairpin loop

Junction (Multiloop)Bulge

Single-Stranded Interior Loop

Stem

Image– Wuchty

Pseudoknot

Dangling end

RNA secondary structureRNA secondary structure

G A

A A G G

A-U U-G C-G A-U G-C

Loop

Stem

wobble pair

canonical pair

Legitimate structurePseudoknots

RNA secondary structure representation

Non-canonical interactions of RNA Non-canonical interactions of RNA secondary-structure elementssecondary-structure elements

Pseudoknot

Kissing hairpins

Hairpin-bulge contact

These patterns are excluded from the prediction schemes as their computation is too intensive.

“Rules for 2D RNA prediction”

• Base Pairs in stems: GOOD

• Additional possible assumptions: e.g., G:C better than A:T

• Bulges, Loops: BAD• Canonical Interactions (base pairs, stems,

bulges, loops): OK• Non canonical interactions (pseudoknots,

kissing hairpins): Forbidden• The more interactions: The better

Predicting RNA secondary Structure

• Allowed base pairing rules (Watson-Crick A:U, G:C, and Wobble pair G:U)

• Sequences may form different structures

• An free energy value is associated with each possible structure

• Predict the structure with the minimal free energy (MFE)

Simplifying Assumptions for Structure Prediction

• RNA folds into one minimum free-energy structure.

• There are no non-canonical interactions.

• The energy of a particular base pair in a double stranded regions is sequence independent– Neighbors have no influence.

Was solved by dynamic programmingZucker and Steigler 1981

Sequence-dependent free-energy (the nearest neighbor model)

U U

C G G C A UG CA UCGAC 3’

U U

C G U A A UG CA UCGAC 3’

Example values:GC GC GC GCAU GC CG UA -2.3 -2.9 -3.4 -2.1

Free energy computationFree energy computation

U UA A G C G C A G C U A A U C G A U A 3’A5’

-0.3

-0.3

-1.1 mismatch of hairpin-2.9 stacking

+3.3 (1 nt bulge) -2.9 stacking

-1.8 stacking

5’ dangling

-0.9 stacking-1.8 stacking

-2.1 stacking

G= -4.6 KCAL/MOL

+5.9 (4 nt loop)

Prediction Programs

• Mfoldhttp://www.bioinfo.rpi.edu/applications/mfold/old/rna/form1.cgi

• Vienna RNA Secondary Structure Predictionhttp://rna.tbi.univie.ac.at/cgi-bin/RNAfold.cgi

Mfold - Suboptimal FoldingMfold - Suboptimal Folding• For any sequence of N nucleotides, the expected

number of structures is greater than 1.8N

• A sequence of 100 nucleotides has ~31025 possible folds. If a computer can calculate 1000 folds/second, it would take 1015 years (age of universe = ~1010 years)!

• Mfold generates suboptimal folds whose free energy fall within a certain range of values. Many of these structures are different in trivial ways. These suboptimal folds can still be useful for designing experiments.

Example:

Output: