RNA secondary structure

1
RNA secondary structure

• RNA is (usually) single-stranded
• The nucleotides want to pair with their
  Watson-Crick complements (AU, GC)
• They may settle for a wobble pair (GU)
• The set of such pairs is the secondary structure
  of the sequence

2
The problem

• Input An RNA sequence R
• Output A predicted secondary structure
• S (ri1, rj1), (ri2, rj2) .. (rin, rjn)

3
Faustian bargain for RNA secondary structure
prediction

• Assume an RNA strand folds to lowest energy
• Three types of base pair interactions (G-C, A-U,
  G-U)
• All structures are nested
• Energies are strictly additive

4
Lowest energy assumption

• There are exponentially many configurations for a
  nucleic acid (or protein) sequence
• A sequence assumes its stable configuration
  quickly (seconds)
• How does it find global minimum quickly?
  (Levenstein paradox)
• Alternative it finds local minimum

5
Base pair interactions

• Atomic interactions too complex to calculate
• Base pair interactions are reasonable compromise

6
Nested structures

• More than 95 of structures are nested, but ..
• Those that arent may well be significant
• Non-nested structures include pseudoknots and
  kissing loops

7
Pseudoknot
8
Kissing loops
9
Loops

• Nested structures are loops
• The size of a loop is the number of unpaired
  nucleotides it contains
• The arity of a loop is the number of interior
  pairs it contains
• Every loop has exactly one closing pair

10
Hairpin loop
Arity 0 (always), size 4 (variable)
11
Hairpin loop -- size
unpaired nucleotides
12
Hairpin loop - closing pair
Closing pair
13
Bulge
Arity 1 (always), size 1 (variable
14
Interior loop
Arity 1 (always), size 2
15
Multiloop
Arity 2 (variable), size 3 (variable)
16
Composite RNA secondary structure
17
Nearest neighbor formula

• Energy is a function of closing base pair and its
  nearest neighbors
• Non-symmetric ( E(XYZW) ¹ E(WZYX) )
• Energies of nested loops are additive
• E(R) E(ri1, ri11, rj-11), (ri12, rj-12) ..
  (ri1n, rj-1n)

18
Loop recurrence relation
E(Si1,j) E(Si,j1) minE(Si,k) E(Si,k), i lt k
lt j E(Li,j)
E(Si,j)
where ...
19
Li,j recurrence relation
Li,j is a hairpin Li,j is a stacked pair Li,j is
an i-bulge Li,j is a j-bulge Li,j is an interior
loop
E(Li,j)
min
20
Hairpin loop
Nearest neighbors