CPSC 545/445 (Autumn 2003) - Class 14: RNA structure
Module 5, Part 1

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5.1 Introduction

recap (from Module 1):

RNAs have many functions in the cell
- intermediate stages of protein synthesis (mRNA, tRNA)
- catalytic role (ribozymes)
- structural/catalytic role (rRNA)

many of these functions crucially depend on the structure


RNA World hypothesis:
RNA existed before DNA and proteins in a world where
organisms had RNA genomes that were replicated 
by RNA catalysts and where catalytic RNAs played
many of the fundamental roles played now by proteins 


levels of RNA structure:
- primary structur = base sequence (A,C,G,U)
- secondary structure = base pairing within an strand
	(and between strands)
- teriary structure = 3-dimensional structure of molecule

secondary structure is one of the most important factors
determining 3d-structure, and hence function

here: focus on secondary structure

experimentally determining RNA structure (even just secondary
structure) is very time-consuming and labour-intensive

=> large incentive to use computational techniques instead


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5.2 RNA secondary structure

RNA strands form secondary structure by means of base-pairing
(mainly Watson-Crick pairing AU, GC,
but others are possible, e.g., GU).

terminology:
  AU, GC = Watson Crick (WC) pairs
  GU = wobble pair
  WC or wobble = canonical pairs
  all others = non-canonical pairs


Example: [slide]


definition:

the secondary structure S of an RNA strand s of length n
is defined as the set of paired base positions in s
such that each base in s is paired with at most one other base,
i.e., forall (i,j) \in S and (i',j') \in S: i=i' iff j=j'


Example: (structure from slide)

(1,49), (2,48), (3,47), (4,46), (5,45), 
(7,18), (8,17), ...
(55,69), (56,68), ...



secondary structure elements:
- stems = helices, composed of neighbouring base pairs = stacked pairs
	(stems form regular, A-form double helix)
- loops:
	- bulges
	- internal loops
	- hairpin loops
	- multibranched loops (multi-loops)
	- pseudoknots

stems, i.e., stacked base pairs, stabilise the structure
by reducing the free energy of the molecule
(low free energy = stable, see also below),
while loops have a destabilising effect (increase free energy).


Example for pseudo-knot: 
(see RNAse P slide)


Formally, an RNA structure is pseudoknotted iff
exist (i,j) \in S, (i',j') \in S: i<i'<j<j'.

An RNA structure that is not pseudoknotted, is called
pseudoknot-free. 

Pseudoknots occur in many biological RNA sequences 
(e.g., rRNA, RNAse P - a well-known ribozyme),
but are often not considered in computational 
RNA secondary structure prediction.

In many ways, pseudoknot-free structures are easier to handle 
algorithmically. (This will be made more precise later.)

 
Pseudoknot-free structures can be conveniently expressed
in the dot-bracket notation:

"." = unpaired base
"(" = paired base (other base involved in the pair is further 3')
")" = paired base (other base involved in the pair is further 5')

Any pseudoknot-free secondary structure S of a strand s of length k
can be expressed by string of length k over {".","(",")"}.


Example: (structure from slide)

GCCGCACGCGAGACCGCG ----- AAGCGGCAUUA ----
(((((.((((....)))) ----- ..))))).... ----



Note: It is easy to specify a context-free grammar for
RNA structures in the dot-bracket notation.


Exercise: Why can pseudoknotted structures not be represented in 
	dot-bracket notation? Is there a context-free grammar
	for pseudoknotted structure?


Alternative graphical representation: 
arcs between paired bases in linear sequence notation


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5.3 comparative sequence analysis approach for predicting secondary structure

homologous RNAs often have common second structure
but very little sequence similarity, since evolutionary
pressure is to preserve function which often depends 
than structure than on sequence (for functional RNAs)

-> compensatory mutations in paired base positions

this can be exploited for predicting RNA secondary structure


basic idea: 
- measure covariation between aligned sequence position to infer
  base pairs in RNA secondary structure


comparative sequence analysis approach:

given: k RNA homologous sequences s_1, ..., s_k

1. compute multiple sequence alignment of s_1, ..., s_k
   Repeat:
2.	guess structure S from current alignment of s_1, ..., s_k
3. 	realign sequences s_1, ..., s_k based on current structure S
   Until no change in structure occured (during the last iteration)


Note: 
- for Step 1 to work reasonably well, s1 ... sk must be sufficiently similar
- for Step 2 to work reasonably well, s1 ... sk must be sufficiently different


How to do Step 2?

quantify covariation (degree of compensatory mutations in a position)
using the concept of mutual information content:

mutual information between columns i and j in alignment:

	M_ij = \sum_{x,y in {A,C,G,U}} f_ij(x,y) log_2 (f_ij(x,y) / (fi(x)*fj(y)))

where	f_i(x) = frequency of base x in column i
	f_j(y) = frequency of base y in column j
	f_ij(x,y) = joint frequency of x,y in columns i,j


Example: 

AGCAAUUGCU
AUCAAUUGAU
AACAAUUGUU
 *      * 

structure: (((....)))

f_2(G)=1/3
f_9(G)=0
f_{2,9}(G,C)=1/3
f_{2,9}(C,G)=0

M_{2,9} = 1/3 * log_2 ((1/3) / (1/3*1/3)) * 3 = 1.585
M_{1,10} = 0	(these positions are perfectly conserved)

Note: M_ij is always >= 0 and <= 2

Paired positions have high mutual information content.


Exercise: give an example for a set of aligned RNA sequences
	for which M_{2,6} = 2


[slide: Figure 10.6]


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Resources:

Durbin et al., Ch.10


Lecture notes from CSE 527, Winter 2000 (Martin Tompa) at U Washington,
http://www.cs.washington.edu/education/courses/527/00wi/lectures/lect16.pdf

http://www.bioinfo.rpi.edu/~zukerm/seqanal-old/node1.html#SECTION00010000000000000000



Further Reading:

http://www.bioinfo.rpi.edu/~zukerm/rna/energy/
http://www.bioinfo.rpi.edu/~zukerm/rna/energy/node2.html
-> turner free energy model


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