RNA secondary structure prediction

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RNA secondary structure prediction

• Introduction
• Examples of RNA molecules
• Secondary structure elements
• Pseudo-knots
• RNA folding
• Nussinov algorithm
• Energy minimization
• Covariance analysis

• RNA secondary structure motifs
• Examples, biological function
• RNA secondary structure patterns

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Basics about RNA (for computer scientists)

• RNA initially synthesized as co-linear copy of
  DNA
• U replaces T (however, U represented as T in
  nucleotide database entries)
• RNA may undergo splicing and other
  post-transcriptional modifications
• Two major RNA classes in cellular organisms
• messenger RNA (mRNA) templates for protein
  synthesis
• structural and catalytic RNAs
• The genome of many viruses (e.g. HIV) consists of
  RNA
• RNA is usually single-stranded (exception a few
  viral genomes)
• RNA folds back onto itself to form short
  base-paired regions
• As in DNA, base-paired regions form anti-parallel
  helices
• Same base-pairing rules as for DNA but U-G pairs
  also permitted

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Examples of structural and/or catalytic RNAs
ribosomal RNA (rRNA) transfer RNA (tRNA) small
nuclear RNA (snRNA. e.g. U1) small nucleolar RNAs
(snoRNA) small cytoplasmic RNA (scRNA, e.g
7SL-RNA) microRNAs (miRNA)
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RNA secondary structure elements Terminology
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Purpose of RNA folding algorithm

• Prediction of the native secondary structure of
  an RNA molecule
• Formally, the secondary structure of an RNA
  consists of all pairs of bases that interact with
  each other, usually through standard Watson-Crick
  base-pairs.
• Recognition of RNA functional motifs
• RNA molecules may contain regulatory motifs that
  interact with RNA-binding proteins
• Such motif may have a conserved secondary
  structure in addition to conserved primary
  structure elements.

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Pseudo-knots
Cause problems to ordinary RNA folding algorithms.
Pseudoknots imply an arrangement of pairs of
interacting base pairs of the type a b a
b Such structure require intersecting lines in
the following type of representation
U U C C G A A G C U C A A C G G G A A A A U G A G
C U
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RNA secondary structure notation

• RNA secondary structures can be specified by a
  sequences of the three letters -,gt,lt.
• Base pairs can be reconstructed as follows
• process sequence from left to right
• if base marked - leave unpaired
• if base marked gt wait
• if base marked lt connect to closest unpaired
  base marked gt on left side

AAGACUUCGGAUCUGGCGACACCC --gtgtgt----lt-ltlt-gtgt-gt---ltltlt
Note works only if no pseudoknots occur.
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Nussinov algorithm Principle
Objective To find the secondary structure with
the maximal number of base pairs under the
pseudo-knot exclusion constraint. Principle Recur
sive procedure (dynamic programming
algorithm). Scoring function sum of base-pair
scores, no penalties for loops Optimal score
computed from the optimal scores of
subsequences. Filling-stage. Scores for
subsequences are recursively computed from and
recorded in a quadratic table. Trace-back Reconst
ruction of filling steps indicates optimal
structure Time-complexity O(N3) Limitations No
pseudo-knots, No constraints on loop
lengths No penalties for bulge loops No
scoring terms for base-pair stacking
inter-actions (see later)
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Nussinov algorithm extension operations
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Nussinov algorithm fill-stage
Scoring system d(i,j) 1 for all RNA
Watson-Crick base-pairs including G-U else d(i,j)
0.
Blue addition of unpaired base 3 or 7
Green addition of paired bases 1,7
Pink joining of substructures 1..4 and 5..8
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Nussinov algorithm trace-back
current record stack 1,9 1,9
1,8 1,8 1,4 5,8 1,4 1,4
2,3 5,8 2,3 2,3 3,2 5,8 3,2
5,8 5,8 5,8 6,7 6,7 6,7 7,6 7,6

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RNA folding by energy minimization
Note a bulge loop does not alter stacking energy!
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Principle of the Zuker algorithm (RNAFOLD)

• Energy minimization using a richer scoring
  system
• Stacking energies scores for overlapping
  dinucleotide pairs
• Bulge loop scores dependent on length
• Hairpin loop scores dependent on length and
  closing pair
• Internal loop scores dependent on length and
  closing pair
• Same principle as Nussinov algorithm but
• Two minimal energy values are stored for each
  subsequence
• W(i,j) best structure on i,j
• V(i,j) best structure on i,j closed by paired
  i,j.
• Computational complexity essentially O(N3)
• (if constraints on maximal loop sizes are applied)

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Energy-parameters used by RNAFOLD
Note Some energy terms (e.g. for the terminal
mismatch of a hairpin) are Missing.
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Prediction of RNA structure by covariance models
Motivation Energy minimization-based approaches
often predict large numbers of alternative RNA
secondary structures with very similar free
energy. A Multiple alignment of related RNAs
potentially reveals base pair interactions
Interacting positions in multiple alignment
positions expected to show co-variation
compatible with standard RNA base-pairing
rules Limitation requires within column
variation. No information is obtained for
completely conserved position.
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Prediction of RNA structure by covariance models
Covariance measure used Mutual information
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Covariance analysis tRNA-Phe
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RNA motifs, signatures, domains, and families

• Terminology
• Motif short RNA regions with partly conserved
  primary and secondary structure, usually with a
  defined function.
• Signature short RNA regions with partly
  conserved primary and secondary structure useful
  for identifying members of an RNA family.
• Domain A larger RNA region with conserved
  secondary structure, usually considered an
  independent folding unit
• Family A family of homologous and/or
  structurally related RNA molecules, e.g. tRNAs.
  
• RNA sequence-structural motifs play a role in
  various biological processes
• Translational control, e.g. iron-response element
  (IRE)
• RNA degradation
• RNA localization (zip-code motifs)

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RNABOB and example of an RNA pattern recognition
program
Characteristics Supports qualitative patterns
(true/false no scores or probabilities) Based
on simple but powerful pattern syntax Fast search
engine Supports non-Watson-Crick type base
interactions Supports pseudo-knots ! Allows for
errors (mismatches) in the pattern.
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RNABOB pattern syntax
S1 h1 s2 h2 s3 h2' h1' h1 00 NNNNNNNNNN h2 00
NNNN S1 0 NN s2 0 R s3 0 ANYA
Example

• The first line indicates the ordering of pattern
  elements
• s1, s2, s3 consist of contiguous unpaired
  sequences
• h1, h1 represent complementary sequence segments
  forming a double helix.
• Lines 2 to 6 contain the descriptions of each
  element
• NNNNNNNNNN means that any base is permitted in
  this structure, the only constraint is that they
  have to respect base-pairing rules2020
• Numbers indicate how many mismatches are allowed
  per element.
• IUPAC codes are used to specify ambiguous
  positions Y CT