RNA Secondary Structure Prediction

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RNA Secondary Structure Prediction

• Lecture 11 June 13, 2006
• Algorithms of Molecular Biology

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Introduction to RNA Sequence/Structure Analysis

• RNAs have many structural and functional uses
• Translation
• Transcription
• RNA splicing
• RNA processing and editing
• cellular localization
• catalysis

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RNA functions

• RNA functions as
• mRNA
• rRNA
• tRNA
• In nuclear export
• Part of spliceosome (snRNA)
• Regulatory molecules (RNAi)
• Enzymes
• Viral genomes
• Retrotransposons
• Medicine

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Biological Functions of Nucleic Acids

• tRNA (transfer RNA, adaptor in translation)
• rRNA (ribosomal RNA, component of ribosome)
• snRNA (small nuclear RNA, component of
  splicesome)
• snoRNA (small nucleolar RNA, takes part in
  processing of rRNA)
• RNase P (ribozyme, processes tRNA)
• SRP RNA (RNA component of signal recognition
  particle)
• ..

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RNA Sequence Analysis

• RNA sequence analysis different from DNA sequence
  analysis
• RNA structures fold and base pair to form
  secondary structures
• not necessarily the sequence but structure
  conservation is most important with RNA

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More Secondary Structures
Secondary Structures of Nucleic Acids
Pseudoknots

• DNA is primarily in duplex form.
• RNA is normally single stranded which can have a
  diverse form of secondary structures other than
  duplex.

Source Cornelis W. A. Pleij in Gesteland, R. F.
and Atkins, J. F. (1993) THE RNA WORLD. Cold
Spring Harbor Laboratory Press.
rRNA Secondary Structure Based on Phylogenetic
Data
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3D Structures of RNACatalytic RNA

• Some structural rules
• Base pairing is stabilizing
• Unpaired sections (loops) destabilize
• 3D conformation with interactions makes up for
  this

Tertiary Structure Of Self-splicing RNA
Secondary Structure Of Self-splicing RNA
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RNA secondary structure

• E. coli Rnase P RNA secondary structure

Image source www.mbio.ncsu.edu/JWB/MB409/lecture/
lecture05/lecture05.htm
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tRNA structure
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RNA Variations

• Variations in RNA sequence maintain base-pairing
  patterns for secondary structures
• when a nucleotide in one base changes, the base
  it pairs to must also change to maintain the same
  structure
• Such variation is referred to as covariation.

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Covariance

• secondary structure prediction in RNA takes into
  account conserved patterns of base-pairing
• Positions of covariance are conserved matches,
  since they maintain the secondary structure
• computationally challenging

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Features of RNA

• RNA polymer composed of a combination of four
  nucleotides
• adenine (A)
• cytosine (C)
• guanine (G)
• uracil (U)

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Features of RNA

• G-C and A-U form complementary hydrogen bonded
  base pairs (canonical Watson-Crick)
• G-C base pairs being more stable (3 hydrogen
  bonds) A-U base pairs less stable (2 bonds)
• non-canonical pairs can occur in RNA -- most
  common is G-U

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Features of RNA

• RNA typically produced as a single stranded
  molecule (unlike DNA)
• Strand folds upon itself to form base pairs
• secondary structure of the RNA

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Features of RNA

• intermediary between a linear molecule and a
  three-dimensional structure
• Secondary structure mainly composed of
  double-stranded RNA regions formed by folding the
  single-stranded RNA molecule back on itself

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Stem Loops (Hairpins)

• Loops generally at least 4 bases long

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Bulge Loops

• occur when bases on one side of the structure
  cannot form base pairs

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Interior Loops

• occur when bases on both sides of the structure
  cannot form base pairs

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Junctions (Multiloops)

• two or more double-stranded regions converge to
  form a closed structure

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Tertiary Interactions

• tertiary interactions can be present as well
• located using covariance analysis

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Kissing Hairpins

• unpaired bases of two separate hairpin loops base
  pair with one another

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Pseudoknots
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Hairpin-Bulge Interactions
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RNA structure prediction methods

• Dot Plot Analysis
• Base-Pair Maximization
• Free Energy Methods
• Covariance Models

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How RNA Prediction Methods Were Developed

• Mount p. 334
• Since Tinoco et al. measured energy associated
  with regions of ss a few energy based algorithms
  were developed
• Nussinov and Jacobson (1980), Zuker and Stiegler
  (1981), Trifonov and Bolshoi (1983) .

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Main approaches to RNA secondary structure
prediction

• Energy minimization
• dynamic programming approach
• does not require prior sequence alignment
• require estimation of energy terms contributing
  to secondary structure
• Comparative sequence analysis
• Using sequence alignment to find conserved
  residues and covariant base pairs.
• most trusted

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Circular Representation

• base pairs of a secondary structure represented
  by a circle
• arc drawn for each base pairing in the structure
• If any arcs cross, a pseudoknot is present

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Circular Representation

• Image source http//www.finchcms.edu/cms/biochem/
  Walters/rna_folding.html

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Circular Representation
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Base-Pair Maximization

• Find structure with the most base pairs
• Efficient dynamic programming approach to this
  problem introduced by Ruth Nussinov (Tel-Aviv,
  1970s).
• Tutorial in the classroom let us try to
  reconstruct Nussinovs algorithm
•  

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Nussinov Algorithm

• Four ways to get the best structure between
  position i and j from the best structures of the
  smaller subsequences
• 1)      Add i,j pair onto best structure found
  for subsequence i1, j-1
• 2)      add unpaired position i onto best
  structure for subsequence i1, j
• 3)      add unpaired position j onto best
  structure for subsequence i, j-1
• 4)      combine two optimal structures i,k and
  k1, j

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Nussinov Algorithm
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Nussinov Algorithm

• compares a sequence against itself in a dynamic
  programming matrix
• Four rules for scoring the structure at a
  particular point
• Since structure folds upon itself, only necessary
  to calculate half the matrix

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Nussinov Algorithm

• Initialization score for matches along main
  diagonal and diagonal just below it are set to
  zero
• Formally, the scoring matrix, M, is initialized
   
• Mii 0 for i 1 to L (L is sequence
  length)
• Mii-1 0 for i 2 to L

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Nussinov Algorithm

• Using the sequence GGGAAAUCC, the matrix now
  looks like the following, such that sequences of
  length 1 will score 0

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Nussinov Algorithm

• Matrix Fill
•  
• Mij max of the following
• Mi1j (ith residue is hanging off by itself)
• Mij-1 (jth residue is hanging off by itself)
• Mi1j-1 S(xi, xj) (ith and jth residue are
  paired if xi complement of xj, then S(xi, xj)
  1 otherwise it is 0.)
• Mij MAXiltkltj (Mik Mk1j) (merging
  two substructures)

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Nussinov Algorithm

• The final filled matrix is as follows

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Nussinov Algorithm

• Traceback (P 271, Durbin et al) leads to the
  following structure

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SCFG Version

• Nussinov algorithm can be converted to a
  stochastic context-free grammar
•  
• S ? aS cS gS uS
• S ? Sa Sc Sg Su
• S ? aSu cSg uSa gSc
• S ? SS

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Nussinov Algorithm

• Web Interface
• http//ludwig-sun2.unil.ch/bsondere/nussinov/

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Nussinov Results
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Evaluation of Maximizing Basepairs

• Simplistic approach
• Does not give accurate structure predictions
• nearest neighbor interactions
• stacking interactions
• loop length preferences

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Free Energy Minimization RNA Structure
Prediction

• All possible choices of complementary sequences
  are considered
• Set(s) providing the most energetically stable
  molecules are chosen
• When RNA is folded, some bases are paired with
  other while others remain free, forming loops
  in the molecule.
• Speaking qualitatively, bases that are bonded
  tend to stabilize the RNA (i.e., have negative
  free energy), whereas unpaired bases form
  destabilizing loops (positive free energy).
• Through thermodynamics experiments, it has been
  possible to estimate the free energy of some of
  the common types of loops that arise.
• Because the secondary structure is related to the
  function of the RNA, we would like to be able to
  predict the secondary structure.
• Given an RNA sequence, the RNA Folding Problem is
  to predict the secondary structure that minimizes
  the total free energy of the folded RNA molecule.

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Prediction of Minimum-Energy RNA Structure is
Limited

• In predicting minimum energy RNA secondary
  structure, several simplifying assumptions are
  made.
• The most likely structure is identical to the
  energetically preferable structure
• Nearest-neighbor energy calculations give
  reliable estimates of an experimentally
  achievable energy measurements
• Usually we can neglect pseudoknots

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Assumptions in secondary Structure Prediction

• most likely structure similar to energetically
  most stable structure
• Energy associated with any position is only
  influenced by local sequence and structure
• Structure formed does not produce pseudoknots

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Inferring Structure By Comparative Sequence
Analysis

• most reliable computational method for
  determining RNA secondary structure
• consider the example from Durbin, et al., p 266
• See an additional lecture of David Mathews

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Predicting Structure From a Single Sequence

• RNA molecule only 200 bases long has 1050
  possible secondary structures
• Find self-complementary regions in an RNA
  sequence using a dot-plot of the sequence against
  its complement
• repeat regions can potentially base pair to form
  secondary structures
• advanced dot-plot techniques incorporate free
  energy measures

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Dot Plot

• Image Source http//www.finchcms.edu/cms/biochem/
  Walters/rna_folding.html

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Energy Minimization Methods

• RNA folding is determined by biophysical
  properties
• Energy minimization algorithm predicts the
  correct secondary structure by minimizing the
  free energy (?G)
• ?G calculated as sum of individual contributions
  of
• loops
• base pairs
• secondary structure elements
• Energies of stems calculated as stacking
  contributions between neighboring base pairs

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Energy Minimization Methods

• Free-energy values (kcal/mole at 37oC ) are as
  follows

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Energy Minimization Methods

• Free-energy values (kcal/mole at 37oC ) are as
  follows

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Energy Minimization Methods

• Given the energy tables, and a folding, the free
  energy can be calculated for a structure

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Calculating Best Structure

• sequence is compared against itself using a
  dynamic programming approach
• similar to the maximum base-paired structure
• instead of using a scoring scheme, the score is
  based upon the free energy values
• Gaps represent some form of a loop
• The most widely used software that incorporates
  this minimum free energy algorithm is MFOLD.

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Free Energy Minimization RNA Structure
Prediction

• http//www.bioinfo.rpi.edu/zukerm/Bio-5495/RNAfol
  d-html/

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Calculating Best Structure

• most widely used software incorporating minimum
  free energy algorithm is MFOLD
• http//www.bioinfo.rpi.edu/applications/mfold/
• http//www.bioinfo.rpi.edu/applications/mfold/old/
  rna/

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Example Sequence

• GCTTACGACCATATCACGTTGAATGCACGC
• CATCCCGTCCGATCTGGCAAGTTAAGCAAC
• GTTGAGTCCAGTTAGTACTTGGATCGGAGA
• CGGCCTGGGAATCCTGGATGTTGTAAGCT

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MFOLD Energy Dot Plot
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Optimal Structure
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Suboptimal Folds

• The correct structure is not necessarily
  structure with optimal free energy
• within a certain threshold of the calculated
  minimum energy
• MFOLD updated to report suboptimal folds

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Comparison of Methods
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Inferring Structure By Comparative Sequence
Analysis

• first step is to calculate a multiple sequence
  alignment
• Requires sequences be similar enough so that they
  can be initially aligned
• Sequences should be dissimilar enough for
  covarying substitutions to be detected
•  

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Mutual Information

• fxi frequency of a base in column i
• fxixj joint (pairwise) frequency of a base
  pair between columns i and j
• Information ranges from 0 and 2 bits
• If i and j are uncorrelated, mutual information
  is 0

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Mutual Information Plot
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Mutual Information Plot
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Frameshifting

• Virology. 2005 Feb 20332(2)498-510
• Programmed ribosomal frameshifting in decoding
  the SARS-CoV genome.
• Baranov PV, Henderson CM, Anderson CB, Gesteland
  RF, Atkins JF, Howard MT.Department of Human
  Genetics, University of Utah, 15 N 2030 E, Room
  7410, Salt Lake City, UT 84112-5330,
  USA.Programmed ribosomal frameshifting is an
  essential mechanism used for the expression of
  orf1b in coronaviruses. Comparative analysis of
  the frameshift region reveals a universal shift
  site U_UUA_AAC, followed by a predicted
  downstream RNA structure in the form of either a
  pseudoknot or kissing stem loops. Frameshifting
  in SARS-CoV has been characterized in cultured
  mammalian cells using a dual luciferase reporter
  system and mass spectrometry. Mutagenic analysis
  of the SARS-CoV shift site and mass spectrometry
  of an affinity tagged frameshift product
  confirmed tandem tRNA slippage on the sequence
  U_UUA_AAC. Analysis of the downstream pseudoknot
  stimulator of frameshifting in SARS-CoV shows
  that a proposed RNA secondary structure in loop
  II and two unpaired nucleotides at the stem
  I-stem II junction in SARS-CoV are important for
  frameshift stimulation. These results demonstrate
  key sequences required for efficient
  frameshifting, and the utility of mass
  spectrometry to study ribosomal frameshifting.

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Frameshifting

• RNA-struct-frameshift.pdf
• frameshifts.pdf
• hepatitisC-frameshift.pdf

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Covariance Models

• 7 approaches to locate covarying sites offered in
  Mount, p225
• key to covariance is mutual information content
• mutual information content can be plotted on a
  motif logo

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Mutual Information

• Image source http//www.cbs.dtu.dk/gorodkin/appl
  /slogo.html

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Covariance Models

• A formal covariance model, COVE, devised by Eddy
  and Durbin
• Provides very accurate results
• extremely slow and unsuitable for searching large
  genomes

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SCFGs

• Stochastic Context Free Grammars (SCFGs) have
  also been used to model RNA secondary structure
• Examples
• tRNAScan-SE
• program created to find snoRNAs
• Grammars are created by using a training set of
  data, and then the grammars are applied to
  potential sequences to see if they fit into the
  language

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SCFGs

• SCFGs allow the detection of sequences belonging
  to a family
• tRNAs
• group I introns
• snoRNAs
• snRNAs

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SCFGs

• base-paired columns modeled by pairwise emitting
  non terminals
• aWu aWa aWc aWg ...
• single-stranded columns modeled by leftwise
  emitting nonterminals (when possible)
• aW cW gW uW ..., when possible

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SCFGs

• Any RNA structure can be reduced to a SCFG (see
  Durbin, et al., p 278-279)

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Transformational Grammars

• First described by linguist Noam Chomsky in the
  1950s.
• (Yes, the same Noam Chomsky who has expressed
  various dissident political views throughout the
  years!)

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Transformational Grammars

• Very important in computer science, most notably
  in compiler design
• Covered in detail in compiler and automaton
  classes

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Transformational Grammars

• Idea take a set of outputs (sentence, RNA
  structure) and determine if it can be produced
  using a set of rules
•  
• consist of a set of symbols and production rules
• The symbols can terminal (emitting) symbols or
  non-terminal symbols

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Grammar for Palindromes

• Consider palindromic DNA sequences
• Five possible terminal symbols A, C, G, T, ?)
  (? represents the blank terminal symbol)

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Grammar for Palindromes

• Production Rules, where S and W are non-terminal
  symbols
•  
• S?W
• W? aWa cWc gWg tWt
• W? a c g t ?

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Derivation of Sequences

• Using these production rules, a derivation of the
  palindromic sequence acttgttca follows
• S ? W ? aWa ? acWca?actWtca ? acttWttca ?
  acttgttca

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Parse Trees

• A context-free grammar can be aligned to a
  sequence using a parse tree
• Root of the tree is the non-terminal start
  symbol, S
• Leaves are terminal symbols
• Internal nodes are the nonterminals
• Leaves can be parsed from left to right to view
  the results of production

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Parse Tree
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RNA Structure SCFG

• S?W
• W? WW (bifurcation)
• W? aWu cWg gWc uWa (stems)
• W? gWu uWg
• W? aW cW gW uW (bulges)
• W? Wa Wc Wg Wu (bulges)
• W? a c g t ?

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Example of SCFG

• structure for the RNA structure for the
  sequence produced by MFOLD, can be constructed
  (5 to 3)
• GCUUACGACCAUAUCACGUUGAAUGCACGCCAUCCCGUCCGAUCUGGCAA
  GUUAAGCAACGUUGAGUCCAGUUAGUACUUGGAUCGGAGACGGCCUGGGA
  AUCCUGGAUGUUGUAAGCU

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Example Construction

• S?
• W?
• Wu?
• gWcu?
• gcWgcu?
• gcuWagcu?
• gcuuWaagcu?
• gcuuaWuaagcu?
• gcuuacWguaagcu?
• gcuuacgWuguaagcu?
• gcuuacgaWuuguaagcu?
• gcuuacgacWguuguaagcu?
• gcuuacgaccWguuguaagcu?
• gcuuacgaccaWguuguaagcu?....

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Other Programs

• RNA Movies
• http//bibiserv.techfak.uni-bielefeld.de/rnamovies
  /
• (Visualization of RNA secondary structure)
• RNA LOGOS
• http//www.cbs.dtu.dk/gorodkin/appl/slogo.html