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Jianlin Cheng, PhD
Associate Professor Computer Science Department University of Missouri, Columbia
RNA Structure Prediction
2013 Based on Gill Bejerano’s CS173 at Stanford and Cheng’s lecture
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Outline • Introduction to non coding RNAs • RNA secondary structure prediction • RNA tertiary structure prediction
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TTATATTGAATTTTCAAAAATTCTTACTTTTTTTTTGGATGGACGCAAAGAAGTTTAATAATCATATTACATGGCATTACCACCATATACATATCCATATCTAATCTTACTTATATGTTGTGGAAATGTAAAGAGCCCCATTATCTTAGCCTAAAAAAACCTTCTCTTTGGAACTTTCAGTAATACGCTTAACTGCTCATTGCTATATTGAAGTACGGATTAGAAGCCGCCGAGCGGGCGACAGCCCTCCGACGGAAGACTCTCCTCCGTGCGTCCTCGTCTTCACCGGTCGCGTTCCTGAAACGCAGATGTGCCTCGCGCCGCACTGCTCCGAACAATAAAGATTCTACAATACTAGCTTTTATGGTTATGAAGAGGAAAAATTGGCAGTAACCTGGCCCCACAAACCTTCAAATTAACGAATCAAATTAACAACCATAGGATGATAATGCGATTAGTTTTTTAGCCTTATTTCTGGGGTAATTAATCAGCGAAGCGATGATTTTTGATCTATTAACAGATATATAAATGGAAAAGCTGCATAACCACTTTAACTAATACTTTCAACATTTTCAGTTTGTATTACTTCTTATTCAAATGTCATAAAAGTATCAACAAAAAATTGTTAATATACCTCTATACTTTAACGTCAAGGAGAAAAAACTATAATGACTAAATCTCATTCAGAAGAAGTGATTGTACCTGAGTTCAATTCTAGCGCAAAGGAATTACCAAGACCATTGGCCGAAAAGTGCCCGAGCATAATTAAGAAATTTATAAGCGCTTATGATGCTAAACCGGATTTTGTTGCTAGATCGCCTGGTAGAGTCAATCTAATTGGTGAACATATTGATTATTGTGACTTCTCGGTTTTACCTTTAGCTATTGATTTTGATATGCTTTGCGCCGTCAAAGTTTTGAACGATGAGATTTCAAGTCTTAAAGCTATATCAGAGGGCTAAGCATGTGTATTCTGAATCTTTAAGAGTCTTGAAGGCTGTGAAATTAATGACTACAGCGAGCTTTACTGCCGACGAAGACTTTTTCAAGCAATTTGGTGCCTTGATGAACGAGTCTCAAGCTTCTTGCGATAAACTTTACGAATGTTCTTGTCCAGAGATTGACAAAATTTGTTCCATTGCTTTGTCAAATGGATCATATGGTTCCCGTTTGACCGGAGCTGGCTGGGGTGGTTGTACTGTTCACTTGGTTCCAGGGGGCCCAAATGGCAACATAGAAAAGGTAAAAGAAGCCCTTGCCAATGAGTTCTACAAGGTCAAGTACCCTAAGATCACTGATGCTGAGCTAGAAAATGCTATCATCGTCTCTAAACCAGCATTGGGCAGCTGTCTATATGAATTAGTCAAGTATACTTCTTTTTTTTACTTTGTTCAGAACAACTTCTCATTTTTTTCTACTCATAACTTTAGCATCACAAAATACGCAATAATAACGAGTAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTTGGATACCTATTCTTGACATGATATGACTACCATTTTGTTATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAGTTGCGAAGTTCTTGGCAAGTTGCCAACTGACGAGATGCAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTTGGATACCTATTCTTGACATGATATGACTACCATTTTGTTATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAGTCATTTGCGAAGTTCTTGGCAAGTTGCCAACTGACGAGATGCAGTTTCCTACGCATAATAAGAATAGGAGGGAATATCAAGCCAGACAATCTATCATTACATTTAAGCGGCTCTTCAAAAAGATTGAACTCTCGCCAACTTATGGAATCTTCCAATGAGACCTTTGCGCCAAATAATGTGGATTTGGAAAAAGAGTATAAGTCATCTCAGAGTAATATAACTACCGAAGTTTATGAGGCATCGAGCTTTGAAGAAAAAGTAAGCTCAGAAAAACCTCAATACAGCTCATTCTGGAAGAAAATCTATTATGAATATGTGGTCGTTGACAAATCAATCTTGGGTGTTTCTATTCTGGATTCATTTATGTACAACCAGGACTTGAAGCCCGTCGAAAAAGAAAGGCGGGTTTGGTCCTGGTACAATTATTGTTACTTCTGGCTTGCTGAATGTTTCAATATCAACACTTGGCAAATTGCAGCTACAGGTCTACAACTGGGTCTAAATTGGTGGCAGTGTTGGATAACAATTTGGATTGGGTACGGTTTCGTTGGTGCTTTTGTTGTTTTGGCCTCTAGAGTTGGATCTGCTTATCATTTGTCATTCCCTATATCATCTAGAGCATCATTCGGTATTTTCTTCTCTTTATGGCCCGTTATTAACAGAGTCGTCATGGCCATCGTTTGGTATAGTGTCCAAGCTTATATTGCGGCAACTCCCGTATCATTAATGCTGAAATCTATCTTTGGAAAAGATTTACAATGATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAGTCATTTGCGAAGTTCTTGGCAAGTTGCCAACTGACGAGATGCAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTTGGATACCTATTCTTGACATGATATGACTACCATTTTGTTATTGTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATAAAG
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“non coding” RNAs (ncRNA)
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Central Dogma of Biology:
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Active forms of “non coding” RNA
reverse transcription
long non-coding RNA
microRNA
rRNA, snRNA, (small nuclear RNA) snoRNA
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What is ncRNA? • Non-coding RNA (ncRNA) is an RNA that functions without being
translated to a protein. • Known roles for ncRNAs:
– RNA catalyzes excision/ligation in introns. – RNA catalyzes the maturation of tRNA. – RNA catalyzes peptide bond formation. – RNA is a required subunit in telomerase. – RNA plays roles in immunity and development (RNAi). – RNA plays a role in dosage compensation. – RNA plays a role in carbon storage. – RNA is a major subunit in the SRP, which is important in protein trafficking. – RNA guides RNA modification.
– RNA can do so many different functions, it is thought in the beginning there was an RNA World, where RNA was both the information carrier and active molecule.
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“non coding” RNAs (ncRNA)
Small structural RNAs (ssRNA)
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AAUUGCGGGAAAGGGGUCAA CAGCCGUUCAGUACCAAGUC UCAGGGGAAACUUUGAGAUG GCCUUGCAAAGGGUAUGGUA AUAAGCUGACGGACAUGGUC CUAACCACGCAGCCAAGUCC UAAGUCAACAGAUCUUCUGU UGAUAUGGAUGCAGUUCA
ssRNA Folds into Secondary and 3D Structures
P 6b
P 6a
P 6
P 4
P 5P 5a
P 5b
P 5 c
120
140
1 6 0
1 8 0
2 0 0
2 2 0
2 4 0
2 6 0
AAU
UGCGGGAAAG
GGGUCA
ACAGCCG UUCAGU
ACCA
AGUCUCAGGGG
AAACUUUGAGAU
GGCCUUGCA A A G G
G U A UGGUA
AUA AGCUGACGGACA
UGGUCC
U
A
A
CCA CGCA
GC
CAAGUCC
UAAGUCAACAGAU C U
UCUGUUGAUAU
GGAUGCA
GU
UC A
Cate, et al. (Cech & Doudna). (1996) Science 273:1678.
Waring & Davies. (1984) Gene 28: 277.
We would like to predict them from sequence.
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For example, tRNA�
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tRNA Activity�
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ssRNA structure rules • Canonical basepairs:
– Watson-Crick basepairs: • G – C • A – U
– Wobble basepair: • G - U
• Stacks: continuous nested basepairs. (energetically favorable)
• Non-basepaired loops: – Hairpin loop – Bulge – Internal loop – Multiloop
• Pseudo-knots
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Ab initio RNA structure prediction: �lots of Dynamic Programming�
• Objective: Maximizing the number of base pairs (Nussinov et al, 1978) �
simple model: δ(i, j) = 1 if allowed fancier model: GC > AU > GU
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Bafna 1
RNA structure �
• Base-pairing defines a secondary structure. The base-pairing is usually non-crossing.�
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S à aSu
S à cSg
S à gSc
S à uSa
S à a
S à c
S à g
S à u
S à SS
1. A CFG
S è aSu
è acSgu
è accSggu
è accuSaggu
è accuSSaggu
è accugScSaggu
è accuggSccSaggu
è accuggaccSaggu
è accuggacccSgaggu
è accuggacccuSagaggu
è accuggacccuuagaggu
2. A derivation of “accuggacccuuagaggu” 3. Corresponding structure
Stochastic context-free grammar�
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Cool algorithmics. Unfortunately…�
– Random DNA (with high GC content) often folds into low-energy structures.�
– We will mention powerful newer methods later on.�
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ssRNA transcription • ssRNAs like tRNAs are usually encoded by short “non coding” genes, that transcribe independently.
• Found in both the UCSC “known genes” track, and as a subtrack of the RepeatMasker track
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“non coding” RNAs (ncRNA)
microRNAs (miRNA/miR)
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MicroRNA (miR)
mRNA
~70nt ~22nt miR match to target mRNA is quite loose.
à a single miR can regulate the expression of hundreds of genes.
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MicroRNA Transcription
mRNA
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MicroRNA Transcription
mRNA
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MicroRNA (miR)
mRNA
~70nt ~22nt miR match to target mRNA is quite loose.
à a single miR can regulate the expression of hundreds of genes.
Computational challenges: Predict miRs. Predict miR targets.
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MicroRNA Therapeutics
mRNA
~70nt ~22nt miR match to target mRNA is quite loose.
à a single miR can regulate the expression of hundreds of genes.
Idea: bolster/inhibit miR production to broadly modulate protein production Hope: “right” the good guys and/or “wrong” the bad guys Challenge: and not vice versa.
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Other Non Coding Transcripts
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lncRNAs (long non coding RNAs)
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Don’t seem to fold into clear structures (or only a sub-region does). Diverse roles only now starting to be understood. à Hard to detect or predict function computationally (currently)
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X chromosome inactivation in mammals
X X X Y
X
Dosage compensation
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Xist – X inactive-specific transcript
Avner and Heard, Nat. Rev. Genetics 2001 2(1):59-67
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Transcripts, transcripts everywhere
Human Genome
Transcribed* (Tx)
Tx from both strands*
* True size of set unknown
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Or are they?
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The million dollar question
Human Genome
Transcribed* (Tx)
Tx from both strands*
* True size of set unknown
Leaky tx? Functional?
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Coding and non-coding gene production
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The cell is constantly making new proteins and ncRNAs. These perform their function for a while, And are then degraded. Newly made coding and non coding gene products take their place.
The picture within a cell is constantly “refreshing”.
To change its behavior a cell can change the repertoire of genes and ncRNAs it makes.
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Cell differentiation
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To change its behavior a cell can change the repertoire of genes and ncRNAs it makes.
That is exactly what happens when cells differentiate during development from stem cells to their different final fates.
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Human manipulation of cell fate
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To change its behavior a cell can change the repertoire of genes and ncRNAs it makes.
We have learned (in a dish) to: 1 control differentiation 2 reverse differentiation 3 hop between different states
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Cell replacement therapies
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We want to use this knowledge to provide a patient with healthy self cells of a needed type.
We have learned (in a dish) to: 1 control differentiation 2 reverse differentiation 3 hop between different states
(iPS = induced pluripotent stem cells)
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How does this happen?
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Different cells in our body hold copies of (essentially) the same genome. Yet they express very different repertoires of proteins and non-coding RNAs. How do cells do it?
A: like they do everything else: using their proteins & ncRNAs…
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Gene Regulation
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Some proteins and non coding RNAs go “back” to bind DNA near genes, turning these genes on and off.
Gene DNA
Proteins
To be continued…
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Review • Central dogma recap
– Genes, proteins and non coding RNAs
• RNA world hypothesis • Small structural RNAs
– Sequence, structure, function – Structure prediction – Transcription mode
• MicroRNAs – Functions – Modes of transcription
• lncRNAs – Xist
• Genome wide (and context wide) transcription – How much? – To what goals?
• Gene transcription and cell identity – Cell differentiation – Human manipulation of cell fates
• Gene regulation control
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Algorithms
http://cs173.stanford.edu [BejeranoWinter12/13] 39
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Jaco de Ridder, 2004
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Junction of Multi-Loop
RNA Secondary Structure
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Tertiary structure elements: Pseudoknots
Pseudoknot: interaction of bases inside a loop with bases outside the loop
Sacha Baginsky, 2005
i1
j1 i2
j2
i1 < i2 < j1 < j2
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RNA Secondary Structure Stability
Structure stability is dependent upon: 1) The number of GC versus AU and GU base pairs (Higher
energy bonds form more stable structures)
2) The number of base pairs in a stem region (longer stems results in more bonds)
3) The number of base pairs in a hairpin loop region (formation of loops with more than 10 or less than 5 bases requires more energy)
4) The number of unpaired bases, whether interior loops or bulges (unpaired bases decrease the stability of the structure)
Jaco de Ridder, 2004
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• Free-energy values (kcal/mole at 37oC ) are as follows:
Sacha Baginsky, 2005
Energy Table for Secondary Structure
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RNA Secondary Structure Prediction Approaches
• Minimum energy: Look for folds with the lowest free energy (most stable) folds. The fold with more negative free energy, is more stable. The free energy of a fold is the addition of free energy of all motifs found in the structure. Require estimation of energy terms.
• Comparative Method: uses multiple sequence alignments of homologous sequences to find conserved regions and covariant base pairs (most trusted if there is enough data)
• Most methods predict secondary structure. Not successful for tertiary structure prediction, which is determined by X-ray and NMR.
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Prediction Assumption of Energy-Based Method
• The most likely structure is similar to the energetically most stable structure
• Energy associated with any position in the structure is only influenced by local sequence and structure (previous pair, not next pair)
• No knots.
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Jaco de Ridder, 2004
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Dynamic programming algorithm
• Recursive definition of the optimal score (We use a simplified scoring function.)
•Initialization of optimal scoring matrix
• Bottom-up approach to fill the scoring matrix (bottom-up because smallest subproblems are solved first). Run from diagonal to diagonal
• Traceback of the matrix to recover the global, optimal solution
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Sacha Baginsky, 2005
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Dynamic Programming Algorithm for RNA Secondary Structure
Prediction • Given a RNA sequence: x1,x2,x3,…,xL and a scoring function a(x,y) • Initialization: E[i,i-1] = 0, E[i,i] = 0 • Recursion: for d = 1,2,3,4,…,L-1 { for ( i = 1; i + d <= L; i++) { j = i + d; E[i,j] = min { E[i+1,j], E[i,j-1], E[i+1,j-1] + a(ri,rj) mini<k<j ( E[i,k] + E[k+1,j] ) } } } Note: i is always smaller than j.
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Dynamic Programming Algorithm for RNA Secondary Structure
Prediction • Given a RNA sequence: x1,x2,x3,…,xL and a scoring function a(x,y) • Initialization: E[i,i-1] = 0, E[i,i] = 0 • Recursion: for d = 1,2,3,4,…,L-1 { for ( i = 1; i + d <= L; i++) { j = i + d; E[i,j] = min { E[i+1,j], E[i,j-1], E[i+1,j-1] + a(ri,rj) mini<k<j ( E[i,k] + E[k+1,j] ) } } } Note: i is always smaller than j.
Time Complexity?
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G G A A A U C C
G 0
G 0 0
A 0 0
A 0 0
A 0 0
U 0 0
C 0 0
C 0 0
i
j 1 2 3 4 5 6 7 8
1
2
3
4
5
6 7
8
A Simple Example Input: GGAAAUCC Scoring Function: a(ri,rj) = -1 if ri and rj form a Watson-Crick base pair. Otherwise, 0.
Initialization
E[i,i-1] = 0, E[i,i] = 0
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G G A A A U C C
G 0 0
G 0 0 0
A 0 0 0
A 0 0 0
A 0 0 -1
U 0 0 0
C 0 0 0
C 0 0
i
j
1 2 3 4 5 6 7 8
1
2
3
4
5
6 7
8
E[1,2] = min( E(1,2-1), E(1+1,2), E[1+1,2-1]+a(1,2) mink(E[1,k]+E[k+1,2] ) = 0
E[5,6] = min( E[5,5], E[6,5]+a(5,6), E[6,6]) mink(E[5,k]+E[k,6]) ) = -1
Fill matrix from diagonal to diagonal
(may set to 0 if two Adjacent ones can’t be paired?)
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G G A A A U C C
G 0 0 0
G 0 0 0 0
A 0 0 0 0
A 0 0 0 -1
A 0 0 -1 -1
U 0 0 0 0
C 0 0 0
C 0 0
i
j
1 2 3 4 5 6 7 8
1
2
3
4
5
6 7
8
E[1,3] = min( E(1,2), E(2,3), E[2,2] + a(G,A) ) = 0
E[4,6] = min ( E[4,5], E[5,6], E[5,5] + a(A,U) ) = -1
Any valid k?
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G G A A A U C C
G 0 0 0 0
G 0 0 0 0 0
A 0 0 0 0 -1
A 0 0 0 -1 -1
A 0 0 -1 -1 -1
U 0 0 0 0
C 0 0 0
C 0 0
i
j
1 2 3 4 5 6 7 8
1
2
3
4
5
6 7
8
E[3,6] = min( E[3,5], E[4,6], E[4,5]+a(A,U), E[3,4]+E[5,6] ) = -1
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G G A A A U C C
G 0 0 0 0 0
G 0 0 0 0 0 -1
A 0 0 0 0 -1 -1
A 0 0 0 -1 -1 -1
A 0 0 -1 -1 -1
U 0 0 0 0
C 0 0 0
C 0 0
i
j
1 2 3 4 5 6 7 8
1
2
3
4
5
6 7
8
E[2,6] = min( E[2,5], E[3,6], E[3,5]+a(G,U), E[2,3]+E[4,6], E[2,4]+E[5,6] ) = -1
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G G A A A U C C
G 0 0 0 0 0 -1
G 0 0 0 0 0 -1 -2
A 0 0 0 0 -1 -1 -1
A 0 0 0 -1 -1 -1
A 0 0 -1 -1 -1
U 0 0 0 0
C 0 0 0
C 0 0
i
j
1 2 3 4 5 6 7 8
1
2
3
4
5
6 7
8
E[2,7] = min ( E[2,6], E[3,7], E[3,6]+a(G,C), E[2,3] + E[4,7], E[2,4] + E[5,7], E[2,5] + E[6,7] ) = -2
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G G A A A U C C
G 0 0 0 0 0 -1 -2
G 0 0 0 0 0 -1 -2 -2
A 0 0 0 0 -1 -1 -1
A 0 0 0 -1 -1 -1
A 0 0 -1 -1 -1
U 0 0 0 0
C 0 0 0
C 0 0
i
j
1 2 3 4 5 6 7 8
1
2
3
4
5
6 7
8
E[1,7] = min( E(1,6), E(2,7), E[2,6] + a(G,C), E[1,2] + E[3,7], E[1,3] + E[4,7], E[1,4] + E[5,7], E[1,5] + E[6,7] ) = -2
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G G A A A U C C
G 0 0 0 0 0 -1 -2 -3
G 0 0 0 0 0 -1 -2 -2
A 0 0 0 0 -1 -1 -1
A 0 0 0 -1 -1 -1
A 0 0 -1 -1 -1
U 0 0 0 0
C 0 0 0
C 0 0
i
j
1 2 3 4 5 6 7 8
1
2
3
4
5
6 7
8
Best score: E[1,8] = E[2,7] + a(G,C)
= -3
Time Complexity?
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G G A A A U C C
G 0 0 0 0 0 -1 -2 -3
G 0 0 0 0 0 -1 -2 -2
A 0 0 0 0 -1 -1 -1
A 0 0 0 -1 -1 -1
A 0 0 -1 -1 -1
U 0 0 0 0
C 0 0 0
C 0 0
i
j
1 2 3 4 5 6 7 8
1
2
3
4
5
6 7
8
Best score: E[1,8] = -3
G C G C A U A
A
Trace Back
G C G C A U A
A
Path 1 Path 2
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Sacha Baginsky, 2005
So in reality, more realistic energy function that considers different loops are needed. But the basic idea of dynamic programming is still applied.
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More information: www.rna.icmb.utexas.edu/METHODS/menu.html
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Representation of RNA secondary structures
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RNA Resources
Web: http://www.imb-jena.de/RNA.html
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RNA Folding Software
• Vienna: http://www.tbi.univie.ac.at/RNA/
• MFold: http://www.bioinfo.rpi.edu/applications/mfold/rna/form1.cgi
• AliFold: http://rna.tbi.univie.ac.at/cgi-bin/alifold.cgi (use aligned sequences)
• Genebee: http://www.genebee.msu.su/services/rna2_reduced.html (alignment)
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Summary of the Course Topic 1 – Template-Based Modeling
• Template-Based Protein Modeling
• Probability of features conditioned on template
• X, Y, Z representation
• Maximum Likelihood • Gradient Descent • Conjugate Gradient Descent
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Topic 2 – Template-Free Modeling
• Template-Free Protein Modeling
• Prior probability: Prob(structure)
• Prob (sequence | structure): P(aai | Ei) or P(aai, aaj | Ei, Ej)
• Maximum a Posterior • Fragment assembly • Simulated Annealing
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Topic 3 – Protein Docking
• Protein Docking • Shape complementarity • Geometric approach • Energy-based approach • Flexible docking • Evaluation methods
• Fourier Transformation • Geometric graph method • Energy optimization • Side chain and backbone flexibility
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Topic 4 - Genome Structure Modeling
• 3D Genome Structure • Chromosome Conformation Capturing
• Hi-C technique • Inter- / intra chromosome contact map
• Chromosomal translocation • Interaction frequency and distance conversion
• Markov Chain Monte Carlo method
• Initialization • Probability of a conformation
• Conformation Perturbation
• Mixing detection • Evaluation
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Topic 5 – RNA Structure Modeling
• Message RNA • Non-coding RNA • No-coding structural RNA (e.g. tRNA)
• microRNA • Non-coding long RNA • RNA Secondary Structure modeling
• Energy or scoring function
• Dynamic programming • Context free grammar approach
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Discussion of Final Presentation and Final Report
• Presentation • Power point slides • Introduction • All four projects • Conclusion
• Report • Title, abstract (0.5 page) • Introduction (~1 page) • Methods (?) • Results and discussions (?)
• Conclusion (~0.5 page) • Bibliography • May 14
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Other Related Courses
• Structural Bioinformatics by Dr. Korkin
• Computational Optimization Methods by me.
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