Lecture 11. RNA Secondary Structure Prediction The Chinese University of Hong Kong CSCI3220...

Lecture 11. RNA Secondary Structure Prediction

The Chinese University of Hong KongCSCI3220 Algorithms for Bioinformatics

CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2015 2

Lecture outline1. From sequences to functions2. RNA secondary structures

Last update: 21-Nov-2015

FROM SEQUENCES TO FUNCTIONSPart 1


From sequences to functions• One of the biggest questions in biology: Can

one tell the function of a molecule (DNA/RNA/protein) from its sequence alone?– Sometimes, but usually not– Easier if we also know the structure– Common believe:

sequence structure function– Of course, also depends on the environment



Molecular structures• Four levels:– Primary structures

• The sequence

– Secondary structures• First formed• Local

– Tertiary structures• Global• “Folds”, “domains”

– Quaternary structures• Multiple molecules


Image credit: http://www.personal.psu.edu/jms5704/blogs/simmons/levels_of_protein_s_c_la_784.jpg


Primary structures• Connections (strong

covalent bonds vs. weak hydrogen bonds)– Which molecules are

connected– Which atoms are

connected– First-level constraints of the

possible structures• Example: Molecules close in

primary structure must also be close in secondary, tertiary and quaternary structures


Image credit: Wikibooks

http://upload.wikimedia.org/wikipedia/commons/e/e4/DNA_chemical_structure.svg


Primary structures• Orientation:

– DNA, RNA: 5’-3’– Amino acids: Amino (N)

terminus to carboxyl (C) terminus• “Residue”: what

remains after a water molecule is expelled


Image credit: http://bealbio.wikispaces.com/file/view/dsDNA.jpg, http://attentionmanagement.ca/userfiles/image/DNA-RNA%20directions.gif, http://www.phschool.com/science/biology_place/biocoach/images/translation/peptbond.gif, http://www.cystinuria.org/resources/education/aminoacids/peptide.gif


DNA secondary structures• Double helix• A-DNA (dehydrated samples)– Right-handed– 11bp per turn

• Most common: B-DNA– Right-handed– 10.5bp per turn

• Z-DNA (some methylated DNA)– Left-handed– 12bp per turn


Image credit: Wikipedia


DNA secondary structures


A-DNA B-DNA Z-DNAImage credit: Wikipedia


RNA secondary structures• Largely possible to be projected onto a 2D

plane


Stem/hairpin loop Stacking pairs Bulge

Image credit: http://www.clcbio.com/scienceimages/rna_prediction/RNA_structure_prediction_web.png

Internal loop Multi-loop Exterior loop

Dangling nucleotides Less stable pair Coaxial stacking


RNA secondary structures• Pseudoknots: complex structures


Image credit: Wikipedia, Sperschneider and Datta, RNA 14(4):630-640, (2008)

http://ureply.mobi/mobile_index.php


Protein secondary structures• Three main types:– -helixes– -sheets– Coils (connectors)


Image credit: http://calcium.uhnres.utoronto.ca/cadherin/images/pub_pages/general/ribbon.jpg, http://www.mun.ca/biology/scarr/MGA2-03-25.jpg


DNA tertiary structures• Wrapped around nucleosomes

formed by histone proteins• Condensed form at beginning

of mitosis and meiosis


Image credit: http://micro.magnet.fsu.edu/cells/nucleus/images/chromatinstructurefigure1.jpg, Wikipedia

http://en.wikipedia.org/wiki/File:Chromatin_Structures.png


RNA tertiary structures• Overall structure of an RNA

– More studied for RNAs that do not translate into proteins -- “non-coding” RNAs

– Example: tRNA




Protein tertiary structures• Complex structures– Mainly caused by weak forces (hydrogen

bonds and hydrophobic interactions)– Occasionally stronger forces (disulfide bonds

between cysteines)

• The CATH hierarchy– Class: composition of secondary structures– Architecture: overall shape– Topology: connection of secondary structures– Homologous: with common ancestor


Image credit: CATH


Quaternary structures• Types:– Protein subunit-protein

sub-unit– Protein-protein– Protein-DNA– Protein-RNA– (Protein-small molecules)– RNA-RNA– ...


Image credit: Wikipedia, http://serrano.crg.es/images/protein_dna1.jpg Protein-DNA interaction

Protein-subunit interaction (Hemoglobin)


Structure and function • Why function depends

on structure?1. Structure itself is the

function (e.g., tubulins)

2. Binding• Complementarity of

interacting structures• Formation of special

bonds


Image credit: http://www.nigms.nih.gov/NR/rdonlyres/54BEAC37-47A9-454A-BC4F-B94EA127FA1E/0/fig1a_large.jpg, http://upload.wikimedia.org/wikimedia/en-labs/7/7f/Protein_Protein_Docking.JPG


Structure and function • Why function depends

on structure? (cont’d)3. Functional group (e.g.,

catalytic site)4. Determining

localization (e.g., transporter membrane proteins)


Image credit: http://www.catalysis-ed.org.uk/principles/images/enzyme_substrate.gif, Spudich , Science 288(5470):1358-1359, 2000

RNA SECONDARY STRUCTURESPart 2


Important RNA classes• Coding:

– Messenger RNAs (mRNAs)• For translating into proteins

• Non-coding:– Ribosomal RNAs (rRNAs)

• Parts of the ribosome complex

– Transfer RNAs (tRNAs)• Delivering free amino acids during translation

– Micro RNAs (miRNAs)• Binding mRNA targets to promote RNA

degradation or repress translation

– Small nucleolar RNAs (snoRNAs)• Guiding chemical modifications of other RNAs

– Small nuclear RNAs (snRNAs)• Involved in mRNA splicing

– Long non-coding RNAs (lncRNAs)• Some involved in gene regulation

– ...


Image source: http://legacy.hopkinsville.kctcs.edu/sitecore/instructors/Jason-Arnold/VLI/Module%201/m1DNAfunction/m1DNAfunction3.html


Importance of RNA structures• Structure is important to many classes of RNA• Examples:


Image sources: http://www.bio.miami.edu/dana/pix/tRNA.jpg, http://lowelab.ucsc.edu/images/CDBox.jpg

tRNA snoRNA


Representing RNA secondary structures

• Formats: (see http://projects.binf.ku.dk/pgardner/bralibase/RNAformats.html):– Dot-bracket format– Stockholm format– ...



Dot-bracket format

• Sequence (nucleotides 10, 20, 30, etc. marked in red):GUGAAUGAUGAAUUUAAUUCUUUGGUCCGUGUUUAUGAUGGGAAGUAAGACCCCCGAUAUGAGUGACAAAAGAGAUGUGGUUGACUAUCACAGUAUCUGACG

• Structure:......((((.......((((((.(((....((((((.((((..........)))).)))))).))).)))))).((((((.....)))))).)))).....


Image credit: Xihao Hu



Predicting RNA secondary structures

• A basic assumption in structure predictions:– Real structure has the lowest free energy

• In a simplified view, more stable bonds lower free energy

• In the case of RNA secondary structures:– Good to form more pairs

• A-U• C-G• Sometimes G-U (a “wobble base pair”)

– Good to form more stable pairs• C-G > A-U > G-U

– Good to have stable sub-structures• E.g., stacking pairs



Predicting RNA secondary structures

• We will assume there are no pseudoknots– With pseudoknots, currently there is no

known algorithm that can find the optimal solution efficiently

• We need two things:1. A thermodynamic model for

computing the free energy of a structure

2. A method for finding the structure with the minimum free energy

– This setting sounds familiar?



A pseudoknot


Further assumptions1. The free energy of a secondary structure is

the sum of the free energies of the sub-structures– Not the sum of individual bases/base pairs, as

one base pair can participate in multiple sub-structures

2. The free energies of the sub-structures are independent



Problem definition• Given an RNA sequence, find a set of base

pairs so that each base is paired at most once• Example:– Input sequence: GUGAAUGAUGAAUUU...ACG– Output set of base pairs:• (7, 97)• (8, 96)• ...• (18, 74)• ...• (81, 87)


Image credit: Xihao Hu


Linear view


1 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 ... 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 ...... 96 97. ( ( ( ( . . . . . . . ( ( ( ( ( ( . ( ... ) . ) ) ) ) ) ) . ( ( ( ( ( ( . . . . . ) ) ) ) ) ) . ) ) ...... ) )


Thermodynamics model• We will consider four types of sub-structures here:– Stacking pairs: both (i, j) and (i+1, j-1) are in the set– Hairpin loop: there is a pair (i, j), where all bases from i+1

to j-1 are not paired– Bulge/Internal loop: there are two pairs (i, j) and (i1, j1),

where i<i1<j1<j, and all bases from i+1 to i1-1 and from j1+1 to j-1 are not paired

– Multi-loop: there are pairs (i, j), (i1, j1), ..., (ik, jk), where i<i1<j1<...<ik<jk<j, and all bases from i+1 to i1-1, from j1+1 to i2-1, ..., jk-1+1 to ik-1 and from jk+1 to j-1 are unpaired

• One base pair can participate in multiple structures



Stacking pairs• Both (i, j) and (i+1,

j-1) are in the set• E.g., i:20, j:72


1 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 ... 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 ...... 96 97i i+1 j-1 j


Hairpin loop• There is a pair (i, j),

where all bases from i+1 to j-1 are not paired

• E.g., i: 81, j: 87


1 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 ... 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 ...... 96 97i j

Image source: http://img.ehowcdn.com/article-new/ds-photo/getty/article/151/226/87820768_XS.jpg


Bulge/Internal loop• Internal loop: There

are two pairs (i, j) and (i1, j1), where i<i1<j1<j, and all bases from i+1 to i1-1 and from j1+1 to j-1 are not paired– Called a bulge if only

one side has unpaired bases

• E.g., i:23, j:69, i1:25, j1:67


1 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 ... 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 ...... 96 97i i1 jj1


Multi-loop• Multi-loop: There are

pairs (i, j), (i1, j1), ..., (ik, jk), where i<i1<j1<...<ik<jk<j, and all bases from i+1 to i1-1, from j1+1 to i2-1, ..., jk-1+1 to ik-1 and from jk+1 to j-1 are unpaired

• E.g., k=2, i:10, j:94, i1:18, j1:74, i2:76, j2:92


1 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 ... 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 ...... 96 97i i1 j1 i2 j2 j



One possible thermodynamic model• Unpaired bases have 0 free energy and all the

terms below have negative free energy• eS(i, j): for the stacking pairs (i, j) and (i+1, j-1)• eH(i, j): for the hairpin loop closed at (i, j)• eBI(i, j, i1, j1): for a bulge or internal loop

enclosed by the pairs (i, j) and (i1, j1)

• eM(i, j, i1, j1, ..., ik, jk): for a multi-loop that consists of the pairs (i, j), (i1, j1), ..., (ik, jk) and satisfying i<i1<j1<...<ik<jk<j



Finding the optimal structure• Dynamic programming• Let s be the RNA sequence with n nucleotides• Tables:– V(j): free energy of the optimal structure for s[1..j]

• Final answer is based on V(n)

– VP(i, j): free energy of the optimal structure for s[i..j] with i and j forming a pair

– VBI(i, j): free energy of the optimal structure for s[i..j] with i and j forming a pair that closes a budge or internal loop

– VM(i, j): free energy of the optimal structure for s[i..j] with i and j forming a pair that closes a multi-loop



Update formulas• V(j): free energy of the optimal structure for

s[1..j]• V(1) = 0• For j > 1,


j...1

i ... j... i-11

j-1

j...1

j is unpaired

j pairs with i

...

...

...

Vሺ𝑗ሻ= minቊVሺ𝑗− 1ሻ 𝑗 is unpairedmin1≤𝑖<𝑗ሼVPሺ𝑖,𝑗ሻ+ Vሺ𝑖 − 1ሻሽ 𝑗 pairs with 𝑖


Update formulas• VP(i, j): free energy of the optimal structure for

s[i..j] with i and j forming a pair • We require that i < j


i ... j...

i ... j... j-1i+1Stacking pairs

i ... j...Hairpin loop

All unpaired

...

...

...

Vpሺ𝑖,𝑗ሻ= minە۔

+eSሺ𝑖,𝑗ሻۓ VPሺ𝑖 + 1,𝑗− 1ሻ ሺ𝑖,𝑗ሻ and ሺ𝑖 + 1,𝑗+ 1ሻ form stacking pairseH(𝑖,𝑗) ሺ𝑖,𝑗ሻ closes a hairpin loopVBIሺ𝑖,𝑗ሻ ሺ𝑖,𝑗ሻ closes an internal loopVMሺ𝑖,𝑗ሻ ሺ𝑖,𝑗ሻ closes a multi loop


Update formulas• VBI(i, j): free energy of the optimal structure

for s[i..j] with i and j forming a pair that closes a budge or internal loop (i.e., i and j take the roles of i1 and j1)


i ... j... ...

i ... j... ...i1 ... j1 ...Budge or internal loop

All unpaired All unpaired

VBIሺ𝑖,𝑗ሻ= min𝑖1,𝑗1:𝑖<𝑖1<𝑗1<𝑗ሼeBIሺ𝑖,𝑗,𝑖1,𝑗1ሻ+ VPሺ𝑖1,𝑗1ሻሽ


Update formulas• VM(i, j): free energy of the optimal structure

for s[i..j] with i and j forming a pair that closes a multi-loop


i ... j... ...

VMሺ𝑖,𝑗ሻ= min𝑖1,𝑗1,…,𝑖k,𝑗𝑘:𝑖<𝑖1<𝑗1<...<𝑖𝑘<𝑗𝑘<𝑗൝eMሺ𝑖,𝑗,𝑖1,𝑗1,…,𝑖𝑘,𝑗𝑘ሻ+ VPሺ𝑖ℎ,𝑗ℎሻ𝑘ℎ=1 ൡ


Time and space requirements

• V: n entries, each takes O(n) time• VP(i, j): O(n2) entries, each takes constant time


Vሺ𝑗ሻ= minቊVሺ𝑗− 1ሻ 𝑗 is unpairedmin1≤𝑖<𝑗ሼVPሺ𝑖,𝑗ሻ+ Vሺ𝑖 − 1ሻሽ 𝑗 pairs with 𝑖

Vpሺ𝑖,𝑗ሻ= minە۔

+eSሺ𝑖,𝑗ሻۓ VPሺ𝑖 + 1,𝑗− 1ሻ ሺ𝑖,𝑗ሻ and ሺ𝑖 + 1,𝑗− 1ሻ form stacking pairseH(𝑖,𝑗) ሺ𝑖,𝑗ሻ closes a hairpin loopVBIሺ𝑖,𝑗ሻ ሺ𝑖,𝑗ሻ closes an internal loopVMሺ𝑖,𝑗ሻ ሺ𝑖,𝑗ሻ closes a multi loop


Time and space requirements

• VBI: O(n2) entries, each takes O(n2) time

• VM: O(n2) entries, each takes O(n2k) time


VBIሺ𝑖,𝑗ሻ= min𝑖1,𝑗1:𝑖<𝑖1<𝑗1<𝑗ሼeBIሺ𝑖,𝑗,𝑖1,𝑗1ሻ+ VPሺ𝑖1,𝑗1ሻሽ VMሺ𝑖,𝑗ሻ= min𝑖1,𝑗1,…,𝑖k,𝑗𝑘:𝑖<𝑖1<𝑗1<...<𝑖𝑘<𝑗𝑘<𝑗൝eMሺ𝑖,𝑗,𝑖1,𝑗1,…,𝑖𝑘,𝑗𝑘ሻ+ VPሺ𝑖ℎ,𝑗ℎሻ𝑘

ℎ=1 ൡ


Time and space requirements• Summary:– V: n entries, each takes O(n) time– VP: O(n2) entries, each takes constant time

– VBI: O(n2) entries, each takes O(n2) time

– VM: O(n2) entries, each takes O(n2k) time

• Total: O(n2) space, O(n2k+2) time– Exponential if k is unbounded– Some approximations could bring the time down

to O(n4) – still huge for large n, but feasible for small or median n



Some remarks• If we allow general pseudoknots, there is

currently no efficient way to find the optimal RNA secondary structure with the minimum free energy

• Other methods to predict RNA secondary structures:– Conservation and covariation• High conservation: 2 and 4• Strong covariation: 1 and 5

– Experimental methods (e.g., RNA footprinting)


12345ACGGUACUGUCCAGGUCCGA


Representing pseudoknots

• Without pseudoknots, RNA secondary structures can be unambiguously represented by dots (single bases) and brackets (base pairs)

– What if there are pseudoknots?– Need more types of brackets


1 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 ... 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 ...... 96 97

. ( ( ( ( . . . . . . . ( ( ( ( ( ( . ( ... ) . ) ) ) ) ) ) . ( ( ( ( ( ( . . . . . ) ) ) ) ) ) . ) ) ...... ) )

Image source: http://ultrastudio.org/upload/RNAPseudoKnot-25005810.jpg

GAAGUACAAUAUGUAACCG.{.((((.....))}))..

CASE STUDY, SUMMARY AND FURTHER READINGS

Epilogue


Case study: Drug finding/design• Drugs are mostly chemicals with a specific

structure that interacts with some biological objects

• Examples:– Inhibiting the activities of an important protein of

bacteria– Blocking the interaction between virus and

receptors of host cell– Simulating the production of a hormone



Case study: Drug finding/design• Suppose we want to identify/design a chemical to

target a particular object (e.g., a protein), we need to make sure that they have tight bindings through a process called docking


Image source: http://vds.cm.utexas.edu/


Case study: Drug finding/design• Computational problem:– Input: a target protein and a list of chemicals– Goal: find a chemical that binds the target well

• Try different locations and orientations• Binding depends on structure and chemistry

– Output: One or more chemicals that bind the target well• Difficulties:– Computational complexity

• Large search space for each protein-chemical combination• Need to try many chemicals

– Need to ensure specificity (not to target other proteins and cause side effects)



Case study: Drug finding/design• There is a game for players to try folding proteins called FoldIt (

http://fold.it/)– Score based on free energy– Real time update of scores and ranks– Players can discuss and share solutions– Resulted in some amazingly good folds as compared to automatic predictions

by computer programs


Image source: http://fold.it/portal/site_files/theme/science/competition.png

http://fold.it/


Summary• Functions depend on structures• Different levels of structures:

– Primary (sequence)– Secondary (local)– Tertiary (global)– Quaternary (interactions)

• RNA secondary structures can be predicted by dynamic programming based on a thermodynamic model

• Important sub-structures– Stacking pairs– Hairpin loops– Internal loops/bulges– Multi-loops– Pseoduknots



Further readings• Chapter 11 of Algorithms in Bioinformatics: A

Practical Introduction– Speed up of algorithm– Algorithm for RNA structure perdition with

pseudoknots– Free slides available

• Parts VII and VIII of Fundamental Concepts of Bioinformatics– Protein folding and protein structure prediction– Docking


http://www.comp.nus.edu.sg/~ksung/algo_in_bioinfo/slides/Ch11_rna_prediction.pdf

Lecture 11. RNA Secondary Structure Prediction The Chinese University of Hong Kong CSCI3220...

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