rna secondary structure prediction

RNA Secondary Structure Prediction

Dong Xu

Computer Science Department271C Life Sciences Center

1201 East Rollins RoadUniversity of Missouri-Columbia

Columbia, MO 65211-2060E-mail: xudong@missouri.edu

573-882-7064 (O)http://digbio.missouri.edu

Final Report

Due on Dec. 8. A numerical score (0-15) will be assigned for

based onClear formulation of the project (2)

Method (4)

Significant results achieved (4)

Discussion (3)

Writing of the project (2)

Final Presentation

Preferably shown in powerpoint file, pdf is fine

Preferably 20 minutes (up to 25 min), plus 5min for questions

15 points for the presentation (introduction, methods, results, discussions)

15 points for software demo Implementation of the software Major functionalities Documentation Perform a test run

Presentation Evaluation

A numerical score (0-15) will be assigned based onDid the student put enough effort? (3)

Is the work interesting or novel? (3)

Is the method technically sound? (3)

Is the discussion insightful? (3)

Is the presentation clear? (3)

Software Demo

A numerical score (0-15) will be assigned based onWhether the program can run using actual

biological data (3)

Documentations (3)

Whether it is easy to use (3)

Performance in accuracy (3)

Performance in computing time and memory usage (3)

Outline

RNA Secondary Structure

Comparative Approach

Base-Pair Maximization

Free Energy Minimization

Local Structure Prediction

RNA Types

siRNA, short interfering RNA; miRNA, microRNA; small temporal RNA stRNA; snoRNA small nucleolar RNA ;snRNA: Small nuclear RNA.

Features of RNA

RNA: polymer composed of a combination of four nucleotidesadenine (A)

cytosine (C)

guanine (G)

uracil (U)

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

RNA Pairs

A-U G-C

G-U

5’ ACCACCUGCUGA 3’

Primary structure:

Secondary Structure

Tertiary structure:

RNA Structure Hierarchy

Secondary Structure Categories

Pseudoknots

Hairpin loop

Internal loop

Bulge loop

Hairpin loop

Stem

Internal loop

Bulge loop

Stem

tRNA structure

Circular Representation

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

Pseudoknot Kissing hairpins Hairpin-bulge

Do not obey “parentheses rule”

Exceptions

Outline

RNA Secondary Structure

Comparative Approach

Base-Pair Maximization

Free Energy Minimization

Local Structure Prediction

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 correlated mutation to be detected

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

ji ji

ji

jixx xx

xx

xxij ff

ffM

,2log

Mutual Information Plot

Mutual Information Plot

Outline

RNA Secondary Structure

Comparative Approach

Base-Pair Maximization

Free Energy Minimization

Local Structure Prediction

Dot Plot

Base-Pair Maximization

Find structure with the most base pairs

Efficient dynamic programming approach to this problem introduced by Nussinov (1970s).

Four ways to get the best structure between position i and j from the best structures of the smaller subsequences

Nussinov Algorithm

1)      Add i,j pair onto best structure found for subsequence i+1, j-1

2)      add unpaired position i onto best structure for subsequence i+1, j

3)      add unpaired position j onto best structure for subsequence i, j-1

4)      combine two optimal structures i,k and k+1, j

Notation:

e(ri,rj) : free energy of a base pair joining ri

and rj

S(i,j) : optimal free energy associated with segment ri…rj

Dynamic Programming - 1

1. i is unpaired, added on toa structure for i+1…j

S(i,j) = S(i+1,j)

2. j is unpaired, added on toa structure for i…j-1

S(i,j) = S(i,j-1)

Dynamic Programming - 2

3. i j paired, added on toa structure for i+1…j-1S(i,j) = S(i+1,j-1)+e(ri,rj)

4. i j paired, but not to each other;the structure for i…j adds together

structures for 2 sub regions, i…k and k+1…j

S(i,j) = max {S(i,k)+S(k+1,j)}i<k<j

Dynamic Programming - 3

Since there are only four cases, the optimal score S(i,j) is just the maximum of the four possibilities:

othereachtonotbutpairedjijkSkiS

pairbasejirrejiS

unpairedrjiS

unpairedrjiS

jiS

jki

ji

j

i

,,),1(),(max

,),()1,1(

)1,(

),1(

max),(

Dynamic Programming - 4

Initialisation:

No close basepairs

A U A C C C U G U G G U A U

A 0 0 0 0

U 0 0 0 0

A 0 0 0 0

C 0 0 0 0

C 0 0 0 0

C 0 0 0 0

U 0 0 0 0

G 0 0 0 0

U 0 0 0 0

G 0 0 0 0

G 0 0 0 0

U 0 0 0

A 0 0

U 0

i

j

Propagation:A U A C C C U G U G G U A U

A 0 0 0 0 0

U 0 0 0 0 0

A 0 0 0 0 2

C 0 0 0 0 3

C 0 0 0 0 0

C 0 0 0 0 3

U 0 0 0 0 1

G 0 0 0 0 1

U 0 0 0 0 2

G 0 0 0 0 1

G 0 0 0 0

U 0 0 0

A 0 0

U 0

j

C5….U9 :

C5 unpaired:S(6,9) = 0

U10 unpaired:S(5,8)=0

C5-U10 pairedS(6,8) +e(C,U)=0

C5 paired, U10 paired:S(5,6)+S(7,9)=0S(5,7)+S(8,9)=0

Propagation:

A U A C C C U G U G G U A U

A 0 0 0 0 0 0 2

U 0 0 0 0 0 2 3

A 0 0 0 0 2 3 5

C 0 0 0 0 3 3 3

C 0 0 0 0 0 3 6

C 0 0 0 0 3 3

U 0 0 0 0 1 1

G 0 0 0 0 1 2

U 0 0 0 0 2 2

G 0 0 0 0 1

G 0 0 0 0

U 0 0 0

A 0 0

U 0

j

C5….G11 :

C5 unpaired:S(6,11) = 3

G11 unpaired:S(5,10)=3

C5-G11 pairedS(6,10)+e(C,G)=6

C5 paired, G11 paired:S(5,6)+S(7,11)=1S(5,7)+S(8,11)=0S(5,8)+S(9,11)=0S(5,9)+S(10,11)=0

Propagation:

A U A C C C U G U G G U A U

A 0 0 0 0 0 0 2 3 5 6 6 8 10 12

U 0 0 0 0 0 2 3 5 6 6 8 10 10

A 0 0 0 0 2 3 5 5 6 8 8 8

C 0 0 0 0 3 3 3 6 6 6 6

C 0 0 0 0 0 3 6 6 6 6

C 0 0 0 0 3 3 3 3 3

U 0 0 0 0 1 1 3 3

G 0 0 0 0 1 2 2

U 0 0 0 0 2 2

G 0 0 0 0 1

G 0 0 0 0

U 0 0 0

A 0 0

U 0

i

j

Traceback:A U A C C C U G U G G U A U

A 0 0 0 0 0 0 2 3 5 6 6 8 10 12

U 0 0 0 0 0 2 3 5 6 6 8 10 10

A 0 0 0 0 2 3 5 5 6 8 8 8

C 0 0 0 0 3 3 3 6 6 6 6

C 0 0 0 0 0 3 6 6 6 6

C 0 0 0 0 3 3 3 3 3

U 0 0 0 0 1 1 3 3

G 0 0 0 0 1 2 2

U 0 0 0 0 2 2

G 0 0 0 0 1

G 0 0 0 0

U 0 0 0

A 0 0

U 0

i

j

A U

U A

A U

C G

C G

C U

U G

AUACCCUGUGGUAU

Total free energy: -12 kcal/mol

Final Prediction

Computational complexity: N3

Does not work with pseudo-knot (would invalidate DP algorithm)

Methods that include pseudo knots:

Rivas and Eddy, JMB 285, 2053 (1999)

These methods are at least N6

Some Notes

Outline

RNA Secondary Structure

Comparative Approach

Base-Pair Maximization

Free Energy Minimization

Local Structure Prediction

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

Example for Thermodynamic Parameters

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.

How well do they perform?

Current RNA folding programs get about 60-70% of base pairs correct, on average: useful, but not yet good.

The problem is the scoring system: thermodynamic model is accurate within 5-10%, and many alternative structures are within 10%.

Possible solution: combination of thermodynamic score with comparative sequence information

Outline

RNA Secondary Structure

Comparative Approach

Base-Pair Maximization

Free Energy Minimization

Local Structure Prediction

RNA Motif in HIV

TAR motif:

Transactivating Response Element

RNA Motifs Associated with Transcription termination

Rho-independent terminator stop the transcription process via its hairpin structure

Algorithm in Rnall

Definition 1. A “match” : canonical base pairs Definition 2. A “mismatch”: non-canonical base pair Definition 3. An “insertion”/“deletion”: nucleotide unpaired

RNA LSS in HIVTAR (30)

DIS (260)

PolyA (82)SD (292)

PSI (319)

Comparative RNA web sitehttp://www.rna.icmb.utexas.edu/

RNA worldhttp://www.imb-jena.de/RNA.html

RNA page by Michael Sukerhttp://www.bioinfo.rpi.edu/~zukerm/rna/

RNA structure database http://www.rnabase.org/

http://ndbserver.rutgers.edu/ (nucleic acid database)http://prion.bchs.uh.edu/bp_type/ (non canonical bases)

RNA structure classificationhttp://scor.berkeley.edu/

RNA visualisationhttp://ndbserver.rutgers.edu/services/download/index.html#rnaview http://rutchem.rutgers.edu/~xiangjun/3DNA/

Some RNA Resource

Reading Assignments

Suggested reading: Chapter 14 in “Current Topics in

Computational Molecular Biology, edited by Tao Jiang, Ying Xu, and Michael Zhang. MIT Press. 2002.”

Optional reading: http://www.bioinfo.rpi.edu

/~zukerm/seqanal/mfold-3.0-manual.pdf