RNA Secondary Structure Prediction Dong Xu Computer Science Department 271C Life Sciences Center 1201 East Rollins Road University of Missouri-Columbia Columbia, MO 65211-2060 E-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 on Clear 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 on Did 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 on Whether 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 nucleotides adenine (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

RNA Structure Hierarchy Primary structure: 5’ ACCACCUGCUGA 3’ Secondary Structure Tertiary structure:

Secondary Structure Categories Hairpin loop Hairpin loop Stem Stem Internal loop Internal loop Bulge loop Bulge loop Pseudoknots

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

Exceptions Pseudoknot Kissing hairpins Hairpin-bulge Do not obey “parentheses rule”

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

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

Dynamic Programming - 1 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 - 2 i is unpaired, added on to a structure for i+1…j S(i,j) = S(i+1,j) j is unpaired, added on to a structure for i…j-1 S(i,j) = S(i,j-1)

Dynamic Programming - 3 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 j paired, added on to a structure for i+1…j-1 S(i,j) = S(i+1,j-1)+e(ri,rj) i<k<j

Dynamic Programming - 4 Since there are only four cases, the optimal score S(i,j) is just the maximum of the four possibilities:

j A U C G Initialisation: No close basepairs i

j A U C G 2 3 1 Propagation: C5….U9 : C5 unpaired: S(6,9) = 0 2 3 1 Propagation: C5….U9 : C5 unpaired: S(6,9) = 0 U10 unpaired: S(5,8)=0 C5-U10 paired S(6,8) +e(C,U)=0 C5 paired, U10 paired: S(5,6)+S(7,9)=0 S(5,7)+S(8,9)=0

j A U C G 2 3 5 6 1 Propagation: C5….G11 : C5 unpaired: S(6,11) = 3 2 3 5 6 1 Propagation: C5….G11 : C5 unpaired: S(6,11) = 3 G11 unpaired: S(5,10)=3 C5-G11 paired S(6,10)+e(C,G)=6 C5 paired, G11 paired: S(5,6)+S(7,11)=1 S(5,7)+S(8,11)=0 S(5,8)+S(9,11)=0 S(5,9)+S(10,11)=0

j A U C G 2 3 5 6 8 10 12 1 Propagation: i

j A U C G 2 3 5 6 8 10 12 1 Traceback: i

Final Prediction AUACCCUGUGGUAU Total free energy: -12 kcal/mol U G C G C U U G AUACCCUGUGGUAU Total free energy: -12 kcal/mol

Some Notes 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

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 HIV TAR (30) DIS (260) PolyA (82) SD (292) PSI (319)

Some RNA Resource Comparative RNA web site http://www.rna.icmb.utexas.edu/ RNA world http://www.imb-jena.de/RNA.html RNA page by Michael Suker http://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 classification http://scor.berkeley.edu/ RNA visualisation http://ndbserver.rutgers.edu/services/download/index.html#rnaview http://rutchem.rutgers.edu/~xiangjun/3DNA/

Suggested reading: Optional reading: Reading Assignments 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