Conserved RNA Structures. Ivo L. Hofacker. Institut for Theoretical Chemistry, University Vienna.
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1 onserved RN Structures Ivo L. Hofacker Institut for Theoretical hemistry, University Vienna Bled, January 2002
2 Energy Directed Folding Predict structures from sequence alone, by minimizing free energy. + works on a single sequence + sophisticated energy model + efficient algorithms, good implementations, many variants - unreliable, at best 70% of predicted pairs correct - gives no information on functional vs. incidental structures.
3 ovariance Methods infer structure from phylogenetic comparison, especially compensatory mutations. + highly accurate predictions + yields conserved (functional) structures - few available programs - requires many sequences with good alignments Obviously a combination energy directed and covariance methods is desirable.
4 Score Functions for omparative Structure Prediction Need to derive a score for a possible pair i, j by comparing columns i and j of the alignment. counting compensatory mutations our alifold covariance score mutual information based on a phylogenetic tree several weird ad hoc methods
5 Mutual Information Entropy of a random variable X with probability distribution p(x) is H(X) = x p(x) log 2 p(x) The mutual information of two distribution is given by M(X; Y ) = H(X) + H(Y ) H(X, Y ) = H(X) H(X Y ) = H(Y ) H(Y X) Obviously we have M(X; Y ) = M(Y ; X) and M(X; Y ) 0 with M(X; Y ) = 0 p(x, y) = p(x)p(y)
6 Mutual Information II Easily computed directly from frequencies in column i and j of alignment: M i,j = x,y f ij (xy) log 2 f ij (xy) f i (x)f j (y) For the 4 letter alphabet = {,,, U}, 0 M ij 2 bits. + ompletely parameter free + No model of sequence evolution or phylogenetic tree needed ± Uses no prior knowledge about secondary structures + can detect tertiary contacts and functional constraints - poor signal to noise for small data sets - only compensatory mutations contribute, consistent mutations ( U) are neglected
7 lifold ovariance Score Let Π α ij = 1 if sequence α can pair positions i, j; d α,β ij hamming distance of α and β at positions i and j (e.g. 0,1, or 2). ij = 1 d α,β N 2 ij Π α ijπ β ij α,β = 1 2N 2 xy,x y f ij (xy)d xy,x y f ij (x y ) where D xy,x y contains d H (xy, x y ) if xy and x y are allowed pairs, else 0. Including a penalty for non-standard pairs set ( B ij = ij ϕ 1 1 N α Π α ij )
8 rtificial Test ase enerate sequences folding into the structure (((.(((...))))))..((.(((...))).)). using RNinverse. MI from 10 sequences MI from 100 sequences
9 rtificial Test ase II omparing mutual information and covariance score from 5 sequences from 10 sequences
10 Scoring with Phylogenetic Tree Idea: Same data pair frequencies may be produced by different histories???? U???? U U U U Single Mutation Multiple Mutations Right scenario gives stronger support for base pair. How to quantify this?
11 Scoring with Phylogenetic Tree Haussler: iven the phylogenetic tree T data d (two columns of the alignment) compute the probability of the data given two models for a) conserved pair b) independent positions. Use the log-odds score: score = log P (d T, pair) P (d T nopair) To calculate P (d model) need to sum over all possible histories. Luckily, this can be done recursively.
12 Recursive calculation of probabilities Let f be the root node of some subtree of T with children r and l; d(f) denotes the data on that subtree. P (d model) = π P (d root = π) P (root = π) P (d(f) f = π) = P (d(r) r = π )P (r = π f = π) π P (d(l) l = π )P (l = π f = π) π Recursion can be started at the leafs whose sequence is known.
13 This tree shows the calculation process used to compute the posterior data probability P(d Model pair ) for the column duo d described in Figure 1. The leaf nodes are initialized from the known nucleotide duo values from d. Other probabilities are derived from descendants according to the inference equation developed above. P( d Model) = P( d( 0 ) = l Model) P( = l Model) l= 0,1 0 ( ) + ( ) = P(d( 0 ) 0 =U) = P(d( 0 ) 0 =) =.0098 P(d( 1 ) 1 =U) = P(d( 1 ) 1 =) =.9781 P(d( 2 ) 2 =U) = P(d( 2 ) 2 =) = P(d( 3 ) 3 =U) = P(d( 3 ) 3 =) = 1.00 P(d( 4 ) 4 =U) = P(d( 4 ) 4 =) = 1.00 P(d( 5 ) 5 =U) = P(d( 5 ) 5 =) = 0.00 P(d( 6 ) 6 =U) = P(d( 6 ) 6 =) = 0.00 Figure 2: alculation Tree for Example (ase 1, Model Pair )
14 Existing Programs I: alidot & pfrali Use Vienna RN Package for predicting secondary structures based on thermodynamic rules. ombine structure prediction and with a standard (clustalw) sequence alignment. Use covariances to rank order base pairs from the prediction and extract predicted conserved structures Best suited for large sequences with interspersed conserved structure motifs.
15 Mcaskill s lgorithm RN Sequencs Ralign (lustal W) Dot Plots Multiple Sequence lignment U 0.99 U U 0.00 U 0.77 U 0.34 sequence and pairing probability ombined Pair Table redibility Ranking Reduce Pair List HEK compensatory mutations onserved sub-structures Flow diagram of alidot
16 lifold Standard dynamic programming with covariance score as bonus energy: E c (S, Ψ) = E(S, Ψ) + cv (i,j) Ψ mfe and partition function algorithm implemented in Vienna RN package. orrectly predicted base pairs for 16S rrn for E. oli. lignment: Ribosomal Database Project [Maidak et al., NR 28: (2000)] lustal W RDB lustal W RDB N raw filled raw filled raw filled raw filled E.coli 16sRN 23sRN N/ 47.2 N/ 52.2 N/ 52.2 N/ B ij
17 UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU Example: E.coli 23S RN from 5 sequences
18 ... ( ( ( ( ( ( ( (.... ( ( ( (. ( ( ( ( ( ) ) ) ) )..... ( ( ( ( ) ) ) ) ) ) ) )..... ( ( ( ( ( ( ( ( (.. ( ( (. ( ( (..... ( ( ( ( ( ( ( ( ( (.... ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (.. ( ( ( ( ( ( ( ( ( ( (... ( {... ( ( ( ( (.. ( ( ( ( ( ( ( ( (.... ) ) ) ) ) ) ) ) )... ) ) ) ) ) ( ( ( ( ( ( ( (..... ( ( (.... ) ) )..... ) ) ).. ) ) ) ) )... }).... ) ) ). ) ) ) ) ) ) ) ).... ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )..... ) ) ). ) ) ).. ) ) ) ) ) ) ) ) )..... ) ) ) ). ) ) ) ) onsensus structure of 14 SRP RN U U U U U U U U U U U U U UU U U UU U U U U U U U U U
19 Eddy s OVE Implements a method to align a set of sequences to a secondary structure. ombined with simple maximum matching algorithm to iteratively improve alignment and consensus structure. lign sequences to structure ompute new consensus structure using maximum matching Information M ij alculate Mutual from alignment
20 Rivas & Eddy s QRN iven an alignment of two sequences, decide whether it s a coding region, structural RN, or neither. For the structural RN case compute the sum over all RN structure s P ( RN) = For any of the three models Bayes rule gives s P ( s, RN)P (s RN) P (Model ) = P ( Model)P (Model)/P ()
21 References Eddy:94 S. R. Eddy and R. Durbin. RN sequence analysis using covariance models. Nucl. cids. Res., 22: , B. ulko and D. Haussler. Using multiple alignents and phylogenetic trees to detect RN secondary structures. Pac. Symp. Biocomput., pages , I. L. Hofacker, M. Fekete,. Flamm, M.. Huynen, S. Rauscher, P. E. Stolorz, and P. F. Stadler. utomatic detection of conserved RN structure elements in complete RN virus genomes. Nucl. cids Res., 26: , I. L. Hofacker, M. Fekete, and P. F. Stadler. Secondary structure prediction for aligned RN sequences. J. Mol. Biol., submitted, SFI Preprint I. L. Hofacker and P. F. Stadler. utomatic detection of conserved base pairing patterns in RN virus genomes. omp. & hem., 23: , E. Rivas and S. R. Eddy. Secondary structure alone is generally not statistically significant for the detection of noncoding RNs. Bioinformatics, 16: , E. Rivas and S. R. Eddy. Noncoding RN gene detection using comparative sequence analysis. BM Bioinformatics, 2(8):19 pages, E. Rivas, R. J. Klein, T.. Jones, and S. R. Eddy. omputational identification of noncoding RNs in e. coli by comparative genomics. urr. Biol., 11: , 2001.
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