RNA Secondary Structure Prediction Using Stochastic Context –Free Grammar And Evolutionary History B. Knudsen and J. Hein Department of Genetics and Ecology.

RNA Secondary Structure Prediction Using Stochastic Context –Free Grammar

And Evolutionary History

B. Knudsen and J. HeinDepartment of Genetics and Ecology

The institute of Biological Sciences

University of Aarhus, Denmark

Presented by Jing CuiNov.22, 2002

Outline of the Lecture

• Introduction• Algorithms

The grammar

Probabilities of columns

Probabilities of an alignment

The full model

• ImplementationThe database

Frequencies

Mutation rates

Grammar parameters

• Results

The test sequencesUsing related

sequencesNeglecting phylogenyWeight of resultsComparison with

other methods

• Conclusion

The limitationsThe improvements

Introduction

• Single sequence e.g. Zuker(1989)

using prior information on RNA structures, through energy functions

not ideal when estimating structures of sequences with known homologs

• Multiple sequences1. Covariance methods (Eddy and Durbin, 1994)

2. Profile stochastic context-free grammars (SCFGs Sakakibara et al. 1994)

Characteristics: do not explicitly take phylogeny into account, and do not use a prior probability distribution of structures

• Maximum weighted matching methods(Cary and Stormo, 1995; Tabaska et al. 1998)

share the above characteristics

• The method used in this paper uses prior knowledge about RNA structure in making a maximum a posteriori

(MAP) estimation of the 2nd structure.

Performed on an alignment of sequences assumed to have identical 2nd structure, i.e. the alignment is assumed to be a structural alignment.

Take the phylogenetic tree of the sequences into account, including branch lengths, using a model of mutation processes in RNA.

The tree can be estimated by a maximum likelihood (ML) method.

• Originating from Goldman et al. (1996)

Predicting protein 2nd structure using HMMs including phylogenetic information

• Difference2nd structure in RNA are not local, like in proteins

SCFGs instead of HMM is used here

• LimitationSCFGs are unable to model crossing interactions, thus pseudoknots cannot be predicted

Algorithm

• Input

an alignment of RNA sequences

• Output single common structure for the sequences

• The modelThe SCFG

The evolutionary model

•The grammara set of variables; some terminal and non-terminal

•Probabilities of columns• Given the tree

A column of non-paring bases is independent of the other columns

Two paring columns is assumed to be independent of any other columns

• P = (pA, pU, pG, pC) the distribution of bases in loop regions of RNA sequences

• The rate matrix

• For base pair (16 by 16) rate matrix

• Given a tree, including branch lengths, the column probabilities are calculated using post-order traversal as described by Felsenstein (1981)

Reversibility of mutations

• Probability of an alignment

The input data: D=(C1, C2, …,Cl)

The model: M

The tree: T

2nd structure: σ

s: a single base

d: a left column of pairs

dc: the right column of the pair

•The core model•The SCFG

•The evolutionary model

The grammar is equivalent to a grammar that generates column in alignments instead of just secondary structure, meaning that for a two-sequence alignment, the production rule covers the following rules:

• The full modelThe ML estimate of the tree, given the model (If no phylogenetic tree)

MAP (Maximum a posteriori) estimation of the most likely 2nd structure

by Bayes theorem

where

P(σ|T,M) is the prior distribution of structures given by the SCFG

Implementation

• The database•The database used for estimating this model should represent RNA structure in general.

• The database should be composed of various types of RNA.

tRNAs database by Sprinzl et al. (1998)

ribosomal RNAs (LSU rRNAs) by De Rijk et al. (1998)

•Frequencies• The single base frequencies were estimated from counts of the bases in the single base positions of the sequences.

• Base pair frequencies were estimated by counting base pairs.

•Mutation rates

For a given pair, P,

tp : the time between sequences

Np: the number of columns in the two-sequence alignment

Ps: the prob. of a base being in a single base position

•Grammar parameters

by inside-outside algorithm (an expectation maximization procedure)on the training set et of secondary structure (Baker, 1979; Lari and Young, 1990)

This is just like the forward-backward algorithm in HMM !!!

Results• The test sequences4 bacterial RNase P RNA seq.

alignment: 385 columns

pair-wise sequence identities 65-92%

• Pseudoknot 68-76 and 368-361; 18-12 and 370-364

• At least 22 positions wrongly predicted in each sequence

•Using related sequences

•Weight of results

by inside and outside variables, calculate the probability that each position is correctly predicted.How certainty the predictions are, assuming that the model is correct.

• Comparison with other methods

• The energy minimization method has more parameters, better results

• COVE (Eddy and Durbin, 1994) with lower accuracy

• This shows the significance of the method described here in situations where only a few sequences are known.

Conclusion

• Limitations• Inability to predict pseudoknots.

• Loop and stem lengths are assumed to be geometrically distributed

The nature of the specific SCFG used here

• A good alignment is needed – hard to solve

• The dynamical programming algorithms are relatively slow. [They have a time complexity of O(N3) with respect to the length of the alignment.]

• Possible improvements

1. Profile SCFGs and covariance models predict 2nd structure at the same time as making alignments

2. Modeling base stacking

3. The evolutionary model

4. Reduce the number of parameters for the rate matrix

Conclusion

Thank you !

Have a nice weekend