1. RNA Secondary Structure Prediction Using Stochastic Context –Free Grammar And Evolutionary History
B. Knudsen and J. Hein
Department of Genetics and Ecology
The institute of Biological Sciences
University of Aarhus, Denmark
Presented by Jing Cui
Nov.22, 2002

2. Outline of the Lecture Introduction Results Algorithms Implementation
The grammar
Probabilities of columns
Probabilities of an alignment
The full model
Implementation
The database
Frequencies
Mutation rates
Grammar parameters
Results
The test sequences
Using related sequences
Neglecting phylogeny
Weight of results
Comparison with other methods
Conclusion
The limitations
The improvements

3. 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 sequences
Covariance methods (Eddy and Durbin, 1994)
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

4. 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
Difference
2nd structure in RNA are not local, like in proteins
SCFGs instead of HMM is used here
Limitation
SCFGs are unable to model crossing interactions, thus pseudoknots cannot be predicted

5. Algorithm Input an alignment of RNA sequences Output
single common structure for the sequences
The model
The SCFG
The evolutionary model

6. The grammar a set of variables; some terminal and non-terminal

8. 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
Reversibility of mutations
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)

9. 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

10. 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:

11. The full model
The 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

12. 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)

13. 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.

14. 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

17. 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 !!!

18. Results The test sequences 4 bacterial RNase P RNA seq.
alignment: 385 columns
pair-wise sequence identities 65-92%

19. Pseudoknot 68-76 and 368-361; 18-12 and 370-364
At least 22 positions wrongly predicted in each sequence

20. Using related sequences

22. 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.

23. 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.

24. 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.]

25. Conclusion Possible improvements
Profile SCFGs and covariance models predict 2nd structure at the same time as making alignments
Modeling base stacking
The evolutionary model
Reduce the number of parameters for the rate matrix

26. Thank you !
Have a nice weekend 