36
Remote RNA homology detection Sean R. Eddy HHMI Janelia Farm Research Campus Probability theory is nothing but common sense reduced to calculation. Laplace (1819)
Remote RNA homology detection
Sean R. Eddy
HHMI Janelia Farm Research Campus
Probability theory is nothing but common sense reduced to calculation.Laplace (1819)
RNAs conserve both secondary structure and sequence
There are many RNA structures of interest
Wade Winkler and Ron Breaker, ChemBioChem 4:1024 2003
Recognizing homologous RNAs is not easy
RNAs have a lot of information in pairwise correlations
Models before algorithms: a short sermon
Prob(data | model, parameters)
Always write down the probability of everything. - Steve Gull
Probabilistic (Bayesian) inference : no arbitrary scores
DJC MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge, 2003
Single residue scores extend to pairwise residue scores
background frequencies of residue a (or residues a,b)
probability of observing residue a (or residues a,b) ‘here’ in the model (‘here’ = aligned to a particular residue, site, or state)
Steve Altschul, J. Mol. Biol. 219:555, 1991
Formal grammars as models of biological sequences
Noam Chomsky, 1958
An SCFG parse tree corresponds to an RNA structure
David Searls, Am. Scientist 80:579, 1992
Probabilistic models of biological sequences
Goal
optimal alignmentP(sequence | model)
EM parameter estimation
memory complexity:time complexity (general):time complexity (as used):
HMM algorithms(sequence)
ViterbiForward
Forward-Backward
O(MN)O(M2N)O(MN)
SCFG algorithms(RNA structure)
CYKInside
Inside-Outside
O(MN2)O(M3N3)O(MN3)
• we can analyze target sequences with secondary structure models;• but the algorithms are computationally expensive.
Richard Durbin, Sean Eddy, Graeme Mitchison, Anders KroghBiological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids
Cambridge, 1998
Covariance models (profile SCFGs): query construction
Infernal User’s Guide, 2007: http://infernal.janelia.org/
CM is organized on a consensus ‘guide tree’
Infernal User’s Guide, 2007: http://infernal.janelia.org/
Each node contains one or more SCFG ‘states’
Infernal User’s Guide, 2007: http://infernal.janelia.org/
CM state graph looks complex but follows simple rules
Infernal User’s Guide, 2007: http://infernal.janelia.org/
Homologous structures: different parses from same model
P(seq, parse tree | CM) is the product of all transition and emission probabilities used by the parse tree
Infernal User’s Guide, 2007: http://infernal.janelia.org/
Structure, parse, alignment : different views of same data
Covariance models (profile SCFGs): summary
• Query is nonpseudoknotted RNA secondary structure/sequence– either consensus of a multiple RNA alignment, or a single RNA structure
• Position-specific scoring parameters are derived from probabilities – easiest: frequencies of events in a deep alignment (maximum likelihood estimation)– usually: maximum a posteriori estimation from counts and a Dirichlet prior– in the limit of one sequence: position-independent substitution matrix
• Generative probabilistic model assigns P(seq, parse tree | CM), by factorizing into a product of transition (indel) and emission probabilities
– affine gap (gap-open, gap-extend)– position-specific, but 0th order Markov: no stacking correlations
• Now, to be useful, we also need:– algorithm for identifying best alignment given a sequence: the CYK algorithm– algorithm for calculating likelihood P(seq | CM): the Inside algorithm
Dynamic programming algorithms for SCFGs
most states:
bifurcation states:
Recursively calculates log probability thatCM subgraph rooted at v generates subsequence i..j.
This is a 3D dynamic programming lattice,requiring O(ML^2) memory.
Bifurcation calculations cost O(L) per cell,and there are O(ML^2) cells in the lattice:so algorithm is O(ML^3) time worst case.
Most models have few bifurcations, sorunning time is between ML^2 and ML^3in practice.
3D SCFG dynamic programming lattices
answer here:root state 0,i=1, j=L complete sequence
initialize here:end states, length 0 subsequences on diagonal
Bacillus subtilis RNase P example (E. coli query)
C. elegans RNase P (found with human RNase P query)
The glycine riboswitch
A glycine-dependent riboswitch that uses cooperative binding to control gene expression.Mandal et al. (Breaker lab), Science 306:275 (2004)
Memory is no longer a limitation, but time is
A memory-efficient dynamic programming algorithm for optimalalignment of a sequence to an RNA secondary structure.
S.R. Eddy, BMC Bioinformatics, 3:18 (2002)
The divide and conquer algorithm (2002): Myers/Miller extended to 3D SCFG lattices.Memory requirement now O(L^2 log M)
Ways to accelerate CM searches
• custom filtering programs (tRNAscan-SE, Lowe and Eddy, 1997)
• BLAST prefilter (Rfam database does this)
• linear profile-HMM filters, including “rigorous filters” (Zasha Weinberg, Larry Ruzzo)
• extend the BLAST algorithm to 3D (Diana Kolbe, work in progress)
• more generally: banded dynamic programming (various strategies possible)
• query-dependent banding (QDB): Nawrocki and Eddy, 2007
QDB algorithm
QDB recursively calculates the probability that a subgraph rooted at state v willgenerate a subsequence of length d, for all v and d, using the generative model.
Subsequence lengths with negligible probability may then be ignored in DP alignment to any target sequence.
Query-dependent banding (QDB) for faster RNA similarity searches.Eric Nawrocki and Sean Eddy, PLoS Computational Biology, in press (2007)
Examples of QDB bands
Query-dependent banding (QDB) for faster RNA similarity searches.Eric Nawrocki and Sean Eddy, PLoS Computational Biology, in press (2007)
CYK dynamic programming with QDB
Query-dependent banding (QDB) for faster RNA similarity searches.Eric Nawrocki and Sean Eddy, PLoS Computational Biology, in press (2007)
One free parameter: negligible probability mass threshold
Query-dependent banding (QDB) for faster RNA similarity searches.Eric Nawrocki and Sean Eddy, PLoS Computational Biology, in press (2007)
Four- to six-fold acceleration
Query-dependent banding (QDB) for faster RNA similarity searches.Eric Nawrocki and Sean Eddy, PLoS Computational Biology, in press (2007)
with QDB, not far from O(MN),the same complexity as BLAST or Smith/Waterman(albeit with a big constant)
QDB has little effect on sensitivity/specificity
BRAliBase III benchmark
Eva Freyhult, Jonathan Bollback, and Paul Gardner, Genome Research 17:117 (2007)
http://hmmer.janelia.org/
http://infernal.janelia.org/
http://pfam.janelia.org/
http://rfam.janelia.org/soon:first release of Easel,
the code library underlying HMMER and Infernal
Software integration & availability: a final sermon
all freely available; currently GPL,soon to be under the (BSD-like) Janelia Software License
HHMI Janelia FarmNow that scientific research has become a regular profession on the payroll of the state, the observer can no longer afford to concentrate for extended periods of time on one subject, and must work even harder. Gone are the days of yore...
Santiago Ramon y Cajal, 1916
http://selab.janelia.org/
Infernal, RNA homology search Diana Kolbe Eric Nawrocki
HMMER, protein homology search Sergi Castellano Alex Coventry
ncRNA genefinding: Jennifer Davila-Aponte Seolkyoung Jung Elena Rivas
secret agent man: Tom Jones
The Rfam Consortiumled by Sam Griffiths-Jones (Sanger, Cambridge UK)
Zasha Weinberg (Yale)Larry Ruzzo (U Washington, Seattle)
Ron Breaker (Yale)Norm Pace (U Colorado, Boulder)
Mixture Dirichlet priors: base pairs
Query-dependent banding (QDB) for faster RNA similarity searches.Eric Nawrocki and Sean Eddy, PLoS Computational Biology, in press (2007)
Mixture Dirichlet priors: singlets
Query-dependent banding (QDB) for faster RNA similarity searches.Eric Nawrocki and Sean Eddy, PLoS Computational Biology, in press (2007)
