Modeling RNA motifs by graph-grammars

Madison (ROC)2 MC-Tools: Functions ( MC-Annotate 3-D ) -> graph ( MC-Cycles graph ) -> [ NCM ] ( MC-Seq graph ) -> [ sequence ] ( MC-Fold sequence ) -> [ graph ] ( MC-Cons [ ( sequence, [ graph ] ) ] ) -> [ graph ] ( MC-Search ( graph, [ 3-D ] ) -> [ 3-D ] ( MC-Sym graph ) -> [ 3-D ]

Madison (ROC)3 MC-Tools: Objects (rat 28S rRNA sarcin/ricin stem-loop) Sequence: GGGUGCUCAGUACGAGAGGAACCGCACCC Graph: Nucleotide cyclic motifs: 3-D structure: Szewczak et al. PNAS(USA) 1993 Lemieux & Major NAR 2006 Parisien, Thibault & Major (in prep.) ( MC-Fold sequence ) -> [ graph ] ( MC-Sym graph ) -> [ 3-D ]

Madison (ROC)4 Graph ( MC-Annotate 3-D ) -> graph Gendron, Lemieux & Major JMB 2001 Lemieux & Major NAR 2002 Leontis & Westhof RNA 2001

Madison (ROC)5 Shortest Cycle Basis C1 C5 C4 C3 C2 X1X1 X2X2 X3X3 X4X4 Y1Y1 Y2Y2 Y3Y3 5’ 3’ ( MC-Cycle graph ) -> [ NCM ] Horton SIAM J Comp 1987 St-Onge et al. NAR 2007

Madison (ROC)6 The Nucleotide Cyclic Motifs (NCM) i.Embrace indistinctly all base pairing types (Watson-Crick and others) ii.Precisely designate how any nucleotide in the sequence relate to others iii.Are joined through a common base pair (context). This helps us predict coherent chains of NCMs and to project them in 3-D. Tentative definition of a motif: “ordered” chain of NCMs. iv.Recur within and across all RNAs v.Are short (< 10 nts; most of 3 to 5 nts) vi.Compose the classical motifs (cf. GRNA tetraloop; sarcin/ricin motif, etc). There are exceptions (cf. AA platform). Lemieux & Major (2006) NAR 34:2340 Parisien, Thibault & Major (in prep.)

Madison (ROC)7 Aim We want a computational model that can encode the valid sequences and structural features of RNA motifs. Hypothesis: A relation between the sequence and the structure of RNA motifs exists.

Madison (ROC)8 Graph Grammars A graph grammar is to a set of graphs what a formal generative grammar is to a set of strings, i.e. a precise and formal description of that set. A graph-grammar consists of a set of rules or productions for transforming graphs. Formally, a graph-grammar, H = {N, , P}, consists of a set of non ‑ terminal symbols, N, a set of terminal symbols, , and a set of production rules, P. Hypothesis: NCMs are “independent” building blocks. Nagl Computing 1976 Nagl In H. Ehrig et al., eds 1987 St-Onge et al. NAR 2007

Madison (ROC)9 ⇒ Sarcin/Ricin Graph Grammar N = {C1, C2, … C5}, the set of NCMs:  = {S1, S2, … S5} the sets of sequences for each NCM: P is a set of consistent assignment of the sequences in  to the NCMs in N (production rules): ARNt levure 23S H. marismortui 16S E. coli ⇒ ⇒ St-Onge et al. NAR 2007

Madison (ROC)10 Sarcin/Ricin Building Blocks C1 : Theoretical : 256 (16 x 16) IMs : 120 (10 x 12) PDB : 7 C2 : Theoretical : 64 (16 x 4) IMs : 40 (10 x 4) PDB : 5 Theoretical : 16 IMs : 10 PDB : 15 A AA U U A A U A C3 : Theoretical : 64 (16 x 4) IMs : 56 (14 x 4) PDB : 2 C4 : Theoretical : 256 (16 x 16) IMs : 160 (16 x 10) PDB : 3 C5 : Theoretical : 64 (16 x 4) IMs : 40 (10 x 4) PDB : 8 A GU G A G U A G A St-Onge et al. NAR 2007

Madison (ROC)11 ( MC-Seq sarcin-ricin-graph ) -> [ sequence ] Sequences supported by the NCMs in the PDB: AGUA-GAAAGUA-AAA GGUA-GAAGGUA-AAA If we remove the instances of the sarcin/ricin motifs ( MC-Search ( sarcin-ricin-graph, [ PDB ] ) ) -> [ 3-D ] Then, the same four sequences are supported => NCMs are found outside the sarcin/ricin context Larose et al. (in prep.) St-Onge et al. NAR 2007

Madison (ROC)12 Graph Grammar Parsing Westhof (personal comm.) St-Onge et al. NAR sequences aligned according to E. coli 23S rRNA structure; site /

Madison (ROC)13 MC-Seq PDB Alignement: 5S, 16S, 23S AGUA-AAA AGUA-GAA GGUA-GAA GGUA-AAA AAUA-AAA AAUA-GAA ACUA-AAA ACUA-GAA ACUA-GAC AGUA-AAC AGUA-CAA AGUA-GAC AGUA-GAU AGUA-GCC AGUA-GGG AGUA-GUG AGUC-GAA AUUA-GAA CGUA-GAA GAUA-GAA GGUA-GAU GUUA-GAA UGUA-GAA UGUA-GAC Isostericity matrices sequences Validation (MC-Seq vs. PDB vs. Alignment) St-Onge et al. NAR 2007

Madison (ROC)14 Perspectives We want to develop a version of MC-Seq that would be useful during the alignment process. PDB does not seem to contain enough structural information yet. To avoid too many sequences, the NCMs (context) are necessary. Two more things need to be considered…

Madison (ROC)15 Sarcin/Ricin (Sequence/Structure Space Is Not Simple) St-Onge et al. (in prep.)

Madison (ROC)16 Modeling In 3-D Might Be Necessary Alignment AUUA-GAA (0.9 Å ) MC-Fold CAUU-AAG (2.1 Å ) St-Onge et al. NAR 2007

Madison (ROC)17 Acknowledgments Martin Larose (Res. assistant) Philippe Thibault (Res. assistant) Patrick Gendron (Res. assistant) Romain Rivière (Postdoc, CS) Véronique Lisi (Ph.D. Molecular Biology) Marc Parisien (Ph.D. Computer Science) Emmanuelle Permal (Ph.D. Bioinformatics) Karine St-Onge (Ph.D. Computer Science) Louis-Philippe Lavoie (M.Sc. Bioinformatics) Maxime Caron (M.Sc. Bioinformatics) Caroline Louis-Jeune (M.Sc. Bioinformatics) Montréal: Pascal Chartrand Gerardo Ferberye Sylvie Hamel Sébastien Lemieux Pascale Legault Luc Desgroseillers Kathy Borden Daniel Lamarre Éric Westhof (Strasbourg) Alain Denise (Paris) Dave Mathews (Rochester)