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Algorithmics of -1 frameshift RNA sequences Michaël Bekaert 1, Laure Bidou 1, Alain Denise 1,2, Guillemette Duchateau-Nguyen 1, Céline Fabret 1 Jean-Paul Forest 2, Christine Froidevaux 2, Isabelle Hatin 1, Jean-Pierre Rousset 1, Michel Termier 1 1 IGM (Institut de Génétique et Microbiologie) 2 LRI (Laboratoire de Recherche en Informatique) Université Paris-Sud, Orsay

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Flow of genetic information transcription translation replication CATATGGATTACATGGTCTAAGAT DNA sequence CAU AUG GAU UAC AUG GUC UAA GAU RNA sequence Protein

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Translation CAU AUG GAU UAC AUG GUC UAA GAU 5’3’ mRNA

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Translation CAU AUG GAU UAC AUG GUC UAA GAU The ribosome reads bases by triplets (or codons) from a START codon ribosome 5’3’

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Translation CAU AUG GAU UAC AUG GUC UAA GAU The ribosome synthetizes one amino-acid per codon 5’3’

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Translation CAU AUG GAU UAC AUG GUC UAA GAU 5’3’

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Translation CAU AUG GAU UAC AUG GUC UAA GAU 5’3’

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Translation CAU AUG GAU UAC AUG GUC UAA GAU 5’3’

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Translation CAU AUG GAU UAC AUG GUC UAA GAU 5’3’

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Translation CAU AUG GAU UAC AUG GUC UAA GAU The synthesis goes on until a STOP codon is read 5’3’ 1 mRNA gives 1 protein

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Experimental fact Some mRNAs encode two distinct proteins with same beginning

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Programmed -1 frameshifting Non-deterministic event ORF1a START 0 STOP 0 0 phase STOP -1 ORF1b -1 phase usual translation -1 frameshift 1 mRNA gives 2 distinct proteins with accurate ratio

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Typical -1 frameshift site [Brierley, 1989] NNX XXY YYZAUG PSP S1 L1L1 S2S2 L2L2 L’1L’1 Slippery sequence Secondary structure 5’ 3’

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IBV frameshift site UAU UUA AACAUG S1 S2 Slippery sequence Pseudoknot 5’ 3’ GGGUAC UGACGAUGGGGUGACGAUGGGG GCUGAUACCCCGCUGAUACCCC A G G C U C G U C C G A G C G UUGC GAAA

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Translation with frameshift UAU UUA AAC GGG UACAUG5’ 3’ UGACGAUGGGGUGACGAUGGGG GCUGAUACCCCGCUGAUACCCC A G G C U C G U C C G A G C G UUGC GAAA

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Translation with frameshift UAU UUA AAC GGG UAC5’ 3’ UGACGAUGGGGUGACGAUGGGG GCUGAUACCCCGCUGAUACCCC A G G C U C G U C C G A G C G UUGC GAAA

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Translation with frameshift UAU UUA AAC GGG UAC5’ 3’ UGACGAUGGGGUGACGAUGGGG GCUGAUACCCCGCUGAUACCCC A G G C U C G U C C G A G C G UUGC GAAA -1 shift

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UA UUU AAA CGG GUA CGG GGU AGC AGU Translation with frameshift 5’ 3’

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UA UUU AAA CGG GUA CGG GGU AGC AGU Translation with frameshift 5’ 3’

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UA UUU AAA CGG GUA CGG GGU AGC AGU Translation with frameshift 5’ 3’

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UA UUU AAA CGG GUA CGG GGU AGC AGU Translation with frameshift 5’ 3’

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Translation : mRNA & ribosome Adapted from Frank et al. by Giedroc et al.

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Biological or random sequences Folded sequences In silico and in vivo validation Folding Wild-type folded sequences Folded and sorted sequences New FS sites Mutant sequences Score matrix RulesVoting Model

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Search for FS sites: the easy part Slippery sequence in -1 phase with START codon ATG N NNN NNXXXYYYZ

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Search for FS sites : the not-so-easy part Search of secondary structure AGGACCT ? Folding

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Example of a folded structure Picture from Lyngso and Pedersen 2000

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Folding algorithms Aligned sequences Zuker’s Rivas & Eddy’s

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Algorithms that require aligned sequences Not relevant to our problem since we only fold one sequence at the same time

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Folding using Zuker’s model Tractable model based on additive energy minimization One sequence gives one folding Bases are either single-stranded or paired with a single other base Matching interactions must not cross (i.e. pseudoknots are not allowed)

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Base-pairs interactions nested disjoint crossing

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Zuker’s algorithm Does not find our pseudoknots, even if the two stems are looked for separately

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Seeking pseudoknots Rivas and Eddy 1999 –extends Zuker’s algorithm –accounts for pseudoknots using a more complex recursion (steep time and memory requirement) –does not work for our problem, probably due to lack of biological experiments to set the thermodynamical parameters

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Orpheo Seeks stems separately with adequate parameters

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Score matrix ATCG A -6 2-6-6 T 2-6-6 0 C -6-6-6 4 G -6 0 4-6

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Smith-Waterman algorithm AGGACCT A000002 G00460 G0 1040 A00 2 C00 C0 T

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Smith-Waterman algorithm AGGACCT A000002 G00460 G0 1040 A00 2 C00 C0 T AGGACCT GGAGGA CCTCCT A

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Finding pseudoknots anyway Scores learnt on wild-type sequences –GC different from CG –GC score in stem 1 = #GC in stem 1 / stem 1 length Accounts for bulges and gaps Needs threshold to select relevant stems

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Typical -1 frameshift site [Brierley, 1989] NNX XXY YYZAUG PSP S1 L1L1 S2S2 L2L2 L’1L’1 Slippery sequence Secondary structure 5’ 3’

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Finding pseudoknots anyway 20 nt 50 nt S1.5’S1.3’ S1.5’S1.3’ HLfrom L2 S2.5’S2.3’

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Orpheo Finds known sites Fast : 2 minutes on both strands of S. cerevisiae Distinguishes 5’ from 3’ and so implicitly accounts for triple interactions Yields around 200 candidates in yeast (including one with 13% efficiency)

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Biological or random sequences Folded sequences In silico and in vivo validation Folding Wild-type folded sequences Folded and sorted sequences New FS sites Mutant folded sequences Score matrix RulesVoting Model

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Example of a rule if SP length 5 and number of Gs in S1.5’ bottom half 3 and number of Gs in S1.5’ 4 and %T in S2.5’ 30 and %C in S2.3’ 75 or % G in S1.5' bottom half 80 and %C in L1 45 or SP length 5 and S1.3' length 6 and %C in S1.3' or SP length 5 and number of Gs in S1.5’ bottom half 3 and %C in S1.3’ 70 and %G in S2.3’ 45 or number of As in S1.5' = 0 and number of As in S2.3' = 0 then %FS 5

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Biological or random sequences Folded sequences In silico and in vivo validation Folding Wild-type folded sequences Folded and sorted sequences New FS sites Mutant folded sequences Score matrix RulesVoting

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Refining the model: Machine learning To identify relevant properties that characterize FS sites Disjunctive learning: all sequences do not frameshift for the same reasons [Giedroc et al., 2000] (or don’t they ? [Michiels et al. 2001])

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Covering and prediction If SP length 5 and number of G in S1.5’ bottom half 3 and number of G in S1.5’ 4 and %T in S2.5’ 35 and %G in S1.5’ 75 then FS rate 5% Covering of examples: 70 % Examples predicted in test set:80 % Counterexamples in test set: 0 %

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Search for protein patterns Goal: to find new frameshift sites outside the known consensus ORF 1 START 0 STOP 0 0 phase STOP -1 ORF 2 -1 phase known proteic patterns

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Validation on random sequences Hypothesis : biologically relevant sequences have been selected and thus are not random If something is relevant, it is apart from the means

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Examples of rule 1 SP length 5 and number of G in S1.5’ bottom half 3 and number of G in S1.5’ 4 and %T in S2.5’ 30 and %C in S2.3’ 75 70 % SP length 5 and number of G in S1.5’ bottom half 3 and %C in S1.5’ 45 and number of T in S2.5’ 1 80 % SP length 5 and S1.5' length 6 and number of G in S1.5’ 4 and number of T in S2.5' 1 and %C in S2.3’ 70 80 %

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Examples of rule 1 SP length 5 and number of G in S1.5’ bottom half 3 and number of G in S1.5’ 4 and %T in S2.5’ 30 and %C in S2.3’ 75 70 % SP length 5 and number of G in S1.5’ bottom half 3 and %C in S1.5’ 45 and number of T in S2.5’ 1 80 % SP length 5 and S1.5' length 6 and number of G in S1.5’ 4 and number of T in S2.5' 1 and %C in S2.3’ 70 80 %

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Experimental results published in Bioinformatics A COMPLETER

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Conclusion and perspectives Spacer: –correlation between primary sequence and FS rate has been established –systematic experimentation going on Learning: –relevant rules –experimentation enriches data –quantitative approach (get real…)

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Example of data IBV family= Coronaviridae genus= Coronavirus name= Infectious avian bronchitis virus gene1= ORF1a gene2= ORF1b article= Review Brierley 1995 wild type= yes modified part= none P= {UUUAAAC} SP= {GGGUAC} S1.5'= {GGGGUAGCAGU} L1= {G} S2.5'= {GAGGCUCG} L1'= {} S1.3'= {GCUGAUACCCC} L2={UUGCUAGUGGAUGUGAUCCUGAUGUUGUAAAG} S2.3'= {CGAGCCUU} S1= { stem1= GGGGTAGCAGT stem2= CCCCATAGTCG stability= -20,7 } S2= { stem1= GAGGCTCG stem2= TTCCGAGC stability= unknown } global stability= unknown definite secondary structure= yes L1.folding= no L1'.folding= no L2.folding= no efficiency= RRL 30% efficiency= XO 30%

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Example of rules if SP length 5 and number of Gs in S1.5’ bottom half 3 and number of Gs in S1.5’ 4 and %T in S2.5’ 30 and %C in S2.3’ 75 or % G in S1.5' bottom half 80 and %C in L1 45 or SP length 5 and S1.3' length 6 and %C in S1.3' or SP length 5 and number of Gs in S1.5’ bottom half 3 and %C in S1.3’ 70 and %G in S2.3’ 45 or number of As in S1.5' = 0 and number of As in S2.3' = 0 then %FS 5

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GloBo: main ideas Takes each example as a seed Agglomerates other examples in subset if least general generalization does not cover counterexamples Heuristically selects subsets to cover all examples

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