RNA$2 nd $structure$predic0on

Transcription

1 RNA$2 nd $structure$predic0on

2 Recall

3 Nucleic Acids - RNA and DNA The carrier of genetic information - The blueprints of proteins

4 Nucleotides Bases Adenine (A) Guanine (G) Cytosine(C) Thymine(T) Uracil (U) Sugars 2'-deoxyribose (in DNA) ribose (in RNA)

5 DNA - deoxyribonucleic acid 5' 3' AGTACG 3' 5' A DNA molecule is two complementary strands of nucleotides DNA: s {A,C,G,T} * RNA: s {A,C,G,U}*

6 The Central Dogma s {A,C,G,T} * s {A,C,G,U} * s {A,C,D,E,F,G,H, I,K,L,M,N,P,Q, R,S,T,V,W,Y} * Everything are strings! A good model of important biology

7 Why? RNA$molecules$can$be$classified$in: messenger$(coding)$rna non?coding$rna trna phenylalanine from yeast tertiary and 2 nd structure The$non?coding$RNAs$have$a$wide$ range$of$func0ons$that$is$(believed$ to$be)$determined$by$its$ter0ary$ structure The$scaffold$for$the$ter0ary$ structure$is$provided$by$the$2 nd $ structure

8 RNA$sequence RNA$(RiboNucleic$Acid)$molecules$are$very$similar$to$DNA$ (DeoxyriboNucleic$Acid)$molecules Each$molecule$is$made$of$a$chain$of$nucleo0des$(bases).$ There$are$only$four$nucleo0des.$ Thus,$the$sequence$(or$primary$structure)$of$the$RNA$ molecule$can$be$represented$as$a$string$over$the$alphabet$ {A,$C,$G,$U} cytosine uracil

9 RNA$2 nd $structure Unlike$DNA,$RNA$is$produced$as$a$single$stranded$molecule$ which$then$folds$to$form$base$pairs$(2 nd $structure) The$typical$base$pairs$are: canonical$(watson$?$crick): A$and$U C$and$G non?canonical: G$and$U RNA$can$have$other$base$pairs$but$they$are$formed$with$ very$low$frequency

10 RNA$2 nd $structure

11 nd RNA$2 $structure

12 RNA$2 nd $structure$representa0on Primary$structure $$Dome U$U$U$G$G$A$U$A$A$A$A Sequence$of$base$pairs {1$T$11,$2$T$10,$3$T$9}$$$ Bracket ($($($.$.$.$.$.$)$)$)$ $$Standard$ $$graphical$ $$representa0on

13 RNA$2 nd $structure$representa0on Vienna format The Vienna format or dot-bracket format is a string notation for a nested RNA structure. An unpaired base is denoted with a dot, a base pair is denoted with an opening and closing bracket. The opening bracket corresponds to the upstream partner, the closing bracket to the downstream partner. The Vienna format cannot denote pseudoknots and is therefore only available as output format. We return a Vienna structure in three lines: a header line starting with a > sign, the RNA sequence on a single line, and the Vienna string on a single line. >Header line AUCGAGAAAUCGAAC..(((...)))...

14 Base$pairs Any$base$can$take$part$in$at$most$one$base$pair Two$base$pairs$can$be$in$one$of$three$configura0ons juxtaposed nested overlapping Overlapping$base$pairs$form$a$pseudoknot A$2 nd $structure$without$pseudoknots$can$be$represented$as$ a$planar$graph

15 RNA$2 nd $structure$predic0on Energy$minimiza0on predict$a$2 nd $structure$of$least$free$energy based$on$primary$structure$only example$nussinov,$zuker's$mfold Compara0ve$structure$predic0on predict$2 nd $structures$for$several$sequences based$on$a$prior$(reliable)$alignment Probabilis0c$models example$scfgs$(stochas0c$context$free$grammars)

16 Nussinov Minimum$energy$ $maximum$number$of$base$pairs Calculate$best$structure$for$small$subsequences$and$work$ outwards$to$larger$and$larger$subsequences Nota.ons seq the$rna$sequence$ $(over$alphabet${a,$c,$g,$u})$$$$ seq[i,6j] the$rna$sequence$from$posi0on$i$to$j str the$best$2 nd $structure$for$seq$ $(over$alphabet${(,$),$.}) str[i,6j]6 the$best$2 nd $structure$for$seq[i,6j] score[i,6j]$ the$number$of$base$pairs$in$str[i,6j]

17 Nussinov i$unpaired$and$str[i+1,6j] $$ $$ $$ $$ $$ $$ str[i,6k]$and$str[k+1,6j]$ for$some$i$<$k$<$j

18 Nussinov j i < score [i, j] ={ {score [i + j] score [i, j ] max score [i + j ] + seq [i] seq [ j ] max i < k < j (score [i, k ] + score [k + j])

19 Nussinov j i < score [i, j] ={ {score [i + j] score [i, j ] max score [i + j ] + seq [i] seq [ j ] max i < k < j (score [i, k ] + score [k + j]) Space?$ Time?$

20 Nussinov j i < score [i, j] ={ {score [i + j] score [i, j ] max score [i + j ] + seq [i] seq [ j ] max i < k < j (score [i, k ] + score [k + j]) Space?$O(n 2 ) Time?$O(n 3 )

21 Nussinov j i < score [i, j] ={ {score [i + j] score [i, j ] max score [i + j ] + seq [i] seq [ j ] max i < k < j (score [i, k ] + score [k + j]) Could$be$BP?Score(seq6[i],$seq[j]) Space?$O(n 2 ) Time?$O(n 3 )

22 Nussinov score [i, j ] = { j i < {score [i + j ] score [i, j ] max score [i + j ] + seq [i ] seq [ j ] max i < k < j (score [i, k ] + score [k + j ])

23 Nussinov score [i, j ] = { j i < {score [i + j ] score [i, j ] max score [i + j ] + seq [i ] seq [ j ] max i < k < j (score [i, k ] + score [k + j ])

24 Backtracking score [i, j ] = ( 4$$ ( 3$$ ( 2$$.$$( 1$$.$$) 1$$ ) 2$$ ) 3$$ ) 4$$. { j i < {score [i + j ] score [i, j ] max score [i + j ] + seq [i ] seq [ j ] max i < k < j (score [i, k ] + score [k + j ])

25 Backtracking score [i, j ] = ( 4$$ ( 3$$ ( 2$$.$$( 1$$.$$) 1$$ ) 2$$ ) 3$$ ) 4$$. { j i < Time?$ {score [i + j ] score [i, j ] max score [i + j ] + seq [i ] seq [ j ] max i < k < j (score [i, k ] + score [k + j ])

26 Backtracking score [i, j ] = ( 4$$ ( 3$$ ( 2$$.$$( 1$$.$$) 1$$ ) 2$$ ) 3$$ ) 4$$. { j i < Time?$O(n 2 ) {score [i + j ] score [i, j ] max score [i + j ] + seq [i ] seq [ j ] max i < k < j (score [i, k ] + score [k + j ])

27 Nussinov vs ($($($.$.$.$.$.$)$)$) ($($($.$($.$)$)$)$)$.

28 True Nussinov VS