lecture11_S2009

lecture11_S2009 - Grammatical Modeling of RNA Secondary...

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Grammatical Modeling of RNA Secondary Structures 18.417 Jérôme Waldispühl, Department of Mathematics, MIT
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RNA secondary structure Set of base pairs = {(A,U),(G,C),(G,U)} The secondary structure is the ensemble of base pairs of the structure.
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RNA secondary structure cgcggggttgatataatataaaaaataat aaataataataataataattatcatcatt tccgacccatattataataatacgggttg gaaatatagatataatatttattatattga tataatacatatatataagttagaggaaa tgttgtttaaaggttaaactgttagattgc aaatctacacatttagagttcgattctctt catttcttatatatatactacccacgcg Primary structure Secondary structure Tertiary structure Central assumption: RNA secondary structure forms before the tertiary structure. Secondary structure prediction is an important step toward 3D structure prediction.
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RNA secondary structure elements
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Energy model: Stacking base pairs Base stacking interactions between the pi orbitals of the bases' aromatic rings contribute to stability. GC stacking interactions with adjacent bases tend to be more favorable. Note: Stacking energy are orientated. 5’ - CG - 3’ 3’ - GC - 5’ 5’ - GC - 3’ 3’ - CG - 5’
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Formal Languages Example: V T ={a,b}, V N ={S}, P={S aSb | ε } L = {ab, aabb, aaabbb, …} S aSb aaSbb aaaSbbb aaa ε bbb aaabbb. A formal language is a set of words (string of letters belonging to an alphabet) generated by a formal grammar. Definition (grammar): G={V T ,V N ,P,S} • V T is a set of terminals (alphabet), • V N is a set of non-terminals (not appearing in the language), • P is a set of production rules α→β with α , β in (V T U V N ) * , • S is the axiom.
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Context-Free Grammars Definition (context-free grammar): G={V T ,V N ,P,S} • V T is a set of terminals (alphabet), • V N is a set of non-terminals, • P is a set of production rules of the form A →α , • S is the axiom. A formal language is a set of words (string of letters belonging to an alphabet) generated by a formal grammar.
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Context-Free Grammars The sequence of the derivation rules is represented as a derivation tree. P = S SS S ( S ) S S + S S S S S x | y | z V T = {x,y,z} V N = {S} +
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Grammatical Modeling RNA secondary structures can be represented using well- bracketed words. GUUGGUUUCUGAACGCCCCUUCAA .((((. ..)).((.(. ..))).)) The language of well-bracketed words is context-free. Thus we can use a context-free grammar to model the secondary structure.
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Grammatical Modeling 1. Non-terminals represent secondary structure elements, 2. Terminals annotate the position of nucleotides in structure.
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Loop decomposition Base pairs?
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This note was uploaded on 06/16/2011 for the course MATH 18.417 taught by Professor Jérômewaldispühl during the Spring '11 term at MIT.

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lecture11_S2009 - Grammatical Modeling of RNA Secondary...

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