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.
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
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.
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} +
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.
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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