lecture8_S2009 - 18.417 Introduction to Computational...

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18.417: Introduction to Computational Structural Biology Evolution of RNA sequences Jerome Waldispuhl Department of Mathematics, MIT
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Principles Figure from (Cowperthwaite&Meyers,2007) Central assumptions: • The structure of a sequence is only determined by its (minimum) free energy. •The structure determines the function. •Evolution tends to preserve and optimize the function.
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Sequence evolution Figure from (Gobel,2000) For short sequences, the set of evolutionary operations can be restricted to: • Insertion • Insertion/Deletion • Mutation We also limit their effect to single nucleotides.
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Modeling the mutation landscape Figure from (Gobel,2000) When the length of the sequence is fixed, the set of operations can be restricted to mutations. The mutation landscape is represented with Hamming graphs, where nodes are the sequences and edges connect sequences differing from one single nucleotide (i.e. 1 mutation).
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Fitness model Figure from (Cowperthwaite&Meyers,2007) Objective: Evaluate the dynamic of the evolution of shapes. Requirement: a metric to compare a predicted structure and a target shape. Models: • simple: The predicted structure is the m.f.e. structure. • plastic: Suboptimal structures can be considered.
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Structure comparison Hamming distance: Base pair distance: Figure from (Schuster&Stadler,2007) Base pair distance is the standard. It corresponds to the number of base pairs we have to remove and add to obtain one structure from the other. Both metrics have to be applied on structures of equal length.
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Neutral network Figure from (Cowperthwaite&Meyers,2007) • A structure is associated to each node (sequence) of the Hamming graph. • Nodes connected and labeled with the same structure form a neutral network. • Introduced by P.Schuster and Vienna group in 1992. Genotype network Phenotype network
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Compatible mutations and structures Figure from (Gobel,2000) • Mutations in neutral networks must conserve the phenotype. • But it is hard to decide if a mutation conserve the m.f.e. structure and hence the phenotype. • The networks have been explored through simulations. • The number of acceptable structures can be recursively computed: Hairpin minimum length ± required and length of stacks bounded ² .
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Role of neutral networks Figure from (Gobel,2000) • Evolution tends to select mutations improving the structure.
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