Improving Free Energy Functions for RNA Folding

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Improving Free Energy Functions for RNA Folding

• RNA Secondary Structure Prediction

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Why RNA is Important

• Machinery of protein construction
• Catalytic role in cells
• May be possible to destroy specific sequences of
  RNA (to interrupt protein production)
• RNase P (Cech/Altman c.1981)

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RNA Structural Levels
Secondary http//anx12.bio.uci.edu/hudel/bs99a/l
ecture21/lecture2_2.html Tertiary
http//www.leeds.ac.uk/bmb/courses/teachers/trnbal
ls.html
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Abstracting the problem
A
G
C
G
C
A
U
C
Zuker (1981) Nucleic Acids Research 9(1) 133-149
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Why it is hard

• Large search space (hard to enumerate)

Hofacker et al. (1994) Monat. Chem. 125 167-188
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Why it is hard

• Secondary structure does not exist.
• Unlike proteins
• Putative structures (prone to revision)
• Quality of Energy Functions
• Discussed later

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Current Algorithms

• Single-Strand
• Minimum Free Energy (Zuker et. al. 1981)
• Partition Functions (McCaskill 1990)
• Comparative Sequence Analysis
• Max. Weighted Matching (Nussinov et. al. 1978)
• Stochastic CFG (Sakikibara et. al. 1994)
• Phylogenetic Trees (Gulko et. al. 1995)
• Statistical Significance (Noller Woese, early
  80s)

See proposal for references
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MFE / Tinoco Hypothesis
The free energy of a secondary structure equals
the sum of the free energies of the loops and
stacked pairs
Tinoco et al. (1971) Nature 230 362-367.
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Proposed System
AAUCG...CUUCUUCCA
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GA (E)
3
1
MFE (E)
AAUCG...CUUCUUCCA
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Step I - Calc MFE Structure

• Given a sequence ? apply the MFE algorithm
• Generates secondary structure S?

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Step II - Structural Similarity

• Given a database of experimentally verified RNA
  structures
• Let Q? be the database structure most similar to
  S?
• Based on RNase P Database (Brown 1999)

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Step III - Construct E

• Create a new energy function

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Discussion on E

• E has global information
• Global information precludes the use of dynamic
  programming (MFE, Partition)
• Leaves (stochastic) combinatorial optimization
• Gradient Descent (no ?E/?S)
• Genetic Algorithms / Simulated Annealing

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Step IV - Genetic Algorithm

• RNA Structural Prediction by GA
• Input sequence ?
• Output structure that maximizes E for ?
• Steady State Genetic Algorithm
• Pseudoknots forbidden (conflicts)
• Fitness -E
• Effect of Similarity(Q?, S?) diminishes with each
  generation (pseudo-SA).

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Genetic Algorithm - Repn.

• Stem-loop representation (Chen et. Al. 2000)
• Window method (EMBOSS Palindrome)

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Genetic Algorithm - Operators

• Mutation
• Add stem from stem pool to a child
• Crossover

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Preliminary Results

• E does not lead to drastic speed up
• Genetic algorithm is very slow
• If initial population generated randomly from
  stem pool.
• Use suboptimal folding for initial population.

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Preliminary Results Explained

• The real structure is usually very similar the
  Tinoco optimal structure.
• View E as a way of choosing among the suboptimal
  structures.

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Future Work

• More testing on the entire RNase P Database (gt
  400 structures)
• Tune E
• Accuracy comparison to MFE and Partition Function
  Algorithms
• Parallelize genetic algorithm

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• END