Improving Free Energy Functions for RNA Folding

RNA Secondary Structure Prediction

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)

RNA Structural Levels

Primary

AAUCG...CUUCUUCCA

Secondary Tertiary

Secondary: http://anx12.bio.uci.edu/~hudel/bs99a/lecture21/lecture2_2.htmlTertiary: http://www.leeds.ac.uk/bmb/courses/teachers/trnballs.html

Abstracting the problem

U

C

C

A G

G

A

C

Zuker (1981) Nucleic Acids Research 9(1) 133-149

Why it is hard

n

nn

E

enOkn

n

8.1]ψ[

)(1

ψ

mer- for RNA sequencessecondary ofnumber ψ

n

5.12/3n

n

Hofacker et al. (1994) Monat. Chem. 125 167-188

• Large search space (hard to enumerate)

Why it is hard

• Secondary structure does not exist.– Unlike proteins– Putative structures (prone to revision)

• Quality of Energy Functions– Discussed later

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 80’s)

See proposal for references

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.

Proposed System

SecondaryStructures

MFE(E)

GA(E’)

AAUCG...CUUCUUCCA

AAUCG...CUUCUUCCA

1

2

3

Step I - Calc MFE Structure

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

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)

Step III - Construct E’

• Create a new energy function:

step)next (see generation

]1,0( where

SES,1

SE'

n

QSimilarityn

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

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).

Genetic Algorithm - Repn.

• Stem-loop representation (Chen et. Al. 2000)

– Window method (EMBOSS Palindrome)

23 52

(23 52 3 3.2)

startend

length

weight

Genetic Algorithm - Operators

• Mutation– Add stem from stem pool to a child

• Crossover

P1

P2

C1

C2

Fit stems of P2 into C1 or C2 randomly.

Placement must be conflict free.

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.

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.

Future Work

• More testing on the entire RNase P Database (> 400 structures)

• Tune E’

• Accuracy comparison to MFE and Partition Function Algorithms

• Parallelize genetic algorithm

END