Geometric Crossovers for Supervised Motif Discovery

1
Geometric Crossovers for Supervised Motif
Discovery

• Rolv Seehuus
• NTNU

2
Motivation and Scope

• Try out the applicability of the geometric
  framework, on a supervised motif discovery
  problem
• Compare its merits to a previously used operator.
  
• In practice, we test on a very easy problem
• that existing software can solve easily
• Value as test case
• Building block for more complex motif discovery
  problems, that current algorithms can not solve
  satisfactory

3
Motif Discovery

• Has become a standard problem in bioinformatics
• Given a set of sequences, figure out what is
  special with it
• by eliciting motifs in the dataset
• Differing by
• Motif model
• Learning algorithms
• Scoring functions

4
The Standard Approach

• Do analysis of the positive set of sequences
• background distribution
• information content
• statistical significance
• Report motif

5
Motif discovery as a classification problem

• Always at least two datasets The positive, and
  the rest
• Choose a negative dataset
• Report motifs best suited to discriminate
• No need to learn a background model
• The statistical significance of the motif can be
  given
• Discriminative motif discovery has received
  increased attention lately

6
Classification problem

• Protein sequences, from the SwissProt database
• Classified according to protein family (as
  specified in the Prosite database)
• Selected six families, that previously have been
  shown to be hard to classify under similar
  circumstances.
• Some of the families can be said to have an
  overrepresented motif as the ones we can train on

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The Potential Negative Data Set

• Huge, compared to the negative
• Quite common in bioinformatics, and an
  interesting problem to cope with in its own right
• In field
• randomly generated sequences
• one set of randomly selected sequences
• random rearrangement of the positive sequences
  (data not shown)
• The best practice was to select the samples
  randomly from the negative set each generation,
  so that their size matches the positive set.

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Motif Model

• Twenty amino acids
• Wildcard

C...C.C..C DMEGACGGSCACSTCHVIVDP
Motif match, positive sequence
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Operators on Motifs

• Unit edit move as mutation
• Mut(A) Insert, Delete or Replace a token
• Substring Swapping Crossover (for comparison)
• Two-point Geometric Crossover

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Geometric Crossover

• Search space have a metric
• Mutation is a move in search space
• Crossover yield children found on the shortest
  path between the parents in search space
• Successfully applied to other problems

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Geometric Crossover for Motifs

• View motifs as sequences
• Basic assumption The edit distance is a good way
  to move around in motif space
• A crossover based on the edit distance, should
  yield a good crossover for motif discovery
• We (arbitrarily) choose unit costs for
  insertions, deletions and substitutions

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Sequence Alignment

• Alignment put spaces (-) in both sequences such
  as they become of the same length
• Seq1 agcacac-a
• Seq2 a-cacacta
• Score 2
• An Optimal alignment is an alignment with minimal
  score
• The score of the optimal alignment of two
  sequences equals their edit distance
• There often are multiple optimal alignments

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Homologous Crossover

1. Pick an optimal alignment for two parent
   sequences
2. Generate a crossover mask as long as the
   alignment
3. Recombine as traditional crossover
4. Remove dashes from offspring

Child1 BANANAS Child2 ANANA
Mask 1101100 Seq1 BANANA- Seq2
-ANANAS SeqA BANANAS SeqB -ANANA-
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Experiments

• Two crossovers with same parameters, and mutation
  only
• Ten fold cross validation
• Partitioned datasets in ten pieces
• Trained on 9/10ths
• Tested the best motif on the remaining test set
• Trained on randomly selected subset of SwissProt
• Tested on entire SwissProt
• Fitness Scaled Pearson correlation of confusion
  matrix

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Dynamic behavior during evolution
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Maximum Values
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Max
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Cytochrome

• Include the following fragment of a highly
  conserved motif CCH
• Which geometric crossover find
• While substring swapping finds CH
• Conservation of length keeps us in the correct
  ballpark
• CH representa local maximum for substring swap

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Ferredoxin

• Contains the following motif C..C..C...CPH
• Which Substring Swap finds
• While Geometric Crossover dont
• Conservation of length keeps us from finding the
  correct motif

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Population Means
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Means
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Classification Performance
Medians, of 10 experiments, for each family
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Classification Performance - II

• Similar for all operators
• Maybe a slight advantage, for the geometric
  crossover if we have
• A highly conserved motif exist
• A ballpark guess on motif length
• Surprisingly, mutation frequently outperforms the
  other operators

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Concluding remarks

• The geometric operator is promising - need work
• It is more length preserving than substring swap
• The geometric operator need a good guess on motif
  length
• Edit move might not be optimal for motif
  discovery?
• even though, it for some problems shows merit.
• Our initial assumption imply an
  insertion/deletion equally often as replacement
  in sequence data
• we are WAY off on that parameter

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Future Work

• Synthetic data with known parameters
• Include character classes and within motif gaps
  in representation
• Modules (composite motifs)
• Expand to position weight matrixes