Setting Up a Replica Exchange Approach to Motif Discovery in DNA

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Setting Up a Replica Exchange Approach to Motif
Discovery in DNA

• Jeffrey Goett
• Advisor
• Professor Sengupta

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Protein Synthesis from DNA
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Binding Sites
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Discovering New Binding Motifs
Motif GCTCAG
ATCG GCTCAG CTAG
CACT GATCAG AGTA
TTCC GCTCTG TAAC
GCTA GCTCAA ATCG
Motif Probability Model
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Modeling Motifs in Sequences
Assume Break into N sequences Each sequence has
one instance of motif embedded in random
background Variations of motif by point mutation,
but not insertion or deletion
ATATCCGTA AATCGAGAC TCGATGTGT CCACCTGCA
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Modeling Motifs in Sequences
The Alignment Starting position of motif in
each sequence
AT ATC CGTA A ATC GAGAC TCG ATG TGT CC ACC TGCA
The Motif Probability Distribution Probability
of each letter occurring at each motif position
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Scoring a Model
Log-likelihood score
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Example Models
A TAT CCGTA AAT CGA GAC TCGATG TGT CC ACC TGCA
AT ATC CGTA A ATC GAGAC TCG ATG TGT CC ACC TGCA
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The Gibbs Sampler
that maximizes
We want to find
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The Gibbs Sampler
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The Gibbs Sampler
Times visited
Over time, the frequency distribution approaches
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Optimization Technique
If we assume areas of local maximization
contribute the most during integration to the
local maximizations of
Biasing our search to these areas may discover
the pj,ro values which maximize faster.
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Multiple Gibbs Samplers
By combining results from Gibbs Samplers begun at
random positions, find maximizing sooner
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Replica Exchange/Parallel Tempering
Low-sensitivity samplers which scout out area
periodically swap with high-sensitivity
samplers good at focused searches if swap appears
promising.
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Controlling Sensitivity
Adjust the relative probability of sampling an xi
by adjusting a new parameter in distribution
Large
Small
Search breadth of space
Focused search of region
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Testing the Sensitivity
Running on randomly generated sequences to see
motifs found, different sensitivity samplers
converge to different scores.
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Predicting Convergence Score
Measure of Similarity magnetization
Ex m.5
Configuration Score energy
m0
m0
m1
m0
m.5
E2J
E2J
E-6J
E2J
E0
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Alignment Analogue
m1
E-9J
A
B
m.77
E-5J
C
m.77
m.77
E-5J
E-5J
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Test Results
L lt alphabetw
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Test Results
L gt alphabetw
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Test Results
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Test Results
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Hidden Motifs Gibbs Sampler
Beta .1
Beta .5
Beta .9
Beta 1.3
Beta 1.7
Beta 2
W5, l500
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Hidden Motifs Replica Exchange
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