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Joint work with Mladen Kolar and Eric Xing
KELLER: Estimating Time Evolving KELLER: Estimating Time Evolving Interactions Between GenesInteractions Between Genes
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Transient Biological Processes
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PPI Network
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Time-Varying Interactions
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The Big-Picture Questions
What are the interactions?
What pathways are activeactive at a particular time point and location?
How will biological networks respond to stimuli (eg. heat shot)?
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Regulation of cell response to stimuli is paramount, but we can usually only measure (or compute) steady-state interactions
Transcriptionalinteractions
Protein—proteininteractions
Biochemicalreactions
▲ Chromatin IP ▲Microarrays
▲ Protein coIP▲ Yeast two-hybrid
▲ Metabolic flux measurements
Transcriptionalinteractions
Protein—proteininteractions
Biochemicalreactions
▲ Chromatin IP ▲Microarrays
▲ Protein coIP▲ Yeast two-hybrid
▲ Metabolic flux measurements
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…
t=1 2 3 T
Current PracticeStatic Networks
Microarray Time Series
Dynamic Bayesian Networks
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Our GoalReverse engineer temporal/spatial-specific
“rewiring” gene networks
Time
t*
n=1
--- what are the difficulties?--- what are the difficulties?
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Two Scenarios
Smoothly evolving networksSmoothly evolving networks Abruptly changing networksAbruptly changing networks
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Scenario I (This paper)Kernel reweighted L1-regularized logistic regression
(KELLER)
Key Idea I: reweighting observations
Key Idea II: regularized neighborhood estimation
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Key IdeaWeight temporally adjacent observations more than
distal observations
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Key IdeaEstimate the neighborhood of each gene separately
via L1-regularized logistic regression
Kernel Reweighting
Log-likelihood
L1-regularization
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Consistency
Theorem 1: Under certain verifiable conditions (omitted here for simplicity), KELLER recovers the true topology of the networks:
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Synthetic data
DBN and static networks do not benefit from more observations
Number of Samples
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Key idea: Temporally Smoothing
Tesla (Amr and Xing, PNAS 2009)
TESLA:
…
Senario II
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Drosophila Life Cycle
Larva
Embryo
Pupa
Adult66 microarrays across
full life cycle
588 genes related to development
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molecular function
biological process
cellular component
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Network Size vs. Clustering Coefficient
mid-embryonic
mid-pupal
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Network Size vs. Clustering Coefficient
mid-embryonic stagetight local clusters
mid-pupal stageloose local clusters
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Interactivity of Gene Sets
27 genes based on ontology
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Interactivity of Gene Sets
25 genes based on ontology
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Transient Gene InteractionsTime
Gene Pairs
Active
Inactive
msn dock
sno Dl
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Transcriptional Factor Cascade
Summary networks 36 transcription factorsNode size its total activity
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TF Cascade – mid-embryonic stage
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TF Cascade – mid-larva stage
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TF Cascade – mid-pupal stage
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TF Cascade – mid-adult stage
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Transient Group Interactions
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ConclusionKELLER for reverse engineering “rewiring” networks
Key advantages:Computationally efficient (scalable to 10Computationally efficient (scalable to 1044 genes) genes)
Global optimal solution is attainableGlobal optimal solution is attainable
Theoretical guaranteeTheoretical guarantee
Glimpse to temporal evolution of gene networks
Many interactions are rewiring and transient
Availability: http://www.sailing.cs.cmu.edu/
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The EndThanks
Travel fellowship:Office of Science (BER), U.S. Department of Energy, Grant No. DE-FG02-06ED64270
Funding: Lane Fellowship,
Questions?
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Interactivity of Gene Sets
30 genes based on ontology
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Timing of Regulatory Program
Galactose
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ChallengesVery small sample size
Experimental data are scarce and costly
Noisy measurement
More genes than microarraysComplexity regularization needed to avoid over-
fitting
Observations no longer iid since the networks are changing!