Le Songlesong@cs.cmu.edu

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:

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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!