Le Song Joint work with Mladen Kolar and Eric Xing KELLER: Estimating Time Evolving Interactions Between Genes

2 Transient Biological Processes

3 3 PPI Network

4 Time-Varying Interactions

5 The Big-Picture Questions What are the interactions? active What pathways are active at a particular time point and location? How will biological networks respond to stimuli (eg. heat shot)?

6 Regulation of cell response to stimuli is paramount, but we can usually only measure (or compute) steady-state interactions

7 … t=1 23T Current Practice Static Networks Microarray Time Series Dynamic Bayesian Networks

8 Our Goal Reverse engineer temporal/spatial-specific “rewiring” gene networks Time t*t* n=1 --- what are the difficulties?

9 Two Scenarios Smoothly evolving networks Abruptly changing networks

10 Scenario I (This paper) Kernel reweighted L1-regularized logistic regression (KELLER) Key Idea I: reweighting observations Key Idea II: regularized neighborhood estimation

11 Key Idea Weight temporally adjacent observations more than distal observations

12 Key Idea Estimate the neighborhood of each gene separately via L1-regularized logistic regression Kernel Reweighting Log-likelihood L1-regularization

13 Consistency Theorem 1: Under certain verifiable conditions (omitted here for simplicity), KELLER recovers the true topology of the networks:

14 Synthetic data DBN and static networks do not benefit from more observations Number of Samples

15 Key idea: Temporally Smoothing Tesla (Amr and Xing, PNAS 2009) TESLA: … Senario II

16 Drosophila Life Cycle Larva Embryo Pupa Adult 66 microarrays across full life cycle 588 genes related to development

17 molecular function biological process cellular component

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40 Network Size vs. Clustering Coefficient mid-embryonic mid-pupal

41 Network Size vs. Clustering Coefficient mid-embryonic stage tight local clusters mid-pupal stage loose local clusters

42 Interactivity of Gene Sets 27 genes based on ontology

43 Interactivity of Gene Sets 25 genes based on ontology

44 Transient Gene Interactions Time Gene Pairs Active Inactive msn  dock sno  Dl

45 Transcriptional Factor Cascade Summary networks 36 transcription factors Node size its total activity

46 TF Cascade – mid-embryonic stage

47 TF Cascade – mid-larva stage

48 TF Cascade – mid-pupal stage

49 TF Cascade – mid-adult stage

50 Transient Group Interactions

51 Conclusion KELLER for reverse engineering “rewiring” networks Key advantages: Computationally efficient (scalable to 10 4 genes) Computationally efficient (scalable to 10 4 genes) Global optimal solution is attainable Global optimal solution is attainable Theoretical guarantee Theoretical guarantee Glimpse to temporal evolution of gene networks Many interactions are rewiring and transient Availability:

52 The End Thanks Travel fellowship: Office of Science (BER), U.S. Department of Energy, Grant No. DE-FG02-06ED64270 Funding: Lane Fellowship, Questions?

53 Interactivity of Gene Sets 30 genes based on ontology

54 Timing of Regulatory Program Galactose

55 Challenges Very small sample size Experimental data are scarce and costly Noisy measurement More genes than microarrays Complexity regularization needed to avoid over- fitting Observations no longer iid since the networks are changing!