Aracne

1. Jorge Viveros Summer 2006 Workshop June 29th, 2006 Aracne

2. Contents • Overview (the problem, the alternatives, ARACNE’s arlgorithm central idea) • Demo (reconstruction of gene regulatory networks for affymatrix gene expression data) • Algorithm details (approximating the mutual information, comparative study results, ARACNE vs Bayesian and Relevance Networks) • Conclusions • Bibliography

3. 1. Overview: ARACNE Algorithm for the Reconstruction of Accurate Cellular Networks “Reverse engineering” or “deconvolution” problem: Samples ga gb ga gb gc gd ge Information-theory + max entropy methods gc gd ge Gene regulatory network

4. (overview, cont’d) Authors A.A. Margolin [1,2], I. Nemenman [2], K. Basso [3], C. Wiggings [2,4], G. Stolovitzky [5], R. Dalla-Favera [3], A. Califano [1,2] [1]Dept. Biomedical informatics, [2]Joint Centers for Sys Biology, [3]Institute for Cancer Genetics, [4]Dept. of Appl. Physics and Appl. Math. Columbia University [5]IBM T.J. Watson Research Center. Main reference: http://www.arxiv.org/abs/q-bio/0410037 BMC Bioinformatics 2006, 7(Suppl 1):S7

5. (overview, cont’d) Goal Understandmammaliannormal cell physiology and complex pathologic phenotypesthrough elucidating gene transcriptional regulatory networks. Thesis Statistical associations between mRNA abundance levels helps to uncovergene regulatory mechanisms.

6. (overview: alternatives) ARACNE vs Clustering ARACNE recovers specific transcriptional interactions but does not attempt to recover all of them (too complex a problem). Genome-wide clustering of gene expression profiles: cannot discern direct (irreducible) from “cascade” transcriptional gene interactions. ga gb gc gd ge a b clustering ARACNE c d e ga,gb gc,gd ge

7. (central idea) Gene network inference edge = (direct) statistical dependency = direct regulatory interaction nodes = genes Temporal gene expression data for higher eukaryotes, difficult to obtain. Only steady-state statistical dependencies are studied. gi gj

8. Accounting for dependence: definition and measurement Gene expression values samples from a joint probability distribution Consider the multi-information = average log-deviation of the joint probability distribution (JPD) from the product of its marginals (also “Kullback-Leibler divergence” (KL-div)). Use maximum entropy methods to approximate JPD by an element of its “m-way” marginal Frechet class (m-way maximum-entropy estimate m-MEE) Use m-MEE to define mth-order connected information (m-cinfo) to account for m-way statistical dependencies (only!). Multi-info = sum of all m-cinfo’s.

9. The multi-information Multi-information (KL-div) JPD “nodes, “expressions” or “genes” Integral if conts case; sum if discrete case Entropy of P(x) JPD not known, approximate it!

10. m-way max entropy estimate of JPD m-MEE , , has the same m-marginals as Lagrange multipliers m-MEE has the following form: Have no analytical solution BUT can be obtained via an iterative Proportional fitting proc (IPFP)

11. Connected and Multi informations mth-order connected information Multi-information Compensate for the lack of knowledge of JPD by using the (truncated!) multi-info to establish and quantify statistical dependencies

12. Detecting a particular m-way interaction M-way interaction contributes to multi-info, iff minimum of interaction multi-information (inter multi-info) over -specific Frechet class is positive. Inter multi-info = and are m-MEE sharing same m-way marginals except for, perhaps, Positivity of minimal inter multi-info  is an irreducible (direct) interaction Thus draw edges coming from nodes and meeting at m-edge vertex.

13. Examples Regulatory cascade (Markov chain) Information processing inequalty generically dependent (similarly, ) generically independent No triplet interactions (coregulation)

14. (examples, cont’d) Other dependencies 2 regulates 1 and 3 OR 1 and 3 regulate 2 jointly does not factor but pairwise marginals do

15. 2. Demo Platforms • caWorkBench2.0 (downloadable through web site) (JAVA) Most developed features: microarray data analysis, pathway analysis and reverse engineering, sequence analysis, transcription factor binding site analysis, pattern discovery. http://amdec-bioinfo.cu-genome.org/html/caWorkBench.htm • Cygwin (for windows). Windows and Linux versions available in web site

16. (Demo) Sample input data file Input_file_name.exp N = 3 # genes M = 2 # microarrays Input file has N+1=4 lines each lines has M+2 (2M+2) fields AffyID HG_U95Av2 SudHL6.CHP ST486.CHP G1 G1 16.477367 0.69939363 20.150969 0.5297595 G2 G2 7.6989274 0.55935365 26.04019 0.5445875 G3 G3 8.8098955 0.5445875 21.554955 0.31372303 Microarray chip names annotation name header line (value,p-value)-chip1

17. (Demo, cont’d) Syntax (Cygwin) ARACNE: algorithm for gene regulatory network computation given microarray data. Usage: aracne aracne GeneExpressionFile [-a | -k | -s | -t | -e | -f] aracne -adj GeneExpressioFile AdjacencyFile [-t | -e] -a accurate | fast [default: accurate] -k gaussian kernel width [accurate method only; default: 0.15] -s Averaging Window step size [fast method only; default: 6] -t Mutual Info. threshold [default: 0] -e DPI tolerance (btw 0 and 1) [default: 1] -f mean stdev [default: no filtering]

18. (Demo, cont’d) Sample output data file input_data_file_name[non-default_param_vals].adj # lines = N = # genes G1:0 8 0.064729 G2:1 2 0.0298643 7 0.0521425 G3:2 1 0.0298643 G4:3 8 0.0427217 G5:4 5 0.403516 G6:5 4 0.403516 6 0.582265 G7:6 5 0.582265 9 0.38039 G8:7 1 0.0521425 8 0.743262 G9:8 0 0.064729 3 0.0427217 7 0.743262 9 0.333104 G10:9 6 0.38039 8 0.333104 5 AffyID ID# MI value Associated gene ID# 4 1 6 9 7 8 10 2 3

19. 3. Algorithm details Incorporate information-theoretic ideas (Markov networks) to model statistical dependencies (cf. [2]) = joint prob dist function of stationary expressions of all genes (i=1,…,N) N = # genes, Z = partition fun (normalization factor), = Hamiltonian, , , , … = interaction potentials (e.g., genes i,j,k do not interact in the model iff = 0. Aim: identify nonzero potentials.

20. (Algorithm details) Aracne’s model First-order approximation: genes are independent 1st order potentials obtained from marginal probabilities (estimated experimentally). ARACNE’s approximation: truncate joint prob dist fun to pairwise potentials In this model non-interacting genes (includes statistically independent genes and genes that do not interact directly, i.e., but ). Reduce number of potential pairwise interactions via realistic biological assumptions.

21. (algorithm details, cont’d) MI estimation Assume two-way interaction: pairwise potentials determine all statistical dependencies. Mutual information (MI) = measure of relatedness = 0 iff MI approximation: G = bivariate standard Gaussian density h = kernel width

22. (algorithm details, cont’d) Some details and technicalities: Transform x, y so and their marginal distributions seem uniform There is not a universal way of choosing h, however the ranking of the MI’s depends only weakly on them.

23. (algorithm details, cont’d)Establishing the network Define thresholdIO to discard MI’s (lower-bound interaction) Shuffle genes across microarray profiles & evaluate MIs for seemingly independent genes, choose IO based on what fraction of MIs falls below the threshold. Data processing inequality: if genes g1 and g2 interact thorugh g3 then ARACNE starts with network so for every edge look at gene triplets and remove edge with smallest MI

24. (algorithm details, cont’d) Establishing the network ARACNE’s algorithmcomplexity: N = number of genes, M = number of samples DPI analysis MI estimation (order of pairwise interactions )

25. Perfect network reconstruction theorems Thm 1:If MI’s are estimated with no errors and true underlying interaction network is a tree with only pairwise interactions then ARACNE will reconstruct it. Thm 2:If Chow-Liu maximum MI info tree is subnetwork of ARACNE’s network then this is the true network. Thm 3: “ARACNE will reconstruct tree-network topologies exactly.”

26. Comparative study results Reconstruction of class of synthetic transcriptional networks by Mendes et al (cf. [1]) and human B lymphocyte genetic network from gene expressions profile data. Performance of ARACNE compared against Bayesian Networks (use LibB package) and Relevance networks (similar to ARACNE but has less accurate MI estimation procedure and less-developed of assigning statistical significance).

27. (results) Synthetic networks 100 genes, 200 interactions organized in two types of networks 1. Erdos-Renyi: each vertex interaction is equally likely 2. Scale-free topology: distribution of vertex connections obeys a power law

28. (results) Performance metrics Pairwise gene interaction is “(True) positive” if their statistical regulatory interaction is directly linked. “(True) negative” if their interaction is not direct. Precision fraction of true interactions correctly inferred (expected success rate in experimental validation of predicted interactions) Recall fraction of true interactions among all inferred ones Performance to be assessed via Precision-Recall curves (PRCs)

29. (results cont’d) PRCs for synthetic data 1 2 ARACNE’s performance above 40% for both models

30. (result con’td) Quantitative results on synthetic data ARACNE recovers far more true connections and predicts far less false ones

31. (results cont’d) Results on Human B cells Assembled expression profile data set of ~340 B lymphocytes from normal, tumor-related and experimentally manipulated populations. Data set was deconvoluted by ARACNE to generate B-cell specific regulatory network of ~129,000 interactions. Validation of the network’s quality was done by comparing inferred interactions with those identified through biochemical methods. See cf [3].

32. Conclusions and Discussions • Algorithm is robust enough for its application in other network reconstruction problems in biology and the social and engineering fields. • Pairwise interaction model  higher-order potential interactions will not be accounted for (ARACNE’s algorithm will open 3-gene loops). • A two-gene interaction will be detected iff there are no alternate paths. • To keep three-gene loops, modify tolerance for edge-removal by introducing tolerance parameter, . • ARACNE’s performance deteriorates as local (true) network topology deviates from a tree (tight loops may be a problem). • ARACNE achieved high precision and substantial recall even for few data points when compared to BN and RN (synthetic data). • ARACNE cannot predict the orientation of the edges of the networks. • The algorithm is suited for more complex (mammalian) networks.

33. Bibliography • P. Mendes, W. Sha, K. Ye. Artificial gene networks for objective comparison of analysis algorithms. Bioinformatics 2003, 19 Suppl 2: II122-II129. • I. Nemenman. Information theory, multivariate dependence and genetic network inference. Technical report: arXiv:q-bio/0406015; 2004. • K. Basso, A.A. Margolin, G. Stolovitzky, U. Klein, R. Dalla-Favera, A. Califano. Reverse engineering of regulatory networks in human B cells. Nature Genetics, 2005, 37(4):382-390.

34. Main web site • Important documentation and relevant publications, application download and support. AMDeC Bionformatics Core Facility at the Columbia Genome Center AMDeC (Academic Medicine Development Company) http://amdec-bioinfo.cu-genome.org/html/ARACNE.htm