Aracne

1
Aracne

• Jorge Viveros
• Summer 2006 Workshop
• June 29th, 2006

2
Contents

1. Overview (the problem, the alternatives, ARACNEs
   arlgorithm central idea)
2. Demo (reconstruction of gene regulatory networks
   for affymatrix gene expression data)
3. Algorithm details (approximating the mutual
   information, comparative study results, ARACNE vs
   Bayesian and Relevance Networks)
4. Conclusions
5. 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, contd) 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/041
0037 BMC Bioinformatics 2006, 7(Suppl 1)S7
5
(overview, contd)
Goal

• Understand mammalian normal cell physiology and
  complex pathologic
• phenotypes through elucidating gene
  transcriptional regulatory networks.
• Thesis
• Statistical associations between mRNA abundance
  levels helps to
• uncover gene 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-cinfos.

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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!
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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)
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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, contd) 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/caWorkBe
  nch.htm
• Cygwin (for windows). Windows and Linux versions
  available in web site

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(Demo) Sample input data
file

• Input_file_name.exp
• N 3 genes
• M 2 microarrays
• Input file has N14 lines
• each lines has M2 (2M2) 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, contd)
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
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(Demo, contd) Sample output data file

• input_data_file_namenon-default_param_vals.adj
• lines N genes
• G10 8 0.064729
• G21 2 0.0298643 7 0.0521425
• G32 1 0.0298643
• G43 8 0.0427217
• G54 5 0.403516
• G65 4 0.403516 6 0.582265
• G76 5 0.582265 9 0.38039
• G87 1 0.0521425 8 0.743262
• G98 0 0.064729 3 0.0427217 7 0.743262 9 0.333104
• G109 6 0.38039 8 0.333104

5
AffyID
ID
Associated gene ID
MI value
1
4
6
9
7
8
10
2
3
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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 (i1,,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.

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(Algorithm details) Aracnes
model

• First-order approximation genes are independent
• 1st order potentials obtained from marginal
  probabilities (estimated
  experimentally).
• ARACNEs 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.

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(algorithm details, contd) 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, contd)

• 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 MIs
• depends only weakly on them.

23
(algorithm details, contd) Establishing
the network

• Define threshold IO to discard MIs
  (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, contd) Establishing the
network
ARACNEs algorithm complexity
N number of genes, M number of samples
DPI analysis MI estimation (order
of pairwise interactions
)
25
Perfect network reconstruction
theorems

• Thm 1 If MIs 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 ARACNEs network then this is the
  true network.
• Thm 3 ARACNE will reconstruct tree-network
  topologies exactly.

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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).

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(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

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(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 contd) PRCs for synthetic
data
1
2
ARACNEs performance above 40 for both models
30
(result contd) Quantitative results on
synthetic data
ARACNE recovers far more true connections and
predicts far less false ones
31
(results contd) 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 networks quality was done by
  comparing inferred interactions
• with those identified through biochemical
  methods.
• See cf 3.

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Conclusions and Discussions

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

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Bibliography

1. P. Mendes, W. Sha, K. Ye. Artificial gene
   networks for objective comparison of analysis
   algorithms. Bioinformatics 2003, 19 Suppl 2
   II122-II129.
2. I. Nemenman. Information theory, multivariate
   dependence and genetic network inference.
   Technical report arXivq-bio/0406015 2004.
3. 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.

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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