Network inference from repeated observations of node sets

Neil Clark, Avi Ma'ayan

Network InferenceProtein-Protein interaction network Cell signaling network

Overview

• Network inference - the deduction of an underlying network of interactions from indirect data.

1. A general class of network inference problem2. Network inference approach3. Application:

1. inference of physical interactions: PPI 2. Inference of gene associations: Stem cell genes3. inference of statistical interactions: Drug/side effect

network

GMT files

The inference problem• Input: a set of entities (genes or proteins or ...) in the form of a

GMT file - the results of experiments, or sampling more generally.

• Assumptions:• 1 An underlying network exists which relates the interactions

between the entities in the GMT file• 2 Each line of the GMT file contains information on the

connectivity of the underlying network

• The problem: Given a GMT file can we extract enough information to resolve the underlying network?

A synthetic example

Approach...• Forget for the moment that we know the underlying network and pretend

we only have the GMT file.

• Attempt to use the accumulation of our course data to infer the fine details of the underlying network.

• Consider the set of all networks that are consistent with our data - there are likely to be many.

• Use an algorithm to sample this ensemble of networks randomly.

• The mean adjacency matrix gives the probability of each link being present within the ensemble.

Inference live!

Information content

Analytic Approximation• When applying this approach to real data typically there are large numbers

of nodes

• Sample space of networks can be very large -> computationally demanding

• Write a simple analytical approximation which mimics the action of the algorithm.

𝑝𝑖𝑗 = 1−ෑ� ቆ1− 2𝛼𝑛𝑖𝑗𝑘ቇ𝑘

Compare analytic approximation

Correction for sampling bias• Destroy any information by a random permutation of the GMT file and

compare the actual edge weight to the distribution of edge weights from the randomly permuted GMT files:

Application to Infer PPIs

Malovannaya A et al. Analysis of the human endogenous coregulator complexome. Cell. 2011 May 27;145(5):787-99

PPI network

Validataion

• Compare inferred PPI network to the following databases: – BioCarta– HPRD PPIInnateDB– IntAct– KEGG– MINT mammalia– MIPS– BioGrid

Comparison

Validation

Validation

Application to stem cells• We used two types of high-throughput data from the ESCAPE

database (www.maayanlab.net/ESCAPE).• Chip X data: from Chip-Chip and Chip-seq experiments.

– 203,190 protein DNA binding interactions in the proximity of coding regions from 48 ESC-relevant source proteins.

• Logof followed by microarray data: A manually compiled database of Protein-mRNA regulatory interactions deriving from loss-of-function gain-of-function followed by microarray profiling.– 154,170 interactions from 16 ESC-relevant regulatory proteins from

loss-of-function studies, and 54 from gain-of-function studies.

Chip X network

Logof network

Combining networks

• Each data source gives a different perspective on the associations between the genes

• New insights may possibly be gained by combining the different perspectives. e.g. small but consistent associations across different perspectives will be revealed by the enhanced signal-to-noise ratio.

𝑝𝑖𝑗 = 1− ෑ� ቆ1− 2𝛼𝑛𝑖𝑗𝑘1ቇ𝑘1 ෑ� ቆ1− 2𝛽𝑛𝑖𝑗𝑘2ቇ𝑘2

ሾ … ሿሾ … ሿ…

Combination of Chip X and Logof

An extension of the approach...

Application II: Inference of Network of statistical relationships in AERS database

• Adverse Event Reporting System (AERS) database contains records of ....

AERS Record 1 Drug 1, Drug 2, ... Side-effect 1, Side-effect 2, ...AERS Record 2 Dug 3, Drug 4, ...Side-effect 3, Side effect 4, ...

… …

AERS sub network

AERS Large-scale Adjacency Matrix

And finally…

Summary• We described a general class of problem in network inference.• A network of physical interactions between proteins is

inferred based on high-throughput IP/MS experiments• The method has been applied to examine associations

between stem-cell genes from multiple perspectives• We have begun to apply the approach to the inference of

statistical interactions between drugs and side-effects based on the AERS database

• More details can be found on the website

�www.maayanlab.net/S2N