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### Introduction to Molecular Networks

BMI/CS 576

www.biostat.wisc.edu/bmi576.html

Sushmita Roy

Nov 27th, 2012

Different types of networks

- Physical networks
- Protein-DNA: interactions between regulatory proteins (transcription factors) and regulatory DNA
- Protein-protein: interactions among proteins
- Signaling networks: interactions between protein and small molecules, and among proteinsthat relay signals from outside the cell to the nucleus
- Functional networks
- metabolic: describe reactions through which enzymes convert substrates to products
- genetic: describe interactions among genes which when genetically perturbed together produce a significant phenotype than individually
- co-expression: describes the dependency between expression patterns of genes under different conditions

Protein-DNA interactions Transcriptional regulatory networks

S. cerevisiae:

E. coli

153 TFs (green & light red), 1319 targets

157 TFs and 4410 targets

Vargas and Santillan, 2008

Detecting protein-DNA interactions

- ChIP-chip
- ChIP-seq
- Promoter scanning of sequence-specific motifs
- DNAseI hypersensitivity maping
- Chromatin marks to identify “regulatory regions” followed by scanning using sequence-specific motifs

Protein-DNA interaction example

- goal: determine the (approximate) locations in the genome where a given protein binds

- ChIP-chip and ChIP-chip binding profiles for transcription factors

Peter Park, Nature Reviews Genetics, 2009

Protein-protein interaction networks

Yeast

Human

Node colors:

Red: lethal, green: non-lethal, yellow: slow growth

Edge colors:

Red:Rualet al., blue: literature

Barabasi et al. 2003, Rual et al. 2005

Detecting protein-protein interactions

- Binary interactions
- Yeast two-hybrid:Uses a transcription factors with two domains: each fused to proteins of interest, and a reporter gene
- Protein Complementation Assay
- Complexes
- Tandem Affinity Purification (TAP) with Mass-spectrometry
- Makes use of a TAP tag attached to a protein of interest. Protein and complex are pulled and purified in two steps.

Yeast two hybrid

TAP

Protein complementation

Shoemaker and Panchenko, 2007, PloS computational biology, Xu et al, Protein Expression and Purification, 2010

Genetic interaction networks

Dixon et al., 2009, Annu. Rev. Genet

Yeast genetic interaction network

Costanzo et al, 2011

Computational challenges in networks

- Identifying the connectivity
- Structure and parameter learning
- Using the connectivity to infer function and activation
- Network-based predictive models
- Analyzing the network structure
- Graph clustering
- Graph properties
- Network motifs

We will study these questions in the context of transcriptional regulatory networks

Network model representations

- Unweighted graphs
- Boolean networks
- Bayesian networks and related graphical models
- Differential equations
- Petri nets
- Constraint-based models
- etc.

Transcriptional gene regulation

Input: Transcription factor level (trans)

Sko1

Hot1

HSP12

Input: Transcription factor binding sites (cis)

Output: mRNA levels

Transcriptional regulatory network connects TFs to target genes

Regulatory network inference from expression

Expression-based network inference

Modeling a regulatory network

Sko1

Hot1

HSP12

X2

X1

Hot1

Sko1

BOOLEAN

LINEAR

DIFF. EQNS

PROBABILISTIC

….

Hot1 regulates HSP12

ψ(X1,X2)

HSP12 is a target of Hot1

HSP12

Y

Function

Structure

Who are the regulators?

How they determine expression levels?

Network inference from expression is a computationally difficult problem

- Given 2 TFs and 3 nodes how many possible networks can there be?

….

Not exhaustive set of possible networks

There can be a total of 26 possible networks.

Why is this problem so hard?

- Assume we have n target genes and mTFs.
- Number of possible edges: nXm
- For example, with 4500 target genes and 300 TFs we have 1.35 million edges!
- Number of possible networks is 2nXm

Need clever methods to address this large space of possibilities.

Two classes of expression-based methods

- Per-gene/direct methods
- Module based methods

Per-gene methods

- Key idea: find the regulators that “best explain” expression of a gene
- Mutual Information
- Context Likelihood of relatedness
- ARACNE
- Probabilistic methods
- Bayesian network: Sparse Candidates
- Regression
- TIGRESS
- GENIE-3

Per-gene methods can be further classified based on how regulators are added

- Pairwise:
- Ask if TF Y and gene X have a high statistical correlation/mutual information
- Examples are CLR and ARACNE
- Higher-order:
- Ask if TFs {Y1,Y2..YK} explain expression of X best
- Regression, Bayesian networks, Dependency networks

Information theory for measuring dependence

- I(X,Y) is the mutual information between two variables
- Knowing X, how much information do I have for Y
- P(Z) is the probability distribution of Z

ARACNE

Getting rid of indirect links:

Target

X2

X1

X3

Regulators

X1

I(X1,X2)

I(X1,X3)

X2

X3

I(X2,X3)

Exclude edges with lowest information in a triplet

I(X2,X3) < min(I(X1,X2),I(X1,X3))

These typically correspond to low mutual information.

Margolin et al 2006

Context Likelihood of Relatedness (CLR)

- For a genejand regulator i, context is defined by the mutual information of j with all other regulators, and mutual information of i with all other target genes.
- Use the contexts to compute two background distributions of mutual information
- Get a z-value for Mij with respect to these distributions.
- Final z-value is the square root of these z-values
- Call an edge is z-value is greater than a cutoff.

Context Likelihood of Relatedness

Mij

i

j

zij is the likelihood of observing Mij from either distribution by chance

Use zij to decide if gene i regulates gene j.

Higher order models for network inference

- Bayesian networks
- Dependency networks

Random variables encode expression levels

Sho1

Msb2

Regulators

X2

X1

X1

Ste20

Y3=f(X1,X2)

X2

Y3

Target

Y3

Structure

Function

Goal: learn the structure and function of these networks

Bayesian networks

- a BN is a Directed Acyclic Graph (DAG) in which
- the nodes denote random variables
- each node X has a conditional probability distribution (CPD) representing P(X | Parents(X))
- the intuitive meaning of an arc from X to Y is that X directly influences Y
- Provides a tractable way to work with large joint distributions

Bayesian networks for representing regulatory networks

…

?

?

?

Regulators (parents)

Yi

Conditional probability distribution (CPD)

Target (child)

Example Bayesian network

Parents

X2

X1

X4

X3

Child

Assume Xi is binary

X5

Needs 25 measurements

No independence assertions

Needs 23 measurements

Independence assertions

A

f

t

Pr(D =t) = 0.9

B

f

t

Pr(D =t) = 0.5

C

f

t

Pr(D =t) = 0.8

Pr(D =t) = 0.5

Representing CPDs for discrete variables- CPDs can be represented using tables or trees
- consider the following case with Boolean variables A, B, C, D

P( D | A, B,C) as a table

Dependency networks: a set of regression problems

Regulators

1

p

1

…

1

?

?

?

1

Yi

X1 …… Xp

=

bj

Yi

d

p

d

Function: Linear regression

Regularization term

Number of genes

Two classes of expression-based methods

- Per-gene/direct methods
- Module based methods

An expression module

Set of genes that are co-expressed in a set of conditions

Genes

Genes

Modules

Genes

Gasch & Eisen, 2002

Module Networks

Revisit the modules

Learn regulators per module

Y2

Y1

Y2

Y1

X1

X2

X2

X1

X2

M1

X1

X3

X4

X4

X3

X4

X3

M2

X5

Y2

Y1

Y2

Y1

X6

X7

X6

X7

X5

X6

X8

X7

X5

X8

X8

M3

Every gene in a module has the same set of regulatory program

Lee et al 2009, Segal et al 03

Modeling the relationship between regulators and targets

- suppose we have a set of (8) genes that all have in their upstream regions the same activator/repressor binding sites

Modeling the relationship between regulators and targets

X1 > e1

Each path captures a mode of regulation

NO

YES

Activating

regulation

X2 > e2

Activating

regulation

YES

NO

Repressing

regulation

Expression of target modeled using Gaussians at each leaf node

Global View of Modules

- modules for common processes often share common
- regulators
- binding site motifs

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