Network Biology- part III - NUS · Association network: Connection matrix ... Generalized Topological overlap matrix and corresponding dissimilarity min( , ) 1 iu uj ij u ij i j ij

Network Biology- part III

Jun Zhu, Ph. D.

Professor of Genomics and Genetic Sciences

Icahn Institute of Genomics and Multi-scale Biology

The Tisch Cancer Institute

Icahn Medical School at Mount Sinai

New York, NY

@IcahnInstitute

http://research.mssm.edu/integrative-network-biology/

Email: [email protected]

Mount Sinai Hospital and Mount Sinai

School of Medicine

in New York City

Mount Sinai Hospital and Mount Sinai

School of Medicine

• Hospital

• Founded in 1852 as a Jewish Hosptical, is one of the oldest and largest teaching hospital in the US

• Located right next to Central Park in Manhattan

• Is the largest hospital in New York City

• Ranked 16th best hospital in 2015

• Medical School

• Founded in 1963

• Merged with New York Univerisity in 1998 as Mount Sinai-NYU medical center

• Independent in 2010

• Ranked 18th best medical school

Mount Sinai Health System

▶ 6,200 physicians, >2,000 residents and

fellows

▶ 36,000 employees

▶ 169,532 inpatient admissions

▶ More than 2,600,000 outpatient visits to

offices and clinics (non-Emergency

Department)

▶ 489,508 Emergency Department visits

▶ 18,000 babies delivered a year

Goals of the workshop

▶ NOT to teach you how to use one method or one

program

▶ Learn from history

▶ Learn about critical thinking

– What you want to achieve?

– What you need to achieve the goal?

– How to abstract a biological problem into

mathematical problem?

– What are underlying assumptions and problems?

Why it is so hard to model biological systems? ▶ The more we learn, the more complicated it becomes!

Post transcriptional regulation

• Splicing (1981)

• RNA editing (1986)

• miRNA mediated regulation (1993)

Post translational regulation

• Phosphorylation

• Glycosaltion

• acetylation It is not one gene to one protein anymore!

Epigenetic regulation : heritable

changes in gene function that cannot

be explained

by changes in DNA sequence

• DNA methylation

• Chromotin structure

Junk DNA?

Gene sets Association

networks

Probabilistic causal

networks

Mechanism

based models

Biological details revealed

Data required to train models

Biological networks/pathways

Observation-> description-> explanation-> prediction

Association network: Connection matrix

▶ Is one gene statistically

associated with another

gene?

▶ A binary symmetric matrix

▶ 1 (red) – two genes are

associated

▶ 0 (black) – two genes are

not associated

▶ Diagonal = 1: genes are

always associated with

themselves!

Topological overlap matrix and corresponding dissimilarity (Ravasz et al 2002)

min( , ) 1

i jij

i j

k kTOM

k k

1ij ijDistTOM TOM

Node i Node j

Association by gene expression correlation

▶ How strong the correlation of mRNA expression levels should be?

– the p-value cutoff for correlation: Bonferroni correction?

• Assuming two expression levels are independent

– FDR (False Discover Rate) by permutation

• No explicit assumption

• Data set specific

detectedpositivestotal

positivesfalseFDR

p-value < total positive false positive FDR

(from data) (from permuted data)

1e-10 40245988 1079 2.68e-5

1e-15 22475531 192 8.54e-6

1e-20 13755681 38 2.76e-6

At p value <1e-20, there are only 38 false positives

so that no module was detected for the permuted data

Pvalue<1e-20 was chosen as threshold

Selecting threshold for Gene-Gene Correlation

(GGC) of 25,000 genes on a microarray chip

weighted coexpression networks

Unsigned Network Signed Network

Zhang & Horvath SAGMB, 2005

Two types of weighted correlation networks

Unsigned

Signed

network, absolute value

| ( , ) |

network preserves sign info

| 0.5 0.5 ( , ) |

ij i j

ij i j

a cor x x

a cor x x

Default values: β=6 for unsigned and β =12 for signed

networks.

Zhang & Horvath SAGMB, 2005

Generalized Connectivity

▶ Gene connectivity = row sum of the adjacency

matrix

– For unweighted networks=number of direct neighbors

– For weighted networks= sum of connection strengths to

other nodes

i ijjk a

Generalized Topological overlap matrix and corresponding dissimilarity

min( , ) 1

iu uj ij

uij

i j ij

a a a

TOMk k a

1ij ijDistTOM TOM

soft thresholding vs hard thresholding?

1. Preserves the continuous information of the co-expression information

2. Results tend to be more robust with regard to different threshold choices

But hard thresholding has its own advantages:

In particular, graph theoretic algorithms from the computer science

community can be applied to the resulting networks

Pros:

Cons:

Making Sense of These Associations

▶ Do a set of genes

connect to each other

similarly?

▶ Hierarchical clustering

reorders the matrix so

that patterns emerge

How to identify modules in an ordered

connection matrix

▶ Identify a largest set

of genes

▶ Most coherent

(connect to each

other)

4267 top genes in BxH liver female rescan qtl overlap (num(p(GGC)<1e-15)>100 ~abs(cor)>0.5886)

,obs

tot

GPCoherence

GP

Lum et al, 2005

Gene sets Association

networks




1. Do they enrich for a

biological function?

2. Do they overlap with any

signatures?

3. Do they correlate with

clinical traits?

4. Do they link to a QTL?

5. Do they enrich for any

transcription factor binding

sites?



1000 2000 3000 4000

1

2

3

4

5

6

7

8

'acyl-CoA binding'

'chromatin remodeling complex'

'respiratory chain complex I‘

'ribosome'

'fibroblast growth factor receptor binding'

'hormone activity'

'positive regulation of phosphorylation' 'glucosyltransferase activity'

'bile acid metabolism'

'carboxy-lyase activity'

'cell-matrix junction'

'B-cell mediated immunity'

'regulation of immune response'

Using the singular value decomposition to define (module) eigengenes

1 2

1 2

1 2

1

(q)

Scale the gene expressions profiles (columns)

( )

( )

( )

(| |,| |, ,| |)

Message: u is the (first) eigengene E

If datX corresponds to the q-th module then

T

m

m

m

datX scale datX

datX UDV

U u u u

V v v v

D diag d d d

(q)E is the q-th module eigengene.

Module eigengenes are very useful

▶ 1) They allow one to relate modules to each other

– Allows one to determine whether modules should be

merged

– Or to define eigengene networks

▶ 2) They allow one to relate modules to clinical traits

and SNPs

– -> avoids multiple comparison problem

▶ 3) They allow one to define a measure of module

membership: kME=cor(x,ME)

Bin Zhang

ARACNE

▶ Reverse engineering of regulatory networks in human B cells.

Basso K, Margolin AA, Stolovitzky G, Klein U, Dalla-Favera R, Califano A.

Nat Genet. 2005 Apr;37(4):382-90. Epub 2005 Mar 20.

▶ ARACNE: an algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context.

Margolin AA, Nemenman I, Basso K, Wiggins C, Stolovitzky G, Dalla Favera R, Califano A.

BMC Bioinformatics. 2006 Mar 20;7 Suppl 1:S7.

http://www.ncbi.nlm.nih.gov/pubmed/15778709



ARACNE: ranking mutual information

Spectral clustering

▶ Useful for sparse network

Adjacency matrix , jiA

, ,i i i j

j

D ADiagonal matrix

Laplacian matrix 1P D A

Cut along the vector

corresponding to the largest

eigen value

Meta-analysis and comparison of association

networks

▶ Integrating multiple data sets into one network

▶ Integrating multiple networks into one network

What Are Common Among Them?

How Do They Differ?

Kai Wang

Mouse and Rat Are Commonly Used Animal

Models in Studying Human Diseases

▶ Understanding their conserved mechanisms is important in predicting whether drug targets identified in mouse and rat will achieve efficacy in humans

▶ Identifying mechanisms that differ among them can help improve the design and interpretation of toxicity studies that involve rodent models

▶ Liver is an important organ for glucose and lipid metabolism, as well as for metabolizing toxic compounds

▶ Gene expression data can be organized into co-expression networks that can shed light on the functional relationship between genes

Wang et al, PLoS Comp Bio., 2009

Existing Methods in the Literature

▶ Meta-analysis approaches

– Parametric meta-analysis

• Combining p-values (Fisher’s Inverse 2 test)

• Fisher-Z statistics (Hedges & Olkin,1985; Rosenthal & Rubin,

1978; DerSimonian & Laird, 1986)

– Non-parametric: order statistics (Stuart et al, 2003)

▶ Network alignment approaches (Kelly et al, 2003, Berg 2006, etc)

– Sub-graph based vs. gene-pair based

– Search for specific network structure of interest


Proposed Semi-nonparametric

Approach: d-statistics

▶ Define effect size, d, as the normalized correlation coefficient to the gene-centric mean correlation

– Gene context specific

– Less assumption needed

– Mean effect size can defined

– Heterogeneity statistics can be used

21

22

1

1

(1) For gene pair , in dataset :

~ 0,1

(2) Mean effect

1,

(3) Statisitical significance

~ 0,1

(4) Homogeneity

~

i k

i k

ij

ij

ijk r

ijk

r

K

ijk

kij d

ij

ij ij

d

K

ijk ij K

k

i j k

d N

d

dK K

dg d K N

Q d d

Distribution of context of gene AA

A

A

A

A

AB

ABd


Meta-analysis Procedures

Compute GGC in single dataset

Gene specific d-transformation

Compute Mean

effect size

Homogeneity?

Differential

Interactions

Yes No

Stat. significance?

Conserved

Interactions

Dataset

specificity


Methods Comparison

▶ Similar results were also obtained using KEGG pathways

101

102

103

104

105

106

107

108

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

# predicted pairs

% p

red

icte

d p

airs s

ha

rin

g G

O a

nn

ota

tio

n

d-statisticsOrder StatisticsCombine P-valueFEM Fisher-ZREM Fisher-ZHumanMouseRat


Conserved Modules Show Better Association

with Human Lipid Traits

▶ Kathiresan et al. A genome-wide association study for blood lipid in the Framingham Heart Study. BMC Medical Genetics 2007, 8:SI7

▶ Association is defined as p-value < 0.001

▶ Genes were selected if marker is within 50kb of the gene

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

p<0.001

p<0.001

% L

ipid

Asso

cia

tin

g G

ene

s

0

1000

2000Module

Siz

e

carboxylic acid metabolic

translation

imm

une response

cell proliferation


Meta-analysis of Differential Interactions between

BxHwt vs. BxH ApoE-/- Mice

▶ A Proof-of-concept case for identifying network changes using the proposed method

– Identical genetic background

– Similarly raised and fed

– ApoE is the only major difference between two mouse strains

▶ 500 differentially connected genes; 1023 differential interactions

▶ Over-represented biological processes were specifically enriched in those which ApoE is known to participates in

Keyword Pvalue Evalue

Bkg

Set

Size

Bkg Set

Count

Input Set

Size

Input Set

Count

cholesterol metabolic process 9.78E-10 5.6E-06 13846 98 ( 0.7%) 375 17 ( 4.5%)

cholesterol biosynthetic process 1.71E-08 9.8E-05 13846 44 ( 0.3%) 375 11 ( 2.9%)

sterol metabolic process 2.08E-08 1.2E-04 13846 119 ( 0.9%) 375 17 ( 4.5%)

sterol biosynthetic process 5.75E-08 3.3E-04 13846 49 ( 0.4%) 375 11 ( 2.9%)

lipid metabolic process 5.77E-08 3.3E-04 13846 999 ( 7.2%) 375 57 (15.2%)

cellular lipid metabolic process 1.39E-07 8.0E-04 13846 845 ( 6.1%) 375 50 (13.3%)

alcohol metabolic process 2.74E-07 1.6E-03 13846 390 ( 2.8%) 375 30 ( 8.0%)


Differentially Connected Genes are Enriched

in Known ApoE Subnetwork

▶ Protein-protein and protein-DNA interactions curated from databases and literature

▶ Differentially connected genes are significantly enriched in the immediate physical network around ApoE (4/21, p < 1E-4), and is still marginally enriched when second neighbors are included (12/356, p < 0.06)


Identification of Differential Interactions Between

Human and Rodent Species

▶ Assume the systems being compared are thoroughly perturbed – Lack of correlation in one system is not due to lack of expression

dynamics

▶ 1,171 differential interactions (among 918 orthologous genes

▶ FDR is estimated to be < 1E-3 using permutation method

▶ 163 of the 1,171 differential interactions are human specific


RXRG Is Identified as A Key Regulator that Differs

Between Human and Rodent Species

▶ The largest sub-network consists of 11 genes, three of them, PIP5K1B, RXRG and ACSBG1, are known to be involved in lipid metabolism

▶ RXRG (Retinoid X receptor ) is: – # 4 most differentially connected

gene

– Involved in 8 human specific interactions, 7 of which are with other top differentially connected genes

– RXRG has previously been associated with hyperlipidemia

– RXRG is a direct upstream regulator of CETP (cholesteryl ester transfer protein), which is a human specific gene that is involved in regulating HDL cholesterol


Conserved Only Both Different Only

0

0.1

0.2

0.3

0.4

0.5

Hum

an-m

ouse K

a/K

s

Evolutionary Difference between Conserved vs.

Differentially Connected Genes

3205 547

479 2726 68

Conserved Different Are differentially connected genes evolve

faster than those involved only in conserved

interactions?

Ka/Ks - ratio of non-synonymous

substitutions rate to synonymous

substitutions rate, which can be

used as an indication of positive

selection on a protein-coding gene

p < 0.131


JointClustering multiple networks

Narayanan et al, PLoS Comp Bio., 2010



Performs better when two networks are different



Identify differences between association

networks ▶ Define a module first

Zhang et al, Cell, 2013

Identify differences between association

networks

▶ Define a differential

connection first

▶ Make no assumption of

module structure a priori

▶ Can identify differential

connections between two

modules

Narayanan et al, Mol. Syst. Biol. 2014

Association

networks

Probabilistic causal

networks




1. How do genes in the same

module interact?

2. How do genes in different

modules interact?

3. Can we make causal

inferences to elucidate

signaling pathway for

disease targets?


Aknowledgements Mount Sinai

Genomics Institute

Eric Schadt

Bin Zhang

Zhidong Tu

Charles Powell

Patrizia Casaccia

Zhu lab

Seungyeul Yoo

Eunjee Lee

Li Wang

Luan Lin

Quan Long

•Icahn Institute of Genomics and Multiscale Biology,

Icahn School of Medicine at Mount Sinai

•Janssen

•Canary Foundation

•Prostate Cancer Foundation

•NIH

•NCI

Supported by:

Boston University

Avrum Spira

Joshua Campbell

U Washington

Roger Baumgarner

Berkerley

Rachel Brem

Princeton

Lenoid Kruglyak

Documents

Network Biology- part III - NUS · Association network: Connection matrix ... Generalized Topological overlap matrix and corresponding dissimilarity min( , ) 1 iu uj ij u ij i j ij