conserved cross-species network modules elucidate th17 t

58
Conserved cross-species network modules elucidate Th17 T-cell differentiation in human and mouse Mohammed El-Kebir, Hayssam Soueidan,Thomas Hume, Daniela Beisser, Marcus Dittrich,Tobias Müller, Guillaume Blin, Jaap Heringa, Macha Nikolski, Lodewyk F. A.Wessels, Gunnar W. Klau ECCB 14 BioNetVisA Workshop 1 “Trouble with mice is you always kill 'em. ” John Steinbeck, Of Mice and Men

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Page 1: Conserved cross-species network modules elucidate Th17 T

Conserved cross-species network modules elucidate Th17 T-cell

differentiation in human and mouse

Mohammed El-Kebir, Hayssam Soueidan, Thomas Hume, Daniela Beisser, Marcus Dittrich, Tobias Müller, Guillaume Blin, Jaap Heringa, Macha Nikolski, Lodewyk F. A. Wessels, Gunnar W. Klau

ECCB 14 BioNetVisA Workshop

1“Trouble with mice is you always kill 'em. ” ― John Steinbeck, Of Mice and Men

Page 2: Conserved cross-species network modules elucidate Th17 T

T Cells

Wikimedia commons Abbas, Cellular & Molecular Immunology, 7th ed

2

Page 3: Conserved cross-species network modules elucidate Th17 T

t

215FUNCTIONAL RESPONSES OF T LYMPHOCYTES

expansion of the respective subsets (described later). In addition, these subsets of T cells differ in the expression of adhesion molecules and receptors for chemokines and other cytokines, which are involved in the migration of distinct subsets to different tissues (see Chapter 10).

Development of TH1, TH2, and TH17 SubsetsDifferentiated TH1, TH2, and TH17 cells all develop from naive CD4+ T lymphocytes, mainly in response to cyto-kines present early during immune responses, and dif-ferentiation involves transcriptional activation and epigenetic modification of cytokine genes. The process of differentiation, which is sometimes referred to as polar-ization of T cells, can be divided into induction, stable commitment, and amplification (Fig. 9-14). Cytokines act on antigen-stimulated T cells to induce the transcription of cytokine genes that are characteristic of differentiation toward each subset. With continued activation, epigen-etic changes occur so that the genes encoding that sub-set’s cytokines are more accessible for activation, and genes that encode cytokines not produced by that subset are rendered inaccessible. Because of these changes, the differentiating T cell becomes progressively committed to one specific pathway. Cytokines produced by any given subset promote the development of this subset and inhibit differentiation toward other CD4+ subpopula-tions. Thus, positive and negative feedback loops contrib-ute to the generation of an increasingly polarized population of effector cells.

There are several important general features of T cell subset differentiation.

! The cytokines that drive the development of CD4+ T cell subsets are produced by APCs (primarily dendritic cells and macrophages) and other immune cells (such as NK cells and basophils or mast cells) present at the site of the immune response. Dendritic cells that encounter

FIGURE 9–13 Properties of TH1, TH2, and TH17 subsets of CD4+ helper T cells. Naive CD4+ T cells may differentiate into distinct subsets of effector cells in response to antigen, costimulators, and cytokines. The columns to the right list the major differences between the best-defined subsets.

Signaturecytokines

Role indiseases

IFNγ

IL-4IL-5IL-13

IL-17AIL-17FIL-22

Immunereactions

Macrophageactivation;

IgG production

Mast cell,eosinophilactivation;

IgE production;"alternative"macrophage

activation

Neutrophilic,monocytic

inflammation

Hostdefense

Intracellularmicrobes

Helminthicparasites

Extracellularbacteria;

fungi

Autoimmunediseases;

tissue damageassociated with

chronic infections

Allergicdiseases

Organ-specificautoimmunity

TH1cell

TH2cell

TH17cell

consists of IgE antibody production and the activation of eosinophils. Along the same lines, in many chronic auto-immune diseases, tissue damage is caused by inflamma-tion with accumulation of neutrophils, macrophages, and T cells, whereas in allergic disorders, the lesions contain abundant eosinophils along with other leukocytes. The realization that all these phenotypically diverse immuno-logic reactions are dependent on CD4+ T cells raised an obvious question: How can the same CD4+ cells elicit such different responses? The answer, as we now know, is that CD4+ T cells consist of subsets of effector cells that produce distinct sets of cytokines, elicit quite different reactions, and are involved in host defense against differ-ent microbes as well as in distinct types of immunologic diseases. The first subsets that were discovered were called TH1 and TH2 (so named because they were the first two subsets identified). It was subsequently found that some inflammatory diseases that were thought to be caused by TH1-mediated reactions were clearly not dependent on this type of T cell, and this realization led to the discovery of TH17 cells (called TH17 because their characteristic cytokine is IL-17). In the next section, we describe the properties of these subsets and how they develop from naive T cells. We will return to their cyto-kine products, effector functions, and roles in cell-mediated immunity in Chapter 10.

The defining characteristics of differentiated subsets of effector cells are the cytokines they produce, the transcrip-tion factors they express, and epigenetic changes in cyto-kine gene loci. These characteristics of TH1, TH2, and TH17 cells are described below.

The signature cytokines produced by the major CD4+ T cell subsets are IFN-γ for TH1 cells; IL-4, IL-5, and IL-13 for TH2 cells; and IL-17 and IL-22 for TH17 cells (see Fig. 9-13). The cytokines produced by these T cell subsets determine their effector functions and roles in diseases. The cytokines also participate in the development and

Abbas, Cellular & Molecular Immunology, 7th ed

T Helper subsets

3

Differentiation

?

Naive Th ! cell

Page 4: Conserved cross-species network modules elucidate Th17 T

Th17 cells: Clinical relevance

• Mucosal immunology :Th17 respond to bacterial and fungal antigens!

• Th17 cells imbalance associated with several autoimmune diseases (Rheumatoid Arthritis, MS, psoriasis, lupus, CD) !

• IL-17-deficient mice are more susceptible to the development of lung melanoma!

• HIV infection specifically depletes Th17 population

4

Page 5: Conserved cross-species network modules elucidate Th17 T

Main questions

• How to modulate Th17 response to self?!

• What are the regulators of Th17 balance?!

• What are the proteins and pathways responsible for proper differentiation of Th17 cells?

How well findings in mouse are transferrable to human immunology?

5

Page 6: Conserved cross-species network modules elucidate Th17 T

Our strategy

• Let’s combine:!

• Human and Mouse Th17 differentiation transcriptomics data!

• Human and Mouse PPI networks!

• Orthology information between Human and Mouse!

• Using an optimization framework !

• To identify conserved cross-species active modules

+ +

Human Mouse

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Page 7: Conserved cross-species network modules elucidate Th17 T

A B

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CCSAM:(1) Activity

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Page 8: Conserved cross-species network modules elucidate Th17 T

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CCSAM:(1I) Modularity

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Page 9: Conserved cross-species network modules elucidate Th17 T

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CCSAM:(1I) Modularity^2

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Page 10: Conserved cross-species network modules elucidate Th17 T

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CCSAM:(III) Conservation

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Page 11: Conserved cross-species network modules elucidate Th17 T

Today

• Material: Gene expression profiling & public datasets!

• Method: Conserved active module !

• Results: Modules identification!

• Regulation at 2h and 72h are well conserved !

• Overall dynamics is conserved!

• Conclusions & future work

11

Page 12: Conserved cross-species network modules elucidate Th17 T

Today

• Material: Gene expression profiling & public datasets!

• Method: Conserved active module !

• Results: Modules identification!

• Regulation at 2h and 72h are well conserved !

• Overall dynamics is conserved!

• Conclusions & future work

12

Page 13: Conserved cross-species network modules elucidate Th17 T

M&M recipe:

• For each species individually:!

• Process RNA-Seq => Count matrix!

• Fit a GLM => estimated coefs!

• For each time point, !

• For each gene:!

• call for DE => p.value!

• Fit a BUM => activity score !

• Get PPI network & orthology relations

13

Page 14: Conserved cross-species network modules elucidate Th17 T

0 6 12 24 48 72

Timepoint (h)

Th0

Th17

CD4+umbilicalcordblood

TGF , IL6, I 1 , anti-IL4, anti-IFN�� �L

anti-IL4, anti-IFN�

BA

C

Th0 Th17

3 % 55 %

FSC

Th0 Th17

250

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p < 0.05

RORC

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D

p < 0.001

IL17F

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Th0Th17p < 0.05

p < 0.001

p < 0.001

Figure 1

0.5; 1; 2; 4

IL17A

Transcriptional profiling of Human & Mouse Th17 cells

Tuomela et al., 2014

• Control Th0 vs Th17!

• 9 time points, RNA-Seq!

• Human: 14,338 mRNAs quantified in the first 72h!

• Mouse: 11,751 mRNAs quantified in the first 72h!

• Matched time points!

• DE called with an edgeR GLM 14

Page 15: Conserved cross-species network modules elucidate Th17 T

Transcription dynamics

-1000

-500

0

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0.5 1 2 4 6 12 24 48 72tp

-N

posLogFC

FALSE

TRUE

Human DE genes, FDR<=0.1, |logFC|>=1

-1000

-500

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1000

0.5 1 2 4 6 12 24 48 72tp

-N

posLogFC

FALSE

TRUE

Mouse DE genes, FDR<=0.1, |logFC|>=1

• Biphasic in both species!

• Seems “stronger” in the mouse samples!

•earliest changes (1/2h!) visible 15

Page 16: Conserved cross-species network modules elucidate Th17 T

AC026803.14+NUCB1 CNP CTD−2154I11.2+RHOBTB3 DTNBP1

FAM71B+HAVCR2+ITK+MED7 FNIP1+RAPGEF6 IFI16 IL6ST

KDSR TAF4B VAV1 ZNRF1

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0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0

0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0

0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0time

counts

is.th17

FALSE

TRUE

Contrasting: Genes DE at time 2

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Page 17: Conserved cross-species network modules elucidate Th17 T

signal⇠ B(a,1)

noise⇠ uniform(0,1)⌘ B(1,1)

p−values (second order statistics)

Den

sity

0.0 0.2 0.4 0.6 0.8 1.0

02

46

810

1214

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0.0 0.2 0.4 0.6 0.8 1.0

0.0

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1.0

quantiles of expected p−values under the mixture model

obse

rved

p−v

alue

s (s

econ

d or

der s

tatis

tics)

signal + noisenoise

p-value

dens

ity

Scores: BUM Model

• Activity (positive and negative) scores derived from !

• p-values distribution!

• described with a beta-uniform mixture model;!

• controlling the FDR!

• using an adj. LL ratio:

s(x,FDR) = log

ax

a�1

a⌧(FDR)

a�1

=(a� 1) (log(x)� log(⌧(FDR)))

17

Estimating the occurrence of false positives and false negatives in microarray studies by approximating and partitioning the empirical distribution of p-values. Pounds 2003

Page 18: Conserved cross-species network modules elucidate Th17 T

Today

• Material: Gene expression profiling & public datasets!

• Method: Conserved active module !

• Results: Modules identification!

• Regulation at 2h and 72h are well conserved !

• Overall dynamics is conserved!

• Conclusions & future work

18

Page 19: Conserved cross-species network modules elucidate Th17 T

PPI Networks

• Obtained from the STRING db!

• Only kept physical interactions!

• Mouse network: 12,121 nodes and 176,462 edges !

• Human network : 14,280 nodes and 197,649 edges

19

Page 20: Conserved cross-species network modules elucidate Th17 T

Orthology relations

• Obtained from ENSEMBL orthology!

• Represented as a bi-partite graph M !

• 85,640 human proteins!

• 49,717 mouse proteins !

• linked by 125,685 edges!

• grouped in 16,736 bicliques (avg size of 8.08, median of 6, SD of 5.97)

A

B

C

D

E

a

b

c

d

e

20

Page 21: Conserved cross-species network modules elucidate Th17 T

M&M recipe (recap)

• For each species individually:!

• Process RNA-Seq => Count matrix!

• Fit a GLM => estimated coefs!

• For each time point, !

• For each gene:!

• call for DE => p.value!

• Fit a BUM => activity score !

• Get PPI network & orthology relations

21

Page 22: Conserved cross-species network modules elucidate Th17 T

Today

• Material: Gene expression profiling & public datasets!

• Method: Conserved active module !

• Results: Modules identification!

• Regulation at 2h and 72h are well conserved !

• Overall dynamics is conserved!

• Conclusions & future work

22

Page 23: Conserved cross-species network modules elucidate Th17 T

Conserved active modules

• Formalized using a constraint modeling approach over boolean variables!

• Constraints are linearized => MILP!

• The MILP is then solved using CPLEX with a branch-and-cut algorithm

A B

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DE

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ab

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d e

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23

Page 24: Conserved cross-species network modules elucidate Th17 T

MILP:?

• A formulation, with:!

• an objective function!

• subject to linear constraints!

• where variables can be constrained to discrete domains ({0,1}, )!

• much harder than on !

• for which exact solutions can be found efficiently in practice

max

x1,x2

S1 · x1 + S2 · x2

Subject to: x1 + x2 L

F1 · x1 + F2 · x2 F

P1 · x1 + P2 · x2 P

x1 � 0, x2 � 0

N

R

24

Page 25: Conserved cross-species network modules elucidate Th17 T

Boolean variables for nodes in solution

A B

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DE

F

ab

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d e

f

g

h

J

K

L

xA

xK

MILP:Variables

25

Page 26: Conserved cross-species network modules elucidate Th17 T

Weighted boolean variables for nodes in solution, objective function:

A B

C

DE

F

ab

c

d e

f

g

h

J

K

L

wAxA

wKxK

MILP:Variables

max

X

v2V1[V2

wvxv

26

Page 27: Conserved cross-species network modules elucidate Th17 T

Boolean variables for conserved nodes

A B

C

DE

F

ab

c

d e

f

g

h

J

K

L

wAxA

mA ma

mBmb

wKxK

MILP:Variables

mu = max

uv2M{xuxv}

27

Page 28: Conserved cross-species network modules elucidate Th17 T

constrained by having e.g more than of nodes being conserved

A B

C

DE

F

ab

c

d e

f

g

h

J

K

L

wAxA

mA ma

mBmb

wKxK

MILP: degree of conservation

⇠P

mvPxv

� 50%

↵ = 50%

28

Page 29: Conserved cross-species network modules elucidate Th17 T

• And satisfying the connectivity constraint:!• Possibly an exponential number of constraints!• Constraints added as needed during optimization

A B

C

DE

F

ab

c

d e

f

g

h

J

K

L

wAxA

mA ma

mBmb

wKxK

MILP: connectivity

29

Page 30: Conserved cross-species network modules elucidate Th17 T

Conserved cross-species network modules

G2 = (V2, E2). The nodes in these networks are labeled by theiractivity—defined by w 2 RV1[V2 . Conserved node pairs are givenby the mapping M ✓ V1 ⇥ V2.

PROBLEM 1 (Conserved active modules). Given G1, G2, w andM , the task is to find a subset of nodes V ⇤

= V

⇤1 [V

⇤2 with V

⇤1 ✓ V1

and V

⇤2 ✓ V2 such that the following properties hold.

• Activity: The sumP

v2V ⇤ wv is maximal. Note that it is up tothe user to normalize the node weights as to prevent a bias inactivity score towards one species.

• Conservation: At least a certain fraction ↵ of the nodes in thesolution must be conserved, that is, |U⇤| � ↵ · |V ⇤| whereU

⇤:= {u 2 V

⇤ | 9v 2 V

⇤: uv 2 M}.

• Modularity: The induced subgraphs G1[V⇤1 ] and G2[V

⇤2 ] are

connected.

There is a trade-off between conservation and activity. If noconservation is enforced (↵ = 0), the solution will correspond totwo independent maximum-weight connected subgraphs therebyachieving maximal overall activity. Conversely, if completeconservation is required (↵ = 1), the solution can only consistof conserved nodes, which may result in smaller overall activity. Theuser controls this trade-off by varying the value of the parameter↵ from 0 to 1. The activity score monotonically decreases withincreasing ↵—see Fig. 2.

Since the maximum-weight connected subgraph problem, whichoccurs as a subproblem for ↵ = 0, is NP-hard (Ideker et al., 2002),the problem of finding conserved active modules is NP-hard as well.

2.2 Integer linear programming approachWe formulate the conserved active modules problem as an integerprogramming (IP) problem in the following way.

max

X

v2V1[V2

wvxv (1)

s.t. mu = max

uv2M{xuxv} u 2 V1 (2)

mv = max

uv2M{xuxv} v 2 V2 (3)

X

v2V1[V2

mv � ↵

X

v2V1[V2

xv (4)

G1[x] and G2[x] are connected (5)

xv,mv 2 {0, 1} v 2 V1 [ V2 (6)

In the following we show that the above formulation satisfies theproperties of activity, conservation and modularity. In addition wegive further details on the actual integer linear program (ILP).

Activity. Variables x 2 {0, 1}V1[V2 encode the presence of nodes inthe solution, i.e., for all v 2 V1 [ V2 we want xv = 1 if v 2 V

⇤ andxv = 0 otherwise. The objective function (1) uses these variables toexpress the activity of the solution, which we aim to maximize.

Conservation. Variables m 2 {0, 1}V1[V2 encode the presence ofconserved nodes in the solution. Recall that a node u 2 V

⇤1 (u 2 V

⇤2 )

that is present in the solution is conserved if there is another nodein the solution v 2 V

⇤2 (v 2 V

⇤1 ) such that the two nodes form

3

-1

3

4

3

-1

3

4

3

-1

3

4

3

-1

3

4

3

-1

3

4

3

-1

3

4

↵ = 0 ↵ = 0.5 ↵ = 1activity: 10 activity: 9 activity: 8

G1 G2 G1 G2 G1 G2

Fig. 2: Trade-off between activity and conservation. Threeoptimal solutions (indicated in yellow) for varying conservationratios ↵ in a toy example instance. Node activities are given nextto the nodes, conserved node pairs are linked by dotted lines. Theactivity of a conserved module is the sum of the activities of itscomprising nodes. The parameter ↵ denotes the minimum fractionof nodes in a solution that must be conserved, i.e. connected by adotted line.

a conserved node pair uv 2 M (vu 2 M ). This corresponds toconstraints (2) and (3). We linearize xuxv , in a standard way, byintroducing binary variables z 2 {0, 1}M such that zuv = xuxv forall uv 2 M :

zuv xu uv 2 M (7)

zuv xv uv 2 M (8)

zuv � xu + xv � 1 uv 2 M (9)

zuv 2 {0, 1} uv 2 M (10)

Subsequently, we model the max function in (2) and (3) as follows.

mu � zuv uv 2 M (11)

mv � zuv uv 2 M (12)

mu X

uv2M

zuv u 2 V1 (13)

mv X

uv2M

zuv v 2 V2 (14)

We model the required degree of conservation by constraint (4).

Modularity. Constraint (5) states that the nodes encoded in thesolution x induce a connected subgraph in both G1 and G2. Thereare many ways to model connectivity, e.g., using flows or cuts(Magnanti and Wolsey, 1995). Cut-based formulations perform betterin practice (Dilkina and Gomes, 2010). Recently, Alvarez-Mirandaet al. (2013) have introduced a cut-based formulation that only usesnode variables. In an empirical study, the authors show that theirformulation outperforms other cut-based formulations. We modelconnectivity along the same lines. Since the constraints that we willdescribe are similar for both graphs, we introduce them only forgraph G1 = (V1, E1).

X

v2V1

yv 1 (15)

3

MILP: Formulation

30

Page 31: Conserved cross-species network modules elucidate Th17 T

Today

• Material: Gene expression profiling & public datasets!

• Method: Conserved active module !

• Results: Modules identification!

• Regulation at 2h and 72h are well conserved !

• Overall dynamics is conserved!

• Conclusions & future work

31

Page 32: Conserved cross-species network modules elucidate Th17 T

CCND1

NTRK1

NR3C1

PTPN1

FURIN

VIM

APBB1IP

PTMS FSCN1

LMNB1

CTLA4

POU2F2

IGF2BP3

SFXN3

ARID5B

PFKFB3

LPP

ELAVL1

BCL3

STAT1

NOTCH1

IL2RB

CD274

SOCS3

TNF

IL23A

IER3

STAT3

ZEB2

CMPK1

PIM1BHLHE40

ETV6

CMPK2

C5AR1

MAPK11

NCK2

BATF

PIM2

DDR1

CEBPZ

DOK2

JAK3

CXCR5

LAG3BCL6

COL1A2

COL18A1

GZMB BATF3

JUNB

2h conserved module

Il2rb

Bcl3Vim

Stat3

Casp6

Socs3

Ctla4

Tbx21

Stat1

Il6stJak3

Apbb1ip

Fyn

Ablim1

Ptpn1

Bcl6

Nr3c1

I l21

Cxcr5

Hif1a

Pou2f2

Lmnb1

Prdm1

Hdac7

Junb

Batf

Cebpz

Lag3

Notch1

Gzmb

Lpp

Phf15

Hmox1

Vhl

Socs1

32

Page 33: Conserved cross-species network modules elucidate Th17 T

IL17F

CCR6

NCALD

IL17RA

LRRN3

ANXA1

CCL20

GPR132

CCR4

CCL5

CYSLTR1

KIF5A

KIF5C

CAMK2B

KIFC3

NCOA2

UCHL1

RYR1

RORC CTSL1COPS5

JUN

MAP3K5

SMAD3

FASLG

FOXP3

PPARG

SMAD7HIF1A

IL24

IL22AP1G1

RORA

IL23R

LMNA

IL12RB2

B2M

IL21

GPR65

KLRD1LTB4R

SOCS3

BCAR3

RUNX1

AHR

FNBP1L PMEPA1CYP1B1

VDRSKILGADD45G NEDD4

KIF26B

GATA3SYN1IL9

NEDD9

IL13

CHN1

FES

CDK5

ICAM1STAT3 IL2RB

CSF2

TGFBI

CD27

PLAUR

MRC2

KLF2 TNFRSF8

TNFRSF12A

FURIN TNFSF8

TRAF5

ITGB7

BASP1RBPJ

THBS1FOXO1

NOTCH1

IL1RNPTGER2PTHLH

IL1R1TUBB3PIK3R1

ATM

IL1A

ATP1B1PDE7B

DPP4

PHLDA1

ELAVL1

ZNF238NCS1

GNAQPFKFB3

PRDM1

SESN3

AQP3

SOS1TIMP1

LPL

MMP2TNF

PTK2

IRS2

GRB7 RDH10

COL15A1

RGS16

CHST3

COL6A3

TIAM2ITGAE

ITGA3JAG2

TNIK

72h conserved module

Dpp4

Itga4

Klrc1

Gap43

Plaur

Itgb7

Klrd1

Il12rb2

Procr

B2m

Rabep1

Furin

Basp1

Rdx

Pdpn

Ap1g1

Tnf

Lum

F3

Klf2

Icam1

Fasl

Rbpsuh-rs3

Lpxn

Camk2b

Ptk2Notch1

Uchl1

Klf3

Srf

Mt2Il17ra

Egln3

RorcIl17f

Il17a

Ltb4r1

Nedd4

Inhba

Cysltr1

Piwil2

Gpr132

Gpr65

Gnaq

Il9

Pik3r1

Cdk5 Syn1

Irs2Lmna

I l24

Il1r1

Epha2

Crem

AtmTgm2

Tec

Fes

Ccl20

Cxcl10Ccl5

Timp1I l22

Ly6aCcr4

Stat6

I l21Hif1a

Il23r

I l10

Map3k5

Csf2

Smad7

Il2rbJag2

Stat3Socs3

Cops5

Tnfrsf8

Bmp7

Cd27

Malt1

Tnfsf8 Ms4a4b

Gadd45gTraf5Rbpj

Ccr5

Cyp1b1

Maf

Ncoa2

Ahr Gata3

RoraKif5c

Kifc3

33

Page 34: Conserved cross-species network modules elucidate Th17 T

Today

• Material: Gene expression profiling & public datasets!

• Method: Conserved active module !

• Results: Modules identification!

• Regulation at 2h and 72h are well conserved !

• Overall dynamics is conserved!

• Conclusions & future work

34

Page 35: Conserved cross-species network modules elucidate Th17 T

2h 4h 24h 48h 72h

0

25

50

75

100

125

0

2

4

6

0

25

50

75

100

125

0

100

200

0

100

200

300

400

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0α

Size

Class Positive, conserved Positive Negative,conserved Negative

Distribution of node classes by alpha

Overall dynamics and solutions

● ●

● ●●

●●

2h 4h 24h 48h 72h

50

100

150

0

2

4

6

0

50

100

150

0

200

400

0

200

400

600

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0α

Scor

e

Species ● ●Human Mouse To optimality ● FALSE TRUE

Module score by alpha

35

Page 36: Conserved cross-species network modules elucidate Th17 T

Today

• Material: Gene expression profiling & public datasets!

• Method: Conserved active module !

• Results: Modules identification!

• Regulation at 2h and 72h are well conserved !

• Overall dynamics is conserved!

• Conclusions & future work

36

Page 37: Conserved cross-species network modules elucidate Th17 T

Conclusions

• Mouse and Human Th17 differentiation processes are well conserved during the first 72h !

• Differentiation happens in two phases, very early (0h--4h) and late (12h--72h) !

• We provide the first formulation of the conserved active module problem as well as an efficient MILP solver !

• Code and recipes available there: http://software.cwi.nl/xheinz!

• PS: We got the same results on an independent data set! 37

Page 38: Conserved cross-species network modules elucidate Th17 T

Future work

• Theoretical results on the computational complexity for specific network topologies!

• Novel formulation for bi-conservation: Conservation between species and across time!

• Non-supervised formulation: Clustering of samples based on conserved active modules

38

Page 39: Conserved cross-species network modules elucidate Th17 T

Thanks!

• Wessels group / NKI!• CWI for the expertise!• CBIB/CGFB for the environment (and computing power!)!• VU Centre for Integrative Bioinformatics!• ERASysBio for the funding!• Riitta Laheesma’s group for the data!• And you for your attention... and for trying the tool:

http://software.cwi.nl/xheinz39

and see you @ poster 7!

Page 40: Conserved cross-species network modules elucidate Th17 T

IL10

IL10RA

IL12RB2

IL13IL16

IL17A

IL17F

IL17RAIL1A

IL1R1

IL1R2

IL2

IL21

IL22

IL23R

IL24

IL2RB

IL4

IL7R

IL9

0.0

2.5

5.0

7.5

10.0

0 5 10hsa

mus

72h: What are the DE IL?

40

Page 41: Conserved cross-species network modules elucidate Th17 T

●●●●●●

●●●●

●●●●●

●●●●●●

●●●●●●●

●●●●●●●●

●●●●

●●●●

● 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

2h

1

1

0.99

0.84

0.79

0.71

0.65

0.46

0.39

0.33

0.15

1

0.99

0.84

0.79

0.71

0.65

0.46

0.39

0.33

0.15

1

0.86

0.81

0.73

0.66

0.48

0.4

0.35

0.15

1

0.94

0.82

0.74

0.53

0.43

0.37

0.18

1

0.88

0.79

0.58

0.45

0.39

0.2

1

0.9

0.66

0.51

0.46

0.22

1

0.75

0.59

0.49

0.21

1

0.78

0.6

0.25

1

0.71

0.26

1

0.33 1

2h

●●●●●●

●●●●

●●

●●●

●●●

●●●

●●

●● 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

4h

1

1

1

1

0.25

0.25

0.25

0.2

0.2

0

0

1

1

1

0.25

0.25

0.25

0.2

0.2

0

0

1

1

0.25

0.25

0.25

0.2

0.2

0

0

1

0.25

0.25

0.25

0.2

0.2

0

0

1

1

1

0.5

0.5

0

0

1

1

0.5

0.5

0

0

1

0.5

0.5

0

0

1

1

0

0

1

0

0

1

1 1

4h

●●●●●●

●●●●

●●●●●

●●●●●●

●●●●●●●

●●●●●●●●

●●●

● 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

24h

1

0.95

0.78

0.69

0.63

0.52

0.49

0.48

0.34

0.18

0

1

0.74

0.73

0.63

0.52

0.49

0.48

0.32

0.17

0

1

0.85

0.69

0.58

0.55

0.53

0.34

0.17

0

1

0.76

0.64

0.57

0.54

0.32

0.16

0.02

1

0.84

0.7

0.66

0.38

0.19

0.02

1

0.78

0.73

0.44

0.25

0.02

1

0.88

0.52

0.25

0

1

0.58

0.28

0

1

0.46

0

1

0 1

24h

●●●●●●

●●●●

●●●●●

●●●●●●

●●●●●●●

●●●●●●●●

●●●●●●●

●●●

● 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

48h

1

1

0.82

0.74

0.69

0.63

0.57

0.51

0.44

0.28

0.01

1

0.82

0.74

0.69

0.63

0.57

0.51

0.44

0.28

0.01

1

0.85

0.78

0.72

0.66

0.58

0.5

0.31

0.01

1

0.91

0.82

0.72

0.64

0.56

0.34

0.01

1

0.91

0.79

0.69

0.6

0.38

0.01

1

0.86

0.75

0.64

0.43

0.01

1

0.81

0.7

0.48

0.01

1

0.8

0.52

0.01

1

0.55

0.01

1

0.02 1

48h

●●●●●●

●●●●

●●●●●

●●●●●●

●●●●●●●

●●●●●●●

●●●

● 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

72h

1

0.89

0.79

0.73

0.68

0.61

0.53

0.45

0.34

0.24

0

1

0.88

0.81

0.76

0.64

0.55

0.49

0.33

0.25

0

1

0.84

0.79

0.67

0.57

0.51

0.36

0.25

0

1

0.91

0.75

0.65

0.56

0.39

0.3

0

1

0.82

0.69

0.61

0.4

0.31

0

1

0.76

0.65

0.45

0.35

0

1

0.8

0.51

0.4

0

1

0.6

0.43

0

1

0.51

0.01

1

0.01 1

72h

Influence of conservation on content

J(A,B) =|A \B||A [B|

41

Page 42: Conserved cross-species network modules elucidate Th17 T

3

-1

3

4

3

-1

3

4

3

-1

3

4

3

-1

3

4

3

-1

3

4

3

-1

3

4

↵ = 0 ↵ = 0.5 ↵ = 1activity: 10 activity: 9 activity: 8

G1 G2 G1 G2 G1 G2

Controls tradeoff between overall activity and conservation

MILP: Conservation tradeoff

42

Page 43: Conserved cross-species network modules elucidate Th17 T

ATP1B1 CHST2 CTSL1 DIXDC1

ITGAE NOTCH1 PFKFB3 PMEPA1

PPP1R16B RYR1 SKIL STAP1

0

500

1000

1500

0

2000

4000

6000

0

4000

8000

12000

010002000300040005000

0

1000

2000

3000

01000020000300004000050000

0

2500

5000

7500

10000

0

1000

2000

3000

0

1000

2000

3000

4000

0

2500

5000

7500

10000

0

2500

5000

7500

0

200

400

600

800

0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0

0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0

0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0 0.5 1.0 2.0 4.06.0 12.0 24.0 48.072.0time

coun

ts

is.th17

FALSE

TRUE

Genes affected at any time

Genes affected at any time point

43

Page 44: Conserved cross-species network modules elucidate Th17 T

T cells response 205SIGNALS FOR T LYMPHOCYTE ACTIVATION

by the T cells themselves and by APCs and other cells at the site of antigen recognition. In this section, we will summarize the nature of antigens recognized by T cells and discuss specific costimulators and their receptors that contribute to T cell activation. Cytokines are discussed later in the chapter.

Recognition of Antigen

Antigen is always the necessary first signal for the activa-tion of lymphocytes, ensuring that the resultant immune response remains specific for the antigen. Because CD4+ and CD8+ T lymphocytes recognize peptide-MHC com-plexes displayed by APCs, they can respond only to protein antigens or chemicals attached to proteins. In addition to the TCR recognizing peptides displayed by MHC molecules, several other T cell surface proteins par-ticipate in the process of T cell activation (see Fig. 7-9, Chapter 7). These include adhesion molecules, which stabilize the interaction of the T cells with APCs, and costimulators, which are described later. The nature of the biochemical signals delivered by antigen receptors and the role of these signals in the functional responses of the T cells are discussed in Chapter 7.

for returning the immune system to a state of equilib-rium, or homeostasis. It occurs mainly because the majority of antigen-activated effector T cells die by apop-tosis. One reason for this is that as the antigen is elimi-nated, lymphocytes are deprived of survival stimuli that are normally provided by the antigen and by the costim-ulators and cytokines produced during inflammatory reactions to the antigen. It is estimated that more than 90% of the antigen-specific T cells that arise by clonal expansion die by apoptosis as the antigen is cleared.

With this overview, we proceed to a discussion of the signals required for T cell activation and the steps that are common to CD4+ and CD8+ T cells. We then describe effector and memory cells in the CD4+ and CD8+ lineages, with emphasis on subsets of CD4+ helper T cells and the cytokines they produce. We conclude with a discussion of the decline of immune responses.

SIGNALS FOR T LYMPHOCYTE ACTIVATION

The proliferation of T lymphocytes and their differentia-tion into effector and memory cells require antigen rec-ognition, costimulation, and cytokines that are produced

FIGURE 9–2 Phases of T cell responses. Antigen recognition by T cells induces cytokine (e.g., IL-2) secretion, particularly in CD4+ T cells, clonal expansion as a result of cell proliferation, and differentiation of the T cells into effector cells or memory cells. In the effector phase of the response, the effector CD4+ T cells respond to antigen by producing cytokines that have several actions, such as the recruitment and activation of leukocytes and activation of B lymphocytes, and CD8+ CTLs respond by killing other cells.

APC

Naive CD4+

T cell EffectorCD4+

T cell

EffectorCD8+ T cell(CTL)

MemoryCD8+

T cell

Activation ofmacrophages,

B cells,other cells;

inflammation

Killing ofinfected

"target cells";macrophage

activation

MemoryCD4+

T cell

Naive CD8+

T cell

Cytokines(e.g., IL-2)

IL-2R

Lymphoid organ Peripheral tissue

Antigenrecognition

Lymphocyteactivation

Clonalexpansion

EffectorfunctionsDifferentiation

Abbas, Cellular & Molecular Immunology, 7th ed 44

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Experimental design

RNA-sequencing

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Page 46: Conserved cross-species network modules elucidate Th17 T

Human exp. design:

Donor

Donor

Donor

Donor

Donor

Donor

Donor

72h48h24h12h6h4h2h1h0.5h

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Th17

72h48h24h12h6h4h2h1h0.5h

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Donor

Donor

Donor

Donor

Donor

Donor

72h48h24h12h6h4h2h1h0.5h

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Th17

72h48h24h12h6h4h2h1h0.5h

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Donor

Donor

Donor

Donor

Donor

Donor

72h48h24h12h6h4h2h1h0.5h

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Th17

72h48h24h12h6h4h2h1h0.5h

46

Page 47: Conserved cross-species network modules elucidate Th17 T

−0.4 −0.2 0.0 0.2 0.4

−0.3

−0.2

−0.1

0.0

0.1

0.2

GLM MDS 0.5h

Dimension 1

Dim

ensi

on 2

Th0_0.5h_rep1

Th0_0.5h_rep2

Th0_0.5h_rep3

Th17_0.5h_rep1

Th17_0.5h_rep2

Th17_0.5h_rep3

Strongest effects: 0.5h

47

Page 48: Conserved cross-species network modules elucidate Th17 T

−0.4 −0.2 0.0 0.2 0.4

−0.2

−0.1

0.0

0.1

0.2

GLM MDS 12h

Dimension 1

Dim

ensi

on 2

Th0_12h_rep1

Th0_12h_rep2

Th0_12h_rep3

Th17_12h_rep1

Th17_12h_rep2

Th17_12h_rep3

Strongest effects: 12h

48

Page 49: Conserved cross-species network modules elucidate Th17 T

−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6

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−0.3

−0.2

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Dim

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Th0_48h_rep1

Th0_48h_rep2

Th0_48h_rep3

Th17_48h_rep1Th17_48h_rep2

Th17_48h_rep3

Strongest effects: 48h

49

Page 50: Conserved cross-species network modules elucidate Th17 T

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Th17_24h_rep1

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Th17_4h_rep3Th17_6h_rep3

Th17_12h_rep3

Th17_24h_rep3

Th17_48h_rep3Th17_72h_rep3

Between all samples

50

Page 51: Conserved cross-species network modules elucidate Th17 T

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2

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51

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Chapter 9 – Activation of T Lymphocytes216

microbes and display microbial antigens are activated to produce cytokines (as well as costimulators, described earlier) as part of innate immune responses to the microbes (see Chapter 4). Different microbes may stimulate dendritic cells to produce distinct sets of cytokines, perhaps because the microbes are recog-nized by different microbial sensors in the cells. Other cells of innate immunity, such as NK cells and mast cells, also produce cytokines that influence the pattern of T cell subset development.

! Stimuli other than cytokines may also influence the pattern of helper T cell differentiation. Some studies indicate that different subsets of dendritic cells selec-tively promote either TH1 or TH2 differentiation; the same principle may be true for TH17 cells. In addition, the genetic makeup of the host is an important deter-minant of the pattern of T cell differentiation. Inbred mice of some strains develop TH2 responses to the same microbes that stimulate TH1 differentiation in most other strains. Strains of mice that develop TH2-dominant responses are susceptible to infections by intracellular microbes (see Chapter 15).

! The distinct cytokine profiles of differentiated cell pop-ulations are controlled by particular transcription factors that activate cytokine gene transcription and by chromatin modifications affecting cytokine gene loci. The transcription factors are themselves activated or induced by cytokines as well as by antigen receptor stimuli. Each subset expresses its own characteristic set of transcription factors. As the subsets become increas-ingly polarized, the gene loci encoding that subset’s signature cytokines undergo histone modifications (changes in methylation and acetylation) and conse-quent chromatin remodeling events, so that these loci are “accessible” and in an “open” chromatin configura-tion, whereas the loci for other cytokines (those not produced by that subset) are in an inaccessible chro-matin state. These epigenetic changes ensure that each subset can produce only its characteristic collection of cytokines. It is likely that epigenetic changes in cyto-kine gene loci correlate with stable phenotypes, and before these changes are established, the subsets may be plastic and convertible.

! Each subset of differentiated effector cells produces cytokines that promote its own development and may suppress the development of the other subsets. This feature of T cell subset development provides a power-ful amplification mechanism. For instance, IFN-γ secreted by TH1 cells promotes further TH1 differentia-tion and inhibits the generation of TH2 and TH17 cells. Similarly, IL-4 produced by TH2 cells promotes TH2

FIGURE 9–14 Development of TH1, TH2, and TH17 subsets. Cytokines produced early in the innate or adaptive immune response to microbes promote the differentiation of naive CD4+ T cells into TH1, TH2, or TH17 cells by activating transcription factors that stimulate production of the cytokines of each subset (the early induction step). Progressive activation leads to stable changes in the expressed genes (commitment), and cytokines promote the development of each population and sup-press the development of the other subsets (amplification). These prin-ciples apply to all three major subsets of CD4+ effector T cells.

Dendriticcell

Cytokinegene expression

Cytokines

Othercells

Cytokinesecretion

Transcriptionfactors

Cytokinereceptor

Naive T cell

Chromatinchanges stable cytokinegene expression

PolarizedTH subset

Inhibitionof other

TH subsets

Induction

Amplification

Commitment

Th cells development & differentiation

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219FUNCTIONAL RESPONSES OF T LYMPHOCYTES

(see Chapter 14), promotes the development of proin-flammatory TH17 cells when other mediators of inflam-mation, such as IL-6 or IL-1, are present. Some experimental results indicate that TGF-β does not directly stimulate TH17 development but is a potent suppressor of TH1 and TH2 differentiation and thus removes the inhibitory effect of these two subsets and allows the TH17 response to develop under the influence of IL-6 or IL-1. According to this idea, the action of TGF-β in promoting TH17 responses is indirect. TH17 cells produce IL-21, which may further enhance their development, provid-ing an amplification mechanism.

The development of TH17 cells is dependent on the transcription factors RORγ t and STAT3 (see Fig. 9-17). TGF-β and the inflammatory cytokines, mainly IL-6 and IL-1, work cooperatively to induce the production of RORγt, a transcription factor that is a member of the retinoic acid receptor family. RORγt is a T cell–restricted protein encoded by the RORC gene, so sometimes the protein may be referred to as RORc. The inflammatory cytokines, notably IL-6, activate the transcription factor STAT3, which functions with RORγt to drive the TH17 response. Mutations in the gene encoding STAT3 are the cause of a rare human immune deficiency disease called Job’s syndrome because patients present with multiple bacterial and fungal abscesses of the skin, resembling the biblical punishments visited on Job. These patients have defective TH17 responses.

TH17 cells appear to be especially abundant in mucosal tissues, particularly of the gastrointestinal tract, suggest-ing that the tissue environment influences the generation of this subset, perhaps by providing high local concentra-tions of TGF-β and other cytokines. This observation also suggests that TH17 cells may be especially important in combating intestinal infections and in the development of intestinal inflammation. The development of TH17 cells in the gastrointestinal tract is also dependent on the local microbial population.

The functions of differentiated effector cells of the CD4+ lineage are mediated by surface molecules, primar-ily CD40 ligand, and by secreted cytokines. We will describe the cytokines produced by differentiated CD4+ effector cells and their functions in Chapter 10.

Differentiation of CD8+ T Cells into Cytotoxic T Lymphocytes

The activation of naive CD8+ T cells requires antigen recognition and second signals, but the nature of the second signals may be different from those for CD4+ cells. We have previously described the role of dendritic cells in presenting antigens to and costimulating naive CD8+ cells.

The full activation of naive CD8+ T cells and their dif-ferentiation into functional CTLs and memory cells may require the participation of CD4+ helper cells. In other words, helper T cells can provide second signals for CD8+ T cells. The requirement for helper cells may vary accord-ing to the type of antigen exposure. In the setting of a strong innate immune response to a microbe, if APCs are directly infected by the microbe, or if cross-presentation

microbes, such as fungi, but also when cells infected with various bacteria and fungi undergo apoptosis and are ingested by dendritic cells. IL-23 may be more important for the proliferation and maintenance of TH17 cells than for their induction. TH17 differentiation is inhibited by IFN-γ and IL-4; therefore, strong TH1 and TH2 responses tend to suppress TH17 development. A surprising aspect of TH17 differentiation is that TGF-β, which is produced by many cell types and is an anti-inflammatory cytokine

FIGURE 9–17 Development of TH17 cells. IL-1 and IL-6 pro-duced by APCs and transforming growth factor-β (TGF-β) produced by various cells activate the transcription factors RORγt and STAT3, which stimulate the differentiation of naive CD4+ T cells to the TH17 subset. IL-23, which is also produced by APCs, especially in response to fungi, stabilizes the TH17 cells. TGF-β may promote TH17 responses indirectly by suppressing TH1 and TH2 cells, both of which inhibit TH17 differentia-tion (not shown in the figure). IL-21 produced by the TH17 cells amplifies this response.

Dendriticcell

Bacteria, fungi

Naive T cell

Sources?

IL-22IL-17

TGF-β

TGF-βIL-6

IL-6IL-1

IL-23

IL-21

Effector functions:InflammationBarrier function

RORγt

TH17 cells

STAT3Th17 cells development & differentiation

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Mice vs Men

• Cells origin? !

• Role of TGFB? !

• Secreted cytokines?

Kobezda et al. (2014). Of mice and men: how animal models advance our understanding of T-cell function in RA. Nat. Reviews. Rheumatology54

Page 55: Conserved cross-species network modules elucidate Th17 T

edgeR GLM

• We fit a model of the like :!

• Here: mean ~ donor + time + treat:time !

• Test for DE by contrasting <=> H0: treat:time ==0 !

• LRT, compare models counts ~ donor + time VS counts ~ donor + time + time:treat

MATERIALS AND METHODS

Biological coefficient of variation

RNA-Seq profiles are formed from n RNA samples. Letpgi be the fraction of all cDNA fragments in the i-thsample that originate from gene g. Let G denotethe total number of genes, so

PGg¼1 !gi ¼ 1 for each

sample. Letffiffiffi"

pg denote the coefficient of variation (CV)

(standard deviation divided by mean) of pgi between thereplicates i. We denote the total number of mapped readsin library i by Ni and the number that map to the g-th geneby ygi. Then

EðygiÞ ¼ #gi ¼ Ni!gi:

Assuming that the count ygi follows a Poisson distributionfor repeated sequencing runs of the same RNA sample, awell known formula for the variance of a mixture distri-bution implies:

varðygiÞ ¼ E! varðyj!Þ½ % þ var! Eðyj!Þ½ % ¼ #gi þ "g#2gi:

Dividing both sides by #2gi gives

CV2ðygiÞ ¼ 1=#gi þ "g:

The first term 1/mgi is the squared CV for the Poissondistribution and the second is the squared CV of the un-observed expression values. The total CV2 therefore is thetechnical CV2 with which pgi is measured plus the bio-logical CV2 of the true pgi. In this article, we call fg thedispersion and

ffiffiffiffiffi"g

pthe biological CV although, strictly

speaking, it captures all sources of the inter-library vari-ation between replicates, including perhaps contributionsfrom technical causes such as library preparation as wellas true biological variation between samples.

GLMs

GLMs are an extension of classical linear models tonon-normally distributed response data (42,43). GLMsspecify probability distributions according to theirmean–variance relationship, for example the quadraticmean–variance relationship specified above for readcounts. Assuming that an estimate is available for fg, sothe variance can be evaluated for any value of mgi, GLMtheory can be used to fit a log-linear model

log#gi ¼ xTi $g þ logNi

for each gene (32,41). Here xi is a vector of covariatesthat specifies the treatment conditions applied to RNAsample i, and bg is a vector of regression coefficients bywhich the covariate effects are mediated for gene g. Thequadratic variance function specifies the negative binomialGLM distributional family. The use of the negativebinomial distribution is equivalent to treating the pgi asgamma distributed.

Fitting the GLMs

The derivative of the log-likelihood with respect to thecoefficients bg is XTzg, where X is the design matrix withcolumns xi and zgi=(ygi' mgi)/(1+fgmgi). The Fisher

information matrix for the coefficients can be written asIg=XTWgX, where Wg is the diagonal matrix of workingweights from standard GLM theory (43). The Fisherscoring iteration to find the maximum likelihoodestimate of bg is therefore $new

g ¼ $oldg þ % with

d=(XTWgX)'1 XTzg. This iteration usually produces an

increase in the likelihood function, but the likelihood canalso decrease representing divergence from the requiredsolution. On the other hand, there always exists astepsize modifier a with 0< a< 1 such that$newg ¼ $old

g þ &% produces an increase in the likelihood.Choosing a so that this is so at each iteration is knownas a line search strategy (44,45).

Fisher’s scoring iteration can be viewed as an approxi-mate Newton-Raphson algorithm, with the Fisher infor-mation matrix approximating the second derivativematrix. The line search strategy may be used with anyapproximation to the second derivative matrix that ispositive definite. Our implemention uses a computationallyconvenient approximation. Without loss of generality, thelinear model can be parametrized so that XTX= I. If this isdone, and if the mgi also happen to be constant over i for agiven gene g, then the information matrix simpifies consid-erably to mg/(1+fgmg) times the identity matrix I. Takingthis as the approximation to the information matrix, theFisher scoring step with line search modification becomessimply d= aXTzg, where the multiplier mg/(1+fgmg) hasbeen absorbed into the stepsize factor a. In this formula-tion, a is no longer constrained to be less than one. In ourimplementation, each gene has its own stepsize a that isincreased or decreased as the iteration proceeds.

Cox–Reid adjusted profile likelihood

The adjusted profile likelihood (APL) for fg is thepenalized log-likelihood

APLgð"gÞ ¼ ‘ð"g; yg; $gÞ '1

2log det Ig:

where yg is the vector of counts for gene g, $g is theestimated coefficient vector, ‘() is the log-likelihoodfunction and Ig is the Fisher information matrix. TheCholesky decomposition (46) provides a numericallystable and efficient algorithm for computing the determin-ant of the information matrix. Specifically, logdet Ig is thesum of the logarithms of the diagonal elements of theCholesky factor R, where Ig=RT R and R is upper tri-angular. The matrix R can be obtained as a by product ofthe QR-decomposition used in standard linear modelfitting. In our implementation, the Cholesky calculationsare carried out in a vectorized fashion, computed for allgenes in parallel.

Simulations

Artificial data sets were generated with negative binomialdistributed counts for a fixed total number of 10 000 genes.The expected count size varied between genes according toa gamma distribution with shape parameter 0.5, an ad hocchoice that happened to mimic the size distribution of thecarcinoma data. The average dispersion was set to 0.16(BCV=0.4). In one simulation, all genes had the same

4290 Nucleic Acids Research, 2012, Vol. 40, No. 10

at Netherlands Cancer Institute on O

ctober 2, 2012http://nar.oxfordjournals.org/

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A

CB D E F

MILP: connectivity constraints

• For each connected component of the current solution S!

• Determine its neighborhood not in S!

• Formulate the two alternatives:!

• It’s expanded towards other CCs!

• Or it’ll be the final module (new variables)

xA xD+yA + yB + yC

xB xD+yA + yB + yC

xC xD+yA + yB + yC

xE xD+yE + yF

xF xD+yE + yF

with yv xv andX

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58