Transcript Modeling Biology From Experimental Data to Predictive Models Ioannis Xenarios Head of Translational Bioinformatics Scientific Computing Serono Pharmaceutical.

Modeling Biology
From Experimental Data to Predictive Models
Ioannis Xenarios
Head of Translational Bioinformatics
Scientific Computing
Serono Pharmaceutical
Standardization is a necessity for biology
MIRIAM
SBML
MIAME
PSI-MI
PSI-MS
MIACE
IL-2
IL-4
IL-5
IL-10
TNFa
IFNg
3
Are We Ready to Model Biology ?
« The flying machine which will really fly might be
Evolved by the combined and continuous efforts of
Mathematicians and mechanicians in from one million
To ten millions years. »
The New York Times, October 9, 1903
« We started assembly today. »
Orville Wright’s Diary, October 9, 1903
From an idea of M. Cassmann
4
The Immune System
5
T helper (Th) cell differentiation
6
OBJECTIVE
 Create a network model of the molecular mechanism
that leads to the differentiation of (precursor) Th0 cells
into (effector) Th1 and Th2 cells
 Analyze some of the dynamical properties of the model
7
Molecular control of Th cell differentiation
Glimcher and Murphy (2000). Genes & Development 14:1693
8
Published models at the molecular level
Höfer et al., 2002.
Proc. Natl. Acad. Sci. USA. 99:9364
Yates et al., 2004. J. Theor. Biol. 231:181
9
Methodology
Use the published molecular data
on wild type and mutants …
… to infer the connectivity
10
The Th network
IFN-g
IL-4
IL-12
IL-18
IFN-
IFN-gR
IL-4R
IL-12R
IL-18R
IFN-R
STAT1
STAT6
STAT4
IRAK
SOCS1
GATA3
T-bet
11
Important aspects
The network is incomplete
Network elements represent functions
Molecular mechanisms are not taken into account
Interactions are not necessarily direct, there may be
other molecules or functions acting in intermediate steps
As a first approach the elements will be considered as
discrete elements with two or three states
12
Generalized logical analysis of networks
Developed by René Thomas and cols.
Thomas (1991). J. Theor. Biol. 153: 1
Thomas et al., (1995). Bull. Math. Biol. 57: 247
WHAT?
It is a qualitative analysis of the dynamical behaviour of a network,
which permits to identify all the steady states of the system
by focusing on the presence of positive and negative feedback loops
in the network.
WHY?
i) Positive loop generate multistationarity, which is the basis
for differentiation
ii) Negative loops generate damped or sustained oscillations, which
is the basis of homeostasis
iii) Steady states of activation are easily identified experimentally
13
Definition
Feedback loops, or feedback circuits,
are defined as circular chains of interactions,
such that each element of a circuit influences
its own future level of activation
Positive loops
A
A
B
A
B
A
C
Negative loops
A
A
B
A
C
B
C
B
A
B
C
15
Dynamical properties of feedback loops
X
X
X
X
Y
Y
Y
Y
X
X
Y
stable steady state
unstable steady state
Y
16
The Th network: Identifying feeback loops
IFN-g
IL-4
IL-12
IL-18
IFN-
IFN-gR
IL-4R
IL-12R
IL-18R
IFN-R
STAT1
STAT6
STAT4
IRAK
SOCS1
GATA3
T-bet
17
IFN-g
IL-4
IFN-gR
IL-4R
IL-12R
STAT1
STAT6
STAT4
18
IFN-g
IL-4
IFN-gR
IL-4R
IL-18R
STAT1
STAT6
IRAK
19
IFN-g
IL-4
IFN-gR
IL-4R
STAT1
STAT6
STAT4
GATA3
20
IFN-g
IL-4
IFN-gR
IL-4R
STAT1
STAT6
GATA3
T-bet
21
IFN-g
IFN-gR
IL-4R
IL-12R
STAT1
STAT6
STAT4
SOCS1
22
IFN-g
IFN-gR
IL-4R
IL-18R
STAT1
STAT6
IRAK
SOCS1
23
IFN-g
IFN-gR
IL-4R
STAT1
STAT6
SOCS1
GATA3
STAT4
24
IFN-g
IFN-gR
IL-4R
STAT1
STAT6
SOCS1
GATA3
T-bet
25
IFN-g
IFN-gR
STAT1
T-bet
26
IFN-g
IFN-gR
IL-4R
IL-12R
STAT1
STAT6
STAT4
SOCS1
T-bet
27
IFN-g
IFN-gR
IL-4R
IL-18R
STAT1
STAT6
IRAK
SOCS1
T-bet
28
IFN-g
IFN-gR
IL-4R
STAT1
STAT6
STAT4
SOCS1
GATA3
T-bet
29
IFN-g
IL-4
IFN-gR
IL-4R
IL-12R
STAT1
STAT6
STAT4
GATA3
T-bet
30
IFN-g
IL-4
IFN-gR
IL-4R
IL-18R
STAT1
STAT6
IRAK
GATA3
T-bet
31
IFN-g
IFN-gR
STAT1
STAT4
GATA3
T-bet
32
IL-4
IL-4R
STAT6
GATA3
33
IL-4R
STAT6
SOCS1
GATA3
T-bet
34
GATA3
T-bet
35
T-bet
36
IL-4
IFN-gR
IL-4R
STAT1
STAT6
SOCS1
GATA3
T-bet
37
IFN-gR
STAT1
SOCS1
38
IFN-gR
STAT1
SOCS1
T-bet
39
The Th network has 22 feedback loops
- 19 positive
- 3 negative
Are they functional?
40
Choice of parameters
Two general strategies
i)
Deductive
What are the sets of parameters that give
functionality to all the loops in the system?
ii) Inductive
Given a set of parameters, what is the behavior
of the system?
41
Levels of node activation
NODE
All elements have a «low» activation level
NODE
IFN-g, IFN-gR, STAT-1 and T-bet have also
an «intermediate» activation level
NODE
All elements have a «high» activation level
42
Dynamical rules for the Th model
Node
Activation state as a function of the regulatory nodes
IFN-g
KIFN-g=l
KIFN-g(IRAK)=l
IL-4
IL-12
IL-18
IFN-
IFN-gR
IL-4R
IL-12R
IL-18R
IFN-R
STAT-1
STAT-6
STAT-4
KIL-4=l
KIL-4(STAT-1m)=l
KIL-4(STAT-1m,GATA-3)=l
KIL-4(STAT-1h)=l
KIL-4(STAT-1h,GATA-3)=l
KIL-12=l
IFN-g
KIL-18=l
KIFN-=l
KIFN-gR=l
KIFN-gR(SOCS-1)=l
KIL-4R=l
KIL-4R(IL-4,SOCS-1)=l
KIL-4R(SOCS-1)=l
KIL-12R=l
KIL-12R(IL-12,STAT-6)=l
KIL-12R(STAT-6)=l
KIL-18R=l
KIL-18R(IL-18,STAT-6)=l
KIL-18R(STAT-6)=l
KIFN-R=l
KSTAT-1=l
KSTAT-6=l
KSTAT-4=l
KSTAT-4(IL-12R,GATA-3)=l
KIFN-g(STAT-4)=m
KIFN-g(STAT-4,T-betm)=m
KIFN-g(IRAK,T-bet m)=m
KIFN-g(T-betm)=m
KIFN-g(STAT-4,IRAK)=h
KIFN-g(STAT-4,IRAK,T-bet m)=h
KIFN-g(STAT-4,IRAK,T-beth)=h
KIFN-g(STAT-4,T-beth)=h
KIFN-g(IRAK,T-beth)=h
KIFN-g(T-beth)=h
KIL-4(GATA-3)=h
KIFN-gR(IFN-gm)=m
KIFN-gR(IFN-gm,SOCS-1)=m
KIFN-gR(IFN-gh,SOCS-1)=m
KIFN-gR(IFN-gh)=h
KIL-4R(IL-4)=h
KIL-12R(IL-12)=h
STAT4
IRAK
KIL-18R(IL-18)=h
T-bet
KIFN-R(IFN-)=h
KSTAT-1(IFN-R)=m
KSTAT-1(IFN-gRm)=m
KSTAT-1(IFN-gRm,IFN-R)=m
KSTAT-1(IFN-gRh)=h
KSTAT-1(IFN-gRh,IFN-R)=h
KSTAT-6(IL-4R)=h
KSTAT-4(IL-12R)=h
43
Writing the transition rules
STAT6
GATA3
GATA3
…
GATA3()=0
GATA3(T-bet)=0
GATA3(STAT6)=1
GATA3(STAT6;T-bet)=0
GATA3(GATA3)=1
GATA3(GATA3;T-bet)=0
GATA3(GATA3;STAT6)=1
GATA3(GATA3;STAT6;T-bet)=0
…
t+1
GATA3
STAT6
T-bet
t
000
001
010
011
100
101
110
111
0
0
1
0
1
0
1
0
T-bet
44
Both Th1 and Th2 switches are functional
IFN-g
IL-4
IL-12
IL-18
IFN-
IFN-gR
IL-4R
IL-12R
IL-18R
IFN-R
STAT1
STAT6
STAT4
IRAK
SOCS1
GATA3
T-bet
45
Th1 and Th2 switches are still functional
IFN-g
IL-4
IL-12
IL-18
IFN-
IFN-gR
IL-4R
IL-12R
IL-18R
IFN-R
STAT1
STAT6
STAT4
IRAK
SOCS1
GATA3
T-bet
46
Th1 and T-bet switches are functional
IFN-g
IL-4
IL-12
IL-18
IFN-
IFN-gR
IL-4R
IL-12R
IL-18R
IFN-R
STAT1
STAT6
STAT4
IRAK
SOCS1
GATA3
T-bet
47
Attenuation of IFN-g signaling (1)
IFN-g
IL-4
IL-12
IL-18
IFN-
IFN-gR
IL-4R
IL-12R
IL-18R
IFN-R
STAT1
STAT6
STAT4
IRAK
SOCS1
GATA3
T-bet
48
Attenuation of IFN-g signaling (2)
IFN-g
IL-4
IL-12
IL-18
IFN-
IFN-gR
IL-4R
IL-12R
IL-18R
IFN-R
STAT1
STAT6
STAT4
IRAK
SOCS1
GATA3
T-bet
49
Predicting : knock out and overexpression
IFN-g
IL-4
IL-12
IL-18
IFN-
IFN-gR
IL-4R
IL-12R
IL-18R
IFN-R
STAT1
STAT6
STAT4
IRAK
SOCS1
GATA3
T-bet
50
Phenotype of mutant models
Models
Attractors
Wild type, IL-12-, IL-18-, IFN--,
IL-12R-, IFN-R-, IL-18R-,
STAT-4-, IRAK-, IL-12-/IL-12RIFN-g-
i) lllllllllllllllll
iii) mllllmllllmlllhlm
ii) hllllmllllmlllhlh
iv) lhllllhllllhlllhl
i) lllllllllllllllll
iii) llllllllllllllhlh
i) lllllllllllllllll
iii) hllllmllllmlllhlh
i) lllllllllllllllll
iii) hlllllllllllllhlh
i) lllllllllllllllll
iii) hllllmllllllllhlh
i) lllllllllllllllll
iii) hllllhllllhlllllh
i) lllllllllllllllll
i) hllllmllllmlllhlh
i) lhllllhllllhlllhl
iii) hhlllmllllmlllhlh
i) mlhllmlhllmlhlhlm
iii) lhhlllhllllhlllhl
i) lllhllllhllllhlll
iii) hllhlmllhlmllhhlh
i) mlllmhlllmhlllhlm
i) hllllhllllhlllhlh
i) hlhhlmlhhlmlhhhlh
iii) lhhhllhllllhlllhl
i) lhllllhllllhlllhl
iii) hllllmhlllmhllhlh
i) mllllmlhllmlhlhlm
iii) lhllllhhlllhlllhl
i) llllllllhllllhlll
iii) hllllmllhlmllhhlh
i) mllllmlllhmlllhlm
i) hllllmllllhlllhlh
i) lhllllhllllhlllhl
iii) hllllmllllmhllhlh
i) lllllllllllllhlll
iii) hllllmllllmllhhlh
i) llllllllllllllhll
iii) hllllmllllmlllhlh
i) lhllllhllllhlllhl
iii) hllllmllllmlllhhh
i) hllllmllllmlllhlh
ii) llllllllllllllhlm
iv) lhllllhllllhlllhl
ii) mllllmllllmlllhlm
IL-4-, IL4R-, STAT6-, GATA3IFN-gRSTAT-1SOCS-1T-betIFN-g+
IL-4+
IL-12+
IL-18+
IFN-+
IFN-gR+
IL-12+/IL-18+
IL-4R+
IL-12R+
IL-18R+
IFN-R+
STAT-1+
STAT-6+
IRAK+
SOCS-1+
GATA3+
T-bet+
ii) mlllllllllllllhlm
iv) lhllllhllllhlllhl
ii) hllllhllllllllhlm
iv) lhllllhllllhlllhl
ii) mllllmllllmlllllm
iv) lhllllhllllhlllhl
ii) lhllllhllllhlllhl
ii) hllllmllllmlllhlm
ii) mhlllmllllmlllhlm
ii) hlhllmlhllmlhlhlh
ii) mllhlmllhlmllhhlm
iv) lhlhllhllllhlllhl
ii) hlllmhlllmhlllhlh
ii) hlhhlmlhhlmlhhhlm
ii) mllllmhlllmhllhlm
ii) hllllmlhllmlhlhlh
ii) mllllmllhlmllhhlm
iv) lhllllhlhllhlhlhl
ii) hllllmlllhmlllhlh
ii) mllllmllllmhllhlm
ii) mllllmllllmllhhlm
iv) lhllllhllllhlhlhl
ii) mllllmllllmlllhlm
ii) mllllmllllmlllhhm
L Mendoza
Biosystems 2006
51
The Th model vs knock-out experiments
IFN-g- cells do not produce IFN-g
Tang et al. (1998). J. Immunol. 160: 5105
But IFN-gR- cells do produce IFN-g
Diehl et al. (2000). Immunity 13: 805
52
The Th model vs knock-out experiments
In the « classical » point of view
53
The Th model vs knock-out experiments
In the « network » point of view
54
Published networks that do not generate Th differentiation
IL-12
IFN-g
Inf.
Resp.
Steroids
IL-4
IL-10
IL-5
TCR
IL-4R
IFN-gR
IL-12
IL-13
STAT6
STAT1
IL-12R
IL-5
GATA3
T-bet
STAT4
IL-4
IFN-g
IL-4
IFN-g
CSIF
IL-2
Ag/
MHC
CD4
Lck
Itk
NFAT
MKK3
TCR
JNK
c-Maf
IL-4R
IL-13
p38/
MAPK
TRAF6
IRAK
JNK2
STAT6
IL-4
ATF2
NFkB
IL-18R
IL-18
GATA3
IL-5
IFN-g
T-bet
STAT4
IL-12R
IL-12
55
Summary of the Generalized Logical Algorithm
PROS
There is enough information to model the Th cell differentiation
The Th model displays the WT known steady states
It describes many null-mutants and constitutive expression types
We can model a network that encompass dozens of molecules
CONS
Feedback loop analysis is a qualitative approach
Extend the model to describe quantitative data
Moving towards a continuous model
56
A semi-quantitative approach
Problem:
There is not « available » quantitative data on the
levels of activity for the molecules of most networks
Solution:
Instead of modeling the absolute levels of the
active forms of the molecules, represent the
normalized values of activation
maximal activity
1
minimal activity
0
time
57
Equations
dxi
 e 0.5h  e  h(ωi 0.5)
 γi xi

dt (1  e 0.5h )(1  e  h(ωi 0.5) )
i 
 1   αn   αn xna   1   βm   βm xm





1
ωi  



i 
a 
  αn  1   αn xn    βm  1   βm xm  
0  xi  1
0  i  1
{xna } is the set of activators of xi
{xna } is the set of inhibitors of xi
h, {a n }, { m }, and {g i } are adjustable parameters
58
Equations
dxi
 e 0.5h  e  h(ωi 0.5)

 γi xi
dt (1  e 0.5h )(1  e  h(ωi 0.5) )
it is a rate equation
with an activation component
and a decay element
59
Equations
dxi
 e 0.5h  e  h(ωi 0.5)

 γi xi
dt (1  e 0.5h )(1  e  h(ωi 0.5) )
60
Equations
i 
 1   αn   αn xna   1   βm   βm xm




ωi  
1




a 
i 
  αn  1   αn xn    βm  1   βm xm  
1
output
more activation and/or
less inhibition
less activation and/or
more inhibition
0
input
1
61
Analyzing the continuous system is complicated
It is a non-linear system, and such systems:
• Don’t have analytical solutions
• Have complex dynamics (may include chaos)
• The steady-states are hard to find
-normally done with using numerical methods,
which
- depend on iterations from an initial point
- don’t necessarily converge
- don’t necessarily find all steady-states
62
The Rossler Attractor
dx
 y  z
dt
dy
 x  ay
dt
dz
 b  cz  xz
dt
63
Analyzing the discrete system is simple
Despite being non-linear:
• Have simple dynamics
• The steady-states are easy to find
- using a method (GLA) that finds all stable steady-states
64
Methodology
xi(t  1 )  g(x1(t)...xn(t))
dx i
 f(x1...xn)
dt
x1(t 0)  0; x2(t 0)  1...
L Mendoza, Tbiomed 2006
65
The Th model
TCR
IL-18
IL-12
IFN-g
IL-4
IL-10
NFAT
IL-18R
IL-12R
IFN-gR
IL-4R
IL-10R
IFN-
IRAK
STAT4
JAK1
STAT6
STAT3
IFN-R
SOCS1
T-bet
STAT1
GATA3
66
Th0 attractor
TCR
IL-18
IL-12
IFN-g
IL-4
IL-10
NFAT
IL-18R
IL-12R
IFN-gR
IL-4R
IL-10R
IFN-
IRAK
STAT4
JAK1
STAT6
STAT3
IFN-R
SOCS1
T-bet
STAT1
GATA3
67
level of activation
Starting at the Th0 attractor
68
Th1 attractor
TCR
IL-18
IL-12
IFN-g
IL-4
IL-10
NFAT
IL-18R
IL-12R
IFN-gR
IL-4R
IL-10R
IFN-
IRAK
STAT4
JAK1
STAT6
STAT3
IFN-R
SOCS1
T-bet
STAT1
GATA3
70
level of activation
Starting at the Th1 attractor
71
Th2 attractor
TCR
IL-18
IL-12
IFN-g
IL-4
IL-10
NFAT
IL-18R
IL-12R
IFN-gR
IL-4R
IL-10R
IFN-
IRAK
STAT4
JAK1
STAT6
STAT3
IFN-R
SOCS1
T-bet
STAT1
GATA3
73
level of activation
Starting at the Th2 attractor
74
Comparison of random and continuous model
50’000 randomly chosen starting nodes values we
ended in
16% Th0
51% Th1
32% Th2
L Mendoza, Tbiomed 2006
76
Stability of the Th0 attractor
IL-4 perturbation
level of activation
IFN-g perturbation
77
Stability of the Th1 attractor
IL-4 perturbation
level of activation
IFN-g perturbation
78
Stability of the Th2 attractor
IFN-g perturbation
level of activation
IL-4 perturbation
79
The constitutive expression of T-bet in Th model
TCR
IL-18
IL-12
IFN-g
IL-4
IL-10
NFAT
IL-18R
IL-12R
IFN-gR
IL-4R
IL-10R
IFN-
IRAK
STAT4
JAK1
STAT6
STAT3
IFN-R
SOCS1
T-bet
STAT1
GATA3
80
Szabo et al. 2000. Cell 100: 655
81
The T-bet+ Th model
level of activation
Th0
82
The T-bet+ Th model
level of activation
Th1
83
The T-bet+ Th model
level of activation
Th2
84
From one « archetypic cell » to many cells
Simulation
With a 1’000
cells
IL4
Random
Initial states
IFNg
Let the system
« run »
IL10
« extract cells »
And identify their
state
85
Cell Culture Results
Th2
New States
Th1
Th0
Cell cultures recapitulates the three final states however
Two novel « intermediary states are observed »
86
Building of a Multi Cellular Model (DTH)
87
Model building and Validation workflow
Which problem?
What data is available?
Which formalism is appropriate?
Y
X
Model as a guide to plan experiments
and to gain knowledge of the biological system
Make an abstraction
Validate against new data
Make predictions
Fit model to data
88
Conclusions
We have developed a standardized methodology to
generate the dynamical behaviour of any cellular networks
This approach is useful when no or little quantitative data are
available
Only the network topology i.e. activation and inhibition
between molecules is necessary.
We extended this approach to multicellular system and
to animal models.
89
Acknowledgments
University of Mexico
Luis Mendoza
EPFL – CS
Giovanni di Micheli
Abishek Garg (Model checking/FPGA)
FP6 Grant ENFIN lead by Ewan Birney
Serono Pharmaceutical
EBI Hinxton (PSI-HUPO)
Massimo de Francesco
Mark Ibberson
David Cregut
Maria Karmirantzou
Francisca Zanoguera
Francois Talabot
Francis Vilbois (MIM)
Henning Hermjakob
Rolf Apweiler
University of Geneva
Sandrine Da Cruz (MIM)
Jean-Claude Martinou (MIM)
University of Lausanne
Manfredo Quadroni (BAF-L/FAS-L)
UCLA-DOE
David Eisenberg
Lukasz Salwinski (DIP-FPGA)
Joyce Xiaquon Duan (LiveDIP)
Charlotte Dean (EPR)
Ralf Landgraf (3DCluster)
University of Texas Austin
Edward M Marcotte
90