Hidde.de-Jong@inrialpes - NTNU
30
Qualitative Analysis of Piecewise-Affine Models of Genetic Regulatory Networks Hidde de Jong INRIA Rhône-Alpes [email protected] HYGEIA PhD School on Hybrid Systems Biology
Transcript of Hidde.de-Jong@inrialpes - NTNU
Qu
alita
tive A
naly
sis
of
Pie
cew
ise-A
ffin
e
Mo
dels
of
Gen
eti
c R
eg
ula
tory
Netw
ork
s
Hid
de
de
Jo
ng
INR
IA R
hô
ne-A
lpes
HY
GE
IA P
hD
Sch
oo
l on
Hyb
rid
Syste
ms B
iolo
gy
2
Ove
rvie
w
1.
Genetic r
egu
lato
ry n
etw
ork
s
2.
Mode
ling o
f genetic r
egu
lato
ry n
etw
ork
s:
obje
ctive a
nd
constr
ain
ts
3.
Pie
ce
wis
e-a
ffin
e m
odels
of
gene
tic r
egula
tory
netw
ork
s
4.
Qualit
ative a
na
lysis
an
d v
erificatio
n o
f pie
cew
ise-a
ffin
e
mode
ls
5.
Genetic N
etw
ork
Analy
zer
(GN
A)
6.
Co
nclu
sio
ns a
nd p
ers
pectives
3
Ba
cte
ria
lce
llan
dp
rote
ins
�P
rote
ins
are
build
ing b
locks o
fcell:
�T
ranspo
rt o
f n
utr
ien
tsa
nd
wa
ste
pro
du
cts
acro
ss
ce
llm
em
bra
ne
�E
xtr
actio
n o
f e
nerg
yfr
om
nu
trie
nts
�C
on
tro
l o
fg
row
tha
nd
div
isio
n
�A
da
pta
tio
n to e
xte
rna
lp
ert
urb
atio
ns
4
Va
ria
tion
in
pro
tein
leve
ls
�P
rote
inle
vels
in c
ell
are
adju
ste
dto
specific
environm
enta
l
cond
itio
ns
Peng, S
him
izu (
2003),
A
pp. M
icro
bio
l. B
iote
chnol., 61:1
63-1
78
Ali
Azam
et al. (
1999),
J.
Bacte
riol., 181(2
0):
6361-6
370
2D
ge
ls
We
ste
rn b
lots
DN
A
mic
roa
rra
ys
5
Syn
thesis
an
dd
eg
rada
tio
no
fp
rote
ins
DN
A
mR
NA
pro
tein
mo
difie
dp
rote
in
transcriptio
n
transla
tio
n
post-
transla
tio
nal
modific
ation
eff
ecto
rm
ole
cu
le
degra
datio
np
rote
ase
RN
A p
oly
me
rase
rib
oso
me
6
Re
gula
tio
no
fsyn
thesis
an
dd
eg
rada
tio
n
RB
S
mR
NA
rib
oso
me
mo
difie
dp
rote
in
kin
ase
pro
tea
se
RN
A p
oly
me
rase
tra
nscri
ptio
n
facto
r
DN
A
sm
all
RN
A
resp
on
se
reg
ula
tor
7
Ge
ne
tic
reg
ula
tory
ne
two
rks
�C
ontr
ol ofpro
tein
syn
thesis
and
degra
datio
ngiv
es
rise
to
gen
eti
cre
gu
lato
ryn
etw
ork
s
Ne
twork
s o
fge
nes, R
NA
s, p
rote
ins, m
eta
bo
lite
s, a
nd
the
irin
tera
ctio
ns
Activation
Str
ess
sig
na
l
CR
P
crpcya
CY
A
fis
FIS
Superc
oili
ng
Top
A
topAG
yrA
B
P1-P
4P
1P
2P2
P1-P
’1
rrn
P1
P2
P
gyrA
BP
tRN
A
rRN
A
GyrI
gyrI
P
rpoS
P1
P2n
lpD
σS
RssB
rssA
PA
PB
rssB
P5
Ca
rbo
nsta
rva
tio
nn
etw
ork
in
E.
co
li
8
An
aly
sis
ofg
en
etic
reg
ula
tory
ne
two
rks
�A
bu
nd
ant
kno
wle
dge o
n c
om
po
nents
and in
tera
ctions o
f
gen
etic r
eg
ula
tory
netw
ork
s
�S
cie
ntific k
now
led
ge
ba
se
s a
nd
da
tab
ase
s
�B
iblio
gra
ph
ic d
ata
ba
se
s
�C
urr
ently n
o u
nders
tand
ing o
f how
glo
bal dynam
ics e
merg
es
from
loca
l in
tera
ctions b
etw
een c
om
pon
ents
�R
espo
nse
of ce
ll to
exte
rna
l str
ess
�D
iffe
ren
tia
tion
of ce
ll d
uri
ng
de
ve
lopm
en
t
�S
hift fr
om
str
uctu
reto
dyn
am
ics
ofnetw
ork
s
«fu
nctio
na
lge
no
mic
s»
, «
inte
gra
tive
bio
log
y»
, «
syste
ms
bio
log
y»
, …
Kitano
(2002),
Scie
nce, 295(5
560):
564
9
Ma
them
atica
lm
eth
od
sa
nd
co
mp
ute
r to
ols
�M
od
elin
gand
sim
ula
tio
nin
dis
pensa
ble
for
dynam
ic a
na
lysis
of
genetic r
egu
lato
ry n
etw
ork
s:
�U
nd
ers
tand
ing
role
ofin
div
idu
alco
mp
one
nts
an
din
tera
ctio
ns
�S
ug
ge
stin
gm
issin
gcom
pon
en
ts a
nd
inte
ractio
ns
�V
ari
ety
ofm
ode
ling
form
alis
ms
exis
t, d
escrib
ing
syste
mon
diffe
rent
levels
of
deta
il
de J
ong
(2002),
J. C
om
put. B
iol., 9(1
): 6
9-1
05
Gra
phs
Boole
an
eq
uations
Diffe
rentia
lequ
ations
Sto
chastic
maste
r equatio
ns
pre
cis
ion
sim
pli
cit
y
10
Co
nstr
ain
tson
mo
delin
gand
sim
ula
tio
n
�C
urr
ent
co
nstr
ain
tson m
odelin
gand
sim
ula
tion:
�K
no
wle
dg
eon
mo
lecu
lar
me
ch
an
ism
sra
re
�Q
uan
tita
tive
in
form
ation
on k
ine
tic
para
me
ters
and
mo
lecu
lar
co
ncen
tra
tio
ns a
bsen
t
�P
ossib
le s
trate
gie
s t
o o
verc
om
e t
he c
onstr
ain
ts
�P
ara
me
ter
estim
atio
n fro
m e
xp
eri
me
nta
l d
ata
�P
ara
me
ter
sen
sitiv
ity a
na
lysis
�M
od
el sim
plif
ica
tio
ns
�In
tuitio
n:
essentia
l pro
pert
ies o
f syste
m d
ynam
ics r
ob
ust
aga
inst
modera
te c
ha
nges in k
inetic p
ara
mete
rs a
nd r
ate
law
s
Ste
lling
et al.
(2004),
Cell,
118(6
):675-8
6
11
Qu
alit
ative
mo
de
ling
an
dsim
ula
tion
�Q
ualita
tive
modelin
g a
nd s
imu
lation o
f la
rge a
nd c
om
ple
x
gen
etic r
eg
ula
tory
netw
ork
s u
sin
g s
imp
lifi
ed
models
�A
pp
lication
s o
fqualit
ative s
imu
lation:
�in
itia
tio
n o
fspo
rula
tio
n in
Ba
cill
us
su
btilis
�q
uoru
m s
ensin
gin
Pseu
dom
on
as
aeru
gin
osa
�o
nse
to
fvir
ule
nce
in
Erw
inia
chry
san
them
i
de J
ong, G
ouzé
et al.
(2004),
Bull.
Math
. B
iol., 66(2
):301-4
0
Batt
et al.
(2007),
Auto
matica, accepte
dfo
r public
ation
de J
ong, G
eis
elm
ann
et al.
(2004),
Bull.
Math
. B
iol., 66(2
):261-3
00
Viretta
and
Fussenegger,
Bio
technol. P
rog., 2
004, 20(3
):6
70
-67
8
Sepulc
hre
et al., J. T
heor.
Bio
l., 2007, 244(2
):239-5
7
12
PA
diffe
ren
tial e
qu
atio
n m
ode
ls
�G
enetic n
etw
ork
s m
od
ele
d b
y c
lass o
f diffe
rentia
l eq
ua
tions
usin
g s
tep
fu
ncti
on
sto
describ
e r
egu
lato
ry inte
ractions
xa
=κas-(xa,
θa2) s-(xb,
θb) –
γ axa
. xb
=κbs-(xa,
θa1) –
γ bxb
.
x : p
rote
incon
cen
tra
tio
n
κ,
γ:
rate
con
sta
nts
θ:
thre
sh
old
co
ncen
tra
tio
n
x
s-(x, θ)
θ01
�D
iffe
rential equ
atio
n m
ode
ls o
f re
gu
lato
ry n
etw
ork
s a
re
pie
cew
ise-a
ffin
e (
PA
)
b
B
a
A
Gla
ss a
nd K
auffm
an (
1973),
J.
Theor.
Bio
l., 39(1
):103-2
9
13
�A
na
lysis
of dynam
ics o
f P
A m
odels
in p
hase s
pace
θa1
0
maxb
θa2
θb
maxa
Ma
them
atica
l a
na
lysis
of P
A m
od
els
xa
=κas-(xa,
θa2) s-(xb,
θb ) –
γ axa
. xb
=κbs-(xa,
θa1) –
γ bxb
.θa1
0
maxb
θa2
θb
maxa
κa/γa
κb/γb
xa
=κa –
γ axa
. xb
=κb –
γ bxb
.
D1
14
�A
na
lysis
of dynam
ics o
f P
A m
odels
in p
hase s
pace
θa1
0
maxb
θa2
θb
maxa
Ma
them
atica
l a
na
lysis
of P
A m
od
els
xa
=κas-(xa,
θa2) s-(xb,
θb ) –
γ axa
. xb
=κbs-(xa,
θa1) –
γ bxb
.
xa
=κa –
γ axa
. xb
=–
γ bxb
.
θa1
0
maxb
θa2
θb
maxa
κa/γa
D5
15
�A
na
lysis
of dynam
ics o
f P
A m
odels
in p
hase s
pace
�E
xte
nsio
n o
f P
A d
iffe
rentia
l eq
ua
tio
ns
to d
iffe
rentia
l in
clu
sio
ns
usin
g F
ilip
pov
appro
ach
θa1
0
maxb
θa2
θb
maxa
Ma
them
atica
l a
na
lysis
of P
A m
od
els
xa
=κas-(xa,
θa2) s-(xb,
θb ) –
γ axa
. xb
=κbs-(xa,
θa1) –
γ bxb
.θa1
0
maxb
θa2
θb
maxa
D3
Gouzé, S
ari (
2002),
Dyn. S
yst., 17(4
):299-3
16
16
�A
na
lysis
of dynam
ics o
f P
A m
odels
in p
hase s
pace
�E
xte
nsio
n o
f P
A d
iffe
rentia
l eq
ua
tio
ns
to d
iffe
rentia
l in
clu
sio
ns
usin
g F
ilip
pov
appro
ach
θa1
0
maxb
θa2
θb
maxa
Ma
them
atica
l a
na
lysis
of P
A m
od
els
xa
=κas-(xa,
θa2) s-(xb,
θb ) –
γ axa
. xb
=κbs-(xa,
θa1) –
γ bxb
.θa1
0
maxb
θa2
θb
maxa
D7
Gouzé, S
ari (
2002),
Dyn. S
yst., 17(4
):299-3
16
17
�P
hase s
pa
ce p
art
itio
n: u
niq
ue d
erivative s
ign p
att
ern
in r
egio
ns
�Q
ualita
tive a
bstr
acti
on
yie
lds s
tate
tra
nsitio
n g
raph
Sh
ift fr
om
con
tin
uo
us to d
iscre
te p
ictu
re o
f n
etw
ork
dyn
am
ics
θa1
0
maxb
θa2
θb
maxa
Qu
alit
ative
ana
lysis
of n
etw
ork
dyn
am
ics
θa1
0
maxb
θa2
θb
maxa
. ..
. ..
xa> 0
xb> 0
xa> 0
xb< 0
xa= 0
xb< 0
D1:
D5:
D7:
D12
D22
D23
D24
D17
D18
D21
D20
D1
D3
D5D7
D9
D15
D27
D26
D25
D11
D13 D14
D2D4 D6 D8
D10
D16
D19
D1
D3
D5
D7
D9
D15
D27
D26
D25
D11
D12
D13
D14
D2
D4
D6
D8
D10
D16
D17
D18
D20
D19
D21
D22
D23
D24
18
�S
tate
tra
nsitio
n g
rap
h in
vari
an
tfo
r para
mete
r constr
ain
ts
Qu
alit
ative
ana
lysis
of n
etw
ork
dyn
am
ics
D1
D3
D11
D12
θa1
0
maxb
θa2
θb
maxa
θa1
0
maxb
θa2
θb
maxa
κa/γa
κb/γb
D1
D11
D12
D3
0 < θa1< θa2 < κa/γa< maxa
0 < θb< κb/γb<maxb
19
�S
tate
tra
nsitio
n g
rap
h in
vari
an
tfo
r para
mete
r constr
ain
ts
Qu
alit
ative
ana
lysis
of n
etw
ork
dyn
am
ics
D1
D3
D11
D12
0 < θa1< θa2 < κa/γa< maxa
0 < θb< κb/γb<maxb
θa1
0
maxb
θa2
θb
maxa
θa1
0
maxb
θa2
θb
maxa
κa/γa
κb/γb
D1
D11
D12
D3
20
�S
tate
tra
nsitio
n g
rap
h in
vari
an
tfo
r para
mete
r constr
ain
ts
Qu
alit
ative
ana
lysis
of n
etw
ork
dyn
am
ics
D1
D3
D11
D12
0 < θa1< θa2 < κa/γa< maxa
0 < θb< κb/γb<maxb
θa1
0
maxb
θa2
θb
maxa
θa1
0
maxb
θa2
θb
maxa
κa/γa
κb/γb
D1
D11
D12
D3
D1
D11
θa1
0
maxb
θa2
θb
maxa
θa1
0
maxb
θa2
θb
maxa
κa/γa
κb/γb
D1D11
D12
D3
0 <
κa/γa< θa1< θa2 < maxa
0 < θb< κb/γb<maxb
21
�P
red
ictio
ns w
ell
ad
apte
d t
o c
om
pariso
n w
ith a
va
ilab
le
experi
menta
l data
: ch
an
ges o
f d
eri
vati
ve s
ign
patt
ern
s
�M
od
el valid
ati
on
: com
pariso
n o
f derivative s
ign p
att
ern
s in
observ
ed a
nd p
red
icte
d b
ehavio
rs
�N
eed f
or
auto
mate
d a
nd e
ffic
ient
too
lsfo
r m
ode
l va
lidatio
n
D1
D3
D5
D7
D9
D15
D27
D26
D25
D11
D12
D13
D14
D2
D4
D6
D8
D10
D16
D17
D18
D20
D19
D21
D22
D23
D24
Va
lida
tio
n o
f q
ua
lita
tive
mo
dels
..
xa< 0
xb> 0
xa> 0
xb> 0
xa= 0
xb= 0
. ..
.D1:
D17:
D18:
Co
ncis
tency?
Yes
0xb
tim
e
tim
e0xa
xa> 0
. xb> 0
.xb> 0
.x a< 0
.
22
�C
om
pute
sta
te tra
nsitio
n g
rap
h a
nd e
xpre
ss d
ynam
ic p
ropert
ies
in t
em
pora
l lo
gic
�U
se o
f m
odel checkers
to v
erify
wheth
er
exp
erim
enta
l d
ata
and
pre
dic
tio
ns a
re c
onsis
tent
Va
lida
tio
n u
sin
g m
od
el ch
eckin
g
Co
ncis
tency?
D1
D3
D5 D7
D9
D15
D27
D26
D25
D11
D12
D13
D14
D2
D4
D6
D10
D16
D17
D18
D20
D19
D21
D22
D23
D24
D8
0xb
tim
e
tim
e0xa
xa> 0
. xb> 0
.xb> 0
.x a< 0
.
Batt
et al.
(2005),
Bio
info
rmatics, 21(s
upp. 1):
i19-2
8
23
�C
om
pute
sta
te tra
nsitio
n g
rap
h a
nd e
xpre
ss d
ynam
ic p
ropert
ies
in t
em
pora
l lo
gic
�U
se o
f m
odel checkers
to v
erify
wheth
er
exp
erim
enta
l d
ata
and
pre
dic
tio
ns a
re c
onsis
tent
Va
lida
tio
n u
sin
g m
od
el ch
eckin
g
D1
D3
D5 D7
D9
D15
D27
D26
D25
D11
D12
D13
D14
D2
D4
D6
D10
D16
D17
D18
D20
D19
D21
D22
D23
D24
D8
Batt
et al.
(2005),
Bio
info
rmatics, 21(s
upp. 1):
i19-2
8
Co
ncis
tency?
0xb
tim
e
tim
e0xa
xa> 0
. xb> 0
.xb> 0
.x a< 0
.
EF(xa> 0
∧xb> 0
∧EF(xa< 0
∧xb> 0) )
..
..
24
�C
om
pute
sta
te tra
nsitio
n g
rap
h a
nd e
xpre
ss d
ynam
ic p
ropert
ies
in t
em
pora
l lo
gic
�U
se o
f m
odel checkers
to v
erify
wheth
er
exp
erim
enta
l d
ata
and
pre
dic
tio
ns a
re c
onsis
tent
Va
lida
tio
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info
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J. M
ath
Bio
l., 52(1
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):336-4
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et al.
(2005),
Bio
info
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27
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igh-levelsp
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uis
ite
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her
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ling
Dru
lhe
et al.
(2006),
Hybrid S
yste
ms: C
om
puta
tion a
nd C
ontr
ol, L
NC
S 3
927, 184-9
9
Muste
rs e
t al.
(2007),
Hybrid S
yste
ms: C
om
puta
tion a
nd C
ontr
ol, L
NC
S 4
416, 727-7
30
28
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ture
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aly
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29
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ork
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ork
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ati
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ars
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sti
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late
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de
ls
30
Co
ntr
ibu
tors
an
d s
pon
so
rs
Gré
gory
Batt, U
niv
ers
ité
Joseph F
ourier,
Gre
noble
Hid
de
de J
ong, IN
RIA
Rhône-A
lpes
Este
lle D
um
as, IN
RIA
Rhône-A
lpes
Hans G
eis
elm
ann, U
niv
ers
ité
Joseph F
ourier,
Gre
noble
Jean-L
uc G
ouzé, IN
RIA
Sophia
-Antipolis
Radu
Mate
escu, IN
RIA
Rhône-A
lpes
Pedro
Monte
ro, IN
RIA
Rhône-A
lpes/IS
T, Lis
bon
Mic
hel P
age, IN
RIA
Rhône-A
lpes/U
niv
ers
ité
Pie
rre M
endès
Fra
nce, G
renoble
Delp
hin
eR
opers
, IN
RIA
Rhône-A
lpes
Tew
fik
Sari,
Univ
ers
ité
de H
aute
Als
ace, M
ulh
ouse
Min
istè
re d
e la R
echerc
he,
IMP
BIO
pro
gra
mE
uro
pean
Com
mis
sio
n,
FP
6, N
ES
T p
rogra
m
INR
IA,
AR
C p
rogra
mA
gence N
ationale
de la
Recherc
he, B
ioS
ys
pro
gra
m
