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

Hidde.de-Jong@inrialpes.fr

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

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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

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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

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l

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P

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Ca

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etw

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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:

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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

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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

. x b=

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

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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 ) –

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. x b=

κbs-(xa,

θa1) –

γ bxb

.θ a1

0

maxb

θa2

θb

maxa

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κb/γb

xa

=κa –

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. x b=

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

. x b=

κbs-(xa,

θa1) –

γ bxb

.

xa

=κa –

γ axa

. x b=–

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

. x b=

κbs-(xa,

θa1) –

γ bxb

.θ a1

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

. x b=

κbs-(xa,

θa1) –

γ bxb

.θ a1

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

. x b> 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

. x b> 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

. x b> 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

n u

sin

g m

od

el ch

eckin

g

D1

D3

D5 D7

D9

D15

D27

D26

D25

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