SLIDE 1 A Dis rete Approa h to Mo del Gene Regulatory Net w
and the Use
F
Logi to Prop
New W et Exp erimen ts Gilles Bernot Univ ersit y
Ni e sophia antipolis, I3S lab
A kno wledgmen ts: Observability Gr
the Epigenomi s Pro je t 1
SLIDE 2 Men u 1. Sim ulation vs. V alidation 2. F
Metho ds for the Mo delling A tivit y 3. Gene Regulatory Net w
& T emp
Logi 4. P edagogi al example: Pseudomonas aeruginosa 2
SLIDE 3 Mathemati al Mo dels and Sim ulation 1. Rigorously en o de sensible kno wledge in to mathemati al form ulae 2.
parameters are w ell dened, e.g. from bio hemi al kno wledge
parameters are limited to some in terv als
parameters are a priori unkno wn 3. P erform lot
sim ulations,
results with kno wn b eha viours, and prop
some redible v alues
the unkno wn parameters whi h pro du e a eptable b eha viours 4. P erform additional sim ulations ree ting no v el situations 5. If they predi t in teresting b eha viours, prop
new biologi al exp erimen ts 6. Simplify the mo del and try to go further 3
SLIDE 4 Mathemati al Mo dels and V alidation Brute for e sim ulations are not the
w a y to use a
W e an
aided en vironmen ts whi h help:
a v
mo dels that an b e tuned ad libitum
v alidate mo dels with a reasonable n um b er
exp erimen ts
dene
mo dels that
b e exp erimen tally refuted
pro v e refutabilit y w.r.t. exp erimen tal apabilities Observability issues: Observability Gr
Epigenomi s Pro je t. 4
SLIDE 5 Men u 1. Sim ulation vs. V alidation 2. F
Metho ds for the Mo delling A tivit y 3. Gene Regulatory Net w
& T emp
Logi 4. P edagogi al example: Pseudomonas aeruginosa 5
SLIDE 6 F
Logi : syn tax/seman ti s/dedu tion
cyan=Computer green=Mathematics
correctness
Rules
proof
Semantics
Models
Syntax Deduction
proved=satisfied
completeness
Formulae red=Computer Science
M | = ϕ Φ ⊢ ϕ
satisfa tion 6
SLIDE 7 Computer Aided Elab
Mo dels F rom biologi al kno wledge and/or biologi al h yp
it
erties: Without stimulus, if gene x has its b asal expr ession level, then it r emains at this level.
del s hemas:
+ + x 1 2 1
y + + 2 1 1 . . . F
logi and formal mo dels allo w us to:
erify h yp
and he k
more pre ise mo dels in remen tally
new biologi al exp erimen ts to e ien tly redu e the n um b er
p
tial mo dels 7
SLIDE 8 The T w
Φ = {ϕ1, ϕ2, · · · , ϕn}
and
M
=
+ + x 1 2 1 . . . 1. Is it p
that Φ and M ? Consisten y
kno wledge and h yp
Means to sele t mo dels b elonging to the s hemas that satisfy Φ .
(∃? M ∈ M | M | = ϕ)
2. If so, is it true in vivo that Φ and M ? Compatibilit y
the sele ted mo dels with the biologi al
je t. Require to prop
exp erimen ts to v alidate (or refute) the sele ted mo del(s).
→
Computer aided pr
and validations 8
SLIDE 9 Men u 1. Sim ulation vs. V alidation 2. F
Metho ds for the Mo delling A tivit y 3. Gene Regulatory Net w
& T emp
Logi 4. P edagogi al example: Pseudomonas aeruginosa 9
SLIDE 10 Multiv alued Regulatory Graphs
y x x y 1 2
+ +
y x x
τ2
1 2
τ1
10
SLIDE 11 Regulatory Net w
(R. Thomas)
Ky
1 2
y
+ + 1 Basal lev el : Kx
x
helps : Kx,x
Ky,x
Absen t y helps : Kx,y Both : Kx,xy (x,y ) Image (0,0)
(Kx,y, Ky)
(0,1)
(Kx, Ky)
(1,0)
(Kx,xy, Ky)
(1,1)
(Kx,x, Ky)
(2,0)
(Kx,xy, Ky,x)
(2,1)
(Kx,x, Ky,x)
11
SLIDE 12 State Graphs (x,y ) Image (0,0)
(Kx,y, Ky)=(2,1)
(0,1)
(Kx, Ky)=(0,1)
(1,0)
(Kx,xy, Ky)=(2,1)
(1,1)
(Kx,x, Ky)=(2,1)
(2,0)
(Kx,xy, Ky,x)=(2,1)
(2,1)
(Kx,x, Ky,x)=(2,1)
y x
1
(1,1) (1,0) (2,0) (2,1) (0,0) (0,1)
1 2
Time has a tree stru ture:
(2,1) (2,1) (1,1) (2,0) (1,0) (0,1) (0,0)
12
SLIDE 13 CTL = Computation T ree Logi A toms =
: (x=2) (y>0) . . . Logi al
es: (ϕ1 ∧ ϕ2)
(ϕ1 = ⇒ ϕ2) · · ·
T emp
es: made
2 hara ters rst hara ter se ond hara ter
A
= for All path hoi es
X
= neXt state
F
= for some Future state
E
= there Exist a hoi e
G
= for all future states (Globally)
U
= Un til AX(y = 1) : the
tration lev el
b elongs to the in terv al 1 in all states dire tly follo wing the
initial state. EG(x = 0) : there exists at least
path from the
initial state where x alw a ys b elongs to its lo w er in terv al. 13
SLIDE 14 Question 1 = Consisten y 1. Dra w all the sensible regulatory graphs with all the sensible threshold allo ations. It denes M . 2. Express in CTL the kno wn b eha vioural prop erties as w ell as the
biologi al h yp
It denes Φ . 3. Automati ally generate all the p
regulatory net w
deriv ed from M a ording to all p
parameters K... . Our soft w are plateform SMBioNet handles this automati ally . 4. Che k ea h
these mo dels against Φ . SMBioNet uses mo del he king to p erform this step. 5. If no mo del surviv e to the previous step, then re onsider the h yp
and p erhaps extend mo del s hemas. . . 6. If at least
mo del surviv es, then the biologi al h yp
are
t. P
parameters K... ha v e b een indire tly established. No w Question 2 has to b e addressed. 14
SLIDE 15 Theoreti al Mo dels ↔ Exp erimen ts CTL form ulae are satised (or refuted) w.r.t. a set
paths from a giv en initial state
an b e tested against the p
paths
the theoreti al mo dels (M |
=Model Checking ϕ )
an b e tested against the biologi al exp erimen ts (Biological _Object |
=Experiment ϕ )
CTL form ulae link theoreti al mo dels and biologi al
je ts together 15
SLIDE 16 Question 2 = V alidation 1. Among all p
form ulae, some are
able i.e., they express a p
result
a p
biologi al exp erimen t. Let Obs b e the set
all
able form ulae. 2. Let Λ b e the set
theorems
and M .
Λ ∩ Obs
is the set
exp erimen ts able to v alidate the surviv
Question 1. Unfortunately it is innite in general. 3. T esting framew
from
s ien e aim at sele ting a nite subsets
these
able form ulae, whi h maximize the han e to refute the surviv
4. These subsets are
to
nev ertheless these testing framew
an b e suitably applied to regulatory net w
16
SLIDE 17 Men u 1. Sim ulation vs. V alidation 2. F
Metho ds for the Mo delling A tivit y 3. Gene Regulatory Net w
& T emp
Logi 4. P edagogi al example: Pseudomonas aeruginosa 17
SLIDE 18 Example : ytoto xi it y (P.aeruginosa ) T erminology ab
phenot yp e mo di ation: Geneti mo di ation: inheritable and not rev ersible (m utation) Epigeneti swit h: inheritable and rev ersible A daptation: not inheritable and rev ersible The biologi al questions (Janine Guespin): is ytoto xi it y in Pseudomonas aeruginosa due to an epigeneti swit h ? [→ ysti brosis℄ 18
SLIDE 19 Cytoto xi it y in P. aeruginosa (Janine Guespin and Mar eline Kaufman)
toxicity
+ ExsA ExsD + Epigeneti h yp
=
→
The p
e feedba k ir uit is fun tional, with a ytoto xi stable state and the
is not ytoto xi .
→
An external signal (in the ysti brosis' lungs)
swit h ExsA from its lo w er stable state to the higher
19
SLIDE 20 Consisten y
the Hyp
toxicity
+ ExsA ExsD + One CTL form ula for ea h stable state:
(ExsA = 2) = ⇒ AXAF(ExsA = 2) (ExsA = 0) = ⇒ AG(¬(ExsA = 2))
Question 1,
pro v ed b y Mo del Che king
→
10 mo dels among the 712 mo dels are extra ted b y SMBioNet Question 2: and in vivo ? . . . 20
SLIDE 21 V alidation
the epigeneti h yp
Question 2 = to v alidate bistationnarit y in vivo Non ytoto xi state:
(ExsA = 0) = ⇒ AG(¬(ExsA = 2))
P. aeruginosa, with a b asal level for ExsA do es not b e
sp
ytotoxi : a tually v alidated Cytoto xi state:
(ExsA = 2) = ⇒ AXAF(ExsA = 2)
Exp erimen tal limitation:
ExsA
an b e saturated but it annot b e measured Exp erimen t: to pulse ExsA and then to test if toxin pr
r emains (⇐
⇒
to v erify a h ysteresis) This exp erimen t an b e automati ally generated 21
SLIDE 22 T
(ExsA=2)=
⇒AXAF
(ExsA=2)
ExsA = 2
annot b e dire tly v eried but toxicity = 1 an b e v eried.
toxicity
+ ExsA ExsD + Lemma: AXAF(ExsA = 2) ⇐
⇒ AXAF(toxicity = 1)
(. . . formal pro
b y
. . . )
→
T
⇒ AXAF(toxicity = 1)
22
SLIDE 23 (ExsA = 2) = ⇒ AXAF(toxicity = 1)
A = ⇒ B
true false true true false false true true Karl P
er: to v alidate = to try to refute thus A=false is useless exp erimen ts m ust b egin with a pulse The pulse for es the ba teria to rea h the initial state ExsA = 2 . If the state w ere not dire tly
trolable w e had to pro v e lemmas:
(ExsA = 2) ⇐ =
(something r e a hable ) General form
a test: (something r e a hable) =
⇒
(something
) 23
SLIDE 24 Con luding Commen ts Beha vioural pr
erties (Φ ) are as m u h imp
t as mo dels (M ) Mo delling is signi an t
with resp e t to the
exp erimen tal r e a hability and
(Obs ) F
pro
an suggest w et exp erimen ts Curren t state
the art / promising pro
ted approa hes:
Hybrid P etri Nets [Sylvie T ron ale, Gilles Bernot & Jean-P aul Comet (Pro du t
automaton)℄
mo dels with dela ys [Olivier Roux &al (HyT e h), Heik e Sieb ert & Alexander Bo kma yr (pro du t
automaton)℄
t programming [Lauren t T rilling & Eri F an hon℄
ards stru tural h yp
[Hans Geiselmann & Hidde de Jong℄ 24
