International Symposium on Symbolic Systems Biology (ISSSB’11)
Shonan Village Center 13-17 November, 2011
Modeling of Signaling Pathways
Based on Petri nets
Hiroshi Matsuno
Graduate School of Science and Engineering
Yamaguchi University
July 4-9, 2004
Feb 22-27, 2009
Petri nets
process algebra
π-calculus
timed automata
probabilistic automata
finite state linear model
differential equations
rule based model
Boolean model
Merits of NII Shonan Meeting
1…
2…
3 Isolated “paradise” with
no distractions
...
Petri nets
...
• Symbolic representation of
systems in graphical manner
In the aims of this meeting …
A secondary aim is to identify ways purely symbolic
methods have been or could be combined with
numerical techniques and applied to emerging
problems in experimental and synthetic biology.
Hybrid Petri Net
Example of hybrid Petri net
flow off
P
m4
T
1
T
1
P
flow on
m6
T
9
1
P
tank
m1
T
P
m2
1
T
3
lever
Lambda phage genetic switch feedback mechanism
Lambda phage genetic switch feedback mechanism
Simulation on Cell Illustrator
Signaling pathways
stimulus
cell membrane
enzyme 1
enzyme 2
・
・
・
cell nuclei
Information transmission from
cell membrane to cell nuclei by
the cascade of enzymes
enzyme n
To control proliferation, differentiation,
and life of cells
signaling pathway components
inactive
MEK4,7
MEK4,7
JNK
JNK
Elk-1
Elk-1
...
Activation Transduction
Component (ATC)
A set of reactions influenced by
an enzyme

inactive
JNK
inactive
Elk-1
MEK4,7
JNK 
Elk-1
...
...
MEK4,7
Petri net model
...
a part of signaling pathway
ATC = Elementary T-invariant
Signaling
Pathway
TERM
Petri net
TERM
A part of signaling pathway
inactive
MEK4,7
MEK4,7
JNK
JNK
Elk-1
...
Elk-1
Elementary
T-invariant
ATC

inactive
JNK
inactive
Elk-1
MEK4,7
JNK 
Elk-1
...
MEK4,7
...
...
Petri net model
Algorithm to find ATC
C. Li, S. Suzuki, Q.-W.Ge, M. Nakata, H. Matsuno, S. Miyano, Structural
modeling and analysis of signaling pathways based on Petri nets, J. Bioinfo.
Comput. Biol. 4(5), pp.1119-1140, 2006..
An Example of signaling pathway modeling
outside of a cell
inside of a cell
Ras-MAPK pathway
Adenylyl cyclase pathway
PLC pathway
G protein signaling pathways
Petri net model of signaling pathway
G protein signaling pathway
Ras-MAPK pathway
Adenylyl cyclase pathway
PLC pathway
Petri net model of G protein signaling pathway
Result of the decomposition
signal flow representation  timed Petri net
ATC representation of pathway
N4
Subnet N9 (MEK activation by Raf-1)
is an important reaction in the pathway.
More than one pathways are working
for producing the same gene product.
PLC pathway
N13
N17
N12
N16
N11 N10
N9
N2
N8
Easy to acquire the characteristics on the
structure of signaling pathways
N15
N7
N6
N1
N3
Adenylyl cyclase pathway
N5
N14
Ras-MAPK pathway
careful three structures of Petri net
tI 1
tI 2
･･･
β1
tI 1
tI m
βm
･･･
β1
α1 α2
f O  f I1 
1
1
tO
 f I2 
αn
2
2
   f Im 
synchronize
m
m
βm
s1
s2
sn
 sk   k
k 1
α3-1
･･･
tO n
m
i 1
f I   i  f O  j
i
β2
p2
αn
tO 2

p1
t2
tO 1
s j  j
n
β1
α2
p
α1 α
2
t1
j
conflict
α3-2
t3
β3
p3
α4
β5
α5
t4
t5
s4   4  s5   5  32   5

1
s5   5
3  5
acyclic
can be used for parameter estimation
p4
Conclusion and future work
• I am very happy to be here,
--- Dagstuhl style meeting in Asia.
• Delay time determination of transitions for
representing signal flow dynamics based on
the structure of the Petri net model and
experimentally obtained data.
• Qualitative characterization of signaling
pathways for biological and medical applications
Collaborators in Yamaguchi Univ.
•Petri net modeling
Qi-Wei Ge
Yuki Murakami
•Experimental data of signaling components
using cell array system
Tomoko Furuya
This research is partially supported by the Ministry of Education,
Science, Sports and Culture, Grant-in-Aid for Scientific Research (B).