Modeling of Signaling Pathways Based on Petri nets

Hiroshi Matsuno

Graduate School of Science and EngineeringYamaguchi University

International Symposium on Symbolic Systems Biology (ISSSB’11) Shonan Village Center 13-17 November, 2011

July 4-9, 2004

Petri netsprocess algebraπ-calculustimed automataprobabilistic automatafinite state linear modeldifferential equationsrule based modelBoolean model

Feb 22-27, 2009

1…2…

3 Isolated “paradise” with no distractions

Merits of NII Shonan Meeting

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

m1

P

m2

P

m4

P

m6

P

T

1 T

3

T

1

T 1T

1

2

9

tank

flow off

flow on

lever

Example of hybrid Petri net

Lambda phage genetic switch feedback mechanism

Lambda phage genetic switch feedback mechanism

Simulation on Cell Illustrator

Signaling pathwaysstimulus

cell membrane

enzyme 1enzyme 1

・・・

cell nuclei

To control proliferation, differentiation, and life of cells

Information transmission from cell membrane to cell nuclei by the cascade of enzymes

enzyme 2enzyme 2

enzyme nenzyme n

signaling pathway components

Petri net model

inactiveJNK

JNK

MEK4,7

. . .

. . .

inactiveElk-1

Elk-1

inactiveMEK4,7

a part of signaling pathway

. . .

. . .

MEK4,7MEK4,7

JNKJNK JNKJNK

MEK4,7MEK4,7. .

.. .

.

Elk-1Elk-1 Elk-1Elk-1Activation Transduction Activation Transduction

Component (ATC)Component (ATC)

Activation Transduction Activation Transduction Component (ATC)Component (ATC)

A set of reactions influenced by an enzyme

A part of signaling pathwayA part of signaling pathway. .

.. .

.

MEK4,7MEK4,7

JNKJNK JNKJNK

MEK4,7MEK4,7

. . .

. . .

Elk-1Elk-1 Elk-1Elk-1

Petri net modelPetri net model

inactiveJNK

JNK

MEK4,7

. . .

. . .

inactiveElk-1

Elk-1

inactiveMEK4,7

ATCATCATCATC

Elementary Elementary T-invariantT-invariant

Elementary Elementary T-invariantT-invariant

ATC = Elementary T-invariantSignaling

Pathway TERM

Petri net TERM

Algorithm to find ATCC. 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

G protein signaling pathwaysG protein signaling pathways

outside of a cell

inside of a cell

Adenylyl cyclase pathway

Ras-MAPK pathway

PLC pathway

Petri net model of G protein signaling pathway

Petri net model of signaling pathway

G protein signaling pathway

Ras-MAPK pathway

PLC pathwayAdenylyl cyclase pathway

Result of the decomposition

signal flow representation timed Petri net

ATC representation of pathway

N1

N2

N3

N4

N5

N6

N7N8

N9

N10N11

N12

N13

N14

N15

N16

N17

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.

Ras-MAPK pathway

PLC pathway

Adenylyl cyclase pathway

Easy to acquire the characteristics on the structure of signaling pathways

careful three structures of Petri net

･･･tI 1

tI 2

tO

β1

βm

α1

αn

α2

1

1

1

IO ff

2

2

2

If

m

m

mIf

synchronize

p

･･･

･･･

tI 1

tI m

tO 1

β1

βm

tO n

α1

αnα

2

tO 2

s1 s2 sn

jOiI ffj

m

i i

1

n

kkk

jj

s

s

1

conflict

t2

t1

t3

t4

t5

α2

β1

β2

β3

α5

β5

α3-1

α4

α3-2

p1

p2

p3

p4

153

523

55

5544

s

ss

acyclic

can be used for parameter estimation

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).