NoPain–Meeting · WorkPackages WP1 Goals Colouredhybrid Petrinets(HPNC) Connectionto WP2 MATLAB...

NoPain – Meeting

Monika Heiner Christian Rohr

Department of Computer ScienceBrandenburg University of Technology Cottbus

http://www-dssz.informatik.tu-cottbus.de

Jan 28, 2014

Work Packages

GoalsWP1Coloured hybridPetri nets (HPN C)

WP2Connection toMATLAB

WP3

Efficient simulationofHPN C

WP4

Design of the“simulation lab”

WP5

Outline of the “simu-lation database”

WP6Implementationof the “simulationdatabase”

WP7 Preparation of theusermanuals

AG Heiner (BTU Cottbus) NoPain Jan 28, 2014

WP3

Efficient simulation of HPN C

a. Predecessor WPs: BTU-WP1, OvGUM-WP1b. Successor WPs: BTU-WP4

Examination of the Petri net models with regard to parallelisationpotentialInvestigation of optimisation possibilities and performancecomparisons with alternative tools, i.e. StochKit2, Cain. . .


Parameter-free simulation

Starting point: The Signaling Petri Net-Based Simulator: ANon-Parametric Strategy for Characterizing the Dynamics ofCell-Specific Signaling NetworksD. Ruths, M. Muller, Jen-Te Tseng, L. Nakhleh, P. T. RamPublished: February 29, 2008; DOI: 10.1371/journal.pcbi.1000005„The key insight behind our approach is the assumption that, whileall network parameters determine the actual signal propagation tosome extent, the network connectivity is the most significant singledeterminant. While this is clearly a gross simplification, severalresearchers have observed that the connectivity of a biologicalnetwork dictates, to a great extent, the network’s dynamics.”



„Simulation of timed Petri nets with variable auto-concurrency”.The least possible time step is 1 time unit.All enabled transitions that are not mutually exclusive, are forced tofire within a time-step, something like maximum step.When the net is filled up with tokens, every transition will fire.



Transition firingGenerate a random sequence of all transitions t ∈ PN .No extra conflict resolution needed, because of serial firing.Maximum step ⊆ random sequences

ExampleRandom sequences:

1 (T1, T3, T2, T4)→ {1, 1, 1, 0}2 (T1, T2, T4, T3)→ {1, 1, 1, 1}3 (T3, T4, T2, T1)→ {1, 1, 0, 0}

Maximum step:1 {T1} → {1, 1, 0, 0}

A B

C

D

T2

T1 T3

T4



Transition firingA transition fires concurrently to itself, i.e. token flow increases.How often a transition concurrently fires depends on its enablednessdegree and is randomly determined.firing rate = random[0, enablness degree]This approximates the stochastic behaviour of mass-action kinetics.

Example(T1, T2, T3, T4)→ {1, 5, 10, 0}T1 = 1→ 0→ {1, 5, 6, 2}T2 = 5→ 4→ {1, 5, 10, 2}T3 = 5→ 2→ {1, 5, 10, 4}T4 = 4→ 4→ {1, 5, 10, 0}

A

5

B

6

C

D

T2

T1 T3

T4


Parameter-free simulationAlgorithm 1 Parameter-free simulation algorithmRequire: PN with initial marking m0, time interval [τ0, τmax], runs rmax

Ensure: marking m at time point τmax

1: for r = 0; r < rmax; r ← r + 1 do2: initRand(seed)3: time τ ← τ0, marking m← m0, Tr ← T4: while τ <= τmax do5: Tr ← random_shuffle(Tr)6: for all transitions tj ∈ Tr do7: e← enablednessDegree(tj ,m)8: f ← random(0, e)9: m← m+ f ∗∆tj

10: end for11: generateResultPoint(τ,m)12: τ ← τ + 113: end while14: end for


ExampleRKIP inhibited ERK Pathway [Gilbert et al. 2006]

Raf1Star

Ns1

RKIP

Ns2

Raf1Star RKIPs3

ERKPP

s9

MEKPP ERKs8

Raf1Star RKIP ERKPP

s4 RKIPP RPs11

MEKPP

Ns7

ERK

Ns5

RKIPP

s6

RP

Ns10

r1 r2

r3 r4

r6 r7 r9 r10r5

r8

r11

RKIP/MEK-ERK signalling pathway [wolkenhauer 2003], [Calder 2005]


RKIP inhibited ERK Pathway

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0

Raf1StarRKIPRaf1Star_RKIP

ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(a) SPN 100 runs (<1s)

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(b) SPN 1,000 runs (<1s)

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(c) SPN 10,000 runs (<1s)

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(d) SPN 100,000 runs (2s)

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(e) QPN 100 runs (<1s)

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(f) QPN 1,000 runs (<1s)

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(g) QPN 10,000 runs (<1s)

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(h) QPN 100,000 runs (3s)

Figure: ERK, N=1



0 10 20 30 40 500

2

4

6

8

10


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP


0 10 20 30 40 500

2

4

6

8

10


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(b) SPN 1,000 runs (<1s)

0 10 20 30 40 500

2

4

6

8

10


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(c) SPN 10,000 runs (8s)

0 10 20 30 40 500

2

4

6

8

10


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(d) SPN 100,000 runs (1m19s)

0 10 20 30 40 500

2

4

6

8

10


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP


0 10 20 30 40 500

2

4

6

8

10


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(f) QPN 1,000 runs (<1s)

0 10 20 30 40 500

2

4

6

8

10


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(g) QPN 10,000 runs (<1s)

0 10 20 30 40 500

2

4

6

8

10


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(h) QPN 100,000 runs (4s)

Figure: ERK, N=10



0 10 20 30 40 500

20

40

60

80

100


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(a) SPN 100 runs (1s)

0 10 20 30 40 500

20

40

60

80

100


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(b) SPN 1,000 runs (9s)

0 10 20 30 40 500

20

40

60

80

100


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(c) SPN 10,000 runs (1m41s)

0 10 20 30 40 500

20

40

60

80

100


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(d) SPN 100,000 runs (17m4s)

0 10 20 30 40 500

20

40

60

80

100


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP


0 10 20 30 40 500

20

40

60

80

100


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(f) QPN 1,000 runs (<1s)

0 10 20 30 40 500

20

40

60

80

100


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(g) QPN 10,000 runs (<1s)

0 10 20 30 40 500

20

40

60

80

100


ERKPPMEKPP_ERK

Raf1Star_RKIP_ERKPP

RKIPP_RP

MEKPPERKRKIPPRP

(h) QPN 100,000 runs (4s)

Figure: ERK, N=100


ExampleMitogen-activated Protein Kinase[Huang et al. 1996], [Gilbert et al. 2007]

e1

e2

k

N

k kkpp

kk

N

kk kkkp

kkk N

kkk e1

kkkp

kkkp e2

kkp

kkp kkkp

kkp ptase

kkpp

kkpp ptase

kkptase

kp

kp kkpp

kp ptase

kpp

kpp ptase

kptase

k k kk k k kk

k k ptase

k k ptase

k kk kkk k kk kkk

k kk ptase k kk ptase

k kkk e1

k kkk e2

a d kkk e1

a d kkk e2

a d kk ptase

a d kk kkk

a d kk ptase

a d kk kkk

a d k kk

a d k ptase

a d k kk

a d k ptase


Mitogen-activated Protein Kinase

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0

kkkkkkkkkpkkpkkppkpkpp

(a) SPN 100 runs (4s)

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0


(b) SPN 1,000 runs (4s)

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0


(c) SPN 10,000 runs (4s)

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0


(d) SPN 100,000 runs (4s)

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0


(e) QPN 100 runs (4s)

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0


(f) QPN 1,000 runs (4s)

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0


(g) QPN 10,000 runs (4s)

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0


(h) QPN 100,000 runs (4s)

Figure: MAPK, N=1



0 10 20 30 40 500.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0



0 10 20 30 40 500.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0


(b) SPN 1,000 runs (<1s)

0 10 20 30 40 500.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0


(c) SPN 10,000 runs (2s)

0 10 20 30 40 500.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0


(d) SPN 100,000 runs (25s)

0 50 100 150 2000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0



0 50 100 150 2000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0


(f) QPN 1,000 runs (<1s)

0 50 100 150 2000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0


(g) QPN 10,000 runs (3s)

0 50 100 150 2000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0


(h) QPN 100,000 runs (33s)

Figure: MAPK, N=4



0 10 20 30 40 500

2

4

6

8

10



0 10 20 30 40 500

2

4

6

8

10


(b) SPN 1,000 runs (<1s)

0 10 20 30 40 500

2

4

6

8

10


(c) SPN 10,000 runs (3s)

0 10 20 30 40 500

2

4

6

8

10


(d) SPN 100,000 runs (39s)

0 100 200 300 400 5000

2

4

6

8

10



0 100 200 300 400 5000

2

4

6

8

10


(f) QPN 1,000 runs (<1s)

0 100 200 300 400 5000

2

4

6

8

10


(g) QPN 10,000 runs (8s)

0 100 200 300 400 5000

2

4

6

8

10


(h) QPN 100,000 runs (1m20s)

Figure: MAPK, N=10


ExampleAngiogenesis [Napione et al. 2009]

Akt

N

AktP3

AktStar

DAG

N

DAGEEnz

N

Gab1 NGP3

GStarP3

GStarP3kP3

GStarPgP3

KdStar

N

KdStar

N

KdStar

N

KdStar

N

KdStar

N

KdStar

N

KdStarG KdStarGP3

KdStarGStar

KdStarGStarP3

KdStarGStarP3k

KdStarGStarP3kP3

KdStarGStarP3kStar

KdStarGStarP3kStarP2

KdStarGStarP3kStarP3

KdStarGStarP3kStarP3P2

KdStarGStarPgKdStarGStarPgP3

KdStarGStarPgStar

KdStarGStarPgStarP2

KdStarGStarPgStarP3

KdStarGStarPgStarP3P2

KdStarPg

KdStarPgStar

KdStarPgStarP2

Pip2

N

Pip2

N

Pip2

N

Pip2

N

Pip2

N

Pip2

N

Pip3

Pip3

Pip3

Pip3

P3k

N

P3k

N

P3k

N

Pg

N

Pg

N

Pg

N

Pg

N

Pten

N

PtP2

PtP3

PtP3P2

k0k1

k10k11

k12 k13

k14

k15

k16 k17

k18

k19

k2

k20

k21

k22 k23

k24

k25k26

k27

k28k29

k3

k30

k31k32

k33

k34k35

k36

k37k38

k39

k4

k40k41

k42

k43k44

k45

k46k47

k48

k49

k5

k50

k51

k52

k53k54

k55

k56k57

k58k59

k6

k60 k61

k62

k63

k7

k8k9

Compound Symbols:

KDR = Kd = n1

Gab1 = G = n3

Pi3k = P3k = n2

PlcGamma = Pg = n4

Pip3 = P3

Pip2 = P2 = n5

Pten = Pt = n6

Enz = E = n7

Akt = n8

Transition k3, k4, k5, k6, k7 are dead


Angiogenesis

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

Pip2Pip3P3kPgPtenPtP2PtP3PtP3P2


0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0


(b) SPN 1,000 runs (<1s)

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0


(c) SPN 10,000 runs (<1s)

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0


(d) SPN 100,000 runs (7s)

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0



0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0


(f) QPN 1,000 runs (<1s)

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0


(g) QPN 10,000 runs (2s)

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0


(h) QPN 100,000 runs (21s)

Figure: ANG, N=1


Angiogenesis

0 20 40 60 80 1000

1

2

3

4

5



0 20 40 60 80 1000

1

2

3

4

5


(b) SPN 1,000 runs (<1s)

0 20 40 60 80 1000

1

2

3

4

5


(c) SPN 10,000 runs (1s)

0 20 40 60 80 1000

1

2

3

4

5


(d) SPN 100,000 runs (13s)

0 20 40 60 80 1000

1

2

3

4

5



0 20 40 60 80 1000

1

2

3

4

5


(f) QPN 1,000 runs (<1s)

0 20 40 60 80 1000

1

2

3

4

5


(g) QPN 10,000 runs (2s)

0 20 40 60 80 1000

1

2

3

4

5


(h) QPN 100,000 runs (22s)

Figure: ANG, N=5


Angiogenesis

0 20 40 60 80 1000

2

4

6

8

10



0 20 40 60 80 1000

2

4

6

8

10


(b) SPN 1,000 runs (<1s)

0 20 40 60 80 1000

2

4

6

8

10


(c) SPN 10,000 runs (2s)

0 20 40 60 80 1000

2

4

6

8

10


(d) SPN 100,000 runs (23s)

0 20 40 60 80 1000

2

4

6

8

10



0 20 40 60 80 1000

2

4

6

8

10


(f) QPN 1,000 runs (<1s)

0 20 40 60 80 1000

2

4

6

8

10


(g) QPN 10,000 runs (2s)

0 20 40 60 80 1000

2

4

6

8

10


(h) QPN 100,000 runs (23s)

Figure: ANG, N=10



ConclusionsMixed results:

1 performance comparable to stochastic simulation, some times better,some time worse

2 correct results for N = 1, contradictory for N > 1Potential solutions:

1 weighted shuffle of transitions2 mass-action kinetics: ct ·

∏p∈•t

(m(p)f(p,t)

)enabledness degree: minp∈•t

(⌊m(p)f(p,t)

⌋)


Milestones

2013 2014 2015

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4

WP1 M1

WP2 M2

WP3 M3

WP4 M4

WP5 M4

WP6 M5

WP7 M6


Next steps...

Model compilation for simulation, i.e. a Petri net model and thesimulation algorithm will be compiled into an executable file.

Performance comparisons with alternative simulation tools, i.e.Stochkit2, Cain, Copasi, StochPy. . .


Thank you for your attention!


NoPain–Meeting · WorkPackages WP1 Goals Colouredhybrid Petrinets(HPNC) Connectionto WP2 MATLAB...

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Transcript of NoPain–Meeting · WorkPackages WP1 Goals Colouredhybrid Petrinets(HPNC) Connectionto WP2 MATLAB...