ROM P P ETRI ETRI N N ETS ETS TO TO P AR TIAL D D IF NTIAL E E QUATI - - PowerPoint PPT Presentation

▶
rom p
SMART_READER_LITE
LIVE PREVIEW

ROM P P ETRI ETRI N N ETS ETS TO TO P AR TIAL D D IF NTIAL E E QUATI - - PowerPoint PPT Presentation

Jan 13, 2023 175 likes •1.09k views

CFSB W ORKSHOP , B ALLIOL C OLLEGE , M ARCH 19 TH 2012 PN & BioModel Engineering F RO ROM P P ETRI ETRI N N ETS ETS TO TO P AR TIAL D D IF NTIAL E E QUATI TIONS ARTIAL IFFERENTIAL AND BE AND BEYOND - B IO - IO M OD EL E E NGIN RING FO FOR

slide-1
SLIDE 1

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

CFSB WORKSHOP, BALLIOL COLLEGE, MARCH 19TH 2012

FRO

ROM P

PETRI

ETRI N

NETS

ETS TO TO

PAR

ARTIAL TIAL D

DIF

IFFERENTIAL NTIAL E

EQUATI

TIONS AND AND BE BEYOND

  • BIO

IOMOD ODEL EL E

ENGIN

NGINEE EERIN RING FO FOR M

MULTI

ULTI-SC SCALE ALE S

SYS

YSTEMS B

BIOL

IOLOGY OGY -

  • Monika Heiner

Brandenburg University of Technology Cottbus David Gilbert Brunel University, Uxbridge/London

slide-2
SLIDE 2

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

OUTLINE

BACKGROUND

  • > modelling, what for ?
  • > how many model types do we need ?
  • > some case studies

FRAMEWORK

  • > unifying paradigms: QPN - SPN - CPN

COLOUR AND MUTLI-SCALE SYSTEM

  • > replication
  • > encoding space

SUMMARY & OUTLOOK

  • > open problems
  • > next steps
slide-3
SLIDE 3

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

BACKGROUND

slide-4
SLIDE 4

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

MODELS IN SYSTEMS BIOLOGY

biosystem natural

model

  • bserved

behaviour predicted behaviour wetlab model-based experiment design experiments formalizing understanding analysis simulation

MOD MODELLI LLING NG

= FO

FORMAL KN KNOWLE LEDGE RE REPRE RESENTAT ATION

(knowledge) model validation

MODE MODEL VA VALIDATION =

= CO

CONFIDENCE INCR INCREASE EASE

slide-5
SLIDE 5

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

MODELS IN SYSTEMS BIOLOGY

biosystem natural

model

  • bserved

behaviour predicted behaviour wetlab model-based experiment design experiments formalizing understanding analysis simulation

MOD MODELLI LLING NG

= FO

FORMAL KN KNOWLE LEDGE RE REPRE RESENTAT ATION

(knowledge) model validation

MODE MODEL VA VALIDATION =

= CO

CONFIDENCE INCR INCREASE EASE

DESCRIPTIV DESCRIPTIVE PR PREDICTIV EDICTIVE EXPLANATO TORY

slide-6
SLIDE 6

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

MODELS IN SYNTHETIC BIOLOGY

MOD MODELLI LLING NG

= BL

BLUEP EPRINT FO FOR SY SYSTEM STEM CON CONSTR TRUCTIO UCTION RE RELIABLE AND AND RO ROBUST ENGINEERING ENGINEERING RE REQUIRE RES VE VERIFIED MODELS MODELS

biosystem synthetic

  • bserved

behaviour predicted behaviour model (blueprint) desired behaviour design construction verification validation verification

slide-7
SLIDE 7

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

WHAT KIND OF MODEL

SHOULD BE USED?

(BIOCHEMICAL NETWORKS)

slide-8
SLIDE 8

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

NETWORK REPRESENTATIONS, EX1

R af-1 M EK ER K1,2 M EK1,2 ER K1,2 B-R af R ap1

cAM P G EF

Akt R eceptor

e.g. 7-TM R

  • tyrosine

kinase

  • SO

S shc grb2 R as PAK R ac PI-3 K R as

cA M P

PKA

cA M P

PD E

cA M P A M P

  • AdC

yc

cA M P A TP

PKA

cA M P

M KP transcription factors

nucleus

cell m em brane cytosol

heterotrim eric G

  • protein

R af-1 R af-1 M EK M EK ER K1,2 ER K1,2 M EK1,2 M EK1,2 ER K1,2 ER K1,2 B-R af B-R af R ap1 R ap1

cAM P G EF cAM P G EF

Akt Akt R eceptor

e.g. 7-TM R

  • tyrosine

kinase

  • SO

S SO S shc shc grb2 grb2 R as R as PAK PAK R ac R ac PI-3 K PI-3 K R as R as

cA M P cA M P

PKA

cA M P

PKA PKA

cA M P cA M P

PD E

cA M P A M P

PD E PD E

cA M P A M P cA M P cA M P A M P

  • AdC

yc

cA M P A TP

  • AdC

yc AdC yc

cA M P A TP cA M P cA M P A TP

PKA

cA M P

PKA PKA

cA M P cA M P

M KP M KP transcription factors transcription factors

nucleus

cell m em brane cytosol

heterotrim eric G

  • protein

F O R M A L S E M A N T I C S

?

A N A L Y S A B I L I T Y

?

E X E C U T I O N ?

slide-9
SLIDE 9

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

NETWORK REPRESENTATIONS, EX2

READABILITY

CAUSALITY ?

U N I Q U E S T R U C T U R E ?

slide-10
SLIDE 10

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

BIO NETWORKS, SOME PROBLEMS

knowledge

  • > PROBLEM 1
  • > uncertain
  • > growing, changing
  • > distributed over independent data bases, papers, journals, . . .

various, mostly ambiguous representations

  • > PROBLEM 2
  • > verbose descriptions
  • > diverse graphical representations
  • > contradictory and / or fuzzy statements

network structure

  • > PROBLEM 3
  • > tend to grow fast
  • > dense, apparently unstructured
  • > hard to read

MODELS ARE PATCHWORKS FULL OF ASSUMPTIONS

slide-11
SLIDE 11

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

BIO NETWORK REPRESENTATIONS SHOULD BE

readable & unambigious

  • > fault avoidant model construction

various abstraction levels locality - causality - concurrency compositional executable

  • > to experience the model, spec. causality

analysable, with unifying power

  • > formal = mathematical representations
  • > high-level description for various analysis approaches

as simple as possible

  • > how many model types do we need ?
slide-12
SLIDE 12

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

MODELLING = ABSTRACTION

hierarchical organisation of components -> model variables genes, molecules, organelles, cells, tissues, organs, organisms functionality of atomic events chemical reactions with/out stoichiometry, conformational change, transport, . . . time qualitative versus quantitative models individual vs population behaviour (hierarchical) space

  • bservables

shape and volume of components biosystem development

slide-13
SLIDE 13

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

BIO NETWORKS

.. .

ARE NETWORKS

OF BIOCHEMICAL

REACTIONS

. . .

NATURALLY EXPRESSIBLE AS

PETRI NETS

2 2 2 2 r1 O2 H+ NADH H2O NAD+

2 NAD+ + 2 H2O -> 2 NADH + 2 H+ + O2

O2 H+ NADH H2O NAD+

hyper-arcs

2 2 2 2

slide-14
SLIDE 14

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

PLACES, TRANSITIONS - SOME BIO INTERPRETATIONS

places

  • > model variables
  • > (bio-) chemical compounds
  • > proteins
  • > protein conformations
  • > complexes
  • > genes, . . . etc.

. . . in different locations transitions

  • > atomic events
  • > (stoichiometric) chemical reaction
  • > complexation / decomplexation
  • > phosphorylation /

dephosphorylation

  • > conformational change
  • > transport step, . . . etc.

. . . in different locations

slide-15
SLIDE 15

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

BIO PETRI NETS - SOME EXAMPLES

slide-16
SLIDE 16

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX1 - Glycolysis and Pentose Phosphate Pathway

Ru5P 4 5 Xu5P R5P 6 S7P GAP 7 E4P F6P 8 GAP 15 NAD+ + Pi G6P F6P 10 ATP ADP FBP 11 12 DHAP 13 14 ATP ADP 9 Gluc 1,3-BPG ATP ADP 16 ATP ADP 19 NAD+ NADH 20 3PG 17 2PG PEP 18 Pyr Lac 2 NADP+ 2 NADPH 4 GSH 2 3 1 2 GSSG NADH

[Reddy 1993]

?? ?? ?? ??

slide-17
SLIDE 17

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX1 - Glycolysis and Pentose Phosphate Pathway

Ru5P 4 5 Xu5P R5P 6 S7P GAP 7 E4P F6P 8 GAP 15 NAD+ + Pi G6P F6P 10 ATP ADP FBP 11 12 DHAP 13 14 ATP ADP 9 Gluc 1,3-BPG ATP ADP 16 ATP ADP 19 NAD+ NADH 20 3PG 17 2PG PEP 18 Pyr Lac 2 NADP+ 2 NADPH 4 GSH 2 3 1 2 GSSG NADH

[Reddy 1993]

  • >
  • > INT

INTERPRETA TATIO TION ?

?

slide-18
SLIDE 18

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX1 - Glycolysis and Pentose Phosphate Pathway

[Reddy 1993] [Heiner 1998] [Koch, Heiner 2010] . . .

Pi Pi NADP+ NADPH GSSG GSH Ru5P Xu5P R5P S7P GAP GAP E4P F6P F6P Gluc G6P FBP DHAP 1,3-BPG 3PG 2PG PEP Pyr Lac ATP ATP ATP ATP ATP ADP ADP ADP ADP ADP NAD+ NAD+ NADH NADH 15 16 17 18 19 20 13 14 12 11 10 9 2 1 3 4 5 6 7 8 2 2 2 2

slide-19
SLIDE 19

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX2 - APOPTOSIS IN MAMMALIAN CELLS

[GON 2003]

Fas-Ligand FADD Procaspase-8 Caspase-8 Bid BidC-Terminal Bax_Bad_Bim Apoptotic_Stimuli Bcl-2_Bcl-xL CytochromeC dATP/ATP Apaf-1 (m20) (m22) Procaspase-9 Caspase-9 Procaspase-3 Caspase-3 DFF CleavedDFF45 DFF40-Oligomer DNA DNA-Fragment Mitochondrion s1 s7 s9 s8 s5 s10 s11 s2 s12 s13 s3 s4 s6

[HEINER, KOCH, WILL 2004]

slide-20
SLIDE 20

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX3 - BIOSENSOR

[GILBERT, HEINER, ROSSER, FULTON, GU, TRYBILO 2008] tf TF + S TF|S phzMS PhzMS PCA TF|S PYO

tf

positive feedback

slide-21
SLIDE 21

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX3 - BIOSENSOR

signal response reporter TF TFS precursor pfb TFS degradation 5 reporter degradation 7 response degradation 9 response production 8 reporter expression 6 TF degradation 2 TF expression 1 TFS disassociation 4 TFS association 3 1'

POSITIVE FEEDBACK

[GILBERT, HEINER, ROSSER, FULTON, GU, TRYBILO 2008]

slide-22
SLIDE 22

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4 - RKIP SIGNALLING PATHWAY

Mitogens Growth factors

Receptor

receptor Ras

k i n a s e

Raf

P P P P

MEK

P

ERK

P P

cytoplasmic substrates Elk SAP

Gene

Mitogens Growth factors

Receptor

receptor

Mitogens Growth factors

Receptor

Mitogens Growth factors

Receptor Receptor

receptor Ras

k i n a s e

Ras

k i n a s e

Ras Ras

k i n a s e

Raf

P P P P

MEK

P

ERK

P P

Raf

P P P P

MEK

P

ERK

P P

cytoplasmic substrates Elk SAP

Gene

cytoplasmic substrates cytoplasmic substrates Elk SAP

Gene

Elk SAP

Gene

Ö one pathwayÖ

slide-23
SLIDE 23

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4 - RKIP SIGNALLING PATHWAY [Cho et al. 2003]

slide-24
SLIDE 24

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4 - RKIP SIGNALLING PATHWAY, PETRI NET

k11 k8 k5 k10 k9 k7 k6 k4 k3 k2 k1 RP s10 RKIP-P s6 ERK s5 MEK-PP s7 RKIP-P_RP s11 Raf-1Star_RKIP_ERK-PP s4 MEK-PP_ERK s8 ERK-PP s9 Raf-1Star_RKIP s3 RKIP s2 Raf-1Star s1

[HEINER, GILBERT 2006] [HEINER, DONALDSON, GILBERT 2010]

mi -> si

slide-25
SLIDE 25

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4 - RKIP SIGNALLING PATHWAY, HIERARCHICAL PETRI NET

k11 k8 k5 RP s10 RKIP-P s6 ERK s5 MEK-PP s7 RKIP-P_RP s11 Raf-1Star_RKIP_ERK-PP s4 MEK-PP_ERK s8 ERK-PP s9 Raf-1Star_RKIP s3 RKIP s2 Raf-1Star s1 k9_k10 k6_k7 k3_k4 k1_k2

[HEINER, GILBERT 2006] [HEINER, DONALDSON, GILBERT 2010]

slide-26
SLIDE 26

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX5 - SIGNALLING CASCADE

Raf RafP MEKP MEKPP MEK ERKP ERKPP ERK Phosphatase3 Phosphatase1 Phosphatase2 RasGTP

slide-27
SLIDE 27

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX5 - SIGNALLING CASCADE

[GILBERT, HEINER, LEHRACK 2007] [HEINER, GILBERT, DONALDSON 2008]

Raf RasGTP Raf_RasGTP RafP RafP_Phase1 MEK_RafP MEKP_RafP MEKP_Phase2 MEKPP_Phase2 ERK ERK_MEKPP ERKP_MEKPP ERKP MEKPP ERKPP_Phase3 ERKP_Phase3 MEKP ERKPP Phase2 Phase3 MEK Phase1 k3 k6 k21 k18 k9 k12 k15 k24 k27 k30 k7/k8 k1/k2 k4/k5 k10/k11 k16/k17 k22/k23 k19/k20 k13/k14 k28/k29 k25/k26
slide-28
SLIDE 28

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX6 - HALOBACTERIUM SALINARUM

[MARWAN, OESTERHELT 1999]

slide-29
SLIDE 29

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX6 - HALOBACTERIUM SALINARUM

[MARWAN 2005]

CheB−P _p0_ CheB _p1_ SR_II360_520 _p2_ SR_II360_520Me _p3_ SR_II480 _p4_ SR_II480Me _p5_ CheR _p6_ CheY−P _p7_ CheY−P _p7_ CheY _p8_ hv487 _p9_ no_hv487 _p10_ Conf2 _p11_ Conf1 _p12_ 44 CheYPbound _p13_ co_CheYP _p14_ 44 co_CheYP _p14_ 44 co_CheYP _p14_ 44 Rccw _p15_ Cccw _p16_ Accw _p17_ Sccw _p18_ Scw _p19_ Acw _p20_ Ccw _p21_ Rcw _p22_ hv373 _p23_ no_hv373 _p24_ SR_I_510Me _p25_ SR_I_510 _p26_ no_hv580 _p27_ hv580 _p28_ CheA−P _p29_ CheA−P _p29_ CheA _p30_ CheA _p30_ CheR _p31_ SR_I_587Me _p32_ SR_I_587 _p33_ SR_I_373Me _p34_ SR_I_373 _p35_ CheB _p36_ CheB P _p37_
  • ff
  • n
t22 t12 kd4 kd3 kd2 ka3 ka2 ka4 t21 t11 kd1 ka1 Tstop_ccw k2_ccw k1_ccw k0_ccw Tstop_cw k2_cw k1_cw k0_cw
  • ff
  • n
  • n
  • ff
44 44 44 44
slide-30
SLIDE 30

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX7 - PAIN SIGNALLING

The nociceptive network is valid!

[B [BLÄ

LÄTK TKE,

, MEY

EYER,

, MARW

ARWAN AN 2

2011]

  • >
  • > A PR

PROT OTEIN EIN-ORIENTED ORIENTED MODULAR MODULAR MODELLING MODELLING CONCE CONCEPT

MODULE MODULES: S: 38 38 PL PLACES ES: 713 TR TRANSIT ITIO IONS: 775 PA PAGES: 325 NE NEST STING DE ING DEPTH PTH: 4

slide-31
SLIDE 31

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

THE FRAMEWORK

slide-32
SLIDE 32

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

CRUCIAL POINT

STATE-DEPENDENT LAMBDA OF RATE FUNCTION STRENGTH OF EXPONENTIAL WAITING TIME CONTINUOUS FLOW

CTMC ODES

  • > supported by, e.g., COPASI, Dizzy, ..., Snoopy
slide-33
SLIDE 33

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

KEY IDEA QUANTITATIVE MODEL = QUALITATIVE MODEL

+

MODELS SHARING STRUCTURE RATE FUNCTIONS

(KINETICS)

slide-34
SLIDE 34

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

FRAMEWORK 2010 QUALITATIVE STOCHASTIC CONTINUOUS time-free timed, quantitative discrete state space continuous state space approximation approximation abstraction abstraction extension extension HYBRID LTS / PO CTL, LTL CTMC CSL, PLTLC ODES PLTLC

slide-35
SLIDE 35

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

ABOUT THE RELATION STOCHASTIC VS CONTINUOUS

slide-36
SLIDE 36

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

STOCHASTIC SIMULATION

slide-37
SLIDE 37

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

STOCHASTIC SIMULATION

slide-38
SLIDE 38

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

STOCHASTIC SIMULATION

slide-39
SLIDE 39

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

DETERMINISTIC SIMULATION

slide-40
SLIDE 40

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

ABOUT THE RELATION QUALITATIVE VS CONTINUOUS

slide-41
SLIDE 41

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX7 - HYPOXIA

  • [Y

[YU ET

ET AL AL.

. 2007]

slide-42
SLIDE 42

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX7 - HYPOXIA

S7 H1F:ARNT:HRE S5 H1F:ARNT S3 H1F S13 H1F:PHD S14 H1FOH S18 H1FOH:VAL S17 VHL S12 PHD S4 ARNT S15 H1F:ARNT:PHD S16 H1FOH:ARNT S6 HRE S22 H1FOH:ARNT:HRE O2 Oxygen O2 Oxygen k1 k2 k12 k13 k14 k19 k18 k20 k4 k3 k15 k16 k17 k21 k22 k6 k5 k29 k30

[H [HEIN

EINER,

, SRI

RIRAM 2

2010]

slide-43
SLIDE 43

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX7 - HYPOXIA

0.5 1 1.5 2 50 100 150 0.5 1 1.5 2 50 100 150 0.5 1 1.5 2 50 100 150

HIF (steady state values)

0.5 1 1.5 2 50 100 150 0.5 1 1.5 2 50 100 150

Oxygen

0.5 1 1.5 2 50 100 150 (a) (b) (d) (f) (e) (c)

k5, k6, k29, k30 (b) + k19 (c) + k4, k21 (d) + k16 (e) + k13

slide-44
SLIDE 44

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX7 - HYPOXIA

S5 H1F:ARNT S3 H1F S13 H1F:PHD S14 H1FOH S18 H1FOH:VAL S17 VHL S12 PHD S4 ARNT S15 H1F:ARNT:PHD S16 H1FOH:ARNT O2 Oxygen O2 Oxygen k1 k2 k12 k14 k18 k20 k3 k15 k17 k22

slide-45
SLIDE 45

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX7 - HYPOXIA

S3 H1F S14 H1FOH S12 PHD k1 A k2 B k18, k20 E k12, k14 C k3, k15, k17, k22 D

slide-46
SLIDE 46

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX7 - HYPOXIA

S12 PHD S14 H1FOH S3 H1F S12 PHD S14 H1FOH S3 H1F S12 PHD S14 H1FOH S3 H1F k2 B k1 A k2 B k1 A k2 B k1 A k18, k20 E k12, k14 C k3, k15, k17, k22 D k18, k20 E k12, k14 C k3, k15, k17, k22 D k18, k20 E k12, k14 C k3, k15, k17, k22 D

slide-47
SLIDE 47

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

FRAMEWORK 2010 QUALITATIVE STOCHASTIC CONTINUOUS time-free timed, quantitative discrete state space continuous state space approximation approximation abstraction abstraction extension extension HYBRID LTS / PO CTL, LTL CTMC CSL, PLTLC ODES PLTLC boundary nodes, SC SB, CPI, CTI, ADT sets STP, bad siphons, etc

slide-48
SLIDE 48

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

. . . AND THEN THERE WAS COLOUR

Kew Gardens, 24/04/2011

slide-49
SLIDE 49

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

COLOURED FRAMEWORK 2011 QUALITATIVE STOCHASTIC CONTINUOUS time-free timed, quantitative discrete state space continuous state space approximation approximation abstraction abstraction extension extension HYBRID LTS / PO CTL, LTL CTMC CSL, PLTLC ODES PLTLC

COLOURED COLOURED COLOURED COLOURED

slide-50
SLIDE 50

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

COLOUR -

WHAT FOR ?

slide-51
SLIDE 51

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX1: PREY - PREDATOR

Prey1 50 Predator1 100 Predator2 100 Prey2 50 reproduction_of_prey consumption_of_prey predator_death predator_death consumption_of_prey reproduction_of_prey 2 2 2 2

sub-system1 sub-system2

slide-52
SLIDE 52

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX1: PREY - PREDATOR

definitions colourset CS = 1-2; var x : CS; better: const SIZE = 2; colourset CS = 1-SIZE; var x : CS; changing SIZE adapts the model to various scenarious

Prey 100 50`all() CS Predator 200 100`all() CS reproduction_of_prey consumption_of_prey predator_death x 2`x 2`x x x x

slide-53
SLIDE 53

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX2 - C. ELEGANS

LS_molecule_E m270 LIN3_Anchorcell m1 LIN15_hyp7 m29 LIN_3_from_hyp7 m28 lin15 AC v4_lin15 v4_LIN_3_from_hyp7 m28 v4_LIN15_hyp7 m29 v4_LS_molecule_E m270 v5_LS_molecule_E m270 v5_LIN15_hyp7 m29 v5_LIN_3_from_hyp7 m28 v5_lin15 v8_lin15 v8_LIN_3_from_hyp7 m28 v8_LIN15_hyp7 m29 v8_LS_molecule_E m270 v7_LS_molecule_E m270 v7_LIN15_hyp7 m29 v7_LIN_3_from_hyp7 m28 v7_lin15 v6_lin15 v6_LIN_3_from_hyp7 m28 v6_LIN15_hyp7 m29 v6_LS_molecule_E m270 p_u2 p_d1 p_s1 p_s10 p_d27 p_s9 p_d26 4_p_d26 4_p_s9 4_p_d27 4_p_s10 4_p_u2 5_p_u2 5_p_s10 5_p_d27 5_p_s9 5_p_d26 8_p_d26 8_p_s9 8_p_d27 8_p_s10 8_p_u2 7_p_u2 7_p_s10 7_p_d27 7_p_s9 7_p_d26 6_p_d26 6_p_s9 6_p_d27 6_p_s10 6_p_u2 VPC_3 VPC_4 VPC_5 VPC_7 VPC_6 VPC_8 parameter 2 30 30 30 30 30 30

[L [LI ET

ET AL AL.

. 2009 009] [B [BON

ONZA ZANNI NNI ET ET AL AL.

. 2009] 2009]

slide-54
SLIDE 54

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX2 - C. ELEGANS

LS_molecule_E CS LS_molecule CS mRNA_of_lst_genes CS Fate_2 CS LIN_12_NotchR_intracellular_N CS LIN12_NotchR_intracellular CS LAG_1 CS LIN12_NotchR_extracellular CS lin12_wt 1 1‘dot Dot lin12_wt 1 1‘dot Dot lin12_gf Dot lin12_gf Dot lin12_gf Dot lst 1 1‘dot Dot lst 1 1‘dot Dot lst 1 1‘dot Dot LS_LIN12 CS Lst_protein CS Lst_protein CS LIN_12 CS Pe1 CS Pe2 CS LIN3_LET23_p_dimer CS LIN3_LET23_p_dimer CS LS_mRNA CS Fate_1 CS Vulval_gene CS LIN31_LIN1_Complex CS LIN_31_a CS LNI_1_a CS MPK_1_active_N CS SEM_5 CS SEM_5_active CS LET60_active CS LET_60 CS MPK_1 CS MPK_1_active_C CS vul 1 1‘dot Dot vul 1 1‘dot Dot vul 1 1‘dot Dot LIN3_LET23_dimer CS LIN3_LET23 CS LET_23 CS lin15 1 1‘dot Dot lin15 1 1‘dot Dot LIN_13_from_hyp7 CS LIN3 CS AC 1 1‘dot Dot AC 1 1‘dot Dot lin12_ko Dot Steady_state_time_Gonad Dot steady_state_time_VPC CS steady_state_time_hyp7 CS LIN3_AC Dot P1 6 1‘all() CS td24 td25 td26 td23 t17 t23 t18 t22 td31 td30 ts10 t20 td27 t21 td29 ts8 t16 t15 [x<>8] ts9 t19 t14 [x<>3] Te1 Te2 Te3 Te4 t13 t12 td20 td15 td13 td18 td19 t11 td17 ts6 td14 t10 td16 t9 td12 td21 td6 td5 td4 t6 td3 ts2 t5 t4 t2 [x<>6] t25 ts3 td7 td8 td10 td9 ts4 t7 td11 ts5 t8 p195 t3 [x=6] td22 ts7 ts1 td1 t1 [x<>6] td2 [x<>6] Tsim3 Tsim1 Tsim2 [x<>6] parameter x x x x x x x x x x x x x x x x x x x 2‘x x x x x x 2‘x x−1 x x x+1 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x dot dot dot 100‘dot dot x dot x x x x x x dot dot dot dot dot dot x x x x x x x x dot dot dot dot dot x x dot dot x x x x x x 3‘x dot x x Simulation Configuration x
slide-55
SLIDE 55

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX3 - HALOBACTERIUM SALINARUM

cl cluster type 1/2: 400/850 PL PLACES ES: : 12,426 12,426 TRANS TRANSITI ITIONS: ONS: 16, 16,577 77 unf unfol

  • ldin

ding: 6 sec 6 sec st stoc

  • ch.
  • h. si

simula latio ion: n: 10- 10-15h 5h

[M [MAR

ARWAN 2

2010]

slide-56
SLIDE 56

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 1D

cAMP_1 cAMP_2 cAMP_3 100 cAMP_4 cAMP_5 t1_1_2 t1_2_1 t1_2_3 t1_3_2 t1_3_4 t1_4_3 t1_4_5 t1_5_4

slide-57
SLIDE 57

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 1D

definitions const D1 = 5; // grid size colorset CS = 1-D1; // grid positions var x,y : CS; function neighbour1D (CS x,a) bool: // a is neighbour of x ( a=x-1 | a=x+1) & (1<=a) & (a<=D1);

cAMP 100`3 CS 100 t1 [neighbour1D(x,y)] x y

slide-58
SLIDE 58

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSSION - 1D, ODES

dc1 dt = k · c2 − k · c1 dc2 dt = k · c1 + k · c3 − 2 · k · c2 dc3 dt = k · c2 + k · c4 − 2 · k · c3 dc4 dt = k · c3 + k · c5 − 2 · k · c4 dc5 dt = k · c4 − k · c5

slide-59
SLIDE 59

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 1D

20 40 60 80 100 2 4 6 8 10 12 14 20 40 60 80 100 cAMP concentration Time Cell in 1D cAMP concentration 20 40 60 80 100

15 GRID POSITIONS

slide-60
SLIDE 60

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 1D

20 40 60 80 100 20 40 60 80 100 120 140 160 20 40 60 80 100 cAMP concentration Time Cell in 1D cAMP concentration 20 40 60 80 100

150 GRID POSITIONS, NO SCALING

slide-61
SLIDE 61

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 1D 150 GRID POSITIONS, SCALING OF INITIAL MARKING AND RATES

20 40 60 80 100 20 40 60 80 100 120 140 160 20 40 60 80 100 cAMP concentration Time Cell in 1D cAMP concentration 20 40 60 80 100

slide-62
SLIDE 62

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D4 NEIGHBOURHOOD

SCHEME

slide-63
SLIDE 63

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D8 NEIGHBOURHOOD

SCHEME

slide-64
SLIDE 64

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D

SCHEME definitions const D1 = 5; // grid size first dimension const D2 = 5; // grid size second dimension colorset CD1 = 1-D1; // row index colorset CD2 = 1-D2; // column index colorset Grid2D = CD1 x CD2; // 2D grid var x, a : CD1; var y, b : CD2;

slide-65
SLIDE 65

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D4 NEIGHBOURHOOD

four neighbours function neighbour2D4 (CD1 x, CD2 y, CD1 a, CD2 b) bool: // (a,b) is one of the up to four neighbours of (x,y) (a=x & b=y-1) | (a=x & b=y+1) | (b=y & a=x-1) | (b=y & a=x+1);

cAMP 100`(3,3) Grid2D 100 t1 [neighbour2D4(x,y,a,b)] (x,y) (a,b)

slide-66
SLIDE 66

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D4 NEIGHBOURHOOD

cAMP__1_1_ cAMP__1_2_ cAMP__1_3_ cAMP__1_4_ cAMP__1_5_ cAMP__2_1_ cAMP__2_2_ cAMP__2_3_ cAMP__2_4_ cAMP__2_5_ cAMP__3_1_ cAMP__3_2_ cAMP__3_3_ 100 cAMP__3_4_ cAMP__3_5_ cAMP__4_1_ cAMP__4_2_ cAMP__4_3_ cAMP__4_4_ cAMP__4_5_ cAMP__5_1_ cAMP__5_2_ cAMP__5_3_ cAMP__5_4_ cAMP__5_5_

slide-67
SLIDE 67

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D8 NEIGHBOURHOOD

eight neighbours function neighbour2D8 (CD1 x, CD2 y, CD1 a, CD2 b) bool: // (a,b) is one of the up to eight neighbours of (x,y) (a=x-1 | a=x | a=x+1) & (b = y-1 | b=y | b=y+1) & (!(a=x & b=y)) & (1<=a & a<=D1) & (1<=b & b<=D2); cAMP 100`(3,3) Grid2D 100 t1 [neighbour2D8(x,y,a,b)] (x,y) (a,b)

slide-68
SLIDE 68

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D8 NEIGHBOURHOOD

100
slide-69
SLIDE 69

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D4 NEIGHBOURHOOD, 15X15

’data.dat.00000000’ matrix 2 4 6 8 10 12 14 2 4 6 8 10 12 14 20 40 60 80 100

slide-70
SLIDE 70

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D4 NEIGHBOURHOOD, 15X15

’data.dat.00000006’ matrix 2 4 6 8 10 12 14 2 4 6 8 10 12 14 2 4 6 8 10 12 14 16 18

slide-71
SLIDE 71

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D4 NEIGHBOURHOOD, 15X15

’data.dat.00000010’ matrix 2 4 6 8 10 12 14 2 4 6 8 10 12 14 1 2 3 4 5 6 7 8 9 10

slide-72
SLIDE 72

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D4 NEIGHBOURHOOD, 15X15

’data.dat.00000015’ matrix 2 4 6 8 10 12 14 2 4 6 8 10 12 14 1 2 3 4 5 6

slide-73
SLIDE 73

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D4 NEIGHBOURHOOD, 15X15

’data.dat.00000020’ matrix 2 4 6 8 10 12 14 2 4 6 8 10 12 14 0.5 1 1.5 2 2.5 3 3.5 4 4.5

slide-74
SLIDE 74

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D4 NEIGHBOURHOOD, 15X15

’data.dat.00000030’ matrix 2 4 6 8 10 12 14 2 4 6 8 10 12 14 0.5 1 1.5 2 2.5 3

slide-75
SLIDE 75

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D4 NEIGHBOURHOOD, 15X15

’data.dat.00000040’ matrix 2 4 6 8 10 12 14 2 4 6 8 10 12 14 0.5 1 1.5 2 2.5

slide-76
SLIDE 76

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D4 NEIGHBOURHOOD, 15X15

’data.dat.00000050’ matrix 2 4 6 8 10 12 14 2 4 6 8 10 12 14 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

slide-77
SLIDE 77

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D4 NEIGHBOURHOOD, 30X30

’data.dat.00000050’ matrix 5 10 15 20 25 5 10 15 20 25 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

slide-78
SLIDE 78

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D4 NEIGHBOURHOOD, 60X60

’data.dat.00000050’ matrix 10 20 30 40 50 10 20 30 40 50 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

slide-79
SLIDE 79

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX4: DIFFUSION - 2D4 NEIGHBOURHOOD, 120X120

’data.dat.00000050’ matrix 20 40 60 80 100 20 40 60 80 100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

slide-80
SLIDE 80

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX5 - PLANAR CELL POLARITY

[B [BIO

IOPPN

PPN 2011] 2011] [CMSB [CMSB 201 2011] 1]

slide-81
SLIDE 81

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX5 - PLANAR CELL POLARITY

(a)

Cell (3,2)

(b) (c) (d)

slide-82
SLIDE 82

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX5 - PLANAR CELL POLARITY

gr grid size: 40 x 40 PL PLACES ES: 164,000 TRANS TRANSITIO TIONS: S: 22 229,6 9,686 un unfol

  • ldi

ding: g: 2 min co cont nt. . simul mulati tion

  • n:

: 2 2 h

[B [BIO

IOPPN

PPN 2011] 2011] [CMSB [CMSB 201 2011] 1]

slide-83
SLIDE 83

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX5 - PLANAR CELL POLARITY

FzFmi_FmiVang CSproximalInter Vang_p 1‘all() CSproximal 336 FmiVang_p CSproximal Pk_p 1‘all() CSproximal 336 1‘all 336 Dsh_p 1‘all() CSproximal 336 FzFmi act p CSproximal FzFmi_p CSproximal FVP_p CSproximal FFD_d CSdistal Dsh_d 1‘all() CSdistal 336 FzFmi_act_d CSdistal ri3 [r=2&a=2|r=1] ri1 [r=2&a=2|r=1] rp1 rp2 rp5 rp6 r 7 ri2 [r=2&a=2|r=1] (((x,y),(a,b)),r) (((x,y),(a,b)),r) ((x,y),(a,b)) ((x,y),(a,b)) ((x,y),(a,b)) ((x,y),(a,b)) ((x,y ((x,y),(a,b)) ((x,y),(a,b)) ((x,y),(a,b)) ((x,y),( ((x,y),(a,b)) ((x,y),(a,b)) ((x,y),(a,b)) ((x,y),(a,b)) ((x,y),(a,b)) ((x,y),(a,b)) ((x,y),(a,b)) ((x,y),(a,b)) ((x,y),(a,b)) ((x,y),(a,b)) ((x,y),(a,b)) ((x,y),(a,b)) (((x,y),(a,b)),r) ((x,y),(a,b)) ((x,y),(1,1))++ ((x,y),(2,1))++ ((x,y),(3,1)) ( ( ( ((x,y),(1,1))++ ((x,y),(2,1))++ ((x,y),(3,1)) NW(x,y,a,b,r)++ SW(x,y,a,b,r) NW(x,y,a,b,r)++ SW(x,y,a,b,r) NW(x,y,a,b,r)++ SW(x,y,a,b,r)
slide-84
SLIDE 84

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

EX6 - MOBILITY / MOTILITY

  • >
  • > GRADIENTS

TS

[D [DAG

AGSTUHL 2

2011]

slide-85
SLIDE 85

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

COLOURED PETRI NETS, MORE APPLICATIONS

get multiple copies of patterns

  • > Halo model, new order of net sizes

encode locality

  • > Ca channel models
  • > cell tissue + communication between cells
  • > motility, gradients, . . .

dynamic membrane systems differentiate between submodels within a master net

  • > T-invariants
  • > generated models in conformance with wet-lab data
  • > mutants
  • > algorithmic folding

. . .

slide-86
SLIDE 86

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

SUMMARY & OUTLOOK

slide-87
SLIDE 87

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

MODELLING = ABSTRACTION

hierarchical organisation of components -> model variables genes, molecules, organelles, cells, tissues, organs, organisms functionality of atomic events chemical reactions with/out stoichiometry, conformational change, transport, . . . time qualitative versus quantitative models individual vs population behaviour (hierarchical) space

  • bservables

shape and volume of components biosystem development

slide-88
SLIDE 88

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

MULTI-SCALE CHALLENGES

repetition ... of components variation spacial organisation hierarchical organisation communication mobility / motility replication / deletion pattern formation differentiation semi-regular/irregular/dynamic organisation

slide-89
SLIDE 89

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

HOW DYNAMIC HAS A MODEL TO BE?

modif modifica cation o tion over time ma er time may inc y include ude

addition/subtraction of model components rewiring yielding new structures parameter modification (e.g. triggered by mutation) model translocation (model passing, nets in nets) reorganizing the hierarchical structure, adding, removing levels

slide-90
SLIDE 90

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

SUMMARY

representation of bio networks by Petri nets

  • > partial order representation
  • > better comprehension
  • > formal semantics
  • > sound analysis techniques
  • > unifying view

purposes

  • > animation
  • > to experience the model
  • > model validation against consistency criteria
  • > to increase confidence
  • > qualitative / quantitative behaviour prediction -> experiment design,

new insights step-wise model development

  • > qualitative model
  • > discrete Petri nets
  • > discrete quantitative model
  • > stochastic Petri nets
  • > continuous quantitative model
  • > continuous Petri nets = ODEs,

hybrid models

  • > locality and space
  • > coloured Petri nets
slide-91
SLIDE 91

PN & BioModel Engineering monika.heiner@tu-cottbus.de March 2012

OUTLOOK

THANKS !

HHTP://WWW-DSSZ.INFORMATIK.TU-COTTBUS.DE