B IOLOGICAL S YSTEMS , B ASICS PN & Systems Biology chemical - - PowerPoint PPT Presentation

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B IOLOGICAL S YSTEMS , B ASICS PN & Systems Biology chemical - - PowerPoint PPT Presentation

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ICATPN 2004, B OLOGNA PN & Systems Biology P ETRI N ET B ASED M ODEL V ALIDATION IN S YSTEMS B IOLOGY Monika Heiner Ina Koch Brandenburg University of Technology Technical University of Applied Sciences Cottbus Berlin Dep. of CS Dep. of

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

ICATPN 2004, BOLOGNA

Monika Heiner Brandenburg University of Technology Cottbus

  • Dep. of CS

Ina Koch Technical University of Applied Sciences Berlin

  • Dep. of Bioinformatics

PETRI NET BASED MODEL VALIDATION

IN SYSTEMS BIOLOGY

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SLIDE 2

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIOLOGICAL SYSTEMS, BASICS

❑ chemical reactions

  • > atomic actions
  • > Petri net transitions

input compounds

  • utput

compounds

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

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

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SLIDE 3

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIOLOGICAL SYSTEMS, BASICS

❑ chemical reactions

  • > atomic actions
  • > Petri net transitions

❑ chemical compounds

  • > Petri net places
  • primary compounds
  • metabolites
  • auxiliary compounds,
  • e. g. electron carrier

ubiquitous -> fusion nodes

  • catalyzing compounds
  • enzymes

input compounds

  • utput

compounds

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

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

r2 y x B A enzyme

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SLIDE 4

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIOLOGICAL SYSTEMS, BASICS

❑ chemical reactions

  • > atomic actions
  • > Petri net transitions

❑ chemical compounds

  • > Petri net places
  • primary compounds
  • metabolites
  • auxiliary compounds,
  • e. g. electron carrier

ubiquitous -> fusion nodes

  • catalyzing compounds
  • enzymes

❑ stoichiometric relations

  • > Petri net arc multiplicities

❑ compounds distribution

  • > marking

input compounds

  • utput

compounds

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

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

r2 y x B A enzyme

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SLIDE 5

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIOLOGICAL SYSTEMS, INTRO

r1 A B

r1: A -> B

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SLIDE 6

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIOLOGICAL SYSTEMS, INTRO

r3 r2 r1 E D C A B

r1: A -> B r2: B -> C + D r3: B -> D + E

  • > alternative reactions
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SLIDE 7

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIOLOGICAL SYSTEMS, INTRO

r3 r4 r7 r6 r2 r1 a F c b c b H G E D C A B

r1: A -> B r2: B -> C + D r4: F -> B + a r3: B -> D + E r6: C + b -> G + c r7: D + b -> H + c

  • > concurrent reactions
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SLIDE 8

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIOLOGICAL SYSTEMS, INTRO

r8 r5 r5_rev r8_rev r3 r4 r7 r6 r2 r1 a F c b c b H G E D C A B

r1: A -> B r2: B -> C + D r4: F -> B + a r3: B -> D + E r5: E + H <-> F r6: C + b -> G + c r7: D + b -> H + c r8: H <-> G

  • > reversible reactions
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SLIDE 9

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIOLOGICAL SYSTEMS, INTRO

r5 r8 r3 r4 r7 r6 r2 r1 a F c b c b H G E D C A B

r1: A -> B r2: B -> C + D r4: F -> B + a r3: B -> D + E r5: E + H <-> F r6: C + b -> G + c r7: D + b -> H + c r8: H <-> G

  • > reversible reactions
  • hierarchical nodes
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SLIDE 10

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIOLOGICAL SYSTEMS, INTRO

2 28 29 29 r11 r5 r8 r3 r10 r9 r4 r7 r6 r2 r1 a K b c c b d a F c b c b H G E D C A B

r1: A -> B r2: B -> C + D r4: F -> B + a r3: B -> D + E r5: E + H <-> F r6: C + b -> G + c r7: D + b -> H + c r8: H <-> G r9: G + b -> K + c + d r10: H + 28a + 29c -> 29b r11: d -> 2a

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SLIDE 11

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIOLOGICAL SYSTEMS, INTRO

2 28 29 29 r11 r5 r8 r3 r10 r9 r4 r7 r6 r2 r1 a K b c c b d a F c b c b H G E D C A B

r1: A -> B r2: B -> C + D r4: F -> B + a r3: B -> D + E r5: E + H <-> F r6: C + b -> G + c r7: D + b -> H + c r8: H <-> G r9: G + b -> K + c + d r10: H + 28a + 29c -> 29b r11: d -> 2a

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SLIDE 12

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIOLOGICAL SYSTEMS, INTRO

2 28 29 29 r11 r5 r8 r3 r10 r9 r4 r7 r6 r2 r1 a K b c c b d a F c b c b H G E D C A B

r1: A -> B r2: B -> C + D r4: F -> B + a r3: B -> D + E r5: E + H <-> F r6: C + b -> G + c r7: D + b -> H + c r8: H <-> G r9: G + b -> K + c + d r10: H + 28a + 29c -> 29b r11: d -> 2a input compound

  • utput compound

stoichiometric relations fusion nodes - auxiliary compounds

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SLIDE 13

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIONETWORKS

❑ networks of chemical reactions ❑ biologically interpreted Petri net

  • > partial order sequences of chemical reactions
  • transforming input into output compounds
  • respecting the given stoichiometric relations
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SLIDE 14

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIONETWORKS

❑ networks of chemical reactions ❑ biologically interpreted Petri net

  • > partial order sequences of chemical reactions
  • transforming input into output compounds
  • respecting the given stoichiometric relations

❑ typical (structural) properties ❑

  • bservation
  • > tend to grow fast

INA ORD HOM NBM PUR CSV SCF CON SC Ft0 tF0 Fp0 pF0 MG SM FC EFC ES N N N Y N N Y N N N Y Y N N N N N DTP CPI CTI B SB REV DSt BSt DTr DCF L LV L&S N N N Y Y ? ? ? ? ? N ? N

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SLIDE 15

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIONETWORKS

❑ networks of chemical reactions ❑ biologically interpreted Petri net

  • > partial order sequences of chemical reactions
  • transforming input into output compounds
  • respecting the given stoichiometric relations

❑ typical (structural) properties ❑

  • bservation
  • > tend to grow fast

INA ORD HOM NBM PUR CSV SCF CON SC Ft0 tF0 Fp0 pF0 MG SM FC EFC ES N N N Y N N Y N N N Y Y N N N N N DTP CPI CTI B SB REV DSt BSt DTr DCF L LV L&S N N N Y Y ? ? ? ? ? N ? N

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIONETWORKS, SOME PROBLEMS

❑ network structure

  • > PROBLEM 1
  • > dense, apparently unstructured
  • > hard to read

❑ knowledge

  • > PROBLEM 2
  • > uncertain
  • > growing, changing
  • > distributed over independent data bases, papers, journals, . . .

❑ various, mostly ambiguous representations

  • > PROBLEM 3
  • > verbose descriptions
  • > diverse graphical representations
  • > contradictory and / or fuzzy statements
  • > some examples
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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK REPRESENTATIONS, EX1

TNF TNFR1 Fas-L Fas DAXX FADD FLIP CrmA Caspase-8 Effector Caspases Caspases-3,-6,-7 Apoptosis Ask1 FADD MADD Procaspase-8 Procaspase-8 JNK MAPK Pathway Bcl-X FAN RIP TRAF2 NSMase

  • > CASE STUDY 1
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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK REPRESENTATIONS, EX1 + EX2

TNF TNFR1 Fas-L Fas DAXX FADD FLIP CrmA Caspase-8 Effector Caspases Caspases-3,-6,-7 Apoptosis Ask1 FADD MADD Procaspase-8 Procaspase-8 JNK MAPK Pathway Bcl-X FAN RIP TRAF2 NSMase

  • > CASE STUDY 1

Death ligand Death receptor FADD Procaspase-8 Caspase-8 Apoptotic Stimuli Apaf-1 Bax, Bad, Bim Bcl-2, Bcl-XL Procaspase-3,-6,-7 Bid Mitochondrion Cytochrome c dATP/ATP Procaspase-9 Active Caspase-9 Procaspase-3,-6,-7 Active Caspase-3,-6,-7 DFF Cleaved DFF45 Oligomer of DFF40 nucleus Chromatin Condensation and Fragmentation

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SLIDE 19

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK REPRESENTATIONS, EX1 + EX2

TNF TNFR1 Fas-L Fas DAXX FADD FLIP CrmA Caspase-8 Effector Caspases Caspases-3,-6,-7 Apoptosis Ask1 FADD MADD Procaspase-8 Procaspase-8 JNK MAPK Pathway Bcl-X FAN RIP TRAF2 NSMase

  • > CASE STUDY 1

Death ligand Death receptor FADD Procaspase-8 Caspase-8 Apoptotic Stimuli Apaf-1 Bax, Bad, Bim Bcl-2, Bcl-XL Procaspase-3,-6,-7 Bid Mitochondrion Cytochrome c dATP/ATP Procaspase-9 Active Caspase-9 Procaspase-3,-6,-7 Active Caspase-3,-6,-7 DFF Cleaved DFF45 Oligomer of DFF40 nucleus Chromatin Condensation and Fragmentation

  • > INHIBITOR

ARCS

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PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK REPRESENTATIONS, EX3

APOPTOSIS

FasL TNFα TNFβ

CD40L

NGF FAP-1 Daxx FADD

TRADD

TRF2 TRF1 TRF3 TRF6 RIP NF-kB I-kB

RAIDD CASP8

Cytc CSP10

CASP11

CASP4 CASP1 CASP6

DFF45 DFF40

CASP3 CASP7 CASP2 CASP9

Apaf-1 Bcl-xL Bcl-2a Hrk Bad Bax Mtd Mcl-1 A-1 Bcl-w DNA fragmentation Fas

TNFR1

CD40 TNFR2 GR

p75LNTR

trkA Nucleus Mitochondria rupture Caspase cascade

Glucocortocoid

  • > CASE STUDY 1

KEGG

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SLIDE 21

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK REPRESENTATIONS, EX3

APOPTOSIS

FasL TNFα TNFβ

CD40L

NGF FAP-1 Daxx FADD

TRADD

TRF2 TRF1 TRF3 TRF6 RIP NF-kB I-kB

RAIDD CASP8

Cytc CSP10

CASP11

CASP4 CASP1 CASP6

DFF45 DFF40

CASP3 CASP7 CASP2 CASP9

Apaf-1 Bcl-xL Bcl-2a Hrk Bad Bax Mtd Mcl-1 A-1 Bcl-w DNA fragmentation Fas

TNFR1

CD40 TNFR2 GR

p75LNTR

trkA Nucleus Mitochondria rupture Caspase cascade

Glucocortocoid

  • > CASE STUDY 1
  • > INHIBITOR

ARCS KEGG

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SLIDE 22

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK REPRESENTATIONS, EX3

APOPTOSIS

FasL TNFα TNFβ

CD40L

NGF FAP-1 Daxx FADD

TRADD

TRF2 TRF1 TRF3 TRF6 RIP NF-kB I-kB

RAIDD CASP8

Cytc CSP10

CASP11

CASP4 CASP1 CASP6

DFF45 DFF40

CASP3 CASP7 CASP2 CASP9

Apaf-1 Bcl-xL Bcl-2a Hrk Bad Bax Mtd Mcl-1 A-1 Bcl-w DNA fragmentation Fas

TNFR1

CD40 TNFR2 GR

p75LNTR

trkA Nucleus Mitochondria rupture Caspase cascade

Glucocortocoid

  • > CASE STUDY 1
  • > INHIBITOR

ARCS

  • > ERROR

KEGG

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SLIDE 23

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK REPRESENTATIONS, EX3

APOPTOSIS

FasL TNFα TNFβ

CD40L

NGF FAP-1 Daxx FADD

TRADD

TRF2 TRF1 TRF3 TRF6 RIP NF-kB I-kB

RAIDD CASP8

Cytc CSP10

CASP11

CASP4 CASP1 CASP6

DFF45 DFF40

CASP3 CASP7 CASP2 CASP9

Apaf-1 Bcl-xL Bcl-2a Hrk Bad Bax Mtd Mcl-1 A-1 Bcl-w DNA fragmentation Fas

TNFR1

CD40 TNFR2 GR

p75LNTR

trkA Nucleus Mitochondria rupture Caspase cascade

Glucocortocoid

  • > CASE STUDY 1
  • > INHIBITOR

ARCS

  • > ERROR
  • > INTERPRETATION ?
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SLIDE 24

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK REPRESENTATIONS, EX4

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

  • > CASE STUDY 3
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SLIDE 25

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK REPRESENTATIONS, EX4

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

?? ??

  • > CASE STUDY 3
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SLIDE 26

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK REPRESENTATIONS, EX4

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

  • > INTERPRETATION ?
  • > CASE STUDY 3
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SLIDE 27

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIONETWORKS, SOME PROBLEMS, CONSEQUENCES

❑ patchwork

  • > likely to be erroneous

❑ long-term purpose

  • > (quantitative) behaviour prediction

❑ necessary intermediate step

  • > model validation
  • > validation criteria ?
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SLIDE 28

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIONETWORKS, SOME PROBLEMS, CONSEQUENCES

❑ patchwork

  • > likely to be erroneous

❑ long-term purpose

  • > (quantitative) behaviour prediction

❑ necessary intermediate step

  • > model validation
  • > validation criteria ?

❑ steady state behaviour

  • > pathways
  • > all possible flows preserving the given compounds distribution
  • > elementary modes = minimal T-invariants

❑ consistency criteria

  • > pathways analysis
  • > CTI
  • > no minimal T-invariant without biological interpretation
  • > no known biological behaviour without corresponding T-invariant
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SLIDE 29

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

BIONETWORKS, SOME PROBLEMS, CONSEQUENCES

❑ patchwork

  • > likely to be erroneous

❑ long-term purpose

  • > (quantitative) behaviour prediction

❑ necessary intermediate step

  • > model validation
  • > validation criteria ?

❑ steady state behaviour

  • > pathways
  • > all possible flows preserving the given compounds distribution
  • > elementary modes = minimal T-invariants

❑ consistency criteria

  • > pathways analysis
  • > CTI
  • > no minimal T-invariant without biological interpretation
  • > no known biological behaviour without corresponding T-invariant
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SLIDE 30

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

T-INVARIANTS, REFRESHMENT

❑ Lautenbach, 1973 ❑ T-invariants

  • > multisets of transitions
  • > integer solutions of

❑ minimal T-invariants

  • > there is no T-invariant with a smaller support
  • > sets of transitions
  • > gcD of all entries is 1

❑ any T-invariant is a non-negative linear combination of minimal ones

  • > multiplication with a positive integer
  • > addition
  • > Division by gcD

❑ Covered by T-Invariants (CTI)

  • > each transition belongs to a T-invariant

Cx 0 x 0 x ≥ , ≠ , =

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SLIDE 31

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK NEEDS ENVIRONMENT BEHAVIOUR

❑ to animate the model

  • > infinite substance flow
  • > deeper insights

❑ to validate the model

  • > consistency criteria

❑ steady flow

  • > input substances
  • > output substances

❑ auxiliary substances

  • > as much as necessary

❑ minimal assumptions

2 28 29 29 r11 r5 r8 r3 r10 r9 r4 r7 r6 r2 r1 a K b c c b d a F c b c b H G E D C A B

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SLIDE 32

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK NEEDS ENVIRONMENT BEHAVIOUR

❑ to animate the model

  • > infinite substance flow
  • > deeper insights

❑ to validate the model

  • > consistency criteria

❑ steady flow

  • > input substances
  • > output substances

❑ auxiliary substances

  • > as much as necessary

❑ minimal assumptions

2 28 29 29 r_a g_a r_c g_c r_b g_b r_K g_A r11 r5 r8 r3 r10 r9 r4 r7 r6 r2 r1 a b c a K b c c b d a F c b c b H G E D C A B

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SLIDE 33

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK WITH ENVIRONMENT BEHAVIOUR

❑ input substances

  • > generating pre-transitions

❑

  • utput substances
  • > consuming post-transitions

❑ auxiliary substances

  • > both

❑ no boundary places, but boundary transitions ❑ transitions without pre-places

  • > live
  • > all post-places are unbounded

❑ steady state behaviour

  • > empty marking reproduction

2 28 29 29 r_a g_a r_c g_c r_b g_b r_K g_A r11 r5 r8 r3 r10 r9 r4 r7 r6 r2 r1 a b c a K b c c b d a F c b c b H G E D C A B

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SLIDE 34

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK, T-INVARIANTS trivial min. T-invariants (5)

❑ boundary transitions of auxiliary compounds

  • > (g_a, r_a), (g_b, r_b),

(g_c, r_c) ❑ reversible reactions

  • > (r5, r5_rev), (r8, r8_rev)

non-trivial min. T-invariants (7)

❑ covering boundary transitions of input / output compounds

  • > i/o-T-invariants

❑ inner cycles

2 28 29 29 r_a g_a r_c g_c r_b g_b r_K g_A r11 r5 r8 r3 r10 r9 r4 r7 r6 r2 r1 a b c a K b c c b d a F c b c b H G E D C A B

  • > CTI
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SLIDE 35

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

NETWORK, I/O-T-INVARIANT

❑ i/o-T-invariant, example 12 | 0.r1 : 1 | 1.r2 : 1, | 3.r8_rev : 1, | 4.r6 : 1, | 5.r7 : 1, | 9.r9 : 2, | 12.r11 : 2, | 13.g_A : 1, | 14.r_K : 2, | 15.g_b : 4, | 18.r_c : 4, | 20.r_a : 4 ❑ sum equation A + 4b -> 2K +4a + 4c

2 28 29 29 r_a g_a r_c g_c r_b g_b r_K g_A r11 r5 r8 r3 r10 r9 r4 r7 r6 r2 r1 a b c a K b c c b d a F c b c b H G E D C A B 2x 2x 2x 4x 4x 4x

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SLIDE 36

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

ENVIRONMENT BEHAVIOUR, THREE STYLES

❑

STYLE 1A

  • > weak assumptions
  • > infinite flow into/out the network

❑

STYLE 1B

  • > firm assumptions
  • > finite, but sufficient reservoir of auxiliary compounds

❑

STYLE 2

  • > strong assumptions
  • > finite, but sufficient reservoir of auxiliary compounds
  • > quantitative relations of input/output compounds

INCREASING STRENGTH

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SLIDE 37

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

ENVIRONMENT BEHAVIOUR, STYLE 1A

❑ weak assumptions ❑ input compounds

  • > generating pre-transitions

❑

  • utput compounds
  • > consuming post-transitions

❑ auxiliary compounds

  • > generating pre-transitions & consuming post-transitions
  • > infinite reservoir

❑ typical properties no assumptions about quantitative relations of input/output compounds

INA ORD HOM NBM PUR CSV SCF CON SC Ft0 tF0 Fp0 pF0 MG SM FC EFC ES N N N Y N N Y N Y Y N N N N N N N DTP CPI CTI B SB REV DSt BSt DTr DCF L LV L&S ? N Y N N ? N ? N n Y Y N

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SLIDE 38

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

ENVIRONMENT BEHAVIOUR, STYLE 1A

❑ weak assumptions ❑ input compounds

  • > generating pre-transitions

❑

  • utput compounds
  • > consuming post-transitions

❑ auxiliary compounds

  • > generating pre-transitions & consuming post-transitions
  • > infinite reservoir

❑ typical properties no assumptions about quantitative relations of input/output compounds

INA ORD HOM NBM PUR CSV SCF CON SC Ft0 tF0 Fp0 pF0 MG SM FC EFC ES N N N Y N N Y N Y Y N N N N N N N DTP CPI CTI B SB REV DSt BSt DTr DCF L LV L&S ? N Y N N ? N ? N n Y Y N

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SLIDE 39

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

ENVIRONMENT BEHAVIOUR, STYLE 1B

❑ firm assumptions ❑ input compounds

  • > generating pre-transitions

❑

  • utput compounds
  • > consuming post-transitions

❑ auxiliary compounds

  • > neither generating pre-transitions nor consuming post-transitions
  • > finite reservoir
  • > P-invariants ( = traps = co-traps )
  • > Which (minimal) initial token distribution makes the net live ?

❑ typically expected properties

  • > see style 1

no assumptions about quantitative relations of input/output compounds

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SLIDE 40

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

ENVIRONMENT BEHAVIOUR, STYLE 2

❑ strong assumptions

  • > quantitative relations of input/output compounds
  • > finite reservoir of auxiliary compounds

❑ typically expected properties ❑ additional model component ❑ How to compute ? For alternative paths ?

INA ORD HOM NBM PUR CSV SCF CON SC Ft0 tF0 Fp0 pF0 MG SM FC EFC ES N N N Y N N Y Y N N N N N N N N N DTP CPI CTI B SB REV DSt BSt DTr DCF L LV L&S ? Y Y Y Y ? N ? N Y Y Y N

input compounds

  • utput

compounds b a e d r e m

  • v

e C B A E D

  • > network sum equation

c g e n e r a t e cycle

aA + bB +cC -> dD + eE

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SLIDE 41

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

ENVIRONMENT BEHAVIOUR, STYLE 2

❑ strong assumptions

  • > quantitative relations of input/output compounds
  • > finite reservoir of auxiliary compounds

❑ typically expected properties ❑ additional model component ❑ How to compute ? For alternative paths ?

INA ORD HOM NBM PUR CSV SCF CON SC Ft0 tF0 Fp0 pF0 MG SM FC EFC ES N N N Y N N Y Y N N N N N N N N N DTP CPI CTI B SB REV DSt BSt DTr DCF L LV L&S ? Y Y Y Y ? N ? N N Y Y N

input compounds

  • utput

compounds b a e d r e m

  • v

e C B A E D

  • > network sum equation

c g e n e r a t e cycle

aA + bB +cC -> dD + eE

slide-42
SLIDE 42

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

CASE STUDIES

❑ case study 1

  • > signal-transduction network - apoptosis
  • > no stoichiometric relations - ordinary place/transition net
  • > many read arcs, resolved for analysis
  • > environment behaviour, style 1A

❑ case study 2

  • > metabolic network - carbon metabolism in potato tuber
  • > stiochiometric relations known - non-ordinary place/transition net
  • > many reversible reactions
  • > environment behaviour, style 1B

❑ case study 3

  • > metabolic network - glycolysis and pentose phosphate metabolism
  • > coloured nets (Design-CPN)
  • > environment behaviour, style 2, computed by prototype tool SY / Genrich
slide-43
SLIDE 43

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

CASE STUDIES

❑ case study 1

  • > 37 P / 45 T
  • > 10 t-inv’s
  • > signal-transduction network - apoptosis
  • > no stoichiometric relations - ordinary place/transition net
  • > many read arcs, resolved for analysis
  • > environment behaviour, style 1A

❑ case study 2

  • > 17 P / 25 T
  • > 19 t-inv’s / 3 p-inv’s
  • > metabolic network - carbon metabolism in potato tuber
  • > stiochiometric relations known - non-ordinary place/transition net
  • > many reversible reactions
  • > environment behaviour, style 1B

❑ case study 3

  • > 32 P / 22 T
  • > 1 t-inv / 39 p-inv’s
  • > metabolic network - glycolysis and pentose phosphate metabolism
  • > coloured nets (Design-CPN)
  • > environment behaviour, style 2, computed by prototype tool SY / Genrich
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SLIDE 44

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

CHALLENGES

❑ extensions

  • > read arcs
  • > inhibitor arcs !?

❑ efficient computation of minimal invariants

  • > exponential complexity
  • > compositional approach ?

❑ analysis of bounded, but not safe non-ordinary nets with inhibitor arcs

  • > huge state spaces, beyond exponential growth (?)
  • > smaller, bounded version of case study 2

1010 states (IDD-based mc tool) ❑ analysis of unbounded nets

  • > besides T-invariant analysis ?

❑ model checking

  • > relevant properties ?

≥

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SLIDE 45

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

OUTLOOK

FURTHER CASE STUDIES

❑ blood clotting (hemostasis versus fibrinolysis) ❑ the whole E. coli pathway ❑ the whole potato tuber pathway ❑ detailed glycolysis in humans ❑ G1/S - phase in mammalian cells ❑ lipoprotein metabolism (liver)

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SLIDE 46

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

OUTLOOK

FURTHER CASE STUDIES

❑ blood clotting

  • > Gerry Neumann / BTU

(hemostasis versus fibrinolysis) ❑ the whole E. coli pathway

  • > Nina Kramer / TFH

❑ the whole potato tuber pathway

  • > Nina Kramer / TFH

❑ detailed glycolysis in humans

  • > Thomas Runge / BTU

❑ G1/S - phase in mammalian cells

  • > Thomas Kaunath / TFH

❑ lipoprotein metabolism (liver)

  • > Daniel Schrödter / BTU
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SLIDE 47

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

SUMMARY

❑ representation of bionetworks by Petri nets

  • > unifying view
  • > animation
  • > model validation against consistency criteria
  • > qualitative/quantitative behaviour prediction

❑ three styles of environment description ❑ steady state behaviour

  • > pathways
  • > T-invariants
  • > elementary modes
  • > minimal T-invariants

❑ consistency criteria

  • > CTI
  • > T-invariant <-> biological interpretation

❑ many challenging questions for analysis techniques

slide-48
SLIDE 48

PN & Systems Biology monika.heiner@informatik.tu-cottbus.de, ina.koch@tfh-berlin.de June 2004

GRAZIE PER LA VOSTRA ATTENZIONE !