SYSTEMS BIOLOGY - A PETRI NET PERSPECTIVE -

ILMENAU, JULY 006 SYSTEMS BIOLOGY - A PETRI NET PERSPECTIVE - WHAT HAVE TECHNICAL AND NATURAL SYSTEMS IN COMMON? Monika Heiner Brandenburg University of Technology Cottbus Dept. of CS

LONG-TERM VISION MEDICAL TREATMENT

LONG-TERM VISION MEDICAL TREATMENT, APPROACH 1- TRIAL-AND-ERROR DRUG PRESCRIPTION??????????

LONG-TERM VISION MEDICAL TREATMENT, APPROACH??????????

LONG-TERM VISION MEDICAL TREATMENT, APPROACH - MODEL-BASED DRUG PRESCRIPTION

WHAT KIND OF MODEL SHOULD BE USED?

BIOLOGICAL FUNCTION?

... BY INTERACTION IN NETWORKS

NETWORK REPRESENTATIONS, EX1 Rap1 camp GEF camp ATP B-Raf AdCyc α camp camp AMP camp PKA Receptor e.g. 7-TMR γ α β heterotrimeric G-protein γ β tyrosine kinase Ras shc SOS grb Raf-1 camp PKA cell membrane Akt Ras Rac PI-3 K PAK MEK1, PDE ERK1, MEK ERK1, MKP cytosol transcription factors nucleus

NETWORK REPRESENTATIONS, EX1 Rap1 camp GEF camp ATP B-Raf MEK1, ERK1, AdCyc camp α camp AMP PDE nucleus transcription factors camp PKA Receptor e.g. 7-TMR γ α β heterotrimeric G-protein γ β MKP tyrosine kinase Ras shc SOS grb camp PKA ERK1, MEK Raf-1 cell membrane Akt Ras PI-3 K cytosol -> FORMAL SEMANTICS? Rac PAK

NETWORK REPRESENTATIONS, EX

NETWORK REPRESENTATIONS, EX -> READABILITY?

WHAT IS A BIOCHEMICAL NETWORK MODEL? structure graph QUALITATIVE kinetics, if you can reaction rates d[raf1*]/dt = k1*m1*m + k*m3 + k5*k4 QUANTITATIVE k1 = 0.53, k = 0.007, k5 = 0.0315 initial conditions concentrations [Raf1*] t=0 = µmolar marking

BIONETWORKS, SOME PROBLEMS knowledge -> PROBLEM 1 -> uncertain -> growing, changing -> time-consuming wet-lab experiments -> some data estimated -> distributed over independent data bases, papers, journals,... various, mostly ambiguous representations -> PROBLEM -> verbose descriptions -> diverse graphical representations -> contradictory and / or fuzzy statements network structure -> PROBLEM 3 -> tend to grow fast -> dense, apparently unstructured -> hard to read

BIONETWORKS, SOME PROBLEMS

FRAMEWORK bionetworks knowledge quantitative modelling understanding quantitative models animation / analysis /simulation model validation quantitative behaviour prediction ODEs

FRAMEWORK bionetworks knowledge qualitative modelling qualitative models animation / analysis understanding model validation qualitative behaviour prediction Petri net theory (invariants) model checking quantitative modelling quantitative parameters understanding quantitative models animation / analysis /simulation model validation quantitative behaviour prediction ODEs

FRAMEWORK bionetworks knowledge qualitative modelling qualitative models animation / analysis understanding model validation qualitative behaviour prediction Petri net theory (invariants) model checking quantitative modelling quantitative parameters quantitative models animation / analysis /simulation understanding model validation quantitative behaviour prediction reachability graph linear unequations linear programming ODEs

BIO PETRI NETS - AN INFORMAL CRASH COURSE

PETRI NETS, BASICS - THE STRUCTURE atomic actions -> Petri net transitions -> chemical reactions NAD + + H O -> NADH + H + + O input compounds NAD + H O r1 NADH H + O output compounds

PETRI NETS, BASICS - THE STRUCTURE atomic actions -> Petri net transitions -> chemical reactions NAD + + H O -> NADH + H + + O input compounds NAD + H O r1 NADH H + O output compounds hyperarc NAD + NADH H O H + O

PETRI NETS, BASICS - THE STRUCTURE atomic actions -> Petri net transitions -> chemical reactions NAD + + H O -> NADH + H + + O input compounds pre-conditions NAD + H O r1 NADH H + O output compounds post-conditions local conditions -> Petri net places -> chemical compounds

PETRI NETS, BASICS - THE STRUCTURE atomic actions -> Petri net transitions -> chemical reactions NAD + + H O -> NADH + H + + O input compounds NAD + H O r1 NADH H + O output compounds local conditions -> Petri net places -> chemical compounds multiplicities -> Petri net arc weights -> stoichiometric relations condition s state -> token(s) in its place -> available amount (e.g. mol) system state -> marking -> compounds distribution

PETRI NETS, BASICS - THE BEHAVIOUR atomic actions -> Petri net transitions -> chemical reactions NAD + + H O -> NADH + H + + O input compounds NAD + H O r1 NADH H + O output compounds

PETRI NETS, BASICS - THE BEHAVIOUR atomic actions -> Petri net transitions -> chemical reactions NAD + + H O -> NADH + H + + O input compounds NAD + H O r1 NADH H + O output compounds FIRING NAD + r1 NADH H + H O O

BIOLOGICAL SYSTEMS, INTRO r1: A -> B r1 A B

BIOLOGICAL SYSTEMS, INTRO r1: A -> B r: B -> C + D r3: B -> D + E r A r1 B r3 C D E -> alternative reactions

BIOLOGICAL SYSTEMS, INTRO r1: A -> B r: B -> C + D r3: B -> D + E r A r1 B r4 a r4: F -> B + a r3 r6: C + b -> G + c C D E F r7: D + b -> H + c r6 b c r7 b c G H -> concurrent reactions

BIOLOGICAL SYSTEMS, INTRO r1: A -> B r: B -> C + D r3: B -> D + E r A r1 B r4 a r4: F -> B + a r5: E + H <-> F r6: C + b -> G + c r7: D + b -> H + c r8: H <-> G G r6 C b c r8_rev r8 r7 D r3 E b c H r5_rev r5 F -> reversible reactions

BIOLOGICAL SYSTEMS, INTRO r1: A -> B r: B -> C + D r3: B -> D + E r A r1 B r4 a r4: F -> B + a r5: E + H <-> F r6: C + b -> G + c C D r3 E r5 F r7: D + b -> H + c r8: H <-> G G r6 b c r8 r7 b c H -> reversible reactions - hierarchical nodes

BIOLOGICAL SYSTEMS, INTRO r1: A -> B r: B -> C + D r3: B -> D + E r A r1 B r4 a r4: F -> B + a r5: E + H <-> F r6: C + b -> G + c C D r3 E r5 F r7: D + b -> H + c r8: H <-> G r9: G + b -> K + c + d r10: H + 8a + 9c -> 9b r11: d -> a r6 G r9 K b c b c d r8 r11 r7 a b c H 8 9 r10 9 b c

BIOLOGICAL SYSTEMS, INTRO r1: A -> B r: B -> C + D r3: B -> D + E r4: F -> B + a 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 + 8a + 9c -> 9b r11: d -> a G K r r6 r9 input compound C b c b c d r8 r11 r7 a output compound D r1 r3 A B b c E H 8 9 r10 9 b c r5 r4 F a stoichiometric relations fusion nodes - auxiliary compounds

BIOLOGICAL SYSTEMS, INTRO INPUT FROM ENVIRONMENT g_a r1: A -> B r: B -> C + D r3: B -> D + E r r1 A B r4 a r4: F -> B + a r5: E + H <-> F r6: C + b -> G + c C D r3 E r5 F r7: D + b -> H + c r8: H <-> G r9: G + b -> K + c + d r10: H + 8a + 9c -> 9b r11: d -> a OUTPUT TO ENVIRONMENT G K r6 r9 r_k b c b c d r8 r11 r7 a b c H 8 9 r10 9 b c g_a g_b g_c a b c r_a r_b r_c

BIOCHEMICAL PETRI NETS, SUMMARY biochemical networks -> networks of (abstract) chemical reactions biochemically interpreted Petri net -> partial order sequences of chemical reactions (= elementary actions) transforming input into output compounds / signals [ respecting the given stoichiometric relations, if any ] -> set of all pathways from the input to the output compounds / signals [ respecting the stoichiometric relations, if any ] pathway -> self-contained partial order sequence of elementary (re-) actions

TYPICAL BASIC STRUCTURES metabolic networks -> substance flows e1 e e3 r1 r r3 signal transduction networks -> signal flows r1 r r3

A CASE STUDY

THE RKIP PATHWAY one pathway Ras Mitogens Growth factors receptor Receptor P P Raf P kinase P P MEK P P ERK cytoplasmic substrates Elk SAP Gene

THE RKIP PATHWAY [Cho et al., CMSB 003]

THE RKIP PATHWAY, PETRI NET Raf-1Star m1 RKIP m k1 k ERK-PP m9 m3 Raf-1Star_RKIP k8 k3 k4 k11 m8 MEK-PP_ERK m4 Raf-1Star_RKIP_ERK-PP m11 RKIP-P_RP k6 k7 k5 k9 k10 m7 MEK-PP m5 ERK m6 RKIP-P m10 RP

THE RKIP PATHWAY, HIERARCHICAL PETRI NET Raf-1Star m1 RKIP m k1_k ERK-PP m9 m3 Raf-1Star_RKIP k8 k3_k4 k11 m8 MEK-PP_ERK m4 m11 RKIP-P_RP Raf-1Star_RKIP_ERK-PP k6_k7 k5 k9_k10 m7 MEK-PP m5 ERK m6 RKIP-P m10 RP

THE RKIP PATHWAY, HIERARCHICAL PETRI NET initial marking Raf-1Star m1 RKIP m k1_k ERK-PP m9 m3 Raf-1Star_RKIP k8 k3_k4 k11 m8 MEK-PP_ERK m4 m11 RKIP-P_RP Raf-1Star_RKIP_ERK-PP k6_k7 k5 k9_k10 m7 MEK-PP m5 ERK m6 RKIP-P m10 RP

THE RKIP PATHWAY, HIERARCHICAL PETRI NET initial marking m7 MEK-PP ERK-PP m9 m8 k8 MEK-PP_ERK k6_k7 Raf-1Star m1 m5 ERK m3 m4 Raf-1Star_RKIP_ERK-PP k5 m m6 RKIP Raf-1Star_RKIP RKIP-P m11 k11 RKIP-P_RP k9_k10 CONSTRUCTED BY PN ANALYSIS k1_k k3_k4 m10 RP

QUALITATIVE ANALYSES

ANALYSIS TECHNIQUES, OVERVIEW static analyses -> no state space construction -> structural properties (graph theory, combinatorial algorithms) -> P / T - invariants (discrete computational geometry), dynamic analyses -> total / partial state space construction -> state space representations: interleaving (RG) / partial order (prefix) -> analysis of general behavioural system properties, e.g. boundedness, liveness, reversibility,... -> model checking of special behavioural system properties, e.g. reachability of a given (sub-) system state [with constraints], reproducability of a given (sub-) system state [with constraints] expressed in temporal logics (CTL / LTL), very flexible, powerful querry language

STATIC ANALYSES

INCIDENCE MATRIX C a representation of the net structure => stoichiometric matrix P T t1... tj... tm p1 C = pi cij cij = (pi, tj) = F(tj,pi) - F(pi, tj) = tj(pi)... pn tj tj = tj(*) matrix entry cij: token change in place pi by firing of transition tj matrix column tj: vector describing the change of the whole marking by firing of tj side-conditions are neglected a x i j enzyme x enzyme-catalysed reaction b cij = 0

P-INVARIANTS, BASICS Lautenbach, 1973 P-invariants -> multisets of places -> integer solutions y of yc = 0, y 0, y 0 minimal P-invariants -> there is no P-invariant with a smaller support -> sets of places -> gcd of all entries is 1 any P-invariant is a non-negative linear combination of minimal ones -> multiplication with a positive integer -> addition -> Division by gcd ky = Covered by P-Invariants (CPI) -> each place belongs to a P-invariant -> CPI => BND (sufficient condition) i a i y i

P-INVARIANTS, INTERPRETATION the firing of any transition has no influence on the weighted sum of tokens on the P-invariant s places -> for all t: the effect of the arcs, removing tokens from a P-invariant s place is equal to the effect of the arcs, adding tokens to a P-invariant s place set of places with -> a constant weighted sum of tokens for all markings m reachable from m 0 ym = ym 0 -> token / compound preservation -> moieties -> a place belonging to a P-invariant is bounded a P-invariant defines a subnet -> the P-invariant s places (the support), + all their pre- and post-transitions + the arcs in between -> pre-sets of supports = post-sets of supports -> self-contained, cyclic

THE RKIP PATHWAY, P-INVARIANTS Raf-1Star m1 RKIP m Raf-1Star m1 RKIP m k1_k k1_k ERK-PP ERK-PP m9 m3 Raf-1Star_RKIP m9 m3 Raf-1Star_RKIP k8 k3_k4 k11 k8 k3_k4 k11 m8 MEK-PP_ERK m4 Raf-1Star_RKIP_ERK-PP m11 RKIP-P_RP m8 MEK-PP_ERK m4 Raf-1Star_RKIP_ERK-PP m11 RKIP-P_RP k6_k7 k5 k9_k10 k6_k7 k5 k9_k10 m7 MEK-PP m5 ERK m6 RKIP-P m10 RP m7 MEK-PP m5 ERK m6 RKIP-P m10 RP Raf-1Star m1 RKIP m k1_k ERK-PP P-INV1: MEK m9 m3 Raf-1Star_RKIP P-INV: RAF-1STAR k8 k3_k4 k11 P-INV3: RP m8 MEK-PP_ERK m4 Raf-1Star_RKIP_ERK-PP m11 RKIP-P_RP P-INV4: ERK k6_k7 k5 k9_k10 P-INV5: RKIP m7 MEK-PP m5 ERK m6 RKIP-P m10 RP

T-INVARIANTS, BASICS Lautenbach, 1973 T-invariants -> multisets of transitions -> integer solutions x of Cx = 0, x 0, x 0 -> Parikh vector 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 kx = Covered by T-Invariants (CTI) -> each transition belongs to a T-invariant -> BND & LIVE => CTI (necessary condition) i a i x i

T-INVARIANTS, INTERPRETATIONS T-invariants = (multi-) sets of transitions = Parikh vector -> zero effect on marking -> reproducing a marking / system state two interpretations 1. relative transition firing rates of transitions occuring permanently & concurrently -> steady state behaviour. partially ordered transition sequence -> behaviour understanding of transitions occuring one after the other -> substance / signal flow a T-invariant defines a subnet -> partial order structure -> the T-invariant s transitions (the support), + all their pre- and post-places + the arcs in between -> pre-sets of supports = post-sets of supports

THE RKIP PATHWAY, NON-TRIVIAL T-INVARIANT -> non-trivial T-invariant + four trivial ones for reversible reactions Raf-1Star m1 RKIP m k1 ERK-PP m9 m3 Raf-1Star_RKIP k8 k3 k11 m8 MEK-PP_ERK m4 m11 RKIP-P_RP Raf-1Star_RKIP_ERK-PP k6 k5 k9 m7 MEK-PP m5 ERK m6 RKIP-P m10 RP

CONSTRUCTION OF THE INITIAL MARKING each P-invariant gets at least one token -> P-invariants are structural deadlocks and traps in signal transduction -> exactly 1 token, corresponding to species conservation -> token in least active state all (non-trivial) T-invariants get realizable -> to make the net live minimal marking -> minimization of the state space

NON-TRIVIAL T-INVARIANT, RUN realizability check under the constructed marking MEK-PP m7 ERK-PP m9 Raf-1Star RKIP m1 m m3 k1 Raf-1Star_RKIP RP m10 T-invariant s unfolding to describe its behaviour -> partial order structure ERK m5 k6 m4 m1 k3 Raf-1Star_RKIP_ERK-PP k5 RKIP-P m6 Raf-1Star k9 labelled condition / event net -> events (boxes) - transition occurences -> conditions (circles) - involved compounds m8 MEK-PP m7 MEK-PP_ERK k8 ERK-PP m9 m3 RKIP m m11 Raf-1Star_RKIP k3 k1 m10 RKIP-P_RP k11 RP occurrence net -> acyclic -> no backward branching conditions -> infinite m8 ERK m5 k6 m4 MEK-PP_ERK k8 m1 Raf-1Star Raf-1Star_RKIP_ERK-PP k5 RKIP-P m6 m11 k9 RKIP-P_RP k11 m7 MEK-PP m9 ERK-PP m RKIP m10 RP monika.heiner@informatik.tu-cottbus.de August 005

DYNAMIC ANALYSES

DYNAMIC ANALYSIS - REACHABILITY GRAPH simple construction algorithm -> nodes - system states -> arcs - the (single) firing transition -> single step firing rule

DYNAMIC ANALYSIS - REACHABILITY GRAPH simple construction algorithm -> nodes - system states -> arcs - the (single) firing transition -> single step firing rule s1

DYNAMIC ANALYSIS - REACHABILITY GRAPH simple construction algorithm -> nodes - system states -> arcs - the (single) firing transition -> single step firing rule s1 s k1

DYNAMIC ANALYSIS - REACHABILITY GRAPH simple construction algorithm -> nodes - system states -> arcs - the (single) firing transition -> single step firing rule s1 k k1 s s3 k3

DYNAMIC ANALYSIS - REACHABILITY GRAPH simple construction algorithm -> nodes - system states -> arcs - the (single) firing transition -> single step firing rule s1 k k1 s k4 k3 s3 s4 k5

RKIP PATHWAY, REACHABILITY GRAPH k s1 k1 k4 s k3 k8 s3 k5 k7 k6 s4 k9 k10 s5 s7 k8 k10 k9 k6 k7 k11 s13 s6 k7 s8 k k11 k10 k9 k8 s1 k11 s11 k6 k1 s9 k9 k10 k k1 k6 k7 k8 s13 s10

MODEL CHECKING, EXAMPLES property 1 Is a given (sub-) marking (system state) reachable? EF ( ERK * RP ); property Liveness of transition k8? AG EF ( MEK-PP_ERK ); property 3 Is it possible to produce ERK-PP neither creating nor using MEK-PP? E (! MEK-PP U ERK-PP ); property 4 Is there cyclic behaviour w.r.t. the presence / absence of RKIP? EG ( ( RKIP -> EF (! RKIP ) ) * (! RKIP -> EF ( RKIP ) ) );

QUALITATIVE ANALYSIS RESULTS, SUMMARY structural decisions of behavioural properties -> static analysis -> CPI -> BND -> ES & DTP -> LIVE CPI & CTI -> all minimal T-invariant / P-invariants enjoy biological interpretation -> non-trivial T-invariant -> partial order description of the essential behaviour reachability graph -> dynamic analysis -> finite -> BND -> the only SCC contains all transitions -> LIVE -> one Strongly Connected Component (SCC) -> REV model checking -> requires professional understanding -> all expected properties are valid

BIONETWORKS, VALIDATION validation criterion 1 -> all expected structural properties hold -> all expected general behavioural properties hold validation criterion -> CTI -> no minimal T-invariant without biological interpretation -> no known biological behaviour without corresponding T-invariant validation criterion 3 -> CPI -> no minimal P-invariant without biological interpretation (?) validation criterion 4 -> all expected special behavioural properties hold -> temporal-logic properties -> TRUE

NOW WE ARE READY FOR SOPHISTICATED QUANTITATIVE ANALYSES!

QUANTITATIVE ANALYSIS quantitative model = qualitative model + quantitative parameters -> known or estimated quantitative parameters

QUANTITATIVE ANALYSIS quantitative model = qualitative model + quantitative parameters -> known or estimated quantitative parameters typical quantitative parameters of bionetworks -> compound concentrations -> real numbers -> reaction rates / fluxes -> concentration-dependent continuous Petri nets p1cont m1 t1cont p3cont m3 tcont continuous nodes! m pcont v1 = k1*m1*m v = k*m3 dm1 / dt = dm / dt = - v1 dm3 / dt = v1 - v ODEs

THE RKIP PATHWAY, CONTINUOUS PETRI NET Raf-1Star m1 RKIP m k1 k ERK-PP m9 m3 Raf-1Star_RKIP k8 k3 k4 k11 m8 MEK-PP_ERK m4 m11 RKIP-P_RP Raf-1Star_RKIP_ERK-PP k6 k7 k5 k9 k10 m7 MEK-PP m5 ERK m6 RKIP-P m10 RP

THE RKIP PATHWAY, CONTINUOUS PETRI NET dm3 = dt Raf-1Star m1 RKIP m k1 k ERK-PP m9 m3 Raf-1Star_RKIP k8 k3 k4 k11 m8 MEK-PP_ERK m4 m11 RKIP-P_RP Raf-1Star_RKIP_ERK-PP k6 k7 k5 k9 k10 m7 MEK-PP m5 ERK m6 RKIP-P m10 RP

THE RKIP PATHWAY, CONTINUOUS PETRI NET dm3 = + r1 dt + r4 Raf-1Star m1 RKIP m k1 k ERK-PP m9 m3 Raf-1Star_RKIP k8 k3 k4 k11 m8 MEK-PP_ERK m4 m11 RKIP-P_RP Raf-1Star_RKIP_ERK-PP k6 k7 k5 k9 k10 m7 MEK-PP m5 ERK m6 RKIP-P m10 RP

THE RKIP PATHWAY, CONTINUOUS PETRI NET dm3 = + r1 dt + r4 m1 m Raf-1Star RKIP - r - r3 k1 k ERK-PP m9 m3 Raf-1Star_RKIP k8 k3 k4 k11 m8 MEK-PP_ERK m4 m11 RKIP-P_RP Raf-1Star_RKIP_ERK-PP k6 k7 k5 k9 k10 m7 m5 m6 m10 MEK-PP ERK RKIP-P RP

THE RKIP PATHWAY, CONTINUOUS PETRI NET dm3 = + k1 * m1 * m dt + r4 m1 m Raf-1Star RKIP - r - r3 k1 k ERK-PP m9 m3 Raf-1Star_RKIP k8 k3 k4 k11 m8 MEK-PP_ERK m4 m11 RKIP-P_RP Raf-1Star_RKIP_ERK-PP k6 k7 k5 k9 k10 m7 m5 m6 m10 MEK-PP ERK RKIP-P RP

THE RKIP PATHWAY, CONTINUOUS PETRI NET dm3 = + k1 * m1 * m dt + k4 * m4 - k * m3 - k3 * m3 * m9 m1 k1 m k Raf-1Star RKIP ERK-PP m9 m3 Raf-1Star_RKIP k8 k3 k4 k11 m8 MEK-PP_ERK m4 m11 RKIP-P_RP Raf-1Star_RKIP_ERK-PP k6 k7 k5 k9 k10 m7 m5 m6 m10 MEK-PP ERK RKIP-P RP

THE QUALITATIVE MODEL BECOMES THE STRUCTURED DESCRIPTION OF THE QUANTITATIVE MODEL!

QUANTITATIVE ANALYSIS 13 Good state configurations Cho et al Biochemist Distribution of `bad' steady states as euclidean distances from the `good' final steady state 13 good state configurations the bad ones

QUANTITATIVE ANALYSIS

CASE STUDY, SUMMARY representation of bionetworks 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 -> new insights two-step model development -> qualitative model -> discrete Petri nets -> quantitative model -> continuous Petri nets = ODEs many challenging open questions

SOME MORE CASE STUDIES

EX1 - Glycolysis and Pentose Phosphate Pathway Ru5P 4 Xu5P [Reddy 1993] 1 GSSG NADPH 3 5 R5P 6 S7P GAP 7 E4P F6P 8 4 GSH NADP + Gluc ATP 9 ADP G6P 10 F6P ATP 11 1 FBP ADP DHAP 13 14 15 GAP NAD + + Pi NAD + NADH ATP ADP ATP ADP NADH Lac 0 Pyr 19 PEP 18 PG 17 3PG 16 1,3-BPG

EX1 - Glycolysis and Pentose Phosphate Pathway GSSG NADPH Ru5P 4 Xu5P S7P E4P 6 7 8 ATP [Reddy 1993] 1 3 5 R5P GAP F6P ADP GSH NADP+ Gluc 9 10 F6P 11 FBP 1 GAP Pi G6P 13 14 NAD ATP ADP ATP ADP DHAP 15 Pi NAD+ NADH ATP ADP ATP ADP NAD Lac 0 Pyr 19 PEP 18 PG 17 3PG 16 1,3 BPG

EX - Carbon Metabolism in Potato Tuber [KOCH; JUNKER; HEINER 005]

EX - Carbon Metabolism in Potato Tuber gesuc esuc SucTrans SPP Inv Suc SuSy 8 UDP Pi SPS Glc Frc UDPglc S6P HK ATP FK ATP 9 ADP 9 ADP UDP PGI PP F6P UGPase 8 Pi 8 9 9 ADP Glyc(b) ATP 9 ATP G6P 9 ATPcons(b) [KOCH; JUNKER; HEINER 005] StaSy(b) starch PP 9 ATP ADP PGM PPase Pi 8 G1P ATP AMP UTP NDPkin AdK ADP 8 Pi 9 ADP rstarch

EX3: APOPTOSIS IN MAMMALIAN CELLS [GON 003]

EX3: APOPTOSIS IN MAMMALIAN CELLS Fas Ligand Apoptotic_Stimuli s7 FADD Procaspase 8 Bax_Bad_Bim Bcl _Bcl xl Apaf 1 s8 s1 Bid BidC Terminal CytochromeC datp/atp s6 Mitochondrion s9 s10 Caspase 8 s5 Procaspase 3 s (m0) Caspase 3 s13 Caspase 9 s11 s3 Procaspase 9 DFF DFF40 Oligomer CleavedDFF45 s1 (m) [GON 003] DNA s4 DNA Fragment [HEINER; KOCH; WILL 004]

EX4 - SWITCH CYCLE HALOBACTERIUM SALINARUM [Marwan; Oesterhelt 1999]

EX4 - SWITCH CYCLE HALOBACTERIUM SALINARUM CheB P _p0_ CheB _p1_ SR_II360_50 _p_ SR_II360_50Me _p3_ SR_II480 _p4_ SR_II480Me _p5_ CheR _p6_ CheY P _p7_ CheY P _p7_ CheY _p8_ hv487 _p9_ no_hv487 _p10_ Conf _p11_ Conf1 _p1_ 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 _p0_ Ccw _p1_ Rcw _p_ hv373 _p3_ no_hv373 _p4_ SR_I_510Me _p5_ SR_I_510 _p6_ no_hv580 _p7_ hv580 _p8_ CheA P _p9_ CheA P _p9_ CheA _p30_ CheA _p30_ CheR _p31_ SR_I_587Me _p3_ SR_I_587 _p33_ SR_I_373Me _p34_ SR_I_373 _p35_ CheB _p36_ CheB P _p37_ off on t t1 kd4 kd3 kd ka3 ka ka4 t1 t11 kd1 ka1 Tstop_ccw k_ccw k1_ccw k0_ccw Tstop_cw k_cw k1_cw k0_cw off on on off 44 44 44 44

WHAT HAVE TECHNICAL AND NATURAL SYSTEMS IN COMMON?

MODEL-BASED SYSTEM ANALYSIS Problem system system properties Petrinetz model model properties

MODEL-BASED SYSTEM ANALYSIS Problem system system properties CONSTRUCTION technical system verification requirement specification Petrinetz model model properties

MODEL-BASED SYSTEM ANALYSIS Problem system system properties UNDERSTANDING biological system validation behaviour prediction known properties unknown properties Petrinetz model model properties

OUTLOOK

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