Model checking : Up to multidimensional / multilevel models David - - PowerPoint PPT Presentation

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Model checking : Up to multidimensional / multilevel models David - - PowerPoint PPT Presentation

Oct 23, 2022 35 likes •530 views

Model checking : Up to multidimensional / multilevel models David Gilbert Computational Design Group Synthetic Biology Brunel University London, UK david.gilbert@brunel.ac.uk www.brunel.ac.uk/people/david-gilbert Collaborative work with

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Model checking : Up to multidimensional / multilevel models

David Gilbert

Computational Design Group Synthetic Biology Brunel University London, UK

david.gilbert@brunel.ac.uk www.brunel.ac.uk/people/david-gilbert Collaborative work with Monika Heiner, Brandenburg Technical University, Cottbus, Germany

david.gilbert@brunel.ac.uk 1 Dagstuhl 17452

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Model Checking

“Formally check whether a model of a biochemical system does what we want it to” Components: model

  • the current description of a biochemical system of interest

property

  • a property which we think the system should have

model checker

  • a program to test whether the model has the property

david.gilbert@brunel.ac.uk 2 Dagstuhl 17452

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SLIDE 3

We We could also check (a (and attempt to [automatically] repair…)

  • Syntactic properties of models
  • Although this is normally done as part of reading in a model into a

mechanised proof system or simulator

  • Checking soundness of the chemical reactions (balance etc)
  • Typos / spelling mistakes of component names, etc…
  • Siphon / trap properties (even in very large networks)

david.gilbert@brunel.ac.uk Dagstuhl 17452 3

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SLIDE 4

To formally express time properties we use a temporal logic

  • "I am hungry.”
  • "I am always hungry", "I will eventually be hungry",
  • "I will be hungry until I eat something”.

Linear time logics restricted to single time line. Branching logics can reason about multiple time lines. “There is a possibility that I will stay hungry forever.” “There is a possibility that eventually I am no longer hungry.” Various logics each with different expressivity:

  • Computational Tree Logic (CTL)
  • Continuous Stochastic Logic (CSL)
  • Linear-time Temporal Logic (LTL)

david.gilbert@brunel.ac.uk 4 Dagstuhl 17452

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SLIDE 5

Model Checking Biochemical Pathway Models

Pathway Model Property

Eg, “Order of peaks is; RafP, MEKPP, ERKPP

Model Checker

Yes/no or probability

predicted behaviour model (knowledge)

  • bserved

behaviour natural biosystem

wetlab experiments Formalising understanding model-based experiment design analysis

david.gilbert@brunel.ac.uk 5 Dagstuhl 17452

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Properties…

Effectively checking over time series behaviour Examples:

  • After 100 seconds the concentration of Protein1 is stable
  • Protein1 peaks and falls
  • Protein1 peaks and stays constant
  • Protein1 peaks before Protein2
  • Protein1 oscillates 4 times in 5,000 seconds
  • Molecules of Protein2 are required for molecules of Protein1 to be created

david.gilbert@brunel.ac.uk 6 Dagstuhl 17452

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SLIDE 7

david.gilbert@brunel.ac.uk 7

Analytical:

  • Exact probabilities & prove properties
  • A model state is an association of #molecules/levels to each of the species
  • Protein1 has 10 molecules & Protein2 has 20 molecules
  • Analytical assesses every state that the model can be in (reachable states)
  • State space can grow even worse than exponentially with increasing

molecules, or even be infinite! Simulative: Instead of analysing the constructed state space:

  • analyse simulation outputs
  • Simulate the model X times and check these simulations
  • Simulation run = finite path through the state space
  • Can’t prove probabilities

Analytical vs Simulative Model Checking

Dagstuhl 17452

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Si Simulative: How/when to check?

In-line: check the observations as they arrive

> Requires complex computational machinery: ‘combine’ simulator & model checker > Good for biochemical observations > Don’t always need to finish the experimental run

Off-line: check observations after all have been generated

> Easier to implement computationally (simulate then check) > Need to always define when to ‘stop’ generating observations

david.gilbert@brunel.ac.uk Dagstuhl 17452 8

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SLIDE 9

Simulation-based Model Checking ‘Behaviour checking’

Eg, “Order of peaks is RafP, MEKPP, ERKPP”

Model Checker Model Property

Yes/no or probability

Lab Model

Behaviour Checker Time series data

predicted behaviour model (blueprint)

  • bserved

behaviour synthetic biosystem design construction validation validation desired behaviour verification

david.gilbert@brunel.ac.uk 9 Dagstuhl 17452

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(P (P)L )LTL L Li Linear r Temporal Lo Logic

  • G (φ )

φ always happens

  • F (φ )

φ happens at some time

  • X (φ )

φ happens in the next time point

  • φ1 U φ2

φ1 happens until φ2 happens

  • Protein stability:

P=? [ time >= 100 à ([Protein] >= 4 ^ [Protein] <= 6) ]

  • Protein concentration rises to a maximum value and then remains constant:

P=? [(d[Protein]> 0) U ( G([Protein] >= 0.99*max[Protein]) ) ]

david.gilbert@brunel.ac.uk 10 Dagstuhl 17452

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SLIDE 11

5

P=?[ F( X > 5 ) ]

=> P = 1 X

MC2 with ODE Output

david.gilber t@brunel.a c.uk

11 david.gilbert@brunel.ac.uk Dagstuhl 17452

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SLIDE 12

5

P=?[ F( X > 5 ) ]

=> P = 4/6 X

MC2 with Gillespie Output

david.gilber t@brunel.a c.uk Systems & Synthetic Biology

david.gilbert@brunel.ac.uk 12 Dagstuhl 17452

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SLIDE 13

Qu Qualit litativ ive to quantit itativ ive desc scrip iptio ions s in in PLTL

  • Qualitative:

Protein rises then falls

  • P=? [ ( d(Protein) > 0 ) U ( G( d(Protein) < 0 ) ) ]
  • Semi-qualitative:

Protein rises then falls to less than 50% of peak concentration

  • P=? [ ( d(Protein) > 0 ) U ( G( d(Protein) < 0 ) ∧ F ( [Protein] < 0.5 ∗ max[Protein] ) ) ]
  • Semi-quantitative:

Protein rises then falls to less than 50% of peak concentration by 60 minutes

  • P=? [ ( d(Protein) > 0 ) U ( G( d(Protein) < 0 ) ∧ F ( time = 60 ∧ Protein < 0.5 ∗ max(Protein) ) ) ]
  • Quantitative:

Protein rises then falls to less than 100µMol by 60 minutes

  • P=? [ ( d(Protein) > 0 ) U ( G( d(Protein) < 0 ) ∧ F ( time = 60 ∧ Protein < 100 ) ) ]

david.gilbert@brunel.ac.uk 13 Dagstuhl 17452

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Mo Model del (b (behaviour) r) se searching

Peaks at least once (rises then falls below 50% max concentration) P>=1[ ErkPP <= 0.50*max(ErkPP) ∧ d(ErkPP) > 0 U ( ErkPP = max(ErkPP) ∧ F( ErkPP <= 0.50*max(ErkPP) ) ) ]

  • Brown
  • Kholodenko
  • Schoeberl

Rises and remains constant (99% max concentration)

P>=1[ErkPP <= 0.50*max(ErkPP) ∧ ( d(ErkPP) > 0 ) U ( G(ErkPP >= 0.99*max(ErkPP)) ) ]

  • Levchenko

Oscillates at least 4 times

P>=1[ F( d(ErkPP) > 0 ∧ F( d(ErkPP) < 0 ∧ … ) ) ]

  • Kholodenko

david.gilbert@brunel.ac.uk 14 Dagstuhl 17452

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SLIDE 15

Mo Model del c chec hecking ng o

  • ver

er l lar arge amo e amoun unt o t of da data

Wh Whol

  • le genom
  • me metab

abol

  • lic mod
  • del (E.c

E.coli)

david.gilbert@brunel.ac.uk 15 Dagstuhl 17452

à Search by behavioural template libraries

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SLIDE 16

PL PLTL pr proper perty ty libr library - me metabo bolit lites es

P>=1 [ G ( [$x] = 0 ) ] always_steadystate_zero P>=1 [ G ( d[$x] = 0 ^ [$x]>0 ) ] always_steadystate_above_zero P>=1 [ G ( d[$x] = 0 ) ] always_steadystate_any_value P>=1 [ F ( G ( [$x]=0 ^ d[$x]=0 ) ) ^ F (d[$x] != 0) ] changing_and_finally_steadystate_of_zero P>=1 [ F ( G ( [$x]>0 ^ d[$x]=0 ) ) ^ F (d[$x] != 0) ] changing_and_finally_steadystate_above_zero P>=1 [ G (d[$x] < 0 ) ] decreasing P>=1 [ G (d[$x] > 0 ) ] Increasing P>=1 [ F( d[$x]>0 ) ^ ( d[$x]>0 U ( G d[$x] < 0 )) ] peaks_and_falls P>=1 [ F( d[$x]<0 ) ^ ( d[$x]<0 U ( G d[$x] > 0 )) ] falls_and_rises P>=1 [ (F ( d[$x] != 0)) ^ ¬( F( G( [$x]=0 ^ d[$x]=0 ) )) ] activity_and_not_finally_steadystate_of_zero P>=1 [ G ( [$x] <= 0.0001 ) ^ ¬ G ( [$x] = 0 ) ] always_low_concentrations_0.0001

16

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SLIDE 17

PL PLTL pr proper perty ty libr library - re reactions

P>=1 [ G ( [$x] = 0 ) ] never_active P>=1 [ F ( [$x] > 0 ) ] sometime_active P>=1 [ G ( d[$x] = 0 ) ] always_steadystate_active_any_value P>=1 [ F ( G ( [$x] > 0 ) ) ] finally_active P>=1 [ F ( G ( [$x] > 0 ^ d[$x]=0 ) ) ] finally_active_steadystate P>=1 [ G ( F ( [$x] > 0 ) ) ] always_active_again P>=1 [ F ( G ( [$x] = 0 ) ) ] finally_inactive P>=1 [ G (d[$x] < 0 ) ] always_decreasing_activity P>=1 [ G (d[$x] > 0 ) ] always_increasing_activity P>=1 [ F( d[$x]>0 ) ^ ( d[$x]>0 U ( G d[$x] < 0 )) ] activity_peaks_and_falls P>=1 [ F( d[$x]<0 ) ^ ( d[$x]<0 U ( G d[$x] > 0 )) ] activity_falls_and_rises P>=1 [ G ( [$x] <= 0.0001 ) ^ ¬ G ( [$x] = 0 ) ] rare_events

17

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Se Searching by by behavioural template libraries

18

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SLIDE 19

Su Subnets

property subnets defined by sets of entities sharing a certain temporal logical property, the composition of which can vary over time functional subnets (subsystems) statically defined by sets of reactions contributing to the same biological function. dead subnets, exhibit no activity from the current time point onwards. Can be an indication of

  • modelling fault,
  • missing information in the network structure (e.g. gaps due to unidentified

genes),

  • unused parts of the network due to the set of environment conditions imposed

(e.g. the growth conditions).

david.gilbert@brunel.ac.uk Computational Synthetic Biology 19

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SLIDE 20

Dy Dynamic ic si simulati tion

M 13dpg c M 2pg c M 3pg c M 6pgc c M 6pgl c M ac c M ac e M acald c M acald e M acon C c M actp c M akg c M akg e M cit c M co2 c M co2 e M dhap c M e4p c M etoh c M etoh e M f6p c M fdp c M for c M for e M fru e M fum c M fum e M g3p c M g6p c M glc D e M gln L c M gln L e M glu L c M glu L e M glx c M h2o c M h2o e M h c M h e M icit c M lac D c M lac D e M mal L c M mal L e M nh4 c M nh4 e M o2 c M o2 e M oaa c M pep c M pi c M pi e M pyr c M pyr e M r5p c M ru5p D c M s7p c M succ c M succ e M xu5p D c M ac b M acald b M akg b M co2 b M etoh b M for b M fru b M fum b M glc D b M gln L b M glu L b M h2o b M h b M lac D b M mal L b M nh4 b M o2 b M pi b M pyr b M succ b M adp c INIT M amp c INIT M atp c INIT M nad c INIT M nadh c INIT M accoa c INIT M coa c INIT M succoa c INIT M nadp c INIT M nadph c INIT M q8 c INIT M q8h2 c INIT in M ac b
  • ut M ac b
in M acald b
  • ut M acald b
in M akg b
  • ut M akg b
in M co2 b
  • ut M co2 b
in M etoh b
  • ut M etoh b
in M for b
  • ut M for b
in M fru b
  • ut M fru b
in M fum b
  • ut M fum b
in M glc D b
  • ut M glc D b
in M gln L b
  • ut M gln L b
in M glu L b
  • ut M glu L b
in M h2o b
  • ut M h2o b
in M h b
  • ut M h b
in M lac D b
  • ut M lac D b
in M mal L b
  • ut M mal L b
in M nh4 b
  • ut M nh4 b
in M o2 b
  • ut M o2 b
in M pi b
  • ut M pi b
in M pyr b
  • ut M pyr b
in M succ b
  • ut M succ b
R ACALD re R ACALD R ACALDt re R ACALDt R ACKr re R ACKr R ACONTa re R ACONTa R ACONTb re R ACONTb R ACt2r re R ACt2r R ADK1 re R ADK1 R AKGDH R AKGt2r re R AKGt2r R ALCD2x re R ALCD2x R ATPM R ATPS4r re R ATPS4r R Biomass Ecoli core w GAM R CO2t re R CO2t R CS R CYTBD R D LACt2 re R D LACt2 R ENO re R ENO R ETOHt2r re R ETOHt2r R EX ac e R EX acald e R EX akg e R EX co2 e re R EX co2 e R EX etoh e R EX for e R EX fru e R EX fum e R EX glc e re R EX glc e R EX gln L e R EX glu L e R EX h e re R EX h e R EX h2o e re R EX h2o e R EX lac D e R EX mal L e R EX nh4 e re R EX nh4 e R EX o2 e re R EX o2 e R EX pi e re R EX pi e R EX pyr e R EX succ e R FBA re R FBA R FBP R FORt2 R FORti R FRD7 R FRUpts2 R FUM re R FUM R FUMt2 2 R G6PDH2r re R G6PDH2r R GAPD re R GAPD R GLCpts R GLNS R GLNabc R GLUDy re R GLUDy R GLUN R GLUSy R GLUt2r re R GLUt2r R GND R H2Ot re R H2Ot R ICDHyr re R ICDHyr R ICL R LDH D re R LDH D R MALS R MALt2 2 R MDH re R MDH R ME1 R ME2 R NADH16 R NADTRHD R NH4t re R NH4t R O2t re R O2t R PDH R PFK R PFL R PGI re R PGI R PGK re R PGK R PGL R PGM re R PGM R PIt2r re R PIt2r R PPC R PPCK R PPS R PTAr re R PTAr R PYK R PYRt2r re R PYRt2r R RPE re R RPE R RPI re R RPI R SUCCt2 2 R SUCCt3 R SUCDi R SUCOAS re R SUCOAS R TALA re R TALA R THD2 R TKT1 re R TKT1 R TKT2 re R TKT2 R TPI re R TPI 4 2 60 2 4 60 4 5 2 60 3 60 2 2 2 4 2 2 2 3 4 2 2 2 3 2 2 4 4 4 13 13 2 60 3 M 13dpg c M 2pg c M 3pg c M 6pgc c M 6pgl c M ac c M ac e M acald c M acald e M acon C c M actp c M akg c M akg e M cit c M co2 c M co2 e M dhap c M e4p c M etoh c M etoh e M f6p c M fdp c M for c M for e M fru e M fum c M fum e M g3p c M g6p c M glc D e M gln L c M gln L e M glu L c M glu L e M glx c M h2o c M h2o e M h c M h e M icit c M lac D c M lac D e M mal L c M mal L e M nh4 c M nh4 e M o2 c M o2 e M oaa c M pep c M pi c M pi e M pyr c M pyr e M r5p c M ru5p D c M s7p c M succ c M succ e M xu5p D c M ac b M acald b M akg b M co2 b M etoh b M for b M fru b M fum b M glc D b M gln L b M glu L b M h2o b M h b M lac D b M mal L b M nh4 b M o2 b M pi b M pyr b M succ b Bio M adp c INIT M amp c INIT M atp c INIT M nad c INIT M nadh c INIT M accoa c INIT M coa c INIT M succoa c INIT M q8 c INIT M q8h2 c INIT M nadp c INIT M nadph c INIT
  • ut M ac b
  • ut M acald b
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in M co2 b
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  • ut M etoh b
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in M fru b in M fum b in M glc D b
  • ut M glc D b
in M gln L b
  • ut M glu L b
in M h2o b
  • ut M h2o b
in M h b
  • ut M h b
  • ut M lac D b
in M mal L b in M nh4 b
  • ut M nh4 b
in M o2 b
  • ut M o2 b
in M pi b
  • ut M pi b
  • ut M pyr b
  • ut M succ b
R ACALD re R ACALD R ACALDt re R ACALDt R ACKr re R ACKr R ACONTa re R ACONTa R ACONTb re R ACONTb R ACt2r re R ACt2r R ADK1 re R ADK1 R AKGDH R AKGt2r re R AKGt2r R ALCD2x re R ALCD2x R ATPM R ATPS4r re R ATPS4r R CO2t re R CO2t R CS R CYTBD R D LACt2 re R D LACt2 R ENO re R ENO R ETOHt2r re R ETOHt2r R EX ac e R EX acald e R EX akg e R EX co2 e re R EX co2 e R EX etoh e R EX for e R EX glc e re R EX glc e R EX glu L e R EX h e re R EX h e R EX h2o e re R EX h2o e R EX lac D e R EX nh4 e re R EX nh4 e R EX o2 e re R EX o2 e R EX pi e re R EX pi e R EX pyr e R EX succ e R FBA re R FBA R FBP R FORt2 R FORti R FRD7 R FUM re R FUM R FUMt2 2 R G6PDH2r re R G6PDH2r R GAPD re R GAPD R GLNS R GLNabc R GLUDy re R GLUDy R GLUN R GLUSy R GLUt2r re R GLUt2r R GND R H2Ot re R H2Ot R ICDHyr re R ICDHyr R ICL R LDH D re R LDH D R MALS R MALt2 2 R MDH re R MDH R ME1 R ME2 R NADH16 R NADTRHD R NH4t re R NH4t R O2t re R O2t R PDH R PFK R PFL R PGI re R PGI R PGK re R PGK R PGL R PGM re R PGM R PIt2r re R PIt2r R PPCK R PTAr re R PTAr R PYK R PYRt2r re R PYRt2r R RPE re R RPE R RPI re R RPI R SUCCt2 2 R SUCCt3 R SUCDi R SUCOAS re R SUCOAS R TALA re R TALA R THD2 R TKT1 re R TKT1 R TKT2 re R TKT2 R TPI re R TPI R EX mal L e R EX gln L e R EX fum e R EX fru e R PPS re R PPS R FRUpts2 re R FRUpts2 R GLCpts re R GLCpts R PPC re R PPC R Biomass Ecoli core w GAM 4 2 60 2 4 60 4 5 2 60 3 60 2 2 2 4 2 2 2 3 2 4 2 2 2 3 2 2 4 4 4 13 13 2 60 3 M 13dpg c M 2pg c M 3pg c M 6pgc c M 6pgl c M ac c M ac e M acald c M acald e M acon C c M actp c M akg c M akg e M cit c M co2 c M co2 e M dhap c M e4p c M etoh c M etoh e M f6p c M fdp c M for c M for e M fru e M fum c M fum e M g3p c M g6p c M glc D e M gln L c M gln L e M glu L c M glu L e M glx c M h2o c M h2o e M h c M h e M icit c M lac D c M lac D e M mal L c M mal L e M nh4 c M nh4 e M o2 c M o2 e M oaa c M pep c M pi c M pi e M pyr c M pyr e M r5p c M ru5p D c M s7p c M succ c M succ e M xu5p D c M ac b M acald b M akg b M co2 b M etoh b M for b M fru b M fum b M glc D b M gln L b M glu L b M h2o b M h b M lac D b M mal L b M nh4 b M o2 b M pi b M pyr b M succ b M adp c INIT M amp c INIT M atp c INIT M nad c INIT M nadh c INIT M accoa c INIT M coa c INIT M succoa c INIT M nadp c INIT M nadph c INIT M q8 c INIT M q8h2 c INIT in M ac b
  • ut M ac b
in M acald b
  • ut M acald b
in M akg b
  • ut M akg b
in M co2 b
  • ut M co2 b
in M etoh b
  • ut M etoh b
in M for b
  • ut M for b
in M fru b
  • ut M fru b
in M fum b
  • ut M fum b
in M glc D b
  • ut M glc D b
in M gln L b
  • ut M gln L b
in M glu L b
  • ut M glu L b
in M h2o b
  • ut M h2o b
in M h b
  • ut M h b
in M lac D b
  • ut M lac D b
in M mal L b
  • ut M mal L b
in M nh4 b
  • ut M nh4 b
in M o2 b
  • ut M o2 b
in M pi b
  • ut M pi b
in M pyr b
  • ut M pyr b
in M succ b
  • ut M succ b
R ACALD re R ACALD R ACALDt re R ACALDt R ACKr re R ACKr R ACONTa re R ACONTa R ACONTb re R ACONTb R ACt2r re R ACt2r R ADK1 re R ADK1 R AKGDH R AKGt2r re R AKGt2r R ALCD2x re R ALCD2x R ATPM R ATPS4r re R ATPS4r R Biomass Ecoli core w GAM R CO2t re R CO2t R CS R CYTBD R D LACt2 re R D LACt2 R ENO re R ENO R ETOHt2r re R ETOHt2r R EX ac e R EX acald e R EX akg e R EX co2 e re R EX co2 e R EX etoh e R EX for e R EX fru e R EX fum e R EX glc e re R EX glc e R EX gln L e R EX glu L e R EX h e re R EX h e R EX h2o e re R EX h2o e R EX lac D e R EX mal L e R EX nh4 e re R EX nh4 e R EX o2 e re R EX o2 e R EX pi e re R EX pi e R EX pyr e R EX succ e R FBA re R FBA R FBP R FORt2 R FORti R FRD7 R FRUpts2 R FUM re R FUM R FUMt2 2 R G6PDH2r re R G6PDH2r R GAPD re R GAPD R GLCpts R GLNS R GLNabc R GLUDy re R GLUDy R GLUN R GLUSy R GLUt2r re R GLUt2r R GND R H2Ot re R H2Ot R ICDHyr re R ICDHyr R ICL R LDH D re R LDH D R MALS R MALt2 2 R MDH re R MDH R ME1 R ME2 R NADH16 R NADTRHD R NH4t re R NH4t R O2t re R O2t R PDH R PFK R PFL R PGI re R PGI R PGK re R PGK R PGL R PGM re R PGM R PIt2r re R PIt2r R PPC R PPCK R PPS R PTAr re R PTAr R PYK R PYRt2r re R PYRt2r R RPE re R RPE R RPI re R RPI R SUCCt2 2 R SUCCt3 R SUCDi R SUCOAS re R SUCOAS R TALA re R TALA R THD2 R TKT1 re R TKT1 R TKT2 re R TKT2 R TPI re R TPI 4 2 60 2 4 60 4 5 2 60 3 60 2 2 2 4 2 2 2 3 4 2 2 2 3 2 2 4 4 4 13 13 2 60 3 M 13dpg c M 2pg c M 3pg c M 6pgc c M 6pgl c M ac c M ac e M acald c M acald e M acon C c M actp c M akg c M akg e M cit c M co2 c M co2 e M dhap c M e4p c M etoh c M etoh e M f6p c M fdp c M for c M for e M fru e M fum c M fum e M g3p c M g6p c M glc D e M gln L c M gln L e M glu L c M glu L e M glx c M h2o c M h2o e M h c M h e M icit c M lac D c M lac D e M mal L c M mal L e M nh4 c M nh4 e M o2 c M o2 e M oaa c M pep c M pi c M pi e M pyr c M pyr e M r5p c M ru5p D c M s7p c M succ c M succ e M xu5p D c M ac b M acald b M akg b M co2 b M etoh b M for b M fru b M fum b M glc D b M gln L b M glu L b M h2o b M h b M lac D b M mal L b M nh4 b M o2 b M pi b M pyr b M succ b Bio M adp c INIT M amp c INIT M atp c INIT M nad c INIT M nadh c INIT M accoa c INIT M coa c INIT M succoa c INIT M q8 c INIT M q8h2 c INIT M nadp c INIT M nadph c INIT
  • ut M ac b
  • ut M acald b
  • ut M akg b
in M co2 b
  • ut M co2 b
  • ut M etoh b
  • ut M for b
in M fru b in M fum b in M glc D b
  • ut M glc D b
in M gln L b
  • ut M glu L b
in M h2o b
  • ut M h2o b
in M h b
  • ut M h b
  • ut M lac D b
in M mal L b in M nh4 b
  • ut M nh4 b
in M o2 b
  • ut M o2 b
in M pi b
  • ut M pi b
  • ut M pyr b
  • ut M succ b
R ACALD re R ACALD R ACALDt re R ACALDt R ACKr re R ACKr R ACONTa re R ACONTa R ACONTb re R ACONTb R ACt2r re R ACt2r R ADK1 re R ADK1 R AKGDH R AKGt2r re R AKGt2r R ALCD2x re R ALCD2x R ATPM R ATPS4r re R ATPS4r R CO2t re R CO2t R CS R CYTBD R D LACt2 re R D LACt2 R ENO re R ENO R ETOHt2r re R ETOHt2r R EX ac e R EX acald e R EX akg e R EX co2 e re R EX co2 e R EX etoh e R EX for e R EX glc e re R EX glc e R EX glu L e R EX h e re R EX h e R EX h2o e re R EX h2o e R EX lac D e R EX nh4 e re R EX nh4 e R EX o2 e re R EX o2 e R EX pi e re R EX pi e R EX pyr e R EX succ e R FBA re R FBA R FBP R FORt2 R FORti R FRD7 R FUM re R FUM R FUMt2 2 R G6PDH2r re R G6PDH2r R GAPD re R GAPD R GLNS R GLNabc R GLUDy re R GLUDy R GLUN R GLUSy R GLUt2r re R GLUt2r R GND R H2Ot re R H2Ot R ICDHyr re R ICDHyr R ICL R LDH D re R LDH D R MALS R MALt2 2 R MDH re R MDH R ME1 R ME2 R NADH16 R NADTRHD R NH4t re R NH4t R O2t re R O2t R PDH R PFK R PFL R PGI re R PGI R PGK re R PGK R PGL R PGM re R PGM R PIt2r re R PIt2r R PPCK R PTAr re R PTAr R PYK R PYRt2r re R PYRt2r R RPE re R RPE R RPI re R RPI R SUCCt2 2 R SUCCt3 R SUCDi R SUCOAS re R SUCOAS R TALA re R TALA R THD2 R TKT1 re R TKT1 R TKT2 re R TKT2 R TPI re R TPI R EX mal L e R EX gln L e R EX fum e R EX fru e R PPS re R PPS R FRUpts2 re R FRUpts2 R GLCpts re R GLCpts R PPC re R PPC R Biomass Ecoli core w GAM 4 2 60 2 4 60 4 5 2 60 3 60 2 2 2 4 2 2 2 3 2 4 2 2 2 3 2 2 4 4 4 13 13 2 60 3 M 13dpg c M 2pg c M 3pg c M 6pgc c M 6pgl c M ac c M ac e M acald c M acald e M acon C c M actp c M akg c M akg e M cit c M co2 c M co2 e M dhap c M e4p c M etoh c M etoh e M f6p c M fdp c M for c M for e M fru e M fum c M fum e M g3p c M g6p c M glc D e M gln L c M gln L e M glu L c M glu L e M glx c M h2o c M h2o e M h c M h e M icit c M lac D c M lac D e M mal L c M mal L e M nh4 c M nh4 e M o2 c M o2 e M oaa c M pep c M pi c M pi e M pyr c M pyr e M r5p c M ru5p D c M s7p c M succ c M succ e M xu5p D c M ac b M acald b M akg b M co2 b M etoh b M for b M fru b M fum b M glc D b M gln L b M glu L b M h2o b M h b M lac D b M mal L b M nh4 b M o2 b M pi b M pyr b M succ b M adp c INIT M amp c INIT M atp c INIT M nad c INIT M nadh c INIT M accoa c INIT M coa c INIT M succoa c INIT M nadp c INIT M nadph c INIT M q8 c INIT M q8h2 c INIT in M ac b
  • ut M ac b
in M acald b
  • ut M acald b
in M akg b
  • ut M akg b
in M co2 b
  • ut M co2 b
in M etoh b
  • ut M etoh b
in M for b
  • ut M for b
in M fru b
  • ut M fru b
in M fum b
  • ut M fum b
in M glc D b
  • ut M glc D b
in M gln L b
  • ut M gln L b
in M glu L b
  • ut M glu L b
in M h2o b
  • ut M h2o b
in M h b
  • ut M h b
in M lac D b
  • ut M lac D b
in M mal L b
  • ut M mal L b
in M nh4 b
  • ut M nh4 b
in M o2 b
  • ut M o2 b
in M pi b
  • ut M pi b
in M pyr b
  • ut M pyr b
in M succ b
  • ut M succ b
R ACALD re R ACALD R ACALDt re R ACALDt R ACKr re R ACKr R ACONTa re R ACONTa R ACONTb re R ACONTb R ACt2r re R ACt2r R ADK1 re R ADK1 R AKGDH R AKGt2r re R AKGt2r R ALCD2x re R ALCD2x R ATPM R ATPS4r re R ATPS4r R Biomass Ecoli core w GAM R CO2t re R CO2t R CS R CYTBD R D LACt2 re R D LACt2 R ENO re R ENO R ETOHt2r re R ETOHt2r R EX ac e R EX acald e R EX akg e R EX co2 e re R EX co2 e R EX etoh e R EX for e R EX fru e R EX fum e R EX glc e re R EX glc e R EX gln L e R EX glu L e R EX h e re R EX h e R EX h2o e re R EX h2o e R EX lac D e R EX mal L e R EX nh4 e re R EX nh4 e R EX o2 e re R EX o2 e R EX pi e re R EX pi e R EX pyr e R EX succ e R FBA re R FBA R FBP R FORt2 R FORti R FRD7 R FRUpts2 R FUM re R FUM R FUMt2 2 R G6PDH2r re R G6PDH2r R GAPD re R GAPD R GLCpts R GLNS R GLNabc R GLUDy re R GLUDy R GLUN R GLUSy R GLUt2r re R GLUt2r R GND R H2Ot re R H2Ot R ICDHyr re R ICDHyr R ICL R LDH D re R LDH D R MALS R MALt2 2 R MDH re R MDH R ME1 R ME2 R NADH16 R NADTRHD R NH4t re R NH4t R O2t re R O2t R PDH R PFK R PFL R PGI re R PGI R PGK re R PGK R PGL R PGM re R PGM R PIt2r re R PIt2r R PPC R PPCK R PPS R PTAr re R PTAr R PYK R PYRt2r re R PYRt2r R RPE re R RPE R RPI re R RPI R SUCCt2 2 R SUCCt3 R SUCDi R SUCOAS re R SUCOAS R TALA re R TALA R THD2 R TKT1 re R TKT1 R TKT2 re R TKT2 R TPI re R TPI 4 2 60 2 4 60 4 5 2 60 3 60 2 2 2 4 2 2 2 3 4 2 2 2 3 2 2 4 4 4 13 13 2 60 3 M 13dpg c M 2pg c M 3pg c M 6pgc c M 6pgl c M ac c M ac e M acald c M acald e M acon C c M actp c M akg c M akg e M cit c M co2 c M co2 e M dhap c M e4p c M etoh c M etoh e M f6p c M fdp c M for c M for e M fru e M fum c M fum e M g3p c M g6p c M glc D e M gln L c M gln L e M glu L c M glu L e M glx c M h2o c M h2o e M h c M h e M icit c M lac D c M lac D e M mal L c M mal L e M nh4 c M nh4 e M o2 c M o2 e M oaa c M pep c M pi c M pi e M pyr c M pyr e M r5p c M ru5p D c M s7p c M succ c M succ e M xu5p D c M ac b M acald b M akg b M co2 b M etoh b M for b M fru b M fum b M glc D b M gln L b M glu L b M h2o b M h b M lac D b M mal L b M nh4 b M o2 b M pi b M pyr b M succ b Bio M adp c INIT M amp c INIT M atp c INIT M nad c INIT M nadh c INIT M accoa c INIT M coa c INIT M succoa c INIT M q8 c INIT M q8h2 c INIT M nadp c INIT M nadph c INIT
  • ut M ac b
  • ut M acald b
  • ut M akg b
in M co2 b
  • ut M co2 b
  • ut M etoh b
  • ut M for b
in M fru b in M fum b in M glc D b
  • ut M glc D b
in M gln L b
  • ut M glu L b
in M h2o b
  • ut M h2o b
in M h b
  • ut M h b
  • ut M lac D b
in M mal L b in M nh4 b
  • ut M nh4 b
in M o2 b
  • ut M o2 b
in M pi b
  • ut M pi b
  • ut M pyr b
  • ut M succ b
R ACALD re R ACALD R ACALDt re R ACALDt R ACKr re R ACKr R ACONTa re R ACONTa R ACONTb re R ACONTb R ACt2r re R ACt2r R ADK1 re R ADK1 R AKGDH R AKGt2r re R AKGt2r R ALCD2x re R ALCD2x R ATPM R ATPS4r re R ATPS4r R CO2t re R CO2t R CS R CYTBD R D LACt2 re R D LACt2 R ENO re R ENO R ETOHt2r re R ETOHt2r R EX ac e R EX acald e R EX akg e R EX co2 e re R EX co2 e R EX etoh e R EX for e R EX glc e re R EX glc e R EX glu L e R EX h e re R EX h e R EX h2o e re R EX h2o e R EX lac D e R EX nh4 e re R EX nh4 e R EX o2 e re R EX o2 e R EX pi e re R EX pi e R EX pyr e R EX succ e R FBA re R FBA R FBP R FORt2 R FORti R FRD7 R FUM re R FUM R FUMt2 2 R G6PDH2r re R G6PDH2r R GAPD re R GAPD R GLNS R GLNabc R GLUDy re R GLUDy R GLUN R GLUSy R GLUt2r re R GLUt2r R GND R H2Ot re R H2Ot R ICDHyr re R ICDHyr R ICL R LDH D re R LDH D R MALS R MALt2 2 R MDH re R MDH R ME1 R ME2 R NADH16 R NADTRHD R NH4t re R NH4t R O2t re R O2t R PDH R PFK R PFL R PGI re R PGI R PGK re R PGK R PGL R PGM re R PGM R PIt2r re R PIt2r R PPCK R PTAr re R PTAr R PYK R PYRt2r re R PYRt2r R RPE re R RPE R RPI re R RPI R SUCCt2 2 R SUCCt3 R SUCDi R SUCOAS re R SUCOAS R TALA re R TALA R THD2 R TKT1 re R TKT1 R TKT2 re R TKT2 R TPI re R TPI R EX mal L e R EX gln L e R EX fum e R EX fru e R PPS re R PPS R FRUpts2 re R FRUpts2 R GLCpts re R GLCpts R PPC re R PPC R Biomass Ecoli core w GAM 4 2 60 2 4 60 4 5 2 60 3 60 2 2 2 4 2 2 2 3 2 4 2 2 2 3 2 2 4 4 4 13 13 2 60 3

min-growth model enhanced-growth model Active (not dead) reactions highlighted in blue. Layouts automatically generated. beginning middle end

david.gilbert@brunel.ac.uk Computational Synthetic Biology 20

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SLIDE 21

What about scaling up?

david.gilbert@brunel.ac.uk 21 Dagstuhl 17452

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SLIDE 22

Or Or s scaling do ng down? n?

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SLIDE 23

Multiscale: from signalling to organs

ODEs

Actin_(MyoP)2 Myosin_P 10 Myosin 100 Drok_act 10 Drok 100 Dsh_act 10 Dsh 100 Fz_Fmi Fmi 10 Ld 10 Fz 10 Fz_act Fmi_Vang FzFmi_FmiVang Pk 10 FzFmi_FmiVangPk Dsh_FzFmi_FmiVang MyoDimer_actin_binding dimerisation dephosphorylation phosphorylation deactivation_drok activation_drok r_2 r_1 activation_Fz rneigh_1 rneigh_2 rInter_1 rInter_2 rInter_3 rInter_4 rInter_5 rInter_7 rInter_6 deactivation_dsh dsh_complex de_dsh_complex 2 Petri nets (coloured, hierarchical)

Monika Heiner Planar Cell Polarity Gao et al (2013). TCCB, 10:2.

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SLIDE 24

Bio Biolo logic gical l Model

  • PCP proteins involved in the intercellular signalling: Flamingo (Fmi) , Frizzled

(Fz), Dishevelled (Dsh), Prickle (Pk) and Van-Gogh (Vang) .

  • A core machinery mediates a competition between the proximal and distal

proteins: Frizzled (Fz), Dishevelled (Dsh), Prickle (Pk) and Van-Gogh (Vang). Flamingo (Fmi) localises at both distal and proximal edges.

  • Feedback loops: cells tent to align cell polarity as asymmetric distribution.

Symmetric distribution Prehair formation

Fmi Vang Pk

Asymmetric distribution

Fmi Fz Dsh

Polarising signalling

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SLIDE 25

Hierarchical Organisation Tissues – cells – ‘compartments’

Hierarchically coloured

Intracellular compartments Tissue (Cells) Cell: (3,2)

Compartment (2,1)

Colourset = {…, {((3,2)(1,1)), ((3,2)(2,1)), ((3,2)(3,1)),……((3,2)(3,3))}, …

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SLIDE 26

Different Compartmentalisation

Systems & Synthetic Biology

26

Symmetric Models 1:1 1:2

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SLIDE 27

HCPN Model for Tissue

(Hierarchically Coloured Petri Net)

Detailed level

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SLIDE 28

PCP: Drosophila Wing Phen enotypes es

Wild type

  • r ‘normal’

phenotype Mutant phenotype

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SLIDE 29

Modelling Mutant Clones

Knock-out: cell clones in which a certain gene is knocked out are induced in the tissue (Biological experiments)

  • no corresponding protein produced.

Petri nets: set the protein concentration zero Coloured Petri Net (repeat, with variations)

  • Big enough patch (tissue): 800 cells
  • Size / shape of clone: 80 cells (10% of the patch) in a circle-like shape

david.gilbert@brunel. ac.uk Systems & Synthetic Biology

29 david.gilbert@brunel.ac.uk 29 Dagstuhl 17452

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SLIDE 30

Mutated tissue Experimental vs In-silico

Systems & Synthetic Biology

30

  • Q. Gao, F. Liu, D. Gilbert, M.

Heiner & D. Tree. CMSB 2011, Paris, France.

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SLIDE 31

Analysis: Clustering of behaviours

Systems & Synthetic Biology

31 david.gilbert@brunel.ac.uk 31 Dagstuhl 17452

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SLIDE 32

Clustering

DBScan with Principal Component Analysis (PCA)

Systems & Synthetic Biology

32

Unbiased model: Grid 40*40 (800 cells)

Feature selection: PCA

Fz- mutant clone model:

A patch of mutated cells lacking Frizzled (Fz) in a wild-type background

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SLIDE 33

Model Checking Primary data

david.gilbert@brunel. ac.uk Systems & Synthetic Biology

33

Wild-type

Fz- mutant clone model

Unlike in the wild-type cells, for the cells distally neighbouring to the Fz- clone the concentration of FFD in the middle distal compartment is always lower than that of the middle proximal compartment:

P=? [time > 0 → G(D2 < P2)]

Moreover, the trace of D2 exhibits a peak followed by a trough, which is not true for P2:

P=?[F(d(D2) > 0 ∧ F(d(D2) < 0 ∧ F(d(D2) > 0)))]

Distally neighbouring to the clone

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SLIDE 34

200 400 600 800 1000 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Time Units Signal Model−BFXWt Cell (20,11) CP2 CD2

Big idea – check cumulative signal!

Systems & Synthetic Biology

34

Time-series of accumulated concentrations of FFD (secondary data) Why?

  • The localisation of PCP signalling at any given time point is the result of the cumulative effect of the

sum over the signalling events until that point.

Primary data

200 400 600 800 1000 100 200 300 400 500 600 Time Units Cumulative Signal Model−BFXWt Cell (20,11) CP2 CD2

Secondary data

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SLIDE 35

Model Checking

Secondary data Fz- mutant clone model

Systems & Synthetic Biology

Wild-type

Wild type cells in the tissue (i.e. away from the clone area).

After short initial period: Always middle distal cumulative[FFD] greater than middle proximal cumulative[FFD]

P=? [time > ε → G(CD2 > CP2)] Wild type cells distally neighbouring to clone in the tissue

After short initial period: Always middle distal cumulative[FFD] less than middle proximal cumulative[FFD]

P=? [time > ε → G(CD2 < CP2)] Hairs grow normally in wild-type, but disturbed in WT distally near clone, influence from the clone

Wild-type distally neighbouring to clone

CD2 CP2 CP2 CD2

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SLIDE 36

Automati tic Generati tion of Te Temporal Log Logic ic Descri ripti tions

We can use PLTLc to characterise the clusters of time series PLTLc statements should be

  • general enough to describe all the time series in a given cluster
  • discriminative enough to distinguish between time series of

different clusters The generation algorithm is based on property patterns (templates)

  • D. Maccagnola, E. Messina, Q. Gao and D. Gilbert, (2012). A Machine Learning Approach for Generating Temporal Logic Classifications of Complex Model Behaviours. Proc Winter

Simulation Conference 2012, IEEE. david.gilbert@brunel.ac.uk 36 Dagstuhl 17452

slide-37
SLIDE 37

Automati tic Generati tion of

  • f TL

TL Descri ripti tions

  • Trend: describes the trend of a time series as a sequence of direction (“increase”, “steady”, “decrease”)

If a cluster shows different trends, they are ordered by frequency (F0 is the most frequent, then F1 and so on) and the cluster trend is defined by: F0 ⋁ F1 ⋁ F2 ⋁ … Example: steady-increase-steady OR steady-increase-decrease-steady d = 0 U d > 0 U (G(d=0)) ⋁ d = 0 U d > 0 U d<0 U (G(d=0))

david.gilbert@brunel.ac.uk 37

  • D. Maccagnola, E. Messina, Q. Gao and D. Gilbert, (2012).

A Machine Learning Approach for Generating Temporal Logic Classifications of Complex Model Behaviours. Proc Winter Simulation Conference, IEEE. Dagstuhl 17452

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SLIDE 38

Automati tic Generati tion of

  • f TL

TL Descri ripti tions

  • Time: identifies the time points when the time series changes its direction, i.e. a set of “direction changes”

Time series with the same trend may have slightly different time patterns We compute a set of time intervals

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SLIDE 39

Automati tic Generati tion of

  • f TL

TL Descri ripti tions

  • Extrema: represents the occurrence of all the local minima and maxima of a time series

The time and value of each extrema can slightly change among the time series in a cluster The extrema of a cluster are defined by a sequence of time and value intervals

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SLIDE 40

Automati tic Generati tion of

  • f TL

TL Descri ripti tions

  • Steady state: represents the value of the time series steady state (if exists)

The value of each steady state can slightly change among the time series in a cluster The steady state of a cluste, if exists, is defined by a value interval

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SLIDE 41

Automati tic Generati tion of

  • f TL

TL Descri ripti tions

  • To evaluate the PLTLc statement, we test it as a temporal logic query over the clusters
  • We use the probability that the statement correctly classifies the time series belonging to cluster i
  • We associate to each statement a “confidence level” Conf :

which indicates its capability to discriminate between time series of cluster i from time series of the most similar cluster j ≠ i.

Evaluation

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SLIDE 42

Re Results

Best clustering result (using DBScan)

Wild Type Tissue Mutated Tissue

  • All the cells have the same behaviour
  • The borders are effect of a biased model
  • The mutated clone is clearly visible
  • Nearby “wild type” cells are INFLUENCED by

the mutated clone

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SLIDE 43

DIS DISCOVE VERE RED D PROP OPERTIE IES

PLTLc EXAMPLE: Behaviour in the INFLUENCED CELLS “The concentration of FFD increases from time zero, reaches its peak between time 30 and 31, and then becomes steady till the end”.

  • Q. Gao, D. Gilbert, M. Heiner, F. Liu, D. Maccagnola and D. Tree, (2013). Multiscale Modelling and Analysis of Planar Cell

Polarity in the Drosophila Wing, IEEE/ACM Transactions on Computational Biology and Bioinformatics, 10:2.

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SLIDE 44

Computational Synthetic Biology 44

From genes to systems

DNA "gene" mRNA Protein sequence Folded Protein

david.gilbert@brunel.ac.uk

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SLIDE 45

Computational Synthetic Biology 45

From system design to genes

DNA "gene" mRNA Protein sequence Folded Protein

david.gilbert@brunel.ac.uk

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SLIDE 46

Ca Can we design sign network k behavio iour base sed on pr protein engineer ein engineering? ing?

46 david.gilbert@brunel.ac.uk Computational Synthetic Biology

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SLIDE 47

model (blueprint) design synthetic biosystem construction verification validation desired behaviour

Sy Synthetic Biology

De Design n & cons nstr truc uct t ne new bio biosystems ms

david.gilbert@brunel.ac.uk 47

  • bserved

behaviour

Wet-lab experiments

predicted behaviour

In-silico experiments

Dagstuhl 17452

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SLIDE 48

So So, , for r cheminform rmatics…? …?

Move from ‘traditional’ factories to cell factories,

ØEmbed the reaction[s] of interest in cellular machinery e.g. metobalism ØRequires ØDesign techniques ØModelling & analysis of large scale networks ØGenome engineering

david.gilbert@brunel.ac.uk Dagstuhl 17452 48

predicted behaviour model (blueprint)

  • bserved

behaviour synthetic biosystem design construction validation validation desired behaviour verification

slide-49
SLIDE 49

Ac Acknowl wledgements

Brunel

  • Pam Gao
  • Ovidiu Parvu
  • Nigel Saunders

Cottbus

  • Monika Heiner

Milan

  • Daniele Maccagnola
  • Enza Messina

david.gilbert@brunel.ac.uk 49

MC2 model checker: http://www.brunel.ac.uk/research/research-areas/research-groups/cssb/software-systems-and-databases/mc2