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School of Informa-on Systems, Compu-ng & Mathema-cs Centre for Systems & Synthe-c Biology BioModel Engineering: The Mul1Scale challenge David Gilbert [email protected] 1
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BioModelEngineering: The Mul1Scalechallengepeople.brunel.ac.uk/~csstdrg/talks/110510DavidGilbertSoC...BioModelEngineering: The Mul1Scalechallenge (DavidGilbert& [email protected]&

May 21, 2018

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Page 1: BioModelEngineering: The Mul1Scalechallengepeople.brunel.ac.uk/~csstdrg/talks/110510DavidGilbertSoC...BioModelEngineering: The Mul1Scalechallenge (DavidGilbert& david.gilbert@brunel.ac.uk&

School  of  Informa-on  Systems,  Compu-ng  &  Mathema-cs  Centre  for  Systems  &  Synthe-c  Biology  

BioModel  Engineering:  The  Mul1Scale  challenge  

 David  Gilbert  

[email protected]   1  

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natural  biosystem  

observed  behaviour  

wetlab  experiments  

model  (knowledge)  

Formalising  understanding  

model-­‐based  experiment  design  

predicted  behaviour   analysis  

Systems  biology  

[email protected]   2  

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BioModel  Engineering  •  Takes  place  at  the  interface  of  compu-ng  science,  

mathema-cs,  engineering  and  biology.    •  A  systema-c  approach  for  designing,  construc1ng  and  

analyzing  computa-onal  models  of  biological  systems.    •  Some  inspira-on  from  efficient  soMware  engineering  

strategies.    

•  Not  engineering  biological  systems  per  se,  but  –  describes  their  structure  and  behaviour,    –  in  par-cular  at  the  level  of  intracellular  molecular  processes,    –  using  computa-onal  tools  and  techniques  in  a  principled  way.    

[email protected]  

Rainer  Breitling,  David  Gilbert,  Monika  Heiner,  Richard  Orton  (2008).  A  structured  approach  for  the  engineering  of  biochemical  network  models,  illustrated  for  signalling  pathways.  Briefings  in  Bioinforma-cs  

David  Gilbert,  Rainer  Breitling,  Monika  Heiner,  and  Robin  Donaldson  (2009).  An  introduc-on  to  BioModel  Engineering,  illustrated  for  signal  transduc-on  pathways,  9th  Interna-onal  Workshop,  WMC  2008,  Edinburgh,  UK  LNCS  Volume  539,  pp13-­‐28  Rainer  Breitling,  Robin  Donaldson,  David  Gilbert,  Monika  Heiner  (2010):  Biomodel  Engineering  -­‐  From  Structure  to  Behavior;  :  Trans.  Comp  Systems  Biology  XII,  Springer  LNBI  5945,  pp.  1-­‐12  

3  

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Biomodel  engineering  

1.  Problem  iden-fica-on  2.  Construc-on  3.  Simula-on  

4.  Analysis  &  interpreta-on  

5.  Management  &  development  

[email protected]   4  

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Biomodel  engineering  

[email protected]   5  

1.  Problem  iden-fica-on  2.   Construc1on  3.   Simula1on  

4.   Analysis  &  interpreta1on  

5.  Management  &  development  

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Qualitative

Stochastic Continuous

 

Approxima-on    

Molecules/Levels CTL, LTL

Markov chain Molecules/Levels Stochastic rates CSL

ODES Concentrations Deterministic rates LTLc

Approxima-on    

DiscreteState Space Continuous State Space

Time-free Timed, Quantitative

Gilbert,  Heiner  and  Lehrack.  ``A  Unifying  Framework  for  Modelling  and  Analysing  Biochemical  Pathways  Using  Petri  Nets.”    Proc  CMSB  2007    

d[A]dt

= −k1 × [A]

Monika  Heiner  

[email protected]   6  

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What  is  a  biochemical  network  model?  

1.  Structure                      graph                          QUALITATIVE  

2.  Kine-cs  (if  you  can)                  reac-on  rates   d[Raf1*]/dt = k1*m1*m2 + k2*m3 + k5*m4 QUANTITATIVE k1 = 0.53; k2 = 0.0072; k5 = 0.0315  

3.  Ini-al  condi-ons                marking  ,  concentra-ons      [Raf1*]t=0=  2  µMolar              QUANTITATIVE  

[email protected]   7  

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[email protected] 8

Petri  nets  

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Simple  enzyma-c  reac-on  

[email protected]   9  

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[email protected]   10  

MA3  model  

A+Ek2

← # #

k1# → # A | Ek6

← # #

k3# → # B | Ek 5← # #

k4# → # B +E

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The  Raf-­‐1/RKIP/ERK  pathway  

[email protected]   11  

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k1   k2  

k3   k4  

k5  k6   k7  

k8  

k9   k10  

k11  

m1  Raf-­‐1*  

m3   Raf-­‐1*/RKIP  

m2  RKIP  

m4  Raf-­‐1*/RKIP/ERK-­‐PP  

m9  ERK-­‐PP  

m5  ERK  

m8   MEK-­‐PP/ERK  

m7  MEK-­‐PP   m6  

RKIP-­‐P  m10  

RP  

m11   RKIP-­‐P/RP  

[email protected]   12  

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k1   k2  

k3   k4  

k5  k6   k7  

k8  

k9   k10  

k11  

m1  Raf-­‐1*  

m3   Raf-­‐1*/RKIP  

m2  RKIP  

m4  Raf-­‐1*/RKIP/ERK-­‐PP  

m9  ERK-­‐PP  

m5  ERK  

m8   MEK-­‐PP/ERK  

m7  MEK-­‐PP   m6  

RKIP-­‐P  m10  

RP  

m11   RKIP-­‐P/RP  

dm3/dt  =          

[email protected]   13  

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k1   k2  

k3   k4  

k5  k6   k7  

k8  

k9   k10  

k11  

m1  Raf-­‐1*  

m3   Raf-­‐1*/RKIP  

m2  RKIP  

m4  Raf-­‐1*/RKIP/ERK-­‐PP  

m9  ERK-­‐PP  

m5  ERK  

m8   MEK-­‐PP/ERK  

m7  MEK-­‐PP   m6  

RKIP-­‐P  m10  

RP  

m11   RKIP-­‐P/RP  

dm3/dt  =  +  r1                                +  r4                                -­‐  r2                                -­‐  r3  

[email protected]   14  

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k1   k2  

k3   k4  

k5  k6   k7  

k8  

k9   k10  

k11  

m1  Raf-­‐1*  

m3   Raf-­‐1*/RKIP  

m2  RKIP  

m4  Raf-­‐1*/RKIP/ERK-­‐PP  

m9  ERK-­‐PP  

m5  ERK  

m8   MEK-­‐PP/ERK  

m7  MEK-­‐PP   m6  

RKIP-­‐P  m10  

RP  

m11   RKIP-­‐P/RP  

dm3/dt  =  +  k1*m1*m2                                  +  r4                                -­‐  r2                                -­‐  r3  

[email protected]   15  

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k1   k2  

k3   k4  

k5  k6   k7  

k8  

k9   k10  

k11  

m1  Raf-­‐1*  

m3   Raf-­‐1*/RKIP  

m2  RKIP  

m4  Raf-­‐1*/RKIP/ERK-­‐PP  

m9  ERK-­‐PP  

m5  ERK  

m8   MEK-­‐PP/ERK  

m7  MEK-­‐PP   m6  

RKIP-­‐P  m10  

RP  

m11   RKIP-­‐P/RP  

dm3/dt  =  +  k1*m1*m2                                +  k4*m4                                -­‐  k2*m3                                -­‐  k3*m3*m9  

[email protected]   16  

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Phosphoryla-on  -­‐  dephosphoryla-on  step  Mass  ac-on  

•  R:  unphosphorylated  form  •  Rp:  phosphorylated  form  •  S:  kinase  •  P:  phosphotase  •  R|S  unphosphorylated+kinase  complex  •  R|P  unphosphorylated+phosphotase  complex  

R   Rp  

S  

P  

R+Sk2

← ⎯ ⎯

k1⎯ → ⎯ R | S k3⎯ → ⎯ Rp + S

R+P kr3← ⎯ ⎯ Rp | Pkr2

⎯ → ⎯

kr1← ⎯ ⎯ Rp +PBreitling,  Gilbert,  Heiner  &  Orton  “A  structured  approach  for  the  engineering  of  biochemical  models,  illustrated  for  signalling  pathways”.    Briefings  in  Bioinforma-cs,  2008  

[email protected]   17  

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Composi-on  Ver-cal  &  horizontal  

Rp  R  

S1  

RRp  RR  

P1  

P2  

Rp  R  

S  

Rpp  

P  2-­‐stage  cascade

1-­‐stage  cascade  double  phosphoryla-on  step

[email protected]   18  

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Phosphoryla-on  cascade  +  feedback  

RRp+S1← ⎯ ⎯ ⎯ → ⎯ RRp | S1

R + RRp | S1← ⎯ ⎯ ⎯ → ⎯ R | RRp | S1 ⎯ → ⎯ RRp | S1

Rp  R  

 S1  

RR  

P1  

P2  

RRp  RRp  

Rp  R  

 S1  

RR  

P1  

P2  

RRp  

Rp  R  

 S1  

RR  

P1  

P2  

RRp+P1← ⎯ ⎯ ⎯ → ⎯ RRp | P1

Rp+ RRp | P1← ⎯ ⎯ ⎯ → ⎯ Rp| RRp | P1 ⎯ → ⎯ RRp | P1

RRp  

Rp  R  

 S1  

RR  

P1  

P2  

RRp+P1← ⎯ ⎯ ⎯ → ⎯ RRp | P1

RRp+S1← ⎯ ⎯ ⎯ → ⎯ RRp | S1

[email protected]   19  

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Networks  •  Gene  regula-on  

•  Metabolic  

•  Signalling    

•  Protein-­‐protein  interac-on    

•  Developmental  

[email protected]   20  

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What  about  scaling  up?  

[email protected]   21  

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Mul-scale  modelling  challenges  •  Repe$$on  –  mul-ple  cells  witha  similar  defini-ons  

•  Varia$on  –  mutants.  

•  Organisa$on  -­‐  regular  or  irregular  paterns  over    spa-al  networks    in  one,  two  or  three  dimensions.  

•  Communica$on  –  between  neighbours  constrained  by  neighbour  rela-on,  and  the  posi-on  in  spa-al  network.  

•  Hierarchical  organisa$on  –cells  containing  compartments.    Enables  abstrac-on  over  level  of  detail  of  components.  

[email protected]   22  

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Mul-scale  from  signalling  to  organs  

Pam  Gao,  David  Tree  

Planar  Cell  Polarity  

[email protected]   23  

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Joint  work  Brunel:  •  Pam  Gao  

•  David  Tree  

CoObus:  •  Monika  Heiner  

•  Fei  Liu  

[email protected]   24  

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Planar  Cell  Polarity  

A  patch  of  cells  (1ssue)  

Wing  (Organ)  

•   Drosophila  wing  hairs  point    distally        virtually  error  free.  •   Hexagonally  packed,  planar  (300,000)  •   PCP:  the  polariza-on  of  a  field  of  cells  within          the  plane  of  a  cell  sheet.  •   Human  pathology:  

 Cochlear  hair  cells   Spina  bifida   Oncogenic  Wnt  pathway    

[email protected]   25  

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Planar  Cell  Polarity  •  The  orienta-on  of  cells  within  the  

plane  of  the  epithelium,  orthogonal  to  the  apical-­‐basal  polarity  of  the  cells.    

•  This  polarisa-on  is  required  for  many  developmental  events  in  both  vertebrates  and  non-­‐  vertebrates.  

•  Defects  in  PCP  in  vertebrates  underlie  developmental  abnormali-es  in  mul-ple  -ssues  including  the  neural  tube,  the  kidney  and  the  inner  ear  

[email protected]   26  

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Biological  Model    •   A  core  machinery  mediates  a  compe--on  between  the  proximal  and  distal  proteins  on        adjacent  surfaces  of  neighboring  cells  and  amplifies  small  differences  to  result  in  a  highly        asymmetric  distribu1on  of  Frizzled  (Fz)  and  Vang.  •   As  a  result  of  the  above  machinery,  Fz  accumulates  on  the  distal  side  of  the  cell,        designa-ng  it  as  the  future  site  for  prehair  forma$on,  while  Vang  accumulates  on  the        proximal  side  of  the  neighbouring  cell.    •   There  are  feedback  loops  func-oning  as  well.  A  consequence  of  these  feedback  loops  is          that  cells  tent  to  align  their  polarity  such  that  each  cell  accumulates  high  levels  of  Fz  on          the  same  side  of  the  cell  and  high  levels  of  Vang  on  the  opposite  side.  

Symmetric  distribu-on  of  protein  complexes  

Asymmetric  distribu-on  of  protein  complexes  

Prehair  forma-on  [email protected]   27  

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Biological  Model  •   An  intracellular  signalling  cascade  func-ons  downstream  of  the  core  machinery,  coupling  signaling  from  the  core  proteins  to  the  cell-­‐type  specific  responses  required  to  generate  PCP  in  the  individual  -ssues.    •   PCP  proteins  Frizzled  (Fz),  Dishevelled  (Dsh),  Prickle  (Pk),  Flamingo  (Fmi)  and  Van-­‐Gogh  (Vang)    

[email protected]   28  

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Biological  Model  •  At  ini-a-on  of  PCP  signalling:  Fmi,  Fz,  Dsh,  Vang  and  Pk  are  all  present  symmetrically  at  

the  cell  membrane.  •   At  the  conclusion  of  PCP  signalling:  Fmi  is  found  at  both  the  proximal  and  distal  cell  

membrane,  Fz  and  Dsh  are  found  exclusively  at  the  distal  cell  membrane  and  Vang  and  Pk  are  found  exclusively  at  the  proximal  cell  membrane.    

•  Communica-on  between  these  proteins  at  cell  boundaries.  Distally  localised  Fmi,  Fz  and  Dsh  recruit  Fmi,  Vang  and  Pk  to  the  proximal  cell  boundary  and  vice  versa.    

[email protected]   29  

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ODEs  

•  Current  model  –  Inter-­‐cellular  signalling:  25  molecular  species  and  23  reac-ons  

–  Kine-c  laws:  mass  ac-on    

[email protected]   30  

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Parameter  Es-ma-on  

Simulated  Annealing  

 

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Coloured  Petri  nets  •  Tokens  dis-nguished  via  their  colours.    •  Each  place  gets  a  colour  set,  specifying  the  kind  of  tokens  

which  can  reside  on  the  place.  •  Each  transi-on  gets  a  guard,  specifying  which  coloured  

tokens  are  required  for  firing.  •  Each  arc  gets  an  arc  inscrip-on  specifying  the  kind  of  

tokens  flowing  through  it  

•  Allows  for  the  discrimina-on  of  species  (molecules,  metabolites,  proteins,  secondary  substances,  genes,  etc.).    

•  Colours  can  be  used  to  dis-nguish  between  sub-­‐popula-ons  of  a  species  in  different  loca-ons  (cytosol,  nucleus  and  so  on).  

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Coloured  Petri  net  •  A  coloured  Petri  net  is  a  tuple  N  =  [P,T,F,Σ,c,g,f,m0],  where:  •  P  is  a  finite,  non-­‐empty  set  of  places.  •  T  is  a  finite,  non-­‐empty  set  of  transi-ons.  •  F  is  a  finite,  non-­‐empty  set  of  directed  arcs.  •  Σ  is  a  finite,  non-­‐empty  set  of  colour  sets.  •  c  :  P  →  Σ  is  a  colour  func-on  that  assigns  to  each  place  p∈P  a  

colourset  c(p)∈Σ.  •  g  :  T  →  EXP  is  a  guard  func-on  that  assigns  to  each  transi-on  t  ∈  T  

a  guard  expression  of  Boolean  type.  •  f  :  F  →  EXP  is  an  arc  func-on  that  assigns  to  each  arc  a  ∈  F  an  arc  

expression  of  a  mul-set  type  c(p)MS,  where  p  is  the  place  connected  to  the  arc  a.  

•  m0  :  P  →  EXP  is  an  ini-alisa-on  func-on  that  assigns  to  each  place  p  ∈  P  an  ini-alisa-on  expression  of  a  mul-set  type  c(p)MS.  

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Coloured  Petri  net  folding  

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Monika  Heiner  &  Fei  Liu  

++      mul-set  addi-on  (+x)    successor  [x=2]  guard  

[x=1](x++(+x))++  [x=2]x  

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Grid  constraints  (rectangular)  neighbour1D(X,  A,  D1):-­‐                  (A=X;  A  =  X+1;  A  =  X-­‐1),                  not(A=X),                  A  <=  D1,                  A  >=  1.    neighbour2D((X,Y),  (A,B),  (D1,D2)):-­‐                  (A=X;  A  =  X+1;  A  =  X-­‐1),                  (B=Y;  B  =  Y+1;  B  =  Y-­‐1),                  not((A=X,B=Y)),                  A  <=  D1,  B  <=  D2,                  A  >=  1,  B  >=  1.    

neighbour3D((X,Y,Z),  (A,B,C),  (D1,D2,D3)):-­‐                  (A=X;  A  =  X+1;  A  =  X-­‐1),                  (B=Y;  B  =  Y+1;  B  =  Y-­‐1),                  (C=Z;  C  =  Z+1;  C  =  Z-­‐1),                  not((A=X,B=Y,C=Z)),                  A  <=  D1,  B  <=  D2,  C  <=  D3,                  A  >=  1,  B  >=  1,  C  >=  1.  

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Single  cell  Abstract  level  

(Labelled  colours  not  about  CPN  colour  sets)  

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DBD_left

C

A

E_left

r3

r4

r1

transport proximalcommunication distal

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CPN  model  for  cells  linked  in  a  pipeline.    

C

CS

B

CS

A3

1‘all()CS

D

CSE

CS

r4

r1 r3

x

x

[x>1]−x

x

x

x

x x

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colourset  CS  =  int  with  1−N,  variable  x:  CS.    The  arc  expression  [x  >  1]−x  indicates  that  the  first  cell  is  not  linked  to  the  last.  

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Spa-al  organisa-on  &  colours  

•  Reflect  organisa-on  by  colour  structure  

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(1,1) (1,2) (1,3) (1,4)

(2,1) (2,2) (2,3) (2,4)

(3,1) (3,2) (3,3) (3,4)

(4,1) (4,2) (4,3) (4,4)

Colourset  =    {(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),  (3,1),  (3,2),  (3,3),  (3,4),                                                  (4,1),  (4,2),  (4,3),  (4,4)  }  

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Hierarchical  organisa-on  

•  Hierarchically  coloured  

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(1,1) (1,2) (1,3) (1,4)

(2,1) (2,2) (2,3) (2,4)

(3,1) (3,2) (3,3) (3,4)

(4,1) (4,2) (4,3) (4,4)

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

(2,2)(1,1) (2,2)(1,2) (2,2)(1,3) (2,2)(2,1) (2,2)(2,2) (2,2)(2,3) (2,2)(3,1) (2,2)(3,2) (2,2)(3,3)

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Wing  -ssue  -ssue:  Cells  with  logical  compartments  

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Petri  net  model  for  single  cell  

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CPN  model  of  cells  with  seven  compartments  in  a  2-­‐D  matrix.  

C CSproximal

E

CSdistal

D

CSdistal

D

CSdistal

B

CSproximal

A

12

1‘all()

CSmiddler1r4 r3NW(x,y,a,b,r) ++

SW(x,y,a,b,r)

((x,y),(a,b))

((x,y),(a,b))

((x,y),(a,b))NW(x,y,a,b,r) ++

SW(x,y,a,b,r)

((x,y),(a,b))

((x,y),(2,2))

((x,y),(2,2))

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•  4  spa-al  regions:  communica-on,  proximal,  transport  and  distal  

•  Seven  virtual  compartments  ((1,  1),  (2,  1),...,  (3,3)).    

•  Each  place  or  transi-on  belongs  to  a  specific  compartment.  

•   NW  and  SW  denote  two  leM  neighbours  of  the  current  cell.  

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Declara-ons  for  the  coloured  Petri  net  model  

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CPN  model  of  PCP  signalling  

FzFmi_FmiVang

CSproximalInter

Fmi_p1‘all()

CSproximal

336

Vang_p

1‘all()

CSproximal

336

FmiVang_p

CSproximal

Pk_p

1‘all()

CSproximal

336

FFDFVP_p

CSproximal

Fz_p

1‘all()

CSproximal

336

Ld_p

1‘all()

CSproximal

336

FFD_p

CSproximal

Dsh_p

1‘all()

CSproximal

336

FzFmi_act_p

CSproximal

FzFmi_pCSproximal

FVP_p

CSproximal

poll2‘all()CSmiddle

224

FFD_dCSdistalFFD_d

CSdistal

Vang_d

1‘all()CSdistal 336

FmiVang_d

CSdistal

Pk_d

1‘all()CSdistal 336

FVP_d

CSdistal

FFDFVP_d

CSdistal

Ld_d

1‘all()

CSdistal

336

Fz_d

1‘all()

CSdistal

336

Fmi_d

1‘all()

CSdistal

336

FzFmi_d

CSdistal

Dsh_d

1‘all()

CSdistal

336

Dsh_d1‘all()

CSdistal

336

FzFmi_act_d

CSdistal

FzFmi_act_d

CSdistal

ri3

[r=2&a=2|r=1]

ri1

[r=2&a=2|r=1]

rp1

rp2

rp5

rp4

rp3

rp9rp8

rp6

rp7

ri2[r=2&a=2|r=1]

rt2

rd11

rd9

rd6

rd7

rd8

rd10

rd1

rd2

rd3

rd5rd4

rt1

rt3

rt6

rt7

rt8rt4

rt9rt5

rt10 P_set1

(((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),(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))

((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))

((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),(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))

((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))

((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),(1,1))++

((x,y),(2,1))++

((x,y),(3,1))

((x,y),(1,1))++

((x,y),(2,1))++

((x,y),(3,1)) ((x,y),(1,3))++

((x,y),(2,3))++

((x,y),(3,3))

((x,y),(1,3))++

((x,y),(2,3))++

((x,y),(3,3))

((x,y),(1,3))++

((x,y),(2,3))++

((x,y),(3,3))

((x,y),(1,3))++

((x,y),(2,3))++

((x,y),(3,3))

((x,y),(1,1))++

((x,y),(2,1))++

((x,y),(3,1))

((x,y),(1,1))++

((x,y),(2,1))++

((x,y),(3,1))

((x,y),(a,b))

((x,y),(a,b))

((x,y),(1,3))++

((x,y),(2,3))++

((x,y),(3,3))

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)

1((x,y),(2,2))

1

((x,y),(2,2))

1

((x,y),(2,2))1((x,y),(2,2))1((x,y),(2,2))

1

((x,y),(2,2))1((x,y),(2,2)) 1

((x,y),(2,2))

1

((x,y),(2,2))

1

((x,y),(2,2))

Proximal DistalTransportCommunication

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FFD  in  one  cell  (3,4)  Con-nuous  simula-on  

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 20 40 60 80 100 120 140 160 180

Con

cent

ratio

n

time

FFD_d_((3,4),(1,3))FFD_d_((3,4),(2,3))FFD_d_((3,4),(3,3))FFD_p_((3,4),(1,3))FFD_p_((3,4),(2,3))FFD_p_((3,4),(3,3))

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FFD  accumulates  at  the  distal  edge  of  the  cell  rather  than  the  proximal  edge  at  the  end  of  signalling.  

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Stochas-c  simula-on    (average  of  10  runs)  

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Some  sta-s-cs  Size Time (seconds)

Grid(M⇥ N) Cells Places Transitions Unfolding Unfolding/Cells Simulation Simulation/Cells

5⇥ 5 12 924 984 0.99 0.0825 13.34 1.1117

10⇥ 10 50 3,850 4,100 3.46 0.0692 235.81 4.7162

15⇥ 15 112 8,624 9,184 8.04 0.0718 1,366.24 12.1986

20⇥ 20 200 15,400 16,400 15.52 0.0776 - -

50⇥ 50 1,250 96,250 102,500 161.48 0.1292 - -

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Size Time (seconds)

Grid(M⇥ N) Cells Places Transitions Unfolding Unfolding/Cells Simulation Simulation/Cells

5⇥ 5 12 924 984 0.99 0.0825 13.34 1.1117

10⇥ 10 50 3,850 4,100 3.46 0.0692 235.81 4.7162

15⇥ 15 112 8,624 9,184 8.04 0.0718 1,366.24 12.1986

20⇥ 20 200 15,400 16,400 15.52 0.0776 - -

50⇥ 50 1,250 96,250 102,500 161.48 0.1292 - -

Size Time (seconds)

Grid(M⇥ N) Cells Places Transitions Unfolding Unfolding/Cells Simulation Simulation/Cells

5⇥ 5 12 924 984 0.99 0.0825 13.34 1.1117

10⇥ 10 50 3,850 4,100 3.46 0.0692 235.81 4.7162

15⇥ 15 112 8,624 9,184 8.04 0.0718 1,366.24 12.1986

20⇥ 20 200 15,400 16,400 15.52 0.0776 - -

50⇥ 50 1,250 96,250 102,500 161.48 0.1292 - -

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Model  Checking    Biochemical  Pathways  

Pathway Model

Property Eg, “Order of peaks is; RafP, MEKPP, ERKPP Model Checker

Yes/no  or    probability  

predicted  behaviour  

model  (knowledge)  

observed  behaviour  

natural  biosystem  

wetlab  experiments  

Formalising  understanding  

model-­‐based  experiment  design  

analysis  

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Simula-on-­‐based  Model  Checking    Biochemical  Pathways  

Model Checker

Model

Property Eg, “Order of peaks is RafP, MEKPP, ERKPP” Yes/no  or    

probability  

Lab Model

Behaviour  Checker  

Time  series  data  

predicted  behaviour  

model  (blueprint)  

observed  behaviour  

synthe-c  biosystem  

design   construc-on  

valida-on  

valida-on  

desired  behaviour  

verifica-on  

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PLTL  language  •  Behaviours  to  be  checked  against  a  model  is  expressed  in  temporal  

logic  

•  We  chose:  Probabilis-c  logic  called  Probabilis-c  Linear-­‐-me  Temporal  Logic  (PLTL)  

•  Main  PLTL  operators:    G  (P)  –  P  always  happens    F  (P)  –  P  happens  at  some  -me    X  (P)  –  P  happens  in  the  next  -me  point    (P1)  U  (P2)  –  P1  happens  un-l  P2  happens    P1  {  P2  }  –  P1  happens  from  the  first  -me  P2  happens  

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Range  of  expressivity  in  PLTL  •  Qualita1ve:    

Protein  rises  then  falls    P=?  [  (  d(Protein)  >  0  )  U  (  G(  d(Protein)  <  0  )  )  ]    

•  Semi-­‐qualita1ve:    Protein  rises  then  falls  to  less  than  50%  of  peak  concentra-on    P=?  [  (  d(Protein)  >  0  )  U  (  G(  d(Protein)  <  0  )  ∧  F  (  [Protein]  <  0.5  ∗  max[Protein]  )  )  ]      

•  Semi-­‐quan1ta1ve:    Protein  rises  then  falls  to  less  than  50%  of  peak  concentra-on  by  60  minutes    P=?  [  (  d(Protein)  >  0  )  U  (  G(  d(Protein)  <  0  )  ∧  F  (  -me  =  60  ∧  Protein  <  0.5  ∗  max(Protein)  )  )  ]    

•  Quan1ta1ve:    Protein  rises  then  falls  to  less  than  100µMol  by  60  minutes    P=?  [  (  d(Protein)  >  0  )  U  (  G(  d(Protein)  <  0  )  ∧  F  (  -me  =  60  ∧  Protein  <  100  )  )  ]    

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Model  searching  Peaks  at  least  once    (rises  then  falls  below  50%  max  concentra-on)  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  concentra-on)  P>=1[ErkPP  <=  0.50*max(ErkPP)  ∧  (  d(ErkPP)  >  0  )  U  (  G(ErkPP  >=  

0.99*max(ErkPP))  )    ]  

•  Levchenko  

Oscillates  at  least  4  1mes  P>=1[    F(  d(ErkPP)  >  0  ∧  F(  d(ErkPP)  <  0  ∧  …  )  )    ]  

•  Kholodenko  

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Model  checking  

For  each  cell  (x,y)  in  the  honeycomb:    AMer  some  ini-alisa-on  phase,  FFD  in  the  middle  distal  logical  compartment  (2,3)  is  always  greater  than  in  the  other  distal  compartments  (1,3)  and  (3,3),  and  will  remain  so:  

P  =?  [G(-me  >  init  →  ([(2,3)]  >  [(1,3)]&[(3,3)]  >  [C]))]    15*15  honeycomb  grid:  112  cells  in  total  Query  holds  for  all  these  cells  except  the  cells  in  the  last  column,  

cells  (2,15)  to  (14,15).  

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0 50 100 150 200−0.0

0.2

0.4

0.6

0.8

1.0FFD_d_((3,4),(1,3))FFD_d_((3,4),(2,3))FFD_d_((3,4),(3,3))

Continuous Result: continuousCPN_detailedModel_3.colcontped

Time

Valu

e

0 50 100 150 200−0.0

0.2

0.4

0.6

0.8

1.0FFD_d_((2,15),(1,3))FFD_d_((2,15),(2,3))FFD_d_((2,15),(3,3))

Continuous Result: continuousCPN_detailedModel_3.colcontped

Time

Valu

e

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Model  checking  For  FFD  in  each  distal  compartment  of  each  cell,  how  many  peaks  exist  in  

their  traces?      

P  =?[F  ((d[x(2,3)]  >  0)&F  ((d[x(2,3)]  <  0)&F  ((d[x(2,3)]  >  0))))]    P  =?[F  ((d[x(2,3)]  >  0)&F  ((d[x(2,3)]  <  0)))]    P  =?[F  ((d[x(2,3)]  >  0))]  

P=?[F(  (d[FFD:(3,4),(1,3)]  >  0)  &  F(  (d[FFD:(3,4),(1,3)]  <  0)))];    Probability:    0.0  P=?[F(  (d[FFD:(3,4),(2,3)]  >  0)  &  F(  (d[FFD:(3,4),(2,3)]  <  0)))];    Probability:    1.0  P=?[F(  (d[FFD:(3,4),(3,3)]  >  0)  &  F(  (d[FFD:(3,4),(3,3)]  <  0)))];    Probability:    0.0  

•  No  (2,3)  peak  in  cells  in  Row  1,  Row  15  and  Column  15  •  Except  these  boundary  cells,  other  cells  have  only  one  peak  •  For  FFD  in  other  distal  compartments,  there  are  no  peaks.  

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Fz  clone  in  WT  background  

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1

Cell position Wild-type Fz- Clone

Row Column Distal Proximal Distal Proximal

3 6 1.72 0.00⇤ 0.37 0.99

4 3 1.72 0.00⇤ 0.37 0.00⇤4 5 2.27 0.00⇤ 0.00 0.00

4 7 1.72 0.00⇤ 0.37 0.99

5 4 2.28 0.00⇤ 0.00 0.00

5 6 2.28 0.00⇤ 0.00 0.00

6 3 1.72 0.00⇤ 0.37 0.00⇤6 5 2.28 0.00⇤ 0.00 0.00

6 7 1.72 0.00⇤ 0.37 1.99

7 4 2.28 0.00⇤ 0.00 0.00

7 6 2.28 0.00⇤ 0.00 0.00

8 3 1.72 0.00⇤ 0.37 0.00⇤8 5 2.28 0.00⇤ 0.00 0.00

8 7 1.72 0.00⇤ 0.37 0.99

9 4 1.72 0.00⇤ 0.37 0.00⇤9 6 1.71 0.00⇤ 0.37 0.99

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Acknowledgements  Brunel:  Pam  Gao            David  Tree  

CoObus:  Monika  Heiner        Fei  Liu  

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PhD  posi1ons  available!  [email protected]