Modelling protein trafficking: progress and challenges

Transcription

1 Modelling protein trafficking: progress and challenges Laboratory for Foundations of Computer Science School of Informatics University of Edinburgh 21 May 2012

2 Outline Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

3 Src protein non-receptor protein tyrosine kinase, member of Src family

4 Src protein non-receptor protein tyrosine kinase, member of Src family in either inactive or active configuration

5 Src protein: inactive and active (Martin, Nature Rev. Mol. Cell Biol. 2, 2001)

6 Src protein non-receptor protein tyrosine kinase, member of Src family in either inactive or active configuration

7 Src protein non-receptor protein tyrosine kinase, member of Src family in either inactive or active configuration active Src at membrane linked to cell motility and adhesion hence important for understanding and treatment of cancer

8 Src protein non-receptor protein tyrosine kinase, member of Src family in either inactive or active configuration active Src at membrane linked to cell motility and adhesion hence important for understanding and treatment of cancer location in normal cell without growth factor (FGF) addition lots of inactive Src in perinuclear region much less active Src on membrane

9 Src protein non-receptor protein tyrosine kinase, member of Src family in either inactive or active configuration active Src at membrane linked to cell motility and adhesion hence important for understanding and treatment of cancer location in normal cell without growth factor (FGF) addition lots of inactive Src in perinuclear region much less active Src on membrane added FGF binds with FGF receptor (FGFR) which becomes active and binds with active Src

10 Src protein non-receptor protein tyrosine kinase, member of Src family in either inactive or active configuration active Src at membrane linked to cell motility and adhesion hence important for understanding and treatment of cancer location in normal cell without growth factor (FGF) addition lots of inactive Src in perinuclear region much less active Src on membrane added FGF binds with FGF receptor (FGFR) which becomes active and binds with active Src location in normal cell after FGF addition lots of inactive Src in perinuclear region increase in amount of active Src on membrane

11 Src protein non-receptor protein tyrosine kinase, member of Src family in either inactive or active configuration active Src at membrane linked to cell motility and adhesion hence important for understanding and treatment of cancer location in normal cell without growth factor (FGF) addition lots of inactive Src in perinuclear region much less active Src on membrane added FGF binds with FGF receptor (FGFR) which becomes active and binds with active Src location in normal cell after FGF addition lots of inactive Src in perinuclear region increase in amount of active Src on membrane how does this happen?

12 Endosomes endosomes: membrane-bound compartments within cells endocytosis: engulfing of molecules by vesicles on the inner side of the membrane, which then merge with endosomes

13 Endosomes endosomes: membrane-bound compartments within cells endocytosis: engulfing of molecules by vesicles on the inner side of the membrane, which then merge with endosomes different types: early, late, recycling, lysosomes role is to sort molecules either for recycling or degradation identify type by Rab family protein and Rho family protein

14 Endosomes endosomes: membrane-bound compartments within cells endocytosis: engulfing of molecules by vesicles on the inner side of the membrane, which then merge with endosomes different types: early, late, recycling, lysosomes role is to sort molecules either for recycling or degradation identify type by Rab family protein and Rho family protein move along microfilaments or microtubules movement is in one direction mostly

15 Endosomes endosomes: membrane-bound compartments within cells endocytosis: engulfing of molecules by vesicles on the inner side of the membrane, which then merge with endosomes different types: early, late, recycling, lysosomes role is to sort molecules either for recycling or degradation identify type by Rab family protein and Rho family protein move along microfilaments or microtubules movement is in one direction mostly vary in contents rather than number or speed

16 Mechanisms experimental research from the Frame laboratory has shown

17 Mechanisms experimental research from the Frame laboratory has shown After stimulation with FGF, Src is found in endosomes throughout the cytoplasm. There is a gradient of inactive Src to active Src from perinuclear region to membrane. Src activation takes place in endosomes. (Sandilands et al, 2004)

18 Mechanisms: gradient from inactive to active (Sandilands et al, Dev. Cell 7, 2004)

19 Mechanisms experimental research from the Frame laboratory has shown After stimulation with FGF, Src is found in endosomes throughout the cytoplasm. There is a gradient of inactive Src to active Src from perinuclear region to membrane. Src activation takes place in endosomes. (Sandilands et al, 2004)

20 Mechanisms experimental research from the Frame laboratory has shown After stimulation with FGF, Src is found in endosomes throughout the cytoplasm. There is a gradient of inactive Src to active Src from perinuclear region to membrane. Src activation takes place in endosomes. (Sandilands et al, 2004) The persistence of active Src at the membrane is inversely related to the quantity of FGF added. (Sandilands et al, 2007)

21 Mechanisms: persistence of response to FGF (Sandilands et al, EMBO Reports 8, 2007)

22 Mechanisms experimental research from the Frame laboratory has shown After stimulation with FGF, Src is found in endosomes throughout the cytoplasm. There is a gradient of inactive Src to active Src from perinuclear region to membrane. Src activation takes place in endosomes. (Sandilands et al, 2004) The persistence of active Src at the membrane is inversely related to the quantity of FGF added. (Sandilands et al, 2007)

23 Mechanisms experimental research from the Frame laboratory has shown After stimulation with FGF, Src is found in endosomes throughout the cytoplasm. There is a gradient of inactive Src to active Src from perinuclear region to membrane. Src activation takes place in endosomes. (Sandilands et al, 2004) The persistence of active Src at the membrane is inversely related to the quantity of FGF added. (Sandilands et al, 2007) In cancerous cells, Src is sequestered in autophagosomes when FAK is absent, to avoid cell death as a result of excess Src not bound to FAK. (Sandilands et al, 2012)

24 Mechanisms: sequestration in autophagosomes b FAK ptyr-416-src Merge FAK +/+ FAK / ure 1 Localization of active Src is altered in the absence of FAK fixed and stained for anti-fak (Sandilands et al, Nature Cell Biology 14, 2012)

25 Modelling protein trafficking modelling aspects dynamic: behaviour, change over time change on addition of FGF spatial: reactions happen in different parts of the cell molecules move within the cell populations: molecular species exist in reasonable numbers each species has a small number of possibilities

26 Modelling protein trafficking modelling aspects dynamic: behaviour, change over time change on addition of FGF spatial: reactions happen in different parts of the cell molecules move within the cell populations: molecular species exist in reasonable numbers each species has a small number of possibilities choice of formalism: process algebras

27 Modelling protein trafficking modelling aspects dynamic: behaviour, change over time change on addition of FGF spatial: reactions happen in different parts of the cell molecules move within the cell populations: molecular species exist in reasonable numbers each species has a small number of possibilities choice of formalism: process algebras modelling challenges concrete: generate hypotheses for further experiment abstract: modelling must be computationally feasible data: very limited

28 Experimental data

29 Experimental data very limited at this stage

30 Experimental data very limited at this stage qualitative: gradient of activity quantitative: persistence of response

31 Experimental data very limited at this stage qualitative: gradient of activity quantitative: persistence of response data from general literature endosomes move along microfilaments and microtubules they move in one direction (mostly) they can move at 1µm/s cells have diameters of between 10µm and 100µm

32 Experimental data very limited at this stage qualitative: gradient of activity quantitative: persistence of response data from general literature endosomes move along microfilaments and microtubules they move in one direction (mostly) they can move at 1µm/s cells have diameters of between 10µm and 100µm both long and short recycling loops time taken for half of short loop: assuming a distance of 10µm then 10 seconds time take for half of long loop: assuming a distance of 20µm then 20 seconds

33 Process algebras history developed to model concurrent computing (mid 1980 s) originally no notion of time or space, some extensions Hillston developed PEPA, stochastic process algebra (1996) Hillston developed ODE interpretation of PEPA (2005)

34 Process algebras history developed to model concurrent computing (mid 1980 s) originally no notion of time or space, some extensions Hillston developed PEPA, stochastic process algebra (1996) Hillston developed ODE interpretation of PEPA (2005) Bio-PEPA, a biological process algebra developed by Ciocchetta and Hillston close match between modelling artificial and natural systems extension of PEPA, functional rates and stoichiometry

35 Process algebras history developed to model concurrent computing (mid 1980 s) originally no notion of time or space, some extensions Hillston developed PEPA, stochastic process algebra (1996) Hillston developed ODE interpretation of PEPA (2005) Bio-PEPA, a biological process algebra developed by Ciocchetta and Hillston close match between modelling artificial and natural systems extension of PEPA, functional rates and stoichiometry Stochastic HYPE, a stochastic hybrid process algebra developed by Bortolussi, Galpin and Hillston from HYPE existing hybrid process algebras treated ODEs monolithically

36 Process algebras (continued) what is a process algebra? compact and elegant formal language behaviour given by semantics defined mathematically classical process algebra: labelled transition systems stochastic process algebra: continuous time Markov chains stochastic hybrid process algebra: piecewise determinsitic Markov processes

37 Process algebras (continued) what is a process algebra? compact and elegant formal language behaviour given by semantics defined mathematically classical process algebra: labelled transition systems stochastic process algebra: continuous time Markov chains stochastic hybrid process algebra: piecewise determinsitic Markov processes why use a process algebra? formalism to describe concurrent behaviour provide an unambiguous and precise description different analyses available from a single description simulation, model checking, CTMC analysis they are mathematically beautiful

38 Bio-PEPA syntax species: reactions, stoichiometry, locations = def (α 1, κ 1 ) op 1 S@L (α n, κ n ) op n S@L where op i {,,,, }

39 Bio-PEPA syntax species: reactions, stoichiometry, locations = def (α 1, κ 1 ) op 1 S@L (α n, κ n ) op n S@L where op i {,,,, }

40 Bio-PEPA syntax species: reactions, stoichiometry, locations = def (α 1, κ 1 ) op 1 S@L (α n, κ n ) op n S@L where op i {,,,, }

41 Bio-PEPA syntax species: reactions, stoichiometry, locations = def (α 1, κ 1 ) op 1 S@L (α n, κ n ) op n S@L where op i {,,,, }

42 Bio-PEPA syntax species: reactions, stoichiometry, locations = def (α 1, κ 1 ) op 1 S@L (α n, κ n ) op n S@L where op i {,,,, } model: quantities of species, interaction between species P = def S 1 (x 1 )... S p (x p )

43 Bio-PEPA syntax species: reactions, stoichiometry, locations = def (α 1, κ 1 ) op 1 S@L (α n, κ n ) op n S@L where op i {,,,, } model: quantities of species, interaction between species P = def S 1 (x 1 )... S p (x p )

44 Bio-PEPA syntax species: reactions, stoichiometry, locations = def (α 1, κ 1 ) op 1 S@L (α n, κ n ) op n S@L where op i {,,,, } model: quantities of species, interaction between species P = def S 1 (x 1 )... S p (x p ) system: includes other information required for modelling L compartments and locations, dimensionality, sizes N species quantities, minimums, maximums, step size K parameter definitions F functional rates for reactions, definition of f α

45 Bio-PEPA syntax species: reactions, stoichiometry, locations = def (α 1, κ 1 ) op 1 S@L (α n, κ n ) op n S@L where op i {,,,, } model: quantities of species, interaction between species P = def S 1 (x 1 )... S p (x p ) system: includes other information required for modelling L compartments and locations, dimensionality, sizes N species quantities, minimums, maximums, step size K parameter definitions F functional rates for reactions, definition of f α process-as-species rather than process-as-molecules

46 Bio-PEPA semantics operational semantics for capability relation c

47 Bio-PEPA semantics operational semantics for capability relation c Prefix rules ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l κ) ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l + κ) ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l) ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l) ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l) κ l N 0 l N κ κ l N 0 l N 0 l N

48 Bio-PEPA semantics operational semantics for capability relation c Prefix rules ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l κ) ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l + κ) ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l) ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l) ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l) κ l N 0 l N κ κ l N 0 l N 0 l N

49 Bio-PEPA semantics operational semantics for capability relation c Prefix rules ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l κ) ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l + κ) ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l) ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l) ((α, κ) S@L)(l) (α,[s@l: (l,κ)]) c S@L(l) κ l N 0 l N κ κ l N 0 l N 0 l N

50 Bio-PEPA semantics (continued) Cooperation for α M P (α,v) c P Q (α,u) c Q α M P Q (α,v::u) M c P Q M

51 Bio-PEPA semantics (continued) Cooperation for α M P (α,v) c P Q (α,u) c Q α M P Q (α,v::u) M c P Q M operational semantics for stochastic relation s V, N, K, F, Comp, P P (α,v) c P (α,fα(v,v,n,k)/h) s V, N, K, F, Comp, P

52 Bio-PEPA semantics (continued) Cooperation for α M P (α,v) c P Q (α,u) c Q α M P Q (α,v::u) M c P Q M operational semantics for stochastic relation s V, N, K, F, Comp, P P (α,v) c P (α,fα(v,v,n,k)/h) s V, N, K, F, Comp, P rate function f α uses information about the species and locations in the string v, together with the species and location information and rate parameters in calculating the actual rate of the reaction

53 Modelling with Bio-PEPA modelled gradient successfully without cycle

54 Modelling with Bio-PEPA modelled gradient successfully without cycle added gradient into model of trafficking with a combined loop gradient component seemed to make model insensitive to changes very difficult to work with, too many parameters

55 Modelling with Bio-PEPA modelled gradient successfully without cycle added gradient into model of trafficking with a combined loop gradient component seemed to make model insensitive to changes very difficult to work with, too many parameters next: combined loop model with abstract gradient

56 Src trafficking: combined loop model FGF membrane FGFR asrc afgfr asrc asrc Src afgfr 20 seconds perinuclear region Src Src

57 Modelling progess with Bio-PEPA modelled gradient successfully without cycle added gradient into model of trafficking with a combined loop gradient component made model insenstive to changes very difficult to work with, too many parameters next: combined loop model with abstract gradient no match with experimental results but useful for discussions

58 Combined loop trafficking model results 1400 asrc at membrane afgfr at membrane Time

59 Modelling progess with Bio-PEPA modelled gradient successfully without cycle added gradient into model of trafficking with a combined loop gradient component made model insenstive to changes very difficult to work with, too many parameters next: combined loop model with abstract gradient no match with experimental results but useful for discussions

60 Modelling progess with Bio-PEPA modelled gradient successfully without cycle added gradient into model of trafficking with a combined loop gradient component made model insenstive to changes very difficult to work with, too many parameters next: combined loop model with abstract gradient no match with experimental results but useful for discussions unnecessary to assume a combined loop for both behaviours found out about short and long recycling loops

61 Modelling progess with Bio-PEPA modelled gradient successfully without cycle added gradient into model of trafficking with a combined loop gradient component made model insenstive to changes very difficult to work with, too many parameters next: combined loop model with abstract gradient no match with experimental results but useful for discussions unnecessary to assume a combined loop for both behaviours found out about short and long recycling loops current: two loop model one short, one long

62 Src trafficking: two loop model FGF membrane FGFR asrc afgfr 10 seconds asrc afgfr asrc Src afgfr 20 seconds perinuclear region Src Src

63 Two loop trafficking model results asrc at membrane afgfr at membrane Time

64 Bio-PEPA Eclipse Plug-in software tool for Bio-PEPA modelling

65 Bio-PEPA Eclipse Plug-in software tool for Bio-PEPA modelling Eclipse front-end and separate back-end library editor for the Bio-PEPA language parser for the Bio-PEPA language User Interface problems view outline view for the reaction-centric view Core static analysis ISBJava time series analysis (ODE, SSA) graphing support via common plugin export facility (SBML; PRISM)

66 Bio-PEPA Eclipse Plug-in software tool for Bio-PEPA modelling Eclipse front-end and separate back-end library editor for the Bio-PEPA language parser for the Bio-PEPA language User Interface problems view outline view for the reaction-centric view Core static analysis ISBJava time series analysis (ODE, SSA) graphing support via common plugin export facility (SBML; PRISM) available for download at case studies, publications, manuals

67 Bio-PEPA Eclipse Plug-in (continued)

68 Simplified Bio-PEPA model active Src at membrane = (bind,1) << + (out sh,150) << + (in sh,75) >> + (in long,100) >> asrc@mb;

69 Simplified Bio-PEPA model active Src at membrane = (bind,1) << + (out sh,150) << + (in sh,75) >> + (in long,100) >> endsome in short recycling loop Endo = (out sh,1) >> Endo + (in sh,1) << Endo +... ;

70 Simplified Bio-PEPA model active Src at membrane = (bind,1) << + (out sh,150) << + (in sh,75) >> + (in long,100) >> endsome in short recycling loop Endo = (out sh,1) >> Endo + (in sh,1) << Endo +... ; model: asrc@mb[initial asrc mb] <*> Endo short@cyto[initial Endo short]

71 Simplified Bio-PEPA model active Src at membrane = (bind,1) << + (out sh,150) << + (in sh,75) >> + (in long,100) >> endsome in short recycling loop Endo = (out sh,1) >> Endo + (in sh,1) << Endo +... ; model: asrc@mb[initial asrc mb] <*> Endo short@cyto[initial Endo short] reactions out sh: 150 asrc -> Endo short in sh: Endo short -> 75 asrc

72 Stochastic HYPE

73 Stochastic HYPE subcomponents ( C1 (V) C n (V) )

74 Stochastic HYPE subcomponents ( C1 (V) C n (V) )

75 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m

76 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m C(V) = def j well-defined subcomponent a j : α j. C(V) + init : α. C(V)

77 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m well-defined subcomponent C(V) = def a j : α j. C(V) + init : α. C(V) j subcomponents are parameterised by variables

78 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m C(V) = def j well-defined subcomponent a j : α j. C(V) + init : α. C(V)

79 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m well-defined subcomponent C(V) = def a j : α j. C(V) + init : α. C(V) j events have event conditions: guards and resets

80 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m well-defined subcomponent C(V) = def a j : α j. C(V) + init : α. C(V) j events have event conditions: guards and resets ec(a j ) = (f (V), V = f (V)) discrete events

81 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m well-defined subcomponent C(V) = def a j : α j. C(V) + init : α. C(V) j events have event conditions: guards and resets ec(a j ) = (f (V), V = f (V)) ec(a j ) = (r, V = f (V)) discrete events stochastic events

82 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m C(V) = def j well-defined subcomponent a j : α j. C(V) + init : α. C(V)

83 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m well-defined subcomponent C(V) = def a j : α j. C(V) + init : α. C(V) j influences are defined by a triple

84 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m well-defined subcomponent C(V) = def a j : α j. C(V) + init : α. C(V) j influences are defined by a triple α j = (ι j, r j, I (V))

85 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m well-defined subcomponent C(V) = def a j : α j. C(V) + init : α. C(V) j influences are defined by a triple α j = (ι j, r j, I (V)) influence names are mapped to variables iv(ι j ) V

86 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m

87 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m

88 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m controller grammar

89 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m controller grammar M ::= a.m 0 M + M

90 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m controller grammar M ::= a.m 0 M + M

91 Stochastic HYPE subcomponents controllers ( C1 (V) C n (V) ) ( ) Con1 Con m controller grammar M ::= a.m 0 M + M Con ::= M Con Con

92 Stochastic HYPE applied to biology a model has n variables defined over R: species quantities

93 Stochastic HYPE applied to biology a model has n variables defined over R: species quantities each subcomponent represents flows affecting a variable: production, binding, activation, degradation, removal

94 Stochastic HYPE applied to biology a model has n variables defined over R: species quantities each subcomponent represents flows affecting a variable: production, binding, activation, degradation, removal each influence represents a specific flow: degradation

95 Stochastic HYPE applied to biology a model has n variables defined over R: species quantities each subcomponent represents flows affecting a variable: production, binding, activation, degradation, removal each influence represents a specific flow: degradation each controller represents sequencing of events: day/night cycle

96 Stochastic HYPE applied to biology a model has n variables defined over R: species quantities each subcomponent represents flows affecting a variable: production, binding, activation, degradation, removal each influence represents a specific flow: degradation each controller represents sequencing of events: day/night cycle each discrete event represents something happening instantaneously when a condition becomes true, with a possible change of values: addition of growth factor

97 Stochastic HYPE applied to biology a model has n variables defined over R: species quantities each subcomponent represents flows affecting a variable: production, binding, activation, degradation, removal each influence represents a specific flow: degradation each controller represents sequencing of events: day/night cycle each discrete event represents something happening instantaneously when a condition becomes true, with a possible change of values: addition of growth factor each stochastic event represents something happening after time has passed, with a possible change of values: transport

98 Stochastic HYPE modelling output of model is a trajectory consisting of continuous paths in R n jumps/changes in values as events happen piecewise deterministic Markov process transition-driven stochastic hybrid automata

99 Stochastic HYPE modelling output of model is a trajectory consisting of continuous paths in R n jumps/changes in values as events happen piecewise deterministic Markov process transition-driven stochastic hybrid automata major differences from Bio-PEPA HYPE allows coordinate model of space rather than explicit abstract locations HYPE allows continuous and stochastic behaviour together likely to be valuable when small quantities of some species

100 Stochastic HYPE modelling output of model is a trajectory consisting of continuous paths in R n jumps/changes in values as events happen piecewise deterministic Markov process transition-driven stochastic hybrid automata major differences from Bio-PEPA HYPE allows coordinate model of space rather than explicit abstract locations HYPE allows continuous and stochastic behaviour together likely to be valuable when small quantities of some species application to protein trafficking work in progress SimHyA simulator

101 The Repressilator synthetic network

102 The Repressilator synthetic network three genes with three inhibitors

103 The Repressilator synthetic network three genes with three inhibitors reporter of green flourescent protein (GFP)

104 The Repressilator synthetic network three genes with three inhibitors reporter of green flourescent protein (GFP) negative feedback cycle

105 The Repressilator synthetic network three genes with three inhibitors reporter of green flourescent protein (GFP) negative feedback cycle each gene produces a protein

106 The Repressilator synthetic network three genes with three inhibitors reporter of green flourescent protein (GFP) negative feedback cycle each gene produces a protein protein inhibits transcription of mrna by another gene

107 The Repressilator synthetic network three genes with three inhibitors reporter of green flourescent protein (GFP) negative feedback cycle each gene produces a protein protein inhibits transcription of mrna by another gene other gene cannot produce its protein

108 The Repressilator synthetic network three genes with three inhibitors reporter of green flourescent protein (GFP) negative feedback cycle each gene produces a protein protein inhibits transcription of mrna by another gene other gene cannot produce its protein quantities of proteins oscillate over time

109 The Repressilator P L lac01 psc101 origin amp R TetR λ ci LacI tetr-lite kan R λp R TetR GFP P L tet01 gfp-aav λ ci-lite laci-lite ColE1 P L tet01 Elowitz and Leibler, Nature 403,

110 The Repressilator Gene A

111 The Repressilator Gene A trsa mrna A

112 The Repressilator Gene A trsa mrna A dm A

113 The Repressilator Gene A trsa mrna A Pr A dm A trla

114 The Repressilator Gene A trsa mrna A Pr A dm A trla dp A

115 The Repressilator Gene A trsa mrna A Pr A dm A trla dp A Gene B trsb mrna B Pr B dm B trlb dp B

116 The Repressilator Gene A trsa mrna A Pr A dm A trla dp A Gene B trsb mrna B Pr B dm B trlb dp B Gene C trsc mrna C Pr C dm C trlc dp C

117 The Repressilator Gene A trsa mrna A Pr A dm A trla dp A Gene B trsb mrna B Pr B dm B trlb dp B Gene C trsc mrna C Pr C dm C trlc dp C

118 The Repressilator Gene A trsa mrna A Pr A dm A trla dp A Gene B trsb mrna B Pr B dm B trlb dp B Gene C trsc mrna C Pr C dm C trlc dp C

119 The Repressilator Gene A trsa mrna A Pr A dm A trla dp A Gene B trsb mrna B Pr B dm B trlb dp B Gene C trsc mrna C Pr C dm C trlc dp C

120 The Repressilator Gene A trsa mrna A Pr A dm A trla dp A Gene B trsb mrna B Pr B dm B trlb dp B Gene C trsc mrna C Pr C dm C trlc dp C

121 The Repressilator Gene A k p Pr A kd Gene B k p Pr B kd Gene C k p Pr C kd

122 The Repressilator in HYPE degradation and production flows for Gene A: G dg A (X ) G pr A def = init : (d A, k d, linear(x )).G dg def = inhibit A : (p A, 0, const).g pr A + express A : (p A, k p, const).g pr A + init : (p A, k p, const).g pr A A (X )

123 The Repressilator in HYPE degradation and production flows for Gene A: G dg A (X ) G pr A def = init : (d A, k d, linear(x )).G dg def = inhibit A : (p A, 0, const).g pr A + express A : (p A, k p, const).g pr A + init : (p A, k p, const).g pr A composed: Gene A (A) = def (G dg A (A) G pr A ) A (X )

124 The Repressilator in HYPE degradation and production flows for Gene A: G dg A (X ) G pr A def = init : (d A, k d, linear(x )).G dg def = inhibit A : (p A, 0, const).g pr A + express A : (p A, k p, const).g pr A + init : (p A, k p, const).g pr A composed: Gene A (A) = def (G dg A (A) controller : Con A G pr A ) A (X ) def = inhibit A.express A.Con A

125 The Repressilator in HYPE degradation and production flows for Gene A: G dg A (X ) G pr A def = init : (d A, k d, linear(x )).G dg def = inhibit A : (p A, 0, const).g pr A + express A : (p A, k p, const).g pr A + init : (p A, k p, const).g pr A composed: Gene A (A) = def (G dg A (A) controller : Con A G pr A ) A (X ) def = inhibit A.express A.Con A influences mapped to variables: iv(d A ) = A iv(p A ) = A

126 The Repressilator in HYPE degradation and production flows for Gene A: G dg A (X ) G pr A def = init : (d A, k d, linear(x )).G dg def = inhibit A : (p A, 0, const).g pr A + express A : (p A, k p, const).g pr A + init : (p A, k p, const).g pr A composed: Gene A (A) = def (G dg A (A) controller : Con A G pr A ) A (X ) def = inhibit A.express A.Con A influences mapped to variables: iv(d A ) = A iv(p A ) = A event conditions: ec(inhibit A ) = (C > p, true) ec(express A ) = (C p, true)

127 The Repressilator protein levels over time (Gene A (A) Gene B (B) Gene C (C)) init.(con A Con B Con C )

128 The Repressilator protein levels over time (Gene A (A) Gene B (B) Gene C (C)) init.(con A Con B Con C ) 110 A B C kp=1.00 k d =0.01

129 Conclusions Biology + Computing =??

130 Conclusions Computing + Biology =??

131 Conclusions Computing + Biology =?? using powerful mathematical models from computer science to model biology and in the longer term, to provide predictions major challenges lack of data, models are often quasi-quantitative getting right level of abstraction for useful models

132 Acknowledgements PEPA Group University of Edinburgh Jane Hillston Stephen Gilmore Allan Clark Maria Luisa Guerriero Federica Ciocchetta Adam Duguid DMG University of Trieste Luca Bortolussi Cancer Research UK Edinburgh Margaret Frame Emma Sandilands

133 Thank you

134 Bio-PEPA syntax two-level syntax

135 Bio-PEPA syntax two-level syntax sequential component, species S ::= (α, κ) op S S + S op {,,,, }

136 Bio-PEPA syntax two-level syntax sequential component, species S ::= (α, κ) op S S + S op {,,,, } α action, reaction name, κ stoichiometric coefficient product, reactant activator, inhibitor, generic modifier

137 Bio-PEPA syntax two-level syntax sequential component, species S ::= (α, κ) op S S + S op {,,,, } α action, reaction name, κ stoichiometric coefficient product, reactant activator, inhibitor, generic modifier

138 Bio-PEPA syntax two-level syntax sequential component, species S ::= (α, κ) op S S + S op {,,,, } α action, reaction name, κ stoichiometric coefficient product, reactant activator, inhibitor, generic modifier model component, system P ::= S(l) P P L

139 Bio-PEPA syntax two-level syntax sequential component, species S ::= (α, κ) op S S + S op {,,,, } α action, reaction name, κ stoichiometric coefficient product, reactant activator, inhibitor, generic modifier model component, system P ::= S(l) P P L

140 Bio-PEPA syntax two-level syntax sequential component, species S ::= (α, κ) op S S + S op {,,,, } α action, reaction name, κ stoichiometric coefficient product, reactant activator, inhibitor, generic modifier model component, system P ::= S(l) P P L

141 Bio-PEPA syntax two-level syntax sequential component, species S ::= (α, κ) op S S + S op {,,,, } α action, reaction name, κ stoichiometric coefficient product, reactant activator, inhibitor, generic modifier model component, system P ::= S(l) P P L need a more constrained form

142 Well-defined Bio-PEPA systems well-defined Bio-PEPA species C = def (α 1, κ 1 )op 1 C +...+(α n, κ n )op n C with all α i s distinct

143 Well-defined Bio-PEPA systems well-defined Bio-PEPA species C = def (α 1, κ 1 )op 1 C +...+(α n, κ n )op n C with all α i s distinct

144 Well-defined Bio-PEPA systems well-defined Bio-PEPA species C = def (α 1, κ 1 )op 1 C +...+(α n, κ n )op n C with all α i s distinct well-defined Bio-PEPA model P = def C 1 (l 1 )... L 1 L m 1 C m (l m ) with all C i s distinct

145 Well-defined Bio-PEPA systems well-defined Bio-PEPA species C = def (α 1, κ 1 )op 1 C +...+(α n, κ n )op n C with all α i s distinct well-defined Bio-PEPA model P = def C 1 (l 1 )... L 1 L m 1 C m (l m ) with all C i s distinct

146 Well-defined Bio-PEPA systems well-defined Bio-PEPA species C = def (α 1, κ 1 )op 1 C +...+(α n, κ n )op n C with all α i s distinct well-defined Bio-PEPA model P = def C 1 (l 1 )... L 1 L m 1 well-defined Bio-PEPA system P = V, N, K, F, Comp, P C m (l m ) with all C i s distinct

147 Well-defined Bio-PEPA systems well-defined Bio-PEPA species C = def (α 1, κ 1 )op 1 C +...+(α n, κ n )op n C with all α i s distinct well-defined Bio-PEPA model P = def C 1 (l 1 )... L 1 L m 1 well-defined Bio-PEPA system P = V, N, K, F, Comp, P C m (l m ) with all C i s distinct well-defined Bio-PEPA model component with levels minimum and maximum concentrations/number of molecules fix step size, convert to minimum and maximum levels species S: 0 to NS levels

148 Example: reaction with enzyme S + E SE P + E

149 Example: reaction with enzyme S + E SE P + E S(lS ) E(l E ) SE(l SE ) P(l P ) where S def = (α, 1) S + (β, 1) S E def = (α, 1) E + (β, 1) E + (γ, 1) E SE def = (α, 1) SE + (β, 1) SE + (γ, 1) SE P def = (γ, 1) P

150 Example: reaction with enzyme S + E SE P + E S(lS ) E(l E ) SE(l SE ) P(l P ) where S def = (α, 1) S + (β, 1) S E def = (α, 1) E + (β, 1) E + (γ, 1) E SE def = (α, 1) SE + (β, 1) SE + (γ, 1) SE P def = (γ, 1) P

151 Example: reaction with enzyme S + E SE P + E S(lS ) E(l E ) SE(l SE ) P(l P ) where S def = (α, 1) S + (β, 1) S E def = (α, 1) E + (β, 1) E + (γ, 1) E SE def = (α, 1) SE + (β, 1) SE + (γ, 1) SE P def = (γ, 1) P

152 Example: reaction with enzyme S + E SE P + E S(lS ) E(l E ) SE(l SE ) P(l P ) where S def = (α, 1) S + (β, 1) S E def = (α, 1) E + (β, 1) E + (γ, 1) E SE def = (α, 1) SE + (β, 1) SE + (γ, 1) SE P def = (γ, 1) P

153 Example: reaction with enzyme S + E SE P + E S(lS ) E(l E ) SE(l SE ) P(l P ) where S def = (α, 1) S + (β, 1) S E def = (α, 1) E + (β, 1) E + (γ, 1) E SE def = (α, 1) SE + (β, 1) SE + (γ, 1) SE P def = (γ, 1) P S E P

154 Example: reaction with enzyme S + E SE P + E S(lS ) E(l E ) SE(l SE ) P(l P ) where S def = (α, 1) S + (β, 1) S E def = (α, 1) E + (β, 1) E + (γ, 1) E SE def = (α, 1) SE + (β, 1) SE + (γ, 1) SE P def = (γ, 1) P S E P S (l S ) E (l E ) P (l P ) where

155 Example: reaction with enzyme S + E SE P + E S(lS ) E(l E ) SE(l SE ) P(l P ) where S def = (α, 1) S + (β, 1) S E def = (α, 1) E + (β, 1) E + (γ, 1) E SE def = (α, 1) SE + (β, 1) SE + (γ, 1) SE P def = (γ, 1) P S E P S (l S ) E (l E ) P (l P ) where S def = (γ, 1) S E def = (γ, 1) E P def = (γ, 1) P

156 Example: reaction with enzyme S + E SE P + E S(lS ) E(l E ) SE(l SE ) P(l P ) where S def = (α, 1) S + (β, 1) S E def = (α, 1) E + (β, 1) E + (γ, 1) E SE def = (α, 1) SE + (β, 1) SE + (γ, 1) SE P def = (γ, 1) P S E P S (l S ) E (l E ) P (l P ) where S def = (γ, 1) S E def = (γ, 1) E P def = (γ, 1) P

157 Example: reaction with enzyme S + E SE P + E S(lS ) E(l E ) SE(l SE ) P(l P ) where S def = (α, 1) S + (β, 1) S E def = (α, 1) E + (β, 1) E + (γ, 1) E SE def = (α, 1) SE + (β, 1) SE + (γ, 1) SE P def = (γ, 1) P S E P S (l S ) E (l E ) P (l P ) where S def = (γ, 1) S E def = (γ, 1) E P def = (γ, 1) P

158 Example: reaction with enzyme, max level 3 state vector (S, E, SE, P) and N S = N E = N SE = N P = 3

159 Example: reaction with enzyme, max level 3 state vector (S, E, SE, P) and N S = N E = N SE = N P = 3 (3, 3, 0, 0) α (2, 2, 1, 0) α (1, 1, 2, 0) α (0, 0, 3, 0) β γ β γ β γ (2, 3, 0, 1) α (1, 2, 1, 1) α (0, 1, 2, 1) β γ (1, 3, 0, 2) β α β γ (0, 2, 1, 2) γ (0, 3, 0, 3)

160 Example: reaction with enzyme, max level 7 state vector S E SE P and N S = N E = N SE = N P = 7 α α α α α α α β γ β γ β γ β γ β γ β γ β γ 6701 α 5611 α 4521 α 3431 α 2341 α 1251 α 0161 β γ β γ β γ β γ β γ β γ 5702 α 4612 α 3522 α 2432 α 1342 α 0252 β γ β γ β γ β γ β γ 4703 α 3613 α 2523 α 1433 α 0342 β γ β γ β γ β γ 3704 α 2614 α 1524 α 0614 β γ β γ β γ 2705 α 1615 α 0525 β γ β γ 1706 α β 0616 γ 0707

161 Parameters initial parameters for species representing basal behaviour no decision species, no added FGF, no active FGFR long recycling loop inactive so no species from it hence only 3 species present initially

162 Parameters initial parameters for species representing basal behaviour no decision species, no added FGF, no active FGFR long recycling loop inactive so no species from it hence only 3 species present initially rate of entry and probability of recycling in each loop

163 Parameters initial parameters for species representing basal behaviour no decision species, no added FGF, no active FGFR long recycling loop inactive so no species from it hence only 3 species present initially rate of entry and probability of recycling in each loop input and output stoichiometry for each loop short loop: input and output the same long loop: output much larger than input

164 Parameters initial parameters for species representing basal behaviour no decision species, no added FGF, no active FGFR long recycling loop inactive so no species from it hence only 3 species present initially rate of entry and probability of recycling in each loop input and output stoichiometry for each loop short loop: input and output the same long loop: output much larger than input creation rate of active Src during basal behaviour binding rate for active Src and active FGFR time to pick up inactive Src in perinuclear region assume time taken in each loop fixed using calculations

165 Parameters (continued) at least 13 unknown parameters not so simple

166 Parameters (continued) at least 13 unknown parameters not so simple enable short recycling loop only find parameters to balance short loop 50% of active Src at membrane 50% of active Src in the short recycling loop 6 parameters not yet specified

167 Parameters (continued) at least 13 unknown parameters not so simple enable short recycling loop only find parameters to balance short loop 50% of active Src at membrane 50% of active Src in the short recycling loop 6 parameters not yet specified enable the long recycling loop guess some parameters enable the doser and see what happens