A Graph Rewriting Calculus: Applications to Biology and Autonomous Systems

Transcription

1 A Graph Rewriting Calculus: Applications to Biology and Autonomous Systems Oana Andrei PhD Defense Institut National Polytechnique de Lorraine INRIA Nancy - Grand-Est & LORIA Adviser: Hélène Kirchner Thanks to Pareo Team, especially to Horatiu Cirstea

2 Formal Methods in Systems Biology Lab experiments suggest new hypotheses biological knowledge, observations Results/ Analysis simulate Model 2

3 Formal Methods in Systems Biology Lab experiments to understand to predict suggest new hypotheses to control biological knowledge, observations Results/ Analysis simulate Model 2

4 Cell Signalling communication between cells cellular processes: proliferation, cell growth, programmed cell death... malfunctions: cancer, diabetes, autoimmunity... 3

5 Cell Signalling stimulus Nucleus communication between cells cellular processes: proliferation, cell growth, programmed cell death... malfunctions: cancer, diabetes, autoimmunity... 3

6 Cell Signalling stimulus Nucleus communication between cells cellular processes: proliferation, cell growth, programmed cell death... malfunctions: cancer, diabetes, autoimmunity... 3

7 Cell Signalling stimulus Nucleus Hello! communication between cells cellular processes: proliferation, cell growth, programmed cell death... malfunctions: cancer, diabetes, autoimmunity... 3

8 Cell Signalling stimulus Nucleus Hello! communication between cells cellular processes: proliferation, cell growth, programmed cell death... 3

9 Cell Signalling stimulus Nucleus Hello! communication between cells cellular processes: proliferation, cell growth, programmed cell death... malfunctions: cancer, diabetes, autoimmunity... 3

10 Cell Signalling stimulus Nucleus Hello! communication between cells cellular processes: proliferation, cell growth, programmed cell death... malfunctions: cancer, diabetes, autoimmunity... Need of good, predictive models for guiding experimentations and drug development. 3

11 Autonomous Systems Living cell are extremely well-organized autonomous systems. [Cardelli 05] Autonomic computing [KephartChess 03] refers to self-manageable systems initially provided with some high-level instructions from administrators. Bio-inspired modeling of distributed systems 4

12 Molecular Complexes as Graphs Protein A Protein B 5

13 Molecular Complexes as Graphs Protein A Protein B 5

14 Molecular Complexes as Graphs Protein A Protein B 5

15 Molecular Complexes as Graphs Protein A Protein B Protein C 5

16 Rule-based Modeling well-suited for modeling bio-molecular interactions, cell-signaling a rule l r defines a class of reactions rewrite strategies control the rule application 6

17 Background Works the graph structure of molecular complexes in the κ-calculus [DanosLaneve 04], BioNetGen [Faeder et al. 05] rule-based modeling of a chemical reactor [Bournez et al. 03] 7

18 Background Works the chemical model of computation, ϒ- calculus, a higher-order chemical calculus [Banatre et al. 05]: a chemical solution where molecules interact freely according to reaction rules, everything is a molecule prod = replace X, Y by X Y prod,3,1,4,5,2 prod,1,4,15,2 * prod, 120 8

19 Background Works the rewriting calculus [CirsteaKirchner 01] : extends first-order term rewriting and the λ-calculus all the basic ingredients of rewriting are explicit objects of the calculus (s(x)+y s(x+y)) (s(5)+s(2)) ρ s(5+s(2)) 9

20 Objective of This Thesis to develop a calculus based on graph rewriting for describing molecules, reactions, and biochemical network generation towards a biochemical calculus: add a biological flavor to the chemical calculus rewrite rules and rewrite strategies property verification for the modeled systems 10

21 Outline An Abstract Biochemical Calculus Port Graph Rewriting A Biochemical Calculus Based on Strategic Port Graph Rewriting Runtime Verification in the Biochemical Calculus Conclusions and Perspectives 11

22 An Abstract Biochemical Calculus Port Graph Rewriting A Biochemical Calculus Based on Strategic Port Graph Rewriting Runtime Verification in the Biochemical Calculus Conclusions and Perspectives 12

23 An Abstract Biochemical Calculus -- the ρ Σ -calculus -- a higher-order rewriting calculus first citizens: structured objects rules (abstractions) rule applications strategies as objects encompasses the rewriting calculus generalizes the ϒ- calculus (abstractions over a class of patterns, not only variables) [AndreiKirchner08a,b,c] 13

24 Basic Syntax structured objects over a monoidal category Σ with an associative and commutative product tensor and ε neutral element (eq. theory ) iterative construction of abstractions and abstract molecules 14

25 Basic Syntax Ex.: the category of graphs Graph structured objects over a monoidal category Σ with an associative and commutative product tensor and ε neutral element (eq. theory ) iterative construction of abstractions and abstract molecules 14

26 Basic Syntax Ex.: the category of graphs Graph structured objects over a monoidal category Σ with an associative and commutative product tensor and ε neutral element (eq. theory ) iterative construction of abstractions and abstract molecules 14

27 Basic Syntax Ex.: the category of graphs Graph structured objects over a monoidal category Σ with an associative and commutative product tensor and ε neutral element (eq. theory ) iterative construction of abstractions and abstract molecules 14

28 Basic Syntax Ex.: the category of graphs Graph structured objects over a monoidal category Σ with an associative and commutative product Ex.: tensor and G1 G2 is a ε neutral element (eq. theory ) graph morphism, arrow iterative construction of abstractions and abstract in Graph molecules 14

29 Basic Syntax Ex.: the category of graphs Graph structured objects over a monoidal category Σ with an associative and commutative product tensor and ε neutral element (eq. theory ) iterative construction of abstractions and abstract molecules 14

30 Basic Syntax Ex.: the category of graphs Graph structured objects over a monoidal category Σ with an associative and commutative product tensor and ε neutral element (eq. theory ) iterative construction of abstractions and abstract molecules 14

31 Interactions M L R Is L R applicable to M? 15

32 Matching submatching equation modulo : solutions have the form such that a submatching algorithm for every instantiation of Σ and 16

33 Matching and Decomposition

34 Matching and Decomposition Pattern i j 17

35 Matching and Decomposition Pattern i j 17

36 Matching and Decomposition Pattern i j 17

37 Matching and Decomposition = Context Subgraph Pattern i j 3 Bridges (neighbourhood information) 17

38 Worlds and Multiverses the molecules in an environment are encapsulated in a world alternative worlds are grouped in a multiverse 18

39 Worlds and Multiverses the molecules in an environment are encapsulated in a world alternative worlds are grouped in a multiverse 18

40 Worlds and Multiverses the molecules in an environment are encapsulated in a world alternative worlds are grouped in a multiverse 18

41 Worlds and Multiverses the molecules in an environment are encapsulated in a world alternative worlds are grouped in a multiverse 18

42 Basic Semantics 19

43 Basic Semantics 19

44 Basic Semantics BANG! 19

45 Basic Semantics BANG! n

46 Making the Application Explicit 20

47 Making the Application Explicit 20

48 Making the Application Explicit 20

49 Making the Application Explicit 20

50 Making the Application Explicit - introducing an explicit object for failure 20

51 Making the Application Explicit - introducing an explicit object for failure 20

52 Strategies enforce confluence and termination control over composing or choosing the abstractions to apply strategy languages: Elan, Stratego, Tom, Maude strategies: Identity, Failure, Sequence, First, Not, IfThenElse, Try, Repeat,... 21

53 Strategies 22

54 Strategies 22

55 Strategies 22

56 Strategies 22

57 Strategy-based Extensions tackling application failure 23

58 Strategy-based Extensions tackling application failure persistent strategies S! if then 23

59 An Abstract Biochemical Calculus Port Graph Rewriting A Biochemical Calculus Based on Strategic Port Graph Rewriting Runtime Verification in the Biochemical Calculus Conclusions and Perspectives 24

60 Port Graphs graphs with multiple edges and loops edges connect to ports of nodes defined over a signature (N,P) category PGraph port graphs as objects node morphisms as arrows [AndreiKirchner07-RULE] 25

61 A Port Graph 26

62 Molecular Complexes as Port Graphs Molecular complex protein site bond interaction Port graph node port edge rewrite rule 27

63 Example: a fragment of the EGFR signaling pathway Initial state: 1:S 2:S 3:S 4:S :R 2 2 6:R :A 28 [AndreiKirchner07-NCA]

64 Port Graph Rewrite Rules 29

65 Port Graph Rewrite Rules 29

66 Port Graph Rewrite Rules 29

67 Port Graph Rewrite Rules 29

68 Port Graph Rewrite Rules 29

69 Port Graph Rewrite Rules 29

70 A Port Graph Rewrite Rule as a Port Graph 30

71 A Port Graph Rewrite Rule as a Port Graph 30

72 A Port Graph Rewrite Rule as a Port Graph 30

73 Example: a fragment of the EGFR signaling pathway i:s j:s 2 DimerS i.j:ds 31

74 Example: a fragment of the EGFR signaling pathway i:s j:s 2 DimerS i.j:ds i:ds j:r DSbindsR i:ds j:r

75 Example: a fragment of the EGFR signaling pathway i:s j:s 2 DimerS i.j:ds i:ds j:r DSbindsR i:ds j:r i:ds j:r DimerR i:ds j:r k:r k:r 31

76 Port Graph Rewriting Relation if such that and 32

77 Port Graph Rewriting G L R 33

78 Port Graph Rewriting G L R 33

79 Port Graph Rewriting G L R G 33

80 Example: a fragment of the EGFR signaling pathway A stable state: 1.2:DS :DS 2 2 5:R 1 1 6:R :A 2 x DimerS 2 x DSbindsR 1 x DimerR 2 x ActivateDR 1 x DRbindsA

81 Term Rewriting Semantics for Port Graph Rewriting a sound and complete axiomatization using algebraic terms prototype in TOM 35 [AndreiKirchner07-RULE]

82 An Abstract Biochemical Calculus Port Graph Rewriting A Biochemical Calculus Based on Strategic Port Graph Rewriting Runtime Verification in the Biochemical Calculus Conclusions and Perspectives 36

83 A Biochemical Calculus Based on Strategic Port Graph Rewriting -- the ρpg-calculus -- instantiated ρ Σ -calculus with the structure of port graphs a (sub)matching algorithm showed the expressivity of the port graph structure by defining the matching and replacement operations 37

84 Applications: Autonomous Systems self-x properties: self-configuration self-protection self-healing self-optimization strategy-based modeling 38 [AndreiKirchner08a,c]

85 Applications: Autonomous Systems 39 A mail delivery system: 1:Network 4:Server 5:Server 3:Server 2:Server 9:Client 8:Client 7:Client 6:Client m 6@2#n 8@4#m s1 s3 s2 s4 i/o c1 c2 out in h c1 c1 c2 c2 h h h out in in in out out h h h h out out out out in in in in

86 Applications: Autonomous Systems - Self-healing 40 i:network k:server s c h i:network k.0:tserver s c h k:server c h if failure(k) SCrash i:network k.0:tserver s1 c h j:server c h s1 l:client h i:network k.0:tserver s1 c h j:server c h s1 l:client h MoveC l@k#m l@j#m

87 Applications: Autonomous Systems - Self-healing k.0:tserver k.0:tserver c in l@_#m SendLocalMess c in m h in h in l:client l:client SCrash; repeat(sendlocalmess); repeat(first(movec, SendAwayIn, SendAwayOut)) 41

88 Applications: Biochemical Networks Initial molecular graph: G = 1:S 2:S 3:S 4:S 5:R 6:R 7:A 42

89 Applications: Biochemical Networks Initial molecular graph: G = 1:S 2:S 3:S 4:S 5:R 6:R 7:A Some possible initial states: DimerS! ActivateDR! G DimerR! DRbindsA! DSbindsR! 42

90 Applications: Biochemical Networks Initial molecular graph: G = 1:S 2:S 3:S 4:S 5:R 6:R 7:A Some possible initial states: DimerS! G ActivateDR! DimerR! G ActivateDR! first(dsbindsr, DimerS)! DimerR DRbindsA! DRbindsA! DSbindsR! 42

91 Applications: Biochemical Networks Initial molecular graph: G = 1:S 2:S 3:S 4:S 5:R 6:R 7:A Some possible initial states: DimerS! ActivateDR! ActivateDR! first(dsbindsr, DimerS)! s G DimerR! G DimerR G DRbindsA! DRbindsA! DSbindsR! s = repeat(seq(first(dsbindsr, DimerS), DimerR,ActivateDR, DRbindsA)) 42

92 An Abstract Biochemical Calculus Port Graph Rewriting A Biochemical Calculus Based on Strategic Port Graph Rewriting Runtime Verification in the Biochemical Calculus Conclusions and Perspectives 43

93 Motivation invariant: rule G G strategy first(g G, X Failure )! remove (G Failure )! or repair (G H)! more: a modal logic with structural and temporal formulas ρ v pg-calculus 44

94 Structural Formulas 45

95 Structural Formulas Structural formulas: 45

96 Structural Formulas Structural formulas: Satisfaction relation: 45

97 Mapping Structural Formulas to Strategies 46

98 Mapping Structural Formulas to Strategies if and only if if and only if 46

99 Temporal Formulas a subset of CTL formulas constructed using: a path quantifier -- A, E a temporal operator -- X, G, F, U structural formula(s) φ 47

100 Temporal Formulas 48

101 Temporal Formulas AGφ 48

102 Temporal Formulas AGφ EFφ 48

103 Runtime Verification W0 W1 W2 W3 49

104 Runtime Verification W0 AGφ W1 W2 W3 49

105 Runtime Verification W0 W1 AGφ AGφ W2 W3 49

106 Runtime Verification W0 W1 W2 AGφ AGφ AGφ W3 49

107 Runtime Verification W0 EFφ W1 W2 W3 50

108 Runtime Verification W0 W1 EFφ EFφ W2 W3 50

109 Runtime Verification W0 W1 W2 EFφ EFφ EFφ W3 50

110 An Abstract Biochemical Calculus Port Graph Rewriting A Biochemical Calculus Based on Strategic Port Graph Rewriting Runtime Verification in the Biochemical Calculus Conclusions and Perspectives 51

111 Conclusions Aim: develop better models of living phenomena and new biologically-inspired computational models 52

112 Conclusions Aim: develop better models of living phenomena and new biologically-inspired computational models a higher-order biochemical calculus port graphs simulation and verification applications to protein-protein interactions and autonomous systems 52

113 Conclusions Aim: develop better models of living phenomena and new biologically-inspired computational models a higher-order biochemical calculus port graphs Strategies! simulation and verification applications to protein-protein interactions and autonomous systems 52

114 Perspectives express other or new strategies, instantiate with various structures (bigraphs) develop efficient simulation methods with graphical interface other types of bio-molecular interactions, stochastic aspects applicability in modeling synthetic biology 53

115 Merci de votre attention!

116 Publications With Hélène Kirchner: A Higher-Order Graph Calculus for Autonomic Computing - GTCIT 08 A Biochemical Calculus Based on Strategic Graph Rewriting - AB 08 Strategic Port Graph Rewriting for Autonomic Computing - TFIT 08 Graph Rewriting and Strategies for Modeling Biochemical Networks - NCA 07 A Rewriting Calculus for Multigraphs with Ports - RULE 07 Strategy-Based Proof Calculus for Membrane Systems - WRLA 08 (with Dorel Lucanu) A rewriting logic framework for operational semantics of membrane systems - TCS 07 (with Gabriel Ciobanu and Dorel Lucanu) Expressing Control Mechanisms of Membranes by Rewriting Strategies - WMC 06 (with Gabriel Ciobanu and Dorel Lucanu)

117 1:6 2:30 1:6 2: : : : :120 repeat(createbondbetweenidenticalports); FusionNodes; repeat(fusionidenticalports)