Formal Languages in the Biochemical Abstract Machine BIOCHAM Franois Fages, INRIA Rocquencourt http:

1
Formal Languages in theBiochemical Abstract
Machine BIOCHAMFrançois Fages, INRIA
Rocquencourt http//contraintes.inria.fr/

• Joint work with
• 
  
• Nathalie Sylvain
  Laurence
• Chabrier-Rivier Soliman
  Calzone
• 
  

2
The Thesis

• Biological model
  Transition system
• Biological property
  Temporal Logic formula
• Biological validation
  Model-checking
• Lincoln et al. 02 Chabrier Fages et al. 03
  Alon et al. 04 Bernot et al. 04
• Model BIOCHAM
  Biological Properties
• - Boolean - simulation
  - CTL
• - Concentration - query evaluation
  - LTL with constraints
• - Population - rule search
  - PCTL with constraints
• - parameter
  search

3
The Thesis

• Biological model
  Transition system
• Biological property
  Temporal Logic formula
• Biological validation
  Model-checking
• Lincoln et al. 02 Chabrier et al. 03 Alon et
  al. 04 Bernot et al. 04
• Model BIOCHAM
  Biological Properties
• - Boolean - simulation
  - CTL
• - Concentration - query evaluation
  - LTL with constraints
• - Population - rule search
  - PCTL with constraints
• - parameter
  search

4
Plan of the Presentation

• Rule-based Language for Modeling Biochemical
  Systems
• Syntax of objects and reactions
• Semantics at 3 abstraction levels Boolean,
  concentrations, populations
• Temporal Logic Language for Formalizing
  Biological Properties
• Computation Tree Logic for the Boolean semantics
• Constraint Linear Time Logic for the
  concentration semantics
• Machine Learning Rules from Temporal Properties
• Learning kinetic parameter values
• Learning reaction rules
• Conclusion on modeling issues of modularity and
  compositionality

5
1. BIOCHAM Syntax of Objects

• O E Elocation
• E compound E-E Ep1,,pn (E)
• S _ OS
• Location symbolic compartment nucleus,
  cytoplasm, membrane, celli
• Compound molecule, gene binding site, abstract
  _at_process
• - binding operator for protein complexes, gene
  binding sites,
• Associative and commutative.
• modification operator for phosphorylated
  sites,
• Set of modified sites (Associative,
  Commutative, Idempotent).
• solution operator (Associative, Commutative,
  Neutral _)

6
Syntax of Rules

• N kinetic for R
• R SgtS abbrev. ACgtB stands
  for ACgtBC
• 
  AltgtB stands for AgtB and BgtA
• Seven main rule schemas
• Complexation A B gt A-B
  Decomplexation A-B gt A B
• Phosphorylation A Cgt Ap
  Dephosphorylation Ap Cgt A
• Synthesis _ Cgt A
  Degradation A Cgt _
• Transport AL1 gt AL2

7
Syntax of Rules

• N kinetic for R
• R SgtS abbrev. ACgtB stands
  for ACgtBC
• 
  AltgtB stands for AgtB and BgtA
• Seven main rule schemas
• Complexation A B gt A-B
  Decomplexation A-B gt A B
• Phosphorylation A Cgt Ap
  Dephosphorylation Ap Cgt A
• Synthesis _ Cgt A
  Degradation A Cgt _
• Transport AL1 gt AL2
• Type inference C is a kinase / phosphatase /
  activated gene
• Type inference topology of locations L1, L2

8
Syntax of Rules

• N kinetic for R
• R SgtS abbrev. ACgtB stands
  for ACgtBC
• 
  AltgtB stands for AgtB and BgtA
• Seven main rule schemas
• Complexation A B gt A-B
  Decomplexation A-B gt A B
• Phosphorylation A Cgt Ap
  Dephosphorylation Ap Cgt A
• Synthesis _ Cgt A
  Degradation A Cgt _
• Transport AL1 gt AL2
• Type inference C is a kinase / phosphatase /
  activated gene
• Type inference topology of locations L1, L2
• Easy import/export SBML format

9
BIOCHAM Semantics of a Rule Set ei for Si gt
Si

• Petri net semantics at three abstraction levels
• Boolean Semantics presence-absence of molecules
• Concurrent Transition System (asynchronous,
  non-deterministic)

10
BIOCHAM Semantics of a Rule Set ei for Si gt
Si

• Petri net semantics at three abstraction levels
• Boolean Semantics presence-absence of molecules
• Concurrent Transition System (asynchronous,
  non-deterministic)
• 2. Concentration Semantics number / volume
• Ordinary Differential Equations or hybrid
  automaton (deterministic)
• dxk/dt SXi1n ri(xk) ei - SXj1n lj(xk)
  ej
• where ri (resp. lj) is the stochiometric
  coefficient of xk in Si (resp. Si) multiplied by
  the volume ratio of the location of xk.

11
BIOCHAM Semantics of a Rule Set ei for Si gt
Si

• Petri net semantics at three abstraction levels
• Boolean Semantics presence-absence of molecules
• Concurrent Transition System (asynchronous,
  non-deterministic)
• 2. Concentration Semantics number / volume
• Ordinary Differential Equations or hybrid
  automaton (deterministic)
• dxk/dt SXi1n ri(xk) ei - SXj1n lj(xk)
  ej
• where ri (resp. lj) is the stochiometric
  coefficient of xk in Si (resp. Si) multiplied by
  the volume ratio of the location of xk.
• 3. Population of molecules number of molecules
• Continuous time Markov chain the eis giving
  transition probabilities

12
Example Cell Cycle Control Model Tyson 91

• k1 for
  _gtCyclin.
• k2Cyclin for Cyclingt_.
• k3CyclinCdc2p1 for CyclinCdc2p1gtCdc
  2p1-Cyclinp1.
• k4pCdc2p1-Cyclinp1 for
• 
  Cdc2p1-Cyclinp1gtCdc2-Cyclinp1.
• k4Cdc2-Cyclinp12Cdc2p1-Cyclinp1
  for
• Cdc2p1-Cyclinp1Cdc2-Cyclin
  p1gtCdc2-Cyclinp1.
• k5Cdc2-Cyclinp1 for Cdc2-Cyclinp1gtCdc
  2p1-Cyclinp1.
• k6Cdc2-Cyclinp1 for Cdc2-Cyclinp1gtCdc
  2Cyclinp1.
• k7Cyclinp1 for Cyclinp1gt_.
• k8Cdc2 for
  Cdc2gtCdc2p1.
• k9Cdc2p1 for Cdc2p1gtCdc2.

13
Interaction Graph
14
Boolean Simulation
15
Concentration Simulation
16
2. Formalizing Biological Properties in Temporal
Logics

• 2.1 Boolean Semantics Computation Tree Logic CTL

17
Biological Properties formalized in CTL

• Initial state biological conditions of
  experiment, mutants etc.
• About reachability
• Can the cell produce some protein P?
  reachable(P)EF(P)
• About pathways
• Is state s2 a necessary checkpoint for reaching
  state s?
• checkpoint(s2,s) ?E(?s2U s)
• About stationnarity
• Is a (partially described) state s a stable
  state? stable(s) AG(s)
• Is s a steady state (with possibility of
  escaping) ? steady(s)EG(s)
• About oscillations
• Can the system exhibit a cyclic behavior w.r.t.
  the presence of P ? oscil(P) EG((P ? EF ?P)
  (?P ? EF P))

18
CTL Properties Satisfied in the Cell Cycle Model

• reachable(Cdc2p1)
• reachable(Cyclin)
• reachable(Cyclinp1)
• reachable(Cdc2-Cyclinp1)
• reachable(Cdc2p1-Cyclinp1)
• oscil(Cdc2)
• oscil(Cdc2p1)
• oscil(Cdc2p1-Cyclinp1)
• oscil(Cyclin)
• AG((!(Cdc2-Cyclinp1))-gtcheckpoint(Cdc2p1-Cyc
  linp1,Cdc2-Cyclinp1))
• Automatically checked / generated by
  model-checking techniques (NuSMV BDD)

19
Temporal Properties with Numerical Constraints

• Constraints over concentrations and derivatives
  as FOL formulae over the reals
• M gt 0.2
• MP gt Q
• d(M)/dt lt 0
• Constraint LTL operators for time X, F, U, G (no
  non-determinism).
• F(Mgt0.2)
• FG(Mgt0.2)
• F (Mgt2 F (d(M)/dtlt0 F (Mlt2
  d(M)/dtgt0 F(d(M)/dtlt0))))
• oscil(M,n)
• Period(A,75) ? t ?v F(T t A v
  d(A)/dt gt 0 X(d(A)/dt lt 0)
• F(T t 75 A v
  d(A)/dt gt 0 X(d(A)/dt lt 0)))
• Model checker and numerical integration
  implemented in Prolog

20
3. Searching Parameters from Temporal Properties

• biocham learn_parameter(k3,k4,(0,200),(0,200)
  ,20,
• 
  oscil(Cdc2-Cyclinp1,3),150).

21
3. Searching Parameters from Temporal Properties

• biocham learn_parameter(k3,k4,(0,200),(0,200)
  ,20,
• 
  oscil(Cdc2-Cyclinp1,3),150).
• First values found
• parameter(k3,10).
• parameter(k4,70).

22
Searching Parameters from Temporal Properties

• biocham learn_parameter(k3,k4,(0,200),(0,200)
  ,20,
• oscil(Cdc2-Cyclinp1,3)
  F(Cdc2-Cyclinp1gt0.15), 150).
• First values found
• parameter(k3,10).
• parameter(k4,120).

23
Learning Rules from CTL Properties

• Theory Revision Algorithm
• ACTL formulae contain only A quantifiers
  checkpoint,
• If false, remains false after adding a rule ?
  delete rule
• Remove a rule on the path given by the model
  checker (why command)
• ECTL formulae contain only E quantifiers
  reachability, oscillation,
• If false, remain false after deleting a rule ?
  add rule
• Unclassified CTL formulae
• Mixed E and A quantifiers
• Correct, terminating but incomplete algorithm
• (only one rule is searched to satisfy ECTL and
  UCTL formulas)

24
Learning Reaction Rules from CTL Specification

• Suppose that the MPF activation rule is
  missing in the model
• biocham delete_rule(MPFpcdc25Cp1,p2gtMPF
  ).
• Rules can be searched to correct the model w.r.t.
  specification
• biocham learn_one_rule(all_elementary_interaction
  _rules).

25
Learning Reaction Rules from CTL Specification

• Suppose that the MPF activation rule is
  missing in the model
• biocham delete_rule(MPFpcdc25Cp1,p2gtMPF
  ).
• Rules can be searched to correct the model w.r.t.
  specification
• biocham learn_one_rule(all_elementary_interaction
  _rules).
• _cdc25Cp1,p2gtMPF
• MPFpcdc25Cp1,p2gtMPF
• CKIMPFpcdc25Cp1,p2gtCKI-MPF

26
Learning Reaction Rules from CTL Specification

• Example finding an intermediary step between MPF
  and APC activation
• biocham absent(X). add_rule(_gtX).
  add_rule(Xgt_).
• biocham add_specs( Ei(reachable(X)),
  Ai(oscil(X)),
• 
  Ai(AG(!APC-gtcheckpoint(X,APC))),
• 
  Ai(AG(!X-gtcheckpoint(MPF,X))) ).
• biocham check_all.
• False. First formula not verified
  Ai(AG(!APC-gt!(E(!X U APC))))
• Biocham searches for revisions of the model
  satisfying the specification
• biocham revise_model.

27
Learning Reaction Rules from CTL Specification

• Example finding an intermediary step between MPF
  and APC activation
• biocham absent(X). add_rule(_gtX).
  add_rule(Xgt_).
• biocham add_specs( Ei(reachable(X)),
  Ai(oscil(X)),
• 
  Ai(AG(!APC-gtcheckpoint(X,APC))),
• 
  Ai(AG(!X-gtcheckpoint(MPF,X))) ).
• biocham check_all.
• False. First formula not verified
  Ai(AG(!APC-gt!(E(!X U APC))))
• Biocham searches for revisions of the model
  satisfying the specification
• biocham revise_model.
• Deletion(s) _MPFgtAPC. _gtX.
• Addition(s) _XgtAPC. _MPFgtX.

28
Conclusion

• Formal languages in BIOCHAM
• Rule language ? modeling biochemical systems
• Temporal logic ? modeling their biological
  properties
• Automated reasoning tools in BIOCHAM
• Checking temporal logic properties ? model
  validation
• Finding parameter values satisfying temporal
  properties
• Finding reaction rules
• Modeling issues of
• Modularity-compositionality ? model re-use in
  different contexts
• Abstraction ? model simplification
• Refinement ? model decomposition