Idea: apply Formal Methods of Program Verification to Systems Biology,

1. Formal Biology of the CellModeling, Computing and Reasoning with ConstraintsFrançois Fages, Constraint Programming Group, INRIA Rocquencourtmailto:Francois.Fages@inria.frhttp://contraintes.inria.fr/ • Idea: apply • Formal Methods of Program Verification to Systems Biology, • Constraint Logic Programming and Constraint-based Model Checking • In course, • Learn bits of Biology through computational models, • Study new formalisms, languages and … implementations.

2. Systems Biology • Multidisciplinary field aiming at getting over • the complexity walls to reason about • biological processes at the system level. • Conferences ICSB, CMSB, … journal TCSB • Virtual cell: emulate high-level biological processes in terms of their biochemical basis at the molecular level (in silico experiments) • Bioinformatics: end 90’s, genomic sequences  post-genomic data (RNA expression, protein synthesis, protein-protein interactions,… ) • Need for a strong effort on: • - the formal representation of biological processes, • - formal tools for modeling and reasoning about their global behavior.

3. Language Approach to Cell Systems Biology • Qualitative models:from diagrammatic notation to • Boolean networks [Thomas 73] • Petri Nets [Reddy 93] • Milner’s π–calculus[Regev-Silverman-Shapiro 99-01, Nagasali et al. 00] • Bio-ambients [Regev-Panina-Silverman-Cardelli-Shapiro 03] • Pathway logic [Eker-Knapp-Laderoute-Lincoln-Meseguer-Sonmez 02] • Transition systems [Chabrier-Chiaverini-Danos-Fages-Schachter 04] • Biochemical abstract machine BIOCHAM-1[Chabrier-Fages 03] • Quantitative models: from differential equation systems to • Hybrid Petri nets [Hofestadt-Thelen 98, Matsuno et al. 00] • Hybrid automata [Alur et al. 01, Ghosh-Tomlin 01] • Hybrid concurrent constraint languages [Bockmayr-Courtois 01] • Rules with continuous dynamics BIOCHAM-2[Chabrier-Fages-Soliman 04]

4. The Biochemical Abstract Machine BIOCHAM • Software environment based on two formal languages: • Biocham Rule Language for Modeling Biochemical Systems • Syntax of molecules, compartments and reactions • Semantics at 3 abstraction levels: Boolean, Concentrations, Populations • Biocham Temporal Logic for Formalizing Biological Properties • CTL for Boolean semantics • Constraint LTL for Concentration semantics • Machine learning Rules and Parameters from Temporal Properties • Learning reaction rules from CTL specification • Learning kinetic parameter values from Constraint-LTL specification • Internship topics: http://contraintes.inria.fr

5. Overview of the Lectures • Introduction. Formal molecules and reactions in BIOCHAM. • Formal biological properties in temporal logic. Symbolic model-checking. • Continuous dynamics. Kinetics and transport models. • Computational models of the cell cycle control. • Abstract interpretation and typing of biochemical networks • Machine learning reaction rules from temporal properties. • Constraint-based model checking. Learning kinetic parameter values. • Constraint Logic Programming approach to protein structure prediction.

6. References • A wonderful textbook: • Molecular Cell Biology. 5th Edition, 1100 pages+CD, Freeman Publ. • Lodish, Berk, Zipursky, Matsudaira, Baltimore, Darnell. Nov. 2003. • Modeling dynamic phenomena in molecular and cellular biology. • Segel. Cambridge Univ. Press. 1987. • Modeling and querying bio-molecular interaction networks. • Chabrier, Chiaverini, Danos, Fages, Schächter. Theoretical Computer Science 04 • The Biochemical Abstract Machine BIOCHAM. Chabrier, Fages, Soliman • http://contraintes.inria.fr/BIOCHAM

7. Map of Course 1 • Introduction • BIOCHAM syntax • Proteins: complexation and phosphorylation • DNA: replication and transcription • Reaction and transport rules • Boolean semantics: concurrent transition system, Kripke structure • States and transitions • Examples: RTK membrane receptors, MAPK signaling pathways

8. 2. Syntax: a Simple Algebra of Cell Molecules • Small molecules: covalent bonds 50-200 kcal/mol • 70% water • 1% ions • 6% amino acids (20), nucleotides (5), • fats, sugars, ATP, ADP, … • Macromolecules: hydrogen bonds, ionic, hydrophobic, Waals 1-5 kcal/mol • Stability and bindings determined by the number of weak bonds: 3D shape • 20% proteins (50-104 amino acids) • RNA (102-104 nucleotides AGCU) • DNA (102-106 nucleotides AGCT)

9. Structure Levels of Proteins • 1) Primary structure: word of n amino acids residues (20n possibilities) • linked with C-N bonds • Example: MPRI • Methionine-Proline-Arginine-Isoleucine • 2) Secondary: word of m a-helix, b-strands, random coils,… (3m-10m) • stabilized by hydrogen bonds H---O • 3) Tertiary 3D structure: spatial folding • stabilized by • hydrophobic • interactions

10. Formal proteins • Cyclin dependent kinase 1 Cdk1 • (free, inactive) • Complex Cdk1-Cyclin B Cdk1–CycB • (low activity) • Phosphorylated form Cdk1~{thr161}-CycB • at site threonine 161 • (high activity) • BIOCHAM syntax

11. Deoxyribonucleic Acid DNA • Primary structure:word over 4 nucleotides • Adenine, Guanine, Cytosine, Thymine • 2) Secondary structure: • double helix of pairs • A--T and C---G stabilized • by hydrogen bonds • DNA replication: separation of the two helices and • production of one complementary strand for each copy

12. DNA: Genome Size

13. DNA: Genome Size 3,200,000,000 pairs of nucleotides single nucleotide polymorphism 1 / 2kb

14. Genome Size

15. Genome Size

16. Transcription: DNA  pre-mRNA  mRNA  Protein • Genes: parts of DNA • Activation: transcription factors bind to the regulatory region of the gene • Transcription: RNA polymerase copies the DNA from start to stop positions into a single stranded pre-mature messenger pRNA • (Alternative)splicing: non coding regions of pRNA are removed giving mature messenger mRNA • Protein synthesis: mRNA moves to cytoplasm and binds to ribosome to assemble a protein • _ =[#E2-E2F13-DP12]=> pRNAcycA

17. BIOCHAM Syntax of Objects • E == compound | E-E | E~{p1,…,pn} • Compound: molecule, #gene binding site, abstract @process… • - : binding operator for protein complexes, gene binding sites, … • Associative and commutative. • ~{…}: modification operator for phosphorylated sites, … • Set of modified sites (Associative, Commutative, Idempotent). • O == E | E::location • Location: symbolic compartment (nucleus, cytoplasm, membrane, …) • S == _ | O+S • + : solution operator (Associative, Commutative, Neutral _)

18. Seven Fundamental Rule Schemas • Complexation: A + B => A-B Decomplexation A-B => A + B • cdk1+cycB => cdk1–cycB • Phosphorylation: A =[C]=> A~{p} Dephosphorylation A~{p} =[C]=> A • Cdk1-CycB =[Myt1]=> Cdk1~{thr161}-CycB • Cdk1~{thr14,tyr15}-CycB =[Cdc25~{Nterm}]=> Cdk1-CycB • Synthesis: _ =[C]=> A. Degradation: A =[C]=> _. • _=[#Ge2-E2f13-Dp12]=>cycA cycE =[@UbiPro]=> _ • (not for cycE-cdk2 which is stable) • Transport: A::L1 => A::L2 • Cdk1~{p}-CycB::cytoplasm=>Cdk1~{p}-CycB::nucleus

19. BIOCHAM Syntax of Reaction Rules • R ::= S=>S | S=[O]=>S | S<=>S | S<=[O]=>S • where A=[C]=>B stands for A+C=>B+C • A<=>B stands for A=>B and B=>A, etc. • N ::= kinetic for R (import/export SBML format) • Three abstraction levels: • Boolean Semantics: presence-absence of molecules • Concurrent Transition System (asynchronous, non-deterministic) • Concentration Semantics: number / volume of diffusion • Ordinary Differential Equations or Hybrid system (deterministic) • Stochastic Semantics: number of molecules • Continuous time Markov chain

20. The Actin-Myosin two-stroke Engine with ATP fuelMyosin + ATP => Myosin-ATP Myosin-ATP => Myosin + ADP • http://www.sci.sdsu.edu/movies

21. The Actin-Myosin two-stroke Engine with ATP fuelMyosin + ATP => Myosin-ATP Myosin-ATP => Myosin + ADP • http://www.sci.sdsu.edu/movies

22. The Actin-Myosin two-stroke Engine with ATP fuelMyosin + ATP => Myosin-ATP Myosin-ATP => Myosin + ADP • http://www.sci.sdsu.edu/movies

23. The Actin-Myosin two-stroke Engine with ATP fuelMyosin + ATP => Myosin-ATP Myosin-ATP => Myosin + ADP • http://www.sci.sdsu.edu/movies http://www-rocq.inria.fr/sosso/icema2

24. Cell to Cell Signaling by Hormones and Receptors • Signals: insulin, adrenaline, steroids, EGF, …, Delta, …, nutriments, light, pressure, … • Receptors: tyrosine kinases, G-protein coupled, Notch, … L + R <=> L-R RAS-GDP =[L-R]=> RAS-GTP

25. Five MAP Kinase Pathways in Budding Yeast(Saccharomyces Cerevisiae)

26. MAPK Signaling Pathways • Input: • RAF • Activated by the receptor • RAF-p14-3-3 + RAS-GTP • => RAF + p14-3-3 + RAS-GDP • Output: • MAPK~{T183,Y185} • moves to the nucleus • phosphorylates a transcription factor • which stimulates gene transcription

27. MAPK Signaling Pathway in BIOCHAM • Pattern variables $P for • Phosphorylation sites • Molecules • with constraints • BIOCHAM rules are expanded in BIOCHAM-0 rules without patterns • RAF + RAFK <=> RAF-RAFK. • RAF-RAFK => RAFK + RAF~{p1}. • RAF~{p1} + RAFPH <=> RAF~{p1}-RAFPH. • RAF~{p1}-RAFPH => RAF + RAFPH. • MEK~$P + RAF~{p1} <=> MEK~$P-RAF~{p1} • where p2 not in $P. • MEK~{p1}-RAF~{p1} => MEK~{p1,p2} + RAF~{p1}. • MEK-RAF~{p1} => MEK~{p1} + RAF~{p1}. • MEKPH + MEK~{p1}~$P <=> MEK~{p1}~$P-MEKPH. • MEK~{p1}-MEKPH => MEK + MEKPH. • MEK~{p1,p2}-MEKPH => MEK~{p1} + MEKPH. • MAPK~$P + MEK~{p1,p2} <=> MAPK~$P-MEK~{p1,p2} • where p2 not in $P. • MAPKPH + MAPK~{p1}~$P <=> MAPK~{p1}~$P-MAPKPH. • MAPK~{p1}-MAPKPH => MAPK + MAPKPH. • MAPK~{p1,p2}-MAPKPH => MAPK~{p1} + MAPKPH. • MAPK-MEK~{p1,p2} => MAPK~{p1} + MEK~{p1,p2}. • MAPK~{p1}-MEK~{p1,p2}=>MAPK~{p1,p2}+MEK~{p1,p2}.

28. Bipartite Proteins-Reactions Graph of MAPK GraphViz http://www.research.att.co/sw/tools/graphviz

29. Random Boolean Simulation of MAPK Signaling

30. Numerical simulation of MAPK in BIOCHAM-2

31. Boolean Semantics • Associate: • Booleanstate variables to molecules • denoting the presence/absence of molecules in the cell or compartment • A Finite concurrent transition system [Shankar 93] to rules (asynchronous) over-approximating the set of all possible behaviors • A reaction A+B=>C+D is translated into 4 transition rules for the possibly complete consumption of reactants: • A+BA+B+C+D • A+BA+B +C+D • A+BA+B+C+D • A+BA+B+C+D

32. Kripke Structure K=(S,R) • Given: • V is a set of state variables, with domain D, • T a set of transition rules between states. • Associate: • a Kripke structure (S,R) where • S=DV is the set of possible states with variables ranging in domain D • RSxS is the total relation induced by T, that is • (A,B) is in R if there exists a transition rule from state A to B • (A,A) is in R if there exist no transition from state A.