1. François Fages MPRI Bio-info 2006 Formal Biology of the Cell Locations, Transport and Signaling François Fages, Constraint Programming Group, INRIA Rocquencourt mailto:Francois.Fages@inria.fr http://contraintes.inria.fr/

2. François Fages MPRI Bio-info 2006 Overview of the Lectures 1.Introduction. Formal molecules and reactions in BIOCHAM. 2.Formal biological properties in temporal logic. Symbolic model-checking. 3.Continuous dynamics. Kinetics models. 4.Learning kinetic parameter values. Constraint-based model checking. 5.Feedback loops, multistationnarity and oscillations [Sriram] 6.Locations, transport and extracellular signaling. 7.…

3. François Fages MPRI Bio-info 2006 Symbolic Locations in BIOCHAM Locations are symbolic notations used for representing mainly Cell compartments: nucleus, cytoplasm, membrane, … Tissues of cells: C1, C2, C3, … Solution S == _ | O+S Object O == E | E::location Element E == name | E-E | E~{p1,…,pn} Declaring the set of possible locations for an element localize p53::[cytoplasm, nucleus]. defines all localized forms: p53, p53::cytoplasm, p53::nucleus

4. François Fages MPRI Bio-info 2006 Transport Rules A::L1 => A::L2 Cdk1~{p}-CycB::cytoplasm => Cdk1~{p}-CycB::nucleus. A~{p}::L1 => A::L2 Mdm-Mdm~{p}::cytoplasm => Mdm-Mdm::nucleus.

5. François Fages MPRI Bio-info 2006 Transport Rules A::L1 => A::L2 Cdk1~{p}-CycB::cytoplasm => Cdk1~{p}-CycB::nucleus. A~{p}::L1 => A::L2 Mdm-Mdm~{p}::cytoplasm => Mdm-Mdm::nucleus. localise Mdm-Mdm::[c,n]. localise Mdm-Mdm~{p}::c. volume_ratio (15,n),(1,c). meaning 15*Vn = 1*Vc (0.5*[Mdm-Mdm::n],15*[Mdm-Mdm~{p}::c]) for Mdm-Mdm::n Mdm-Mdm~{p}::c. shorthand for 15*Mdm-Mdm::n Mdm-Mdm~{p}::c.

6. François Fages MPRI Bio-info 2006 Volume Ratios for the Concentration Semantics A set of BIOCHAM reaction rules {e i for S i => S’ i | i=1,…,n} is interpreted in the concentration semantics by the system of ODEs: dx k /dt = Σ Xi=1 n r i (x k ) * e i − Σ Xj=1 n l j (x k ) * e j where r i (resp. l j ) is the stochiometric coefficient of x k in S’ i (resp. S i ) multiplied by the volume ratio of the location of x k.

7. François Fages MPRI Bio-info 2006 Example: DNA Repair Control by p53/mdm2 Vogelstein et al. 2000

8. François Fages MPRI Bio-info 2006 Observed p53/mdm2 Oscillations after Irradiation Damped oscillations after strong irradiation Delay and no oscillations after weak irradiation Lev Bar-Or et al. (2000)

9. François Fages MPRI Bio-info 2006 Single Cell Behaviors « Analogic » « Digital » From Lahav et al. (2004) Geva-Zatorsky et al. (2006)

10. François Fages MPRI Bio-info 2006 Interaction and Influence Schemas Ciliberto et al. 2005 Kaufman et al. 2006

11. François Fages MPRI Bio-info 2006 Effect of Ionizing Radiation (IR) on DNA Irradiation: 0.2*[IR] for IR => _. DNA damage: 0.18*[IR] for _ =[IR]=> damaged_dna.

12. François Fages MPRI Bio-info 2006 Effect of Ionizing Radiation (IR) on DNA Irradiation: 0.2*[IR] for IR => _. DNA damage: 0.18*[IR] for _ =[IR]=> damaged_dna. DNA repair: 0.017*([p53]+[p53-u]+[p53-u-u]) *[damaged_dna]/(1+[damaged_dna]) for damaged_dna => dna.

13. François Fages MPRI Bio-info 2006 Synthesis and Degradation of p53 (0.055, 0.0055*[p53]) for _ p53.

14. François Fages MPRI Bio-info 2006 Synthesis and Degradation of p53 (0.055, 0.0055*[p53]) for _ p53. P53 degradation is accelerated by Mdm2::n through ubiquitination 8.8 *[p53]*[Mdm-Mdm::n] for p53 =[Mdm-Mdm::n]=> p53-u. 2.5*[p53-u] for p53-u => p53. 0.0055*[p53-u] for p53-u => _.

15. François Fages MPRI Bio-info 2006 Synthesis and Degradation of p53 (0.055, 0.0055*[p53]) for _ p53. P53 degradation is accelerated by Mdm2::n through ubiquitination 8.8 *[p53]*[Mdm-Mdm::n] for p53 =[Mdm-Mdm::n]=> p53-u. 2.5*[p53-u] for p53-u => p53. 0.0055*[p53-u] for p53-u => _. 8.8*[p53-u]*[Mdm-Mdm::n] for p53-u =[Mdm-Mdm::n]=> p53-u-u. 2.5*[p53-u-u] for p53-u-u => p53-u. 8.0055*[p53-u-u] for p53-u-u => _.

16. François Fages MPRI Bio-info 2006 Synthesis and Degradation of Mdm2 in the Cytoplasm P53 promotes the transcription of Mdm2 0.0015+0.006/(1.2^3/(([p53]+[p53-u]+[p53-u-u])^3)) _ =[p53]=> Mdm-Mdm::c.

17. François Fages MPRI Bio-info 2006 Synthesis and Degradation of Mdm2 in the Cytoplasm P53 promotes the transcription of Mdm2 0.0015+0.006/(1.2^3/(([p53]+[p53-u]+[p53-u-u])^3)) _ =[p53]=> Mdm-Mdm::c. 0.05*[Mdm-Mdm::c]/(0.01+[p53]+[p53-u]+[p53-u-u]) for Mdm-Mdm::c => Mdm-Mdm~{p}::c. 6*[Mdm-Mdm~{p}::c] for Mdm-Mdm~{p}::c => Mdm-Mdm::c.

18. François Fages MPRI Bio-info 2006 Synthesis and Degradation of Mdm2 in the Cytoplasm P53 promotes the transcription of Mdm2 0.0015+0.006/(1.2^3/(([p53]+[p53-u]+[p53-u-u])^3)) _ =[p53]=> Mdm-Mdm::c. 0.05*[Mdm-Mdm::c]/(0.01+[p53]+[p53-u]+[p53-u-u]) for Mdm-Mdm::c => Mdm-Mdm~{p}::c. 6*[Mdm-Mdm~{p}::c] for Mdm-Mdm~{p}::c => Mdm-Mdm::c. 0.01*[Mdm-Mdm~{p}::c] for Mdm-Mdm~{p}::c => _. 0.01*[Mdm-Mdm::c] for Mdm-Mdm::c => _.

19. François Fages MPRI Bio-info 2006 Transport and Degradation of mdm2 in the Nucleus (14*[Mdm-Mdm~{p}::c], 0.5*[Mdm-Mdm::n]) for Mdm-Mdm~{p}::c Mdm-Mdm::n. 0.01*[Mdm-Mdm::n] for Mdm-Mdm::n => _.

20. François Fages MPRI Bio-info 2006 Transport and Degradation of mdm2 in the Nucleus (14*[Mdm-Mdm~{p}::c], 0.5*[Mdm-Mdm::n]) for Mdm-Mdm~{p}::c Mdm-Mdm::n. 0.01*[Mdm-Mdm::n] for Mdm-Mdm::n => _. DNA damage accelerates the degradation of Mdm2::n by auto-ubiquitination (ATM and ATR kinases) 0.01*[damaged_dna]*[Mdm-Mdm::n]/(0.2+[damaged_dna]) for Mdm-Mdm::n =[damaged_dna]=> _.

21. François Fages MPRI Bio-info 2006 Simulation of Irradiation and DNA Repair p53/mdm2 model of Ciliberto et al. 2005

22. François Fages MPRI Bio-info 2006 Cell Differentiation by Delta-Notch Signaling Xenopus embryonic skin [Ghosh, Tomlin 2001]

23. François Fages MPRI Bio-info 2006 Delta-Notch Lateral Signaling Delta and Notch proteins are transmembrane proteins Delta acts as a ligand and Notch as a receptor

24. François Fages MPRI Bio-info 2006 Delta-Notch Lateral Signaling Delta and Notch proteins are transmembrane proteins Delta acts as a ligand and Notch as a receptor Notch production is triggered by high Delta levels in neigboring cells

25. François Fages MPRI Bio-info 2006 Delta-Notch Lateral Signaling Delta and Notch proteins are transmembrane proteins Delta acts as a ligand and Notch as a receptor Notch production is triggered by high Delta levels in neigboring cells Delta production is triggered by low Notch concentration in the same cell

26. François Fages MPRI Bio-info 2006 Delta-Notch Lateral Signaling Delta and Notch proteins are transmembrane proteins Delta acts as a ligand and Notch as a receptor Notch production is triggered by high Delta levels in neigboring cells Delta production is triggered by low Notch concentration in the same cell Notch and Delta are degraded.

27. François Fages MPRI Bio-info 2006 Delta-Notch Lateral Signaling Delta and Notch proteins are transmembrane proteins Delta acts as a ligand and Notch as a receptor Notch production is triggered by high Delta levels in neigboring cells Delta production is triggered by low Notch concentration in the same cell Notch and Delta are degraded. At the steady state, a cell has either the Delta phenotype or the Notch

28. François Fages MPRI Bio-info 2006 Four Possible States Delta expressed and Notch inhibited Vd=0.2 Vn=0.5 D>Vd N<Vn Delta and Notch expressed D>Vd N>Vn Delta inhibited and Notch expressed D Vn Delta and Notch inhibited D<Vd N<Vn

29. François Fages MPRI Bio-info 2006 Delta-Notch on a Loop of 20 Cells localise D::[c1,c2,c3,c4,…,c20]. localise N::[c1,c2,c3,c4,…,c20].

30. François Fages MPRI Bio-info 2006 Delta-Notch on a Loop of 20 Cells localise D::[c1,c2,c3,c4,…,c20]. localise N::[c1,c2,c3,c4,…,c20]. Delta production and degradation for all cells if [N::c1]>0.5 then 0,0 else 0,[D::c1] for _ D::c1.

31. François Fages MPRI Bio-info 2006 Delta-Notch on a Loop of 20 Cells localise D::[c1,c2,c3,c4,…,c20]. localise N::[c1,c2,c3,c4,…,c20]. Delta production and degradation for all cells if [N::c1]>0.5 then 0,0 else 0,[D::c1] for _ D::c1. Notch production and degradation for a one neighbor cell if [D::c2]<0.2 then 0,0 else 0,[N::c1] for _ N::c1.

32. François Fages MPRI Bio-info 2006 Delta-Notch on a Loop of 20 Cells localise D::[c1,c2,c3,c4,…,c20]. localise N::[c1,c2,c3,c4,…,c20]. Delta production and degradation for all cells if [N::c1]>0.5 then 0,0 else 0,[D::c1] for _ D::c1. Notch production and degradation for a one neighbor cell if [D::c2]<0.2 then 0,0 else 0,[N::c1] for _ N::c1. Notch production and degradation for a two neighbors cell if [D::c1]+[D::c3]<0.2 then 0,0 else 0,[N::c2] for _ N::c2.

33. François Fages MPRI Bio-info 2006 Delta-Notch on a Square Grid of 36 Cells Delta production and degradation for all cells if [N::c1]>0.5 then 0,0 else 0,[D::c1] for _ D::c1. Notch production and degradation for a four neighbors cell if [D::c21]+[D::c23]+[D::c12]+[D::c32]<0.2 then 0,0 else 0,[N::c22] for _ N::c22.

34. François Fages MPRI Bio-info 2006 Life = Auto-activation + Degradation