G7

Formal Biology of the Cell Locations, Transport and SignalingFrançois Fages, Constraint Programming Group, INRIA Rocquencourt mailto:Francois.Fages@inria.frhttp://contraintes.inria.fr/: 

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/

Overview of the Lectures: 

Overview of the Lectures Introduction. Formal molecules and reactions in BIOCHAM. Formal biological properties in temporal logic. Symbolic model-checking. Continuous dynamics. Kinetic models. Learning kinetic parameter values. Constraint-based model checking. Abstract Interpretation for systems biology I: hierarchy of semantics Abstract Interpretation for systems biology II: types Locations, transport and intercellular signalling Inferring reaction rules from temporal properties … Protein structure prediction in constraint logic programming

Symbolic Locations in BIOCHAM: 

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

Transport Rules: 

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.

Transport Rules: 

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.

Volume Ratios for the Concentration Semantics: 

Volume Ratios for the Concentration Semantics A set of BIOCHAM reaction rules {ei for Si => S’i | i=1,…,n} is interpreted in the concentration semantics by the system of ODEs: dxk/dt = ΣXi=1n ri(xk) * ei − ΣXj=1n lj(xk) * ej where ri (resp. lj) is the stochiometric coefficient of xk in S’i (resp. Si) multiplied by the volume ratio of the location of xk.

Example: DNA Repair Control by p53/mdm2: 

Example: DNA Repair Control by p53/mdm2 Vogelstein et al. 2000

Observed p53/mdm2 Oscillations after Irradiation: 

Observed p53/mdm2 Oscillations after Irradiation Damped oscillations after strong irradiation Delay and no oscillations after weak irradiation Lev Bar-Or et al. (2000)

Single Cell Behaviors: 

Single Cell Behaviors « Analogic » « Digital » From Lahav et al. (2004) Geva-Zatorsky et al. (2006)

Interaction and Influence Schemas: 

Interaction and Influence Schemas Ciliberto et al. 2005 Kaufman et al. 2006

Effect of Ionizing Radiation (IR) on DNA : 

Effect of Ionizing Radiation (IR) on DNA Irradiation: 0.2*[IR] for IR => _. DNA damage: 0.18*[IR] for _ =[IR]=> damaged_dna.

Effect of Ionizing Radiation (IR) on DNA : 

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.

Synthesis and Degradation of p53: 

Synthesis and Degradation of p53 (0.055, 0.0055*[p53]) for _<=> p53.

Synthesis and Degradation of p53: 

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 => _.

Synthesis and Degradation of p53: 

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 => _.

Synthesis and Degradation of Mdm2 in the Cytoplasm: 

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.

Synthesis and Degradation of Mdm2 in the Cytoplasm: 

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.

Synthesis and Degradation of Mdm2 in the Cytoplasm: 

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 => _.

Transport and Degradation of mdm2 in the Nucleus: 

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 => _.

Transport and Degradation of mdm2 in the Nucleus: 

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]=> _.

Simulation of Irradiation and DNA Repair: 

Simulation of Irradiation and DNA Repair p53/mdm2 model of Ciliberto et al. 2005

Reaction and Inferred Influence Graph: 

Reaction and Inferred Influence Graph Some inhibitions are hidden in the (non monotonic) kinetic expressions

Cell Differentiation by Delta-Notch Signaling: 

Cell Differentiation by Delta-Notch Signaling Xenopus embryonic skin [Ghosh, Tomlin 2001]

Delta-Notch Lateral Signaling: 

Delta-Notch Lateral Signaling Delta and Notch proteins are transmembrane proteins Delta acts as a ligand and Notch as a receptor

Delta-Notch Lateral Signaling: 

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-Notch Lateral Signaling: 

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

Delta-Notch Lateral Signaling: 

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.

Delta-Notch Lateral Signaling: 

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

Four Possible States: 

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<Vd N>Vn Delta and Notch inhibited D<Vd N<Vn

Delta-Notch on a Loop of 20 Cells: 

Delta-Notch on a Loop of 20 Cells localise D::[c1,c2,c3,c4,…,c20]. localise N::[c1,c2,c3,c4,…,c20].

Delta-Notch on a Loop of 20 Cells: 

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.

Delta-Notch on a Loop of 20 Cells: 

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.

Delta-Notch on a Loop of 20 Cells: 

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.

Delta-Notch on a Square Grid of 36 Cells: 

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.

Morphogenesis : Auto-activation + Degradation: 

Morphogenesis : Auto-activation + Degradation