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François Fages MPRI Bio-info 2005 Formal Biology of the Cell Locations, Transport and Signaling François Fages, Constraint Programming Group, INRIA Rocquencourt

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François Fages MPRI Bio-info 2005 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.Computational models of the cell cycle control [L. Calzone]. 5.Mixed models of the cell cycle and the circadian cycle [L. Calzone]. 6.Machine learning reaction rules from temporal properties. 7.Learning kinetic parameter values. Constraint-based model checking. 8.Protein structure prediction with Constraint Logic Programming. 9.Locations, transport and signaling.

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François Fages MPRI Bio-info 2005 Symbolic Locations in BIOCHAM Locations are symbolic notations used for representing mainly Cell compartments: nucleus, cytoplasm, membrane, … Tissues of cells: C1, C2, … 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

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François Fages MPRI Bio-info 2005 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.

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François Fages MPRI Bio-info 2005 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.

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François Fages MPRI Bio-info 2005 Example: DNA Repair Control by p53/mdm2 Vogelstein et al. 2000

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François Fages MPRI Bio-info 2005 Observed p53/mdm2 Oscillations after Irradiation Damped oscillations after strong irradiation Delay and no oscillations after weak irradiation Lev Bar-Or et al. (2000)

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François Fages MPRI Bio-info 2005 Single Cell Behaviors « Analogic » « Digital » From Lahav et al. (2004) Geva-Zatorsky et al. (2006)

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François Fages MPRI Bio-info 2005 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.

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

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François Fages MPRI Bio-info 2005 Synthesis and Degradation of p53 (0.055, *[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 => p *[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 *[p53-u-u] for p53-u-u => _.

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François Fages MPRI Bio-info 2005 Synthesis and Degradation of Mdm2 in the Cytoplasm P53 promotes the transcription of Mdm /(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 => _.

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François Fages MPRI Bio-info 2005 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]=> _.

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

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François Fages MPRI Bio-info 2005 Cell Differentiation by Delta-Notch Signaling Xenopus embryonic skin [Ghosh, Tomlin 2001]

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François Fages MPRI Bio-info 2005 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

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François Fages MPRI Bio-info 2005 Four Possible States Delta expressed and Notch inhibited Vd=0.2 Vn=0.5 D>Vd N

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François Fages MPRI Bio-info 2005 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 (-[D::c1]) else (1-[D::c1]) for_ => D::c1. Notch production and degradation for a one neighbor cell if [D::c2]<0.2 then (-[N::c1]) else (1-[N::c1]) for _ => N::c1. Notch production and degradation for a two neighbors cell if [D::c1]+[D::c3]<0.2 then (-[N::c2]) else (1-[N::c2]) for _ => N::c2.

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François Fages MPRI Bio-info 2005 Delta-Notch on a Square Grid of 36 Cells Delta production and degradation for all cells if [N::c1]>0.5 then (-[D::c1]) else (1-[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 (-[N::c22]) else (1-[N::c22]) for _ => N::c22.

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François Fages MPRI Bio-info 2005 Life = Auto-activation + Degradation

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