Formal Biology of the Cell
Locations, Transport and Signaling
François Fages,
Constraint Programming Group,
INRIA Rocquencourt
mailto:[email protected]
http://contraintes.inria.fr/
François Fages
MPRI Bio-info 2005
Overview of the Lectures
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Introduction. Formal molecules and reactions in BIOCHAM.
Formal biological properties in temporal logic. Symbolic model-checking.
Continuous dynamics. Kinetics models.
Computational models of the cell cycle control [L. Calzone].
Mixed models of the cell cycle and the circadian cycle [L. Calzone].
Machine learning reaction rules from temporal properties.
Learning kinetic parameter values. Constraint-based model checking.
Protein structure prediction with Constraint Logic Programming.
Locations, transport and signaling.
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
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.
François Fages
MPRI Bio-info 2005
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.
François Fages
MPRI Bio-info 2005
Example: DNA Repair Control by p53/mdm2
Vogelstein et al. 2000
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Observed p53/mdm2 Oscillations after Irradiation
Damped oscillations after strong irradiation
Delay and no oscillations
after weak irradiation
François Fages
Lev Bar-Or et al. (2000)
MPRI Bio-info 2005
Single Cell Behaviors
« Analogic »
« Digital »
From Lahav et al. (2004) Geva-Zatorsky et al. (2006)
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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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MPRI Bio-info 2005
Interaction and Influence Schemas
Ciliberto et al. 2005
Kaufman et al. 2006
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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 => _.
François Fages
MPRI Bio-info 2005
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 => _.
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]=> _.
François Fages
MPRI Bio-info 2005
Simulation of Irradiation and DNA Repair
p53/mdm2 model of Ciliberto et al. 2005
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Cell Differentiation by Delta-Notch Signaling
Xenopus embryonic skin
[Ghosh, Tomlin 2001]
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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
François Fages
MPRI Bio-info 2005
Four Possible States
Delta expressed and Notch inhibited
D>Vd N<Vn
Vd=0.2 Vn=0.5
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
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.
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.
François Fages
MPRI Bio-info 2005
Life = Auto-activation + Degradation
François Fages
MPRI Bio-info 2005