François Fages MPRI Bio-info 2006 Formal Biology of the Cell Locations, Transport and Signaling François Fages, Constraint Programming Group, INRIA Rocquencourt

François Fages MPRI Bio-info 2006

Formal Biology of the Cell

Locations, Transport and Signaling

François Fages, Constraint Programming Group,

INRIA Rocquencourt mailto:[email protected]://contraintes.inria.fr/


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. …


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

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

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

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=1

n 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

Vogelstein et al. 2000


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

« Analogic »

« Digital »

From Lahav et al. (2004) Geva-Zatorsky et al. (2006)


Interaction and Influence Schemas

Ciliberto et al. 2005

Kaufman et al. 2006


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

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

(0.055, 0.0055*[p53]) for _<=> p53.



(0.055, 0.0055*[p53]) for _<=> p53.

P53 degradation is accelerated by Mdm2::n through ubiquitination8.8 *[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 => _.



(0.055, 0.0055*[p53]) for _<=> p53.

P53 degradation is accelerated by Mdm2::n through ubiquitination8.8 *[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

P53 promotes the transcription of Mdm2

0.0015+0.006/(1.2^3/(([p53]+[p53-u]+[p53-u-u])^3))

_ =[p53]=> Mdm-Mdm::c.




0.0015+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.




0.0015+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

(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

(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

p53/mdm2 model of Ciliberto et al. 2005


Cell Differentiation by Delta-Notch Signaling

Xenopus embryonic skin

[Ghosh, Tomlin 2001]


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.







Notch and Delta are degraded.

At the steady state, a cell has either the Delta phenotype or the Notch


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

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.







_ <=> 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.







_ <=> 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


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.


Life = Auto-activation + Degradation

Documents

François Fages MPRI Bio-info 2006 Formal Biology of the Cell Locations, Transport and Signaling François Fages, Constraint Programming Group, INRIA Rocquencourt