We will first describe the biological problems we are facing (building a model of a Biological Pathway), before talking about the usual methods used by computer scientist to tackle such problems. We will finally describe the stochastic modeling used in IPAL for the biological pathways, and explain the decomposition framework we are developing to speed up the computations.

1. Using formal models in analysis of
Biological Pathways
Prof. P.S. Thiagarajan NUS
Liu Bing and S. Akshay Postdocs NUS
Sucheendra Palaniappan PhD student NUS
Subra Biswas and Alexandre Gouaillard BMRC
Blaise Genest CNRS
Bruno Karelovic CNRS Master student

2. Studying Pathway dynamics
 Methods: ODEs , Stochastic approaches, Petri Net…
2

3. EGF-NGF Pathway
3

4. EGF-NGF Pathway as ODEs
ODE (differential equations) for « Smooth » behaviors
(enough reactants or enough cells)
4

5. Akt Signaling Pathway
Growth
Factors
Bcl-2 will factors then
Phosphorylated will bind
Akt and PDK will AKT will
Activated PI3K will
PI3K will then get then
Growth then dimerize
with besurface receptors
then Bax at to into cellto
translocate Mitochondrial
phosphorylate membrane
recruited to the
to cell freedthePIP2
cytoplasm where it is
membrane,where Akt
membrane activated
PIP3 it is preventing
where P
phosphorylate Bad
apoptosis
phosphorylated PI3K P
PIP2 P
P P
GTP P
Ras Akt
P21 P
Activated - Kinase Interaction of Phosphatase
PI3K
Raf1
Raf1 and Inhibitors such as LYAkt
P
P
MEK
MEK PDK1
P
P
ERK Bax
ERK P
Bax
Bad
Na+/H+ Exchangers Bad
Bad
P Bad
Bcl-2
Bcl-2
Mitochondria
Growth Factors can also
activate the MAPK
pathway at the same time
5

6. What we want to obtain:
6

7. What Biologists have and
want
Have: Hypothesised diagram of interactions (see previous slide)
Want: Is it correct (enough)?
Have: Some (few, noisy) data for concentration of some species at some
(few,noisy) time point + some (few, noisy) rates of reactions.
0.6
0.4
Concentration of 1 molecule
over time, with 3 data points 0.2
0.0
1 8 15 22 29 36 43 50 57 64 71 78 85 92 99
Want: model fitting experiments

8. What Biologists want
Want: if model correct, in silico predictions
Reaction 2 and 5
blocked
In silico
model
computations
0.6
0.4
0.2
Interesting? Do wet lab experiments, with drugs 0.0
blocking reaction 2 and 5 to confirm 1 8 15 22 29 36 43 50 57 64 71 78 85 92 99

9. Mass action law
V1
S1 + S2 2P
V2
dP = k1. [S1] [S2] – k2 [P]2
Unknown!
(can be known in vitro with these molecules only,
but in the cell/in a cell population different)
+ no close form solutions: Simulate ODE by taking small time step
9

10. Determining Parameter Values
 Experimental measurements
 Expensive
 Not possible to measure all the parameters
 In vitro measurements may not reflect the actual
physiological conditions in the cell (Minton, 2001)
 Cell population-based measurements are not very
accurate +Noisy (Kim & Price, 2010)
Akt*
10

11. Parameter Estimation
 Goal:
 Find values of parameter so that model prediction
generated by simulations using these values can
match experimental data
krbNGF = 0.33, KmAkt = 0.16, kpRaf1 = 0.42 … … target
krbNGF = 0.49, KmAkt = 0.08, kpRaf1 = 0.97 … …
krbNGF = 0.88, KmAkt = 0.21, kpRaf1 = 0.05 … …
Time
11

12. Global Methods
 Evolutionary strategy
 Genetic algorithm
 Simulated annealing
 Particle swarm optimization
12

13. Dynamic Bayesian Network (DBN)
ODE DBN
……. Et Et+1 Et+2
dS
= −k1.S .E + k 2 .ES …….
dt St+2
St St+1
dE
= −k1.S .E + (k 2 + k3 ).ES
dt
ESt ESt+1 ESt+2
dES
= k1.S .E − (k 2 + k3 ).ES
dt
dP ……. Pt Pt+1 Pt+2
…….
= k3 .ES
dt t t+1 t+2
Liu.et.al [ TCS 2011]
• Discretize time domain into finite time points
• Discretize the value domain of each species
=> Probability distribution
13

14. Validation of the DBN wrt. ODE (Contd)
2.7 1.5
pJAK2 pEpoR
1.8 1
0.9 0.5
0 0
1 21 41 61 81 1 21 41 61 81
actSHP1 mSHP1
12 3.6
8 2.4
4
1.2
0
1 21 41 61 81 0
1 21 41 61 81
14

15. Semantics of DBN
E0 E1 E2
……… Et-1 Et
S0 S1 S2
……… St-1 St
Exponential
Complexity
………
ES0 ES1 ES2 Est-1 ESt
………
P0 P1 P2 Pt-1 Pt
15 Joint at time t-1

16. Pathway Decomposition
Decomposition: Akt/MAPK Pathway
 Decompositional approach
 Treat components one by one in
order to feed the computation to next
steps.
 But: seldom all theoretically valid
fragments are small enough
 => resort to approximation to find
not so bad
experimental decomposition
(Bruno’s work)
HFPN model of the Akt / MAPK pathway (Koh et al 2006)
16

17. Pathway Decomposition
Decomposition
Approximate probability distributions
in 2 different ways.
Best: 2sd way is “more exact”
(that we have).
Assume the similar approx
distributions to be the exact ones
If none, 2 “better” approximations.
Delete the similar approx and
decompose again (less constraints)…
17

18. Conclusion
• Formal models can be helpful in bioinformatics:
Compact representation
Structurally decompose pathway in pieces.
Error Analysis …
High dimension: we need approximations, be pragmatic
=> be optimistic! Believe the fastest will work.
(ODE vs Gillpesie, FF vs HFF vs exact etc)
=> then validation to be sure we don’t do nonsense.
=> if we do nonsense, then work more.

19. Problem: Size = 5^32 states
⇒ Resort to approximated computation and representation.
Ususally: Factored Frontier (FF): all species independant.
New: Hybrid FF, between FF and exact

20. Biological Applications
TLR4 signalling pathway with new components.
Important pathway for the Human immune system
Involved in Sepsis (complex disease,
characterized by whole-body inflammatory response)
Collaboration with
A*STAR/SiGN (Biopolis)
(Groups of Subra Biswas
and of Alexandre Gouaillard)

21. Future?
Medical image not always sufficient to detect accurately pathology
Multimode analysis (tissular, molecular)
Image not always conclusive Molecular information
not always sufficient
⇒ Add molecular information => may need number of cells
with some form, multi modal analysis

22. Near Future?
In between: population of cells
Experimental data = image analysis
Modeling: local forces (cellular automata)
+ biochemical reactions (apopthosis = death of cells)
+ cell division
With P.S. Thiagarajan (NUS) and Gregory Batt (INRIA Rocquencourt)

23. Akt-MAPK Pathway as a Petri Net
Serum
R
1
Ract
For discrete behaviors
DPI
46
NOX5
Rint (few molecules in a cell,
ROS
3
LY294002
2
need to count them 1 by 1)
47
Ras 15 Rasa Pak 48 Pakp PI3K 4 PI3Ka
16 49 5
Leads to stochastic behaviors
17 18 PIP2 6 PIP3 AKTcyto
PTEN 7 (each cell can evolve in 2
Raf Rafp
19 20 PDK1cyto 50
8 9
different ways at random)
21 22 24 25 51 PDK1
PDK2
PIP3.AKT
10
MEK MEKp MEKpp
PIP3.AKTp
23 26 12 11
13
27 29 PIP3.AKTpp 14
ERK ERKp ERKpp
PP2A
Ex: pathogene
28 30
34 35 37 38 evading host response)
Badp112 Badp136 Bax 40 Baxcyto
MKP3
Bad
31 32
36 39 41
Bcl2.Bax
42 44
P90RSK 33 P90RSKp Bcl2.Bad
43 45
Bcl2
23