Results of a brief study to model MAPK pathway with ODEs and Petri Nets.

1. Dynamic Models:
Modeling Cervical Cancer via Notch and JAK-STAT with Petri
Nets and ODEs
Biafra Ahanonu

2. Motivation
 Dynamic models provide a method of viewing how a
system evolves after a perturbation
 Biological diagrams are static or the system
becomes too complex to make intuitive (qualitative)
predictions
 Simple?
 No

3. Motivation
 Dynamic models allow discovery of gaps in
knowledge or modeling

4. Motivation
 How do you decide which part of the pathway to
block that produces the best results?
Hornberg
(2005)

5. Objective
 Construct petri net representations of pathways from
literature
 Clearly define how common reactions will be
represented
 Convert transitions into chemical reactions
 Chemical reactions into reaction rates
 Reaction rates converted to ordinary differential
equations
 Quantitative (stochastic) simulation
 Modular

6. Outline
 Cervical Cancer
 Petri Nets
 Notch
 JAK/STAT
 Model
 Literature Applications of the Model
 Neumann (2010)
 Aguda (2004)
 Sasagawa (2005)
 Software
 Conclusions
 Comments

7. Cervical Cancer
 Cervical Cancer is one of the leading causes of
cancer deaths among females worldwide
 HPV is present in 99% of cases
 Why does cervical cancer occur? How is HPV
implicated it is onset?
 Notch and JAK-STAT pathways have been seen to
promote cervical tumor growth
 Model these pathways to study how and where
interference can prevent oncogenic activity

8. Cervical Cancer
 JAK/STAT Pathway
 Aberrant STAT3/STAT5 signaling
 Notch Pathway
 HPV E6 and E7 protein upregulation of Notch-1
 Constitutive Notch activations leads to anti-
differentiation and anti-apoptotic behaviour

9. JAK/STAT Pathway 9,10

10. Notch Pathway 7,8

12. Model
 Search literature for pathways
 KEGG
 Science’s Signal
 Papers
 Convert to Petri Net

13. Model
 Create a guide that states exactly how each
transition and its places are converted to chemical
equations
 Simple reactions
 More Complex reactions

14. Model
 We are not trying to model detailed interactions
 e.g. we could try to model the interaction of arginine,
Mn(II) ions, sulfate, etc. at the λPP active site
 But that would be wasting time
 Phosphatases, transferases, kinases, etc. act via
different mecanisms at the atomic level
 We are only interested in the rate at which they
change things

15. Model
 Next, we wish to observe the rate that each chemical
reaction changes components

16. Model
 Once we have rates for each reaction, we can create
ODEs for each component

17. Model
 We now need to find the rate constants
 Rate constants are sometimes hard to obtain
 In the literature they are also in different units and
some use disassociation, rate or other constants
 Possible to estimate parameters; it has been found
that many biological systems allow for order of
magnitude parameter value changes before it affects
the system

18. Model
 Dynamic model is then produced
 A steady state basically means that there is no net
change in the amount of some molecule
 A stable model is one in which the components do
not blow-up to infinity
 (Maybe) Interesting behaviour emerges…

19. Model
 Decrease initial Notch concentration by 100

20. Model
 Stochastic ODEs
 Continuously vary the parameters around some set
mean

21. Applications
 What can we learn from application of the model?
 Neumann (2010)
 Aguda (2004)
 Sasagawa (2005)

22. Applications
 Neumann (2010)
 Models allow you to focus in on critical components

23. Applications
 Simulation captures data

24. Applications
 Clear sorting of reactions and parameters, replicate

25. Applications
 Aguda (2004)

26. Applications
 Convert pathway to kinetics
 Michaelis-Menten
 Determine rates associated
with each components
 Conservation Equation
 Note, necessity/style (Dr.
Hoops)
 Initial values
 Rate Constants

27. Applications
 Similar to Ferrell (1996)
Simulation Experimental

28. Applications
 Sasagawa (2005)

29. Applications
 Notice, there is not an exact match, but the trends
are the same

30. Applications
 They could thus conclude
by which pathway each
growth factor acted and
the mechanism

31. Software
 Berkeley Madonna
 COPASI
 PIPE
 Gepasi
 CellDesigner
 Jdesigner
 Matlab (dde23)
 xpp

32. Software
 COPASI
 Overview: Input chemical equations, rate constants
and initial concentrations to yield ODEs and
simulations
 Advantage: Quick and interface is easy
 Disadvantage: Simulation is not reliable, unsure about
mass conservation
 Gepasi
 Overview: Same as COPASI
 Advantage: Relatively quick and not much clutter
 Disadvantage: Not as many options, flaky simulator

33. Software
 Berkeley Madonna
 Overview: Numerical solutions to systems of ODEs
 Advantage: Quick and options for parameter
variation, time delayed and stochastic ODEs
 Disadvantage: Some knowledge of code required
 PIPE
 Overview: Creation of petri nets
 Advantage: Quick and painless
 Disadvantage: Limited options, can’t give more than
one place the same name, crashes, those pesky 1s

34. Software
 CellDesigner
 Overview: Diagram pathway, input kinetic equations,
simulate
 Advantage: Allows a start to finish approach from pathway
model construction to simulation
 Disadvantage: Pathways are not easily readable,
trustworthiness of simulations
 Jdesigner
 Overview: Diagram pathways, input kinetic equations,
simulate
 Advantage: Easy to use and allows simulation
 Disadvantage: Can have at most three reactants per
reaction, diagrams are vague

35. Software
 Matlab (dde23)
 Overview: Simulate (time delayed) ODEs
 Advantage: Matlab is widely used, has a time-delay
ODE solver (package)
 Disadvantage: Requires some coding knowledge, GUI
is not human friendly
 xpp
 Overview: Solve time delayed ODEs
 Advantage: Solves ODEs
 Disadvantage: GUI not human friendly

36. Conclusions
 Dynamic models allow us to view how a system
evolves
 We can test mechanics of a pathway as well as
parameter values
 Ratio between, say, concentrations may be important
 Time-delayed ODEs are strongly recommended
 Capture true behaviour of biological systems
 Direct construction of ODEs from pathway may be
recommended

37. Conclusions
 Petri nets are unambiguous graphical
representations
 Easily convertible to ODEs
 Notch and JAK-STAT are reasonable pathways to
model to test the methadology
 Cervical cancer can be induced by aberrant
signaling of these pathways
 We should be able to model the pathways and then
tweak various parts of the model to find parameters
with the highest sensitivity

38. Comments
 Specify exactly what you want from a model
beforehand
 Look in literature to get an estimate of a range of
plausible values
 Do not make a model just to fit the data, make a
model to test out a mechanistic theory

39. Report
 A more detailed discussion of everything in this
presentation is included in a report summarizing this
project

40. Useful Links
 http://www.ebi.ac.uk/biomodels-main/
 http://www.jjj.bio.vu.nl/database/index.html
 http://www.brc.dcs.gla.ac.uk/
 http://www.gepasi.org/gep3dwld.html
 http://www.informatik.uni-hamburg.de/TGI/PetriNets/
 http://www.informatik.uni-
hamburg.de/TGI/PetriNets/tools/quick.html