Modeling MAPK with ODEs and Petri Nets


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

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Modeling MAPK with ODEs and Petri Nets

  1. 1. Dynamic Models:Modeling Cervical Cancer via Notch and JAK-STAT with Petri Nets and ODEs Biafra Ahanonu
  2. 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. 3. Motivation Dynamic models allow discovery of gaps in knowledge or modeling
  4. 4. Motivation How do you decide which part of the pathway to block that produces the best results? Hornberg (2005)
  5. 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. 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. 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. 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. 9. JAK/STAT Pathway 9,10
  10. 10. Notch Pathway 7,8
  11. 11. Model Search literature for pathways  KEGG  Science’s Signal  Papers Convert to Petri Net
  12. 12. Model Create a guide that states exactly how each transition and its places are converted to chemical equations  Simple reactions  More Complex reactions
  13. 13. 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
  14. 14. Model Next, we wish to observe the rate that each chemical reaction changes components
  15. 15. Model Once we have rates for each reaction, we can create ODEs for each component
  16. 16. 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
  17. 17. 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…
  18. 18. Model Decrease initial Notch concentration by 100
  19. 19. Model Stochastic ODEs  Continuously vary the parameters around some set mean
  20. 20. Applications What can we learn from application of the model?  Neumann (2010)  Aguda (2004)  Sasagawa (2005)
  21. 21. Applications Neumann (2010) Models allow you to focus in on critical components
  22. 22. Applications Simulation captures data
  23. 23. Applications Clear sorting of reactions and parameters, replicate
  24. 24. Applications Aguda (2004)
  25. 25. Applications Convert pathway to kinetics  Michaelis-Menten Determine rates associated with each components Conservation Equation  Note, necessity/style (Dr. Hoops) Initial values Rate Constants
  26. 26. Applications Similar to Ferrell (1996) Simulation Experimental
  27. 27. Applications Sasagawa (2005)
  28. 28. Applications Notice, there is not an exact match, but the trends are the same
  29. 29. Applications They could thus conclude by which pathway each growth factor acted and the mechanism
  30. 30. Software Berkeley Madonna COPASI PIPE Gepasi CellDesigner Jdesigner Matlab (dde23) xpp
  31. 31. 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
  32. 32. 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
  33. 33. 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
  34. 34. 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
  35. 35. 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
  36. 36. 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
  37. 37. 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
  38. 38. Report A more detailed discussion of everything in this presentation is included in a report summarizing this project
  39. 39. Useful Links http://www.informatik.uni-