Dynamic Models:Modeling Cervical Cancer via Notch and JAK-STAT
with Petri Nets and ODEs
Biafra Ahanonu
MotivationDynamic models provide a method of viewing
how a system evolves after a perturbationBiological diagrams are static or the system
becomes too complex to make intuitive (qualitative) predictions
Simple?No
MotivationDynamic models allow discovery of gaps in
knowledge or modeling
MotivationHow do you decide which part of the pathway
to block that produces the best results?
Hornberg (2005)
ObjectiveConstruct petri net representations of
pathways from literatureClearly define how common reactions will be
representedConvert transitions into chemical reactionsChemical reactions into reaction ratesReaction rates converted to ordinary
differential equationsQuantitative (stochastic) simulation Modular
OutlineCervical CancerPetri Nets
NotchJAK/STAT
ModelLiterature Applications of the Model
Neumann (2010)Aguda (2004)Sasagawa (2005)
SoftwareConclusionsComments
Cervical CancerCervical Cancer is one of the leading causes
of cancer deaths among females worldwideHPV 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
Cervical CancerJAK/STAT Pathway
Aberrant STAT3/STAT5 signalingNotch Pathway
HPV E6 and E7 protein upregulation of Notch-1Constitutive Notch activations leads to anti-
differentiation and anti-apoptotic behaviour
JAK/STAT Pathway9,10
Notch Pathway7,8
ModelSearch literature for pathways
KEGGScienceβs SignalPapers
Convert to Petri Net
ModelCreate a guide that states exactly how each
transition and its places are converted to chemical equationsSimple reactionsMore Complex reactions
[πΈ1 ]+ [ππππ‘πππ ]β [πΈ1 ]+[ππππ‘πππβπ]
ModelWe are not trying to model detailed
interactionse.g. we could try to model the interaction of
arginine, Mn(II) ions, sulfate, etc. at the Ξ»PP active site
But that would be wasting timePhosphatases, transferases, kinases, etc. act
via different mecanisms at the atomic levelWe are only interested in the rate at which they
change things
ModelNext, we wish to observe the rate that each
chemical reaction changes components
[πΈ 1 ]+ [ππππ‘πππ ]βπ1 [πΈ 1βππππ‘πππ ]βπ2 [πΈ1 ]+[ππππ‘πππβπ ]
ModelOnce we have rates for each reaction, we can
create ODEs for each component
π [πΆπ ]ππ‘
=β π£πππππ’ππ‘πππββ π£ππππ π’πππ‘πππ
π [πΈ1 ]ππ‘
=π£2βπ£1=π2 [πΈ1βππππ‘πππ]βπ1 [πΈ1 ] [ππππ‘πππ ]+πβ 1 [πΈ1βππππ‘πππ ]
ModelWe now need to find the rate constantsRate 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
ModelDynamic model is then producedA 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 emergesβ¦
ModelDecrease initial Notch concentration by 100
ModelStochastic ODEs
Continuously vary the parameters around some set mean
ApplicationsWhat can we learn from application of the
model?Neumann (2010)Aguda (2004)Sasagawa (2005)
ApplicationsNeumann (2010)Models allow you to focus in on critical
components
ApplicationsSimulation captures data
ApplicationsClear sorting of reactions and parameters,
replicate
ApplicationsAguda (2004)
ApplicationsConvert pathway to
kineticsMichaelis-Menten
Determine rates associated with each components
Conservation EquationNote, necessity/style (Dr.
Hoops)Initial valuesRate Constants
ApplicationsSimilar to Ferrell (1996)
Simulation Experimental
ApplicationsSasagawa (2005)
ApplicationsNotice, there is not an exact match, but the
trends are the same
ApplicationsThey could thus
conclude by which pathway each growth factor acted and the mechanism
SoftwareBerkeley MadonnaCOPASIPIPEGepasiCellDesignerJdesignerMatlab (dde23)xpp
SoftwareCOPASI
Overview: Input chemical equations, rate constants and initial concentrations to yield ODEs and simulations
Advantage: Quick and interface is easyDisadvantage: Simulation is not reliable, unsure
about mass conservationGepasi
Overview: Same as COPASIAdvantage: Relatively quick and not much
clutterDisadvantage: Not as many options, flaky
simulator
SoftwareBerkeley 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
PIPEOverview: Creation of petri netsAdvantage: Quick and painlessDisadvantage: Limited options, canβt give more
than one place the same name, crashes, those pesky 1s
SoftwareCellDesigner
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
JdesignerOverview: Diagram pathways, input kinetic equations,
simulateAdvantage: Easy to use and allows simulationDisadvantage: Can have at most three reactants per
reaction, diagrams are vague
SoftwareMatlab (dde23)
Overview: Simulate (time delayed) ODEsAdvantage: Matlab is widely used, has a time-
delay ODE solver (package)Disadvantage: Requires some coding
knowledge, GUI is not human friendlyxpp
Overview: Solve time delayed ODEsAdvantage: Solves ODEsDisadvantage: GUI not human friendly
ConclusionsDynamic models allow us to view how a
system evolvesWe can test mechanics of a pathway as well
as parameter valuesRatio between, say, concentrations may be
importantTime-delayed ODEs are strongly
recommendedCapture true behaviour of biological systems
Direct construction of ODEs from pathway may be recommended
ConclusionsPetri nets are unambiguous graphical
representationsEasily convertible to ODEsNotch and JAK-STAT are reasonable pathways
to model to test the methadologyCervical cancer can be induced by aberrant
signaling of these pathwaysWe should be able to model the pathways and
then tweak various parts of the model to find parameters with the highest sensitivity
CommentsSpecify exactly what you want from a model
beforehandLook in literature to get an estimate of a
range of plausible valuesDo not make a model just to fit the data,
make a model to test out a mechanistic theory
ReportA more detailed discussion of everything in
this presentation is included in a report summarizing this project
Useful Linkshttp://www.ebi.ac.uk/biomodels-main/http://www.jjj.bio.vu.nl/database/index.htmlhttp://www.brc.dcs.gla.ac.uk/http://www.gepasi.org/gep3dwld.htmlhttp://www.informatik.uni-hamburg.de/TGI/Pet
riNets/
http://www.informatik.uni-hamburg.de/TGI/PetriNets/tools/quick.html
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