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

KEGGScience’s 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

[𝐸1 ]+ [𝑃𝑟𝑜𝑡𝑒𝑖𝑛 ]→ [𝐸1 ]+[𝑃𝑟𝑜𝑡𝑒𝑖𝑛−𝑝]

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 λPP 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

[𝐸 1 ]+ [𝑃𝑟𝑜𝑡𝑒𝑖𝑛 ]⇌𝑘1 [𝐸 1∗𝑃𝑟𝑜𝑡𝑒𝑖𝑛 ]→𝑘2 [𝐸1 ]+[𝑃𝑟𝑜𝑡𝑒𝑖𝑛−𝑝 ]

ModelOnce we have rates for each reaction, we can

create ODEs for each component

𝑑 [𝐶𝑖 ]𝑑𝑡

=∑ 𝑣𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛−∑ 𝑣𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛

𝑑 [𝐸1 ]𝑑𝑡

=𝑣2−𝑣1=𝑘2 [𝐸1∗𝑃𝑟𝑜𝑡𝑒𝑖𝑛]−𝑘1 [𝐸1 ] [𝑃𝑟𝑜𝑡𝑒𝑖𝑛 ]+𝑘− 1 [𝐸1∗𝑃𝑟𝑜𝑡𝑒𝑖𝑛 ]

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 emerges…

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, can’t 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