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Discovery and Assesment of New Target Sites for Anti-HIV
TherapiesProblem given by:
Sanjive Qazi, Gustavus Adolphus College, U.S.A.
Working group:Chris Breward, Math. Inst., University of Oxford,
U.K.Jane Heffernan, York University, Canada.Robert M. Miura, New
Jersey Institute of Technology, U.S.A.Neal Madras, York University,
Canada.John Ockendon, OCIAM Math. Inst. , University of Oxford,
U.K.Mads Peter Srensen, DTU Mathematics, Tech. Univ. of Denmark.Bob
Anderssen, CSIRO, Mathematical and Information Sciences,
Australia.Roderick Melnik, Wilfrid Laurier University, Canada.Mark
McGuinness, Victoria University, New Zealand.
Fields-MITACS Industrial Problem-Solving WorkshopAugust 11 15,
2008
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IntroductionThe HIV viruses infect cells by endocytosis and
takes over parts of the cells reaction pathways in order to
reproduce itself and spread the infection.
One such pathway is the mammalian inflammatory signaling, which
invoke NF-B as the principal transcription factor.
A treatment against HIV could be based on blocking the NF-B
pathway by a suitably designed drug.
The aim of the current project is to investigate the feasibility
of this idea by using mathematical modelling of the NF-B
pathway.
Fields-MITACS Industrial Problem-Solving WorkshopAugust 11 15,
2008
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Outline
Cartoon model of the inflammatory pathway. How HIV attacks
mammalian cells through e.g. TNF signalling. The role of IKK and
the TNF receptor in the cell membrane. Mathematical model of the
NF-B pathway. The role of IKK signaling. Fixed points and
stability. Numerical examples. Extended mathematical model. Fixed
points and stability. Numerical examples. Outlook and further
work.
Fields-MITACS Industrial Problem-Solving WorkshopAugust 11 15,
2008
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*HIV Life Cycle
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*Drug Therapy
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Cartoon of the NF-B pathwayFields-MITACS Industrial
Problem-Solving WorkshopAugust 11 15, 2008
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Reaction scheme
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Mathematical descriptionUse law of mass action for each of the
reactionsAssume constant concentration of D, and combine with
k5
We get An after the fact from A=A*-Ac-AB
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Mathematical descriptionParameter values come from literature
(means that someone else guessed them!)
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*Steady StateHas unique physical fixed point for all positive
parameter values.Stable at given parameter values (in general:
Jacobian at fixed point has positive determinant, negative trace,
no positive real eigenvalues).
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*Numerics
k5=02k5
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*Numerics
2k5 k5=0
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Cartoon number 2 of the NF-B pathway
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Modified reaction scheme
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Modified reaction scheme contd
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Mathematical descriptionUse law of mass action for each of the
reactions
Concentration of TNF is rolled up into k6
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Mathematical description
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Steady states and stability
Has unique physical fixed point for the given parameter values,
as well as for all smaller (nonnegative) values of k6) and k5).
Stable at given parameter values (other values not checked).
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*Numerics
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*Numerics
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*Numerics
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*Future Work27 variable modelSystematic reduction to see if it
corresponds with our 7 variable modelControl modelConsider problem
as optimal control with mu and lambda as the control
parametersUnclear what to minimizeSensitivity analysisVary
rates
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Reference: Cheong et.al. Understanding NF-B signaling via
mathematical modeling, Molecular Sytems Biology 4:192,
2008.Fields-MITACS Industrial Problem-Solving WorkshopAugust 11 15,
2008Reference: Krishna et.al. Minimal model of spiky oscillations
in NF-B signaling, PNAS 103(29), 10840-10845, 2006.
Reference: Chan et.al. Quantitative ianalysis of human
immunodeficiency virus type 1-infected CD4+ cell proteome: Journal
of Virology, 7571-7583, 2007.
Reference: Lipniacki et.al. Mathematical model of NF-B
regulatory module, Journal of Theoretcal Biology 228, 195-215,
2004.
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Summary and outlookHIV viruses take over host cellular pathways
for their reproduction. One such pathway is the NF-B pathway.
Cartoon modeling of the NF-B pathway.
Mathematical modeling for clearifying the underlying regulatory
pathway dynamics and hopefully summarizing abundant experimental
observations.
Mathematical modling as a tool for rational guided drug
targeting.
Extended complex models and mode reduction of bio chemical
complexity. Fields-MITACS Industrial Problem-Solving WorkshopAugust
11 15, 2008
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