1 / 24

Discovery and Assesment of New Target Sites for Anti-HIV Therapies

Discovery and Assesment of New Target Sites for Anti-HIV Therapies. Problem 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.

johnmmoore
Download Presentation

Discovery and Assesment of New Target Sites for Anti-HIV Therapies

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Discovery and Assesment of New Target Sites for Anti-HIV Therapies Problem 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 Sørensen, 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 Workshop August 11 – 15, 2008

  2. Introduction The HIV virusesinfectcells by endocytosis and takes over parts of the cellsreactionpathwaysin order to reproduceitself and spread the infection. One suchpathway is the mammalianinflammatorysignaling, whichinvoke NF-κB as the principal transcription factor. A treatmentagainst HIV couldbebasedonblocking the NF-κB pathwayby a suitablydesigned drug. The aim of the currentproject is to investigate the feasibility of thisidea by usingmathematicalmodelling of the NF-κB pathway. Fields-MITACS Industrial Problem-Solving Workshop August 11 – 15, 2008

  3. 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-κB 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 Workshop August 11 – 15, 2008

  4. HIV Protease Fusion Reverse Transcriptase Viral RNA Viral RNA Transcribed to DNA RNA + Viral Proteins Released Viral DNA Incorporated Into Host Genome New Proteins from Viral DNA CD4 receptor Budding of New Virion Protease Enables Capsid Assembly CD4 T-cell HIV Life Cycle

  5. HIV Protease Fusion Reverse Transcriptase Viral RNA Viral RNA Transcribed to DNA RNA + Viral Proteins Released Viral DNA Incorporated Into Host Genome New Proteins from Viral DNA CD4r Budding of New Virion Protease Enables Capsid Assembly CD4 T-cell Drug Therapy

  6. Cartoon of the NF-κB pathway Fields-MITACS Industrial Problem-Solving Workshop August 11 – 15, 2008

  7. Reaction scheme

  8. Mathematicaldescription Use law of mass action for each of the reactions Assume constant concentration of D, and combine with k5 We get An after the fact from A=A*-Ac-AB

  9. Mathematicaldescription Parameter values come from literature (means that someone else guessed them!)

  10. Steady State Has 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).

  11. Numerics k5=0 2k5

  12. Numerics k5=0 2k5

  13. Cartoonnumber 2 of the NF-κB pathway

  14. Modifiedreactionscheme

  15. Modified reaction scheme cont’d

  16. Mathematicaldescription Use law of mass action for each of the reactions Concentration of TNF is rolled up into k6

  17. Mathematicaldescription

  18. Steadystates 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).

  19. Numerics

  20. Numerics

  21. Numerics

  22. Future Work 27 variable model Systematic reduction to see if it corresponds with our 7 variable model Control model Consider problem as optimal control with mu and lambda as the control parameters Unclear what to minimize Sensitivity analysis Vary rates

  23. Reference: Krishna et.al. Minimal model of spiky oscillations in NF-κB signaling, PNAS 103(29), 10840-10845, 2006. Reference: Chanet.al. Quantitativeianalysis of human immunodeficiency virus type 1-infected CD4+ cellproteome: … Journal of Virology, 7571-7583, 2007. Reference: Lipniackiet.al. Mathematical model of NF-κB regulatorymodule, Journal of TheoretcalBiology 228, 195-215, 2004. Reference: Cheonget.al. Understanding NF-κB signaling via mathematicalmodeling, MolecularSytemsBiology 4:192, 2008. Fields-MITACS Industrial Problem-Solving Workshop August 11 – 15, 2008

  24. Summary and outlook HIV viruses take over host cellular pathways for their reproduction. One such pathway is the NF-κB pathway. Cartoon modeling of the NF-κB 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 Workshop August 11 – 15, 2008

More Related