HIV/AIDS: How Mathematics Has Saved Lives

1. HIV/AIDS: How Mathematics HasSaved Lives Alan S. Perelson, PhD Theoretical Biology & BiophysicsLos Alamos National LaboratoryLos Alamos, NM asp@lanl.gov

2. People living with HIV (2005) TOTAL: 40.3 (36.7–45.3) million

3. Deaths resulting from HIV (2005) TOTAL: 3.1 (2.8–3.6) million

4. New infections with HIV (2005) TOTAL: 4.9 (4.3–6.6) million

5. Mathematics entered the field

6. No treatment

7. Drug Therapy • Medical: a means of interfering with viral replication – treat or cure disease • Mathematical: a means of perturbing a system and uncovering its dynamics

10. Model of HIV Infection k Infection Rate pVirions/d T* T Productively Infected Cell Target Cell c d Death Clearance

12. Model of HIV Infection Parameters Variables

13. Model Used for Drug Perturbation Studies Drug efficacy eRTePI Subscripts: “I”: infectious “NI”: non-infectious From HIV-Dynamics in Vivo: …, Perelson, et al, Science, 1996

14. Solution of Model Equations Assuming 100% Efficacy of Protease Inhibitor Therapy Solution has two parameters: c – clearance rate of virus d – death rate of infected cells

15. HIV-1: FirstPhase Kinetics Perelson et al. Science 271, 1582 1996

18. - 1 hr 1010 to 1012 virions/d from 107 to 109 T cells

19. Implications • HIV infection is not a slow process • Virus replicates rapidly and is cleared rapidly – can compute to maintain set point level > 1010 virions produced/day • Cells infected by HIV are killed rapidly • Rapid replication implies HIV can mutate and become drug resistant

21. Combination therapy

22. HIV-1: Two Phase KineticsCombination Therapy Perelson et al. Nature 387, 186 (1997)

23. Perelson & Ho, Nature 1997

24. HIV-1: Two Phase Kinetics Perelson et al. Nature 387, 186 (1997)

27. Basic Biology of HIV-1 In Vivo Revealed by Modeling Contribution to viral load >1010/day 93-99% 1-7% t1/2 < 1 hr 0.7 d 14 d Virions: Infected T cells: Infected long-lived cells: < 1 % Latently infected T cells: months - years

28. Implications • Due to long-lived infected cell populations, would need to treat HIV infected individuals for many years with 100% effective drugs to eradicate the virus. Initial estimates were 3-4 years of treatment, new estimates at least 10 years. • But, do not have 100% effective therapy

29. Is eradication possible? • Not known. Current therapy may not stop all ongoing replication, so viral reservoirs such as long-lived cells and latently infected cells may constantly be regenerated. • Recent reports show massive early infection in gut associated lymphoid tissue – 50-80% of CD4+ cells killed in these tissues in the first weeks of infection. Both “resting” and activated cells are infected. • Spatial models and meta-population models needed. Replication may only be occurring in some locals, e.g., “drug sanctuaries”.

30. Summary • Modeling has been used to analyze the many possible sources of HIV • What was once thought to be a a simple “slow” infection has now been shown to involve at least 4 time scales: • Clearance of free virus ~ 1 hr • Lifespan of virus producing CD4+ T cells ~ 1 day • Lifespan of long-lived infected cells ~ a few weeks • Lifespan of latently infected cells ~ between 6 - 44 months • Modeling also helped reveal the in vivo relative efficacy of drug regimes and the need for combination therapy.

31. Vaccines for HIV

32. Cytotoxic T Lymphocytes CTLs can kill virus-infected cells. Here, a CTL (arrow) is attacking and killing a much larger influenza virus-infected target cell. http://www.cellsalive.com/

33. “CTL inducing” vaccine Barouch et al. Science290, 486-492 (2000)

34. Viral Kinetics Controls (die) Viral load Vaccinees (live) Barouch et al Science 290, 486-492 (2000) day

35. What about Cytotoxic T Lymphocyte (CTL) kinetics? CTL are a type of CD8+ T cell In these experiments the number of HIV specific CD8 cells was measured.

36. CD8 response to HIV About 10x higher at peak Vaccinees controls

37. We expect a vaccine to prevent infection • A vaccine should create ‘memory’ T cells • The memory cells should respond earlier and faster than ‘naïve’ T cells • THIS IS NOT OCCURRING HERE

38. Vaccinees controls No increase in CTL numbers in vaccinees prior to day 10

39. Viral Kinetics Controls Viral load Vaccinees day No difference in viral kinetics up to day 10

40. Vaccinees controls 0.73 ± 0.22 day-1 0.94 ± 0.22 day-1 No significant difference in CTL growth rates between controls and vaccinees.

41. Abdel-Motal et al. Virol. 333: 226 (2005) V V V CTL

42. Why is there a delay in CTL expansion? • May be due to intrinsic delay in getting enough infection and antigen presentation to stimulate a response Is this delay the reason that this vaccine does not protect against infection?

43. Non-sterilizingvaccines Viralload time Viral load reducing Progression slowing Barouch et al, Science, 290, pp486-492 (2000) (figure 3c)

44. Benefits Vaccinated individuals, if infected live longer Lower viral loads, thus less likely to transmit infection Risks Continued infections Increased sexual risk behavior Viral ‘escape’ and transmission Loss of vaccine effect What’s the impact of such vaccines?

45. No treatment

46. Unresolved Problems • What causes T cell depletion? • What determines the 10 year timescale? • What determines the setpoint? • Are immune responses important in protection against HIV? • Can we develop a vaccine or a cure for HIV infection?

47. Collaborators • David Ho – Aaron Diamond AIDS Research Center, Rockefeller • Miles Davenport, UNSW • Ruy Ribeiro, LANL • Many students, postdocs at LANL: A. Neumann, D. Callaway, L. Jones, L. Rong, T. Reluga, …