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Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
Mathematical models of CD8 T cell responses: measuring CD8 T ...
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  • 1. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Mathematical models of CD8 T cell responses: measuring CD8 T cell mediated killing in vivo Vitaly V. Ganusov Los Alamos National Laboratory Los Alamos, NM, USA 1 / 55
  • 2. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Outline 1 Immunology 101 Immune system 2 Killing in acute viral infections Experimental details Model 3 Killing in chronic viral infections Problem Experiments and Analysis Conclusions 4 Appendix I LCMV infection 5 Appendix II PyV infection 6 Extra Pictures 2 / 55
  • 3. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Outline 1 Immunology 101 Immune system 2 Killing in acute viral infections Experimental details Model 3 Killing in chronic viral infections Problem Experiments and Analysis Conclusions 4 Appendix I LCMV infection 5 Appendix II PyV infection 6 Extra Pictures 3 / 55
  • 4. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Focus of this talk: CD8 T cells CD8+ T cells (T-killers, Cytotoxic T Lymphocytes (CTLs)) have the major function to kill virus-infected cells. CD8 T cells recognize viral antigens (epitopes) that are presented on the surface of infected cells. 4 / 55
  • 5. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Killing by CD8 T cells in vivo Killing in vivo Mempel et al Immunity 2006 5 / 55
  • 6. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra CD8 T cells and viral clearance LCMV Armstrong LCMV clone 13 107 107 NP396 NP396 106 106 populations populations 105 105 104 CD8 cells spleen 104 viral load, PFU ml 103 103 2 CD8 cells spleen 10 102 viral load, PFU ml 1 1 10 10 0 20 40 60 80 0 20 40 60 80 time, days time, days 6 / 55
  • 7. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Topics to discuss Acute viral infections: quantifying cytotoxic efficacy of CD8 T cells in vivo Chronic viral infections: is failure to clear chronic infection due to inefficient CD8 T cell response? 7 / 55
  • 8. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Outline 1 Immunology 101 Immune system 2 Killing in acute viral infections Experimental details Model 3 Killing in chronic viral infections Problem Experiments and Analysis Conclusions 4 Appendix I LCMV infection 5 Appendix II PyV infection 6 Extra Pictures 8 / 55
  • 9. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Measuring effector functions of CD8+ T cells Most of effector functions of T cells are currently measured ex vivo or after cell culturing in vitro. Effector functions in vivo and ex vivo can differ. We propose a quantitative framework for estimation of killing efficacy of T cells based on the in vivo cytotoxicity assay. Barber et al. JI 2003 9 / 55
  • 10. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Spleen Some details Spleen is a secondary lymphoid organ. Lymphocytes enter and leave spleen via blood. T cell responses take place in the white pulp of the spleen (which is only 10 to 20% of whole spleen). 10 / 55
  • 11. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Spleen Some details Spleen is a secondary lymphoid organ. Lymphocytes enter and leave spleen via blood. T cell responses take place in the white pulp of the spleen (which is only 10 to 20% of whole spleen). 10 / 55
  • 12. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Measuring killing in vivo Target cells (splenocytes) are labeled with different concentrations of CFSE. A subpopulation of target cells is pulsed with a peptide (to which CD8 T cells are specific). Pulsed and unpulsed target cells are transferred into new syngenic host (generally i.v.) harboring epitope-specific CD8 T cells. Killing is measured by the reduction in the ratio of peptide-pulsed to unpulsed percent of pulsed targets (generally in the spleen). Barber et al. JI 2003; Regoes et al. PNAS 2007 11 / 55
  • 13. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Measuring killing in vivo: FACS Ratio of pulsed to unpulsed R = 0.15/0.84 : 44.7/54.5 ≈ 0.22 Percent cells killed L = 1 − R = 78% Ingulli Meth Mol Biol 2007 12 / 55
  • 14. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Measuring killing in mice infected with LCMV Setup Three target cell populations were transferred into mice infected 8 days (or 30 to 100 days) previously with LCMV-Arm: unpulsed, cells pulsed with NP396 and GP276 epitopes of LCMV. Killing was measured in the spleen in several time points. Barber et al. JI 2003 13 / 55
  • 15. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Measuring killing in mice infected with LCMV Setup Three target cell populations were transferred into mice infected 8 days (or 30 to 100 days) previously with LCMV-Arm: unpulsed, cells pulsed with NP396 and GP276 epitopes of LCMV. Killing was measured in the spleen in several time points. Barber et al. JI 2003 13 / 55
  • 16. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Research questions For the data of Barber et al. 2003 What are the half-life times of peptide-pulsed targets in acutely infected and LCMV-immune mice? How does the death rate of targets scale with the magnitude of the CD8 T cell response? What are the per capita efficacy of memory and effector CD8 T cells at killing peptide-pulsed targets? Ganusov and De Boer J Virol (2008); Ganusov et al. (in prep) 14 / 55
  • 17. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Complied Data 106 NP396 pulsed unpulsed acute 100 memory unpulsed spleen 1 10 5 10 2 acute 10 memory 3 10 104 0 50 100 150 200 250 0 50 100 150 200 250 min min Barber et al. JI 2003; Regoes et al. PNAS 2007 15 / 55
  • 18. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Recruitment of unpulsed targets into spleen where SB (0) = 5 × 106 cells and S(0) = 0. 16 / 55
  • 19. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Recruitment of unpulsed targets into spleen dSB (t) = −(δ + σ + )SB (t), dt dS(t) = σSB (t) − S(t). dt where SB (0) = 5 × 106 cells and S(0) = 0. 16 / 55
  • 20. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Killing of peptide-pulsed targets in the spleen where similarly, TB (0) = 5 × 106 cells and T (0) = 0, and K is the death rate of peptide-pulsed targets. 17 / 55
  • 21. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Killing of peptide-pulsed targets in the spleen dTB (t) = −(δ + σ + )TB (t), dt dT (t) = σTB (t) − ( + K)T (t). dt where similarly, TB (0) = 5 × 106 cells and T (0) = 0, and K is the death rate of peptide-pulsed targets. 17 / 55
  • 22. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Predictions on dynamics of target cells c S(t) = e− t − e−dt , d− T (t) (d − ) e−dt − e−( +K)t R(t) = = , S(t) ( + K − d) e− t − e−dt where d = δ + + σ is the rate of cell removal from the blood, and c = SB (0)σ is the initial rate of migration of cells into the spleen. 18 / 55
  • 23. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Predictions on dynamics of target cells c S(t) = e− t − e−dt , d− T (t) (d − ) e−dt − e−( +K)t R(t) = = , S(t) ( + K − d) e− t − e−dt where d = δ + + σ is the rate of cell removal from the blood, and c = SB (0)σ is the initial rate of migration of cells into the spleen. 2.5 d 0.02 100 d 0.02 c 5000 cells spleen, 105 Ε 0 pulsed unpulsed 2 1 10 1.5 2 10 1 Ε 0 K 0.01 0.005 3 K 0.08 0.5 Ε 10 Ε 0.01 K 0.2 0 4 K 1 10 0 50 100 150 200 0 50 100 150 200 time, min time, min 18 / 55
  • 24. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Fits of the model to data: killing killing of NP396-pulsed targets 100 acute NP396 100 memory NP396 pulsed unpulsed pulsed unpulsed 1 10 2 10 1 10 3 10 0 50 100 150 200 250 0 50 100 150 200 250 min min killing of GP276-pulsed targets 100 acute GP276 100 memory GP276 pulsed unpulsed pulsed unpulsed 1 10 2 10 1 10 3 10 0 50 100 150 200 250 0 50 100 150 200 250 min min 19 / 55
  • 25. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Fits of the model to data: recruitment acute memory acute memory 106 106 unpulsed spleen unpulsed spleen 105 105 104 104 0 50 100 150 200 250 0 50 100 150 200 250 min min 20 / 55
  • 26. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Robust quantitative results Half-life times of pulsed targets T1/2 = 2 and 14 minutes for NP396 and GP276-pulsed targets in acutely infected mice. T1/2 = 48 minutes and 2.9 hour for NP396 and GP276-pulsed targets in memory mice. Ganusov and De Boer J Virol (2008) 21 / 55
  • 27. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Robust quantitative results Half-life times of pulsed targets T1/2 = 2 and 14 minutes for NP396 and GP276-pulsed targets in acutely infected mice. T1/2 = 48 minutes and 2.9 hour for NP396 and GP276-pulsed targets in memory mice. Recruitment rate of recruitment of targets into the spleen is proportional to the spleen size. Ganusov and De Boer J Virol (2008) 21 / 55
  • 28. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Specific (testable) predictions of the model The model predicts a relatively slow removal of cells from the blood (T1/2 ≈ 2 h). This allows for the biphasic decline in the ratio of pulsed to unpulsed targets. In the model, due to a rapid preparation-induced cell death, only 2 × 105 targets (or less than 5% of injected cells) are able to migrate to other tissues (beside spleen). About 9% of injected splenocytes are predicted to home to the spleen in 24 hours. Ganusov and De Boer J Virol 2008 22 / 55
  • 29. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Estimating the per capita killing efficacy Death rate K and CD8 T cell numbers K = kEi (mass-action) kEi K = (saturation in E) 1 + cE Ei kEi K = (decrease with T) 1 + cT T i kEi K = (E/T ratio) E i + cT T i where Ei and Ti is the frequency of effector and target cells in the spleen, respectively. 23 / 55
  • 30. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Additional (adoptive transfer) experiments Prediction If killing follows the law of mass-action, estimated death rate of targets should be proportional to the density of antigen-specific CD8 T cells. 24 / 55
  • 31. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Death rate vs. CD8 T cell density A B death rate K, 1 min death rate K, 1 min NP396 NP396 GP276 GP276 1 GP33 1 GP33 10 10 2 10 10 2 3 10 3 10 10 1 100 105 106 107 % of epitope specific CD8 T cells # of epitope specific CD8 T cells Results: Linear regression suggests that K = kE 1 . Ganusov et al. (in prep) 25 / 55
  • 32. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Per capita killing vs CD8 T cell density A 6 B 5 NP396 NP396 cell min GP276 GP276 5 GP33 4 GP33 K E, 1 min 4 3 3 8 2 K E, 10 2 1 1 0 0 10 1 100 105 106 107 % of epitope specific CD8 T cells # of epitope specific CD8 T cells Results: Killing is simply proportional to the frequency (or number) of antigen-specific CD8 T cells in the spleen. The average killing efficacy of CD8+ T cells is 2.33 min−1 (panel A) or 2.62 × 10−8 cell−1 min−1 (panel B). Ganusov et al. (in prep) 26 / 55
  • 33. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Does this all make sense? Results: We found that LCMV-specific CD8 T cells rapidly clear peptide-pulsed targets from the spleen. NP396-specific effectors kill half of the targets in 2 minutes. The death rate of targets is roughly independent of the T cell specificity and simply proportional to the magnitude of the antigen-specific CD8 T cell response. 27 / 55
  • 34. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Does this all make sense? Results: We found that LCMV-specific CD8 T cells rapidly clear peptide-pulsed targets from the spleen. NP396-specific effectors kill half of the targets in 2 minutes. The death rate of targets is roughly independent of the T cell specificity and simply proportional to the magnitude of the antigen-specific CD8 T cell response. Problems with results: In vitro and in vivo studies found that it takes 10-60 minutes for CD8 T cell to kill a target cell which seems to be incompartible with the 2 min half-life estimated. Given 10-15 min handeling time for the kill, how can the estimated death rate of targets be simply proportional to the density of T cells? 27 / 55
  • 35. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Outline 1 Immunology 101 Immune system 2 Killing in acute viral infections Experimental details Model 3 Killing in chronic viral infections Problem Experiments and Analysis Conclusions 4 Appendix I LCMV infection 5 Appendix II PyV infection 6 Extra Pictures 28 / 55
  • 36. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Chronic viral infections LCMV Armstrong LCMV Clone 13 107 107 NP396 NP396 106 106 populations populations 105 105 4 10 CD8 cells spleen 104 viral load, PFU ml 3 10 103 CD8 cells spleen 102 102 viral load, PFU ml 101 101 0 20 40 60 80 0 20 40 60 80 time, days time, days Problems: How can viruses establish a state of persistent infection? 29 / 55
  • 37. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra How can viruses establish a persistent infection? Immune response is efficient (on per cell basis) but small. Immune response is large but inefficient On per cell basis, killing is impaired (e.g., IL-10 production by virus-infected cells) Killing of virus-infected cells is inefficient (e.g., latency)? 30 / 55
  • 38. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Acute vs. chronic LCMV Conclusion: During LCMV infection, effector to target ratio determines the outcome of infection (clearance vs. persistence). It is unknown, however, if the functionality of LCMV-specific CD8 T cells is also impaired during the acute phase of LCMV clone 13 infection. 31 / 55
  • 39. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Chronic infection with Polyoma virus (PyV) 107 106 cells,virus 105 104 CD8 T cells spleen 103 PFU mg 2 10 101 100 0 10 20 30 40 50 days since infection Biology: Polyoma virus is a natural pathogen of mice causing persistent infection. CD8 T cell response is important in the early control of the virus dynamics. How PyV establishes a persistent infection is not completely understood. 32 / 55
  • 40. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Killing efficacy of PyV-specific CD8 T cells Transfer targets (peptide-pulsed and unpulsed) into PyV-infected mice at different times after the infection. Measure percent of targets killed at different times after cell transfer. Estimate the death rate of targets due to CD8 T cell mediated killing. Byers et al. JI 2003 33 / 55
  • 41. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Mathematical model c S(t) = e− t − e−dt , d− T (t) (d − ) e−dt − e−( +K)t R(t) = = , S(t) ( + K − d) e− t − e−dt where d = δ + + σ is the rate of cell removal from the blood, and c = SB (0)σ is the initial rate of migration of cells into the spleen. 34 / 55
  • 42. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Model fits to data A 106 B 100 pulsed unpulsed unpulsed spleen 105 1 10 104 acute acute chronic chronic 2 103 10 0 50 100 150 200 250 0 50 100 150 200 250 min min Results: The half-life time of peptide-pulsed targets at the peak of the MT389-specific CD8+ T cell response is 15 minutes. During the chronic phase, half of MT389-expressing targets were eliminated in 47 minutes. Per capita killing efficacy of PyV-specific effectors (k = 4 min−1 ) is similar to that of LCMV-specific effectors. 35 / 55
  • 43. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra No change in the killing efficacy over time 101 acute chronic 1 kmax , min 100 0 25 50 75 100 125 150 175 days after infection −Kmax t where kmax = Kmax /E, Kmax = (1−e Rt ) and E is frequency of PyV-specific CD8 T cells in the spleen. Ganusov et al. (in prep) 36 / 55
  • 44. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Killing efficacy at lower peptide concentrations 1 ΜM 0.1 ΜM 100 100 pulsed unpulsed pulsed unpulsed 1 10 acute acute chronic 1 chronic 10 0 50 100 150 200 250 0 50 100 150 200 250 min min 0.01 ΜM 0.001 ΜM 100 pulsed unpulsed pulsed unpulsed 0 10 acute acute chronic chronic 0 50 100 150 200 250 0 50 100 150 200 250 min min 37 / 55
  • 45. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Killing efficacy at lower peptide concentrations ˆ kpn 101 acute k= chronic hn + pn 100 ˆ k, 1 min where k is the maximal killing efficacy of MT389-specific CD8+ T cells, p is 1 10 the peptide concentration used to 2 pulse target cells, h is the peptide 10 3 10 10 2 10 1 100 101 peptide concentration, ΜM concentration at which killing is half-maximal, and n is the power of the Hill function. 38 / 55
  • 46. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Killing efficacy at lower peptide concentrations ˆ kpn 101 acute k= chronic hn + pn 100 ˆ k, 1 min where k is the maximal killing efficacy of MT389-specific CD8+ T cells, p is 1 10 the peptide concentration used to 2 pulse target cells, h is the peptide 10 3 10 10 2 10 1 100 101 peptide concentration, ΜM concentration at which killing is half-maximal, and n is the power of the Hill function. Conclusion: Persistence of PyV could arise due to low level expression of viral proteins but not due to low killing efficacy of T cells. Ganusov et al. (in prep) 38 / 55
  • 47. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Conclusions The developmed framework allows estimation of the killing efficacy of the antiviral CD8 T cell response in the spleen. Killing in the spleen by effector CD8 T cells is rapid with most of targets being killed in minutes after transfer. Killing of targets in the spleen follows the law of mass-action whereby the death rate of targets is simply proportional to the density of epitope-specific CD8 T cells. Persistence of chronic PyV infection could arise due to a low level expression of viral proteins, and as the consequence, to a low killing efficacy by PyV-specific CD8 T cells. PyV-specific CD8 T cells are effective killers at high peptide concentrations and do not loose their ability to kill over the time. 39 / 55
  • 48. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Acknowledgments and Contributions Acute LCMV infection Rob De Boer (Utrecht) and Daniel Barber (NIH) Chronic PyV infection Tony Byers (VaxDesign) and Aron Luckacher (Emory) Funding Marie Curie Incoming International Fellowship (FP6), HFSP grant RGP0010/2004 (Rob De Boer), and Director’s post-doctoral fellowship (LANL). 40 / 55
  • 49. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra I hope that you’re not completely bored Post-doc position available: At the Department of Microbiology of the University of Tennessee in Knoxville starting March-April 2010 for at least 2 years. 41 / 55
  • 50. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Outline 1 Immunology 101 Immune system 2 Killing in acute viral infections Experimental details Model 3 Killing in chronic viral infections Problem Experiments and Analysis Conclusions 4 Appendix I LCMV infection 5 Appendix II PyV infection 6 Extra Pictures 42 / 55
  • 51. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Recruitment of targets into the spleen A B 106 acute 106 memory unpulsed spleen unpulsed spleen 5 60 15 90 30 120 60 240 105 120 105 270 240 270 104 104 0 1 108 2 108 3 108 4 108 0 5 107 1 108 1.5 108 2 108 splenocytes splenocytes 43 / 55
  • 52. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Killing of targets in the spleen A B 0.25 eff NP396 eff GP276 log predicted R 0.2 log predicted R 0.5 0.75 0.4 1 0.6 1.25 0.8 1.5 t 5 t 5 t 15 1 t 15 1.75 t 30 t 30 t 60 t 60 t 120 1.2 t 120 2 t 240 t 240 t 270 t 270 3 2.5 2 1.5 1 0.5 0 1.5 1.25 1 0.75 0.5 0.25 log observed R log observed R C D mem NP396 mem GP276 0.2 log predicted R log predicted R 0.1 0.4 0.2 0.6 t t 60 90 0.3 t 60 t 90 0.8 t 120 t 120 t 240 t 240 t 270 t 270 0.4 1 1 0.8 0.6 0.4 0.2 0 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 log observed R log observed R 44 / 55
  • 53. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Parameter estimates for the in vivo killing Parameter Mean Low 95% CI High 95% CI , min−1 4.71 × 10−3 3.34 × 10−3 6.17 × 10−3 αA , min−1 7.17 × 10−12 5.58 × 10−12 9.22 × 10−12 αM , min−1 1.30 × 10−11 0.92 × 10−11 1.89 × 10−11 KN P , min−1 a 3.45 × 10−1 2.59 × 10−1 4.56 × 10−1 KGP , min−1 a 5.0 × 10−2 3.80 × 10−2 6.41 × 10−2 KN P , min−1 m 1.44 × 10−2 1.10 × 10−2 1.82 × 10−2 KGP , min−1 m 4.15 × 10−3 3.21 × 10−3 5.52 × 10−3 45 / 55
  • 54. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Point estimates of the half-life time By assuming slow migration of targets into the spleen (i.e., at the limit d, e → 0), we obtain the maximum estimate of the death rate of pulsed targets Kmax 1 − e−Kmax t0 R0 = Kmax t0 By assuming very rapid migration of targets into the spleen (i.e., at the limit d → ∞), we obtain the minimal estimate of the death rate of pulsed targets Kmin ln R0 Kmin = − t0 Half-life times are calculated as log(2) T1/2 = K 46 / 55
  • 55. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Point estimates of the half-life time 104 Eff NP396 104 Eff GP276 103 103 T1 2 , min T1 2 , min 102 102 101 101 100 100 0 50 100 150 200 250 0 50 100 150 200 250 time after cell transfer, min time after cell transfer, min 104 Mem NP396 104 Mem GP276 3 3 10 10 T1 2 , min 2 T1 2 , min 10 102 101 101 100 100 0 50 100 150 200 250 0 50 100 150 200 250 time after cell transfer, min time after cell transfer, min 46 / 55
  • 56. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Parameter estimates from the adoptive transfer experiments Parameter Mean 95% CIs E/T E, % E, 106 cells Transferred α, 10−11 min−1 2.14 1.88–6.16 , 10−3 min−1 1.1 0.4–1.6 δ, 10−2 min−1 1.0 0.7–4.3 k1 , min−1 1.77 0.91–2.12 0.14 0.06 0.05 106 γ1 1.84 1.47–2.78 0.09 0.04 0.03 k2 , min−1 1.77 0.91–2.12 0.34 0.18 0.10 2 × 106 γ2 0.55 0.36–0.81 0.25 0.15 0.09 k3 , min−1 3.08 1.6–3.9 23.7 0.87 0.68 107 γ3 0.3 0.26–0.39 9.48 1.25 1.05 k4 , min−1 1.77 0.91–2.12 44.4 1.54 1.43 2 × 107 47 / 55
  • 57. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Alternative models explaining the data Efflux of targets migrated to the spleen, back to the blood. long retention of cells in the blood (T1/2 ≈ 1.9 h); short average residence time in the spleen (T1/2 ≈ 2 h); 60-70% of injected targets migrate to other organs. Loss of recognition of peptide-pulsed targets by CTLs rapid removal of cells from the blood (T1/2 = 40 min); rapid loss of recognition of peptide-pulsed targets by CTLs (T1/2 ≈ 4 h). 48 / 55
  • 58. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Alternative models explaining the data Efflux of targets migrated to the spleen, back to the blood. long retention of cells in the blood (T1/2 ≈ 1.9 h); short average residence time in the spleen (T1/2 ≈ 2 h); 60-70% of injected targets migrate to other organs. Loss of recognition of peptide-pulsed targets by CTLs rapid removal of cells from the blood (T1/2 = 40 min); rapid loss of recognition of peptide-pulsed targets by CTLs (T1/2 ≈ 4 h). More experimental data are need to discriminate between alternative models! 48 / 55
  • 59. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Estimated killing efficacy A 4 B 3 effector memory 2.5 kGP33 , per min 3 2 ΓGP33 2 1.5 1 1 0.5 0 0 106 2 106 107 2 107 106 2 106 107 P14 cells transferred P14 cells transferred Results: These results suggest that there is a minimal change in the killing efficacy of GP33-specific effector CD8 T cells (with an average of 2.10 ± 0.17 per minute) with the number of effector cells transferred. In contrast, the per capita efficacy of memory CD8 T cells (average 1.72 ± 0.44 per minute) declines at high numbers of transferred memory cells. Ganusov et al. (in prep) 49 / 55
  • 60. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Outline 1 Immunology 101 Immune system 2 Killing in acute viral infections Experimental details Model 3 Killing in chronic viral infections Problem Experiments and Analysis Conclusions 4 Appendix I LCMV infection 5 Appendix II PyV infection 6 Extra Pictures 50 / 55
  • 61. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Statistical model n −(log Si −log S(ti ))2 n −(log Ri −log R(ti ))2 1 2s2 1 2s2 L(S, R|p) = e 1 × e 2 i=1 2πs2 1 i=1 2πs2 2 where Si and S(ti ) are the measured and predicted number of unpulsed targets in the spleen at time ti after cell transfer, respectively, and Ri and R(ti ) are the measured and predicted ratio of peptide-pulsed to unpulsed targets in the spleen at time ti after cell transfer, respectively, s1 and s2 are the standard deviation of the errors in the recruitment and killing data, respectively, n is the number of measurements, and p is the vector of model parameters to be estimated from the data. Ganusov et al. (in prep) 51 / 55
  • 62. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Parameter estimates: high peptide concentration parameter acute chronic σ, 10−4 min−1 3.96 (2.90–5.37) δ, 10−3 min−1 4.92 (2.95–7.04) k, min−1 4.16 (3.42–4.84) 1.90 (1.65–2.18) 52 / 55
  • 63. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Parameter estimates: k vs. peptide concentration parameter acute chronic d, 10−3 min−1 5.83 (3.61–8.78) ˆ k, min−1 3.50 (2.93–4.04) 1.89 (1.58–2.16) h, µM 0.19 (0.10–0.37) 0.08 (0.04–0.14) 53 / 55
  • 64. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Outline 1 Immunology 101 Immune system 2 Killing in acute viral infections Experimental details Model 3 Killing in chronic viral infections Problem Experiments and Analysis Conclusions 4 Appendix I LCMV infection 5 Appendix II PyV infection 6 Extra Pictures 54 / 55
  • 65. Immunology 101 Killing in acute viral infections Killing in chronic viral infections Appendix I Appendix II Extra Killing by CD8 T cells in vitro Killing in vitro 55 / 55

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