1. Understanding granuloma formation in TB using different mathematical and biological scales Denise Kirschner, Ph.D. Dept. of Microbiology/Immunology Univ. of Michigan Medical School

2. Outline of Presentation Introduction to TB immunobiology Studying the host-pathogen interaction Experimental Methods ODE model, 2-compartmental model, metapopulation model, agent-based model Granuloma Structure and Function Results Compare dynamics and bifurcation parameters for each approach

3. Mycobacterium tuberculosis 1/3 of the world infected 3 million+ die each year no clear understanding of distinction between different disease trajectories: Exposure No infection Infection Latent disease Reactivation Acute disease 70% 30% 95% 5% 5-10%

5. HUMAN GRANULOMA- snap shot

7. Cell mediated immunity in M. tuberculosis infection What elements of the host-mycobacterial dynamical system contribute to different disease outcomes once exposed? Hypothesis: components of the cell mediated immune response determine either latency or active disease (primary or reactivation) Wigginton and Kirschner J Immunology 166:1951-1976, 2001

8. Cell- mediated Immunity: Activated M  s Humoral- mediated immunity

9. Complex interactions between cytokines and T cells : black=production, green=upregulation, red=downregulation

10. Experimental Approach Build a virtual model of human TB describing temporal changes in broncoalveolar lavage fluid (BAL) to predict mechanisms underlying different disease outcomes Use model to ask questions about the system

11. Methodology for TB Model Describe separate cellular and cytokine interactions Translate into mathematical expressions nonlinear ordinary differential equations Estimate rates of interactions from data (parameter estimation) Simulate model and validate with data Perform virtual experiments

12. Variables tracked in our model: Macrophages: resting, activated, chronically infected T cells: Th0, Th1, Th2 Cytokines: IFN-  IL-4, IL-10, IL-12 Bacteria: both extracellular and intracellular Define 4 submodels

18. Parameter Estimation: inclusion of experimental data Estimated from literature giving weight to humans or human cells and to M. tuberculosis over other mycobacteria species Units are cells/ml or pg/ml of BAL Sensitivity and Uncertainty analyses can be performed to test these values or estimate values for unknown parameters

19. Example: estimating growth rate of M. tuberculosis in vitro estimates for doubling times of H37Rv lab strain within macrophages ranged from 28 hours to 96 hours In mouse lung tissue, H37Rv estimated to have a doubling time of 63.2 hours We can estimate the growth rates of intracellular vs. extracellular growth rates from these values (rate=ln2/doub. time )

20. Model Outcomes: Virtual infection within humans over 500 days No infection - resting macrophages are at their average value in lung (3x10 5 /ml) (negative control) Clearance - a small amount of bacteria are introduced and infection is cleared (PPD-) latent TB (a few macrophages harbor all - may miss them in biopsy) Active, primary TB

25. What determines these different outcomes? *Detailed Uncertainty and Sensitivity Analyses on all parameters in the system zLatin Hypercube Sampling zPartial Rank Correlation

26. Varying T cell killing of infected macrophages Total T cells Total bacteria

27. Factors leading to different disease outcomes-Model 1 Production of IL-4 Rates of macrophage activation, deactivation and infection Rate T cells lyse infected macrophages Rate extracellular bacteria are killed by activated macrophages *Production of IFN-  from NK and CD8 cells

28. Virtual Deletion and Depletion Experiments: Deletion: mimic knockout (disruption) experiments where the element is removed from the system at day 0. Ask: what parameters contribute to achieving latency? Depletion: mimic depletion of an element by setting it to zero after latency is achieved. Ask: what maintains latency after it has been achieved?

29. Depletion Experiments IFN-  : progress to active disease within 500 days IL-12: still able to maintain latency; much higher bacterial load IL-10:

30. IL-10 Depletion

31. Multiple Compartments- spatial component within the immune system zSite of infection- lung zLymph nodes- site of adaptive immunity zTrafficking between sites zSpecialized cells: Dendritic cells zImmune priming zActivation and differentiation  Marino, S and Kirschner, D. The Role of Dendritic cells in the Human Immune Response to Mycobacterium tuberculosis in the lung and lymph node. Journal of Theoretical Biology, (in press), 2004. – and another submitted.

33. Factors leading to different disease outcomes-Model 2 Rates of macrophage activation, deactivation and infection Rate T cells lyse infected macrophages Production of IFN-  from NK and CD8 cells DC-T cell interaction rates, IL-12 prod. rate, DC turnover rate, DC migration rate Growth Rate of extracellular bacteria Rate new Th0 cells migrate out of LN to inf. site

34. Importance of A Spatial Response at the site: Granuloma formation? Cells respond to chemotatic signals Other? Granuloma function? ‘wall off’ infection – bacterial spread Minimize tissue damage Provide a localized environment for cell to cell interactions

35. Host response to M.tb- development of granuloma: DTH/Th1 response Large necrotic Small solid

36. Spatio-temporal models of granuloma formation Metapopulation Model (Drs. S. Ganguli & D. Gammack) Agent based model (Drs. J. Segovia-Juarez & S. Ganguli) PDE model- tracked only innate immunity and early macrophage response (Dr. D. Gammack) Gammack D, Doering C, and Kirschner D. Macrophage response to Mycobacterium tuberculosis infection. Journal of Mathematical Biology. Vol 48( 2) February 2004, Pages: 218 - 242.

37. Metapopulation Modeling Ganguli S, Gammack D, and Kirschner D. A metapopulation model of granuloma formation in the lung during infection with M. tuberculosis. (Submitted)

38. Discrete Spatial Model of Granuloma Development Partition space: nxn lattice of compartments Model diffusion between compartments movement based on local differences (gradient) Probabilistic movement Model interactions within compartments Existing temporal model n 2 Systems of ODEs 10mm x10mm

39. Modeling diffusion Example: Chemokine C diffuses out from a source C

40. Modeling diffusion Example: Chemokine C diffuses out from a source Diffusion of macrophages M is biased towards higher concentrations of C C M

41. Metapopulation model: simulation of containment

42. Factors leading to different disease outcomes-Model 3 Rates of macrophage activation, deactivation and infection Rate T cells lyse infected macrophages Rate extracellular bacteria are killed by activated macrophages Growth rate of extracellular bacteria Rate of recruitment of Macrophages and T cells via chemokine Rate that activated macrophages and T cells move about the infection site Rate of chemokine diffusion

43. Agent Based Modeling Jose Segovia-Juarez, Suman Ganguli and D. Kirschner. An agent based model of granuloma formation in the lung during infection with M. tuberculosis (submitted).

44. Model Agents DISCRETE ENTITIES Cells Macrophages in different states: Activated, Resting, Infected and Chronically infected Effector T cells CONTINUOUS ENTITIES Chemokine Extracellular mycobacteria

45. Macrophage state diagram

46. Model Framework: lattice with agents and continuous entities Vascular sources of cells

47. Rules: an example Resting macrophage phagocytosis

48. Rules: an example Macrophage activation by T cells

49. Granuloma formation-solid Resting macrophages Infected macrophages Chronically infected m. Activated macrophage Bacteria T cells Necrosis

50. Granuloma formation-necrotic Resting macrophages Infected macrophages Chronically infected m. Activated macrophage Bacteria T cells Necrosis

51. Granuloma formation- clearance Resting macrophages Infected macrophages Chronically infected m. Activated macrophage Bacteria T cells Necrosis 2x2 mm sq.

52. Adaptive Immunity: T cell arrival delay to infectionsite Panel A: parameters that lead to containment Panel B: parameters that least to disseminative disease

53. How robust are the simulations with stochastic elements?

54. Factors determining successful granuloma formation-Model 4 Rate of recruitment of Macrophages and T cells via chemokine Rate that activated macrophages and T cells move about the infection site Rate of chemokine diffusion zIntracellular bacteria load that converts macrophages chronically infected zNumber of times it takes to count region as necrotic zNumber of initial resting macrophages

55. Can we determine granuloma function from form? zResults indicate that how the granuloma forms and is maintained can determine whether infection is contained or spreads locally within the lung zThis is dependent on a number of factors: yCrowding of cells within the granuloma xThis does not allow for T cells to penetrate and activate macrophages yNecrotic regions containing bacteria xThis walls off bacteria from macrophages and spread

56. Can we predict the human outcome? *How do we extrapolate from a single granuloma to predict infection outcome? *Emile et al(1997) in J. of Path. Identified 14 patients with BCG-disease each of whom had either latent, suppressed infection or acute disease. All granulomas were distinct and uniform within the two groups (solid or caseated)

57. Present work- expanding our ABM studies zCollaborating with studies on NHP models of TB zExploring specific role of cytokines and specific cellular subsets in granuloma formation zHeterogeneous lattice representing the lung environment z3-D representation of the granuloma

58. Acknowledgments Kirschner Lab Jose S.-Juarez, PhD David Gammack, PhD Simeone Marino, PhD Suman Ganguli, PhD Ping Ye, PhD Seema Bajaria, MS Ian Joseph Christian Ray Stewart Chang Dhruv Sud Joe Waliga NIH and The Whitaker Foundation Collaborators: JoAnne Flynn (Pitt) John Chan (Albert Einstein)

59. Present Work- cellular level Include in the temporal BAL model: CD8+ T cells and TNF-  D. Sud) IL-10 as a regulator of the immune response (S. Marino)

60. Present Work: intracellular level Temporal specificity by M. tuberculosis inhibiting antigen presentation in macrophages (S. Chang) The balance of activation, killing and iron homeostasis in determining M. tuberculosis survival within a macrophage (Christian Ray)