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

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

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

HUMAN GRANULOMA- snap shot

Cell mediated immunity in
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

Cellmediated
Immunity:
Activated
M
F s
Humoralmediated immunity

cytokines and T cells : green=upregulation, red=downregulation black=production,

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

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

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

Parameter Estimation: inclusion of experimental data
• Estimated from literature giving weight to humans or human cells and to species
M. tuberculosis over other mycobacteria
• 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

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 )

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

What determines these different outcomes?
*Detailed Uncertainty and Sensitivity
Analyses on all parameters in the system
 Latin Hypercube Sampling
 Partial Rank Correlation

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

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 IFNg from NK and CD8 cells

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?

Depletion Experiments
• IFNg : progress to active disease within
500 days
• IL-12: still able to maintain latency; much higher bacterial load
• IL-10:

Multiple Compartments- spatial component within the immune system
 Site of infection- lung
 Lymph nodes- site of adaptive immunity
 Trafficking between sites
 Specialized cells: Dendritic cells
 Immune priming
 Activation 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.

Factors leading to different disease outcomes-Model 2
•
•
• Rates of macrophage activation, deactivation and infection
Rate T cells lyse infected macrophages
Production of IFNg 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

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

Host response to M.tbdevelopment of granuloma:
DTH/Th1 response
Large necrotic
Small solid

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
.

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

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

Modeling diffusion
Example:
• Chemokine C diffuses out from a source
C

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

Metapopulation model: simulation of containment

•
•
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

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

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

Macrophage state diagram

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

Rules: an example
Resting macrophage phagocytosis

Rules: an example
Macrophage activation by T cells

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

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

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

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

How robust are the simulations with stochastic elements?

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
 Intracellular bacteria load that converts macrophages chronically infected
 Number of times it takes to count region as necrotic
 Number of initial resting macrophages

Can we determine granuloma function from form?
 Results indicate that how the granuloma forms and is maintained can determine whether infection is contained or spreads locally within the lung
 This is dependent on a number of factors:
 Crowding of cells within the granuloma
 This does not allow for T cells to penetrate and activate macrophages
 Necrotic regions containing bacteria
 This walls off bacteria from macrophages and spread

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)

Present work- expanding our ABM studies
 Collaborating with studies on NHP models of TB
 Exploring specific role of cytokines and specific cellular subsets in granuloma formation
 Heterogeneous lattice representing the lung environment
 3-D representation of the granuloma

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
Acknowledgments
NIH and The Whitaker Foundation
•Collaborators: JoAnne Flynn (Pitt)
•John Chan (Albert Einstein)

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

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)