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Modeling early events in Francisella tularensis pathogenesis.

Gillard JJ, Laws TR, Lythe G, Molina-París C - Front Cell Infect Microbiol (2014)

Bottom Line: The model is mechanistic and governed by a small number of experimentally verifiable parameters.The mean and variance of these distributions are determined by model parameters with a precise biological interpretation, providing new mechanistic insights into the determinants of immune and bacterial kinetics.Insights into the dynamics of macrophage suppression and activation gained by the model can be used to explore the potential benefits of interventions that stimulate macrophage activation.

View Article: PubMed Central - PubMed

Affiliation: Defence Science and Technology Laboratory Porton Down, Salisbury, UK.

ABSTRACT
Computational models can provide valuable insights into the mechanisms of infection and be used as investigative tools to support development of medical treatments. We develop a stochastic, within-host, computational model of the infection process in the BALB/c mouse, following inhalational exposure to Francisella tularensis SCHU S4. The model is mechanistic and governed by a small number of experimentally verifiable parameters. Given an initial dose, the model generates bacterial load profiles corresponding to those produced experimentally, with a doubling time of approximately 5 h during the first 48 h of infection. Analytical approximations for the mean number of bacteria in phagosomes and cytosols for the first 24 h post-infection are derived and used to verify the stochastic model. In our description of the dynamics of macrophage infection, the number of bacteria released per rupturing macrophage is a geometrically-distributed random variable. When combined with doubling time, this provides a distribution for the time taken for infected macrophages to rupture and release their intracellular bacteria. The mean and variance of these distributions are determined by model parameters with a precise biological interpretation, providing new mechanistic insights into the determinants of immune and bacterial kinetics. Insights into the dynamics of macrophage suppression and activation gained by the model can be used to explore the potential benefits of interventions that stimulate macrophage activation.

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Comparison of the stochastic model with the analytic approximations derived in section 3.2. Upper plot: number of bacteria in macrophage phagosomes as a function of time, for the first 24 h post-infection. Lower plot: number of bacteria in macrophage cytosols as a function of time, for the first 24 h post-infection. The two figures show, in blue, one standard error range of numerical values from 10 realizations and, in green, the formulae calculated from (2b) and (4). The initial number of F. tularensis bacteria is Poisson distributed with mean N = 100. The alveolar space initially contains M = 104 macrophages, ρ = 0.01, ϕ = 2.0, β = 0.15 μ = 0.01, γ = 0.1, ν = 0.01 and δ = 0.001. The time unit is an hour.
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Figure 5: Comparison of the stochastic model with the analytic approximations derived in section 3.2. Upper plot: number of bacteria in macrophage phagosomes as a function of time, for the first 24 h post-infection. Lower plot: number of bacteria in macrophage cytosols as a function of time, for the first 24 h post-infection. The two figures show, in blue, one standard error range of numerical values from 10 realizations and, in green, the formulae calculated from (2b) and (4). The initial number of F. tularensis bacteria is Poisson distributed with mean N = 100. The alveolar space initially contains M = 104 macrophages, ρ = 0.01, ϕ = 2.0, β = 0.15 μ = 0.01, γ = 0.1, ν = 0.01 and δ = 0.001. The time unit is an hour.

Mentions: The solution of (4) is compared with numerical results in Figure 5. The agreement between the stochastic model and analytic approximations provide a further verification that the model is representing the infection mechanisms appropriately.


Modeling early events in Francisella tularensis pathogenesis.

Gillard JJ, Laws TR, Lythe G, Molina-París C - Front Cell Infect Microbiol (2014)

Comparison of the stochastic model with the analytic approximations derived in section 3.2. Upper plot: number of bacteria in macrophage phagosomes as a function of time, for the first 24 h post-infection. Lower plot: number of bacteria in macrophage cytosols as a function of time, for the first 24 h post-infection. The two figures show, in blue, one standard error range of numerical values from 10 realizations and, in green, the formulae calculated from (2b) and (4). The initial number of F. tularensis bacteria is Poisson distributed with mean N = 100. The alveolar space initially contains M = 104 macrophages, ρ = 0.01, ϕ = 2.0, β = 0.15 μ = 0.01, γ = 0.1, ν = 0.01 and δ = 0.001. The time unit is an hour.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4263195&req=5

Figure 5: Comparison of the stochastic model with the analytic approximations derived in section 3.2. Upper plot: number of bacteria in macrophage phagosomes as a function of time, for the first 24 h post-infection. Lower plot: number of bacteria in macrophage cytosols as a function of time, for the first 24 h post-infection. The two figures show, in blue, one standard error range of numerical values from 10 realizations and, in green, the formulae calculated from (2b) and (4). The initial number of F. tularensis bacteria is Poisson distributed with mean N = 100. The alveolar space initially contains M = 104 macrophages, ρ = 0.01, ϕ = 2.0, β = 0.15 μ = 0.01, γ = 0.1, ν = 0.01 and δ = 0.001. The time unit is an hour.
Mentions: The solution of (4) is compared with numerical results in Figure 5. The agreement between the stochastic model and analytic approximations provide a further verification that the model is representing the infection mechanisms appropriately.

Bottom Line: The model is mechanistic and governed by a small number of experimentally verifiable parameters.The mean and variance of these distributions are determined by model parameters with a precise biological interpretation, providing new mechanistic insights into the determinants of immune and bacterial kinetics.Insights into the dynamics of macrophage suppression and activation gained by the model can be used to explore the potential benefits of interventions that stimulate macrophage activation.

View Article: PubMed Central - PubMed

Affiliation: Defence Science and Technology Laboratory Porton Down, Salisbury, UK.

ABSTRACT
Computational models can provide valuable insights into the mechanisms of infection and be used as investigative tools to support development of medical treatments. We develop a stochastic, within-host, computational model of the infection process in the BALB/c mouse, following inhalational exposure to Francisella tularensis SCHU S4. The model is mechanistic and governed by a small number of experimentally verifiable parameters. Given an initial dose, the model generates bacterial load profiles corresponding to those produced experimentally, with a doubling time of approximately 5 h during the first 48 h of infection. Analytical approximations for the mean number of bacteria in phagosomes and cytosols for the first 24 h post-infection are derived and used to verify the stochastic model. In our description of the dynamics of macrophage infection, the number of bacteria released per rupturing macrophage is a geometrically-distributed random variable. When combined with doubling time, this provides a distribution for the time taken for infected macrophages to rupture and release their intracellular bacteria. The mean and variance of these distributions are determined by model parameters with a precise biological interpretation, providing new mechanistic insights into the determinants of immune and bacterial kinetics. Insights into the dynamics of macrophage suppression and activation gained by the model can be used to explore the potential benefits of interventions that stimulate macrophage activation.

Show MeSH
Related in: MedlinePlus