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IL7 receptor signaling in T cells: A mathematical modeling perspective

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Interleukin‐7 (IL7) plays a nonredundant role in T cell survival and homeostasis, which is illustrated in the severe T cell lymphopenia of IL7‐deficient mice, or demonstrated in animals or humans that lack expression of either the IL7Rα or γ c chain, the two subunits that constitute the functional IL7 receptor. Remarkably, IL7 is not expressed by T cells themselves, but produced in limited amounts by radio‐resistant stromal cells. Thus, T cells need to constantly compete for IL7 to survive. How T cells maintain homeostasis and further maximize the size of the peripheral T cell pool in face of such competition are important questions that have fascinated both immunologists and mathematicians for a long time. Exceptionally, IL7 downregulates expression of its own receptor, so that IL7‐signaled T cells do not consume extracellular IL7, and thus, the remaining extracellular IL7 can be shared among unsignaled T cells. Such an altruistic behavior of the IL7Rα chain is quite unique among members of the γ c cytokine receptor family. However, the consequences of this altruistic signaling behavior at the molecular, single cell and population levels are less well understood and require further investigation. In this regard, mathematical modeling of how a limited resource can be shared, while maintaining the clonal diversity of the T cell pool, can help decipher the molecular or cellular mechanisms that regulate T cell homeostasis. Thus, the current review aims to provide a mathematical modeling perspective of IL7‐dependent T cell homeostasis at the molecular, cellular and population levels, in the context of recent advances in our understanding of the IL7 biology. This article is categorized under: Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models Biological Mechanisms > Cell Signaling Models of Systems Properties and Processes > Mechanistic Models Analytical and Computational Methods > Computational Methods
An example of shared molecular components in immune signaling: competition for the γc chain by the IL7Rα and IL15Rβ chains (adapted from Palmer et al. ())
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Left plot: fraction of bound [IL7R]b, f7, as defined by Equation (1), for different values of the initial concentration of [IL7](t = 0). Different colors correspond to different values of the initial concentration of [IL15](t = 0), as shown in the legend. Middle plot: fraction of bound [IL7R]b, f7, as in the left panel, but as a function of the initial concentration of [IL15](t = 0). Right plot: steady state values for the bound complexes, [IL7R]b and [IL15R]b, as a function of the initial γc chain expression, γc(t = 0). The parameters have been taken from Palmer et al. () and have been summarized in Table
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Effect of signaling altruism on the amount of available extracellular (free) IL7. Left plot: effect of ϕ for κs = 103 on for different values of Nc. Right plot: effect of κs for ϕ = ϕthreshold/2 on for different values of Nc. Model parameters are summarized in Table . Different colors correspond to different values of the number of cells, Nc, in the experiment
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Effect of altruism on the amount of free IL7R. Left plot: effect of ϕ for κs = 103 on for different values of Nc. Right plot: effect of κs for ϕ = ϕthreshold/2 on for different values of Nc. Model parameters are summarized in Table . Different colors correspond to different values of the number of cells, Nc, in the experiment
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Immune signaling at the population level: possible transitions between the four subsets of the peripheral CD8+ T cell pool. We impose μ1 > μ2; that is, CD5lo T cells have prolonged survival in a cytokine independent environment. In the mathematical model the parameter λ corresponds to the per cell division rate. λ1 is the per cell division rate for CD5hi CD8+ T cells and λ2 is the per cell division rate for CD5lo CD8+ T cells, with λ1 > λ2 (Palmer et al., ). We assume that after a division event, there is a significant drop in the level of IL7R expressed on the surface of a cell, since daughter cells inherit, on average, half of the IL7 receptors expressed by their mother cell. Finally, ϕ corresponds to the basal upregulation rate of IL7R expression and is assumed to be independent of the extracellular IL7 concentration. ϕ1 is the per cell IL7R upregulation rate for CD5hi CD8+ T cells and ϕ2 is the per cell IL7R upregulation for CD5lo CD8+ T cells
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Effect of the parameter α on the severity of the threshold functions (see Equation (12)). Note that for α = 0 (black line) the threshold functions are constant and equal to . On the other hand, for α ≫ 1 the functions are almost discontinuous and the thresholds rather sharp
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Numerical study for a total time of 2 weeks with low IL7 production, ν = 1 and a soft threshold, α = 5. On the right plot, we see the T cell population is dominated by the subset of CD5lo T cells. Note the reasonable agreement between the deterministic model (ODE) and the stochastic simulations (SSA). On the left plot, we follow the extracellular IL7 concentration in time. On the middle plot, we follow the four cellular populations in time. On the right plot, we follow the two cellular populations, as defined by their CD5 expression in time
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Numerical study for a total time of 2 weeks with medium IL7 production, ν = 5 and a soft threshold, α = 5. On the right plot, we see the T cell population is dominated by the subset of CD5lo T cells. Note that a deterministic (ODE) approach cannot precisely reproduce the stochastic behavior (SSA). On the left plot, we follow the extracellular IL7 concentration in time. On the middle plot, we follow the four cellular populations in time. On the right plot, we follow the two cellular populations, as defined by their CD5 expression in time
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Numerical study for a total time of 2 weeks with high IL7 production, ν = 25 and a soft threshold, α = 5. On the right plot, we see the T cell population is dominated by the subset of CD5hi T cells. Note that a deterministic (ODE) approach is able to reproduce the stochastic behavior (SSA). On the left plot, we follow the extracellular IL7 concentration in time. On the middle plot, we follow the four cellular populations in time. On the right plot, we follow the two cellular populations, as defined by their CD5 expression in time
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Numerical study for a total time of 2 weeks with high IL7 production, ν = 25 and a soft threshold, α = 5. This study also considers the role of IL7 degradation (with rate δ = 20 h−1). On the right plot, we see the T cell population is dominated by the subset of CD5lo T cells. Note that a deterministic (ODE) approach cannot precisely reproduce the stochastic behavior (SSA) observed. On the left plot, we follow the extracellular IL7 concentration in time. On the middle plot, we follow the four cellular populations in time. On the right plot, we follow the two cellular populations, as defined by their CD5 expression in time
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Numerical study for a total time of 2 weeks with high IL7 production, ν = 5 for two values of α: α = 0 (top row) and α = 50 (bottom row). On the left plot, we follow the extracellular IL7 concentration in time. On the middle plot, we follow the four cellular populations in time. On the right plot, we follow the two cellular populations, as defined by their CD5 expression in time
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Histogram of the steady state of CD5 high subpopulation (black) and CD5 low subpopulation (red) for ν = 5 and α = 5 (left) or α = 50 (right). The blue dashed vertical line is a guide to the eye to show the line where the fraction of each subpopulation is 50%
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Models of Systems Properties and Processes > Mechanistic Models
Biological Mechanisms > Cell Signaling
Analytical and Computational Methods > Computational Methods
Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

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