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Register a new userA mathematical model of the effects of aging on naive T-cell population and diversity
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The human adaptive immune response is known to weaken in advanced age, resulting in increased severity of pathogen-born illness, poor vaccine efficacy, and a higher prevalence of cancer in the elderly. Age-related erosion of the T-cell compartment has been implicated as a likely cause, but the underlying mechanisms driving this immunosenescence have not been quantitatively modeled and systematically analyzed. T-cell receptor diversity, or the extent of pathogen-derived antigen responsiveness of the T-cell pool, is known to diminish with age, but inherent experimental difficulties preclude accurate analysis on the full organismal level. In this paper, we formulate a mechanistic mathematical model of T-cell population dynamics on the immunoclonal subpopulation level, which provides quantitative estimates of diversity. We define different estimates for diversity that depend on the individual number of cells in a specific immunoclone. We show that diversity decreases with age primarily due to diminished thymic output of new T-cells and the resulting overall loss of small immunoclones.
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The set of T cells that express the same T cell receptor (TCR) sequence represents a T cell clone. The number of different naive T cell clones in an organism reflects the number of different T cell receptors (TCRs) arising from recombination of the V(D)J gene segments during T cell development in the thymus. TCR diversity and more specifically, the clone abundance distribution is an important factor in immune function. Specific recombination patterns occur more frequently than others while subsequent interactions between TCRs and self-antigens are known to trigger proliferation and sustain naive T cell survival. These processes are TCR-dependent, leading to clone-dependent thymic export and naive T cell proliferation rates. Using a mean-field approximation to the solution of a regulated birth-death-immigration model and a modification arising from sampling, we systematically quantify how TCR-dependent heterogeneities in immigration and proliferation rates affect the shape of clone abundance distributions (the number of different clones that are represented by a specific number of cells, or clone counts). By comparing predicted clone counts derived from our heterogeneous birth-death-immigration model with experimentally sampled clone abundances, we show that although heterogeneity in immigration rates causes very little change to predicted clone-counts, significant heterogeneity in proliferation rates is necessary to generate the observed abundances with reasonable physiological parameter values. Our analysis provides constraints among physiological parameters that are necessary to yield predictions that qualitatively match the data. Assumptions of the model and potentially other important mechanistic factors are discussed.
Naive human T cells are produced in the thymus, which atrophies abruptly and severely in response to physical or psychological stress. To understand how an instance of stress affects the size and diversity of the peripheral naive T cell pool, we derive a mean-field autonomous ODE model of T cell replenishment that allows us to track the clone abundance distribution (the mean number of different TCRs each represented by a specific number of cells). We identify equilibrium solutions that arise at different rates of T cell production, and derive analytic approximations to the dominant eigenvalues and eigenvectors of the problem linearized about these equilibria. From the forms of the eigenvalues and eigenvectors, we estimate rates at which counts of clones of different sizes converge to and depart from equilibrium values--that is, how the number of clones of different sizes adjust to the changing rate of T cell production. Under most physiologically realistic realizations of our model, the dominant eigenvalue (representing the slowest dynamics of the clone abundance distribution) scales as a power law in the thymic output for low output levels, but saturates at higher T cell production rates. Our analysis provides a framework for quantitatively understanding how the clone abundance distributions evolve under small changes in the overall T cell production rate by the thymus.
Complete understanding of the mechanisms regulating the proliferation and differentiation that takes place during human immune CD8+ T cell responses is still lacking. Human clinical data is usually limited to blood cell counts, yet the initiation of these responses occurs in the draining lymph nodes; antigen-specific effector and memory CD8+ T cells generated in the lymph nodes migrate to those tissues where they are required. We use approximate Bayesian computation with deterministic mathematical models of CD8+ T cell populations (naive, central memory, effector memory and effector) and yellow fever virus vaccine data to infer the dynamics of these CD8+ T cell populations in three spatial compartments: draining lymph nodes, circulation and skin. We have made use of the literature to obtain rates of division and death for human CD8+ T cell population subsets and thymic export rates. Under the decreasing potential hypothesis for differentiation during an immune response, we find that, as the number of T cell clonotypes driven to an immune response increases, there is a reduction in the number of divisions required to differentiate from a naive to an effector CD8+ T cell, supporting the division of labour hypothesis observed in murine studies. We have also considered the reverse differentiation scenario, the increasing potential hypothesis. The decreasing potential model is better supported by the yellow fever virus vaccine data.
Adoptive Cell Transfer therapy of cancer is currently in full development and mathematical modeling is playing a critical role in this area. We study a stochastic model developed by Baar et al. in 2015 for modeling immunotherapy against melanoma skin cancer. First, we estimate the parameters of the deterministic limit of the model based on biological data of tumor growth in mice. A Nonlinear Mixed Effects Model is estimated by the Stochastic Approximation Expectation Maximization algorithm. With the estimated parameters, we head back to the stochastic model and calculate the probability that the T cells all get exhausted during the treatment. We show that for some relevant parameter values, an early relapse is due to stochastic fluctuations (complete T cells exhaustion) with a non negligible probability. Then, focusing on the relapse related to the T cell exhaustion, we propose to optimize the treatment plan (treatment doses and restimulation times) by minimizing the T cell exhaustion probability in the parameter estimation ranges.
The hypothalamic-pituitary-adrenal (HPA) axis is a neuroendocrine system that regulates numerous physiological processes. Disruptions in the activity of the HPA axis are correlated with many stress-related diseases such as post-traumatic stress disorder (PTSD) and major depressive disorder. In this paper, we characterize normal and diseased states of the HPA axis as basins of attraction of a dynamical system describing the inhibition of peptide hormones such as corticotropin-releasing hormone (CRH) and adrenocorticotropic hormone (ACTH) by circulating glucocorticoids such as cortisol (CORT). In addition to including key physiological features such as ultradian oscillations in cortisol levels and self-upregulation of CRH neuron activity, our model distinguishes the relatively slow process of cortisol-mediated CRH biosynthesis from rapid trans-synaptic effects that regulate the CRH secretion process. Crucially, we find that the slow regulation mechanism mediates external stress-driven transitions between the stable states in novel, intensity, duration, and timing-dependent ways. These results indicate that the timing of traumatic events may be an important factor in determining if and how patients will exhibit hallmarks of stress disorders. Our model also suggests a mechanism whereby exposure therapy of stress disorders such as PTSD may act to normalize downstream dysregulation of the HPA axis.
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