How Naive T-Cell Clone Counts Are Shaped By Heterogeneous Thymic Output and Homeostatic Proliferation

Abstract

The specificity of T cells is that each T cell has only one T cell receptor (TCR). A T cell clone represents a collection of T cells with the same TCR sequence. Thus, the number of different T cell clones in an organism reflects the number of different T cell receptors (TCRs) that arise 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, are important factors in immune functions. 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. We describe the heterogeneous steady-state population of naive T cells (those that have not yet been antigenically triggered) by using a mean-field model of a regulated birth-death-immigration process. After accounting for random sampling, we investigate 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 using reasonable physiological parameter values and fitting predicted clone counts to experimentally sampled clone abundances, we show that realistic levels of heterogeneity in immigration rates cause very little change to predicted clone-counts, but that modest heterogeneity in proliferation rates can generate the observed clone abundances. 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.

Finding meaningful and workable applied mathematics problems in science

“…For researchers in mathematics, communication and collaboration with experimental biologists might not be smooth at the beginning, since the thinking modes are different. I also participated in other projects on population dynamics [1,23,6,36].…”

Mathematical Characterization of Private and Public Immune Repertoire Sequences

“…Such a model translates the fundamental underlying recombination process into a population of T cells with TCR i and total population in individual m . The connection between and might be described by population dynamics models, deterministic or stochastic, such as those presented in [15].…”

“…Besides thymic selection and subsequent death, activation, and proliferation occur differently across individuals 1 ≤ m ≤ M , described by model parameters θ , N (m) might be described by population dynamics models, deterministic or stochastic, such as those presented in [15].…”

Inferring the T-cells repertoire dynamics of healthy individuals

“…Yet, processes such as homeostasis [3] and unspecific signals in both naive and memory subrepertoires result in frequency changes of background clones. Many first-principles models of naive T cells dynamics have been proposed to study the balance between thymic output and peripheral proliferation and death [2,4,[13][14][15]. The role of competition for antigens between T cells has been pointed out [16], as well the effect of crossreactivity [17] (the ability for one T cell to recognize different antigens), the relative size of a primary versus secondary response to similar antigens [18], or the effect of beneficial mutations [19].…”