Dynamics of T Cell Receptor Distributions Following Acute Thymic Atrophy and Resumption

TL;DR

This study develops a mathematical model to analyze how acute thymic atrophy and subsequent recovery affect the diversity and distribution of naive T cell clones, providing insights into immune system dynamics under stress.

Contribution

The paper introduces a mean-field ODE model that captures T cell clone distribution dynamics during thymic atrophy and recovery, with analytic approximations for eigenvalues and eigenvectors.

Findings

Eigenvalues scale as a power law at low thymic output

Clone distribution dynamics depend on thymic output rate

Model predicts saturation of clone diversity at high T cell production

Abstract

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.