# How heterogeneous thymic output and homeostatic proliferation shape naive T cell receptor clone abundance distributions

## TL;DR

This study models how heterogeneity in thymic output and T cell proliferation influences naive T cell receptor clone abundance distributions, revealing that proliferation heterogeneity is key to matching observed data.

## Contribution

It introduces a mean-field birth-death-immigration model incorporating TCR-dependent heterogeneity, highlighting proliferation variability as crucial for clone abundance patterns.

## Key findings

- Heterogeneity in proliferation rates significantly impacts clone abundance distributions.
- Immigration rate heterogeneity has minimal effect on predicted clone counts.
- Model constraints align with experimental clone abundance data.

## Abstract

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.