Stochastic descriptors to study the fate and potential of naive T\xa0cell clonotypes in the periphery

J R Artalejo,A Gómez-Corral,C Molina-París,M López-García

doi:10.1007/s00285-016-1020-6

Abstract

The population of naive T cells in the periphery is best described by determining both its T cell receptor diversity, or number of clonotypes, and the sizes of its clonal subsets. In this paper, we make use of a previously introduced mathematical model of naive T cell homeostasis, to study the fate and potential of naive T cell clonotypes in the periphery. This is achieved by the introduction of several new stochastic descriptors for a given naive T cell clonotype, such as its maximum clonal size, the time to reach this maximum, the number of proliferation events required to reach this maximum, the rate of contraction of the clonotype during its way to extinction, as well as the time to a given number of proliferation events. Our results show that two fates can be identified for the dynamics of the clonotype: extinction in the short-term if the clonotype experiences too hostile a peripheral environment, or establishment in the periphery in the long-term. In this second case the probability mass function for the maximum clonal size is bimodal, with one mode near one and the other mode far away from it. Our model also indicates that the fate of a recent thymic emigrant (RTE) during its journey in the periphery has a clear stochastic component, where the probability of extinction cannot be neglected, even in a friendly but competitive environment. On the other hand, a greater deterministic behaviour can be expected in the potential size of the clonotype seeded by the RTE in the long-term, once it escapes extinction.

Highlights

T cells are the set of lymphocytes characterised by the expression of a specialised receptor, called the T cell receptor (TCR)
An adult mouse has a homeostatic population of 108 naive T cells (Mason 1998) and a TCR diversity estimated around 2× (Zarnitsyna et al 2013), and a healthy adult human has a homeostatic population of 1011 naive T cells (Hazenberg et al 2003) distributed in 2.5 × different TCR specificities (Zarnitsyna et al 2013; Johnson et al 2014)
In this paper we have analysed the fate of a given naive T cell clonotype or a recent thymic emigrant, when competing with pre-established peripheral T cell clonotypes for homeostatic proliferation signals

Summary

Introduction

T cells are the set of lymphocytes characterised by the expression of a specialised receptor, called the T cell receptor (TCR). T cells can be classified in “families” (or clonotypes) according to the molecular structure of the TCR they display on their membrane (Murphy et al 2008). The number of T cells in the adaptive immune system of an adult human tends to a stationary “homeostatic” distribution (McLean et al 1997; Freitas and Rocha 2000), specified by its size (the total number of T cells) and TCR diversity (the number of different clonotypes or TCR molecular structures). An adult mouse has a homeostatic population of 108 naive T cells (Mason 1998) and a TCR diversity estimated around 2× (Zarnitsyna et al 2013), and a healthy adult human has a homeostatic population of 1011 naive T cells (Hazenberg et al 2003) distributed in 2.5 × different TCR specificities (Zarnitsyna et al 2013; Johnson et al 2014)

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Conclusion