Lythe, G and Molina-París, C (2018) Some deterministic and stochastic mathematical models of naive T-cell homeostasis. Immunological Reviews, 285 (1). pp. 206-217. ISSN 0105-2896
Abstract
Humans live for decades, whereas mice live for months. Over these long timescales, naïve T cells die or divide infrequently enough that it makes sense to approximate death and division as instantaneous events. The population of T cells in the body is naturally divided into clonotypes; a clonotype is the set of cells that have identical T‐cell receptors. While total numbers of cells, such as naïve CD4+ T cells, are large enough that ordinary differential equations are an appropriate starting point for mathematical models, the numbers of cells per clonotype are not. Here, we review a number of basic mathematical models of the maintenance of clonal diversity. As well as deterministic models, we discuss stochastic models that explicitly track the integer number of naïve T cells in many competing clonotypes over the lifetime of a mouse or human, including the effect of waning thymic production. Experimental evaluation of clonal diversity by bulk high‐throughput sequencing has many difficulties, but the use of single‐cell sequencing is restricted to numbers of cells many orders of magnitude smaller than the total number of T cells in the body. Mathematical questions associated with extrapolating from small samples are therefore key to advances in understanding the diversity of the repertoire of T cells. We conclude with some mathematical models on how to advance in this area.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Keywords: | aging; competition; computational models; extinction sampling; single‐cell sequencing; stochastic |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Jul 2018 11:46 |
Last Modified: | 11 Aug 2019 00:40 |
Status: | Published |
Publisher: | Wiley |
Identification Number: | 10.1111/imr.12696 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:133020 |