Sampling from T Cell Receptor Repertoires

Ferrarini, Marco; Molina-Parı́s, Carmen; Lythe, Grant

doi:10.1007/978-3-319-45833-5_3

Cited by 4 publications

(2 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Suppose that an unbiased random sample of m cells is taken, and sequenced, from a total repertoire of S cells. Let us start with the probability that one particular cell in the repertoire is part of the sample:

q = \frac{m}{S} .

In naïve repertoire single‐cell sequencing q ≪ 1, because m , approximately 10 2 –10 3 , is much smaller than S , approximately 10 7 (mice) or 10 11 (humans). We seek a relationship between n i , the number of cells of type i in the repertoire, and s i , the number of cells of type i in the sample.…”

Section: How Many Tcr Clonotypes Are Maintained?mentioning

confidence: 99%

See 1 more Smart Citation

Some deterministic and stochastic mathematical models of naïve T‐cell homeostasis

Lythe

Molina-Parı́s

2018

Immunological Reviews

Self Cite

View full text Add to dashboard Cite

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.

show abstract

q = \frac{m}{S} .

Section: How Many Tcr Clonotypes Are Maintained?mentioning

confidence: 99%

“…For the distribution of values of s i ,

Φ false(z false) = {false\sum}_{k = 0}^{\infty} Prob false[s_{i} = k false] z^{n}

. Assuming that qn i ≪ 1, the relationship between ϕ ( z ) and Φ( z ) is:

Φ (z) = ϕ (1 - q + q z) .

…”

Section: How Many Tcr Clonotypes Are Maintained?mentioning

confidence: 99%

Some deterministic and stochastic mathematical models of naïve T‐cell homeostasis

Lythe

Molina-Parı́s

2018

Immunological Reviews

Self Cite

View full text Add to dashboard Cite

show abstract

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

Dessalles

D’Orsogna

Chou³

2019

Preprint

View full text Add to dashboard Cite

The set of T cells that express the same T cell receptor (TCR) sequence represent 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, 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). By comparing predicted clone abundances derived from our heterogeneous birth-death-immigration model with experimentally sampled clone abundances, we quantify the heterogeneity necessary to generate the observed abundances. Our findings indicate that heterogeneity in proliferation rates is more likely the mechanism underlying the observed clone abundance distributions than heterogeneity in immigration rates. Author SummaryThe abundance distribution of different T cell receptors (TCRs) expressed on naive T cells depends on their rates of thymic output, homeostatic proliferation, and death. However, measured TCR count distributions do not match, even qualitatively, those predicted from a multiclone birth death-immigration process when constant birth, death, and immigration rates are used (a neutral model). We show how non-neutrality in the birth-death-immigration process, where naive T cells with different TCRs are produced and proliferate with a distribution of rates shape the predicted sampled clone abundance distributions (the clone counts). Using physiological parameters, we find that heterogeneity in proliferation rates, and not in thymic output rates, is the main determinant in generating the observed clone counts. These findings are consistent with proliferation-driven maintenance of the T cell population in humans.

show abstract

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

et al. 2022

View full text Add to dashboard Cite

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.

show abstract

Sampling from T Cell Receptor Repertoires

Cited by 4 publications

References 25 publications

Some deterministic and stochastic mathematical models of naïve T‐cell homeostasis

Some deterministic and stochastic mathematical models of naïve T‐cell homeostasis

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

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

Contact Info

Product

Resources

About