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Cited by 175T-cell and B-cell ImmunologyArtificial Immune Systems ApplicationsEvolution and Genetic Dynamics

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How many TCR clonotypes does a body maintain?

Open access
Lythe, Grant, Callard, Robin E., Hoare, Rollo L., Molina-París, Carmen·2016·Journal of Theoretical Biology
DOI 10.1016/j.jtbi.2015.10.016PMC PMC4678146
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Abstract

We consider the lifetime of a T cell clonotype, the set of T cells with the same T cell receptor, from its thymic origin to its extinction in a multiclonal repertoire. Using published estimates of total cell numbers and thymic production rates, we calculate the mean number of cells per TCR clonotype, and the total number of clonotypes, in mice and humans. When there is little peripheral division, as in a mouse, the number of cells per clonotype is small and governed by the number of cells with identical TCR that exit the thymus. In humans, peripheral division is important and a clonotype may survive for decades, during which it expands to comprise many cells. We therefore devise and analyse a computational model of homeostasis of a multiclonal population. Each T cell in the model competes for self pMHC stimuli, cells of any one clonotype only recognising a small fraction of the many subsets of stimuli. A constant mean total number of cells is maintained by a balance between cell division and death, and a stable number of clonotypes by a balance between thymic production of new clonotypes and extinction of existing ones. The number of distinct clonotypes in a human body may be smaller than the total number of naive T cells by only one order of magnitude.

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Graphical abstract
Graphical abstract CC BY · PubMed Central
Fig. 1 Representation of connections between N=30 T cell clonotypes and M=40 self pMHC subsets. An arrow connecting a red ball to a green ball indicates that the self pMHC stimulates division of cells in the T cell clonotype. The connections between clonotypes and self pMHCs are assigned randomly with probability p=0.1. That is, each entry of the matrix A, independently, is equal to 1 with probability p and equal to 0 with probability 1−p. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Fig. 1 Representation of connections between N=30 T cell clonotypes and M=40 self pMHC subsets. An arrow connecting a red ball to a green ball indicates that the self pMHC stimulates division of cells in the T cell clonotype. The connections between clonotypes and self pMHCs are assigned randomly with probability p=0.1. That is, each entry of the matrix A, independently, is equal to 1 with probability p and equal to 0 with probability 1−p. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)CC BY · PubMed Central
Fig. 2 Predicted steady-state number of distinct clonotypes. The value of N⁎ is the product of the rate of production of new clonotypes, θ, and the mean lifetime of a clonotype, (16). The dotted lines are (7), valid in the weak-thymus limit. The parameter α=nθθ/γM measures the strength of thymic production relative to peripheral division. Three values of nθ are shown. We use γM/μ=10¹¹ cells, approximately equal to the number of naive CD4+ T cells in a human.
Fig. 2 Predicted steady-state number of distinct clonotypes. The value of N⁎ is the product of the rate of production of new clonotypes, θ, and the mean lifetime of a clonotype, (16). The dotted lines are (7), valid in the weak-thymus limit. The parameter α=nθθ/γM measures the strength of thymic production relative to peripheral division. Three values of nθ are shown. We use γM/μ=10¹¹ cells, approximately equal to the number of naive CD4+ T cells in a human.CC BY · PubMed Central
Fig. 3 A numerical solution of the competition model without thymic production. The left panel shows the total number of T cells, as a function of time. (The total number of cells continues to fluctuate about the same mean for times later than shown.) The right panel shows the number of surviving clonotypes, N(t), with a logarithmic time scale. The dotted line is (14). One time unit is the mean lifetime of a T cell in the absence of division stimulus, taken to be one year in a human body. The parameters are μ=1.0, γ=10, M=1000; T cell clonotype-pMHC connections were assigned randomly with probability p=0.1 at the beginning of the run. The initial conditions are N(0)=200 and ni(0)=25 for each i.
Fig. 3 A numerical solution of the competition model without thymic production. The left panel shows the total number of T cells, as a function of time. (The total number of cells continues to fluctuate about the same mean for times later than shown.) The right panel shows the number of surviving clonotypes, N(t), with a logarithmic time scale. The dotted line is (14). One time unit is the mean lifetime of a T cell in the absence of division stimulus, taken to be one year in a human body. The parameters are μ=1.0, γ=10, M=1000; T cell clonotype-pMHC connections were assigned randomly with probability p=0.1 at the beginning of the run. The initial conditions are N(0)=200 and ni(0)=25 for each i.CC BY · PubMed Central
Fig. 4 Diagrammatic representation of the competition model. Each green ball represents a set of T cells; each red ball, a set of self pMHC complexes. An arrow (link) connecting a red ball to a green indicates that T cells of the clonotype recognise the self pMHC subset. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Fig. 4 Diagrammatic representation of the competition model. Each green ball represents a set of T cells; each red ball, a set of self pMHC complexes. An arrow (link) connecting a red ball to a green indicates that T cells of the clonotype recognise the self pMHC subset. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)CC BY · PubMed Central
Fig. 5 A numerical solution of the exact clonal competition model without thymic input. In the top panel, the average number of self pMHCs recognised by a clonotype, ϕ¯(t), and the average number of clonotypes recognising a pMHC, C¯(t), are shown as a function of time. Due to extinction of clonotypes, ϕ¯(t) increases and C¯(t) decreases. The middle panel shows histograms of the 2000 values of |Cq|, at the start and end of the realisation. The bottom panel shows the histograms of values of ϕ at the start (1000 clonotypes) and end (168 clonotypes). T cell clonotype-pMHC connections are assigned randomly with probability p=0.05. The remaining parameter values are μ=1.0, γ=10, M=2000. The initial conditions are N(0)=1000 and ni(0)=10∀i.
Fig. 5 A numerical solution of the exact clonal competition model without thymic input. In the top panel, the average number of self pMHCs recognised by a clonotype, ϕ¯(t), and the average number of clonotypes recognising a pMHC, C¯(t), are shown as a function of time. Due to extinction of clonotypes, ϕ¯(t) increases and C¯(t) decreases. The middle panel shows histograms of the 2000 values of |Cq|, at the start and end of the realisation. The bottom panel shows the histograms of values of ϕ at the start (1000 clonotypes) and end (168 clonotypes). T cell clonotype-pMHC connections are assigned randomly with probability p=0.05. The remaining parameter values are μ=1.0, γ=10, M=2000. The initial conditions are N(0)=1000 and ni(0)=10∀i.CC BY · PubMed Central
Fig. 6 Competition is more important than chance in determining which clonotypes survive. Of the initial 1000 clonotypes, on average only 50 survive. Ten independent realisations were carried out with the same connection matrix A; the fates of clonotypes i=390 to i=610 (horizontal axes) are illustrated. The upper panel shows the values of ϕi for the subset of clonotypes. (Each i has the same value of ϕi in each realisation.) In the lower panel, the vertical axis is the realisation number. A blue rectangle at position i in realisation j indicates that the clonotype has survived to t=10⁴ in that realisation. Many clonotypes never survive; some usually do. The parameter values are γ=10, M=1000, p=0.1. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Fig. 6 Competition is more important than chance in determining which clonotypes survive. Of the initial 1000 clonotypes, on average only 50 survive. Ten independent realisations were carried out with the same connection matrix A; the fates of clonotypes i=390 to i=610 (horizontal axes) are illustrated. The upper panel shows the values of ϕi for the subset of clonotypes. (Each i has the same value of ϕi in each realisation.) In the lower panel, the vertical axis is the realisation number. A blue rectangle at position i in realisation j indicates that the clonotype has survived to t=10⁴ in that realisation. Many clonotypes never survive; some usually do. The parameter values are γ=10, M=1000, p=0.1. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)CC BY · PubMed Central
Fig. 7 Scaling of the dynamics with the size of the self pMHC environment. Different numerical runs, with M=1600, M=3200 and M=6400, without thymic input. In each case, pM=100, μ=1, N(0)=1/4M and γ=10. In the vertical axis on the right, the number of surviving clonotypes, as a function of time, is multiplied by p. The product pM is the mean number of self pMHC recognised by a single TCR clonotype; the product pN is the mean number of clonotypes that recognise a single self pMHC.
Fig. 7 Scaling of the dynamics with the size of the self pMHC environment. Different numerical runs, with M=1600, M=3200 and M=6400, without thymic input. In each case, pM=100, μ=1, N(0)=1/4M and γ=10. In the vertical axis on the right, the number of surviving clonotypes, as a function of time, is multiplied by p. The product pM is the mean number of self pMHC recognised by a single TCR clonotype; the product pN is the mean number of clonotypes that recognise a single self pMHC.CC BY · PubMed Central
Fig. 8 Input of new clonotypes from the thymus, while barely affecting the total number of cells, determines the late-time number of surviving clonotypes. For comparison with adult human homeostasis, time is measured in years. The thymic output rates are θ=0.1 year−1 (blue), θ=1 year−1 (green), θ=10 year−1 (red), θ=100 year−1 (black) and θ=400 year−1 (cyan). The remaining parameter values are M=4000, pM=100, γ=10 year−1, μ=1 year−1, nθ=4 in all cases. The histograms on the right show, for θ=10 year−1, the distribution of survival times of clonotypes from the thymus and the distribution of ni(t) for surviving clonotypes. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Fig. 8 Input of new clonotypes from the thymus, while barely affecting the total number of cells, determines the late-time number of surviving clonotypes. For comparison with adult human homeostasis, time is measured in years. The thymic output rates are θ=0.1 year−1 (blue), θ=1 year−1 (green), θ=10 year−1 (red), θ=100 year−1 (black) and θ=400 year−1 (cyan). The remaining parameter values are M=4000, pM=100, γ=10 year−1, μ=1 year−1, nθ=4 in all cases. The histograms on the right show, for θ=10 year−1, the distribution of survival times of clonotypes from the thymus and the distribution of ni(t) for surviving clonotypes. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)CC BY · PubMed Central
Fig. 9 Total number of cells, and total number of surviving clonotypes, as a function of time. Stimulus rates of the self pMHC, γq, are drawn from a log-normal distribution. The values of σ are the ratio of the standard deviation to the mean value of 10 year−1. In the case σ=1, the standard deviation is equal to the mean. The remaining parameter values are M=4000, pM=100, θ=400 year−1, μ=1 year−1 and nθ=4.
Fig. 9 Total number of cells, and total number of surviving clonotypes, as a function of time. Stimulus rates of the self pMHC, γq, are drawn from a log-normal distribution. The values of σ are the ratio of the standard deviation to the mean value of 10 year−1. In the case σ=1, the standard deviation is equal to the mean. The remaining parameter values are M=4000, pM=100, θ=400 year−1, μ=1 year−1 and nθ=4.CC BY · PubMed Central

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Research works printed but not linked: 2

  1. Hershberg, 2003, What is the basis of the immune systems specificity?, Math. Model. Comput. Biol. Med., 377
  2. Merrill, 1994, Development of the T-cell repertoire, Rocky Mt. J. Math., 24, 214

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Metadata

Authors
Lythe, G., Callard, R. E., Hoare, R. L., & Molina-París, C.
Affiliations
  • University of Leeds (GB)
  • University College London (GB)
Corresponding author
Lythe, Grant
ORCID
Venue
Journal of Theoretical Biology
Publisher
Elsevier BV
Published
2016-01
Volume
389
Pages
214-224
ISSN
0022-5193 (ISSN-L)
DOI
10.1016/j.jtbi.2015.10.016
PMC
PMC4678146
OpenAlex
W2141312574
Cited by
175
References
134
Citations by year
2026: 10 · 2025: 13 · 2024: 14 · 2023: 25 · 2022: 26 · 2021: 22 · 2020: 22 · 2019: 15 · 2018: 13 · 2017: 11 · 2016: 4
FWCI
4.59
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal of Theoretical Biology (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • White Rose Research Online (University of Leeds, The University of Sheffield, University of York) (acceptedVersion)
  • UCL Discovery (University College London) (submittedVersion)
Funders
BBSRC Research Development Fellowship (BB/G023395/1)
Topics
  • Life Sciences › Immunology and Microbiology › Immunology › T-cell and B-cell Immunology
  • Physical Sciences › Computer Science › Artificial Intelligence › Artificial Immune Systems Applications
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
Keywords
T cell clonotypes, T cell receptor repertoire, thymic output, naive T cells
MeSH terms
Algorithms, Animals, Cell Division, Computer Simulation, Homeostasis, Humans, Immunologic Memory, Models, Theoretical, Receptors, Antigen, T-Cell, Stochastic Processes, T-Lymphocytes, Thymus Gland, Mice

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