Post-thymectomy dynamics of PTK7⁺ naive CD4⁺ T cells in a model where residual thymic production alone maintains cell numbers.

<p>Residual thymic production of ∼15% and ∼45% is required to reproduce the observed persistence of PTK7<b>⁺</b> T cells in subjects thymectomised at age 2 and 14 years, respectively. Each curve corresponds to a constant rate of maturation from PTK7<b>⁺</b> to PTK7⁻ naive T cells, as described in legend. Filled circles: observations by Haines & colleagues <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049554#pone.0049554-Haines1" target="_blank">[5]</a>.</p

Implications of thymectomy.

<p>Post-thymic age distribution of PTK7<b>⁺</b> naive CD4<b>⁺</b> T cells at days 0, 50 and 100 following thymectomy in a 2 and 14 year old, calculated using the homogeneous (<b>blue</b>) and heterogeneous (<b>red</b>) models.</p

Homogeneous rate of PTK7+ T cell maturation.

<p>(<b>A–B</b>) Decline in PTK7<b>⁺</b> naive CD4<b>⁺</b> T cells post-thymectomy predicted by a range of density-dependent functions and clinical observations made by Haines et al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049554#pone.0049554-Haines1" target="_blank">[5]</a>. (<b>C</b>) Age-related change in PTK7+ T cells with age predicted by the same family of density-dependent maturation functions combined with independent estimates of thymic export <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049554#pone.0049554-Bains2" target="_blank">[26]</a>. Filled circles are experimental observations from Haines et al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049554#pone.0049554-Haines1" target="_blank">[5]</a>. Grey region: a family of functions defined by <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049554#pone.0049554.e040" target="_blank">equation (9</a>) (where ) that encompasses observation in thymectomised individuals aged 2 and 14 years.</p

Survivorship of circulating PTK7⁺ T cells estimated by bi-exponential (left column) and lognormal distributions (right column).

<p>(<b>A</b>) PTK7 survivorship functions. Black lines: estimated survivorship using best-fit parameters. Grey regions: a family of feasible survivorship functions that encompass observations in both healthy and thymectomised individuals. (<b>B–C</b>) Decline in PTK7<b>⁺</b> naive CD4<b>⁺</b> T cells post-thymectomy predicted by survivorship functions and clinical observations following thymectomy at age 2 and 14 years (filled circles). (<b>D</b>) PTK7<b>⁺</b> naive CD4<b>⁺</b> T cell numbers in healthy individuals from birth to age 60 years simulated using feasible survivorship functions and independent estimates of thymic export <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049554#pone.0049554-Bains2" target="_blank">[26]</a>. Experimental observations (filled circles) are as published by Haines et al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049554#pone.0049554-Haines1" target="_blank">[5]</a>.</p

Experimental observations of PTK7⁺ T cells from Haines et al.

<p><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049554#pone.0049554-Haines1" target="_blank">[<b>5</b>]</a><b>. </b><b>A:</b> Frequency of PTK7<b>⁺</b> naive CD4<b>⁺</b> T cells in healthy individuals aged 0 to 60 years. <b>B:</b> Frequency of PTK7<b>⁺</b> naive CD4<b>⁺</b> T cells before and after thymectomy in subjects aged 2 and 14 years.</p

Implications of thymectomy.

<p>Predicted size of the residual PTK7<b>⁺</b> naive CD4<b>⁺</b> T cell population following thymectomy at different ages, as a percentage of expected PTK7<b>⁺</b> numbers in age-matched non-thymectomised individuals, according to the heterogeneous model (using best-fit parameters for a bi-exponential distribution guided by data from thymectomised individuals; , , ).</p

PTK7⁺ dynamics in a healthy individual.

<p>Post-thymic age distribution of PTK7<b>⁺</b> naive CD4<b>⁺</b> T cells, in typical 1, 10, 30 and 60 year olds, calculated using the homogeneous (<b>blue</b>) and heterogeneous (<b>red</b>) models. The homogeneous model predicts an exponential distribution of post-thymic age (mean post-thymic age ∼0.25 years in a 60 year old subject); the heterogeneous model predicts an increasingly broad post-thymic age distribution (and significant accumulation of veteran PTK7<b>⁺</b> cells) in aged individuals (mean post-thymic age ∼15 years in a 60 year old subject).</p

Model of post-thymic maturation of cells within the naive CD4⁺ T cell population.

<p>Survivorship of PTK7<b>⁺</b> T cells within the naive T cell pool reflects the proportion of cells that express PTK7, and are detectable in the blood, as a function of time since leaving the thymus (illustrative plot). Changes in the survivorship function might arise from maturation into PTK7⁻naive T cells, division, or death.</p

Comparison of models explaining naive T-cell dynamics in busulfan chimeras.

(A) Generating busulfan chimeras. (B) Fitting the incumbent, adaptation, and selection models to naive CD4 and CD8 counts from busulfan chimeras made in recipients of different ages. (C) Simultaneous fits to the normalised chimerism in the peripheral naive CD4 and CD8 pools. Colours indicate different age groups of recipient mice. The predictions shown were generated using the mode of the age within each group. Data are provided in S2 Data. BMT, bone marrow transplant.</p

Models of naive T-cell homeostasis.

<p>(A) A simple random birth–death model, with both processes occuring at rates that are constant over time and identical for all cells. (B) A model of density-dependent homeostasis in which every cell’s homeostatic fitness declines equally with total population size, due to resource competition or other forms of quorum-sensing. (C) A model of adaptation in which every cell’s fitness increases progressively with its post-thymic age. We assume that post-thymic age is inherited by a dividing cell’s offspring. (D) A model in which T cells are generated with a distribution of intrinsic, constant, and heritable fitnesses. Over time, selection acts on this distribution. (E) A variant of the selection model, in which the naive pool comprises numerically stable, self-renewing ‘incumbent’ cells generated early in life and ‘displaceable’ cells that are continually replaced by new emigrants from the thymus.</p