Supra-normal TREC content during naive T cell recovery induced by the thymus. We consider the following model for TREC+ naive T cells,
N+, and total naive T cells,
N:

. Thus,
C=
N+/
N is the TREC content per naive T cell. Considering a human adult, the thymic output, σ, should be small. We assumed a thymic production of σ = 0.032 cell/µl/day corresponding to a fractional output of less than 10
−4 /day (taking a count of 400 CD4+ T cells per µl for a normal individual 11). The parameter α was set to 1/8 to represent the TREC content of RTE (e.g., cord blood cells) 31. Since naive T cells are long-lived we give them a half-life of two years by setting
dN=0.001 day
−1, and if naive T cell numbers ultimately approach a normal steady state of
N=400 cells after the transient recovery phase, one can solve that
p=0.00092 day
−1. At the steady state the normal TREC content is
C=0.01 /cell (see the horizontal line in Panel (a)). For simplicity we start with no TREC+ cells (i.e.,
N+(0)=0). The three lines correspond to three initial populations sizes:
N=10 (solid line),
N=50 (dashed line),
N=200 (dash-dotted line).