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From pre-DP, post-DP, SP4, and SP8 Thymocyte Cell Counts to a Dynamical Model of Cortical and Medullary Selection.

Sawicka M, Stritesky GL, Reynolds J, Abourashchi N, Lythe G, Molina-París C, Hogquist KA - Front Immunol (2014)

Bottom Line: Thymic development is characterized by (i) an extremely low success rate, and (ii) the selection of a functional and self-tolerant T cell repertoire.The stable steady state of the model for the pre-DP, post-DP, and SP populations is identified with the experimentally measured cell counts from 5.5- to 17-week-old mice.In the post-DP compartment, 91.7% undergo death by negative selection, 4.7% become CD4 SP, and 3.6% become CD8 SP.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Mathematics, School of Mathematics, University of Leeds , Leeds , UK.

ABSTRACT
Cells of the mature αβ T cell repertoire arise from the development in the thymus of bone marrow precursors (thymocytes). αβ T cell maturation is characterized by the expression of thousands of copies of identical αβ T cell receptors and the CD4 and/or CD8 co-receptors on the surface of thymocytes. The maturation stages of a thymocyte are: (1) double negative (DN) (TCR(-), CD4(-) and CD8(-)), (2) double positive (DP) (TCR(+), CD4(+) and CD8(+)), and (3) single positive (SP) (TCR(+), CD4(+) or CD8(+)). Thymic antigen presenting cells provide the appropriate micro-architecture for the maturation of thymocytes, which "sense" the signaling environment via their randomly generated TCRs. Thymic development is characterized by (i) an extremely low success rate, and (ii) the selection of a functional and self-tolerant T cell repertoire. In this paper, we combine recent experimental data and mathematical modeling to study the selection events that take place in the thymus after the DN stage. The stable steady state of the model for the pre-DP, post-DP, and SP populations is identified with the experimentally measured cell counts from 5.5- to 17-week-old mice. We make use of residence times in the cortex and the medulla for the different populations, as well as recently reported asymmetric death rates for CD4 and CD8 SP thymocytes. We estimate that 65.8% of pre-DP thymocytes undergo death by neglect. In the post-DP compartment, 91.7% undergo death by negative selection, 4.7% become CD4 SP, and 3.6% become CD8 SP. Death by negative selection in the medulla removes 8.6% of CD4 SP and 32.1% of CD8 SP thymocytes. Approximately 46.3% of CD4 SP and 27% of CD8 SP thymocytes divide before dying or exiting the thymus.

No MeSH data available.


Time evolution of the thymocyte populations in the second model. The different trajectories correspond to the parameter values and ranges described in Table 2.
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Figure 5: Time evolution of the thymocyte populations in the second model. The different trajectories correspond to the parameter values and ranges described in Table 2.

Mentions: The sensitivity analysis (see Section 3.3) and the variability of the selection rates derived from it (see Section 3.4) give us the confidence to conclude, that our parameter estimation is robust. We are aware that the experimental data we have made use of [steady state thymocyte cell counts (26)] do not provide the exquisite time resolution described in Ref. (21). However, the supporting mathematical model described in Section 2.2, allows us to obtain the time evolution of the thymocyte populations, once the parameters have been estimated. In Figure 5, we plot the time evolution of the total number of cells in each compartment of the mathematical model: pre-DP, post-DP, CD4 SP, and CD8 SP thymocytes. We start with no cells at time zero, ni(t = 0) = 0 for i = 1, 2, 4, 8. Trajectories have been plotted for a period of 6 weeks and have been computed for every permutation of the parameter set presented in Table 2. The subset of parameters shared with the simple model (ϕ, φ1, μ1, μ2), were fixed at their mean values. Thus, 548 distinct parameter sets were generated. The system of equations (6) was solved using a fourth order Runge–Kutta method (Python source code).


From pre-DP, post-DP, SP4, and SP8 Thymocyte Cell Counts to a Dynamical Model of Cortical and Medullary Selection.

Sawicka M, Stritesky GL, Reynolds J, Abourashchi N, Lythe G, Molina-París C, Hogquist KA - Front Immunol (2014)

Time evolution of the thymocyte populations in the second model. The different trajectories correspond to the parameter values and ranges described in Table 2.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3924582&req=5

Figure 5: Time evolution of the thymocyte populations in the second model. The different trajectories correspond to the parameter values and ranges described in Table 2.
Mentions: The sensitivity analysis (see Section 3.3) and the variability of the selection rates derived from it (see Section 3.4) give us the confidence to conclude, that our parameter estimation is robust. We are aware that the experimental data we have made use of [steady state thymocyte cell counts (26)] do not provide the exquisite time resolution described in Ref. (21). However, the supporting mathematical model described in Section 2.2, allows us to obtain the time evolution of the thymocyte populations, once the parameters have been estimated. In Figure 5, we plot the time evolution of the total number of cells in each compartment of the mathematical model: pre-DP, post-DP, CD4 SP, and CD8 SP thymocytes. We start with no cells at time zero, ni(t = 0) = 0 for i = 1, 2, 4, 8. Trajectories have been plotted for a period of 6 weeks and have been computed for every permutation of the parameter set presented in Table 2. The subset of parameters shared with the simple model (ϕ, φ1, μ1, μ2), were fixed at their mean values. Thus, 548 distinct parameter sets were generated. The system of equations (6) was solved using a fourth order Runge–Kutta method (Python source code).

Bottom Line: Thymic development is characterized by (i) an extremely low success rate, and (ii) the selection of a functional and self-tolerant T cell repertoire.The stable steady state of the model for the pre-DP, post-DP, and SP populations is identified with the experimentally measured cell counts from 5.5- to 17-week-old mice.In the post-DP compartment, 91.7% undergo death by negative selection, 4.7% become CD4 SP, and 3.6% become CD8 SP.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Mathematics, School of Mathematics, University of Leeds , Leeds , UK.

ABSTRACT
Cells of the mature αβ T cell repertoire arise from the development in the thymus of bone marrow precursors (thymocytes). αβ T cell maturation is characterized by the expression of thousands of copies of identical αβ T cell receptors and the CD4 and/or CD8 co-receptors on the surface of thymocytes. The maturation stages of a thymocyte are: (1) double negative (DN) (TCR(-), CD4(-) and CD8(-)), (2) double positive (DP) (TCR(+), CD4(+) and CD8(+)), and (3) single positive (SP) (TCR(+), CD4(+) or CD8(+)). Thymic antigen presenting cells provide the appropriate micro-architecture for the maturation of thymocytes, which "sense" the signaling environment via their randomly generated TCRs. Thymic development is characterized by (i) an extremely low success rate, and (ii) the selection of a functional and self-tolerant T cell repertoire. In this paper, we combine recent experimental data and mathematical modeling to study the selection events that take place in the thymus after the DN stage. The stable steady state of the model for the pre-DP, post-DP, and SP populations is identified with the experimentally measured cell counts from 5.5- to 17-week-old mice. We make use of residence times in the cortex and the medulla for the different populations, as well as recently reported asymmetric death rates for CD4 and CD8 SP thymocytes. We estimate that 65.8% of pre-DP thymocytes undergo death by neglect. In the post-DP compartment, 91.7% undergo death by negative selection, 4.7% become CD4 SP, and 3.6% become CD8 SP. Death by negative selection in the medulla removes 8.6% of CD4 SP and 32.1% of CD8 SP thymocytes. Approximately 46.3% of CD4 SP and 27% of CD8 SP thymocytes divide before dying or exiting the thymus.

No MeSH data available.