Modeling the development of the post-natal mouse thymus in the absence of bone marrow progenitors

Daniela Zaharie,Radu D Moleriu,Felix A Mic

doi:10.1038/srep36159

Abstract

Many mathematical models have been published with the purpose of explaining aspects of T-cell development in the thymus. In this manuscript we adapted a four-compartment model of the thymus and used a range of mathematical approaches with the aim of explaining the dynamics of the four main thymocyte populations in the mouse thymus, from the emergence of the first fetal thymocyte until the death of the animal. At various pre-natal and post-natal stages we investigated experimentally the number and composition of thymocytes populations, their apoptosis and proliferation, along with data from literature, to create and validate the model. In our model the proliferation processes are characterized by decreasing proliferation rates, which allows us to model the natural involution of the thymus. The best results were obtained when different sets of parameters were used for the fetal and post-natal periods, suggesting that birth may induce a discontinuity in the modeled processes. Our model is able to model the development of both pre-natal and post-natal thymocyte populations. Also, our findings showed that the post-natal thymus is able to develop in the absence of the daily input of bone marrow progenitors, providing more evidence to support the autonomous development of the post-natal thymus.

Highlights

Many mathematical models have been published with the purpose of explaining aspects of T-cell development in the thymus
The current view of thymocyte developmental flow in the thymus indicates that bone marrow progenitors enter the thymus on a daily basis where they first generate DN thymocytes that subsequently turn into DP ones that undergo intense proliferation, differentiation and apoptosis as they generate the mature SP4/SP8 thymocytes, which are exported as functional T-cells from the thymus
To further investigate the fitting quality of the modeling, we examined the correspondence between the time points of the appearance of the DN thymocyte population in the fetal thymus as obtained using the simulations of all four models, and those reported in the literature[3,4,5,7,8,9]

Summary

Introduction

Many mathematical models have been published with the purpose of explaining aspects of T-cell development in the thymus In this manuscript we adapted a four-compartment model of the thymus and used a range of mathematical approaches with the aim of explaining the dynamics of the four main thymocyte populations in the mouse thymus, from the emergence of the first fetal thymocyte until the death of the animal. At various pre-natal and post-natal stages we investigated experimentally the number and composition of thymocytes populations, their apoptosis and proliferation, along with data from literature, to create and validate the model. Data on the dynamics of thymocyte apoptosis in the adult mouse thymus[16] and the composition of the four main thymocyte populations in the pre-natal thymus at several stages[17,18] were obtained from the literature. The change over time in the number of precursors in the pre-natal thymus appears to follow a logistic type of growth[19]

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Conclusion