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and 
TCR Excision Circles in Naive T Cells1
Department of Theoretical Biology, Utrecht University, Utrecht, The Netherlands
Due to homeostasis total naive T cell numbers remain fairly constant over life despite a gradual involution of the thymus. The contribution of the thymus to maintaining naive T cell pools is typically measured with TCR excision circles (TRECs) that are formed in thymocytes. The mechanisms underlying thymic involution are poorly understood. Some data suggest that thymocytes undergo fewer divisions in old (small) than young (large) thymi, and other data suggest that the number of TRECs per thymocyte is independent of age. If thymic involution were associated with a decreased number of divisions of the thymocytes, this would markedly complicate the interpretation of TREC data. To study this we develop a mathematical model in which the division rate of thymocytes decreases with increasing age. We describe the dilution of TRECs formed during the arrangement of both chains of the TCR by division of thymocytes, recent thymic emigrants, and mature naive T cells. The model behavior is complicated as TREC contents in naive T cells can increase with age due to decreased dilution in the thymus. Because our model is consistent with current data on the effects of age and thymectomy on TRECs in peripheral T cells, we conclude that aging may well affect thymocyte division, which markedly complicates the interpretation of TREC data. It is possible, but more difficult, to let the model be consistent with the rapid changes in 
and 
TRECs observed shortly after HIV infection.
The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
1 This work was supported in part by the Netherlands Organization for Scientific Research (VICI Grant 016.048.603; to R.J.D.B.) and the Human Frontier Science Program (Grant RGP0010/2004).
2 Current address: Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Heidelberglaan 100, 3584 CX Utrecht, The Netherlands.
3 Address correspondence and reprint requests to Dr. Rob J. de Boer, Department of Theoretical Biology, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands. E-mail address: R.J.DeBoer{at}bio.uu.nl
4 Abbreviations used in this paper: TREC, TCR excision circle; sj, signal-joint; RTE, recent thymic emigrant.
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