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Rob J. de Boer

Mathematical Models of Human CD4+ T Cell Population Kinetics

Rob J. de Boer

We review how mathematical models help the interpretation of data measuring CD4\+ T cell kinetics by two recently developed techniques. Mathematical models are developed for the average content of T cell receptor excision circles (TRECs), and the average telomeric restriction fragment (TRF) length in T cells in the peripheral blood. Changes in the TRECs were supposed to indicate changes in thymic production. The rate at which naive and memory CD4\+ T cells erode their telomeres was supposed to reflect their respective division rates. Analyzing the mathematical models we show that rapid changes in the TRECs per naive T cell are most likely due to changes in the division rates, and that the rates of telomere erosion fail to reflect naive and memory division rates. The models are applied to explain why rheumatoid arthritis (RA) patients have abnormal TRECs and telomeres.

Figure 1
Figure 1: A scheme of a model where we keep track of the number of divisions a cell has made. Each box ni represents the number of T cells that have gone through precisely i cell divisions. N is the total number of T cells. The arrows α and δ represent division and death rates, respectively. Both may be arbitrary homeostatic functions of the total T cell density, i.e., α is some decreasing, and δ some increasing function of the total number of T cells N = ∑i ni. Two linear examples are depicted in the figure.

 

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