The rescaling method for quantifying the turnover of cell populations

The dynamic nature of immune responses requires the development of appropriate experimental and theoretical tools to quantitatively estimate the division and death rates which determine the turnover of immune cells. A number of papers have used experimental data from BrdU and D-glucose labels together with a simple random birth-death model to quantify the turnover of immune cells focusing on HIV/SIV infections [Mohri et al. 279 (1998) 1223-1227, Hellerstein et al. 5 (1999) 83-89, Bonhoeffer et al. 164 (2000) 5049-5054, Mohri et al. 87 (2001) 1277-1287]. We show how uncertainties in the assumptions of the random birth-death model may lead to substantial errors in the parameters estimated. We then show how more accurate estimates can be obtained from the more recent CFSE data which allow to track the number of divisions each cell has undergone. Specifically, we: (i) describe a general stage-structured model of cell division where the probabilities of division and death are functions of time since the previous division; (ii) develop a rescaling method to identify invariant parameters (i.e. the ones that are independent of the specific functions describing division and death); (iii) show how these invariant parameters can be estimated, and (iv) illustrate this technique by applying it to CFSE data taken from the literature.