Modelling deuterium labelling of lymphocytes with temporal and/or kinetic heterogeneity

To study the kinetics of lymphocytes, models have divided the cell population into subpopulations with different turnover rates. These have been called ‘kinetic heterogeneity models’ so as to distinguish them from ‘temporal heterogeneity models’, in which a cell population may have different turnover rates at different times, e.g. when resting versus when activated. We model labelling curves for temporally heterogeneous populations, and predict that they exhibit equal biphasic up- and downslopes. We show when cells divide only once upon activation, these slopes are dominated by the slowest exponent, yielding underestimates of the average turnover rate. When cells undergo more than one division, the labelling curves allow fitting of the two exponential slopes in the temporal heterogeneity model. The same data can also be described with a two-compartment kinetic heterogeneity model. In both instances, the average turnover rate is correctly estimated. Because both models assume a different cell biology but describe the data equally well, the parameters of either model have no simple biological interpretation, as each parameter could reflect a combination of parameters of another biological process. Thus, even if there are sufficient data to reliably estimate all exponentials, one can only accurately estimate an average turnover rate. We illustrate these issues by re-fitting labelling data from healthy and HIV-infected individuals.