Explicit Kinetic Heterogeneity: Mathematical Models for Interpretation of Deuterium Labeling of Heterogeneous Cell Populations
Figure 3
Model predictions for gamma-distributed turnover rates.
We have plotted the changes in the fraction of labeled DNA according to the kinetic heterogeneity model with gamma-distributed turnover rates (eqn. (4)) with average turnover rate /day on a linear (panel A) or logarithmic (panel B) scale. Predicted changes are shown for different values of the shape parameter
. Larger values of
correspond to a more symmetric distribution (Panel C). For low values of the shape parameter
, the loss of labeled DNA after label cessation is biphasic, which is most clearly visible on a logarithmic scale for
(panel B). This characteristic of the kinetic heterogeneity model differs from the Asymptote models which have a constant per capita rate at which labeled DNA is lost. Note that for shape parameters
, the distribution of turnover rates
becomes extremely skewed with most cells undergoing hardly any division and relatively few cells undergoing extremely many rounds of division (panel C). Panel D gives the cumulative contribution of sub-populations with a particular turnover rate
to the average rate of turnover of the population
. The vertical line shows the value of the average proliferation rate
. For high values of the shape parameter (
), the cell sub-populations with turnover rates that are somewhat lower or higher than
give the main contribution to the average turnover rate. In contrast, for low values of
(
), the major contribution to the average turnover rate comes from sub-populations with extremely rapid turnover rates (
); about 50% of the average turnover is due to a few sub-populations with turnover rates that exceed 10 per day, which is biologically unrealistic.