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Explicit Kinetic Heterogeneity: Mathematical Models for Interpretation of Deuterium Labeling of Heterogeneous Cell Populations

Figure 4

Fits of artificial (simulated) data with various models.

We have fitted artificial data (black dots) with the Asymptote model (eqn. (1), solid black lines), the Exponential model, in which a fraction of the cells have exponentially distributed turnover rates (eqn. (8), small red dashed lines), and the Gamma model with gamma distributed turnover rates (eqn. (4), large green dashed lines). Data were generated using the Gamma model (panel A&B), the Exponential model (panel C&D) and the Two-populations model (panel E&F, Eqn. (2)), respectively. Thin blue lines show the exact curves of the models that were used to generate the data. The different models were fitted to 11 datapoints taken from these predicted curves after having added noise to these data points. Noise was added by a relative change of the predicted value with a normally distributed error (with standard deviation of the distribution ). The models were fitted to data from artificial labeling experiments in which the label was administered for 7 (left panels) or 15 (right panels) days. Parameter estimates providing the best fit are shown in Table S1, and the corresponding estimates of the average rates of cell turnover are shown in Figure 5. Parameters used to generate the data are also given in Table S1.

doi: https://doi.org/10.1371/journal.pcbi.1000666.g004