FIGURE 3.

Empirical parameter formulas for varying doxorubicin concentrations. The proposed empirical formulas indicated at the top of each panel (A–E) were fit to the median of the corresponding parameter distributions obtained from fitting the single-dose model to the varying concentration datasets from Experiment 1 (Table 1). $C$ denotes doxorubicin concentration in nM, while ${\alpha }_i$ ( $i=\mathrm{1,2},\dots$ ) are empirical parameters. The distributions of the single-dose model parameters are represented with black boxplots, in which outliers are represented as black circles. The resulting curves from fitting the empirical parameter formulas are shown as purple solid lines, and their corresponding 95% confidence intervals are plotted as purple dashed lines. Panel (A) shows the parameter formula for the fraction of surviving cells ( $f_s$ ). Panel (B) shows the parameter formula for the proliferation rate of the surviving tumor cells ( $g_s$ ). Panel (C) shows the parameter formula for the proliferation rate of the irreversibly damaged tumor cells ( $g_d$ ). In panels (A–C), we observe that as the drug concentration increases, the corresponding single-dose model parameter values decrease exponentially. Panel (D) shows the parameter formula for the doxorubicin-induced death rate of irreversibly damaged cells ( $k_d$ ), which we approximated with an equation based on a Morse-potential relationship. Panel (E) shows the parameter formula for the doxorubicin-induced death delay rate of irreversibly damaged cells ( ${\gamma }_d$ ), which increases and then plateaus as the drug concentration increases. Median and range of quality of fit metrics for the empirical parameter formulas (n = 5) are NRMSE: 17.65 [5.45, 153.6], $R^{\mathit{2}}$ : 0.91 [0.78, 0.98], PCC: 0.95 [0.88, 0.99], and CCC: 0.85 [0.78, 0.88].