Table 1.

Mathematical models to describe dynamic drug sensitivity data: We present the equations used for each of the three different structural models that were fit to the time-resolved drug sensitivity assays.

Description	Model equation	Variables and parameters
Single static model	$V_{\sin gstat}(d)=\frac{V_{\max }}{1+\exp \left(m_{ss}(d-c_{ss})\right)}$	V = fraction of cells viable in population Vmax = maximum viability of cell population (baseline viability at dose = 0 µM) d = dose of doxorubicin (µM) mss = slope of loss of viability as dose increases, mss = $\frac{1}{\mathrm{\sigma }}$ css = LD50 to describe all data assuming no change in time d = dose of doxorubicin (µM)
Single dynamic model	$V_{sindyn}(d,t)=\frac{V_{\max }}{1+\exp \left(m_{sd}(t)(d-c_{sd}(t))\right)}$	msd(t) = slope of loss of viability as dose increases msd(t) = $\frac{1}{\mathrm{\sigma }(t)}$ for each population csd (t) = LD50 to describe data at each time point
Two population dynamic model	$V_{twopop}(d,t)=V_{\max }\left(\frac{f_{sens}(t)}{1+\exp (m_{sens}(d-c_{sens})}+\frac{1-f_{sens}(t)}{1+\exp (m_{res}(d-c_{res})}\right)$	msens(t) = slope of loss of viability as dose increases, msens(t) = $\frac{1}{\mathrm{\sigma }(sens)}$, mres(t) = slope of loss of viability as dose increases, mres(t) = $\frac{1}{\mathrm{\sigma }(res)}$csens = LD50 to describe sensitive population cres = LD50 to describe resistant population

The column labeled, “Model equation” provides the functional form of the equation, with t representing a parameter that was fit to the data set at each time point measured. The column labeled, “Variables and parameters” describes the variables used in terms of their physical meaning and their relation to the time-resolved drug sensitivity assays.