Fig 1.
Schematic illustration of model structures with curves for total cell number (black) partitioned into resistant (red) and sensitive (green) fractions.
Regions of the curves are marked to show the effects of key model parameters (A). The effects of three different models of k are shown for model 1 with an exponential time delay on k (B), model 2 with a linear time delay on k (C) or model 3 with no time delay on k (D).
Table 1.
Parameters were either calibrated from growth data (see Methods - Model Calibration) or determined from longitudinal cell growth data (see Methods - Quantification of tr).
Table 2.
Summary of model assumptions in models selected for further analysis.
Fig 2.
Micrograph example illustrating doxorubicin induced proliferation delay.
In this example demonstrating a doxorubicin induced proliferation delay, after exposure to 150 nM doxorubicin at time 0 (A) MCF7 cells stop proliferating and remain in arrest for 315 hours. At 14 days (B), cells have died off in the intervening time, and proliferation has not occurred, and at 21 days (C), proliferation has produced a small patch of cells indicated by the red arrow; proliferation then continues and produces a patch of hundreds of cells by 28 days (D). Untreated cells grow to confluence in approximately four days.
Fig 3.
Cell population response to doxorubicin regimens.
Population level response to 24 hour doxorubicin exposures is quantified as doxorubicin concentration varies in the MCF7 cell line (A), the BT474 cell line (D), and the MDA-MB-231 cell line (G), as the interval between two 24 hour doxorubicin exposures varies at 75 nM in the MCF7 cell line (B), at 35 nM in the BT474 cell line (E), and at 200 nM in the MDA-MB-231 cell line (H), and as the number of sequential 24 hour doxorubicin exposures varies at a two day interval and 75 nM in the MCF7 cell line (C), at a zero day interval (continuous exposure) and 35 nM in the BT474 cell line (F), and at a two day interval and 200 nM in the MDA-MB-231 cell line (I). Each curve represents the average of six (A, D, G) or 12 (B, C, E, F, H, I) replicate samples, and 95% confidence intervals are marked by the shaded regions. All curves are aligned such that t = 0 is the beginning of the final drug exposure for that treatment group.
Fig 4.
Percentage of non-recovering replicate cell populations.
The percentage of replicate cultures which did not recover during the course of the experiment is shown as doxorubicin concentration varies in the MCF7 cell line (A), the BT474 cell line (D), and the MDA-MB-231 cell line (G), as the interval between two 24 hour doxorubicin exposures varies at 75 nM in the MCF7 cell line (B), at 35 nM in the BT474 cell line (E), and at 200 nM in the MDA-MB-231 cell line (H), and as the number of sequential 24 hour doxorubicin exposures varies at a two day interval and 75 nM in the MCF7 cell line (C), at a zero day interval (continuous exposure) and 35 nM in the BT474 cell line (F), and at a two day interval and 200 nM in the MDA-MB-231 cell line (I). Each value is the percentage of 6 (A, D, G) or 12 (B, C, E, F, H, I) replicates.
Fig 5.
Proliferation delay, tr varies with dosing regimen.
Length of growth arrest of resistant cells (tr) is displayed as a Tukey box-and-whiskers plot as doxorubicin concentration varies in the MCF7 cell line (A), the BT474 cell line (D), and the MDA-MB-231 cell line (G), as the interval between two 24 hour doxorubicin exposures varies at 75 nM in the MCF7 cell line (B), at 35 nM in the BT474 cell line (E), and at 200 nM in the MDA-MB-231 cell line (H), and as the number of sequential 24 hour doxorubicin exposures varies at a two day interval and 75 nM in the MCF7 cell line (C), at a zero day interval (continuous exposure) and 35 nM in the BT474 cell line (F), and at a two day interval and 200 nM in the MDA-MB-231 cell line (I). The number of replicates in each group varies between 3 and 12; all replicates in which recovery is observed are included (see Fig 4).
Fig 6.
Examples of model fitting demonstrate the ability of model 1 to capture long term dynamics.
Examples of model fitting are shown for a single replicate culture in the MCF7 (A), BT474 (B), and MDA-MB-231 (C) cell lines. The curve represents a response to the doxorubicin concentration used in serial treatment within the cell line– 75 nM for the MCF7 line, 35 nM for the BT474 cell line, and 200 nM for the MDA-MB-231 cell line. Data is shown as open blue circles, while the best-fit curve for model 1 (the total number of sensitive and resistant cells) is shown in black, with the resistant and sensitive compartments shown in red and green respectively.
Table 3.
Leave-one-out cross validation.
The performance of model 1 at predicting data excluded from the training set is broken down by cell line and whether the replicate culture recovered or not (see Fig 4).
Fig 7.
Critical time is estimated based on the best fit to model 1 for each replicate culture in the MCF7 cell lines and shown as a Tukey box-and-whiskers plot as doxorubicin concentration varies in the MCF7 cell line (A), the BT474 cell line (D), and the MDA-MB-231 cell line (G), as the interval between two 24 hour doxorubicin exposures varies at 75 nM in the MCF7 cell line (B), at 35 nM in the BT474 cell line (E), and at 200 nM in the MDA-MB-231 cell line (H), and as the number of sequential 24 hour doxorubicin exposures varies at a two day interval and 75 nM in the MCF7 cell line (C), at a zero day interval (continuous exposure) and 35 nM in the BT474 cell line (F), and at a two day interval and 200 nM in the MDA-MB-231 cell line (I). The number of replicates in each group varies between 3 and 12; all replicates in which recovery is observed are included. The 95% confidence interval on the mean is shown by the shaded region.
Table 4.
Summary of model assumptions tested in model identifiability analysis.