Supplementary Table S3 shows ratio of each schedule to the standard schedule at day 100 for simulated cell lines

A, B, Posterior prediction of the total cell count. Each panel shows the posterior predicted total number of live cells over 5 days for a specific combination of palbociclib and fulvestrant for −DOX (A) and +DOX (B) cells. The line represents the median posterior predicted live cell count value over 5 days and the gray shaded area corresponds to the 95% credible interval of the posterior predictive values. The datapoints represent the observed cell counts from the drug synergy experiments used to train the model. The concentration of palbociclib increases across the columns and is denoted at the top of each column; the concentration of fulvestrant increases down the rows and is denoted to the right of each row. The unit of drug concentrations is nmol/L. C, D, The posterior predictive number of cells in each phase of the cell cycle for −DOX (C) and +DOX (D) cells treated with fulvestrant and palbociclib in combination. Each panel corresponds to a specific dose of fulvestrant and palbociclib. The line represents the median posterior predictive value and the shaded area corresponds to the 95% credible interval of the posterior predictive values. The datapoints represent the observed cell phase counts from the cell-cycle analysis experiments used to train the model. The concentrations of fulvestrant and palbociclib increase across the columns and are denoted at the top of each column. Red, blue, and green represent the G0–G1, S, and G2–M phases, respectively. See Supplementary Fig. S5 and S6 for more sets of drug concentrations.

In silico clinical trial schedules of palbociclib

Supplementary Fig. S1 shows an illustration of multistage cell-cycle model with m = 4

HER2 counting at a single cell level

Supplementary Fig. S7 shows posterior prediction of effective drug model parameters

In silico trial predictions of multiple palbociclib treatment administration schedules in combination with fulvestrant. For −DOX cells (A) and for +DOX cells (B), The panels show the box plots for the number of cells at day 100. The p-values were computed using the Wilcoxon test. In each panel, we only show the largest two p-values. The p-values not shown in the panels, for the rest of pairs of treatment schedules, are all smaller than 1e − 15 in A and 1e − 13 in B. For −DOX cells (C) and for +DOX cells (D), The panels show the waterfall charts for 150 random samples from the group of 1,500 simulations in descending order of cell number at day 100. For −DOX cells (E) and for +DOX cells (F), The panels show the predictions of in silico cell growth trajectories by taking the ratio of each schedule to the standard schedule (daily, 125 mg, 3 weeks on, 1 week off). The shaded area corresponds to the 95% credible interval of the posterior predictive values.

Supplementary Fig. S11 shows in silico simulation of palbociclib resistant MCF7 cell line

Supplementary Table S2 shows quantifications of cell growth rates

Supplementary Table S1 shows parameter distributions for model inference

Supplementary Appendix S3 shows multistage model versus logistic model

Pharmacodynamics of palbociclib and fulvestrant. A–D, In each panel, the y-axis represents the ratio of the G1-to-S transition rate treated by palbociclib/fulvestrant to the G1-to-S transition rate in control (zero drug concentration) and the x-axis represents drug concentrations in the unit of nmol/L. The gray shaded area corresponds to the 95% credible interval of the posterior predictive values. A, Fulvestrant only in −DOX cells. B, Palbociclib only in −DOX cells. C, Fulvestrant only in +DOX cells. D, Palbociclib only in +DOX cells. E and F are the surface plots for G1–S TR50 (z-axis) with respect to the combinations of palbociclib (x-axis) and fulvestrant (y-axis). E, For −DOX cells: because the response to fulvestrant is extremely sensitive, the unit is rescaled to 1e−6 nmol/L; palbocilib is in the unit of nmol/L. F, For +DOX cells: the units of palbociclib and fulvestrant are both in nmol/L.

Supplementary Fig. S9 shows in silico trial predictions of multiple palbociclib treatment administration schedules in combination with fulvestrant

Supplementary Fig. S4 shows using LOOIC to determine number of stages m

IC50s versus G1–S TR50 of palbociclib and fulvestrant

Supplementary Fig. S6 shows posterior prediction of the cell cycle phase counts

Supplementary Fig. S5 shows posterior prediction of the total cell count

Supplementary Fig. S13 shows in silico simulation of new cell lines - 1

Supplementary Fig. S15 shows in silico simulation of new cell lines - 3

Abstract Cyclin-dependent kinases 4/6 (CDK4/6) inhibitors such as palbociclib are approved for the treatment of metastatic estrogen receptor–positive (ER+) breast cancer in combination with endocrine therapies and significantly improve outcomes in patients with this disease. However, given the large number of possible pairwise drug combinations and administration schedules, it remains unclear which clinical strategy would lead to best survival. Here, we developed a computational, cell cycle–explicit model to characterize the pharmacodynamic response to palbociclib-fulvestrant combination therapy. This pharmacodynamic model was parameterized, in a Bayesian statistical inference approach, using in vitro data from cells with wild-type estrogen receptor (WT-ER) and cells expressing the activating missense ER mutation, Y537S, which confers resistance to fulvestrant. We then incorporated pharmacokinetic models derived from clinical data into our computational modeling platform. To systematically compare dose administration schedules, we performed in silico clinical trials based on integrating our pharmacodynamic and pharmacokinetic models as well as considering clinical toxicity constraints. We found that continuous dosing of palbociclib is more effective for lowering overall tumor burden than the standard, pulsed-dose palbociclib treatment. Importantly, our mathematical modeling and statistical analysis platform provides a rational method for comparing treatment strategies in search of optimal combination dosing strategies of other cell-cycle inhibitors in ER+ breast cancer. Significance: We created a computational modeling platform to predict the effects of fulvestrant/palbocilib treatment on WT-ER and Y537S-mutant breast cancer cells, and found that continuous treatment schedules are more effective than the standard, pulsed-dose palbociclib treatment schedule.