Fig 2: Model evaluation and experimental validation of tumor response kinetics in mice under different drug treatment strategies.a Simulated efficacy of different drug regimens used in clinical practice, including lapatinib plus capecitabine, pyrotinib plus capecitabine and single T-DM1. b Simulated antitumor effects of the new combination regimen of lapatinib or pyrotinib plus T-DM1 versus classic lapatinib or pyrotinib plus capecitabine. c Simulated tumor growth inhibition (TGI) in response to combinations of lapatinib or pyrotinib with T-DM1 over a range of doses (lapatinib 20–100 mg/kg qd, pyrotinib 6–30 mg/kg qd, and T-DM1 2–10 mg/kg q3w, respectively). Tumor volumes were analyzed after three treatment cycles (e.g., on day 62). d QSP model prediction and in-house experimental validation of tumor growth kinetics in vivo in response to combination regimen of pyrotinib (10 mg/kg) plus T-DM1 (10 mg/kg); S, simulation; D, experimental data. e Simulated antitumor effects of sequential therapies of lapatinib or pyrotinib plus capecitabine followed by T-DM1 or T-DM1 followed by lapatinib or pyrotinib plus capecitabine. f The drug administration protocol of the in vivo mouse xenograft experiments (L, lapatinib; C, capecitabine; P, pyrotinib; see Methods section for details). g QSP model prediction and in-house experimental validation of tumor growth kinetics in vivo in response to sequential regimen between T-DM1 and lapatinib plus capecitabine; S, simulation; D, experimental data. h Simulated tumor growth trends under single lapatinib or pyrotinib, NRG1 (representing the overexpression-induced resistant scenario), and the combination as well as in the presence of HER3 mAb. i Simulated tumor growth trends under single lapatinib, PI3K inhibitor and their combination when tumor growth is highly dependent on the PI3K/AKT pathway. See the legends for the detailed dosage and frequency of administrations, where a treatment cycle is 21 days and d1–d14 means capecitabine is administered on days 1–14 of each cycle.

Fig 3: Effect of pyrotinib treatment on ErbB signaling in SKBR3 cells and corresponding model calibration.a Dose-dependent inhibition of EGFR after pyrotinib and EGF treatment for 60 min. b Dose-dependent inhibition of HER3 after pyrotinib and NRG1 treatment for 60 min. c Dose-dependent inhibition of HER4 after pyrotinib and NRG1 treatment for 60 min. d Dose-dependent inhibition of ERK after pyrotinib and EGF treatment for 60 min. e Dose-dependent inhibition of ERK after pyrotinib and NRG1 treatment for 60 min. f HER2 expression in response to pyrotinib treatment. g HER3 expression in response to pyrotinib treatment. a–g Contains immunoblots showing differential regulation of ErbB signaling proteins under various treatment conditions and the immunoblot data (n = 3) were quantified and used as calibration data; GAPDH levels were used as controls. Y axes are relative expression levels, with (a–e) normalized to their respective control condition (e.g., pyrotinib 0 nM) and (f, g) normalized to their respective maximum values. S, simulation; D, experimental data.

Fig 4: Sensitivity analysis and simulation of diverse treatment responses reflecting heterogeneous individual phenotypes.Partial rank correlation coefficients (PRCC) indices for parameters that significantly impact tumor volume (with absolute PRCC values greater than 0.05) under (a) NRG1 overexpression, (b) lapatinib plus capecitabine and (c) single agent T-DM1 conditions. The positive or negative signs of PRCC values represent a positive or negative effect on the model output. d Model simulations of tumor growth inhibition (TGI) after one cycle of treatment (e.g., TGI measured on day 20) using 13 different regimens for the four different response phenotypes, with blue representing a phenotype sensitive to all treatments, red—resistant to single T-DM1, green—resistant to lapatinib plus capecitabine, and black—resistant to all existing clinical standard therapies (lapatinib or pyrotinib plus capecitabine, single agent T-DM1 and T-DXd). The dosages are given as follows: lapatinib 100 mg/kg, qd; pyrotinib 30 mg/kg, qd; capecitabine 400 mg/kg, d1–d14 (e.g., days 1–14 of a 21-day cycle); T-DM1 30 mg/kg, q3w; T-DXd 10 mg/kg, q3w.

Fig 5: Model calibration of phospho-receptors and downstream PI3K/AKT, Ras/MAPK signal transduction at the cell level.a EGF (100 ng/mL) induces activation of EGFR. NRG1 (b 50 ng/mL, c 200 ng/mL) induces activation of HER3 and HER4. d EGF (20 ng/mL) induces activation of downstream AKT. e NRG1 (10 ng/mL) induces activation of downstream AKT. EGF (f 100 ng/mL, g 50 ng/mL) induces activation of downstream Raf and ERK axis. h NRG1 (10 ng/mL) induces activation of downstream ERK. Lapatinib induces time-dependent and dose-dependent inhibition of (i–l) HER2, (m–p) HER3 and downstream (q–s) AKT, (t–v) ERK. w NRG1 (50 ng/mL) reduces HER3 expression. x Lapatinib induces HER3 expression. a–x All data are from experiments in the SKBR3 cell line, except in (c) (MCF7, HER2 0–1+) and (f) (BT20 transfected with ErbB2). Y axes are relative expression levels (normalized to their respective maximum values). Lap condition 1, simultaneous addition of lapatinib and NRG1 (50 ng/mL) for 15 min; Lap condition 2, lapatinib alone for 15 min; Lap condition 3, NRG1 (50 ng/mL) for 15 min followed by lapatinib for 15 min; S, simulation; D, experimental data; Ctr, control/untreated condition.