Fig. 1

Schematics of cell proliferation model and proteomics-based cell cycle and apoptosis model of PANC-1 cells exposed to paclitaxel and birinapant. a Model structure for PANC-1 cell growth inhibition by paclitaxel and birinapant, alone and combined. B: birinapant; P: paclitaxel. The cell number N (blue circle) increases as cells proliferate in an exponential manner, with net growth rate constant k_G. Concentration-dependent cytotoxic signals for the two drugs are modeled by nonlinear Hill functions with transduction delays (rounded rectangles), and mediate removal of cells (cell killing; downward blue arrow) from the population. The killing signals are additive. The Ψ drug interaction term is fixed to 1 for single-drug treatment but is fitted for drug combinations. b Structure of the proteomics-based cell cycle and apoptosis model for cells exposed to birinapant (B) and paclitaxel (P). The BRP/PTX combination is represent as B&P. Pink boxes: proteins quantified by proteomics; grey boxes: proteins measured by western blot; circles: cells in different cell cycle stages or undergoing apoptosis. Activation of a protein/signal is denoted by a black arrow, inhibition by a red bar. Each live cell progresses through G₀/G₁, S, and G₂/M phases and divides into two progeny cells. Live cells can also undergo spontaneous apoptosis (Apo). Birinapant acts by accelerating degradation of cIAP1, an inhibitor of apoptosis. Paclitaxel-induced mitotic arrest (MA) is mediated by ELYS, and the mitotically-arrested cells are prone to apoptosis, regulated by cIAP1, BAX, Bcl2, and the delayed signal of ASPP2. The mitotically-arrested cells may also undergo mitotic slippage and become polyploid cells (PL). The transition rate constants between the cell cycle stages and to apoptosis are represented by the ‘k’ parameters, described in Table 1