Cell response heterogeneity upon drug treatment is a leading cause of reduced drug efficacy in preclinical cancer research. Although single-cell studies have revealed the depth of cellular heterogeneity observed between in tumor cells, the regulatory impact of cell variability on therapeutic response remains unclear. Here, we present a new ODE model of the extrinsic apoptosis initiation by death-ligands. This model is calibrated on fluorescent time-trajectories (FRET) of hundreds of clonal HeLa cells treated with different amounts of Tumor necrosis factor-related apoptosis-inducing ligand (TRAIL). By highlighting the different steps in the regulation of apoptosis, and the associated timeline, we locate an initial cell fate decision just after TRAIL binding and the presence of additional regulation at the receptor that only benefits the drug-sensitive population. Then, our study provides evidence that increasing the dose of TRAIL actually has small effects within each population (resistant or sensitive) but rather accentuates the differences between the two, affecting the population dynamics in two different ways depending on their response to the drug. Finally, the distribution of 3 parameters of our mechanistic model, according to the cell drug response, suggests the existence of an determinant threshold in C8 dynamics, independent of the drug dose, that distinguishes cells drug-resistant or sensitive, that could be used to control or predict cell drug-response in the future.