Highlights d Mathematical modeling enables integration of heterogeneous data d Single-cell modeling captures a binary decision process d Multiple sources of cell-to-cell variability exist in erythroid progenitor cells d Minimal amount of active STAT5 is sufficient for erythroid progenitor cell survival

Highlights• Mathematical modeling enables integration of heterogeneous data • Single-cell modeling captures binary decision process • Multiple sources of cell-to-cell variability in erythroid progenitor cells • Minimal amount of active STAT5 sufficient for survival of erythroid progenitor cells Summary Survival or apoptosis is a binary decision in individual cells. Yet, at the cell population level, a graded increase in survival of CFU-E cells is observed upon stimulation with Erythropoietin (Epo). To identify components of JAK2/STAT5 signal transduction that contribute to the graded population response, a cell population-level model calibrated with experimental data was extended to study the behavior in single cells. The single-cell model showed that the high cell-to-cell variability in nuclear phosphorylated STAT5 is caused by variability in the amount of EpoR:JAK2 complexes and of SHP1 as well as the extent of nuclear import due to the large variance in the cytoplasmic volume of CFU-E cells. 24 to 118 pSTAT5 molecules in the nucleus for 120 min are sufficient to ensure cell survival. Thus, variability in membraneassociated processes are responsible to convert a switch-like behavior at the single-cell level to a graded population level response.

Mixed effect modeling is widely used to study cell-to-cell and patient-to-patient variability. The population statistics of mixed effect models is usually approximated using Dirac mixture distributions obtained using Monte-Carlo, quasi Monte-Carlo, and sigma point methods.Here, we propose the use of a method based on the Cramér-von Mises Distance, which has been introduced in the context of filtering. We assess the accuracy of the different methods using several problems and provide the first scalability study for the Cramér-von Mises Distance method. Our results indicate that for a given number of points, the method based on the modified Cramér-von Mises Distance method tends to achieve a better approximation accuracy than Monte-Carlo and quasi Monte-Carlo methods. In contrast to sigma-point methods, the method based on the modified Cramér-von Mises Distance allows for a flexible number of points and a more accurate approximation for nonlinear problems.