Cell-to-cell variability in JAK2/STAT5 pathway components and cytoplasmic volumes define survival threshold in erythroid progenitor cells

Abstract

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.

Mathematical modeling of variability in intracellular signaling

“…A first approach is often to visualize the data in a two-or three-dimensional space, employing linear or nonlinear dimension reduction methods (Figure 1A). These tech-Levine et al 22 Luo and Zhao 21 Lun et al 26 statistical mechanistic network analysis clustering dimension reduction Loos et al 34 Hasenauer et al 33 Dixit et al 37 Spencer et al 1 Pyne et al 24 Qiu et al 20 Filippi et al 31 Palaniappan et al 29 Kallenberger et al 30 Dharmarajan et al Slack et al 16 Johnsson et al 23 Sachs et al 25 Adlung et al 32…”

“…To distinguish these, additional statistical assumptions are made about the system. This yields a likelihood function, which either describes the whole population density 33,34,31 or the deviance between the statistical moments of the data and those predicted by the model 32 . The likelihood function can then by maximized 33,34,32 , and, e.g., subsequently be used to calculate profile likelihoods to assess the uncertainty of the estimated population parameters.…”

“…This yields a likelihood function, which either describes the whole population density 33,34,31 or the deviance between the statistical moments of the data and those predicted by the model 32 . The likelihood function can then by maximized 33,34,32 , and, e.g., subsequently be used to calculate profile likelihoods to assess the uncertainty of the estimated population parameters. Alternatively, sampling is performed and the likelihood function is, e.g., incorporated into a Bayesian setting with a prior distribution for the population parameters 31,34 , and uncertainty can directly be assessed from samples of the posterior distribution.…”

“…Even though it is in principle possible for many of the approaches to integrate different data types, only few publications 30,32 actually used single-cell data together with population average data. Here, a key challenge is to choose the weighting of the data sets.…”