Heterogeneity reduces sensitivity of cell death for TNF-stimuli

Abstract

Background: Apoptosis is a form of programmed cell death essential for the maintenance of homeostasis and the removal of potentially damaged cells in multicellular organisms. By binding its cognate membrane receptor, TNF receptor type 1 (TNF-R1), the proinflammatory cytokine Tumor Necrosis Factor (TNF) activates pro-apoptotic signaling via caspase activation, but at the same time also stimulates nuclear factor κB (NF-κB)-mediated survival pathways. Differential dose-response relationships of these two major TNF signaling pathways have been described experimentally and using mathematical modeling. However, the quantitative analysis of the complex interplay between pro- and anti-apoptotic signaling pathways is an open question as it is challenging for several reasons: the overall signaling network is complex, various time scales are present, and cells respond quantitatively and qualitatively in a heterogeneous manner.

Results: This study analyzes the complex interplay of the crosstalk of TNF-R1 induced pro- and anti-apoptotic signaling pathways based on an experimentally validated mathematical model. The mathematical model describes the temporal responses on both the single cell level as well as the level of a heterogeneous cell population, as observed in the respective quantitative experiments using TNF-R1 stimuli of different strengths and durations. Global sensitivity of the heterogeneous population was quantified by measuring the average gradient of time of death versus each population parameter. This global sensitivity analysis uncovers the concentrations of Caspase-8 and Caspase-3, and their respective inhibitors BAR and XIAP, as key elements for deciding the cell's fate. A simulated knockout of the NF-κB-mediated anti-apoptotic signaling reveals the importance of this pathway for delaying the time of death, reducing the death rate in the case of pulse stimulation and significantly increasing cell-to-cell variability.

Conclusions: Cell ensemble modeling of a heterogeneous cell population including a global sensitivity analysis presented here allowed us to illuminate the role of the different elements and parameters on apoptotic signaling. The receptors serve to transmit the external stimulus; procaspases and their inhibitors control the switching from life to death, while NF-κB enhances the heterogeneity of the cell population. The global sensitivity analysis of the cell population model further revealed an unexpected impact of heterogeneity, i.e. the reduction of parametric sensitivity.

Figure 1

Illustration of the Signaling Pathways and Interactions Initiated by TNF-R1. Ligand stimulated TNF-R1 activates two major signaling pathways, pro- and anti-apoptotic cellular responses (red and blue background, respectively). The ligand-receptor interaction and signal complex formation is outlined in the green area.

Figure 2

Experimentally obtained Dynamic Dose-Responses. (A) NF-κB in the nucleus after 1 ng/ml and 10 ng/ml TNF for 30 minute pulse or continuous stimulation, as shown by EMSA at different time points. Oct-1 served as loading control. (B) Caspase-3 activity assay for continuous stimulation of 1 ng/ml TNF (solid lines) measured 4-8 h post stimulus. Control experiments without TNF (magenta) and with the caspase inhibitor Z-VAD-fmk (dashed lines). (C) and (D) Cell viability over time for 10 different TNF concentrations (0-100 ng/ml TNF). The surfaces connect the measured data points. Continuous (C) and 30 minute pulse (D) stimulations, both including error bars from three independent experiments. The isoclines (lines connecting points of same cell viability) are shown projected onto the 0% planes.

Figure 3

Simulations of the Single Cell Model. (A) and (B) Single cell time course simulations of relative NF-κB translocation into the nucleus and Caspase-3 activation for TNF concentrations in the range of 0.01 - 100 ng/ml; (A) for continuous TNF stimulation and (B) for 30 minute TNF pulse stimulation. Relative activities represent the concentration time courses divided by their maximum values. For NF-κB, the relative activity is color coded such that blue depicts a low, yellow a medium and red a high nuclear accumulation. For Caspase-3, the color of a complete trajectory stands for the time of death: early death in red, late death in yellow, cell survival in green.

Figure 4

Cell Population Sensitivity Analysis. (A) - (F) Time of death for 2500 cells with lognormally distributed production rates, plotted as a projection versus one of these rates normalized by its nominal value. Cells not dying within 100 hours post stimulus with TNF are classified as survivors and plotted as magenta or cyan dot in the zone "> 100" at a random ordinate, the others are plotted as red or blue dot. The number of dying cells is approximated using robust linear regression (black solid lines) and an estimate of the standard deviation of the error (black dash-dotted lines). (A), (C), (E) continuous stimulation with 10 ng/ml TNF. (B), (D), (F) 30 minute pulse stimulation with 10 ng/ml TNF. (A) - (B) projection with respect to the production rate of TNF receptors, (C) - (D) to IκBα mRNA expression and (E) - (F) to XIAP production.

Figure 5

Sensitivity and Heterogeneity Analysis of Wild Type and NF-κB Knockout Model. (A) - (B) Global sensitivity measures defined as the slope of the linear correlation of time of death versus each population parameters, obtained using robust linear regression on a log-log plot. Dots: cell population sensitivity, stars: sensitivity of the nominal cell. The color coding highlights the slope value: the more red the higher the magnitude of the sensitivity, and the vertical black lines connect cell population and nominal cell sensitivities of the same parameter. (A) continuous stimulation, (B) 30 minutes pulse stimulation. (C) - (D) Cell viability as a function of time for different continuous stimulation of TNF concentrations (1, 3, 10, 30 ng/ml). (C) Solid lines: wild type cell population, dashed lines: without activation of the NF-κB-pathway. (D) Box plots of the distribution of the time of death within the cell population for different TNF concentrations. The solid red line depicts the median values of the cell populations; blue box: second and third quartiles; dashed line: whiskers with a maximum length of 1.5 interquartile range; red pluses: outliers. White background: wild type cells, grey background: cells without NF-κB activation.