Heterogeneity reduces sensitivity of cell death for TNF-Stimuli

Abstract

BackgroundApoptosis 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.ResultsThis 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.ConclusionsCell 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.

The Experimental Side of Parameter Estimation

“…Calcium propagation was one of the first systems in which microinjection experiments [42] were utilised in the development of mathematical models, see for example [51,61]. Other systems where microinjection experiments where used are transport across the cell membrane [4] and apoptosis signalling, see [45] and Fig. 5.18, which measures the dependence of the time of death on the injected amount of caspase-3 in KYM-1 cells.…”

“…The first one is the already mentioned TNFinduced pro-and anti-apoptotic signalling [45]. The other is [40], which studies how the pseudo-phosphatase STYX regulates ERK signalling and affects cell migration and differentiation in HeLa and PC12 cells, respectively.…”

“…While some parameters can be observed in a steady-state, for example the steady-state protein concentrations, other parameters are only visible during transient perturbations. In the model of TNF-induced pro-and anti-apoptotic signalling [45] illustrated in (Fig. 5.1) whose states are concentrations of proteins and mRNA's, roughly half of the flows are zero in the absence of TNF, as of the 106 reactions, only 52 are non-zero: 30 turnover reactions and 22 reactions linked to the shuttling between cytoplasm and nucleus of the transcription factor nuclear factor kappa B (NF-κB).…”

“…If the enzyme amount is constant small compared to the substrate amount, the substrate will be consumed linearly over time. [45] continuous measurements of the activity of caspase-3 for samples taken at different time points post stimulation. From these measurements, the actual enzymatic activity needs to be inferred and corresponds to the slope of the measured curves.…”

Systems‐based understanding of pharmacological responses with combinations of multidisciplinary methodologies

“…Systems biology markup language (SBML) is one of the de facto languages used to describe molecular network pathways; rate equations governing chemical/biological reactions can be described in an SBML-compliant format, which makes simulations easy to perform [29]. Indeed, many reports provide systems biology maps in SBMLcompliant formats [30][31][32]. In addition, several software platforms are available that enable the easy editing of SMBL maps using graphical user interfaces (Table 2) [33].…”