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.

In systems biology, models often contain a large number of unknown or only roughly known parameters that must be identified. This work examines the question of whether or not these parameters can in fact be estimated from available measurements. We consider identifiability of unknown parameters in biochemical reaction networks obtained from first-principles-modeling of metabolic and signal transduction networks. Such systems consist of continuous time, nonlinear differential equations. Several methods exist for answering the question of identifiability for such systems; many of which restate the question of identifiability as one of observability. We consider the application of such methods to a representative biological system: the NF-κB signal transduction pathway. It is shown that existing observability based strategies, which rely on finding an analytical solution, require significant simplifications to be applicable to systems biology problems which are often not feasible. For this reason, a new method based on the use of an 'empirical observability Gramian' for checking identifiability is proposed. This method is demonstrated through the use of a simple biological example.

(2 nd ed.) ISBN: 978-1-934115-02-2 (BSB)

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