Identifying fragilities in biochemical networks: robust performance analysis of Fas signaling-induced apoptosis

Proper control of apoptotic signaling is critical to immune response and development in multicellular organisms. Two tools from control engineering are applied to a mathematical model of Fas ligand signaling-induced apoptosis. Structured singular value analysis determines the volume in parameter space within which the system parameters may exist and still maintain efficacious signaling, but is limited to linear behaviors. Sensitivity analysis can be applied to nonlinear systems but is difficult to relate to performance criteria. Thus, structured singular value analysis is used to quantify performance during apoptosis rejection, ensuring that the system remains sensitive but not overly so to apoptotic stimuli. Sensitivity analysis is applied when the system has switched to the death-inducing, apoptotic steady state to determine parameters significant to maintaining the bistability. The analyses reveal that the magnitude of the death signal is fragile to perturbations in degradation parameters (failures in the ubiquitin/proteasome mechanism) while the timing of signal expression can be tuned by manipulating local parameters. Simultaneous parameter uncertainty highlights apoptotic fragility to disturbances in the ubiquitin/proteasome system. Sensitivity analysis reveals that the robust signaling characteristics of the apoptotic network is due to network architecture, and the apoptotic signaling threshold is best manipulated by interactions upstream of the apoptosome.