Mathematical modeling reveals threshold mechanism in CD95-induced apoptosis

Abstract

Mathematical modeling is required for understanding the complex behavior of large signal transduction networks. Previous attempts to model signal transduction pathways were often limited to small systems or based on qualitative data only. Here, we developed a mathematical modeling framework for understanding the complex signaling behavior of CD95(APO-1/Fas)-mediated apoptosis. Defects in the regulation of apoptosis result in serious diseases such as cancer, autoimmunity, and neurodegeneration. During the last decade many of the molecular mechanisms of apoptosis signaling have been examined and elucidated. A systemic understanding of apoptosis is, however, still missing. To address the complexity of apoptotic signaling we subdivided this system into subsystems of different information qualities. A new approach for sensitivity analysis within the mathematical model was key for the identification of critical system parameters and two essential system properties: modularity and robustness. Our model describes the regulation of apoptosis on a systems level and resolves the important question of a threshold mechanism for the regulation of apoptosis.

Sensitivity analysis approaches applied to systems biology models

“…Bentele et al [4] proposed a WALS coefficient to measure the global parameter sensitivities. The concept of this method is similar to the Morris sensitivity analysis method.…”

“…In addition, sensitivity analysis is important in model development. It helps us to test whether a model prediction is dependent on the model assumptions and guide parameter estimation and experimental design [4]. Sensitivity analysis is also useful for model simplification by quantifying the dependence of model outputs on its inputs.…”

Thresholds in transient dynamics of signal transduction pathways

“…As it has been discussed in the introduction sigmoidal stimulus-response curves have been related to activation thresholds of biochemical networks [8,11,12,13,14,15,16,17]. So far, experimental and modeling efforts have focused on sigmoidal stimulus-response curves in the steady state.…”

“…We here consider a stimulus as either some external input, say extracellular ligands, as well as initial condition (concentrations) of intracellular signaling proteins [15]. An example for an extracellular stimulus is the gene transcription network studied in this work.…”

“…Ferrell has concluded, on the basis of experimental data, that the MAPK cascade is optimized to convert a graded input into a switch-like output [9]. Ultrasensitive responses leading to sigmoidal stimulusresponse curves have been related to activation thresholds of biochemical networks in the literature [8,11,12,13,14,15,16,17]. Experimental measurements in networks with multiple phosphorylations have shown that the stimulus has to exceed a threshold concentration to activate downstream events [10,11,12,13].…”