Bistability Analyses of a Caspase Activation Model for Receptor-induced Apoptosis

Abstract

Apoptosis is an important physiological process crucially involved in development and homeostasis of multicellular organisms. Although the major signaling pathways have been unraveled, a detailed mechanistic understanding of the complex underlying network remains elusive. We have translated here the current knowledge of the molecular mechanisms of the deathreceptor-activated caspase cascade into a mathematical model. A reduction down to the apoptotic core machinery enables the application of analytical mathematical methods to evaluate the system behavior within a wide range of parameters. Using parameter values from the literature, the model reveals an unstable status of survival indicating the need for further control. Based on recent publications we tested one additional regulatory mechanism at the level of initiator caspase activation and demonstrated that the resulting system displays desired characteristics such as bistability. In addition, the results from our model studies allowed us to reconcile the fast kinetics of caspase 3 activation observed at the single cell level with the much slower kinetics found at the level of a cell population.Apoptosis is a genetically defined major form of programmed cell death enabling the organism to remove unwanted cells, e.g. during embryonal development and after immune responses, to select educated immune cells and to eliminate virally infected and transformed cells (1, 2). Enhanced or inhibited apoptotic cell death can be involved in severe pathological alterations, including developmental defects, autoimmune diseases, neurodegeneration, or cancer. Extrinsic and intrinsic apoptotic pathways can be distinguished, although partly employing overlapping signal transduction pathways. A hallmark of the ongoing apoptotic process is the activation of a family of aspartatedirected cysteine proteases, the caspases. Caspases are produced as proenzymes and become activated upon cleavage (3). Activation of caspases finally dismantles the cells via the cleavage of important regulatory and structural proteins and enables phagocytic removal of the dying cell (4). A simplified outline of the extrinsic pathway of apoptosis induction after death receptor stimulation is depicted in Fig. 1.Mathematical modeling and systems theory can provide valuable tools to get insight into complex dynamical systems, to test hypotheses, and to identify weak points (5, 6). Previous modeling approaches in apoptosis focused on the extrinsically triggered pathways, resulting in complex models (7,8). The model parameters were fitted to data derived from cell population studies showing caspase activation in a range from 30 min to several hours. These models can describe and nicely illustrate certain aspects of the signal transduction pathway. However, more recent experimental results performed at the single cell level show that the majority of caspases are activated within a very short time interval (Ͻ15 min) (9 -12).Obviously, the single cell level is relevant for a mechanistic understanding. With the focus...

Dynamics of outer mitochondrial membrane permeabilization during apoptosis

“…10,11,[36][37][38][39] Time-lapse fluorescence imaging of living cells, a noninvasive method appropriate to measure the real-time kinetics of apoptotic processes, can directly be linked with mathematical models of intracellular apoptosis signaling. 10,40 The mathematical model proposed here for the mechanism of spatial MOMP waves builds on the lex parsimoniae, otherwise also known as the principle of Occam's razor.…”

Systems biology and the integration of mechanistic explanation and mathematical explanation

“…Explaining stability under a range of variation in parameter values again requires mathematical modeling. The Eissing et al (2004) study discussed does such an analysis (for more details see Eissing et al, 2005), as do other systems biological studies of bistability in the context of apoptosis (Bagci et al, 2006;Cui et al, 2008;Ho & Harrington, 2010). The bistability modeling by Legewie et al (2006) includes both the extrinsic (death receptor initiated) and intrinsic (mitochondrion initiated) apoptosis pathway.…”

“…2 in one column. ] The mathematical model by Eissing et al (2004) analyzes bistability. Based on the network of biochemical pathways downstream of the death receptor stimulus shown in Fig.…”

Unraveling cellular pathways contributing to drug-induced liver injury by dynamical modeling

“…In their bistability analysis of this simple model, the 'alive' stage of the cell was unstable for biologically reasonable parameter values, implying that cells would go into apoptosis with only a little bit of noise. Eissing et al [110] therefore suggest that caspase-8 needs a similar negative feedback loop as caspase-3 has via IAP. In the case of caspase-8, this role could be played by bifunctional apoptosis regulator (BAR), i.e.…”

“…Eissing et al [110] analyzed the bistability of the caspase cell-extrinsic pathway, because this is a mandatory property of the apoptotic pathway: On the one hand, cells should be resistant against minor fluctuations in signal in order not to trigger apoptosis by accident. On the other hand, when a cell is prompted into apoptosis, it should not be possible to revert back.…”