Kinetic modeling, phase diagrams analysis, and quantitative single-cell experiments are combined to investigate how multiple factors, including the XIAP:caspase-3 ratio and ligand concentration, regulate receptor-mediated apoptosis.
Based on protein expression levels, Lyapunov-based phase diagrams predict which pathways are required for a cell to undergo receptor-mediated cell death.Multiple inter-dependent factors, including the XIAP:caspase-3 ratio and ligand concentration, regulate the requirement for mitochondrial outer membrane permeabilization during receptor-mediated apoptosis.The E3 ubiquitin ligase activity of XIAP is essential for maintaining the ‘snap-action' regulation of effector caspase activity.Cell-to-cell variability in protein expression gives rise to mixed phenotypes in cell lines that map close to boundaries (separatrices) identified by Lyapunov exponent analysis.
In mammalian cells, extrinsic (receptor-mediated) apoptosis is triggered by binding of extracellular death ligands such as tumor necrosis factor (TNF) and TRAIL (TNF-related apoptosis-inducing ligand) to cognate receptors. When death receptors are activated, death inducing signaling complexes (DISCs) assemble causing activation and cleavage of initiator pro-caspases-8 and -10, which then cleave effector pro-caspases-3 and -7 in a multi-enzyme cascade (Riedl and Shi, 2004). Active effector caspases digest essential cellular proteins and activate the CAD nucleases that cleave genomic DNA, thereby killing cells. This cascade of DISC assembly followed by initiator and then effector caspase activation is sufficient to kill so-called type I cells (e.g. B lymphocytes), but most cell types exhibit a type II behavior in which mitochondrial outer membrane permeabilization (MOMP) is an essential step in the march to death (Scaffidi et al, 1998; Barnhart et al, 2003; Letai, 2008). Identifying factors that determine whether cells are type I or II is of practical and theoretical interest. From a practical perspective, whether a cell requires MOMP for apoptosis determines the potency of Bcl2 and similar oncogenes, the efficacy of anti-Bcl2 drugs such as navitoclax (ABT-263), and the sensitivity of cells to TRAIL and anti-TRAIL receptor antibodies, which are also investigational anti-cancer drugs (Newsom-Davis et al, 2009). From a theoretical perspective, the type I versus II choice exemplifies a common situation in mammalian cells in which overlapping signaling pathways play a greater or lesser role in controlling cell fate depending on cell type: it is remarkable that a simple three-step (receptor→initiator caspase→effector caspase) process is sufficient to trigger apoptosis in some cell types but that a much more complex route involving MOMP is required in others.
Attempts to understand why some cells require MOMP for cell death and others do not have identified differences in the oligomeric state of death ligand receptors and the efficiency of DISC formation as important variables. In cells in which DISCs form efficiently, initiator caspases are cleaved rapidly and sufficient effector pro-caspases are processed into their active forms to kill cells (type I cells; Scaffidi et al, 1999b). In type II cells, DISC formation seems to be less efficient, and it has been proposed that MOMP is required to amplify weak initiator caspase signals and thereby generate lethal effector caspase levels (Barnhart et al, 2003). However, it has recently become apparent that XIAP also plays a role in type I versus II choice: in XIAP knockout mice, liver cells switch from a type II to a type I phenotype (Jost et al, 2009) and XIAP is observed to be involved in the survival of type I cells treated with death ligands in culture (Maas et al, 2010).
In this paper, we attempt to place these observations in a quantitative context by analyzing a computational model of extrinsic cell death using a method drawn from dynamical system analysis, direct finite-time Lyapunov exponent (DLE) analysis. Our implementation of DLE analysis relates changes in the concentrations of protein in a model to an outcome several hours later. We computed DLEs for six regulators of apoptosis over a range of concentrations determined experimentally to represent a natural range of variation in parental or genetically modified tumor cell lines. This generated a phase space onto which individual cell lines could be mapped using quantitative immunoblotting data. Cell-to-cell variation was estimated by flow cytometry and also mapped onto the phase space. The most interesting regions of the space were those in which a small change in one or more initial protein concentration resulted in a dramatic change in phenotype. Such a boundary or separatrix was observed in slices of phase space corresponding XIAP versus pro-caspase-3 concentration (the [XIAP]:[caspase-3] ratio). In cells in which the ratio is low, a type I phenotype is predicted to occur; when the ratio is high, a type II phenotype is favored; and in cell lines that lie close to the separatrix, cell-to-cell variability is expected, with some cells exhibiting a type I phenotype and others a type II behavior. DLE analysis shows that the [XIAP]:[caspase-3] ratio is not the only controlling factor in type I versus II control: as receptor activity or ligand concentration increase, the position of the separatrix changes so as to expand the region in which the type I phenotype is favored.
We tested these predictions by manipulating XIAP and ligand levels in multiple cell lines and then followed cell death by imaging, flow cytometry, or clonogenic assays. We observed that when XIAP was knocked out (by homologous recombination) in the HCT116 colorectal cancer line, cells shifted from a pure type II to a type I phenotype, as predicted from the DLE phase diagram. SKW6.4 B-cell lymphoma cells were predicted to lie at a position in phase space that is insensitive to XIAP levels (within the range achievable by over-expression) and we confirmed this experimentally. Finally, T47D breast cancer cells were predicted—and observed—to straddle the separatrix and to exhibit cell-to-cell variability in fate, with some cells showing a type I and others a type II phenotype. As the concentration of TRAIL was increased, the ratio of type I to type II T47D cells increased, confirming the prediction that this ratio is controlled in a multi-factorial manner.
To extend our approach to mutations that change protein activity rather than protein level, we simulated the effects of changing rate constants that control ubiquitylation of caspase-3 following its binding to XIAP. We generated cells carrying a truncated form of XIAP that lacks the RING domain (XIAPΔRING) and cannot mediate the ubiquitylation of caspase-3 (this truncation leaves the affinity of XIAP for caspase-3 unchanged). We predicted and demonstrated experimentally that expression of XIAPΔRING disrupts normal snap-action control over caspase-3 activation. Our findings not only advance understanding of extrinsic apoptosis but also constitute a proof of principle for an approach to quantitative modeling of dynamic regulatory processes in diverse cell types.
Receptor-mediated apoptosis proceeds via two pathways: one requiring only a cascade of initiator and effector caspases (type I behavior) and the second requiring an initiator–effector caspase cascade and mitochondrial outer membrane permeabilization (type II behavior). Here, we investigate factors controlling type I versus II phenotypes by performing Lyapunov exponent analysis of an ODE-based model of cell death. The resulting phase diagrams predict that the ratio of XIAP to pro-caspase-3 concentrations plays a key regulatory role: type I behavior predominates when the ratio is low and type II behavior when the ratio is high. Cell-to-cell variability in phenotype is observed when the ratio is close to the type I versus II boundary. By positioning multiple tumor cell lines on the phase diagram we confirm these predictions. We also extend phase space analysis to mutations affecting the rate of caspase-3 ubiquitylation by XIAP, predicting and showing that such mutations abolish all-or-none control over activation of effector caspases. Thus, phase diagrams derived from Lyapunov exponent analysis represent a means to study multi-factorial control over a complex biochemical pathway.