Modeling a snap-action, variable-delay switch controlling extrinsic cell death

Abstract

When exposed to tumor necrosis factor (TNF) or TNF-related apoptosis-inducing ligand (TRAIL), a closely related death ligand and investigational therapeutic, cells enter a protracted period of variable duration in which only upstream initiator caspases are active. A subsequent and sudden transition marks activation of the downstream effector caspases that rapidly dismantle the cell. Thus, extrinsic apoptosis is controlled by an unusual variable-delay, snap-action switch that enforces an unambiguous choice between life and death. To understand how the extrinsic apoptosis switch functions in quantitative terms, we constructed a mathematical model based on a mass-action representation of known reaction pathways. The model was trained against experimental data obtained by live-cell imaging, flow cytometry, and immunoblotting of cells perturbed by protein depletion and overexpression. The trained model accurately reproduces the behavior of normal and perturbed cells exposed to TRAIL, making it possible to study switching mechanisms in detail. Model analysis shows, and experiments confirm, that the duration of the delay prior to effector caspase activation is determined by initiator caspase-8 activity and the rates of other reactions lying immediately downstream of the TRAIL receptor. Sudden activation of effector caspases is achieved downstream by reactions involved in permeabilization of the mitochondrial membrane and relocalization of proteins such as Smac. We find that the pattern of interactions among Bcl-2 family members, the partitioning of Smac from its binding partner XIAP, and the mechanics of pore assembly are all critical for snap-action control.

Figure 1. Process Diagram of the Death Receptor Network Modeled in This Study

(A) The convention of Kitano et al. [94] is followed. The major features of the network are highlighted by color: gray, receptor module; blue, direct caspase cascade; green, positive feedback loop; yellow, mitochondrial feed-forward loop. (B) A condensed alternate representation of the network.

Figure 2. Dynamics of Caspase Activation in Cells Treated with TNF or TRAIL

(A) Time-lapse images of HeLa cells expressing EC-RP treated with 50 ng/ml TRAIL. Imaging was performed at 465 nm and 535 nm; cleavage of EC-RP caused a shift in the 465/535 ratio that was pseudo-colored as a shift from blue to yellow. Inset numbers indicate the time in hours after treatment with TRAIL. (B) Time courses of EC-RP cleavage in individual HeLa cells treated with 250, 50, or 10 ng/ml TRAIL; five cells are shown for each dose. Cell-to-cell variation in dynamics for a single dose is observed reproducibly and is not a consequence of imprecision in the assay. (C) Idealized single-cell time course for EC-RP cleavage, showing relationships among T_d (delay time), T_s (switch time), and f (fraction substrate cleaved). (D, E) Frequency distributions for T_d (D) and T_s (E) determined by live-cell microscopy in EC-RP-expressing HeLa cells treated with varying concentrations of death ligand (n > 100 for each condition); binning intervals were 30 min (E), or 5 min (F). (F) Flow cytometry of PARP cleavage, as assayed with an antibody selective for PARP cleaved at Asp214 by C3 and C7, in HeLa cells treated with 10 to 250 ng/ml TRAIL for 1–9 h as indicated. Colored regions underlying the histogram represent intervals used to discretize data into PARP cleavage levels of <5% (green), 5%–25% (yellow), or >25% (gray; percentages are relative to the median fluorescence intensity of the fully positive population). (G) Discretized flow cytometry data. The fraction of cells having low, intermediate, or high PARP cleavage is color-coded to match the intervals in (F). (H) Immunoblot analysis of PARP cleavage in HeLa cells treated with 10 to 250 ng/ml TRAIL. (I) Quantitation of the cleaved 89 kDa form of PARP for blots shown in (H).

Figure 3. Simulation-Based Approach to Data Fusion for Three Different Measures of Caspase Activity

(A, B, C, D) Simulated live-cell (top, twenty individual cells shown as blue lines), immunoblot (top, red lines), raw flow cytometry (middle, computed from 10,000 simulated live-cell profiles), and discretized flow cytometry data (bottom) for four different sets of switching parameters: (A) Baseline, corresponding to 250 ng/ml TRAIL; (B) an increase in mean T_d to 240 min. (C) An increase in T_s to 100 min (D) or a decrease in f to 0.1. (E, F, G) Concordance of data on EC substrate cleavage as obtained from immunoblot, flow cytometry, and live-cell assays in HeLa cells treated with 250 ng/ml (E), 50 ng/ml (F), or 10 ng/ml (G) TRAIL. Values for immunoblots are derived from quantitating the cleaved 89 kDa form of PARP by immunoblot; flow cytometry values represent the percentage of cPARP-positive cells computed as described in the legend of Figure 2, and live cell data were computed as the cumulative percentages of dead cells for populations of >150 cells. To facilitate comparisons, all three signals were normalized to their final value.

Figure 4. Training Data Derived from Live-Cell Microscopy

(A) Simulation of T_d (left) or T_s and f (right) as a function of TRAIL dose (lines) alongside corresponding experimental values (points with error bars indicating standard deviations). For predicted values of T_d, an envelope of constant coefficient of variation is shown, as estimated from experimental data (CV ≈ 20%); the source of variation is not known. (B) Composite plot of IC-RP and EC-RP cleavage for >50 cells treated with 50 ng/ml TRAIL in the presence of CHX and aligned by the average time of MOMP (left panel) and model-based simulation of the corresponding species (right panel). Data in the left panel were originally reported elsewhere [15].

Figure 5. Training the Model on Network-Wide Perturbations

First column: perturbation values measured by immunoblot (see Figure S2). Second column: comparison of EARM v1.0-simulated and experimentally derived values for T_s, T_d, f, and T_c. Simulated values were computed by EARM v1.0 with the perturbation conditions indicated in the first column. Experimental values were derived by fitting the simFACS data model to discretized flow cytometry data (See Materials and Methods and Protocol S2 for details). Third column: comparison of EARM v1.0-simulated cPARP cleavage (red) to time courses derived from flow cytometry using a data model (blue). Blue curves were produced by Equation (1) parameterized with the experimental T_s, T_d, and f values shown in the second column. The dashed line in the control condition shows simulation under non-siRNA conditions; all other simulations were performed under siRNA conditions (see “Linking Models and Experiment Via Perturbation” for details). Fourth column: comparison of experimental (blue) and predicted (red) flow cytometry plots at the indicated time points (see Figure S3 for comparisons of all time points). Predicted flow cytometry data were produced by simFACS data simulation using the EARM v1.0-simulated values for T_s, T_d, and f shown in the second column. Raw data for several of the conditions shown were originally reported elsewhere [15].

Figure 6. Prediction of the Transition from Graded to Switch-Like Kinetics

For simplicity, positive feedback was omitted in all simulations by setting [C6]₀ = 0; results with positive feedback produce highly similar conclusions and can be found in Figure S4. (A) Overlay of multiple species. To accommodate the wide range of concentrations, some species are scaled according to the values in parentheses in the caption. (B) The same data as in (A) except that each vertical axis is scaled independently to better depict the full dynamic range for each species. The pink vertical line denotes the duration of MOMP. The estimated LD₅₀ for caspase activity (corresponding to ∼10% PARP cleavage) [15] is denoted by a dashed line in the cPARP plot; the gray shaded region denotes points in time after this lethal dose has been reached and cells are already destined to die. (C) Simulated time courses for C8*, tBid, Bax*, and mitochondrial pores as in (A) shown on a truncated vertical axis to display the times at which each species achieves a concentration of one molecule/cell. The full time course for mitochondrial Smac/CyC is shown as a dashed line on a full vertical axis (right) to show MOMP. (D) Top panel, simulation of the total number of MOMP pores as in (A) (green) in comparison to the subset of pores bound to Smac or CyC during the process of release (red). Bottom panel, simulation of released Smac/CyC as in (A) (pink) and the discrete-time derivative of the release reaction (red). (E) Live-cell imaging of IMS-RP (red) and GFP-Bax (green) in the same cell. Frames correspond to 30-s intervals, with the first frame of MOMP denoted by a pink box. Partial mitochondrial localization of IMS-RP following MOMP is an artifact of the overexpressed reporter; endogenous CyC is fully cytosolic at this point, as determined by immunofluorescence (not shown). (F) Quantitation of Bax pores (top) and rate of IMS-RP release (bottom) for two cells (orange curves correspond to the cell shown in [E]); puncta and rate of release were quantified as described in Materials and Methods. (G) Live-cell images for the cell in (E) shown at higher zoom and with pseudocoloring to highlight the temporal and spatial relationship between Bax puncta and IMS-RP release. Frames correspond to 30-s intervals; the magnified region (yellow box) encompasses the area of the cell in which both GFP-Bax puncta and IMS-RP release are first visible.

Figure 7. Rapid MOMP Independent of the Rapid Phase of Initiator Activity

(A) Simulated values for the average rate of C8 substrate cleavage during the early (pre-MOMP) and late (post-MOMP) phases (left axis) and T_s of MOMP (right axis). Simulations were performed under conditions corresponding to stimulation by 2 ng/ml TRAIL. (B) Live-cell measurements of IC-RP cleavage and IMS-RP release in control or Smac-depleted cells treated with 10 or 2 ng/ml TRAIL. IC-RP and IMS-RP signals were normalized individually to allow comparison on the same axes. (C) Schematic diagram of potential feedback pathways regulating MOMP. The data shown in (B) are inconsistent with snap-action behavior resulting from feedback loops that act upstream of Bid cleavage (red arrows) but do not rule out the possibility that snap-action may arise from feedback loops that act downstream of Bid (green arrows). Some of the depicted loops are hypothetical and are shown for logical completeness.

Figure 8. Control of T_d by C8

(A) Simulation of C8 substrate cleavage (tBid, top) and free mitochondrial Bcl-2 (bottom) in comparison to Smac/CyC release at 4 TRAIL concentrations (spanning approximately 0.2 to 200 ng/ml). Red circles indicate the level of tBid or Bcl-2 when Smac/CyC release is 50% complete. (B) Live-cell measurement of IC-RP cleavage and IMS-RP release in individual cells stimulated with 250, 50, or 10 ng/ml TRAIL. IC-RP and IMS-RP signals were normalized individually to allow comparison on the same axes. Circles outlined in red indicate the IC-RP signal at the time of IMS-RP release. (C) Averaged IC-RP cleavage for ten to 50 HeLa cells treated with 0 (black line), 50 (blue), or 250 (red) ng/ml TRAIL (as indicated) in the presence of cycloheximide. At each dose of TRAIL, time-courses were aligned by the average time of MOMP (indicated by symbols with red outlines). (D) Average IC-RP cleavage in 50 Hela cells treated with 250 ng/ml TRAIL in the presence of 10 or 2 μM C8 inhibitor. Time courses for cells treated with 2 μM inhibitor were aligned at the average time of MOMP. Average time courses from (C) are shown for comparison in light blue, green, and gray. In (C) and (D), MOMP did not occur in cells not treated with TRAIL or treated with TRAIL in the presence of 10 μM inhibitor, and time courses were aligned by the time of TRAIL treatment

Figure 9. Role of the Apoptosome in Snap-Action C3 Activation

(A–C) Simulation of the time course of C3 (EC) substrate cleavage in control cells (A), or cells lacking C9 (B), or Apaf-1 (C). For each condition, simulations were performed using baseline conditions for Smac (black lines), or 5-fold overexpression of Smac (red lines). (D) Simulation of f as a function of initial concentrations of Smac and the apoptosome; for simplicity, the apoptosome components C9 and Apaf-1 were assumed to be present at equal concentrations. Orange dotted line indicates the region where [XIAP]₀ = [Smac]₀ + [apoptosome]₀; numbered circles and cyan arrows indicate the positions of the indicated conditions. Point 1a corresponds to the baseline model, in which either Smac or Apaf-1 knockdown leads to a decrease in f, while point 1b corresponds to the baseline model with 5-fold higher Smac, in which Apaf-1 depletion does not reduce f. (E, F) Simulation of the time course of PARP cleavage in cells in which apoptosome function has been altered so that it cannot process pro-C3 (E) or so that it cannot bind XIAP (F).

Figure 10. Role of C6 in Modulating the Duration of Pre-MOMP Delay (T_d)

(A) Simulation showing the effect on T_d of increasing the levels of [C6]₀ 10- (green line) or 100-fold (blue lines) above baseline values (black line) or of eliminating C6 altogether (red line). (B–D) Simulations showing concentrations of total C8* (purple lines) and the subset of C8* generated by DISC (red lines) or by C6* (blue lines) at three different doses of TRAIL. The bottom panels magnify the period immediately before and after snap-action switching; bar plots to the right depict levels of DISC- or C6*-generated C8* (normalized to a total C8* value of 1.0) at the time of MOMP onset (dotted vertical lines).

Figure 11. Role of Network Topology in Generating Snap-Action Behavior

Models representing varying topologies of the MOMP module were analyzed for snap-action behavior. For each model, the input species (C8*) was introduced at values ranging from 1 to 10³ molecules/cell, and the resulting release behavior of Smac determined by simulation (middle column). The kinetic characteristics T_s, T_d, and T_on (defined as the time at which Smac release reached 1% of its final value) for Smac release were determined from these simulations as a function of input strength (right column). Note that f = 1 in all cases and therefore T_c = T_s. Binding of Bid to Bcl-2 was omitted for simplicity, although this interaction is included in the full EARM v1.0. (A) Basic motif model. Simulations are shown for parameter sets representing physiologically realistic rate constants (gray) and for irreversible, faster-than-diffusion binding (orange) for Bax-Bcl-2 association, and T_s, T_d, and T_on curves shown only for physiologically realistic values. The inset plot in the right column shows the expected behavior for an idealized variable-delay snap-action switch. (B) Model of known topology, including Bid cleavage. (C) Model including Bax oligomerization. (D) Model including separate mitochondrial reaction compartment. (E) Model corresponding to the MOMP module in EARM v1.0. Note that the cytosolic pool of Bcl-2 anti-apoptotic proteins, which binds to tBid in EARM v1.0, has been omitted for simplicity. (F) Model as in (F), but with rate constants for Bax oligomerization and insertion adjusted to represent positive cooperativity.